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a/docs/examples/kernel/davinci.txt b/docs/examples/kernel/davinci.txt deleted file mode 100644 index 377d8dc..0000000 --- a/docs/examples/kernel/davinci.txt +++ /dev/null @@ -1,32118 +0,0 @@ -The Project Gutenberg EBook of The Notebooks of Leonardo Da Vinci, Complete -by Leonardo Da Vinci -(#3 in our series by Leonardo Da Vinci) - -Copyright laws are changing all over the world. Be sure to check the -copyright laws for your country before downloading or redistributing -this or any other Project Gutenberg eBook. - -This header should be the first thing seen when viewing this Project -Gutenberg file. Please do not remove it. Do not change or edit the -header without written permission. - -Please read the "legal small print," and other information about the -eBook and Project Gutenberg at the bottom of this file. Included is -important information about your specific rights and restrictions in -how the file may be used. You can also find out about how to make a -donation to Project Gutenberg, and how to get involved. - - -**Welcome To The World of Free Plain Vanilla Electronic Texts** - -**eBooks Readable By Both Humans and By Computers, Since 1971** - -*****These eBooks Were Prepared By Thousands of Volunteers!***** - - -Title: The Notebooks of Leonardo Da Vinci, Complete - -Author: Leonardo Da Vinci - -Release Date: Jan, 2004 [EBook #5000] -[Yes, we are more than one year ahead of schedule] -[Most recently updated June 26, 2002] - -Edition: 10 - -Language: English - -Character set encoding: ASCII - -*** START OF THE PROJECT GUTENBERG EBOOK, THE NOTEBOOKS OF LEONARDO DA - VINCI, COMPLETE *** - - - - -This eBook was produced by Charles Aldarondo and the Distributed -Proofreaders team. - - - -The Notebooks of Leonardo Da Vinci - -Volume 1 - -Translated by Jean Paul Richter - -1888 - - - - - - -PREFACE. - - - - - -A singular fatality has ruled the destiny of nearly all the most -famous of Leonardo da Vinci's works. Two of the three most important -were never completed, obstacles having arisen during his life-time, -which obliged him to leave them unfinished; namely the Sforza -Monument and the Wall-painting of the Battle of Anghiari, while the -third--the picture of the Last Supper at Milan--has suffered -irremediable injury from decay and the repeated restorations to -which it was recklessly subjected during the XVIIth and XVIIIth -centuries. Nevertheless, no other picture of the Renaissance has -become so wellknown and popular through copies of every description. - -Vasari says, and rightly, in his Life of Leonardo, "that he laboured -much more by his word than in fact or by deed", and the biographer -evidently had in his mind the numerous works in Manuscript which -have been preserved to this day. To us, now, it seems almost -inexplicable that these valuable and interesting original texts -should have remained so long unpublished, and indeed forgotten. It -is certain that during the XVIth and XVIIth centuries their -exceptional value was highly appreciated. This is proved not merely -by the prices which they commanded, but also by the exceptional -interest which has been attached to the change of ownership of -merely a few pages of Manuscript. - -That, notwithstanding this eagerness to possess the Manuscripts, -their contents remained a mystery, can only be accounted for by the -many and great difficulties attending the task of deciphering them. -The handwriting is so peculiar that it requires considerable -practice to read even a few detached phrases, much more to solve -with any certainty the numerous difficulties of alternative -readings, and to master the sense as a connected whole. Vasari -observes with reference to Leonardos writing: "he wrote backwards, -in rude characters, and with the left hand, so that any one who is -not practised in reading them, cannot understand them". The aid of a -mirror in reading reversed handwriting appears to me available only -for a first experimental reading. Speaking from my own experience, -the persistent use of it is too fatiguing and inconvenient to be -practically advisable, considering the enormous mass of Manuscripts -to be deciphered. And as, after all, Leonardo's handwriting runs -backwards just as all Oriental character runs backwards--that is -to say from right to left--the difficulty of reading direct from the -writing is not insuperable. This obvious peculiarity in the writing -is not, however, by any means the only obstacle in the way of -mastering the text. Leonardo made use of an orthography peculiar to -himself; he had a fashion of amalgamating several short words into -one long one, or, again, he would quite arbitrarily divide a long -word into two separate halves; added to this there is no punctuation -whatever to regulate the division and construction of the sentences, -nor are there any accents--and the reader may imagine that such -difficulties were almost sufficient to make the task seem a -desperate one to a beginner. It is therefore not surprising that the -good intentions of some of Leonardo s most reverent admirers should -have failed. - -Leonardos literary labours in various departments both of Art and of -Science were those essentially of an enquirer, hence the analytical -method is that which he employs in arguing out his investigations -and dissertations. The vast structure of his scientific theories is -consequently built up of numerous separate researches, and it is -much to be lamented that he should never have collated and arranged -them. His love for detailed research--as it seems to me--was the -reason that in almost all the Manuscripts, the different paragraphs -appear to us to be in utter confusion; on one and the same page, -observations on the most dissimilar subjects follow each other -without any connection. A page, for instance, will begin with some -principles of astronomy, or the motion of the earth; then come the -laws of sound, and finally some precepts as to colour. Another page -will begin with his investigations on the structure of the -intestines, and end with philosophical remarks as to the relations -of poetry to painting; and so forth. - -Leonardo himself lamented this confusion, and for that reason I do -not think that the publication of the texts in the order in which -they occur in the originals would at all fulfil his intentions. No -reader could find his way through such a labyrinth; Leonardo himself -could not have done it. - -Added to this, more than half of the five thousand manuscript pages -which now remain to us, are written on loose leaves, and at present -arranged in a manner which has no justification beyond the fancy of -the collector who first brought them together to make volumes of -more or less extent. Nay, even in the volumes, the pages of which -were numbered by Leonardo himself, their order, so far as the -connection of the texts was concerned, was obviously a matter of -indifference to him. The only point he seems to have kept in view, -when first writing down his notes, was that each observation should -be complete to the end on the page on which it was begun. The -exceptions to this rule are extremely few, and it is certainly -noteworthy that we find in such cases, in bound volumes with his -numbered pages, the written observations: "turn over", "This is the -continuation of the previous page", and the like. Is not this -sufficient to prove that it was only in quite exceptional cases that -the writer intended the consecutive pages to remain connected, when -he should, at last, carry out the often planned arrangement of his -writings? - -What this final arrangement was to be, Leonardo has in most cases -indicated with considerable completeness. In other cases this -authoritative clue is wanting, but the difficulties arising from -this are not insuperable; for, as the subject of the separate -paragraphs is always distinct and well defined in itself, it is -quite possible to construct a well-planned whole, out of the -scattered materials of his scientific system, and I may venture to -state that I have devoted especial care and thought to the due -execution of this responsible task. - -The beginning of Leonardo's literary labours dates from about his -thirty-seventh year, and he seems to have carried them on without -any serious interruption till his death. Thus the Manuscripts that -remain represent a period of about thirty years. Within this space -of time his handwriting altered so little that it is impossible to -judge from it of the date of any particular text. The exact dates, -indeed, can only be assigned to certain note-books in which the year -is incidentally indicated, and in which the order of the leaves has -not been altered since Leonardo used them. The assistance these -afford for a chronological arrangement of the Manuscripts is -generally self evident. By this clue I have assigned to the original -Manuscripts now scattered through England, Italy and France, the -order of their production, as in many matters of detail it is highly -important to be able to verify the time and place at which certain -observations were made and registered. For this purpose the -Bibliography of the Manuscripts given at the end of Vol. II, may be -regarded as an Index, not far short of complete, of all Leonardo s -literary works now extant. The consecutive numbers (from 1 to 1566) -at the head of each passage in this work, indicate their logical -sequence with reference to the subjects; while the letters and -figures to the left of each paragraph refer to the original -Manuscript and number of the page, on which that particular passage -is to be found. Thus the reader, by referring to the List of -Manuscripts at the beginning of Volume I, and to the Bibliography at -the end of Volume II, can, in every instance, easily ascertain, not -merely the period to which the passage belongs, but also exactly -where it stood in the original document. Thus, too, by following the -sequence of the numbers in the Bibliographical index, the reader may -reconstruct the original order of the Manuscripts and recompose the -various texts to be found on the original sheets--so much of it, -that is to say, as by its subject-matter came within the scope of -this work. It may, however, be here observed that Leonardo s -Manuscripts contain, besides the passages here printed, a great -number of notes and dissertations on Mechanics, Physics, and some -other subjects, many of which could only be satisfactorily dealt -with by specialists. I have given as complete a review of these -writings as seemed necessary in the Bibliographical notes. - -In 1651, Raphael Trichet Dufresne, of Paris, published a selection -from Leonardo's writings on painting, and this treatise became so -popular that it has since been reprinted about two-and-twenty times, -and in six different languages. But none of these editions were -derived from the original texts, which were supposed to have been -lost, but from early copies, in which Leonardo's text had been more -or less mutilated, and which were all fragmentary. The oldest and on -the whole the best copy of Leonardo's essays and precepts on -Painting is in the Vatican Library; this has been twice printed, -first by Manzi, in 1817, and secondly by Ludwig, in 1882. Still, -this ancient copy, and the published editions of it, contain much -for which it would be rash to hold Leonardo responsible, and some -portions--such as the very important rules for the proportions of -the human figure--are wholly wanting; on the other hand they contain -passages which, if they are genuine, cannot now be verified from any -original Manuscript extant. These copies, at any rate neither give -us the original order of the texts, as written by Leonardo, nor do -they afford any substitute, by connecting them on a rational scheme; -indeed, in their chaotic confusion they are anything rather than -satisfactory reading. The fault, no doubt, rests with the compiler -of the Vatican copy, which would seem to be the source whence all -the published and extensively known texts were derived; for, instead -of arranging the passages himself, he was satisfied with recording a -suggestion for a final arrangement of them into eight distinct -parts, without attempting to carry out his scheme. Under the -mistaken idea that this plan of distribution might be that, not of -the compiler, but of Leonardo himself, the various editors, down to -the present day, have very injudiciously continued to adopt this -order--or rather disorder. - -I, like other enquirers, had given up the original Manuscript of the -Trattato della Pittura for lost, till, in the beginning of 1880, I -was enabled, by the liberality of Lord Ashburnham, to inspect his -Manuscripts, and was so happy as to discover among them the original -text of the best-known portion of the Trattato in his magnificent -library at Ashburnham Place. Though this discovery was of a fragment -only--but a considerable fragment--inciting me to further search, -it gave the key to the mystery which had so long enveloped the first -origin of all the known copies of the Trattato. The extensive -researches I was subsequently enabled to prosecute, and the results -of which are combined in this work, were only rendered possible by -the unrestricted permission granted me to investigate all the -Manuscripts by Leonardo dispersed throughout Europe, and to -reproduce the highly important original sketches they contain, by -the process of "photogravure". Her Majesty the Queen graciously -accorded me special permission to copy for publication the -Manuscripts at the Royal Library at Windsor. The Commission Centrale -Administrative de l'Institut de France, Paris, gave me, in the most -liberal manner, in answer to an application from Sir Frederic -Leighton, P. R. A., Corresponding member of the Institut, free -permission to work for several months in their private collection at -deciphering the Manuscripts preserved there. The same favour which -Lord Ashburnham had already granted me was extended to me by the -Earl of Leicester, the Marchese Trivulsi, and the Curators of the -Ambrosian Library at Milan, by the Conte Manzoni at Rome and by -other private owners of Manuscripts of Leonardo's; as also by the -Directors of the Louvre at Paris; the Accademia at Venice; the -Uffizi at Florence; the Royal Library at Turin; and the British -Museum, and the South Kensington Museum. I am also greatly indebted -to the Librarians of these various collections for much assistance -in my labours; and more particularly to Monsieur Louis Lalanne, of -the Institut de France, the Abbate Ceriani, of the Ambrosian -Library, Mr. Maude Thompson, Keeper of Manuscripts at the British -Museum, Mr. Holmes, the Queens Librarian at Windsor, the Revd Vere -Bayne, Librarian of Christ Church College at Oxford, and the Revd A. -Napier, Librarian to the Earl of Leicester at Holkham Hall. - -In correcting the Italian text for the press, I have had the -advantage of valuable advice from the Commendatore Giov. Morelli, -Senatore del Regno, and from Signor Gustavo Frizzoni, of Milan. The -translation, under many difficulties, of the Italian text into -English, is mainly due to Mrs. R. C. Bell; while the rendering of -several of the most puzzling and important passages, particularly in -the second half of Vol. I, I owe to the indefatigable interest taken -in this work by Mr. E. J. Poynter R. A. Finally I must express my -thanks to Mr. Alfred Marks, of Long Ditton, who has most kindly -assisted me throughout in the revision of the proof sheets. - -The notes and dissertations on the texts on Architecture in Vol. II -I owe to my friend Baron Henri de Geymuller, of Paris. - -I may further mention with regard to the illustrations, that the -negatives for the production of the "photo-gravures" by Monsieur -Dujardin of Paris were all taken direct from the originals. - -It is scarcely necessary to add that most of the drawings here -reproduced in facsimile have never been published before. As I am -now, on the termination of a work of several years' duration, in a -position to review the general tenour of Leonardos writings, I may -perhaps be permitted to add a word as to my own estimate of the -value of their contents. I have already shown that it is due to -nothing but a fortuitous succession of unfortunate circumstances, -that we should not, long since, have known Leonardo, not merely as a -Painter, but as an Author, a Philosopher, and a Naturalist. There -can be no doubt that in more than one department his principles and -discoveries were infinitely more in accord with the teachings of -modern science, than with the views of his contemporaries. For this -reason his extraordinary gifts and merits are far more likely to be -appreciated in our own time than they could have been during the -preceding centuries. He has been unjustly accused of having -squandered his powers, by beginning a variety of studies and then, -having hardly begun, throwing them aside. The truth is that the -labours of three centuries have hardly sufficed for the elucidation -of some of the problems which occupied his mighty mind. - -Alexander von Humboldt has borne witness that "he was the first to -start on the road towards the point where all the impressions of our -senses converge in the idea of the Unity of Nature" Nay, yet more -may be said. The very words which are inscribed on the monument of -Alexander von Humboldt himself, at Berlin, are perhaps the most -appropriate in which we can sum up our estimate of Leonardo's -genius: - -"Majestati naturae par ingenium." - -LONDON, April 1883. - -F. P. R. - - - - - - - -CONTENTS OF VOLUME I. - - - - - -PROLEGOMENA AND GENERAL INTRODUCTION TO THE BOOK ON PAINTING - -Clavis Sigillorum and Index of Manuscripts.--The author's intention -to publish his MSS. (1).--The preparation of the MSS. for -publication (2).--Admonition to readers (3).--The disorder in the -MSS. (4).--Suggestions for the arrangement of MSS. treating of -particular subjects (5--8).--General introductions to the book on -painting (9--13).--The plan of the book on painting (14--17).--The -use of the book on painting (18).--Necessity of theoretical -knowledge (19, 20).--The function of the eye (21--23).--Variability -of the eye (24).--Focus of sight (25).--Differences of perception by -one eye and by both eyes (26--29).--The comparative size of the -image depends on the amount of light (30--39). - -II. - -LINEAR PERSPECTIVE - -General remarks on perspective (40--41).--The elements of -perspective:--of the point (42--46).--Of the line (47--48).--The -nature of the outline (49).--Definition of perspective (50).--The -perception of the object depends on the direction of the eye -(51).--Experimental proof of the existence of the pyramid of sight -(52--55).--The relations of the distance point to the vanishing -point (55--56).--How to measure the pyramid of vision (57).--The -production of the pyramid of vision (58--64).--Proof by experiment -(65--66).--General conclusions (67).--That the contrary is -impossible (68).--A parallel case (69).--The function of the eye, as -explained by the camera obscura (70--71).--The practice of -perspective (72--73).--Refraction of the rays falling upon the eye -(74--75).--The inversion of the images (76).--The intersection of -the rays (77--82).--Demonstration of perspective by means of a -vertical glass plane (83--85.)--The angle of sight varies with the -distance (86--88).--Opposite pyramids in juxtaposition (89).--On -simple and complex perspective (90).--The proper distance of objects -from the eye (91--92).--The relative size of objects with regard to -their distance from the eye (93--98).--The apparent size of objects -denned by calculation (99--106).--On natural perspective (107--109). - -III. - -SIX BOOKS ON LIGHT AND SHADE - -GENERAL INTRODUCTION.--Prolegomena (110).--Scheme of the books on -light and shade (111).--Different principles and plans of treatment -(112--116).--Different sorts of light (117--118).--Definition of -the nature of shadows (119--122).--Of the various kinds of shadows -(123--125).--Of the various kinds of light (126--127).--General -remarks (128--129).--FIRST BOOK ON LIGHT AND SHADE.--On the nature -of light (130--131).--The difference between light and lustre -(132--135).--The relations of luminous to illuminated bodies (136). ---Experiments on the relation of light and shadow within a room -(137--140).--Light and shadow with regard to the position of the -eye (141--145).--The law of the incidence of light -(146--147).--SECOND BOOK ON LIGHT AND SHADE.--Gradations of strength -in the shadows (148--149).--On the intensity of shadows as dependent -on the distance from the light (150--152).--On the proportion of -light and shadow (153--157).--THIRD BOOK ON LIGHT AND -SHADE.--Definition of derived shadow (158--159).--Different sorts of -derived shadows (160--162).--On the relation of derived and primary -shadow (163--165).--On the shape of derived shadows (166--174).--On -the relative intensity of derived shadows (175--179).--Shadow as -produced by two lights of different size (180--181).--The effect of -light at different distances (182).--Further complications in the -derived shadows (183--187).--FOURTH BOOK ON LIGHT AND SHADE.--On the -shape of cast shadows (188--191).--On the outlines of cast shadows -(192--195).--On the relative size of cast shadows (196. -197).--Effects on cast shadows by the tone of the back ground -(198).--A disputed proposition (199).--On the relative depth of -cast shadows (200--202).--FIFTH BOOK ON LIGHT AND -SHADE.--Principles of reflection (203. 204).--On reverberation -(205).--Reflection on water (206. 207).--Experiments with the mirror -(208--210).--Appendix:--On shadows in movement (211--212).--SIXTH -BOOK ON LIGHT AND SHADE.--The effect of rays passing through holes -(213. 214).--On gradation of shadows (215. 216).--On relative -proportion of light and shadows (216--221). - -IV. - -PERSPECTIVE OF DISAPPEARANCE - -Definition (222. 223).--An illustration by experiment (224).--A -guiding rule (225).---An experiment (226).--On indistinctness at -short distances (227--231).--On indistinctness at great distances -(232--234).--The importance of light and shade in the Prospettiva -de' perdimenti (235--239).--The effect of light or dark backgrounds -on the apparent size of objects (240--250).--Propositions on -Prospettiva de' perdimenti from MS. C. (250--262). - -V. - -THEORY OF COLOURS - -The reciprocal effects of colours on objects placed opposite each -other (263--271).--Combination of different colours in cast shadows -(272).--The effect of colours in the camera obscura (273. 274).--On -the colours of derived shadows (275. 276).--On the nature of colours -(277. 278).--On gradations in the depth of colours (279. 280).--On -the reflection of colours (281--283).--On the use of dark and light -colours in painting (284--286).--On the colours of the rainbow -(287--288). - -VI. - -PERSPECTIVE OF COLOUR AND AERIAL PERSPECTIVE - -General rules (289--291).--An exceptional case (292).--An experiment -(293).--The practice of the Prospettiva de' colori (294).--The rules -of aerial perspective (295--297).--On the relative density of the -atmosphere (298--299).--On the colour of the atmosphere (300--307). - -VII. - -ON THE PROPORTIONS AND ON THE MOVEMENTS OF THE HUMAN FIGURE - -Preliminary observations (308. 309).--Proportions of the head and -face (310--318).--Proportions of the head seen in front -(319--321).--Proportions of the foot (322--323).--Relative -proportions of the hand and foot (324).--Relative proportions of -the foot and of the face (325--327).--Proportions of the leg -(328--331).--On the central point of the whole body (332).--The -relative proportions of the torso and of the whole figure -(333).--The relative proportions of the head and of the torso -(334).--The relative proportions of the torso and of the leg (335. -336).--The relative proportions of the torso and of the foot -(337).--The proportions of the whole figure (338--341).--The torso -from the front and back (342).--Vitruvius' scheme of proportions -(343).--The arm and head (344).--Proportions of the arm -(345--349).--The movement of the arm (350--354).--The movement of -the torso (355--361).--The proportions vary at different ages -(362--367).--The movement of the human figure (368--375).--Of -walking up and down (375--379).--On the human body in action -(380--388).--On hair falling down in curls (389).--On draperies - -(390--392). - -VIII. - -BOTANY FOR PAINTERS, AND ELEMENTS OF LANDSCAPE PAINTING - -Classification of trees (393).--The relative thickness of the -branches to the trunk (394--396).--The law of proportion in the -growth of the branches (397--402).--The direction of growth -(403--407).--The forms of trees (408--411).--The insertion of the -leaves (412--419).--Light on branches and leaves (420--422).--The -proportions of light and shade in a leaf (423--426).--Of the -transparency of leaves (427--429).--The gradations of shade and -colour in leaves (430--434).--A classification of trees according to -their colours (435).--The proportions of light and shade in trees -(436--440).--The distribution of light and shade with reference to -the position of the spectator (441--443).--The effects of morning -light (444--448).--The effects of midday light (449).--The -appearance of trees in the distance (450--451).--The cast shadow of -trees (452. 453).--Light and shade on groups of trees -(454--457).--On the treatment of light for landscapes -(458--464).--On the treatment of light for views of towns -(465--469).--The effect of wind on trees (470--473).--Light and -shade on clouds (474--477).--On images reflected in water (478).--Of -rainbows and rain (479. 480).--Of flower seeds (481). - -IX. - -THE PRACTICE OF PAINTING - -I. MORAL PRECEPTS FOR THE STUDENT OF PAINTING.--How to ascertain the -dispositions for an artistic career (482).--The course of -instruction for an artist (483--485).--The study of the antique -(486. 487).--The necessity of anatomical knowledge (488. 489).--How -to acquire practice (490).--Industry and thoroughness the first -conditions (491--493.)--The artist's private life and choice of -company (493. 494).--The distribution of time for studying (495-- -497).--On the productive power of minor artists (498--501).--A -caution against one-sided study (502).--How to acquire universality -(503--506).--Useful games and exercises (507. 508).--II. THE -ARTIST'S STUDIO.--INSTRUMENTS AND HELPS FOR THE APPLICATION OF -PERSPECTIVE.--ON JUDGING OF A PICTURE.--On the size of the studio -(509).--On the construction of windows (510--512).--On the best -light for painting (513--520).--On various helps in preparing a -picture (521--530).--On the management of works (531. 532).--On the -limitations of painting (533--535).--On the choice of a position -(536. 537).--The apparent size of figures in a picture (538. -539).--The right position of the artist, when painting and of the -spectator (540--547).--III. THE PRACTICAL METHODS OF LIGHT AND SHADE -AND AERIAL PERSPECTIVE.--Gradations of light and shade (548).--On -the choice of light for a picture (549--554).--The distribution of -light and shade (555--559).--The juxtaposition of light and shade -(560. 561).--On the lighting of the background (562--565).--On the -lighting of white objects (566).--The methods of aerial perspective -(567--570).--IV. OF PORTRAIT AND FIGURE PAINTING.--Of sketching -figures and portraits (571. 572).--The position of the head -(573).--Of the light on the face (574--576).--General suggestions -for historical pictures (577--581).--How to represent the -differences of age and sex (582. 583).--Of representing the emotions -(584).--Of representing imaginary animals (585).--The selection of -forms (586--591).--How to pose figures (592).--Of appropriate -gestures (593--600).--V. SUGGESTIONS FOR COMPOSITIONS.--Of painting -battle-pieces (601--603).--Of depicting night-scenes (604).--Of -depicting a tempest (605. 606).--Of representing the deluge -(607--609).--Of depicting natural phenomena (610. 611).--VI. THE -ARTIST'S MATERIALS.--Of chalk and paper (612--617).--On the -preparation and use of colours (618--627).--Of preparing the panel -(628).--The preparation of oils (629--634).--On varnishes (635-- -637).--On chemical _materials (638--650).--VII. PHILOSOPHY AND -HISTORY OF THE ART OF PAINTING.--The relation of art and nature -(651. 652).--Painting is superior to poetry (653. 654).--Painting is -superior to sculpture (655. 656).--Aphorisms (657--659).--On the -history of painting (660. 661).--The painter's scope (662). - -X. - -STUDIES AND SKETCHES FOR PICTURES AND DECORATIONS - -On pictures of the Madonna (663).--Bernardo di Bandino's portrait -(664).--Notes on the Last Supper (665--668).--On the battle of -Anghiari (669).--Allegorical representations referring to the duke -of Milan (670--673).--Allegorical representations -(674--678).--Arrangement of a picture (679).--List of drawings -(680).--Mottoes and Emblems (681--702). - - - - - - -The author's intention to publish his MSS. - -1. - -How by a certain machine many may stay some time under water. And -how and wherefore I do not describe my method of remaining under -water and how long I can remain without eating. And I do not publish -nor divulge these, by reason of the evil nature of men, who would -use them for assassinations at the bottom of the sea by destroying -ships, and sinking them, together with the men in them. Nevertheless -I will impart others, which are not dangerous because the mouth of -the tube through which you breathe is above the water, supported on -air sacks or cork. - -[Footnote: The leaf on which this passage is written, is headed with -the words _Casi_ 39, and most of these cases begin with the word -'_Come_', like the two here given, which are the 26th and 27th. 7. -_Sughero_. In the Codex Antlanticus 377a; 1170a there is a sketch, -drawn with the pen, representing a man with a tube in his mouth, and -at the farther end of the tube a disk. By the tube the word -'_Channa_' is written, and by the disk the word '_sughero_'.] - -The preparation of the MSS. for publication. - -2. - -When you put together the science of the motions of water, remember -to include under each proposition its application and use, in order -that this science may not be useless.-- - -[Footnote: A comparatively small portion of Leonardo's notes on -water-power was published at Bologna in 1828, under the title: "_Del -moto e misura dell'Acqua, di L. da Vinci_".] - -Admonition to readers. - -3. - -Let no man who is not a Mathematician read the elements of my work. - -The disorder in the MSS. - -4. - -Begun at Florence, in the house of Piero di Braccio Martelli, on the -22nd day of March 1508. And this is to be a collection without -order, taken from many papers which I have copied here, hoping to -arrange them later each in its place, according to the subjects of -which they may treat. But I believe that before I am at the end of -this [task] I shall have to repeat the same things several times; -for which, O reader! do not blame me, for the subjects are many and -memory cannot retain them [all] and say: 'I will not write this -because I wrote it before.' And if I wished to avoid falling into -this fault, it would be necessary in every case when I wanted to -copy [a passage] that, not to repeat myself, I should read over all -that had gone before; and all the more since the intervals are long -between one time of writing and the next. - -[Footnote: 1. In the history of Florence in the early part of the -XVIth century _Piero di Braccio Martelli_ is frequently mentioned as -_Commissario della Signoria_. He was famous for his learning and at -his death left four books on Mathematics ready for the press; comp. -LITTA, _Famiglie celebri Italiane_, _Famiglia Martelli di -Firenze_.--In the Official Catalogue of MSS. in the Brit. Mus., New -Series Vol. I., where this passage is printed, _Barto_ has been -wrongly given for Braccio. - -2. _addi 22 di marzo 1508_. The Christian era was computed in -Florence at that time from the Incarnation (Lady day, March 25th). -Hence this should be 1509 by our reckoning. - -3. _racolto tratto di molte carte le quali io ho qui copiate_. We -must suppose that Leonardo means that he has copied out his own MSS. -and not those of others. The first thirteen leaves of the MS. in the -Brit. Mus. are a fair copy of some notes on physics.] - -Suggestions for the arrangement of MSS treating of particular -subjects.(5-8). - -5. - -Of digging a canal. Put this in the Book of useful inventions and in -proving them bring forward the propositions already proved. And this -is the proper order; since if you wished to show the usefulness of -any plan you would be obliged again to devise new machines to prove -its utility and thus would confuse the order of the forty Books and -also the order of the diagrams; that is to say you would have to mix -up practice with theory, which would produce a confused and -incoherent work. - -6. - -I am not to blame for putting forward, in the course of my work on -science, any general rule derived from a previous conclusion. - -7. - -The Book of the science of Mechanics must precede the Book of useful -inventions.--Have your books on anatomy bound! [Footnote: 4. The -numerous notes on anatomy written on loose leaves and now in the -Royal collection at Windsor can best be classified in four Books, -corresponding to the different character and size of the paper. When -Leonardo speaks of '_li tua libri di notomia_', he probably means -the MSS. which still exist; if this hypothesis is correct the -present condition of these leaves might seem to prove that he only -carried out his purpose with one of the Books on anatomy. A borrowed -book on Anatomy is mentioned in F.O.] - -8. - -The order of your book must proceed on this plan: first simple -beams, then (those) supported from below, then suspended in part, -then wholly [suspended]. Then beams as supporting other weights -[Footnote: 4. Leonardo's notes on Mechanics are extraordinarily -numerous; but, for the reasons assigned in my introduction, they -have not been included in the present work.]. - -General introductions to the book on Painting (9-13). - -9. - -INTRODUCTION. - -Seeing that I can find no subject specially useful or -pleasing--since the men who have come before me have taken for their -own every useful or necessary theme--I must do like one who, being -poor, comes last to the fair, and can find no other way of providing -himself than by taking all the things already seen by other buyers, -and not taken but refused by reason of their lesser value. I, then, -will load my humble pack with this despised and rejected -merchandise, the refuse of so many buyers; and will go about to -distribute it, not indeed in great cities, but in the poorer towns, -taking such a price as the wares I offer may be worth. [Footnote: It -need hardly be pointed out that there is in this 'Proemio' a covert -irony. In the second and third prefaces, Leonardo characterises his -rivals and opponents more closely. His protest is directed against -Neo-latinism as professed by most of the humanists of his time; its -futility is now no longer questioned.] - -10. - -INTRODUCTION. - -I know that many will call this useless work [Footnote: 3. questa -essere opera inutile. By opera we must here understand libro di -pittura and particularly the treatise on Perspective.]; and they -will be those of whom Demetrius [Footnote: 4. Demetrio. "With regard -to the passage attributed to Demetrius", Dr. H. MULLER STRUBING -writes, "I know not what to make of it. It is certainly not -Demetrius Phalereus that is meant and it can hardly be Demetrius -Poliorcetes. Who then can it be--for the name is a very common one? -It may be a clerical error for Demades and the maxim is quite in the -spirit of his writings I have not however been able to find any -corresponding passage either in the 'Fragments' (C. MULLER, _Orat. -Att._, II. 441) nor in the Supplements collected by DIETZ (_Rhein. -Mus._, vol. 29, p. 108)." - -The same passage occurs as a simple Memorandum in the MS. Tr. 57, -apparently as a note for this '_Proemio_' thus affording some data -as to the time where these introductions were written.] declared -that he took no more account of the wind that came out their mouth -in words, than of that they expelled from their lower parts: men who -desire nothing but material riches and are absolutely devoid of that -of wisdom, which is the food and the only true riches of the mind. -For so much more worthy as the soul is than the body, so much more -noble are the possessions of the soul than those of the body. And -often, when I see one of these men take this work in his hand, I -wonder that he does not put it to his nose, like a monkey, or ask me -if it is something good to eat. - -[Footnote: In the original, the Proemio di prospettiva cioe -dell'uffitio dell'occhio (see No. 21) stands between this and the -preceding one, No. 9.] - -INTRODUCTION. - -I am fully concious that, not being a literary man, certain -presumptuous persons will think that they may reasonably blame me; -alleging that I am not a man of letters. Foolish folks! do they not -know that I might retort as Marius did to the Roman Patricians -[Footnote 21: _Come Mario disse ai patriti Romani_. "I am unable to -find the words here attributed by Leonardo to Marius, either in -Plutarch's Life of Marius or in the Apophthegmata (_Moralia_, -p.202). Nor do they occur in the writings of Valerius Maximus (who -frequently mentions Marius) nor in Velleius Paterculus (II, 11 to -43), Dio Cassius, Aulus Gellius, or Macrobius. Professor E. -MENDELSON of Dorpat, the editor of Herodian, assures me that no such -passage is the found in that author" (communication from Dr. MULLER -STRUBING). Leonardo evidently meant to allude to some well known -incident in Roman history and the mention of Marius is the result -probably of some confusion. We may perhaps read, for Marius, -Menenius Agrippa, though in that case it is true we must alter -Patriti to Plebei. The change is a serious one. but it would render -the passage perfectly clear.] by saying: That they, who deck -themselves out in the labours of others will not allow me my own. -They will say that I, having no literary skill, cannot properly -express that which I desire to treat of [Footnote 26: _le mie cose -.... che d'altra parola_. This can hardly be reconciled with Mons. -RAVAISSON'S estimate of L. da Vinci's learning. "_Leonard de Vinci -etait un admirateur et un disciple des anciens, aussi bien dans -l'art que dans la science et il tenait a passer pour tel meme aux -yeux de la posterite._" _Gaz. des Beaux arts. Oct. 1877.]; but they -do not know that my subjects are to be dealt with by experience -rather than by words [Footnote 28: See Footnote 26]; and -[experience] has been the mistress of those who wrote well. And so, -as mistress, I will cite her in all cases. - -11. - -Though I may not, like them, be able to quote other authors, I shall -rely on that which is much greater and more worthy:--on experience, -the mistress of their Masters. They go about puffed up and pompous, -dressed and decorated with [the fruits], not of their own labours, -but of those of others. And they will not allow me my own. They will -scorn me as an inventor; but how much more might they--who are not -inventors but vaunters and declaimers of the works of others--be -blamed. - -INTRODUCTION. - -And those men who are inventors and interpreters between Nature and -Man, as compared with boasters and declaimers of the works of -others, must be regarded and not otherwise esteemed than as the -object in front of a mirror, when compared with its image seen in -the mirror. For the first is something in itself, and the other -nothingness.--Folks little indebted to Nature, since it is only by -chance that they wear the human form and without it I might class -them with the herds of beasts. - -12. - -Many will think they may reasonably blame me by alleging that my -proofs are opposed to the authority of certain men held in the -highest reverence by their inexperienced judgments; not considering -that my works are the issue of pure and simple experience, who is -the one true mistress. These rules are sufficient to enable you to -know the true from the false--and this aids men to look only for -things that are possible and with due moderation--and not to wrap -yourself in ignorance, a thing which can have no good result, so -that in despair you would give yourself up to melancholy. - -13. - -Among all the studies of natural causes and reasons Light chiefly -delights the beholder; and among the great features of Mathematics -the certainty of its demonstrations is what preeminently (tends to) -elevate the mind of the investigator. Perspective, therefore, must -be preferred to all the discourses and systems of human learning. In -this branch [of science] the beam of light is explained on those -methods of demonstration which form the glory not so much of -Mathematics as of Physics and are graced with the flowers of both -[Footnote: 5. Such of Leonardo's notes on Optics or on Perspective -as bear exclusively on Mathematics or Physics could not be included -in the arrangement of the _libro di pittura_ which is here presented -to the reader. They are however but few.]. But its axioms being laid -down at great length, I shall abridge them to a conclusive brevity, -arranging them on the method both of their natural order and of -mathematical demonstration; sometimes by deduction of the effects -from the causes, and sometimes arguing the causes from the effects; -adding also to my own conclusions some which, though not included in -them, may nevertheless be inferred from them. Thus, if the Lord--who -is the light of all things--vouchsafe to enlighten me, I will treat -of Light; wherefore I will divide the present work into 3 Parts -[Footnote: 10. In the middle ages--for instance, by ROGER BACON, by -VITELLONE, with whose works Leonardo was certainly familiar, and by -all the writers of the Renaissance Perspective and Optics were not -regarded as distinct sciences. Perspective, indeed, is in its widest -application the science of seeing. Although to Leonardo the two -sciences were clearly separate, it is not so as to their names; thus -we find axioms in Optics under the heading Perspective. According to -this arrangement of the materials for the theoretical portion of the -_libro di pittura_ propositions in Perspective and in Optics stand -side by side or occur alternately. Although this particular chapter -deals only with Optics, it is not improbable that the words _partiro -la presente opera in 3 parti_ may refer to the same division into -three sections which is spoken of in chapters 14 to 17.]. - -The plan of the book on Painting (14--17). - -14. - -ON THE THREE BRANCHES OF PERSPECTIVE. - -There are three branches of perspective; the first deals with the -reasons of the (apparent) diminution of objects as they recede from -the eye, and is known as Diminishing Perspective.--The second -contains the way in which colours vary as they recede from the eye. -The third and last is concerned with the explanation of how the -objects [in a picture] ought to be less finished in proportion as -they are remote (and the names are as follows): - -Linear Perspective. The Perspective of Colour. The Perspective of -Disappearance. - -[Footnote: 13. From the character of the handwriting I infer that -this passage was written before the year 1490.]. - -15. - -ON PAINTING AND PERSPECTIVE. - -The divisions of Perspective are 3, as used in drawing; of these, -the first includes the diminution in size of opaque objects; the -second treats of the diminution and loss of outline in such opaque -objects; the third, of the diminution and loss of colour at long -distances. - -[Footnote: The division is here the same as in the previous chapter -No. 14, and this is worthy of note when we connect it with the fact -that a space of about 20 years must have intervened between the -writing of the two passages.] - -16. - -THE DISCOURSE ON PAINTING. - -Perspective, as bearing on drawing, is divided into three principal -sections; of which the first treats of the diminution in the size of -bodies at different distances. The second part is that which treats -of the diminution in colour in these objects. The third [deals with] -the diminished distinctness of the forms and outlines displayed by -the objects at various distances. - -17. - -ON THE SECTIONS OF [THE BOOK ON] PAINTING. - -The first thing in painting is that the objects it represents should -appear in relief, and that the grounds surrounding them at different -distances shall appear within the vertical plane of the foreground -of the picture by means of the 3 branches of Perspective, which are: -the diminution in the distinctness of the forms of the objects, the -diminution in their magnitude; and the diminution in their colour. -And of these 3 classes of Perspective the first results from [the -structure of] the eye, while the other two are caused by the -atmosphere which intervenes between the eye and the objects seen by -it. The second essential in painting is appropriate action and a due -variety in the figures, so that the men may not all look like -brothers, &c. - -[Footnote: This and the two foregoing chapters must have been -written in 1513 to 1516. They undoubtedly indicate the scheme which -Leonardo wished to carry out in arranging his researches on -Perspective as applied to Painting. This is important because it is -an evidence against the supposition of H. LUDWIG and others, that -Leonardo had collected his principles of Perspective in one book so -early as before 1500; a Book which, according to the hypothesis, -must have been lost at a very early period, or destroyed possibly, -by the French (!) in 1500 (see H. LUDWIG. L. da Vinci: _Das Buch van -der Malerei_. Vienna 1882 III, 7 and 8).] - -The use of the book on Painting. - -18. - -These rules are of use only in correcting the figures; since every -man makes some mistakes in his first compositions and he who knows -them not, cannot amend them. But you, knowing your errors, will -correct your works and where you find mistakes amend them, and -remember never to fall into them again. But if you try to apply -these rules in composition you will never make an end, and will -produce confusion in your works. - -These rules will enable you to have a free and sound judgment; since -good judgment is born of clear understanding, and a clear -understanding comes of reasons derived from sound rules, and sound -rules are the issue of sound experience--the common mother of all -the sciences and arts. Hence, bearing in mind the precepts of my -rules, you will be able, merely by your amended judgment, to -criticise and recognise every thing that is out of proportion in a -work, whether in the perspective or in the figures or any thing -else. - -Necessity of theoretical knowledge (19. 20). - -19. - -OF THE MISTAKES MADE BY THOSE WHO PRACTISE WITHOUT KNOWLEDGE. - -Those who are in love with practice without knowledge are like the -sailor who gets into a ship without rudder or compass and who never -can be certain whether he is going. Practice must always be founded -on sound theory, and to this Perspective is the guide and the -gateway; and without this nothing can be done well in the matter of -drawing. - -20. - -The painter who draws merely by practice and by eye, without any -reason, is like a mirror which copies every thing placed in front of -it without being conscious of their existence. - -The function of the eye (21-23). - -21. - -INTRODUCTION TO PERSPECTIVE:--THAT IS OF THE FUNCTION OF THE EYE. - -Behold here O reader! a thing concerning which we cannot trust our -forefathers, the ancients, who tried to define what the Soul and -Life are--which are beyond proof, whereas those things, which can at -any time be clearly known and proved by experience, remained for -many ages unknown or falsely understood. The eye, whose function we -so certainly know by experience, has, down to my own time, been -defined by an infinite number of authors as one thing; but I find, -by experience, that it is quite another. [Footnote 13: Compare the -note to No. 70.] - -[Footnote: In section 13 we already find it indicated that the study -of Perspective and of Optics is to be based on that of the functions -of the eye. Leonardo also refers to the science of the eye, in his -astronomical researches, for instance in MS. F 25b '_Ordine del -provare la terra essere una stella: Imprima difinisce l'occhio'_, -&c. Compare also MS. E 15b and F 60b. The principles of astronomical -perspective.] - -22. - -Here [in the eye] forms, here colours, here the character of every -part of the universe are concentrated to a point; and that point is -so marvellous a thing ... Oh! marvellous, O stupendous Necessity--by -thy laws thou dost compel every effect to be the direct result of -its cause, by the shortest path. These [indeed] are miracles;... - -In so small a space it can be reproduced and rearranged in its whole -expanse. Describe in your anatomy what proportion there is between -the diameters of all the images in the eye and the distance from -them of the crystalline lens. - -23. - -OF THE 10 ATTRIBUTES OF THE EYE, ALL CONCERNED IN PAINTING. - -Painting is concerned with all the 10 attributes of sight; which -are:--Darkness, Light, Solidity and Colour, Form and Position, -Distance and Propinquity, Motion and Rest. This little work of mine -will be a tissue [of the studies] of these attributes, reminding the -painter of the rules and methods by which he should use his art to -imitate all the works of Nature which adorn the world. - -24. - -ON PAINTING. - -Variability of the eye. - -1st. The pupil of the eye contracts, in proportion to the increase -of light which is reflected in it. 2nd. The pupil of the eye expands -in proportion to the diminution in the day light, or any other -light, that is reflected in it. 3rd. [Footnote: 8. The subject of -this third proposition we find fully discussed in MS. G. 44a.]. The -eye perceives and recognises the objects of its vision with greater -intensity in proportion as the pupil is more widely dilated; and -this can be proved by the case of nocturnal animals, such as cats, -and certain birds--as the owl and others--in which the pupil varies -in a high degree from large to small, &c., when in the dark or in -the light. 4th. The eye [out of doors] in an illuminated atmosphere -sees darkness behind the windows of houses which [nevertheless] are -light. 5th. All colours when placed in the shade appear of an equal -degree of darkness, among themselves. 6th. But all colours when -placed in a full light, never vary from their true and essential -hue. - -25. - -OF THE EYE. - -Focus of sight. - -If the eye is required to look at an object placed too near to it, -it cannot judge of it well--as happens to a man who tries to see the -tip of his nose. Hence, as a general rule, Nature teaches us that an -object can never be seen perfectly unless the space between it and -the eye is equal, at least, to the length of the face. - -Differences of perception by one eye and by both eyes (26-29). - -26. - -OF THE EYE. - -When both eyes direct the pyramid of sight to an object, that object -becomes clearly seen and comprehended by the eyes. - -27. - -Objects seen by one and the same eye appear sometimes large, and -sometimes small. - -28. - -The motion of a spectator who sees an object at rest often makes it -seem as though the object at rest had acquired the motion of the -moving body, while the moving person appears to be at rest. - -ON PAINTING. - -Objects in relief, when seen from a short distance with one eye, -look like a perfect picture. If you look with the eye _a_, _b_ at -the spot _c_, this point _c_ will appear to be at _d_, _f_, and if -you look at it with the eye _g_, _h_ will appear to be at _m_. A -picture can never contain in itself both aspects. - -29. - -Let the object in relief _t_ be seen by both eyes; if you will look -at the object with the right eye _m_, keeping the left eye _n_ shut, -the object will appear, or fill up the space, at _a_; and if you -shut the right eye and open the left, the object (will occupy the) -space _b_; and if you open both eyes, the object will no longer -appear at _a_ or _b_, but at _e_, _r_, _f_. Why will not a picture -seen by both eyes produce the effect of relief, as [real] relief -does when seen by both eyes; and why should a picture seen with one -eye give the same effect of relief as real relief would under the -same conditions of light and shade? - -[Footnote: In the sketch, _m_ is the left eye and _n_ the right, -while the text reverses this lettering. We must therefore suppose -that the face in which the eyes _m_ and _n_ are placed is opposite -to the spectator.] - -30. - -The comparative size of the image depends on the amount of light -(30-39). - -The eye will hold and retain in itself the image of a luminous body -better than that of a shaded object. The reason is that the eye is -in itself perfectly dark and since two things that are alike cannot -be distinguished, therefore the night, and other dark objects cannot -be seen or recognised by the eye. Light is totally contrary and -gives more distinctness, and counteracts and differs from the usual -darkness of the eye, hence it leaves the impression of its image. - -31. - -Every object we see will appear larger at midnight than at midday, -and larger in the morning than at midday. - -This happens because the pupil of the eye is much smaller at midday -than at any other time. - -32. - -The pupil which is largest will see objects the largest. This is -evident when we look at luminous bodies, and particularly at those -in the sky. When the eye comes out of darkness and suddenly looks up -at these bodies, they at first appear larger and then diminish; and -if you were to look at those bodies through a small opening, you -would see them smaller still, because a smaller part of the pupil -would exercise its function. - -[Footnote: 9. _buso_ in the Lomb. dialect is the same as _buco_.] - -33. - -When the eye, coming out of darkness suddenly sees a luminous body, -it will appear much larger at first sight than after long looking at -it. The illuminated object will look larger and more brilliant, when -seen with two eyes than with only one. A luminous object will appear -smaller in size, when the eye sees it through a smaller opening. A -luminous body of an oval form will appear rounder in proportion as -it is farther from the eye. - -34. - -Why when the eye has just seen the light, does the half light look -dark to it, and in the same way if it turns from the darkness the -half light look very bright? - -35. - -ON PAINTING. - -If the eye, when [out of doors] in the luminous atmosphere, sees a -place in shadow, this will look very much darker than it really is. -This happens only because the eye when out in the air contracts the -pupil in proportion as the atmosphere reflected in it is more -luminous. And the more the pupil contracts, the less luminous do the -objects appear that it sees. But as soon as the eye enters into a -shady place the darkness of the shadow suddenly seems to diminish. -This occurs because the greater the darkness into which the pupil -goes the more its size increases, and this increase makes the -darkness seem less. - -[Footnote 14: _La luce entrera_. _Luce_ occurs here in the sense of -pupil of the eye as in no 51: C. A. 84b; 245a; I--5; and in many -other places.] - -36. - -ON PERSPECTIVE. - -The eye which turns from a white object in the light of the sun and -goes into a less fully lighted place will see everything as dark. -And this happens either because the pupils of the eyes which have -rested on this brilliantly lighted white object have contracted so -much that, given at first a certain extent of surface, they will -have lost more than 3/4 of their size; and, lacking in size, they -are also deficient in [seeing] power. Though you might say to me: A -little bird (then) coming down would see comparatively little, and -from the smallness of his pupils the white might seem black! To this -I should reply that here we must have regard to the proportion of -the mass of that portion of the brain which is given up to the sense -of sight and to nothing else. Or--to return--this pupil in Man -dilates and contracts according to the brightness or darkness of -(surrounding) objects; and since it takes some time to dilate and -contract, it cannot see immediately on going out of the light and -into the shade, nor, in the same way, out of the shade into the -light, and this very thing has already deceived me in painting an -eye, and from that I learnt it. - -37. - -Experiment [showing] the dilatation and contraction of the pupil, -from the motion of the sun and other luminaries. In proportion as -the sky is darker the stars appear of larger size, and if you were -to light up the medium these stars would look smaller; and this -difference arises solely from the pupil which dilates and contracts -with the amount of light in the medium which is interposed between -the eye and the luminous body. Let the experiment be made, by -placing a candle above your head at the same time that you look at a -star; then gradually lower the candle till it is on a level with the -ray that comes from the star to the eye, and then you will see the -star diminish so much that you will almost lose sight of it. - -[Footnote: No reference is made in the text to the letters on the -accompanying diagram.] - -38. - -The pupil of the eye, in the open air, changes in size with every -degree of motion from the sun; and at every degree of its changes -one and the same object seen by it will appear of a different size; -although most frequently the relative scale of surrounding objects -does not allow us to detect these variations in any single object we -may look at. - -39. - -The eye--which sees all objects reversed--retains the images for -some time. This conclusion is proved by the results; because, the -eye having gazed at light retains some impression of it. After -looking (at it) there remain in the eye images of intense -brightness, that make any less brilliant spot seem dark until the -eye has lost the last trace of the impression of the stronger light. - -_II. - -Linear Perspective. - -We see clearly from the concluding sentence of section 49, where the -author directly addresses the painter, that he must certainly have -intended to include the elements of mathematics in his Book on the -art of Painting. They are therefore here placed at the beginning. In -section 50 the theory of the "Pyramid of Sight" is distinctly and -expressly put forward as the fundamental principle of linear -perspective, and sections 52 to 57 treat of it fully. This theory of -sight can scarcely be traced to any author of antiquity. Such -passages as occur in Euclid for instance, may, it is true, have -proved suggestive to the painters of the Renaissance, but it would -be rash to say any thing decisive on this point. - -Leon Battista Alberti treats of the "Pyramid of Sight" at some -length in his first Book of Painting; but his explanation differs -widely from Leonardo's in the details. Leonardo, like Alberti, may -have borrowed the broad lines of his theory from some views commonly -accepted among painters at the time; but he certainly worked out its -application in a perfectly original manner. - -The axioms as to the perception of the pyramid of rays are followed -by explanations of its origin, and proofs of its universal -application (58--69). The author recurs to the subject with endless -variations; it is evidently of fundamental importance in his -artistic theory and practice. It is unnecessary to discuss how far -this theory has any scientific value at the present day; so much as -this, at any rate, seems certain: that from the artist's point of -view it may still claim to be of immense practical utility. - -According to Leonardo, on one hand, the laws of perspective are an -inalienable condition of the existence of objects in space; on the -other hand, by a natural law, the eye, whatever it sees and wherever -it turns, is subjected to the perception of the pyramid of rays in -the form of a minute target. Thus it sees objects in perspective -independently of the will of the spectator, since the eye receives -the images by means of the pyramid of rays "just as a magnet -attracts iron". - -In connection with this we have the function of the eye explained by -the Camera obscura, and this is all the more interesting and -important because no writer previous to Leonardo had treated of this -subject_ (70--73). _Subsequent passages, of no less special interest, -betray his knowledge of refraction and of the inversion of the image -in the camera and in the eye_ (74--82). - -_From the principle of the transmission of the image to the eye and -to the camera obscura he deduces the means of producing an -artificial construction of the pyramid of rays or--which is the same -thing--of the image. The fundamental axioms as to the angle of sight -and the vanishing point are thus presented in a manner which is as -complete as it is simple and intelligible_ (86--89). - -_Leonardo distinguishes between simple and complex perspective_ (90, -91). _The last sections treat of the apparent size of objects at -various distances and of the way to estimate it_ (92--109). - -General remarks on perspective (40-41). - -40. - -ON PAINTING. - -Perspective is the best guide to the art of Painting. - -[Footnote: 40. Compare 53, 2.] - -41. - -The art of perspective is of such a nature as to make what is flat -appear in relief and what is in relief flat. - -The elements of perspective--Of the Point (42-46). - -42. - -All the problems of perspective are made clear by the five terms of -mathematicians, which are:--the point, the line, the angle, the -superficies and the solid. The point is unique of its kind. And the -point has neither height, breadth, length, nor depth, whence it is -to be regarded as indivisible and as having no dimensions in space. -The line is of three kinds, straight, curved and sinuous and it has -neither breadth, height, nor depth. Hence it is indivisible, -excepting in its length, and its ends are two points. The angle is -the junction of two lines in a point. - -43. - -A point is not part of a line. - -44. - -OF THE NATURAL POINT. - -The smallest natural point is larger than all mathematical points, -and this is proved because the natural point has continuity, and any -thing that is continuous is infinitely divisible; but the -mathematical point is indivisible because it has no size. - -[Footnote: This definition was inserted by Leonardo on a MS. copy on -parchment of the well-known _"Trattato d'Architettura civile e -militare"_ &c. by FRANCESCO DI GIORGIO; opposite a passage where the -author says: _'In prima he da sapere che punto e quella parie della -quale he nulla--Linia he luncheza senza apieza; &c.] - -45. - -1, The superficies is a limitation of the body. 2, and the -limitation of a body is no part of that body. 4, and the limitation -of one body is that which begins another. 3, that which is not part -of any body is nothing. Nothing is that which fills no space. - -If one single point placed in a circle may be the starting point of -an infinite number of lines, and the termination of an infinite -number of lines, there must be an infinite number of points -separable from this point, and these when reunited become one again; -whence it follows that the part may be equal to the whole. - -46. - -The point, being indivisible, occupies no space. That which occupies -no space is nothing. The limiting surface of one thing is the -beginning of another. 2. That which is no part of any body is called -nothing. 1. That which has no limitations, has no form. The -limitations of two conterminous bodies are interchangeably the -surface of each. All the surfaces of a body are not parts of that -body. - -Of the line (47-48). - -47. - -DEFINITION OF THE NATURE OF THE LINE. - -The line has in itself neither matter nor substance and may rather -be called an imaginary idea than a real object; and this being its -nature it occupies no space. Therefore an infinite number of lines -may be conceived of as intersecting each other at a point, which has -no dimensions and is only of the thickness (if thickness it may be -called) of one single line. - -HOW WE MAY CONCLUDE THAT A SUPERFICIES TERMINATES IN A POINT? - -An angular surface is reduced to a point where it terminates in an -angle. Or, if the sides of that angle are produced in a straight -line, then--beyond that angle--another surface is generated, -smaller, or equal to, or larger than the first. - -48. - -OF DRAWING OUTLINE. - -Consider with the greatest care the form of the outlines of every -object, and the character of their undulations. And these -undulations must be separately studied, as to whether the curves are -composed of arched convexities or angular concavities. - -49. - -The nature of the outline. - -The boundaries of bodies are the least of all things. The -proposition is proved to be true, because the boundary of a thing is -a surface, which is not part of the body contained within that -surface; nor is it part of the air surrounding that body, but is the -medium interposted between the air and the body, as is proved in its -place. But the lateral boundaries of these bodies is the line -forming the boundary of the surface, which line is of invisible -thickness. Wherefore O painter! do not surround your bodies with -lines, and above all when representing objects smaller than nature; -for not only will their external outlines become indistinct, but -their parts will be invisible from distance. - -50. - -Definition of Perspective. - -[Drawing is based upon perspective, which is nothing else than a -thorough knowledge of the function of the eye. And this function -simply consists in receiving in a pyramid the forms and colours of -all the objects placed before it. I say in a pyramid, because there -is no object so small that it will not be larger than the spot where -these pyramids are received into the eye. Therefore, if you extend -the lines from the edges of each body as they converge you will -bring them to a single point, and necessarily the said lines must -form a pyramid.] - -[Perspective is nothing more than a rational demonstration applied -to the consideration of how objects in front of the eye transmit -their image to it, by means of a pyramid of lines. The _Pyramid_ is -the name I apply to the lines which, starting from the surface and -edges of each object, converge from a distance and meet in a single -point.] - -[Perspective is a rational demonstration, by which we may -practically and clearly understand how objects transmit their own -image, by lines forming a Pyramid (centred) in the eye.] - -Perspective is a rational demonstration by which experience confirms -that every object sends its image to the eye by a pyramid of lines; -and bodies of equal size will result in a pyramid of larger or -smaller size, according to the difference in their distance, one -from the other. By a pyramid of lines I mean those which start from -the surface and edges of bodies, and, converging from a distance -meet in a single point. A point is said to be that which [having no -dimensions] cannot be divided, and this point placed in the eye -receives all the points of the cone. - -[Footnote: 50. 1-5. Compare with this the Proem. No. 21. The -paragraphs placed in brackets: lines 1-9, 10-14, and 17--20, are -evidently mere sketches and, as such, were cancelled by the writer; -but they serve as a commentary on the final paragraph, lines 22-29.] - -51. - -IN WHAT WAY THE EYE SEES OBJECTS PLACED IN FRONT OF IT. - -The perception of the object depends on the direction of the eye. - -Supposing that the ball figured above is the ball of the eye and let -the small portion of the ball which is cut off by the line _s t_ be -the pupil and all the objects mirrored on the centre of the face of -the eye, by means of the pupil, pass on at once and enter the pupil, -passing through the crystalline humour, which does not interfere in -the pupil with the things seen by means of the light. And the pupil -having received the objects, by means of the light, immediately -refers them and transmits them to the intellect by the line _a b_. -And you must know that the pupil transmits nothing perfectly to the -intellect or common sense excepting when the objects presented to it -by means of light, reach it by the line _a b;_ as, for instance, by -the line _b c_. For although the lines _m n_ and _f g_ may be seen -by the pupil they are not perfectly taken in, because they do not -coincide with the line _a b_. And the proof is this: If the eye, -shown above, wants to count the letters placed in front, the eye -will be obliged to turn from letter to letter, because it cannot -discern them unless they lie in the line _a b;_ as, for instance, in -the line _a c_. All visible objects reach the eye by the lines of a -pyramid, and the point of the pyramid is the apex and centre of it, -in the centre of the pupil, as figured above. - -[Footnote: 51. In this problem the eye is conceived of as fixed and -immovable; this is plain from line 11.] - -Experimental proof of the existence of the pyramid of sight (52-55). - -52. - -Perspective is a rational demonstration, confirmed by experience, -that all objects transmit their image to the eye by a pyramid of -lines. - -By a pyramid of lines I understand those lines which start from the -edges of the surface of bodies, and converging from a distance, meet -in a single point; and this point, in the present instance, I will -show to be situated in the eye which is the universal judge of all -objects. By a point I mean that which cannot be divided into parts; -therefore this point, which is situated in the eye, being -indivisible, no body is seen by the eye, that is not larger than -this point. This being the case it is inevitable that the lines -which come from the object to the point must form a pyramid. And if -any man seeks to prove that the sense of sight does not reside in -this point, but rather in the black spot which is visible in the -middle of the pupil, I might reply to him that a small object could -never diminish at any distance, as it might be a grain of millet or -of oats or of some similar thing, and that object, if it were larger -than the said [black] spot would never be seen as a whole; as may be -seen in the diagram below. Let _a_. be the seat of sight, _b e_ the -lines which reach the eye. Let _e d_ be the grains of millet within -these lines. You plainly see that these will never diminish by -distance, and that the body _m n_ could not be entirely covered by -it. Therefore you must confess that the eye contains within itself -one single indivisible point _a_, to which all the points converge -of the pyramid of lines starting from an object, as is shown below. -Let _a_. _b_. be the eye; in the centre of it is the point above -mentioned. If the line _e f_ is to enter as an image into so small -an opening in the eye, you must confess that the smaller object -cannot enter into what is smaller than itself unless it is -diminished, and by diminishing it must take the form of a pyramid. - -53. - -PERSPECTIVE. - -Perspective comes in where judgment fails [as to the distance] in -objects which diminish. The eye can never be a true judge for -determining with exactitude how near one object is to another which -is equal to it [in size], if the top of that other is on the level -of the eye which sees them on that side, excepting by means of the -vertical plane which is the standard and guide of perspective. Let -_n_ be the eye, _e f_ the vertical plane above mentioned. Let _a b c -d_ be the three divisions, one below the other; if the lines _a n_ -and _c n_ are of a given length and the eye _n_ is in the centre, -then _a b_ will look as large as _b c. c d_ is lower and farther off -from _n_, therefore it will look smaller. And the same effect will -appear in the three divisions of a face when the eye of the painter -who is drawing it is on a level with the eye of the person he is -painting. - -54. - -TO PROVE HOW OBJECTS REACH THE EYE. - -If you look at the sun or some other luminous body and then shut -your eyes you will see it again inside your eye for a long time. -This is evidence that images enter into the eye. - -The relations of the distance points to the vanishing point (55-56). - -55. - -ELEMENTS OF PERSPECTIVE. - -All objects transmit their image to the eye in pyramids, and the -nearer to the eye these pyramids are intersected the smaller will -the image appear of the objects which cause them. Therefore, you may -intersect the pyramid with a vertical plane [Footnote 4: _Pariete_. -Compare the definitions in 85, 2-5, 6-27. These lines refer -exclusively to the third diagram. For the better understanding of -this it should be observed that _c s_ must be regarded as -representing the section or profile of a square plane, placed -horizontally (comp. lines 11, 14, 17) for which the word _pianura_ -is subsequently employed (20, 22). Lines 6-13 contain certain -preliminary observations to guide the reader in understanding the -diagram; the last three seem to have been added as a supplement. -Leonardo's mistake in writing _t denota_ (line 6) for _f denota_ has -been rectified.] which reaches the base of the pyramid as is shown -in the plane _a n_. - -The eye _f_ and the eye _t_ are one and the same thing; but the eye -_f_ marks the distance, that is to say how far you are standing from -the object; and the eye _t_ shows you the direction of it; that is -whether you are opposite, or on one side, or at an angle to the -object you are looking at. And remember that the eye _f_ and the eye -_t_ must always be kept on the same level. For example if you raise -or lower the eye from the distance point _f_ you must do the same -with the direction point _t_. And if the point _f_ shows how far the -eye is distant from the square plane but does not show on which side -it is placed--and, if in the same way, the point _t_ show _s_ the -direction and not the distance, in order to ascertain both you must -use both points and they will be one and the same thing. If the eye -_f_ could see a perfect square of which all the sides were equal to -the distance between _s_ and _c_, and if at the nearest end of the -side towards the eye a pole were placed, or some other straight -object, set up by a perpendicular line as shown at _r s_--then, I -say, that if you were to look at the side of the square that is -nearest to you it will appear at the bottom of the vertical plane _r -s_, and then look at the farther side and it would appear to you at -the height of the point _n_ on the vertical plane. Thus, by this -example, you can understand that if the eye is above a number of -objects all placed on the same level, one beyond another, the more -remote they are the higher they will seem, up to the level of the -eye, but no higher; because objects placed upon the level on which -your feet stand, so long as it is flat--even if it be extended into -infinity--would never be seen above the eye; since the eye has in -itself the point towards which all the cones tend and converge which -convey the images of the objects to the eye. And this point always -coincides with the point of diminution which is the extreme of all -we can see. And from the base line of the first pyramid as far as -the diminishing point - -[Footnote: The two diagrams above the chapter are explained by the -first five lines. They have, however, more letters than are referred -to in the text, a circumstance we frequently find occasion to -remark.] - -56. - -there are only bases without pyramids which constantly diminish up -to this point. And from the first base where the vertical plane is -placed towards the point in the eye there will be only pyramids -without bases; as shown in the example given above. Now, let _a b_ -be the said vertical plane and _r_ the point of the pyramid -terminating in the eye, and _n_ the point of diminution which is -always in a straight line opposite the eye and always moves as the -eye moves--just as when a rod is moved its shadow moves, and moves -with it, precisely as the shadow moves with a body. And each point -is the apex of a pyramid, all having a common base with the -intervening vertical plane. But although their bases are equal their -angles are not equal, because the diminishing point is the -termination of a smaller angle than that of the eye. If you ask me: -"By what practical experience can you show me these points?" I -reply--so far as concerns the diminishing point which moves with you ---when you walk by a ploughed field look at the straight furrows -which come down with their ends to the path where you are walking, -and you will see that each pair of furrows will look as though they -tried to get nearer and meet at the [farther] end. - -[Footnote: For the easier understanding of the diagram and of its -connection with the preceding I may here remark that the square -plane shown above in profile by the line _c s_ is here indicated by -_e d o p_. According to lines 1, 3 _a b_ must be imagined as a plane -of glass placed perpendicularly at _o p_.] - -57. - -How to measure the pyramid of vision. - -As regards the point in the eye; it is made more intelligible by -this: If you look into the eye of another person you will see your -own image. Now imagine 2 lines starting from your ears and going to -the ears of that image which you see in the other man's eye; you -will understand that these lines converge in such a way that they -would meet in a point a little way beyond your own image mirrored in -the eye. And if you want to measure the diminution of the pyramid in -the air which occupies the space between the object seen and the -eye, you must do it according to the diagram figured below. Let _m -n_ be a tower, and _e f_ a, rod, which you must move backwards and -forwards till its ends correspond with those of the tower [Footnote -9: _I sua stremi .. della storre_ (its ends ... of the tower) this -is the case at _e f_.]; then bring it nearer to the eye, at _c d_ -and you will see that the image of the tower seems smaller, as at _r -o_. Then [again] bring it closer to the eye and you will see the rod -project far beyond the image of the tower from _a_ to _b_ and from -_t_ to _b_, and so you will discern that, a little farther within, -the lines must converge in a point. - -The Production of pyramid of Vision (58-60). - -58. - -PERSPECTIVE. - -The instant the atmosphere is illuminated it will be filled with an -infinite number of images which are produced by the various bodies -and colours assembled in it. And the eye is the target, a loadstone, -of these images. - -59. - -The whole surface of opaque bodies displays its whole image in all -the illuminated atmosphere which surrounds them on all sides. - -60. - -That the atmosphere attracts to itself, like a loadstone, all the -images of the objects that exist in it, and not their forms merely -but their nature may be clearly seen by the sun, which is a hot and -luminous body. All the atmosphere, which is the all-pervading -matter, absorbs light and heat, and reflects in itself the image of -the source of that heat and splendour and, in each minutest portion, -does the same. The Northpole does the same as the loadstone shows; -and the moon and the other planets, without suffering any -diminution, do the same. Among terrestrial things musk does the same -and other perfumes. - -61. - -All bodies together, and each by itself, give off to the surrounding -air an infinite number of images which are all-pervading and each -complete, each conveying the nature, colour and form of the body -which produces it. - -It can clearly be shown that all bodies are, by their images, -all-pervading in the surrounding atmosphere, and each complete in -itself as to substance form and colour; this is seen by the images -of the various bodies which are reproduced in one single perforation -through which they transmit the objects by lines which intersect and -cause reversed pyramids, from the objects, so that they are upside -down on the dark plane where they are first reflected. The reason of -this is-- - -[Footnote: The diagram intended to illustrate the statement (Pl. II -No. i) occurs in the original between lines 3 and 4. The three -circles must be understood to represent three luminous bodies which -transmit their images through perforations in a wall into a dark -chamber, according to a law which is more fully explained in 75?81. -So far as concerns the present passage the diagram is only intended -to explain that the images of the three bodies may be made to -coalesce at any given spot. In the circles are written, -giallo--yellow, biacho--white, rosso--red. - -The text breaks off at line 8. The paragraph No.40 follows here in -the original MS.] - -62. - -Every point is the termination of an infinite number of lines, which -diverge to form a base, and immediately, from the base the same -lines converge to a pyramid [imaging] both the colour and form. No -sooner is a form created or compounded than suddenly infinite lines -and angles are produced from it; and these lines, distributing -themselves and intersecting each other in the air, give rise to an -infinite number of angles opposite to each other. Given a base, each -opposite angle, will form a triangle having a form and proportion -equal to the larger angle; and if the base goes twice into each of -the 2 lines of the pyramid the smaller triangle will do the same. - -63. - -Every body in light and shade fills the surrounding air with -infinite images of itself; and these, by infinite pyramids diffused -in the air, represent this body throughout space and on every side. -Each pyramid that is composed of a long assemblage of rays includes -within itself an infinite number of pyramids and each has the same -power as all, and all as each. A circle of equidistant pyramids of -vision will give to their object angles of equal size; and an eye at -each point will see the object of the same size. The body of the -atmosphere is full of infinite pyramids composed of radiating -straight lines, which are produced from the surface of the bodies in -light and shade, existing in the air; and the farther they are from -the object which produces them the more acute they become and -although in their distribution they intersect and cross they never -mingle together, but pass through all the surrounding air, -independently converging, spreading, and diffused. And they are all -of equal power [and value]; all equal to each, and each equal to -all. By these the images of objects are transmitted through all -space and in every direction, and each pyramid, in itself, includes, -in each minutest part, the whole form of the body causing it. - -64. - -The body of the atmosphere is full of infinite radiating pyramids -produced by the objects existing in it. These intersect and cross -each other with independent convergence without interfering with -each other and pass through all the surrounding atmosphere; and are -of equal force and value--all being equal to each, each to all. And -by means of these, images of the body are transmitted everywhere and -on all sides, and each receives in itself every minutest portion of -the object that produces it. - -Proof by experiment (65-66). - -65. - -PERSPECTIVE. - -The air is filled with endless images of the objects distributed in -it; and all are represented in all, and all in one, and all in each, -whence it happens that if two mirrors are placed in such a manner as -to face each other exactly, the first will be reflected in the -second and the second in the first. The first being reflected in the -second takes to it the image of itself with all the images -represented in it, among which is the image of the second mirror, -and so, image within image, they go on to infinity in such a manner -as that each mirror has within it a mirror, each smaller than the -last and one inside the other. Thus, by this example, it is clearly -proved that every object sends its image to every spot whence the -object itself can be seen; and the converse: That the same object -may receive in itself all the images of the objects that are in -front of it. Hence the eye transmits through the atmosphere its own -image to all the objects that are in front of it and receives them -into itself, that is to say on its surface, whence they are taken in -by the common sense, which considers them and if they are pleasing -commits them to the memory. Whence I am of opinion: That the -invisible images in the eyes are produced towards the object, as the -image of the object to the eye. That the images of the objects must -be disseminated through the air. An instance may be seen in several -mirrors placed in a circle, which will reflect each other endlessly. -When one has reached the other it is returned to the object that -produced it, and thence--being diminished--it is returned again to -the object and then comes back once more, and this happens -endlessly. If you put a light between two flat mirrors with a -distance of 1 braccio between them you will see in each of them an -infinite number of lights, one smaller than another, to the last. If -at night you put a light between the walls of a room, all the parts -of that wall will be tinted with the image of that light. And they -will receive the light and the light will fall on them, mutually, -that is to say, when there is no obstacle to interrupt the -transmission of the images. This same example is seen in a greater -degree in the distribution of the solar rays which all together, and -each by itself, convey to the object the image of the body which -causes it. That each body by itself alone fills with its images the -atmosphere around it, and that the same air is able, at the same -time, to receive the images of the endless other objects which are -in it, this is clearly proved by these examples. And every object is -everywhere visible in the whole of the atmosphere, and the whole in -every smallest part of it; and all the objects in the whole, and all -in each smallest part; each in all and all in every part. - -66. - -The images of objects are all diffused through the atmosphere which -receives them; and all on every side in it. To prove this, let _a c -e_ be objects of which the images are admitted to a dark chamber by -the small holes _n p_ and thrown upon the plane _f i_ opposite to -these holes. As many images will be produced in the chamber on the -plane as the number of the said holes. - -67. - -General conclusions. - -All objects project their whole image and likeness, diffused and -mingled in the whole of the atmosphere, opposite to themselves. The -image of every point of the bodily surface, exists in every part of -the atmosphere. All the images of the objects are in every part of -the atmosphere. The whole, and each part of the image of the -atmosphere is [reflected] in each point of the surface of the bodies -presented to it. Therefore both the part and the whole of the images -of the objects exist, both in the whole and in the parts of the -surface of these visible bodies. Whence we may evidently say that -the image of each object exists, as a whole and in every part, in -each part and in the whole interchangeably in every existing body. -As is seen in two mirrors placed opposite to each other. - -68. - -That the contrary is impossible. - -It is impossible that the eye should project from itself, by visual -rays, the visual virtue, since, as soon as it opens, that front -portion [of the eye] which would give rise to this emanation would -have to go forth to the object and this it could not do without -time. And this being so, it could not travel so high as the sun in a -month's time when the eye wanted to see it. And if it could reach -the sun it would necessarily follow that it should perpetually -remain in a continuous line from the eye to the sun and should -always diverge in such a way as to form between the sun and the eye -the base and the apex of a pyramid. This being the case, if the eye -consisted of a million worlds, it would not prevent its being -consumed in the projection of its virtue; and if this virtue would -have to travel through the air as perfumes do, the winds would bent -it and carry it into another place. But we do [in fact] see the mass -of the sun with the same rapidity as [an object] at the distance of -a braccio, and the power of sight is not disturbed by the blowing of -the winds nor by any other accident. - -[Footnote: The view here refuted by Leonardo was maintained among -others by Bramantino, Leonardo's Milanese contemporary. LOMAZZO -writes as follows in his Trattato dell' Arte della pittura &c. -(Milano 1584. Libr. V cp. XXI): Sovviemmi di aver gia letto in certi -scritti alcune cose di Bramantino milanese, celebratissimo pittore, -attenente alla prospettiva, le quali ho voluto riferire, e quasi -intessere in questo luogo, affinche sappiamo qual fosse l'opinione -di cosi chiaro e famoso pittore intorno alla prospettiva . . Scrive -Bramantino che la prospettiva e una cosa che contrafa il naturale, e -che cio si fa in tre modi - -Circa il primo modo che si fa con ragione, per essere la cosa in -poche parole conclusa da Bramantino in maniera che giudico non -potersi dir meglio, contenendovi si tutta Parte del principio al -fine, io riferiro per appunto le proprie parole sue (cp. XXII, Prima -prospettiva di Bramantino). La prima prospettiva fa le cose di -punto, e l'altra non mai, e la terza piu appresso. Adunque la prima -si dimanda prospettiva, cioe ragione, la quale fa l'effetto dell' -occhio, facendo crescere e calare secondo gli effetti degli occhi. -Questo crescere e calare non procede della cosa propria, che in se -per esser lontana, ovvero vicina, per quello effetto non puo -crescere e sminuire, ma procede dagli effetti degli occhi, i quali -sono piccioli, e percio volendo vedere tanto gran cosa_, bisogna che -mandino fuora la virtu visiva, _la quale si dilata in tanta -larghezza, che piglia tutto quello che vuoi vedere, ed_ arrivando a -quella cosa la vede dove e: _e da lei agli occhi per quello circuito -fino all' occhio, e tutto quello termine e pieno di quella cosa_. - -It is worthy of note that Leonardo had made his memorandum refuting -this view, at Milan in 1492] - -69. - -A parallel case. - -Just as a stone flung into the water becomes the centre and cause of -many circles, and as sound diffuses itself in circles in the air: so -any object, placed in the luminous atmosphere, diffuses itself in -circles, and fills the surrounding air with infinite images of -itself. And is repeated, the whole every-where, and the whole in -every smallest part. This can be proved by experiment, since if you -shut a window that faces west and make a hole [Footnote: 6. Here the -text breaks off.] . . - -[Footnote: Compare LIBRI, _Histoire des sciences mathematiques en -Italie_. Tome III, p. 43.] - -The function of the eye as explained by the camera obscura (70. 71). - -70. - -If the object in front of the eye sends its image to the eye, the -eye, on the other hand, sends its image to the object, and no -portion whatever of the object is lost in the images it throws off, -for any reason either in the eye or the object. Therefore we may -rather believe it to be the nature and potency of our luminous -atmosphere which absorbs the images of the objects existing in it, -than the nature of the objects, to send their images through the -air. If the object opposite to the eye were to send its image to the -eye, the eye would have to do the same to the object, whence it -might seem that these images were an emanation. But, if so, it would -be necessary [to admit] that every object became rapidly smaller; -because each object appears by its images in the surrounding -atmosphere. That is: the whole object in the whole atmosphere, and -in each part; and all the objects in the whole atmosphere and all of -them in each part; speaking of that atmosphere which is able to -contain in itself the straight and radiating lines of the images -projected by the objects. From this it seems necessary to admit that -it is in the nature of the atmosphere, which subsists between the -objects, and which attracts the images of things to itself like a -loadstone, being placed between them. - -PROVE HOW ALL OBJECTS, PLACED IN ONE POSITION, ARE ALL EVERYWHERE -AND ALL IN EACH PART. - -I say that if the front of a building--or any open piazza or -field--which is illuminated by the sun has a dwelling opposite to -it, and if, in the front which does not face the sun, you make a -small round hole, all the illuminated objects will project their -images through that hole and be visible inside the dwelling on the -opposite wall which may be made white; and there, in fact, they will -be upside down, and if you make similar openings in several places -in the same wall you will have the same result from each. Hence the -images of the illuminated objects are all everywhere on this wall -and all in each minutest part of it. The reason, as we clearly know, -is that this hole must admit some light to the said dwelling, and -the light admitted by it is derived from one or many luminous -bodies. If these bodies are of various colours and shapes the rays -forming the images are of various colours and shapes, and so will -the representations be on the wall. - -[Footnote: 70. 15--23. This section has already been published in the -"_Saggio delle Opere di Leonardo da Vinci_" Milan 1872, pp. 13, 14. -G. Govi observes upon it, that Leonardo is not to be regarded as the -inventor of the Camera obscura, but that he was the first to explain -by it the structure of the eye. An account of the Camera obscura -first occurs in CESARE CESARINI's Italian version of Vitruvius, pub. -1523, four years after Leonardo's death. Cesarini expressly names -Benedettino Don Papnutio as the inventor of the Camera obscura. In -his explanation of the function of the eye by a comparison with the -Camera obscura Leonardo was the precursor of G. CARDANO, Professor -of Medicine at Bologna (died 1576) and it appears highly probable -that this is, in fact, the very discovery which Leonardo ascribes to -himself in section 21 without giving any further details.] - -71. - -HOW THE IMAGES OF OBJECTS RECEIVED BY THE EYE INTERSECT WITHIN THE -CRYSTALLINE HUMOUR OF THE EYE. - -An experiment, showing how objects transmit their images or -pictures, intersecting within the eye in the crystalline humour, is -seen when by some small round hole penetrate the images of -illuminated objects into a very dark chamber. Then, receive these -images on a white paper placed within this dark room and rather near -to the hole and you will see all the objects on the paper in their -proper forms and colours, but much smaller; and they will be upside -down by reason of that very intersection. These images being -transmitted from a place illuminated by the sun will seem actually -painted on this paper which must be extremely thin and looked at -from behind. And let the little perforation be made in a very thin -plate of iron. Let _a b e d e_ be the object illuminated by the sun -and _o r_ the front of the dark chamber in which is the said hole at -_n m_. Let _s t_ be the sheet of paper intercepting the rays of the -images of these objects upside down, because the rays being -straight, _a_ on the right hand becomes _k_ on the left, and _e_ on -the left becomes _f_ on the right; and the same takes place inside -the pupil. - -[Footnote: This chapter is already known through a translation into -French by VENTURI. Compare his '_Essai sur les ouvrages -physico-mathematiques de L. da Vinci avec des fragments tires de ses -Manuscrits, apportes de l'Italie. Lu a la premiere classe de -l'Institut national des Sciences et Arts.' Paris, An V_ (1797).] - -The practice of perspective (72. 73). - -72. - -In the practice of perspective the same rules apply to light and to -the eye. - -73. - -The object which is opposite to the pupil of the eye is seen by that -pupil and that which is opposite to the eye is seen by the pupil. - -Refraction of the rays falling upon the eye (74. 75) - -74. - -The lines sent forth by the image of an object to the eye do not -reach the point within the eye in straight lines. - -75. - -If the judgment of the eye is situated within it, the straight lines -of the images are refracted on its surface because they pass through -the rarer to the denser medium. If, when you are under water, you -look at objects in the air you will see them out of their true -place; and the same with objects under water seen from the air. - -The intersection of the rays (76-82). - -76. - -The inversion of the images. - -All the images of objects which pass through a window [glass pane] -from the free outer air to the air confined within walls, are seen -on the opposite side; and an object which moves in the outer air -from east to west will seem in its shadow, on the wall which is -lighted by this confined air, to have an opposite motion. - -77. - -THE PRINCIPLE ON WHICH THE IMAGES OF BODIES PASS IN BETWEEN THE -MARGINS OF THE OPENINGS BY WHICH THEY ENTER. - -What difference is there in the way in which images pass through -narrow openings and through large openings, or in those which pass -by the sides of shaded bodies? By moving the edges of the opening -through which the images are admitted, the images of immovable -objects are made to move. And this happens, as is shown in the 9th -which demonstrates: [Footnote 11: _per la 9a che dicie_. When -Leonardo refers thus to a number it serves to indicate marginal -diagrams; this can in some instances be distinctly proved. The ninth -sketch on the page W. L. 145 b corresponds to the middle sketch of -the three reproduced.] the images of any object are all everywhere, -and all in each part of the surrounding air. It follows that if one -of the edges of the hole by which the images are admitted to a dark -chamber is moved it cuts off those rays of the image that were in -contact with it and gets nearer to other rays which previously were -remote from it &c. - -OF THE MOVEMENT OF THE EDGE AT THE RIGHT OR LEFT, OR THE UPPER, OR -LOWER EDGE. - -If you move the right side of the opening the image on the left will -move [being that] of the object which entered on the right side of -the opening; and the same result will happen with all the other -sides of the opening. This can be proved by the 2nd of this which -shows: all the rays which convey the images of objects through the -air are straight lines. Hence, if the images of very large bodies -have to pass through very small holes, and beyond these holes -recover their large size, the lines must necessarily intersect. - -[Footnote: 77. 2. In the first of the three diagrams Leonardo had -drawn only one of the two margins, et _m_.] - -78. - -Necessity has provided that all the images of objects in front of -the eye shall intersect in two places. One of these intersections is -in the pupil, the other in the crystalline lens; and if this were -not the case the eye could not see so great a number of objects as -it does. This can be proved, since all the lines which intersect do -so in a point. Because nothing is seen of objects excepting their -surface; and their edges are lines, in contradistinction to the -definition of a surface. And each minute part of a line is equal to -a point; for _smallest_ is said of that than which nothing can be -smaller, and this definition is equivalent to the definition of the -point. Hence it is possible for the whole circumference of a circle -to transmit its image to the point of intersection, as is shown in -the 4th of this which shows: all the smallest parts of the images -cross each other without interfering with each other. These -demonstrations are to illustrate the eye. No image, even of the -smallest object, enters the eye without being turned upside down; -but as it penetrates into the crystalline lens it is once more -reversed and thus the image is restored to the same position within -the eye as that of the object outside the eye. - -79. - -OF THE CENTRAL LINE OF THE EYE. - -Only one line of the image, of all those that reach the visual -virtue, has no intersection; and this has no sensible dimensions -because it is a mathematical line which originates from a -mathematical point, which has no dimensions. - -According to my adversary, necessity requires that the central line -of every image that enters by small and narrow openings into a dark -chamber shall be turned upside down, together with the images of the -bodies that surround it. - -80. - -AS TO WHETHER THE CENTRAL LINE OF THE IMAGE CAN BE INTERSECTED, OR -NOT, WITHIN THE OPENING. - -It is impossible that the line should intersect itself; that is, -that its right should cross over to its left side, and so, its left -side become its right side. Because such an intersection demands two -lines, one from each side; for there can be no motion from right to -left or from left to right in itself without such extension and -thickness as admit of such motion. And if there is extension it is -no longer a line but a surface, and we are investigating the -properties of a line, and not of a surface. And as the line, having -no centre of thickness cannot be divided, we must conclude that the -line can have no sides to intersect each other. This is proved by -the movement of the line _a f_ to _a b_ and of the line _e b_ to _e -f_, which are the sides of the surface _a f e b_. But if you move -the line _a b_ and the line _e f_, with the frontends _a e_, to the -spot _c_, you will have moved the opposite ends _f b_ towards each -other at the point _d_. And from the two lines you will have drawn -the straight line _c d_ which cuts the middle of the intersection of -these two lines at the point _n_ without any intersection. For, you -imagine these two lines as having breadth, it is evident that by -this motion the first will entirely cover the other--being equal -with it--without any intersection, in the position _c d_. And this -is sufficient to prove our proposition. - -81. - -HOW THE INNUMERABLE RAYS FROM INNUMERABLE IMAGES CAN CONVERGE TO A -POINT. - -Just as all lines can meet at a point without interfering with each -other--being without breadth or thickness--in the same way all the -images of surfaces can meet there; and as each given point faces the -object opposite to it and each object faces an opposite point, the -converging rays of the image can pass through the point and diverge -again beyond it to reproduce and re-magnify the real size of that -image. But their impressions will appear reversed--as is shown in -the first, above; where it is said that every image intersects as it -enters the narrow openings made in a very thin substance. - -Read the marginal text on the other side. - -In proportion as the opening is smaller than the shaded body, so -much less will the images transmitted through this opening intersect -each other. The sides of images which pass through openings into a -dark room intersect at a point which is nearer to the opening in -proportion as the opening is narrower. To prove this let _a b_ be an -object in light and shade which sends not its shadow but the image -of its darkened form through the opening _d e_ which is as wide as -this shaded body; and its sides _a b_, being straight lines (as has -been proved) must intersect between the shaded object and the -opening; but nearer to the opening in proportion as it is smaller -than the object in shade. As is shown, on your right hand and your -left hand, in the two diagrams _a_ _b_ _c_ _n_ _m_ _o_ where, the -right opening _d_ _e_, being equal in width to the shaded object _a_ -_b_, the intersection of the sides of the said shaded object occurs -half way between the opening and the shaded object at the point _c_. -But this cannot happen in the left hand figure, the opening _o_ -being much smaller than the shaded object _n_ _m_. - -It is impossible that the images of objects should be seen between -the objects and the openings through which the images of these -bodies are admitted; and this is plain, because where the atmosphere -is illuminated these images are not formed visibly. - -When the images are made double by mutually crossing each other they -are invariably doubly as dark in tone. To prove this let _d_ _e_ _h_ -be such a doubling which although it is only seen within the space -between the bodies in _b_ and _i_ this will not hinder its being -seen from _f_ _g_ or from _f_ _m_; being composed of the images _a_ -_b_ _i_ _k_ which run together in _d_ _e_ _h_. - -[Footnote: 81. On the original diagram at the beginning of this -chapter Leonardo has written "_azurro_" (blue) where in the -facsimile I have marked _A_, and "_giallo_" (yellow) where _B_ -stands.] - -[Footnote: 15--23. These lines stand between the diagrams I and III.] - -[Footnote: 24--53. These lines stand between the diagrams I and II.] - -[Footnote: 54--97 are written along the left side of diagram I.] - -82. - -An experiment showing that though the pupil may not be moved from -its position the objects seen by it may appear to move from their -places. - -If you look at an object at some distance from you and which is -below the eye, and fix both your eyes upon it and with one hand -firmly hold the upper lid open while with the other you push up the -under lid--still keeping your eyes fixed on the object gazed at--you -will see that object double; one [image] remaining steady, and the -other moving in a contrary direction to the pressure of your finger -on the lower eyelid. How false the opinion is of those who say that -this happens because the pupil of the eye is displaced from its -position. - -How the above mentioned facts prove that the pupil acts upside down -in seeing. - -[Footnote: 82. 14--17. The subject indicated by these two headings is -fully discussed in the two chapters that follow them in the -original; but it did not seem to me appropriate to include them -here.] - -Demostration of perspective by means of a vertical glass plane -(83-85). - -83. - -OF THE PLANE OF GLASS. - -Perspective is nothing else than seeing place [or objects] behind a -plane of glass, quite transparent, on the surface of which the -objects behind that glass are to be drawn. These can be traced in -pyramids to the point in the eye, and these pyramids are intersected -on the glass plane. - -84. - -Pictorial perspective can never make an object at the same distance, -look of the same size as it appears to the eye. You see that the -apex of the pyramid _f c d_ is as far from the object _c_ _d_ as the -same point _f_ is from the object _a_ _b_; and yet _c_ _d_, which is -the base made by the painter's point, is smaller than _a_ _b_ which -is the base of the lines from the objects converging in the eye and -refracted at _s_ _t_, the surface of the eye. This may be proved by -experiment, by the lines of vision and then by the lines of the -painter's plumbline by cutting the real lines of vision on one and -the same plane and measuring on it one and the same object. - -85. - -PERSPECTIVE. - -The vertical plane is a perpendicular line, imagined as in front of -the central point where the apex of the pyramids converge. And this -plane bears the same relation to this point as a plane of glass -would, through which you might see the various objects and draw them -on it. And the objects thus drawn would be smaller than the -originals, in proportion as the distance between the glass and the -eye was smaller than that between the glass and the objects. - -PERSPECTIVE. - -The different converging pyramids produced by the objects, will -show, on the plane, the various sizes and remoteness of the objects -causing them. - -PERSPECTIVE. - -All those horizontal planes of which the extremes are met by -perpendicular lines forming right angles, if they are of equal width -the more they rise to the level of eye the less this is seen, and -the more the eye is above them the more will their real width be -seen. - -PERSPECTIVE. - -The farther a spherical body is from the eye the more you will see -of it. - -The angle of sight varies with the distance (86-88) - -86. - -A simple and natural method; showing how objects appear to the eye -without any other medium. - -The object that is nearest to the eye always seems larger than -another of the same size at greater distance. The eye _m_, seeing -the spaces _o v x_, hardly detects the difference between them, and -the. reason of this is that it is close to them [Footnote 6: It is -quite inconceivable to me why M. RAVAISSON, in a note to his French -translation of this simple passage should have remarked: _Il est -clair que c'est par erreur que Leonard a ecrit_ per esser visino _au -lieu de_ per non esser visino. (See his printed ed. of MS. A. p. -38.)]; but if these spaces are marked on the vertical plane _n o_ -the space _o v_ will be seen at _o r_, and in the same way the space -_v x_ will appear at _r q_. And if you carry this out in any place -where you can walk round, it will look out of proportion by reason -of the great difference in the spaces _o r_ and _r q_. And this -proceeds from the eye being so much below [near] the plane that the -plane is foreshortened. Hence, if you wanted to carry it out, you -would have [to arrange] to see the perspective through a single hole -which must be at the point _m_, or else you must go to a distance of -at least 3 times the height of the object you see. The plane _o p_ -being always equally remote from the eye will reproduce the objects -in a satisfactory way, so that they may be seen from place to place. - -87. - -How every large mass sends forth its images, which may diminish -through infinity. - -The images of any large mass being infinitely divisible may be -infinitely diminished. - -88. - -Objects of equal size, situated in various places, will be seen by -different pyramids which will each be smaller in proportion as the -object is farther off. - -89. - -Perspective, in dealing with distances, makes use of two opposite -pyramids, one of which has its apex in the eye and the base as -distant as the horizon. The other has the base towards the eye and -the apex on the horizon. Now, the first includes the [visible] -universe, embracing all the mass of the objects that lie in front of -the eye; as it might be a vast landscape seen through a very small -opening; for the more remote the objects are from the eye, the -greater number can be seen through the opening, and thus the pyramid -is constructed with the base on the horizon and the apex in the eye, -as has been said. The second pyramid is extended to a spot which is -smaller in proportion as it is farther from the eye; and this second -perspective [= pyramid] results from the first. - -90. - -SIMPLE PERSPECTIVE. - -Simple perspective is that which is constructed by art on a vertical -plane which is equally distant from the eye in every part. Complex -perspective is that which is constructed on a ground-plan in which -none of the parts are equally distant from the eye. - -91. - -PERSPECTIVE. - -No surface can be seen exactly as it is, if the eye that sees it is -not equally remote from all its edges. - -92. - -WHY WHEN AN OBJECT IS PLACED CLOSE TO THE EYE ITS EDGES ARE -INDISTINCT. - -When an object opposite the eye is brought too close to it, its -edges must become too confused to be distinguished; as it happens -with objects close to a light, which cast a large and indistinct -shadow, so is it with an eye which estimates objects opposite to it; -in all cases of linear perspective, the eye acts in the same way as -the light. And the reason is that the eye has one leading line (of -vision) which dilates with distance and embraces with true -discernment large objects at a distance as well as small ones that -are close. But since the eye sends out a multitude of lines which -surround this chief central one and since these which are farthest -from the centre in this cone of lines are less able to discern with -accuracy, it follows that an object brought close to the eye is not -at a due distance, but is too near for the central line to be able -to discern the outlines of the object. So the edges fall within the -lines of weaker discerning power, and these are to the function of -the eye like dogs in the chase which can put up the game but cannot -take it. Thus these cannot take in the objects, but induce the -central line of sight to turn upon them, when they have put them up. -Hence the objects which are seen with these lines of sight have -confused outlines. - -The relative size of objects with regard to their distance from the -eye (93-98). - -93. - -PERSPECTIVE. - -Small objects close at hand and large ones at a distance, being seen -within equal angles, will appear of the same size. - -94. - -PERSPECTIVE. - -There is no object so large but that at a great distance from the -eye it does not appear smaller than a smaller object near. - -95. - -Among objects of equal size that which is most remote from the eye -will look the smallest. [Footnote: This axiom, sufficiently clear in -itself, is in the original illustrated by a very large diagram, -constructed like that here reproduced under No. 108. - -The same idea is repeated in C. A. I a; I a, stated as follows: -_Infra le cose d'equal grandeza quella si dimostra di minor figura -che sara piu distante dall' ochio_.--] - -96. - -Why an object is less distinct when brought near to the eye, and why -with spectacles, or without the naked eye sees badly either close or -far off [as the case may be]. - -97. - -PERSPECTIVE. - -Among objects of equal size, that which is most remote from the eye -will look the smallest. - -98. - -PERSPECTIVE. - -No second object can be so much lower than the first as that the eye -will not see it higher than the first, if the eye is above the -second. - -PERSPECTIVE. - -And this second object will never be so much higher than the first -as that the eye, being below them, will not see the second as lower -than the first. - -PERSPECTIVE. - -If the eye sees a second square through the centre of a smaller one, -that is nearer, the second, larger square will appear to be -surrounded by the smaller one. - -PERSPECTIVE--PROPOSITION. - -Objects that are farther off can never be so large but that those in -front, though smaller, will conceal or surround them. - -DEFINITION. - -This proposition can be proved by experiment. For if you look -through a small hole there is nothing so large that it cannot be -seen through it and the object so seen appears surrounded and -enclosed by the outline of the sides of the hole. And if you stop it -up, this small stopping will conceal the view of the largest object. - -The apparent size of objects defined by calculation (99-105) - -99. - -OF LINEAR PERSPECTIVE. - -Linear Perspective deals with the action of the lines of sight, in -proving by measurement how much smaller is a second object than the -first, and how much the third is smaller than the second; and so on -by degrees to the end of things visible. I find by experience that -if a second object is as far beyond the first as the first is from -the eye, although they are of the same size, the second will seem -half the size of the first and if the third object is of the same -size as the 2nd, and the 3rd is as far beyond the second as the 2nd -from the first, it will appear of half the size of the second; and -so on by degrees, at equal distances, the next farthest will be half -the size of the former object. So long as the space does not exceed -the length of 20 braccia. But, beyond 20 braccia figures of equal -size will lose 2/4 and at 40 braccia they will lose 9/10, and 19/20 -at 60 braccia, and so on diminishing by degrees. This is if the -picture plane is distant from you twice your own height. If it is -only as far off as your own height, there will be a great difference -between the first braccia and the second. - -[Footnote: This chapter is included in DUFRESNE'S and MANZI'S -editions of the Treatise on Painting. H. LUDWIG, in his commentary, -calls this chapter "_eines der wichtigsten im ganzen Tractat_", but -at the same time he asserts that its substance has been so -completely disfigured in the best MS. copies that we ought not to -regard Leonardo as responsible for it. However, in the case of this -chapter, the old MS. copies agree with the original as it is -reproduced above. From the chapters given later in this edition, -which were written at a subsequent date, it would appear that -Leonardo corrected himself on these points.] - -100. - -OF THE DIMINUTION OF OBJECTS AT VARIOUS DISTANCES. - -A second object as far distant from the first as the first is from -the eye will appear half the size of the first, though they be of -the same size really. - -OF THE DEGREES OF DIMINUTION. - -If you place the vertical plane at one braccio from the eye, the -first object, being at a distance of 4 braccia from your eye will -diminish to 3/4 of its height at that plane; and if it is 8 braccia -from the eye, to 7/8; and if it is 16 braccia off, it will diminish -to 15/16 of its height and so on by degrees, as the space doubles -the diminution will double. - -101. - -Begin from the line _m f_ with the eye below; then go up and do the -same with the line _n f_, then with the eye above and close to the 2 -gauges on the ground look at _m n_; then as _c m_ is to _m n_ so -will _n m_ be to _n s_. - -If _a n_ goes 3 times into _f b, m p_ will do the same into _p g_. -Then go backwards so far as that _c d_ goes twice into _a n_ and _p -g_ will be equal to _g h_. And _m p_ will go into _h p_ as often as -_d c_ into _o p_. - -[Footnote: The first three lines are unfortunately very obscure.] - -102. - -I GIVE THE DEGREES OF THE OBJECTS SEEN BY THE EYE AS THE MUSICIAN -DOES THE NOTES HEARD BY THE EAR. - -Although the objects seen by the eye do, in fact, touch each other -as they recede, I will nevertheless found my rule on spaces of 20 -braccia each; as a musician does with notes, which, though they can -be carried on one into the next, he divides into degrees from note -to note calling them 1st, 2nd, 3rd, 4th, 5th; and has affixed a name -to each degree in raising or lowering the voice. - -103. - -PERSPECTIVE. - -Let _f_ be the level and distance of the eye; and _a_ the vertical -plane, as high as a man; let _e_ be a man, then I say that on the -plane this will be the distance from the plane to the 2nd man. - -104. - -The differences in the diminution of objects of equal size in -consequence of their various remoteness from the eye will bear among -themselves the same proportions as those of the spaces between the -eye and the different objects. - -Find out how much a man diminishes at a certain distance and what -its length is; and then at twice that distance and at 3 times, and -so make your general rule. - -105. - -The eye cannot judge where an object high up ought to descend. - -106. - -PERSPECTIVE. - -If two similar and equal objects are placed one beyond the other at -a given distance the difference in their size will appear greater in -proportion as they are nearer to the eye that sees them. And -conversely there will seem to be less difference in their size in -proportion as they are remote from the eve. - -This is proved by the proportions of their distances among -themselves; for, if the first of these two objects were as far from -the eye, as the 2nd from the first this would be called the second -proportion: since, if the first is at 1 braccia from the eye and the -2nd at two braccia, two being twice as much as one, the first object -will look twice as large as the second. But if you place the first -at a hundred braccia from you and the second at a hundred and one, -you will find that the first is only so much larger than the second -as 100 is less than 101; and the converse is equally true. And -again, the same thing is proved by the 4th of this book which shows -that among objects that are equal, there is the same proportion in -the diminution of the size as in the increase in the distance from -the eye of the spectator. - -On natural perspective (107--109). - -107. - -OF EQUAL OBJECTS THE MOST REMOTE LOOK THE SMALLEST. - -The practice of perspective may be divided into ... parts [Footnote -4: _in_ ... _parte_. The space for the number is left blank in the -original.], of which the first treats of objects seen by the eye at -any distance; and it shows all these objects just as the eye sees -them diminished, without obliging a man to stand in one place rather -than another so long as the plane does not produce a second -foreshortening. - -But the second practice is a combination of perspective derived -partly from art and partly from nature and the work done by its -rules is in every portion of it, influenced by natural perspective -and artificial perspective. By natural perspective I mean that the -plane on which this perspective is represented is a flat surface, -and this plane, although it is parallel both in length and height, -is forced to diminish in its remoter parts more than in its nearer -ones. And this is proved by the first of what has been said above, -and its diminution is natural. But artificial perspective, that is -that which is devised by art, does the contrary; for objects equal -in size increase on the plane where it is foreshortened in -proportion as the eye is more natural and nearer to the plane, and -as the part of the plane on which it is figured is farther from the -eye. - -And let this plane be _d e_ on which are seen 3 equal circles which -are beyond this plane _d e_, that is the circles _a b c_. Now you -see that the eye _h_ sees on the vertical plane the sections of the -images, largest of those that are farthest and smallest of the -nearest. - -108. - -Here follows what is wanting in the margin at the foot on the other -side of this page. - -Natural perspective acts in a contrary way; for, at greater -distances the object seen appears smaller, and at a smaller distance -the object appears larger. But this said invention requires the -spectator to stand with his eye at a small hole and then, at that -small hole, it will be very plain. But since many (men's) eyes -endeavour at the same time to see one and the same picture produced -by this artifice only one can see clearly the effect of this -perspective and all the others will see confusion. It is well -therefore to avoid such complex perspective and hold to simple -perspective which does not regard planes as foreshortened, but as -much as possible in their proper form. This simple perspective, in -which the plane intersects the pyramids by which the images are -conveyed to the eye at an equal distance from the eye is our -constant experience, from the curved form of the pupil of the eye on -which the pyramids are intersected at an equal distance from the -visual virtue. - -[Footnote 24: _la prima di sopra_ i. e. the first of the three -diagrams which, in the original MS., are placed in the margin at the -beginning of this chapter.] - -109. - -OF A MIXTURE OF NATURAL AND ARTIFICIAL PERSPECTIVE. - -This diagram distinguishes natural from artificial perspective. But -before proceeding any farther I will define what is natural and what -is artificial perspective. Natural perspective says that the more -remote of a series of objects of equal size will look the smaller, -and conversely, the nearer will look the larger and the apparent -size will diminish in proportion to the distance. But in artificial -perspective when objects of unequal size are placed at various -distances, the smallest is nearer to the eye than the largest and -the greatest distance looks as though it were the least of all; and -the cause of this is the plane on which the objects are represented; -and which is at unequal distances from the eye throughout its -length. And this diminution of the plane is natural, but the -perspective shown upon it is artificial since it nowhere agrees with -the true diminution of the said plane. Whence it follows, that when -the eye is somewhat removed from the [station point of the] -perspective that it has been gazing at, all the objects represented -look monstrous, and this does not occur in natural perspective, -which has been defined above. Let us say then, that the square _a b -c d_ figured above is foreshortened being seen by the eye situated -in the centre of the side which is in front. But a mixture of -artificial and natural perspective will be seen in this tetragon -called _el main_ [Footnote 20: _el main_ is quite legibly written in -the original; the meaning and derivation of the word are equally -doubtful.], that is to say _e f g h_ which must appear to the eye of -the spectator to be equal to _a b c d_ so long as the eye remains in -its first position between _c_ and _d_. And this will be seen to -have a good effect, because the natural perspective of the plane -will conceal the defects which would [otherwise] seem monstrous. - -_III._ - -_Six books on Light and Shade._ - -_Linear Perspective cannot be immediately followed by either the_ -"prospettiva de' perdimenti" _or the_ "prospettiva de' colori" _or -the aerial perspective; since these branches of the subject -presuppose a knowledge of the principles of Light and Shade. No -apology, therefore, is here needed for placing these immediately -after Linear Perspective._ - -_We have various plans suggested by Leonardo for the arrangement of -the mass of materials treating of this subject. Among these I have -given the preference to a scheme propounded in No._ III, _because, -in all probability, we have here a final and definite purpose -expressed. Several authors have expressed it as their opinion that -the Paris Manuscript_ C _is a complete and finished treatise on -Light and Shade. Certainly, the Principles of Light and Shade form -by far the larger portion of this MS. which consists of two separate -parts; still, the materials are far from being finally arranged. It -is also evident that he here investigates the subject from the point -of view of the Physicist rather than from that of the Painter._ - -_The plan of a scheme of arrangement suggested in No._ III _and -adopted by me has been strictly adhered to for the first four Books. -For the three last, however, few materials have come down to us; and -it must be admitted that these three Books would find a far more -appropriate place in a work on Physics than in a treatise on -Painting. For this reason I have collected in Book V all the -chapters on Reflections, and in Book VI I have put together and -arranged all the sections of MS._ C _that belong to the book on -Painting, so far as they relate to Light and Shade, while the -sections of the same MS. which treat of the_ "Prospettiva de' -perdimenti" _have, of course, been excluded from the series on Light -and Shade._ - -[Footnote III: This text has already been published with some slight -variations in Dozio's pamphlet _Degli scritti e disegni di Leonardo -da Vinci_, Milan 1871, pp. 30--31. Dozio did not transcribe it from -the original MS. which seems to have remained unknown to him, but -from an old copy (MS. H. 227 in the Ambrosian Library).] - -GENERAL INTRODUCTION. - -Prolegomena. - -110. - -You must first explain the theory and then the practice. First you -must describe the shadows and lights on opaque objects, and then on -transparent bodies. - -Scheme of the books on Light and shade. - -111. - -INTRODUCTION. - -[Having already treated of the nature of shadows and the way in -which they are cast [Footnote 2: _Avendo io tractato._--We may -suppose that he here refers to some particular MS., possibly Paris -C.], I will now consider the places on which they fall; and their -curvature, obliquity, flatness or, in short, any character I may be -able to detect in them.] - -Shadow is the obstruction of light. Shadows appear to me to be of -supreme importance in perspective, because, without them opaque and -solid bodies will be ill defined; that which is contained within -their outlines and their boundaries themselves will be -ill-understood unless they are shown against a background of a -different tone from themselves. And therefore in my first -proposition concerning shadow I state that every opaque body is -surrounded and its whole surface enveloped in shadow and light. And -on this proposition I build up the first Book. Besides this, shadows -have in themselves various degrees of darkness, because they are -caused by the absence of a variable amount of the luminous rays; and -these I call Primary shadows because they are the first, and -inseparable from the object to which they belong. And on this I will -found my second Book. From these primary shadows there result -certain shaded rays which are diffused through the atmosphere and -these vary in character according to that of the primary shadows -whence they are derived. I shall therefore call these shadows -Derived shadows because they are produced by other shadows; and the -third Book will treat of these. Again these derived shadows, where -they are intercepted by various objects, produce effects as various -as the places where they are cast and of this I will treat in the -fourth Book. And since all round the derived shadows, where the -derived shadows are intercepted, there is always a space where the -light falls and by reflected dispersion is thrown back towards its -cause, it meets the original shadow and mingles with it and modifies -it somewhat in its nature; and on this I will compose my fifth Book. -Besides this, in the sixth Book I will investigate the many and -various diversities of reflections resulting from these rays which -will modify the original [shadow] by [imparting] some of the various -colours from the different objects whence these reflected rays are -derived. Again, the seventh Book will treat of the various distances -that may exist between the spot where the reflected rays fall and -that where they originate, and the various shades of colour which -they will acquire in falling on opaque bodies. - -Different principles and plans of treatment (112--116). - -112. - -First I will treat of light falling through windows which I will -call Restricted [Light] and then I will treat of light in the open -country, to which I will give the name of diffused Light. Then I -will treat of the light of luminous bodies. - -113. - -OF PAINTING. - -The conditions of shadow and light [as seen] by the eye are 3. Of -these the first is when the eye and the light are on the same side -of the object seen; the 2nd is when the eye is in front of the -object and the light is behind it. The 3rd is when the eye is in -front of the object and the light is on one side, in such a way as -that a line drawn from the object to the eye and one from the object -to the light should form a right angle where they meet. - -114. - -OF PAINTING. - -This is another section: that is, of the nature of a reflection -(from) an object placed between the eye and the light under various -aspects. - -115. - -OF PAINTING. - -As regards all visible objects 3 things must be considered. These -are the position of the eye which sees: that of the object seen -[with regard] to the light, and the position of the light which -illuminates the object, _b_ is the eye, _a_ the object seen, _c_ the -light, _a_ is the eye, _b_ the illuminating body, _c_ is the -illuminated object. - -116. - -Let _a_ be the light, _b_ the eye, _c_ the object seen by the eye -and in the light. These show, first, the eye between the light and -the body; the 2nd, the light between the eye and the body; the 3rd -the body between the eye and the light, _a_ is the eye, _b_ the -illuminated object, _c_ the light. - -117. - -OF PAINTING. - -OF THE THREE KINDS OF LIGHT THAT ILLUMINATE OPAQUE BODIES. - -The first kind of Light which may illuminate opaque bodies is called -Direct light--as that of the sun or any other light from a window or -flame. The second is Diffused [universal] light, such as we see in -cloudy weather or in mist and the like. The 3rd is Subdued light, -that is when the sun is entirely below the horizon, either in the -evening or morning. - -118. - -OF LIGHT. - -The lights which may illuminate opaque bodies are of 4 kinds. These -are: diffused light as that of the atmosphere, within our horizon. -And Direct, as that of the sun, or of a window or door or other -opening. The third is Reflected light; and there is a 4th which is -that which passes through [semi] transparent bodies, as linen or -paper or the like, but not transparent like glass, or crystal, or -other diaphanous bodies, which produce the same effect as though -nothing intervened between the shaded object and the light that -falls upon it; and this we will discuss fully in our discourse. - -Definition of the nature of shadows (119--122). - -119. - -WHAT LIGHT AND SHADOW ARE. - -Shadow is the absence of light, merely the obstruction of the -luminous rays by an opaque body. Shadow is of the nature of -darkness. Light [on an object] is of the nature of a luminous body; -one conceals and the other reveals. They are always associated and -inseparable from all objects. But shadow is a more powerful agent -than light, for it can impede and entirely deprive bodies of their -light, while light can never entirely expel shadow from a body, that -is from an opaque body. - -120. - -Shadow is the diminution of light by the intervention of an opaque -body. Shadow is the counterpart of the luminous rays which are cut -off by an opaque body. - -This is proved because the shadow cast is the same in shape and size -as the luminous rays were which are transformed into a shadow. - -121. - -Shadow is the diminution alike of light and of darkness, and stands -between darkness and light. - -A shadow may be infinitely dark, and also of infinite degrees of -absence of darkness. - -The beginnings and ends of shadow lie between the light and darkness -and may be infinitely diminished and infinitely increased. Shadow is -the means by which bodies display their form. - -The forms of bodies could not be understood in detail but for -shadow. - -122. - -OF THE NATURE OF SHADOW. - -Shadow partakes of the nature of universal matter. All such matters -are more powerful in their beginning and grow weaker towards the -end, I say at the beginning, whatever their form or condition may be -and whether visible or invisible. And it is not from small -beginnings that they grow to a great size in time; as it might be a -great oak which has a feeble beginning from a small acorn. Yet I may -say that the oak is most powerful at its beginning, that is where it -springs from the earth, which is where it is largest (To return:) -Darkness, then, is the strongest degree of shadow and light is its -least. Therefore, O Painter, make your shadow darkest close to the -object that casts it, and make the end of it fading into light, -seeming to have no end. - -Of the various kinds of shadows. (123-125). - -123. - -Darkness is absence of light. Shadow is diminution of light. -Primitive shadow is that which is inseparable from a body not in the -light. Derived shadow is that which is disengaged from a body in -shadow and pervades the air. A cast transparent shadow is that which -is surrounded by an illuminated surface. A simple shadow is one -which receives no light from the luminous body which causes it. A -simple shadow begins within the line which starts from the edge of -the luminous body _a b_. - -124. - -A simple shadow is one where no light at all interferes with it. - -A compound shadow is one which is somewhat illuminated by one or -more lights. - -125. - -WHAT IS THE DIFFERENCE BETWEEN A SHADOW THAT IS INSEPARABLE FROM A -BODY AND A CAST SHADOW? - -An inseparable shadow is that which is never absent from the -illuminated body. As, for instance a ball, which so long as it is in -the light always has one side in shadow which never leaves it for -any movement or change of position in the ball. A separate shadow -may be and may not be produced by the body itself. Suppose the ball -to be one braccia distant from a wall with a light on the opposite -side of it; this light will throw upon the wall exactly as broad a -shadow as is to be seen on the side of the ball that is turned -towards the wall. That portion of the cast shadow will not be -visible when the light is below the ball and the shadow is thrown up -towards the sky and finding no obstruction on its way is lost. - -126. - -HOW THERE ARE 2 KINDS OF LIGHT, ONE SEPARABLE FROM, AND THE OTHER -INSEPARABLE FROM BODIES. - -Of the various kinds of light (126, 127). - -Separate light is that which falls upon the body. Inseparable light -is the side of the body that is illuminated by that light. One is -called primary, the other derived. And, in the same way there are -two kinds of shadow:--One primary and the other derived. The primary -is that which is inseparable from the body, the derived is that -which proceeds from the body conveying to the surface of the wall -the form of the body causing it. - -127. - -How there are 2 different kinds of light; one being called diffused, -the other restricted. The diffused is that which freely illuminates -objects. The restricted is that which being admitted through an -opening or window illuminates them on that side only. - -[Footnote: At the spot marked _A_ in the first diagram Leonardo -wrote _lume costretto_ (restricted light). At the spot _B_ on the -second diagram he wrote _lume libero_ (diffused light).] - -General remarks (128. 129). - -128. - -Light is the chaser away of darkness. Shade is the obstruction of -light. Primary light is that which falls on objects and causes light -and shade. And derived lights are those portions of a body which are -illuminated by the primary light. A primary shadow is that side of a -body on which the light cannot fall. - -The general distribution of shadow and light is that sum total of -the rays thrown off by a shaded or illuminated body passing through -the air without any interference and the spot which intercepts and -cuts off the distribution of the dark and light rays. - -And the eye can best distinguish the forms of objects when it is -placed between the shaded and the illuminated parts. - -129. - -MEMORANDUM OF THINGS I REQUIRE TO HAVE GRANTED [AS AXIOMS] IN MY -EXPLANATION OF PERSPECTIVE. - -I ask to have this much granted me--to assert that every ray -passing through air of equal density throughout, travels in a -straight line from its cause to the object or place it falls upon. - -FIRST BOOK ON LIGHT AND SHADE. - -On the nature of light (130. 131). - -130. - -The reason by which we know that a light radiates from a single -centre is this: We plainly see that a large light is often much -broader than some small object which nevertheless--and although the -rays [of the large light] are much more than twice the extent [of -the small body]--always has its shadow cast on the nearest surface -very visibly. Let _c f_ be a broad light and _n_ be the object in -front of it, casting a shadow on the plane, and let _a b_ be the -plane. It is clear that it is not the broad light that will cast the -shadow _n_ on the plane, but that the light has within it a centre -is shown by this experiment. The shadow falls on the plane as is -shown at _m o t r_. - -[Footnote 13: In the original MS. no explanatory text is placed -after this title-line; but a space is left for it and the text -beginning at line 15 comes next.] Why, to two [eyes] or in front of -two eyes do 3 objects appear as two? - -Why, when you estimate the direction of an object with two sights -the nearer appears confused. I say that the eye projects an infinite -number of lines which mingle or join those reaching it which come to -it from the object looked at. And it is only the central and -sensible line that can discern and discriminate colours and objects; -all the others are false and illusory. And if you place 2 objects at -half an arm's length apart if the nearer of the two is close to the -eye its form will remain far more confused than that of the second; -the reason is that the first is overcome by a greater number of -false lines than the second and so is rendered vague. - -Light acts in the same manner, for in the effects of its lines -(=rays), and particularly in perspective, it much resembles the eye; -and its central rays are what cast the true shadow. When the object -in front of it is too quickly overcome with dim rays it will cast a -broad and disproportionate shadow, ill defined; but when the object -which is to cast the shadow and cuts off the rays near to the place -where the shadow falls, then the shadow is distinct; and the more so -in proportion as the light is far off, because at a long distance -the central ray is less overcome by false rays; because the lines -from the eye and the solar and other luminous rays passing through -the atmosphere are obliged to travel in straight lines. Unless they -are deflected by a denser or rarer air, when they will be bent at -some point, but so long as the air is free from grossness or -moisture they will preserve their direct course, always carrying the -image of the object that intercepts them back to their point of -origin. And if this is the eye, the intercepting object will be seen -by its colour, as well as by form and size. But if the intercepting -plane has in it some small perforation opening into a darker -chamber--not darker in colour, but by absence of light--you will see -the rays enter through this hole and transmitting to the plane -beyond all the details of the object they proceed from both as to -colour and form; only every thing will be upside down. But the size -[of the image] where the lines are reconstructed will be in -proportion to the relative distance of the aperture from the plane -on which the lines fall [on one hand] and from their origin [on the -other]. There they intersect and form 2 pyramids with their point -meeting [a common apex] and their bases opposite. Let _a b_ be the -point of origin of the lines, _d e_ the first plane, and _c_ the -aperture with the intersection of the lines; _f g_ is the inner -plane. You will find that _a_ falls upon the inner plane below at -_g_, and _b_ which is below will go up to the spot _f_; it will be -quite evident to experimenters that every luminous body has in -itself a core or centre, from which and to which all the lines -radiate which are sent forth by the surface of the luminous body and -reflected back to it; or which, having been thrown out and not -intercepted, are dispersed in the air. - -131. - -THE RAYS WHETHER SHADED OR LUMINOUS HAVE GREATER STRENGTH AND EFFECT -AT THEIR POINTS THAN AT THEIR SIDES. - -Although the points of luminous pyramids may extend into shaded -places and those of pyramids of shadow into illuminated places, and -though among the luminous pyramids one may start from a broader base -than another; nevertheless, if by reason of their various length -these luminous pyramids acquire angles of equal size their light -will be equal; and the case will be the same with the pyramids of -shadow; as may be seen in the intersected pyramids _a b c_ and _d e -f_, which though their bases differ in size are equal as to breadth -and light. - -[Footnote: 51--55: This supplementary paragraph is indicated as being -a continuation of line 45, by two small crosses.] - -The difference between light and lustre (132--135). - -132. - -Of the difference between light and lustre; and that lustre is not -included among colours, but is saturation of whiteness, and derived -from the surface of wet bodies; light partakes of the colour of the -object which reflects it (to the eye) as gold or silver or the like. - -133. - -OF THE HIGHEST LIGHTS WHICH TURN AND MOVE AS THE EYE MOVES WHICH -SEES THE OBJECT. - -Suppose the body to be the round object figured here and let the -light be at the point _a_, and let the illuminated side of the -object be _b c_ and the eye at the point _d_: I say that, as lustre -is every where and complete in each part, if you stand at the point -_d_ the lustre will appear at _c_, and in proportion as the eye -moves from _d_ to _a_, the lustre will move from _c_ to _n_. - -134. - -OF PAINTING. - -Heigh light or lustre on any object is not situated [necessarily] in -the middle of an illuminated object, but moves as and where the eye -moves in looking at it. - -135. - -OF LIGHT AND LUSTRE. - -What is the difference between light and the lustre which is seen on -the polished surface of opaque bodies? - -The lights which are produced from the polished surface of opaque -bodies will be stationary on stationary objects even if the eye on -which they strike moves. But reflected lights will, on those same -objects, appear in as many different places on the surface as -different positions are taken by the eye. - -WHAT BODIES HAVE LIGHT UPON THEM WITHOUT LUSTRE? - -Opaque bodies which have a hard and rough surface never display any -lustre in any portion of the side on which the light falls. - -WHAT BODIES WILL DISPLAY LUSTRE BUT NOT LOOK ILLUMINATED? - -Those bodies which are opaque and hard with a hard surface reflect -light [lustre] from every spot on the illuminated side which is in a -position to receive light at the same angle of incidence as they -occupy with regard to the eye; but, as the surface mirrors all the -surrounding objects, the illuminated [body] is not recognisable in -these portions of the illuminated body. - -136. - -The relations of luminous to illuminated bodies. - -The middle of the light and shade on an object in light and shade is -opposite to the middle of the primary light. All light and shadow -expresses itself in pyramidal lines. The middle of the shadow on any -object must necessarily be opposite the middle of its light, with a -direct line passing through the centre of the body. The middle of -the light will be at _a_, that of the shadow at _b_. [Again, in -bodies shown in light and shade the middle of each must coincide -with the centre of the body, and a straight line will pass through -both and through that centre.] - -[Footnote: In the original MS., at the spot marked _a_ of the first -diagram Leonardo wrote _primitiuo_, and at the spot marked -_c_--_primitiva_ (primary); at the spot marked _b_ he wrote -_dirivatiuo_ and at _d deriuatiua_ (derived).] - -Experiments on the relation of light and shadow within a room -(137--140). - -137. - -SHOWS HOW LIGHT FROM ANY SIDE CONVERGES TO ONE POINT. - -Although the balls _a b c_ are lighted from one window, -nevertheless, if you follow the lines of their shadows you will see -they intersect at a point forming the angle _n_. - -[Footnote: The diagram belonging to this passage is slightly -sketched on Pl. XXXII; a square with three balls below it. The first -three lines of the text belonging to it are written above the sketch -and the six others below it.] - -138. - -Every shadow cast by a body has a central line directed to a single -point produced by the intersection of luminous lines in the middle -of the opening and thickness of the window. The proposition stated -above, is plainly seen by experiment. Thus if you draw a place with -a window looking northwards, and let this be _s f_, you will see a -line starting from the horizon to the east, which, touching the 2 -angles of the window _o f_, reaches _d_; and from the horizon on the -west another line, touching the other 2 angles _r s_, and ending at -_c_; and their intersection falls exactly in the middle of the -opening and thickness of the window. Again, you can still better -confirm this proof by placing two sticks, as shown at _g h_; and you -will see the line drawn from the centre of the shadow directed to -the centre _m_ and prolonged to the horizon _n f_. - -[Footnote: _B_ here stands for _cerchio del' orizonte tramontano_ on -the original diagram (the circle of the horizon towards the North); -_A_ for _levante_ (East) and _C_ for _ponete_ (West).] - -139. - -Every shadow with all its variations, which becomes larger as its -distance from the object is greater, has its external lines -intersecting in the middle, between the light and the object. This -proposition is very evident and is confirmed by experience. For, if -_a b_ is a window without any object interposed, the luminous -atmosphere to the right hand at _a_ is seen to the left at _d_. And -the atmosphere at the left illuminates on the right at _c_, and the -lines intersect at the point _m_. - -[Footnote: _A_ here stands for _levante_ (East), _B_ for _ponente_ -(West).] - -140. - -Every body in light and shade is situated between 2 pyramids one -dark and the other luminous, one is visible the other is not. But -this only happens when the light enters by a window. Supposing _a b_ -to be the window and _r_ the body in light and shade, the light to -the right hand _z_ will pass the object to the left and go on to -_p_; the light to the left at _k_ will pass to the right of the -object at _i_ and go on to _m_ and the two lines will intersect at -_c_ and form a pyramid. Then again _a_ _b_ falls on the shaded body -at _i_ _g_ and forms a pyramid _f_ _i_ _g_. _f_ will be dark because -the light _a_ _b_ can never fall there; _i_ _g_ _c_ will be -illuminated because the light falls upon it. - -Light and shadow with regard to the position of the eye (141--145). - -141. - -Every shaded body that is larger than the pupil and that interposes -between the luminous body and the eye will be seen dark. - -When the eye is placed between the luminous body and the objects -illuminated by it, these objects will be seen without any shadow. - -[Footnote: The diagram which in the original stands above line 1 is -given on Plate II, No 2. Then, after a blank space of about eight -lines, the diagram Plate II No 3 is placed in the original. There is -no explanation of it beyond the one line written under it.] - -142. - -Why the 2 lights one on each side of a body having two pyramidal -sides of an obtuse apex leave it devoid of shadow. - -[Footnote: The sketch illustrating this is on Plate XLI No 1.] - -143. - -A body in shadow situated between the light and the eye can never -display its illuminated portion unless the eye can see the whole of -the primary light. - -[Footnote: _A_ stands for _corpo_ (body), _B_ for _lume_ (light).] - -144. - -The eye which looks (at a spot) half way between the shadow and the -light which surrounds the body in shadow will see that the deepest -shadows on that body will meet the eye at equal angles, that is at -the same angle as that of sight. - -[Footnote: In both these diagrams _A_ stands for _lume_ (light) _B_ -for _ombra_ (shadow).] - -145. - -OF THE DIFFERENT LIGHT AND SHADE IN VARIOUS ASPECTS AND OF OBJECTS -PLACED IN THEM. - -If the sun is in the East and you look towards the West you will see -every thing in full light and totally without shadow because you see -them from the same side as the sun: and if you look towards the -South or North you will see all objects in light and shade, because -you see both the side towards the sun and the side away from it; and -if you look towards the coming of the sun all objects will show you -their shaded side, because on that side the sun cannot fall upon -them. - -The law of the incidence of light. - -146. - -The edges of a window which are illuminated by 2 lights of equal -degrees of brightness will not reflect light of equal brightness -into the chamber within. - -If _b_ is a candle and _a c_ our hemisphere both will illuminate the -edges of the window _m_ _n_, but light _b_ will only illuminate _f -g_ and the hemisphere _a_ will light all of _d e_. - -147. - -OF PAINTING. - -That part of a body which receives the luminous rays at equal angles -will be in a higher light than any other part of it. - -And the part which the luminous rays strike between less equal -angles will be less strongly illuminated. - -SECOND BOOK ON LIGHT AND SHADE. - -Gradations of strength in the shadows (148. 149). - -148. - -THAT PORTION OF A BODY IN LIGHT AND SHADE WILL BE LEAST LUMINOUS -WHICH IS SEEN UNDER THE LEAST AMOUNT OF LIGHT. - -That part of the object which is marked _m_ is in the highest light -because it faces the window _a d_ by the line _a f_; _n_ is in the -second grade because the light _b d_ strikes it by the line _b e_; -_o_ is in the third grade, as the light falls on it from _c d_ by -the line _c h_; _p_ is the lowest light but one as _c d_ falls on it -by the line _d v_; _q_ is the deepest shadow for no light falls on -it from any part of the window. - -In proportion as _c d_ goes into _a d_ so will _n r s_ be darker -than _m_, and all the rest is space without shadow. - -[Footnote: The diagram belonging to this chapter is No. 1 on Plate -III. The letters _a b e d_ and _r_ are not reproduced in facsimile -of the original, but have been replaced by ordinary type in the -margin. 5-12. The original text of these lines is reproduced within -the diagram.--Compare No 275.] - -149. - -The light which falls on a shaded body at the acutest angle receives -the highest light, and the darkest portion is that which receives it -at an obtuse angle and both the light and the shadow form pyramids. -The angle _c_ receives the highest grade of light because it is -directly in front of the window _a b_ and the whole horizon of the -sky _m x_. The angle _a_ differs but little from _c_ because the -angles which divide it are not so unequal as those below, and only -that portion of the horizon is intercepted which lies between _y_ -and _x_. Although it gains as much on the other side its line is -nevertheless not very strong because one angle is smaller than its -fellow. The angles _e i_ will have less light because they do not -see much of the light _m s_ and the light _v x_ and their angles are -very unequal. Yhe angle _k_ and the angle _f_ are each placed -between very unequal angles and therefore have but little light, -because at _k_ it has only the light _p t_, and at _f_ only _t q_; -_o g_ is the lowest grade of light because this part has no light at -all from the sky; and thence come the lines which will reconstruct a -pyramid that is the counterpart of the pyramid _c_; and this pyramid -_l_ is in the first grade of shadow; for this too is placed between -equal angles directly opposite to each other on either side of a -straight line which passes through the centre of the body and goes -to the centre of the light. The several luminous images cast within -the frame of the window at the points _a_ and _b_ make a light which -surrounds the derived shadow cast by the solid body at the points 4 -and 6. The shaded images increase from _o g_ and end at 7 and 8. - -[Footnote: The diagram belonging to this chapter is No. 2 on Plate -III. In the original it is placed between lines 3 and 4, and in the -reproduction these are shown in part. The semi circle above is -marked _orizonte_ (horizon). The number 6 at the left hand side, -outside the facsimile, is in the place of a figure which has become -indistinct in the original.] - -On the intensity of shadows as dependent on the distance from the -light (150-152). - -150. - -The smaller the light that falls upon an object the more shadow it -will display. And the light will illuminate a smaller portion of the -object in proportion as it is nearer to it; and conversely, a larger -extent of it in proportion as it is farther off. - -A light which is smaller than the object on which it falls will -light up a smaller extent of it in proportion as it is nearer to it, -and the converse, as it is farther from it. But when the light is -larger than the object illuminated it will light a larger extent of -the object in proportion as it is nearer and the converse when they -are farther apart. - -151. - -That portion of an illuminated object which is nearest to the source -of light will be the most strongly illuminated. - -152. - -That portion of the primary shadow will be least dark which is -farthest from the edges. - -The derived shadow will be darker than the primary shadow where it -is contiguous with it. - -On the proportion of light and shade (153-157). - -153. - -That portion of an opaque body will be more in shade or more in -light, which is nearer to the dark body, by which it is shaded, or -to the light that illuminates it. - -Objects seen in light and shade show in greater relief than those -which are wholly in light or in shadow. - -154. - -OF PERSPECTIVE. - -The shaded and illuminated sides of opaque objects will display the -same proportion of light and darkness as their objects [Footnote 6: -The meaning of _obbietti_ (objects) is explained in no 153, lines -1-4.--Between the title-line and the next there is, in the -original, a small diagram representing a circle described round a -square.]. - -155. - -OF PAINTING. - -The outlines and form of any part of a body in light and shade are -indistinct in the shadows and in the high lights; but in the -portions between the light and the shadows they are highly -conspicuous. - -156. - -OF PAINTING. - -Among objects in various degrees of shade, when the light proceeds -from a single source, there will be the same proportion in their -shadows as in the natural diminution of the light and the same must -be understood of the degrees of light. - -157. - -A single and distinct luminous body causes stronger relief in the -object than a diffused light; as may be seen by comparing one side -of a landscape illuminated by the sun, and one overshadowed by -clouds, and so illuminated only by the diffused light of the -atmosphere. - -THIRD BOOK ON LIGHT AND SHADE. - -Definition of derived shadow (158. 159). - -158. - -Derived shadow cannot exist without primary shadow. This is proved -by the first of this which says: Darkness is the total absence of -light, and shadow is an alleviation of darkness and of light, and it -is more or less dark or light in proportion as the darkness is -modified by the light. - -159. - -Shadow is diminution of light. - -Darkness is absence of light. - -Shadow is divided into two kinds, of which the first is called -primary shadow, the second is derived shadow. The primary shadow is -always the basis of the derived shadow. - -The edges of the derived shadow are straight lines. - -[Footnote: The theory of the _ombra_ dirivativa_--a technical -expression for which there is no precise English equivalent is -elaborately treated by Leonardo. But both text and diagrams (as Pl. -IV, 1-3 and Pl. V) must at once convince the student that the -distinction he makes between _ombra primitiva_ and _ombra -dirivativa_ is not merely justifiable but scientific. _Ombra -dirivativa_ is by no means a mere abstract idea. This is easily -proved by repeating the experiment made by Leonardo, and by filling -with smoke the room in which the existence of the _ombra dirivativa_ -is investigated, when the shadow becomes visible. Nor is it -difficult to perceive how much of Leonardo's teaching depended on -this theory. The recognised, but extremely complicated science of -cast shadows--_percussione dell' ombre dirivative_ as Leonardo -calls them--is thus rendered more intelligible if not actually -simpler, and we must assume this theory as our chief guide through -the investigations which follow.] - -The darkness of the derived shadow diminishes in proportion as it is -remote from the primary shadow. - -Different sorts of derived shadows (160-162). - -160. - -SHADOW AND LIGHT. - -The forms of shadows are three: inasmuch as if the solid body which -casts the shadow is equal (in size) to the light, the shadow -resembles a column without any termination (in length). If the body -is larger than the light the shadow resembles a truncated and -inverted pyramid, and its length has also no defined termination. -But if the body is smaller than the light, the shadow will resemble -a pyramid and come to an end, as is seen in eclipses of the moon. - -161. - -OF SIMPLE DERIVED SHADOWS. - -The simple derived shadow is of two kinds: one kind which has its -length defined, and two kinds which are undefined; and the defined -shadow is pyramidal. Of the two undefined, one is a column and the -other spreads out; and all three have rectilinear outlines. But the -converging, that is the pyramidal, shadow proceeds from a body that -is smaller than the light, and the columnar from a body equal in -size to the light, and the spreading shadow from a body larger than -the light; &c. - -OF COMPOUND DERIVED SHADOWS. - -Compound derived shadows are of two kinds; that is columnar and -spreading. - -162. - -OF SHADOW. - -Derived shadows are of three kinds of which one is spreading, the -second columnar, the third converging to the point where the two -sides meet and intersect, and beyond this intersection the sides are -infinitely prolonged or straight lines. And if you say, this shadow -must terminate at the angle where the sides meet and extend no -farther, I deny this, because above in the first on shadow I have -proved: that a thing is completely terminated when no portion of it -goes beyond its terminating lines. Now here, in this shadow, we see -the converse of this, in as much as where this derived shadow -originates we obviously have the figures of two pyramids of shadow -which meet at their angles. Hence, if, as [my] opponent says, the -first pyramid of shadow terminates the derivative shadow at the -angle whence it starts, then the second pyramid of shadow--so says -the adversary--must be caused by the angle and not from the body in -shadow; and this is disproved with the help of the 2nd of this which -says: Shadow is a condition produced by a body casting a shadow, and -interposed between this shadow and the luminous body. By this it is -made clear that the shadow is not produced by the angle of the -derived shadow but only by the body casting the shadow; &c. If a -spherical solid body is illuminated by a light of elongated form the -shadow produced by the longest portion of this light will have less -defined outlines than that which is produced by the breadth of the -same light. And this is proved by what was said before, which is: -That a shadow will have less defined outlines in proportion as the -light which causes it is larger, and conversely, the outlines are -clearer in proportion as it is smaller. - -[Footnote: The two diagrams to this chapter are on Plate IV, No. 1.] - -On the relation of derived and primary shadow (163-165). - -163. - -The derived shadow can never resemble the body from which it -proceeds unless the light is of the same form and size as the body -causing the shadow. - -The derived shadow cannot be of the same form as the primary shadow -unless it is intercepted by a plane parallel to it. - -164. - -HOW A CAST SHADOW CAN NEVER BE OF THE SAME SIZE AS THE BODY THAT -CASTS IT. - -If the rays of light proceed, as experience shows, from a single -point and are diffused in a sphere round this point, radiating and -dispersed through the air, the farther they spread the wider they -must spread; and an object placed between the light and a wall is -always imaged larger in its shadow, because the rays that strike it -[Footnote: 7. The following lines are wanting to complete the -logical connection.] would, by the time they have reached the wall, -have become larger. - -165. - -Any shadow cast by a body in light and shade is of the same nature -and character as that which is inseparable from the body. The centre -of the length of a shadow always corresponds to that of the luminous -body [Footnote 6: This second statement of the same idea as in the -former sentence, but in different words, does not, in the original, -come next to the foregoing; sections 172 and 127 are placed between -them.]. It is inevitable that every shadow must have its centre in a -line with the centre of the light. - -On the shape of derived shadows (166-174). - -166. - -OF THE PYRAMIDAL SHADOW. - -The pyramidal shadow produced by a columnar body will be narrower -than the body itself in proportion as the simple derived shadow is -intersected farther from the body which casts it. - -[Footnote 166: Compare the first diagram to No. 161. If we here -conceive of the outlines of the pyramid of shadow on the ground as -prolonged beyond its apex this gives rise to a second pyramid; this -is what is spoken of at the beginning of No. 166.] - -167. - -The cast shadow will be longest when the light is lowest. - -The cast shadow will be shortest when the light is highest. - -168. - -Both the primary and derived shadow will be larger when caused by -the light of a candle than by diffused light. The difference between -the larger and smaller shadows will be in inverse proportion to the -larger and smaller lights causing them. - -[Footnote: In the diagrams _A_ stands for _celo_ (sky), _B_ for -_cadela_ (candle).] - -169. - -ALL BODIES, IN PROPORTION AS THEY ARE NEARER TO, OR FARTHER FROM THE -SOURCE OF LIGHT, WILL PRODUCE LONGER OR SHORTER DERIVED SHADOWS. - -Among bodies of equal size, that one which is illuminated by the -largest light will have the shortest shadow. Experiment confirms -this proposition. Thus the body _m_ _n_ is surrounded by a larger -amount of light than the body _p q_, as is shown above. Let us say -that _v c a b d x_ is the sky, the source of light, and that _s t_ -is a window by which the luminous rays enter, and so _m n_ and _p q_ -are bodies in light and shade as exposed to this light; _m n_ will -have a small derived shadow, because its original shadow will be -small; and the derivative light will be large, again, because the -original light _c d_ will be large and _p q_ will have more derived -shadow because its original shadow will be larger, and its derived -light will be smaller than that of the body _m n_ because that -portion of the hemisphere _a b_ which illuminates it is smaller than -the hemisphere _c d_ which illuminates the body _m n_. - -[Footnote: The diagram, given on Pl. IV, No. 2, stands in the -original between lines 2 and 7, while the text of lines 3 to 6 is -written on its left side. In the reproduction of this diagram the -letter _v_ at the outer right-hand end has been omitted.] - -170. - -The shadow _m_ bears the same proportion to the shadow _n_ as the -line _b c_ to the line _f c_. - -171. - -OF PAINTING. - -Of different shadows of equal strength that which is nearest the eye -will seem the least strong. - -Why is the shadow _e a b_ in the first grade of strength, _b c_ in -the second; _c d_ in the third? The reason is that as from _e a b_ -the sky is nowhere visible, it gets no light whatever from the sky, -and so has no direct [primary] light. _b c_ faces the portion of the -sky _f g_ and is illuminated by it. _c d_ faces the sky at _h k_. _c -d_, being exposed to a larger extent of sky than _b c_, it is -reasonable that it should be more lighted. And thus, up to a certain -distance, the wall _a d_ will grow lighter for the reasons here -given, until the darkness of the room overpowers the light from the -window. - -172. - -When the light of the atmosphere is restricted [by an opening] and -illuminates bodies which cast shadows, these bodies being equally -distant from the centre of the window, that which is most obliquely -placed will cast the largest shadow beyond it. - -173. - -These bodies standing apart in a room lighted by a single window -will have derivative shadows more or less short according as they -are more or less opposite to the window. Among the shadows cast by -bodies of equal mass but at unequal distances from the opening by -which they are illuminated, that shadow will be the longest of the -body which is least in the light. And in proportion as one body is -better illuminated than another its shadow will be shorter than -another. The proportion _n m_ and _e v k_ bear to _r t_ and _v x_ -corresponds with that of the shadow _x_ to 4 and _y_. - -The reason why those bodies which are placed most in front of the -middle of the window throw shorter shadows than those obliquely -situated is:--That the window appears in its proper form and to the -obliquely placed ones it appears foreshortened; to those in the -middle, the window shows its full size, to the oblique ones it -appears smaller; the one in the middle faces the whole hemisphere -that is _e f_ and those on the side have only a strip; that is _q r_ -faces _a b_; and _m n_ faces _c d_; the body in the middle having a -larger quantity of light than those at the sides is lighted from a -point much below its centre, and thus the shadow is shorter. And the -pyramid _g_ 4 goes into _l y_ exactly as often as _a b_ goes into _e -f_. The axis of every derivative shadow passes through 6 1/2 -[Footnote 31: _passa per_ 6 1/2 (passes through 6 1/2). The meaning -of these words is probably this: Each of the three axes of the -derived shadow intersects the centre (_mezzo_) of the primary shadow -(_ombra originale_) and, by prolongation upwards crosses six lines. - -This is self evident only in the middle diagram; but it is equally -true of the side figures if we conceive of the lines 4 _f_, _x n v -m_, _y l k v_, and 4 _e_, as prolonged beyond the semicircle of the -horizon.] and is in a straight line with the centre of the primary -shadow, with the centre of the body casting it and of the derivative -light and with the centre of the window and, finally, with the -centre of that portion of the source of light which is the celestial -hemisphere, _y h_ is the centre of the derived shade, _l h_ of the -primary shadow, _l_ of the body throwing it, _l k_ of the derived -light, _v_ is the centre of the window, _e_ is the final centre of -the original light afforded by that portion of the hemisphere of the -sky which illuminates the solid body. - -[Footnote: Compare the diagram on Pl. IV, No. 3. In the original -this drawing is placed between lines 3 and 22; the rest, from line 4 -to line 21, is written on the left hand margin.] - -174. - -THE FARTHER THE DERIVED SHADOW IS PROLONGED THE LIGHTER IT BECOMES. - -You will find that the proportion of the diameter of the derived -shadow to that of the primary shadow will be the same as that -between the darkness of the primary shadow and that of the derived -shadow. - -[Footnote 6: Compare No. 177.] Let _a b_ be the diameter of the -primary shadow and _c d_ that of the derived shadow, I say that _a -b_ going, as you see, three times into _d c_, the shadow _d c_ will -be three times as light as the shadow _a b_. [Footnote 8: Compare -No. 177.] - -If the size of the illuminating body is larger than that of the -illuminated body an intersection of shadow will occur, beyond which -the shadows will run off in two opposite directions as if they were -caused by two separate lights. - -On the relative intensity of derived shadows (175-179). - -175. - -ON PAINTING. - -The derived shadow is stronger in proportion as it is nearer to its -place of origin. - -176. - -HOW SHADOWS FADE AWAY AT LONG DISTANCES. - -Shadows fade and are lost at long distances because the larger -quantity of illuminated air which lies between the eye and the -object seen tints the shadow with its own colour. - -177. - -_a b_ will be darker than _c d_ in proportion as _c d_ is broader -than _a b_. - -[Footnote: In the original MS. the word _lume_ (light) is written at -the apex of the pyramid.] - -178. - -It can be proved why the shadow _o p c h_ is darker in proportion as -it is nearer to the line _p h_ and is lighter in proportion as it is -nearer to the line _o c_. Let the light _a b_, be a window, and let -the dark wall in which this window is, be _b s_, that is, one of the -sides of the wall. - -Then we may say that the line _p h_ is darker than any other part of -the space _o p c h_, because this line faces the whole surface in -shadow of [Footnote: In the original the diagram is placed between -lines 27 and 28.] the wall _b s_. The line _o c_ is lighter than the -other part of this space _o p c h_, because this line faces the -luminous space _a b_. - -Where the shadow is larger, or smaller, or equal the body which -casts it. - -[First of the character of divided lights. [Footnote 14: _lumi -divisi_. The text here breaks off abruptly.] - -OF THE COMPOUND SHADOW _F, R, C, H_ CAUSED BY A SINGLE LIGHT. - -The shadow _f r c h_ is under such conditions as that where it is -farthest from its inner side it loses depth in proportion. To prove -this: - -Let _d a_, be the light and _f n_ the solid body, and let _a e_ be -one of the side walls of the window that is _d a_. Then I -say--according to the 2nd [proposition]: that the surface of any -body is affected by the tone of the objects surrounding it,--that -the side _r c_, which faces the dark wall _a e_ must participate of -its darkness and, in the same way that the outer surface which faces -the light _d a_ participates of the light; thus we get the outlines -of the extremes on each side of the centre included between them.] - -This is divided into four parts. The first the extremes, which -include the compound shadow, secondly the compound shadow between -these extremes. - -179. - -THE ACTION OF THE LIGHT AS FROM ITS CENTRE. - -If it were the whole of the light that caused the shadows beyond the -bodies placed in front of it, it would follow that any body much -smaller than the light would cast a pyramidal shadow; but experience -not showing this, it must be the centre of the light that produces -this effect. - -[Footnote: The diagram belonging to this passage is between lines 4 -and 5 in the original. Comp. the reproduction Pl. IV, No. 4. The -text and drawing of this chapter have already been published with -tolerable accuracy. See M. JORDAN: "_Das Malerbuch des Leonardo da -Vinci_". Leipzig 1873, P. 90.] - -PROOF. - -Let _a b_ be the width of the light from a window, which falls on a -stick set up at one foot from _a c_ [Footnote 6: _bastone_ (stick). -The diagram has a sphere in place of a stick.]. And let _a d_ be the -space where all the light from the window is visible. At _c e_ that -part of the window which is between _l b_ cannot be seen. In the -same way _a m_ cannot be seen from _d f_ and therefore in these two -portions the light begins to fail. - -Shadow as produced by two lights of different size (180. 181). - -180. - -A body in light and shade placed between two equal lights side by -side will cast shadows in proportion to the [amount of] light. And -the shadows will be one darker than the other in proportion as one -light is nearer to the said body than the other on the opposite -side. - -A body placed at an equal distance between two lights will cast two -shadows, one deeper than the other in proportion, as the light which -causes it is brighter than the other. - -[Footnote: In the MS. the larger diagram is placed above the first -line; the smaller one between l. 4 & 5.] - -181. - -A light which is smaller than the body it illuminates produces -shadows of which the outlines end within [the surface of] the body, -and not much compound shadow; and falls on less than half of it. A -light which is larger than the body it illuminates, falls on more -than half of it, and produces much compound shadow. - -The effect of light at different distances. - -182. - -OF THE SHADOW CAST BY A BODY PLACED BETWEEN 2 EQUAL LIGHTS. - -A body placed between 2 equal lights will cast 2 shadows of itself -in the direction of the lines of the 2 lights; and if you move this -body placing it nearer to one of the lights the shadow cast towards -the nearer light will be less deep than that which falls towards the -more distant one. - -Further complications in the derived shadows (183-187). - -183. - -The greatest depth of shadow is in the simple derived shadow because -it is not lighted by either of the two lights _a b, c d_. - -The next less deep shadow is the derived shadow _e f n_; and in this -the shadow is less by half, because it is illuminated by a single -light, that is _c d_. - -This is uniform in natural tone because it is lighted throughout by -one only of the two luminous bodies [10]. But it varies with the -conditions of shadow, inasmuch as the farther it is away from the -light the less it is illuminated by it [13]. - -The third degree of depth is the middle shadow [Footnote 15: We -gather from what follows that _q g r_ here means _ombra media_ (the -middle shadow).]. But this is not uniform in natural tone; because -the nearer it gets to the simple derived shadow the deeper it is -[Footnote 18: Compare lines 10-13], and it is the uniformly gradual -diminution by increase of distance which is what modifies it -[Footnote 20: See Footnote 18]: that is to say the depth of a shadow -increases in proportion to the distance from the two lights. - -The fourth is the shadow _k r s_ and this is all the darker in -natural tone in proportion as it is nearer to _k s_, because it gets -less of the light _a o_, but by the accident [of distance] it is -rendered less deep, because it is nearer to the light _c d_, and -thus is always exposed to both lights. - -The fifth is less deep in shadow than either of the others because -it is always entirely exposed to one of the lights and to the whole -or part of the other; and it is less deep in proportion as it is -nearer to the two lights, and in proportion as it is turned towards -the outer side _x t_; because it is more exposed to the second light -_a b_. - -[Footnote: The diagram to this section is given on Pl. V. To the -left is the facsimile of the beginning of the text belonging to it.] - -184. - -OF SIMPLE SHADOWS. - -Why, at the intersections _a_, _b_ of the two compound shadows _e f_ -and _m e_, is a simple shadow pfoduced as at _e h_ and _m g_, while -no such simple shadow is produced at the other two intersections _c -d_ made by the very same compound shadows? - -ANSWER. - -Compound shadow are a mixture of light and shade and simple shadows -are simply darkness. Hence, of the two lights _n_ and _o_, one falls -on the compound shadow from one side, and the other on the compound -shadow from the other side, but where they intersect no light falls, -as at _a b_; therefore it is a simple shadow. Where there is a -compound shadow one light or the other falls; and here a difficulty -arises for my adversary since he says that, where the compound -shadows intersect, both the lights which produce the shadows must of -necessity fall and therefore these shadows ought to be neutralised; -inasmuch as the two lights do not fall there, we say that the shadow -is a simple one and where only one of the two lights falls, we say -the shadow is compound, and where both the lights fall the shadow is -neutralised; for where both lights fall, no shadow of any kind is -produced, but only a light background limiting the shadow. Here I -shall say that what my adversary said was true: but he only mentions -such truths as are in his favour; and if we go on to the rest he -must conclude that my proposition is true. And that is: That if both -lights fell on the point of intersection, the shadows would be -neutralised. This I confess to be true if [neither of] the two -shadows fell in the same spot; because, where a shadow and a light -fall, a compound shadow is produced, and wherever two shadows or two -equal lights fall, the shadow cannot vary in any part of it, the -shadows and the lights both being equal. And this is proved in the -eighth [proposition] on proportion where it is said that if a given -quantity has a single unit of force and resistance, a double -quantity will have double force and double resistance. - -DEFINITION. - -The intersection _n_ is produced by the shadows caused by the light -_b_, because this light _b_ produces the shadow _x b_, and the -shadow _s b_, but the intersection _m_ is produced by the light _a_ -which causes the shadow _s a_, and the shadow _x a_. - -But if you uncover both the lights _a b_, then you get the two -shadows _n m_ both at once, and besides these, two other, simple -shadows are produced at _r o_ where neither of the two lights falls -at all. The grades of depth in compound shadows are fewer in -proportion as the lights falling on, and crossing them are less -numerous. - -186. - -Why the intersections at _n_ being composed of two compound derived -shadows, forms a compound shadow and not a simple one, as happens -with other intersections of compound shadows. This occurs, according -to the 2nd [diagram] of this [prop.] which says:--The intersection -of derived shadows when produced by the intersection of columnar -shadows caused by a single light does not produce a simple shadow. -And this is the corollary of the 1st [prop.] which says:--The -intersection of simple derived shadows never results in a deeper -shadow, because the deepest shadows all added together cannot be -darker than one by itself. Since, if many deepest shadows increased -in depth by their duplication, they could not be called the -_deepest_ shadows, but only part-shadows. But if such intersections -are illuminated by a second light placed between the eye and the -intersecting bodies, then those shadows would become compound -shadows and be uniformly dark just as much at the intersection as -throughout the rest. In the 1st and 2nd above, the intersections _i -k_ will not be doubled in depth as it is doubled in quantity. But in -this 3rd, at the intersections _g n_ they will be double in depth -and in quantity. - -187. - -HOW AND WHEN THE SURROUNDINGS IN SHADOW MINGLE THEIR DERIVED SHADOW -WITH THE LIGHT DERIVED FROM THE LUMINOUS BODY. - -The derived shadow of the dark walls on each side of the bright -light of the window are what mingle their various degrees of shade -with the light derived from the window; and these various depths of -shade modify every portion of the light, except where it is -strongest, at _c_. To prove this let _d a_ be the primary shadow -which is turned towards the point _e_, and darkens it by its derived -shadow; as may be seen by the triangle _a e d_, in which the -angle _e_ faces the darkened base _d a e_; the point _v_ faces the -dark shadow _a s_ which is part of _a d_, and as the whole is -greater than a part, _e_ which faces the whole base [of the -triangle], will be in deeper shadow than _v_ which only faces part -of it. In consequence of the conclusion [shown] in the above -diagram, _t_ will be less darkened than _v_, because the base of the -_t_ is part of the base of the _v_; and in the same way it follows -that _p_ is less in shadow than _t_, because the base of the _p_ is -part of the base of the _t_. And _c_ is the terminal point of the -derived shadow and the chief beginning of the highest light. - -[Footnote: The diagram on Pl. IV, No. 5 belongs to this passage; but -it must be noted that the text explains only the figure on the -right-hand side.] - -FOURTH BOOK ON LIGHT AND SHADE. - -On the shape of the cast shadows (188-191). - -188. - -The form of the shadow cast by any body of uniform density can never -be the same as that of the body producing it. [Footnote: Comp. the -drawing on PI. XXVIII, No. 5.] - -189. - -No cast shadow can produce the true image of the body which casts it -on a vertical plane unless the centre of the light is equally -distant from all the edges of that body. - -190. - -If a window _a b_ admits the sunlight into a room, the sunlight will -magnify the size of the window and diminish the shadow of a man in -such a way as that when the man makes that dim shadow of himself, -approach to that which defines the real size of the window, he will -see the shadows where they come into contact, dim and confused from -the strength of the light, shutting off and not allowing the solar -rays to pass; the effect of the shadow of the man cast by this -contact will be exactly that figured above. - -[Footnote: It is scarcely possible to render the meaning of this -sentence with strict accuracy; mainly because the grammatical -construction is defective in the most important part--line 4. In the -very slight original sketch the shadow touches the upper arch of the -window and the correction, here given is perhaps not justified.] - -191. - -A shadow is never seen as of uniform depth on the surface which -intercepts it unless every portion of that surface is equidistant -from the luminous body. This is proved by the 7th which says:--The -shadow will appear lighter or stronger as it is surrounded by a -darker or a lighter background. And by the 8th of this:--The -background will be in parts darker or lighter, in proportion as it -is farther from or nearer to the luminous body. And:--Of various -spots equally distant from the luminous body those will always be in -the highest light on which the rays fall at the smallest angles: The -outline of the shadow as it falls on inequalities in the surface -will be seen with all the contours similar to those of the body that -casts it, if the eye is placed just where the centre of the light -was. - -The shadow will look darkest where it is farthest from the body that -casts it. The shadow _c d_, cast by the body in shadow _a b_ which -is equally distant in all parts, is not of equal depth because it is -seen on a back ground of varying brightness. [Footnote: Compare the -three diagrams on Pl. VI, no 1 which, in the original accompany this -section.] - -On the outlines of cast shadows (192-195). - -192. - -The edges of a derived shadow will be most distinct where it is cast -nearest to the primary shadow. - -193. - -As the derived shadow gets more distant from the primary shadow, the -more the cast shadow differs from the primary shadow. - -194. - -OF SHADOWS WHICH NEVER COME TO AN END. - -The greater the difference between a light and the body lighted by -it, the light being the larger, the more vague will be the outlines -of the shadow of that object. - -The derived shadow will be most confused towards the edges of its -interception by a plane, where it is remotest from the body casting -it. - -195. - -What is the cause which makes the outlines of the shadow vague and -confused? - -Whether it is possible to give clear and definite outlines to the -edges of shadows. - -On the relative size of shadows (196. 197). - -196. - -THE BODY WHICH IS NEAREST TO THE LIGHT CASTS THE LARGEST SHADOW, AND -WHY? - -If an object placed in front of a single light is very close to it -you will see that it casts a very large shadow on the opposite wall, -and the farther you remove the object from the light the smaller -will the image of the shadow become. - -WHY A SHADOW LARGER THAN THE BODY THAT PRODUCES IT BECOMES OUT OF -PROPORTION. - -The disproportion of a shadow which is larger than the body -producing it, results from the light being smaller than the body, so -that it cannot be at an equal distance from the edges of the body -[Footnote 11: H. LUDWIG in his edition of the old copies, in the -Vatican library--in which this chapter is included under Nos. 612, -613 and 614 alters this passage as follows: _quella parte ch'e piu -propinqua piu cresce che le distanti_, although the Vatican copy -agrees with the original MS. in having _distante_ in the former and -_propinque_ in the latter place. This supposed amendment seems to me -to invert the facts. Supposing for instance, that on Pl. XXXI No. 3. -_f_ is the spot where the light is that illuminates the figure there -represented, and that the line behind the figure represents a wall -on which the shadow of the figure is thrown. It is evident, that in -that case the nearest portion, in this case the under part of the -thigh, is very little magnified in the shadow, and the remoter -parts, for instance the head, are more magnified.]; and the portions -which are most remote are made larger than the nearer portions for -this reason [Footnote 12: See Footnote 11]. - -WHY A SHADOW WHICH IS LARGER THAN THE BODY CAUSING IT HAS -ILL-DEFINED OUTLINES. - -The atmosphere which surrounds a light is almost like light itself -for brightness and colour; but the farther off it is the more it -loses this resemblance. An object which casts a large shadow and is -near to the light, is illuminated both by that light by the luminous -atmosphere; hence this diffused light gives the shadow ill-defined -edges. - -197. - -A luminous body which is long and narrow in shape gives more -confused outlines to the derived shadow than a spherical light, and -this contradicts the proposition next following: A shadow will have -its outlines more clearly defined in proportion as it is nearer to -the primary shadow or, I should say, the body casting the shadow; -[Footnote 14: The lettering refers to the lower diagram, Pl. XLI, -No. 5.] the cause of this is the elongated form of the luminous body -_a c_, &c. [Footnote 16: See Footnote 14]. - -Effects on cast shadows by the tone of the back ground. - -198. - -OF MODIFIED SHADOWS. - -Modified shadows are those which are cast on light walls or other -illuminated objects. - -A shadow looks darkest against a light background. The outlines of a -derived shadow will be clearer as they are nearer to the primary -shadow. A derived shadow will be most defined in shape where it is -intercepted, where the plane intercepts it at the most equal angle. - -Those parts of a shadow will appear darkest which have darker -objects opposite to them. And they will appear less dark when they -face lighter objects. And the larger the light object opposite, the -more the shadow will be lightened. - -And the larger the surface of the dark object the more it will -darken the derived shadow where it is intercepted. - -A disputed proposition. - -199. - -OF THE OPINION OF SOME THAT A TRIANGLE CASTS NO SHADOW ON A PLANE -SURFACE. - -Certain mathematicians have maintained that a triangle, of which the -base is turned to the light, casts no shadow on a plane; and this -they prove by saying [5] that no spherical body smaller than the -light can reach the middle with the shadow. The lines of radiant -light are straight lines [6]; therefore, suppose the light to be _g -h_ and the triangle _l m n_, and let the plane be _i k_; they say -the light _g_ falls on the side of the triangle _l n_, and the -portion of the plane _i q_. Thus again _h_ like _g_ falls on the -side _l m_, and then on _m n_ and the plane _p k_; and if the whole -plane thus faces the lights _g h_, it is evident that the triangle -has no shadow; and that which has no shadow can cast none. This, in -this case appears credible. But if the triangle _n p g_ were not -illuminated by the two lights _g_ and _h_, but by _i p_ and _g_ and -_k_ neither side is lighted by more than one single light: that is -_i p_ is invisible to _h g_ and _k_ will never be lighted by _g_; -hence _p q_ will be twice as light as the two visible portions that -are in shadow. - -[Footnote: 5--6. This passage is so obscure that it would be rash to -offer an explanation. Several words seem to have been omitted.] - -On the relative depth of cast shadows (200-202). - -200. - -A spot is most in the shade when a large number of darkened rays -fall upon it. The spot which receives the rays at the widest angle -and by darkened rays will be most in the dark; a will be twice as -dark as b, because it originates from twice as large a base at an -equal distance. A spot is most illuminated when a large number of -luminous rays fall upon it. d is the beginning of the shadow _d f_, -and tinges _c_ but _a_ little; _d e_ is half of the shadow _d f_ and -gives a deeper tone where it is cast at _b_ than at _f_. And the -whole shaded space _e_ gives its tone to the spot _a_. [Footnote: -The diagram here referred to is on Pl. XLI, No. 2.] - -201. - -_A n_ will be darker than _c r_ in proportion to the number of times -that _a b_ goes into _c d_. - -202. - -The shadow cast by an object on a plane will be smaller in -proportion as that object is lighted by feebler rays. Let _d e_ be -the object and _d c_ the plane surface; the number of times that _d -e_ will go into _f g_ gives the proportion of light at _f h_ to _d -c_. The ray of light will be weaker in proportion to its distance -from the hole through which it falls. - -FIFTH BOOK ON LIGHT AND SHADE. - -Principles of reflection (203. 204). - -203. - -OF THE WAY IN WHICH THE SHADOWS CAST BY OBJECTS OUGHT TO BE DEFINED. - -If the object is the mountain here figured, and the light is at the -point _a_, I say that from _b d_ and also from _c f_ there will be -no light but from reflected rays. And this results from the fact -that rays of light can only act in straight lines; and the same is -the case with the secondary or reflected rays. - -204. - -The edges of the derived shadow are defined by the hues of the -illuminated objects surrounding the luminous body which produces the -shadow. - -On reverberation. - -205. - -OF REVERBERATION. - -Reverberation is caused by bodies of a bright nature with a flat and -semi opaque surface which, when the light strikes upon them, throw -it back again, like the rebound of a ball, to the former object. - -WHERE THERE CAN BE NO REFLECTED LIGHTS. - -All dense bodies have their surfaces occupied by various degrees of -light and shade. The lights are of two kinds, one called original, -the other borrowed. Original light is that which is inherent in the -flame of fire or the light of the sun or of the atmosphere. Borrowed -light will be reflected light; but to return to the promised -definition: I say that this luminous reverberation is not produced -by those portions of a body which are turned towards darkened -objects, such as shaded spots, fields with grass of various height, -woods whether green or bare; in which, though that side of each -branch which is turned towards the original light has a share of -that light, nevertheless the shadows cast by each branch separately -are so numerous, as well as those cast by one branch on the others, -that finally so much shadow is the result that the light counts for -nothing. Hence objects of this kind cannot throw any reflected light -on opposite objects. - -Reflection on water (206. 207). - -206. - -PERSPECTIVE. - -The shadow or object mirrored in water in motion, that is to say in -small wavelets, will always be larger than the external object -producing it. - -207. - -It is impossible that an object mirrored on water should correspond -in form to the object mirrored, since the centre of the eye is above -the surface of the water. - -This is made plain in the figure here given, which demonstrates that -the eye sees the surface _a b_, and cannot see it at _l f_, and at -_r t_; it sees the surface of the image at _r t_, and does not see -it in the real object _c d_. Hence it is impossible to see it, as -has been said above unless the eye itself is situated on the surface -of the water as is shown below [13]. - -[Footnote: _A_ stands for _ochio_ [eye], _B_ for _aria_ [air], _C_ -for _acqua_ [water], _D_ for _cateto_ [cathetus].--In the original -MS. the second diagram is placed below line 13.] - -Experiments with the mirror (208-210). - -208. - -THE MIRROR. - -If the illuminated object is of the same size as the luminous body -and as that in which the light is reflected, the amount of the -reflected light will bear the same proportion to the intermediate -light as this second light will bear to the first, if both bodies -are smooth and white. - -209. - -Describe how it is that no object has its limitation in the mirror -but in the eye which sees it in the mirror. For if you look at your -face in the mirror, the part resembles the whole in as much as the -part is everywhere in the mirror, and the whole is in every part of -the same mirror; and the same is true of the whole image of any -object placed opposite to this mirror, &c. - -210. - -No man can see the image of another man in a mirror in its proper -place with regard to the objects; because every object falls on [the -surface of] the mirror at equal angles. And if the one man, who sees -the other in the mirror, is not in a direct line with the image he -will not see it in the place where it really falls; and if he gets -into the line, he covers the other man and puts himself in the place -occupied by his image. Let _n o_ be the mirror, _b_ the eye of your -friend and _d_ your own eye. Your friend's eye will appear to you at -_a_, and to him it will seem that yours is at _c_, and the -intersection of the visual rays will occur at _m_, so that either of -you touching _m_ will touch the eye of the other man which shall be -open. And if you touch the eye of the other man in the mirror it -will seem to him that you are touching your own. - -Appendix:--On shadows in movement (211. 212). - -211. - -OF THE SHADOW AND ITS MOTION. - -When two bodies casting shadows, and one in front of the other, are -between a window and the wall with some space between them, the -shadow of the body which is nearest to the plane of the wall will -move if the body nearest to the window is put in transverse motion -across the window. To prove this let _a_ and _b_ be two bodies -placed between the window _n m_ and the plane surface _o p_ with -sufficient space between them as shown by the space _a b_. I say -that if the body _a_ is moved towards _s_ the shadow of the body _b_ -which is at _c_ will move towards _d_. - -212. - -OF THE MOTION OF SHADOWS. - -The motion of a shadow is always more rapid than that of the body -which produces it if the light is stationary. To prove this let _a_ -be the luminous body, and _b_ the body casting the shadow, and _d_ -the shadow. Then I say that in the time while the solid body moves -from _b_ to _c_, the shadow _d_ will move to _e_; and this -proportion in the rapidity of the movements made in the same space -of time, is equal to that in the length of the space moved over. -Thus, given the proportion of the space moved over by the body _b_ -to _c_, to that moved over by the shadow _d_ to _e_, the proportion -in the rapidity of their movements will be the same. - -But if the luminous body is also in movement with a velocity equal -to that of the solid body, then the shadow and the body that casts -it will move with equal speed. And if the luminous body moves more -rapidly than the solid body, the motion of the shadow will be slower -than that of the body casting it. - -But if the luminous body moves more slowly than the solid body, then -the shadow will move more rapidly than that body. - -SIXTH BOOK ON LIGHT AND SHADE. - -The effect of rays passing through holes (213. 214). - -213. - -PERSPECTIVE. - -If you transmit the rays of the sun through a hole in the shape of a -star you will see a beautiful effect of perspective in the spot -where the sun's rays fall. - -[Footnote: In this and the following chapters of MS. C the order of -the original paging has been adhered to, and is shown in -parenthesis. Leonardo himself has but rarely worked out the subject -of these propositions. The space left for the purpose has -occasionally been made use of for quite different matter. Even the -numerous diagrams, most of them very delicately sketched, lettered -and numbered, which occur on these pages, are hardly ever explained, -with the exception of those few which are here given.] - -214. - -No small hole can so modify the convergence of rays of light as to -prevent, at a long distance, the transmission of the true form of -the luminous body causing them. It is impossible that rays of light -passing through a parallel [slit], should not display the form of -the body causing them, since all the effects produced by a luminous -body are [in fact] the reflection of that body: The moon, shaped -like a boat, if transmitted through a hole is figured in the surface -[it falls on] as a boatshaped object. [Footnote 8: In the MS. a -blank space is left after this question.] Why the eye sees bodies at -a distance, larger than they measure on the vertical plane?. - -[Footnote: This chapter, taken from another MS. may, as an -exception, be placed here, as it refers to the same subject as the -preceding section.] - -On gradation of shadows (215. 216). - -215. - -Although the breadth and length of lights and shadow will be -narrower and shorter in foreshortening, the quality and quantity of -the light and shade is not increased nor diminished. - -[3]The function of shade and light when diminished by -foreshortening, will be to give shadow and to illuminate an object -opposite, according to the quality and quantity in which they fall -on the body. - -[5]In proportion as a derived shadow is nearer to its penultimate -extremities the deeper it will appear, _g z_ beyond the intersection -faces only the part of the shadow [marked] _y z_; this by -intersection takes the shadow from _m n_ but by direct line it takes -the shadow _a m_ hence it is twice as deep as _g z_. _Y x_, by -intersection takes the shadow _n o_, but by direct line the shadow -_n m a_, therefore _x y_ is three times as dark as _z g_; _x f_, by -intersection faces _o b_ and by direct line _o n m a_, therefore we -must say that the shadow between _f x_ will be four times as dark as -the shadow _z g_, because it faces four times as much shadow. - -Let _a b_ be the side where the primary shadow is, and _b c_ the -primary light, _d_ will be the spot where it is intercepted,_f g_ -the derived shadow and _f e_ the derived light. - -And this must be at the beginning of the explanation. - -[Footnote: In the original MS. the text of No. 252 precedes the one -given here. In the text of No. 215 there is a blank space of about -four lines between the lines 2 and 3. The diagram given on Pl. VI, -No. 2 is placed between lines 4 and 5. Between lines 5 and 6 there -is another space of about three lines and one line left blank -between lines 8 and 9. The reader will find the meaning of the whole -passage much clearer if he first reads the final lines 11--13. -Compare also line 4 of No. 270.] - -On relative proportion of light and shadows (216--221). - -216. - -That part of the surface of a body on which the images [reflection] -from other bodies placed opposite fall at the largest angle will -assume their hue most strongly. In the diagram below, 8 is a larger -angle than 4, since its base _a n_ is larger than _e n_ the base of -4. This diagram below should end at _a n_ 4 8. [4]That portion of -the illuminated surface on which a shadow is cast will be brightest -which lies contiguous to the cast shadow. Just as an object which is -lighted up by a greater quantity of luminous rays becomes brighter, -so one on which a greater quantity of shadow falls, will be darker. - -Let 4 be the side of an illuminated surface 4 8, surrounding the -cast shadow _g e_ 4. And this spot 4 will be lighter than 8, because -less shadow falls on it than on 8. Since 4 faces only the shadow _i -n_; and 8 faces and receives the shadow _a e_ as well as _i n_ which -makes it twice as dark. And the same thing happens when you put the -atmosphere and the sun in the place of shade and light. - -[12] The distribution of shadow, originating in, and limited by, -plane surfaces placed near to each other, equal in tone and directly -opposite, will be darker at the ends than at the beginning, which -will be determined by the incidence of the luminous rays. You will -find the same proportion in the depth of the derived shadows _a n_ -as in the nearness of the luminous bodies _m b_, which cause them; -and if the luminous bodies were of equal size you would still -farther find the same proportion in the light cast by the luminous -circles and their shadows as in the distance of the said luminous -bodies. - -[Footnote: The diagram originally placed between lines 3 and 4 is on -Pl. VI, No. 3. In the diagram given above line 14 of the original, -and here printed in the text, the words _corpo luminoso_ [luminous -body] are written in the circle _m_, _luminoso_ in the circle _b_ -and _ombroso_ [body in shadow] in the circle _o_.] - -217. - -THAT PART OF THE REFLECTION WILL BE BRIGHTEST WHERE THE REFLECTED -RAYS ARE SHORTEST. - -[2] The darkness occasioned by the casting of combined shadows will -be in conformity with its cause, which will originate and terminate -between two plane surfaces near together, alike in tone and directly -opposite each other. - -[4] In proportion as the source of light is larger, the luminous and -shadow rays will be more mixed together. This result is produced -because wherever there is a larger quantity of luminous rays, there -is most light, but where there are fewer there is least light, -consequently the shadow rays come in and mingle with them. - -[Footnote: Diagrams are inserted before lines 2 and 4.] - -218. - -In all the proportions I lay down it must be understood that the -medium between the bodies is always the same. [2] The smaller the -luminous body the more distinct will the transmission of the shadows -be. - -[3] When of two opposite shadows, produced by the same body, one is -twice as dark as the other though similar in form, one of the two -lights causing them must have twice the diameter that the other has -and be at twice the distance from the opaque body. If the object is -lowly moved across the luminous body, and the shadow is intercepted -at some distance from the object, there will be the same relative -proportion between the motion of the derived shadow and the motion -of the primary shadow, as between the distance from the object to -the light, and that from the object to the spot where the shadow is -intercepted; so that though the object is moved slowly the shadow -moves fast. - -[Footnote: There are diagrams inserted before lines 2 and 3 but they -are not reproduced here. The diagram above line 6 is written upon as -follows: at _A lume_ (light), at _B obbietto_ (body), at _C ombra -d'obbietto_ (shadow of the object).] - -219. - -A luminous body will appear less brilliant when surrounded by a -bright background. - -[2] I have found that the stars which are nearest to the horizon -look larger than the others because light falls upon them from a -larger proportion of the solar body than when they are above us; and -having more light from the sun they give more light, and the bodies -which are most luminous appear the largest. As may be seen by the -sun through a mist, and overhead; it appears larger where there is -no mist and diminished through mist. No portion of the luminous body -is ever visible from any spot within the pyramid of pure derived -shadow. - -[Footnote: Between lines 1 and 2 there is in the original a large -diagram which does not refer to this text. ] - -220. - -A body on which the solar rays fall between the thin branches of -trees far apart will cast but a single shadow. - -[2] If an opaque body and a luminous one are (both) spherical the -base of the pyramid of rays will bear the same proportion to the -luminous body as the base of the pyramid of shade to the opaque -body. - -[4] When the transmitted shadow is intercepted by a plane surface -placed opposite to it and farther away from the luminous body than -from the object [which casts it] it will appear proportionately -darker and the edges more distinct. - -[Footnote: The diagram which, in the original, is placed above line -2, is similar to the one, here given on page 73 (section 120).--The -diagram here given in the margin stands, in the original, between -lines 3 and 4.] - -221. - -A body illuminated by the solar rays passing between the thick -branches of trees will produce as many shadows as there are branches -between the sun and itself. - -Where the shadow-rays from an opaque pyramidal body are intercepted -they will cast a shadow of bifurcate outline and various depth at -the points. A light which is broader than the apex but narrower than -the base of an opaque pyramidal body placed in front of it, will -cause that pyramid to cast a shadow of bifurcate form and various -degrees of depth. - -If an opaque body, smaller than the light, casts two shadows and if -it is the same size or larger, casts but one, it follows that a -pyramidal body, of which part is smaller, part equal to, and part -larger than, the luminous body, will cast a bifurcate shadow. - -[Footnote: Between lines 2 and 3 there are in the original two large -diagrams.] - -_IV._ - -_Perspective of Disappearance._ - -_The theory of the_ "Prospettiva de' perdimenti" _would, in many -important details, be quite unintelligible if it had not been led up -by the principles of light and shade on which it is based. The word_ -"Prospettiva" _in the language of the time included the principles -of optics; what Leonardo understood by_ "Perdimenti" _will be -clearly seen in the early chapters, Nos._ 222--224. _It is in the -very nature of the case that the farther explanations given in the -subsequent chapters must be limited to general rules. The sections -given as_ 227--231 _"On indistinctness at short distances" have, it -is true, only an indirect bearing on the subject; but on the other -hand, the following chapters,_ 232--234, _"On indistinctness at -great distances," go fully into the matter, and in chapters_ -235--239, _which treat "Of the importance of light and shade in the -Perspective of Disappearance", the practical issues are distinctly -insisted on in their relation to the theory. This is naturally -followed by the statements as to "the effect of light or dark -backgrounds on the apparent size of bodies"_ (_Nos._ 240--250). _At -the end I have placed, in the order of the original, those sections -from the MS._ C _which treat of the "Perspective of Disappearance" -and serve to some extent to complete the treatment of the subject_ -(251--262). - -Definition (222. 223). - -222. - -OF THE DIMINISHED DISTINCTNESS OF THE OUTLINES OF OPAQUE BODIES. - -If the real outlines of opaque bodies are indistinguishable at even -a very short distance, they will be more so at long distances; and, -since it is by its outlines that we are able to know the real form -of any opaque body, when by its remoteness we fail to discern it as -a whole, much more must we fail to discern its parts and outlines. - -223. - -OF THE DIMINUTION IN PERSPECTIVE OF OPAQUE OBJECTS. - -Among opaque objects of equal size the apparent diminution of size -will be in proportion to their distance from the eye of the -spectator; but it is an inverse proportion, since, where the -distance is greater, the opaque body will appear smaller, and the -less the distance the larger will the object appear. And this is the -fundamental principle of linear perspective and it -follows:--[11]every object as it becomes more remote loses first -those parts which are smallest. Thus of a horse, we should lose the -legs before the head, because the legs are thinner than the head; -and the neck before the body for the same reason. Hence it follows -that the last part of the horse which would be discernible by the -eye would be the mass of the body in an oval form, or rather in a -cylindrical form and this would lose its apparent thickness before -its length--according to the 2nd rule given above, &c. [Footnote 23: -Compare line 11.]. - -If the eye remains stationary the perspective terminates in the -distance in a point. But if the eye moves in a straight [horizontal] -line the perspective terminates in a line and the reason is that -this line is generated by the motion of the point and our sight; -therefore it follows that as we move our sight [eye], the point -moves, and as we move the point, the line is generated, &c. - -An illustration by experiment. - -224. - -Every visible body, in so far as it affects the eye, includes three -attributes; that is to say: mass, form and colour; and the mass is -recognisable at a greater distance from the place of its actual -existence than either colour or form. Again, colour is discernible -at a greater distance than form, but this law does not apply to -luminous bodies. - -The above proposition is plainly shown and proved by experiment; -because: if you see a man close to you, you discern the exact -appearance of the mass and of the form and also of the colouring; if -he goes to some distance you will not recognise who he is, because -the character of the details will disappear, if he goes still -farther you will not be able to distinguish his colouring, but he -will appear as a dark object, and still farther he will appear as a -very small dark rounded object. It appears rounded because distance -so greatly diminishes the various details that nothing remains -visible but the larger mass. And the reason is this: We know very -well that all the images of objects reach the senses by a small -aperture in the eye; hence, if the whole horizon _a d_ is admitted -through such an aperture, the object _b c_ being but a very small -fraction of this horizon what space can it fill in that minute image -of so vast a hemisphere? And because luminous bodies have more power -in darkness than any others, it is evident that, as the chamber of -the eye is very dark, as is the nature of all colored cavities, the -images of distant objects are confused and lost in the great light -of the sky; and if they are visible at all, appear dark and black, -as every small body must when seen in the diffused light of the -atmosphere. - -[Footnote: The diagram belonging to this passage is placed between -lines 5 and 6; it is No. 4 on Pl. VI. ] - -A guiding rule. - -225. - -OF THE ATMOSPHERE THAT INTERPOSES BETWEEN THE EYE AND VISIBLE -OBJECTS. - -An object will appear more or less distinct at the same distance, in -proportion as the atmosphere existing between the eye and that -object is more or less clear. Hence, as I know that the greater or -less quantity of the air that lies between the eye and the object -makes the outlines of that object more or less indistinct, you must -diminish the definiteness of outline of those objects in proportion -to their increasing distance from the eye of the spectator. - -An experiment. - -226. - -When I was once in a place on the sea, at an equal distance from the -shore and the mountains, the distance from the shore looked much -greater than that from the mountains. - -On indistinctness at short distances (227-231). - -227. - -If you place an opaque object in front of your eye at a distance of -four fingers' breadth, if it is smaller than the space between the -two eyes it will not interfere with your seeing any thing that may -be beyond it. No object situated beyond another object seen by the -eye can be concealed by this [nearer] object if it is smaller than -the space from eye to eye. - -228. - -The eye cannot take in a luminous angle which is too close to it. - -229. - -That part of a surface will be better lighted on which the light -falls at the greater angle. And that part, on which the shadow falls -at the greatest angle, will receive from those rays least of the -benefit of the light. - -230. - -OF THE EYE. - -The edges of an object placed in front of the pupil of the eye will -be less distinct in proportion as they are closer to the eye. This -is shown by the edge of the object _n_ placed in front of the pupil -_d_; in looking at this edge the pupil also sees all the space _a c_ -which is beyond the edge; and the images the eye receives from that -space are mingled with the images of the edge, so that one image -confuses the other, and this confusion hinders the pupil from -distinguishing the edge. - -231. - -The outlines of objects will be least clear when they are nearest to -the eye, and therefore remoter outlines will be clearer. Among -objects which are smaller than the pupil of the eye those will be -less distinct which are nearer to the eye. - -On indistinctness at great distances (232-234). - -232. - -Objects near to the eye will appear larger than those at a distance. - -Objects seen with two eyes will appear rounder than if they are seen -with only one. - -Objects seen between light and shadow will show the most relief. - -233. - -OF PAINTING. - -Our true perception of an object diminishes in proportion as its -size is diminished by distance. - -234. - -PERSPECTIVE. - -Why objects seen at a distance appear large to the eye and in the -image on the vertical plane they appear small. - -PERSPECTIVE. - -I ask how far away the eye can discern a non-luminous body, as, for -instance, a mountain. It will be very plainly visible if the sun is -behind it; and could be seen at a greater or less distance according -to the sun's place in the sky. - -[Footnote: The clue to the solution of this problem (lines 1-3) is -given in lines 4-6, No. 232. Objects seen with both eyes appear -solid since they are seen from two distinct points of sight -separated by the distance between the eyes, but this solidity cannot -be represented in a flat drawing. Compare No. 535.] - -The importance of light and shade in the perspective of -disappearance (235-239). - -235. - -An opaque body seen in a line in which the light falls will reveal -no prominences to the eye. For instance, let _a_ be the solid body -and _c_ the light; _c m_ and _c n_ will be the lines of incidence of -the light, that is to say the lines which transmit the light to the -object _a_. The eye being at the point _b_, I say that since the -light _c_ falls on the whole part _m n_ the portions in relief on -that side will all be illuminated. Hence the eye placed at _c_ -cannot see any light and shade and, not seeing it, every portion -will appear of the same tone, therefore the relief in the prominent -or rounded parts will not be visible. - -236. - -OF PAINTING. - -When you represent in your work shadows which you can only discern -with difficulty, and of which you cannot distinguish the edges so -that you apprehend them confusedly, you must not make them sharp or -definite lest your work should have a wooden effect. - -237. - -OF PAINTING. - -You will observe in drawing that among the shadows some are of -undistinguishable gradation and form, as is shown in the 3rd -[proposition] which says: Rounded surfaces display as many degrees -of light and shade as there are varieties of brightness and darkness -reflected from the surrounding objects. - -238. - -OF LIGHT AND SHADE. - -You who draw from nature, look (carefully) at the extent, the -degree, and the form of the lights and shadows on each muscle; and -in their position lengthwise observe towards which muscle the axis -of the central line is directed. - -239. - -An object which is [so brilliantly illuminated as to be] almost as -bright as light will be visible at a greater distance, and of larger -apparent size than is natural to objects so remote. - -The effect of light or dark backgrounds on the apparent size of -objects (240-250). - -240. - -A shadow will appear dark in proportion to the brilliancy of the -light surrounding it and conversely it will be less conspicuous -where it is seen against a darker background. - -241. - -OF ORDINARY PERSPECTIVE. - -An object of equal breadth and colour throughout, seen against a -background of various colours will appear unequal in breadth. - -And if an object of equal breadth throughout, but of various -colours, is seen against a background of uniform colour, that object -will appear of various breadth. And the more the colours of the -background or of the object seen against the ground vary, the -greater will the apparent variations in the breadth be though the -objects seen against the ground be of equal breadth [throughout]. - -242. - -A dark object seen against a bright background will appear smaller -than it is. - -A light object will look larger when it is seen against a background -darker than itself. - -243. - -OF LIGHT. - -A luminous body when obscured by a dense atmosphere will appear -smaller; as may be seen by the moon or sun veiled by mists. - -OF LIGHT. - -Of several luminous bodies of equal size and brilliancy and at an -equal distance, that will look the largest which is surrounded by -the darkest background. - -OF LIGHT. - -I find that any luminous body when seen through a dense and thick -mist diminishes in proportion to its distance from the eye. Thus it -is with the sun by day, as well as the moon and the other eternal -lights by night. And when the air is clear, these luminaries appear -larger in proportion as they are farther from the eye. - -244. - -That portion of a body of uniform breadth which is against a lighter -background will look narrower [than the rest]. - -[4] _e_ is a given object, itself dark and of uniform breadth; _a b_ -and _c d_ are two backgrounds one darker than the other; _b c_ is a -bright background, as it might be a spot lighted by the sun through -an aperture in a dark room. Then I say that the object _e g_ will -appear larger at _e f_ than at _g h_; because _e f_ has a darker -background than _g h_; and again at _f g_ it will look narrower from -being seen by the eye _o_, on the light background _b c_. [Footnote -12: The diagram to which the text, lines 1-11, refers, is placed in -the original between lines 3 and 4, and is given on Pl. XLI, No. 3. -Lines 12 to 14 are explained by the lower of the two diagrams on Pl. -XLI, No. 4. In the original these are placed after line 14.] That -part of a luminous body, of equal breadth and brilliancy throughout, -will look largest which is seen against the darkest background; and -the luminous body will seem on fire. - -245. - -WHY BODIES IN LIGHT AND SHADE HAVE THEIR OUTLINES ALTERED BY THE -COLOUR AND BRIGHTNESS OF THE OBJECTS SERVING AS A BACKGROUND TO -THEM. - -If you look at a body of which the illuminated portion lies and ends -against a dark background, that part of the light which will look -brightest will be that which lies against the dark [background] at -_d_. But if this brighter part lies against a light background, the -edge of the object, which is itself light, will be less distinct -than before, and the highest light will appear to be between the -limit of the background _m f_ and the shadow. The same thing is seen -with regard to the dark [side], inasmuch as that edge of the shaded -portion of the object which lies against a light background, as at -_l_, it looks much darker than the rest. But if this shadow lies -against a dark background, the edge of the shaded part will appear -lighter than before, and the deepest shade will appear between the -edge and the light at the point _o_. - -[Footnote: In the original diagram _o_ is inside the shaded surface -at the level of _d_.] - -246. - -An opaque body will appear smaller when it is surrounded by a highly -luminous background, and a light body will appear larger when it is -seen against a darker background. This may be seen in the height of -buildings at night, when lightning flashes behind them; it suddenly -seems, when it lightens, as though the height of the building were -diminished. For the same reason such buildings look larger in a -mist, or by night than when the atmosphere is clear and light. - -247. - -ON LIGHT BETWEEN SHADOWS - -When you are drawing any object, remember, in comparing the grades -of light in the illuminated portions, that the eye is often deceived -by seeing things lighter than they are. And the reason lies in our -comparing those parts with the contiguous parts. Since if two -[separate] parts are in different grades of light and if the less -bright is conterminous with a dark portion and the brighter is -conterminous with a light background--as the sky or something -equally bright--, then that which is less light, or I should say -less radiant, will look the brighter and the brighter will seem the -darker. - -248. - -Of objects equally dark in themselves and situated at a considerable -and equal distance, that will look the darkest which is farthest -above the earth. - -249. - -TO PROVE HOW IT IS THAT LUMINOUS BODIES APPEAR LARGER, AT A -DISTANCE, THAN THEY ARE. - -If you place two lighted candles side by side half a braccio apart, -and go from them to a distance 200 braccia you will see that by the -increased size of each they will appear as a single luminous body -with the light of the two flames, one braccio wide. - -TO PROVE HOW YOU MAY SEE THE REAL SIZE OF LUMINOUS BODIES. - -If you wish to see the real size of these luminous bodies, take a -very thin board and make in it a hole no bigger than the tag of a -lace and place it as close to your eye as possible, so that when you -look through this hole, at the said light, you can see a large space -of air round it. Then by rapidly moving this board backwards and -forwards before your eye you will see the light increase [and -diminish]. - -Propositions on perspective of disappearance from MS. C. (250-262). - -250. - -Of several bodies of equal size and equally distant from the eye, -those will look the smallest which are against the lightest -background. - -Every visible object must be surrounded by light and shade. A -perfectly spherical body surrounded by light and shade will appear -to have one side larger than the other in proportion as one is more -highly lighted than the other. - -251. - -PERSPECTIVE. - -No visible object can be well understood and comprehended by the -human eye excepting from the difference of the background against -which the edges of the object terminate and by which they are -bounded, and no object will appear [to stand out] separate from that -background so far as the outlines of its borders are concerned. The -moon, though it is at a great distance from the sun, when, in an -eclipse, it comes between our eyes and the sun, appears to the eyes -of men to be close to the sun and affixed to it, because the sun is -then the background to the moon. - -252. - -A luminous body will appear more brilliant in proportion as it is -surrounded by deeper shadow. [Footnote: The diagram which, in the -original, is placed after this text, has no connection with it.] - -253. - -The straight edges of a body will appear broken when they are -conterminous with a dark space streaked with rays of light. -[Footnote: Here again the diagrams in the original have no -connection with the text.] - -254. - -Of several bodies, all equally large and equally distant, that which -is most brightly illuminated will appear to the eye nearest and -largest. [Footnote: Here again the diagrams in the original have no -connection with the text.] - -255. - -If several luminous bodies are seen from a great distance although -they are really separate they will appear united as one body. - -256. - -If several objects in shadow, standing very close together, are seen -against a bright background they will appear separated by wide -intervals. - -257. - -Of several bodies of equal size and tone, that which is farthest -will appear the lightest and smallest. - -258. - -Of several objects equal in size, brightness of background and -length that which has the flattest surface will look the largest. A -bar of iron equally thick throughout and of which half is red hot, -affords an example, for the red hot part looks thicker than the -rest. - -259. - -Of several bodies of equal size and length, and alike in form and in -depth of shade, that will appear smallest which is surrounded by the -most luminous background. - -260. - -DIFFERENT PORTIONS OF A WALL SURFACE WILL BE DARKER OR BRIGHTER IN -PROPORTION AS THE LIGHT OR SHADOW FALLS ON THEM AT A LARGER ANGLE. - -The foregoing proposition can be clearly proved in this way. Let us -say that _m q_ is the luminous body, then _f g_ will be the opaque -body; and let _a e_ be the above-mentioned plane on which the said -angles fall, showing [plainly] the nature and character of their -bases. Then: _a_ will be more luminous than _b_; the base of the -angle _a_ is larger than that of _b_ and it therefore makes a -greater angle which will be _a m q_; and the pyramid _b p m_ will be -narrower and _m o c_ will be still finer, and so on by degrees, in -proportion as they are nearer to _e_, the pyramids will become -narrower and darker. That portion of the wall will be the darkest -where the breadth of the pyramid of shadow is greater than the -breadth of the pyramid of light. - -At the point _a_ the pyramid of light is equal in strength to the -pyramid of shadow, because the base _f g_ is equal to the base _r -f_. At the point _d_ the pyramid of light is narrower than the -pyramid of shadow by so much as the base _s f_ is less than the base -_f g_. - -Divide the foregoing proposition into two diagrams, one with the -pyramids of light and shadow, the other with the pyramids of light -[only]. - -261. - -Among shadows of equal depth those which are nearest to the eye will -look least deep. - -262. - -The more brilliant the light given by a luminous body, the deeper -will the shadows be cast by the objects it illuminates. - -_V._ - -_Theory of colours._ - -_Leonardo's theory of colours is even more intimately connected with -his principles of light and shade than his Perspective of -Disappearance and is in fact merely an appendix or supplement to -those principles, as we gather from the titles to sections_ 264, -267_, and _276_, while others again_ (_Nos._ 281, 282_) are headed_ -Prospettiva. - -_A very few of these chapters are to be found in the oldest copies -and editions of the Treatise on Painting, and although the material -they afford is but meager and the connection between them but -slight, we must still attribute to them a special theoretical value -as well as practical utility--all the more so because our knowledge -of the theory and use of colours at the time of the Renaissance is -still extremely limited._ - -The reciprocal effects of colours on objects placed opposite each -other (263-272). - -263. - -OF PAINTING. - -The hue of an illuminated object is affected by that of the luminous -body. - -264. - -OF SHADOW. - -The surface of any opaque body is affected by the colour of -surrounding objects. - -265. - -A shadow is always affected by the colour of the surface on which it -is cast. - -266. - -An image produced in a mirror is affected by the colour of the -mirror. - -267. - -OF LIGHT AND SHADE. - -Every portion of the surface of a body is varied [in hue] by the -[reflected] colour of the object that may be opposite to it. - -EXAMPLE. - -If you place a spherical body between various objects that is to say -with [direct] sunlight on one side of it, and on the other a wall -illuminated by the sun, which wall may be green or of any other -colour, while the surface on which it is placed may be red, and the -two lateral sides are in shadow, you will see that the natural -colour of that body will assume something of the hue reflected from -those objects. The strongest will be [given by] the luminous body; -the second by the illuminated wall, the third by the shadows. There -will still be a portion which will take a tint from the colour of -the edges. - -268. - -The surface of every opaque body is affected by the colour of the -objects surrounding it. But this effect will be strong or weak in -proportion as those objects are more or less remote and more or less -strongly [coloured]. - -269. - -OF PAINTING. - -The surface of every opaque body assumes the hues reflected from -surrounding objects. - -The surface of an opaque body assumes the hues of surrounding -objects more strongly in proportion as the rays that form the images -of those objects strike the surface at more equal angles. - -And the surface of an opaque body assumes a stronger hue from the -surrounding objects in proportion as that surface is whiter and the -colour of the object brighter or more highly illuminated. - -270. - -OF THE RAYS WHICH CONVEY THROUGH THE AIR THE IMAGES OF OBJECTS. - -All the minutest parts of the image intersect each other without -interfering with each other. To prove this let _r_ be one of the -sides of the hole, opposite to which let _s_ be the eye which sees -the lower end _o_ of the line _n o_. The other extremity cannot -transmit its image to the eye _s_ as it has to strike the end _r_ -and it is the same with regard to _m_ at the middle of the line. The -case is the same with the upper extremity _n_ and the eye _u_. And -if the end _n_ is red the eye _u_ on that side of the holes will not -see the green colour of _o_, but only the red of _n_ according to -the 7th of this where it is said: Every form projects images from -itself by the shortest line, which necessarily is a straight line, -&c. - -[Footnote: 13. This probably refers to the diagram given under No. -66.] - -271. - -OF PAINTING. - -The surface of a body assumes in some degree the hue of those around -it. The colours of illuminated objects are reflected from the -surfaces of one to the other in various spots, according to the -various positions of those objects. Let _o_ be a blue object in full -light, facing all by itself the space _b c_ on the white sphere _a b -e d e f_, and it will give it a blue tinge, _m_ is a yellow body -reflected onto the space _a b_ at the same time as _o_ the blue -body, and they give it a green colour (by the 2nd [proposition] of -this which shows that blue and yellow make a beautiful green &c.) -And the rest will be set forth in the Book on Painting. In that Book -it will be shown, that, by transmitting the images of objects and -the colours of bodies illuminated by sunlight through a small round -perforation and into a dark chamber onto a plane surface, which -itself is quite white, &c. - -But every thing will be upside down. - -Combination of different colours in cast shadows. - -272. - -That which casts the shadow does not face it, because the shadows -are produced by the light which causes and surrounds the shadows. -The shadow caused by the light _e_, which is yellow, has a blue -tinge, because the shadow of the body _a_ is cast upon the pavement -at _b_, where the blue light falls; and the shadow produced by the -light _d_, which is blue, will be yellow at _c_, because the yellow -light falls there and the surrounding background to these shadows _b -c_ will, besides its natural colour, assume a hue compounded of -yellow and blue, because it is lighted by the yellow light and by -the blue light both at once. - -Shadows of various colours, as affected by the lights falling on -them. That light which causes the shadow does not face it. - -[Footnote: In the original diagram we find in the circle _e_ -"_giallo_" (yellow) and the cirle _d_ "_azurro"_ (blue) and also -under the circle of shadow to the left "_giallo_" is written and -under that to the right "_azurro_". - -In the second diagram where four circles are placed in a row we find -written, beginning at the left hand, "_giallo_" (yellow), "_azurro_" -(blue), "_verde_" (green), "_rosso_" (red).] - -The effect of colours in the camera obscura (273-274). - -273. - -The edges of a colour(ed object) transmitted through a small hole -are more conspicuous than the central portions. - -The edges of the images, of whatever colour, which are transmitted -through a small aperture into a dark chamber will always be stronger -than the middle portions. - -274. - -OF THE INTERSECTIONS OF THE IMAGES IN THE PUPIL OF THE EYE. - -The intersections of the images as they enter the pupil do not -mingle in confusion in the space where that intersection unites -them; as is evident, since, if the rays of the sun pass through two -panes of glass in close contact, of which one is blue and the other -yellow, the rays, in penetrating them, do not become blue or yellow -but a beautiful green. And the same thing would happen in the eye, -if the images which were yellow or green should mingle where they -[meet and] intersect as they enter the pupil. As this does not -happen such a mingling does not exist. - -OF THE NATURE OF THE RAYS COMPOSED OF THE IMAGES OF OBJECTS, AND OF -THEIR INTERSECTIONS. - -The directness of the rays which transmit the forms and colours of -the bodies whence they proceed does not tinge the air nor can they -affect each other by contact where they intersect. They affect only -the spot where they vanish and cease to exist, because that spot -faces and is faced by the original source of these rays, and no -other object, which surrounds that original source can be seen by -the eye where these rays are cut off and destroyed, leaving there -the spoil they have conveyed to it. And this is proved by the 4th -[proposition], on the colour of bodies, which says: The surface of -every opaque body is affected by the colour of surrounding objects; -hence we may conclude that the spot which, by means of the rays -which convey the image, faces--and is faced by the cause of the -image, assumes the colour of that object. - -On the colours of derived shadows (275. 276). - -275. - -ANY SHADOW CAST BY AN OPAQUE BODY SMALLER THAN THE LIGHT CAUSING THE -SHADOW WILL THROW A DERIVED SHADOW WHICH IS TINGED BY THE COLOUR OF -THE LIGHT. - -Let _n_ be the source of the shadow _e f_; it will assume its hue. -Let _o_ be the source of _h e_ which will in the same way be tinged -by its hue and so also the colour of _v h_ will be affected by _p_ -which causes it; and the shadow of the triangle _z k y_ will be -affected by the colour of _q_, because it is produced by it. [7] In -proportion as _c d_ goes into _a d_, will _n r s_ be darker than -_m_; and the rest of the space will be shadowless [11]. _f g_ is -the highest light, because here the whole light of the window _a d_ -falls; and thus on the opaque body _m e_ is in equally high light; -_z k y_ is a triangle which includes the deepest shadow, because the -light _a d_ cannot reach any part of it. _x h_ is the 2nd grade of -shadow, because it receives only 1/3 of the light from the window, -that is _c d_. The third grade of shadow is _h e_, where two thirds -of the light from the window is visible. The last grade of shadow is -_b d e f_, because the highest grade of light from the window falls -at _f_. - -[Footnote: The diagram Pl. III, No. 1 belongs to this chapter as -well as the text given in No. 148. Lines 7-11 (compare lines 8-12 of -No. 148) which are written within the diagram, evidently apply to -both sections and have therefore been inserted in both.] - -276. - -OF THE COLOURS OF SIMPLE DERIVED SHADOWS. - -The colour of derived shadows is always affected by that of the body -towards which they are cast. To prove this: let an opaque body be -placed between the plane _s c t d_ and the blue light _d e_ and the -red light _a b_, then I say that _d e_, the blue light, will fall on -the whole surface _s c t d_ excepting at _o p_ which is covered by -the shadow of the body _q r_, as is shown by the straight lines _d q -o e r p_. And the same occurs with the light _a b_ which falls on -the whole surface _s c t d_ excepting at the spot obscured by the -shadow _q r_; as is shown by the lines _d q o_, and _e r p_. Hence -we may conclude that the shadow _n m_ is exposed to the blue light -_d e_; but, as the red light _a b_ cannot fall there, _n m_ will -appear as a blue shadow on a red background tinted with blue, -because on the surface _s c t d_ both lights can fall. But in the -shadows only one single light falls; for this reason these shadows -are of medium depth, since, if no light whatever mingled with the -shadow, it would be of the first degree of darkness &c. But in the -shadow at _o p_ the blue light does not fall, because the body _q r_ -interposes and intercepts it there. Only the red light _a b_ falls -there and tinges the shadow of a red hue and so a ruddy shadow -appears on the background of mingled red and blue. - -The shadow of _q r_ at _o p_ is red, being caused by the blue light -_d e_; and the shadow of _q r_ at _o' p'_ is blue being caused by -the red light _a b_. Hence we say that the blue light in this -instance causes a red derived shadow from the opaque body _q' r'_, -while the red light causes the same body to cast a blue derived -shadow; but the primary shadow [on the dark side of the body itself] -is not of either of those hues, but a mixture of red and blue. - -The derived shadows will be equal in depth if they are produced by -lights of equal strength and at an equal distance; this is proved. -[Footnote 53: The text is unfinished in the original.] - -[Footnote: In the original diagram Leonardo has written within the -circle _q r corpo obroso_ (body in shadow); at the spot marked _A, -luminoso azzurro_ (blue luminous body); at _B, luminoso rosso_ (red -luminous body). At _E_ we read _ombra azzurra_ (blue tinted shadow) -and at _D ombra rossa_ (red tinted shadow).] - -On the nature of colours (277. 278). - -277. - -No white or black is transparent. - -278. - -OF PAINTING. - -[Footnote 2: See Footnote 3] Since white is not a colour but the -neutral recipient of every colour [Footnote 3: _il bianco non e -colore ma e inpotentia ricettiva d'ogni colore_ (white is not a -colour, but the neutral recipient of every colour). LEON BATT. -ALBERTI "_Della pittura_" libro I, asserts on the contrary: "_Il -bianco e'l nero non sono veri colori, ma sono alteratione delli -altri colori_" (ed. JANITSCHEK, p. 67; Vienna 1877).], when it is -seen in the open air and high up, all its shadows are bluish; and -this is caused, according to the 4th [prop.], which says: the -surface of every opaque body assumes the hue of the surrounding -objects. Now this white [body] being deprived of the light of the -sun by the interposition of some body between the sun and itself, -all that portion of it which is exposed to the sun and atmosphere -assumes the colour of the sun and atmosphere; the side on which the -sun does not fall remains in shadow and assumes the hue of the -atmosphere. And if this white object did not reflect the green of -the fields all the way to the horizon nor get the brightness of the -horizon itself, it would certainly appear simply of the same hue as -the atmosphere. - -On gradations in the depth of colours (279. 280). - -279. - -Since black, when painted next to white, looks no blacker than when -next to black; and white when next to black looks no whiter than -white, as is seen by the images transmitted through a small hole or -by the edges of any opaque screen ... - -280. - -OF COLOURS. - -Of several colours, all equally white, that will look whitest which -is against the darkest background. And black will look intensest -against the whitest background. - -And red will look most vivid against the yellowest background; and -the same is the case with all colours when surrounded by their -strongest contrasts. - -On the reflection of colours (281-283). - -281. - -PERSPECTIVE. - -Every object devoid of colour in itself is more or less tinged by -the colour [of the object] placed opposite. This may be seen by -experience, inasmuch as any object which mirrors another assumes the -colour of the object mirrored in it. And if the surface thus -partially coloured is white the portion which has a red reflection -will appear red, or any other colour, whether bright or dark. - -PERSPECTIVE. - -Every opaque and colourless body assumes the hue of the colour -reflected on it; as happens with a white wall. - -282. - -PERSPECTIVE. - -That side of an object in light and shade which is towards the light -transmits the images of its details more distinctly and immediately -to the eye than the side which is in shadow. - -PERSPECTIVE. - -The solar rays reflected on a square mirror will be thrown back to -distant objects in a circular form. - -PERSPECTIVE. - -Any white and opaque surface will be partially coloured by -reflections from surrounding objects. - -[Footnote 281. 282: The title line of these chapters is in the -original simply _"pro"_, which may be an abbreviation for either -_Propositione_ or _Prospettiva_--taking Prospettiva of course in its -widest sense, as we often find it used in Leonardo's writings. The -title _"pro"_ has here been understood to mean _Prospettiva_, in -accordance with the suggestion afforded by page 10b of this same -MS., where the first section is headed _Prospettiva_ in full (see -No. 94), while the four following sections are headed merely _"pro"_ -(see No. 85).] - -283. - -WHAT PORTION OF A COLOURED SURFACE OUGHT IN REASON TO BE THE MOST -INTENSE. - -If _a_ is the light, and _b_ illuminated by it in a direct line, -_c_, on which the light cannot fall, is lighted only by reflection -from _b_ which, let us say, is red. Hence the light reflected from -it, will be affected by the hue of the surface causing it and will -tinge the surface _c_ with red. And if _c_ is also red you will see -it much more intense than _b_; and if it were yellow you would see -there a colour between yellow and red. - -On the use of dark and light colours in painting (284--286). - -284. - -WHY BEAUTIFUL COLOURS MUST BE IN THE [HIGHEST] LIGHT. - -Since we see that the quality of colour is known [only] by means of -light, it is to be supposed that where there is most light the true -character of a colour in light will be best seen; and where there is -most shadow the colour will be affected by the tone of that. Hence, -O Painter! remember to show the true quality of colours in bright -lights. - -285. - -An object represented in white and black will display stronger -relief than in any other way; hence I would remind you O Painter! to -dress your figures in the lightest colours you can, since, if you -put them in dark colours, they will be in too slight relief and -inconspicuous from a distance. And the reason is that the shadows of -all objects are dark. And if you make a dress dark there is little -variety in the lights and shadows, while in light colours there are -many grades. - -286. - -OF PAINTING. - -Colours seen in shadow will display more or less of their natural -brilliancy in proportion as they are in fainter or deeper shadow. - -But if these same colours are situated in a well-lighted place, they -will appear brighter in proportion as the light is more brilliant. - -THE ADVERSARY. - -The variety of colours in shadow must be as great as that of the -colours in the objects in that shadow. - -THE ANSWER. - -Colours seen in shadow will display less variety in proportion as -the shadows in which they lie are deeper. And evidence of this is to -be had by looking from an open space into the doorways of dark and -shadowy churches, where the pictures which are painted in various -colours all look of uniform darkness. - -Hence at a considerable distance all the shadows of different -colours will appear of the same darkness. - -It is the light side of an object in light and shade which shows the -true colour. - -On the colours of the rainbow (287. 288). - -287. - -Treat of the rainbow in the last book on Painting, but first write -the book on colours produced by the mixture of other colours, so as -to be able to prove by those painters' colours how the colours of -the rainbow are produced. - -288. - -WHETHER THE COLOURS OF THE RAINBOW ARE PRODUCED BY THE SUN. - -The colours of the rainbow are not produced by the sun, for they -occur in many ways without the sunshine; as may be seen by holding a -glass of water up to the eye; when, in the glass--where there are -those minute bubbles always seen in coarse glass--each bubble, even -though the sun does not fall on it, will produce on one side all the -colours of the rainbow; as you may see by placing the glass between -the day light and your eye in such a way as that it is close to the -eye, while on one side the glass admits the [diffused] light of the -atmosphere, and on the other side the shadow of the wall on one side -of the window; either left or right, it matters not which. Then, by -turning the glass round you will see these colours all round the -bubbles in the glass &c. And the rest shall be said in its place. - -THAT THE EYE HAS NO PART IN PRODUCING THE COLOURS OF THE RAINBOW. - -In the experiment just described, the eye would seem to have some -share in the colours of the rainbow, since these bubbles in the -glass do not display the colours except through the medium of the -eye. But, if you place the glass full of water on the window sill, -in such a position as that the outer side is exposed to the sun's -rays, you will see the same colours produced in the spot of light -thrown through the glass and upon the floor, in a dark place, below -the window; and as the eye is not here concerned in it, we may -evidently, and with certainty pronounce that the eye has no share in -producing them. - -OF THE COLOURS IN THE FEATHERS OF CERTAIN BIRDS. - -There are many birds in various regions of the world on whose -feathers we see the most splendid colours produced as they move, as -we see in our own country in the feathers of peacocks or on the -necks of ducks or pigeons, &c. - -Again, on the surface of antique glass found underground and on the -roots of turnips kept for some time at the bottom of wells or other -stagnant waters [we see] that each root displays colours similar to -those of the real rainbow. They may also be seen when oil has been -placed on the top of water and in the solar rays reflected from the -surface of a diamond or beryl; again, through the angular facet of a -beryl every dark object against a background of the atmosphere or -any thing else equally pale-coloured is surrounded by these rainbow -colours between the atmosphere and the dark body; and in many other -circumstances which I will not mention, as these suffice for my -purpose. - -_VI._ - -_'Prospettiva de' colri' (Perspective of Colour)_ - -_and_ - -_'Prospettiva aerea' (Aerial Perspective)._ - -_Leonardo distinctly separates these branches of his subject, as may -be seen in the beginning of No._ 295. _Attempts have been made to -cast doubts on the results which Leonardo arrived at by experiment -on the perspective of colour, but not with justice, as may be seen -from the original text of section_ 294. - -_The question as to the composition of the atmosphere, which is -inseparable from a discussion on Aerial Perspective, forms a -separate theory which is treated at considerable length. Indeed the -author enters into it so fully that we cannot escape the conviction -that he must have dwelt with particular pleasure on this part of his -subject, and that he attached great importance to giving it a -character of general applicability._ - -General rules (289--291). - -289. - -The variety of colour in objects cannot be discerned at a great -distance, excepting in those parts which are directly lighted up by -the solar rays. - -290. - -As to the colours of objects: at long distances no difference is -perceptible in the parts in shadow. - -291. - -OF THE VISIBILITY OF COLOURS. - -Which colour strikes most? An object at a distance is most -conspicuous, when it is lightest, and the darkest is least visible. - -An exceptional case. - -292. - -Of the edges [outlines] of shadows. Some have misty and ill defined -edges, others distinct ones. - -No opaque body can be devoid of light and shade, except it is in a -mist, on ground covered with snow, or when snow is falling on the -open country which has no light on it and is surrounded with -darkness. - -And this occurs [only] in spherical bodies, because in other bodies -which have limbs and parts, those sides of limbs which face each -other reflect on each other the accidental [hue and tone] of their -surface. - -An experiment. - -293. - -ALL COLOURS ARE AT A DISTANCE UNDISTINGUISHABLE AND UNDISCERNIBLE. - -All colours at a distance are undistinguishable in shadow, because -an object which is not in the highest light is incapable of -transmitting its image to the eye through an atmosphere more -luminous than itself; since the lesser brightness must be absorbed -by the greater. For instance: We, in a house, can see that all the -colours on the surface of the walls are clearly and instantly -visible when the windows of the house are open; but if we were to go -out of the house and look in at the windows from a little distance -to see the paintings on those walls, instead of the paintings we -should see an uniform deep and colourless shadow. - -The practice of the prospettiva de colori. - -294. - -HOW A PAINTER SHOULD CARRY OUT THE PERSPECTIVE OF COLOUR IN -PRACTICE. - -In order to put into practice this perspective of the variation and -loss or diminution of the essential character of colours, observe at -every hundred braccia some objects standing in the landscape, such -as trees, houses, men and particular places. Then in front of the -first tree have a very steady plate of glass and keep your eye very -steady, and then, on this plate of glass, draw a tree, tracing it -over the form of that tree. Then move it on one side so far as that -the real tree is close by the side of the tree you have drawn; then -colour your drawing in such a way as that in colour and form the two -may be alike, and that both, if you close one eye, seem to be -painted on the glass and at the same distance. Then, by the same -method, represent a second tree, and a third, with a distance of a -hundred braccia between each. And these will serve as a standard and -guide whenever you work on your own pictures, wherever they may -apply, and will enable you to give due distance in those works. [14] -But I have found that as a rule the second is 4/5 of the first when -it is 20 braccia beyond it. - -[Footnote: This chapter is one of those copied in the Manuscript of -the Vatican library Urbinas 1270, and the original text is rendered -here with no other alterations, but in the orthography. H. LUDWIG, -in his edition of this copy translates lines 14 and 15 thus: "_Ich -finde aber als Regel, dass der zweite um vier Funftel des ersten -abnimmt, wenn er namlich zwanzig Ellen vom ersten entfernt ist -(?)"_. He adds in his commentary: "_Das Ende der Nummer ist wohl -jedenfalls verstummelt_". However the translation given above shows -that it admits of a different rendering.] - -The rules of aerial perspective (295--297). - -295. - -OF AERIAL PERSPECTIVE. - -There is another kind of perspective which I call Aerial -Perspective, because by the atmosphere we are able to distinguish -the variations in distance of different buildings, which appear -placed on a single line; as, for instance, when we see several -buildings beyond a wall, all of which, as they appear above the top -of the wall, look of the same size, while you wish to represent them -in a picture as more remote one than another and to give the effect -of a somewhat dense atmosphere. You know that in an atmosphere of -equal density the remotest objects seen through it, as mountains, in -consequence of the great quantity of atmosphere between your eye and -them--appear blue and almost of the same hue as the atmosphere -itself [Footnote 10: _quado il sole e per leuante_ (when the sun is -in the East). Apparently the author refers here to morning light in -general. H. LUDWIG however translates this passage from the Vatican -copy "_wenn namlich die Sonne (dahinter) im Osten steht_".] when the -sun is in the East [Footnote 11: See Footnote 10]. Hence you must -make the nearest building above the wall of its real colour, but the -more distant ones make less defined and bluer. Those you wish should -look farthest away you must make proportionately bluer; thus, if one -is to be five times as distant, make it five times bluer. And by -this rule the buildings which above a [given] line appear of the -same size, will plainly be distinguished as to which are the more -remote and which larger than the others. - -296. - -The medium lying between the eye and the object seen, tinges that -object with its colour, as the blueness of the atmosphere makes the -distant mountains appear blue and red glass makes objects seen -beyond it, look red. The light shed round them by the stars is -obscured by the darkness of the night which lies between the eye and -the radiant light of the stars. - -297. - -Take care that the perspective of colour does not disagree with the -size of your objects, hat is to say: that the colours diminish from -their natural [vividness] in proportion as the objects at various -distances dimmish from their natural size. - -On the relative density of the atmosphere (298--290). - -298. - -WHY THE ATMOSPHERE MUST BE REPRESENTED AS PALER TOWARDS THE LOWER -PORTION. - -Because the atmosphere is dense near the earth, and the higher it is -the rarer it becomes. When the sun is in the East if you look -towards the West and a little way to the South and North, you will -see that this dense atmosphere receives more light from the sun than -the rarer; because the rays meet with greater resistance. And if the -sky, as you see it, ends on a low plain, that lowest portion of the -sky will be seen through a denser and whiter atmosphere, which will -weaken its true colour as seen through that medium, and there the -sky will look whiter than it is above you, where the line of sight -travels through a smaller space of air charged with heavy vapour. -And if you turn to the East, the atmosphere will appear darker as -you look lower down because the luminous rays pass less freely -through the lower atmosphere. - -299. - -OF THE MODE OF TREATING REMOTE OBJECTS IN PAINTING. - -It is easy to perceive that the atmosphere which lies closest to the -level ground is denser than the rest, and that where it is higher -up, it is rarer and more transparent. The lower portions of large -and lofty objects which are at a distance are not much seen, because -you see them along a line which passes through a denser and thicker -section of the atmosphere. The summits of such heights are seen -along a line which, though it starts from your eye in a dense -atmosphere, still, as it ends at the top of those lofty objects, -ceases in a much rarer atmosphere than exists at their base; for -this reason the farther this line extends from your eye, from point -to point the atmosphere becomes more and more rare. Hence, O -Painter! when you represent mountains, see that from hill to hill -the bases are paler than the summits, and in proportion as they -recede beyond each other make the bases paler than the summits; -while, the higher they are the more you must show of their true form -and colour. - -On the colour of the atmosphere (300-307). - -300. - -OF THE COLOUR OF THE ATMOSPHERE. - -I say that the blueness we see in the atmosphere is not intrinsic -colour, but is caused by warm vapour evaporated in minute and -insensible atoms on which the solar rays fall, rendering them -luminous against the infinite darkness of the fiery sphere which -lies beyond and includes it. And this may be seen, as I saw it by -any one going up [Footnote 5: With regard to the place spoken of as -_M'oboso_ (compare No. 301 line 20) its identity will be discussed -under Leonardo's Topographical notes in Vol. II.] Monboso, a peak of -the Alps which divide France from Italy. The base of this mountain -gives birth to the four rivers which flow in four different -directions through the whole of Europe. And no mountain has its base -at so great a height as this, which lifts itself almost above the -clouds; and snow seldom falls there, but only hail in the summer, -when the clouds are highest. And this hail lies [unmelted] there, so -that if it were not for the absorption of the rising and falling -clouds, which does not happen twice in an age, an enormous mass of -ice would be piled up there by the hail, and in the middle of July I -found it very considerable. There I saw above me the dark sky, and -the sun as it fell on the mountain was far brighter here than in the -plains below, because a smaller extent of atmosphere lay between the -summit of the mountain and the sun. Again as an illustration of the -colour of the atmosphere I will mention the smoke of old and dry -wood, which, as it comes out of a chimney, appears to turn very -blue, when seen between the eye and the dark distance. But as it -rises, and comes between the eye and the bright atmosphere, it at -once shows of an ashy grey colour; and this happens because it no -longer has darkness beyond it, but this bright and luminous space. -If the smoke is from young, green wood, it will not appear blue, -because, not being transparent and being full of superabundant -moisture, it has the effect of condensed clouds which take distinct -lights and shadows like a solid body. The same occurs with the -atmosphere, which, when overcharged with moisture appears white, and -the small amount of heated moisture makes it dark, of a dark blue -colour; and this will suffice us so far as concerns the colour of -the atmosphere; though it might be added that, if this transparent -blue were the natural colour of the atmosphere, it would follow that -wherever a larger mass air intervened between the eye and the -element of fire, the azure colour would be more intense; as we see -in blue glass and in sapphires, which are darker in proportion as -they are larger. But the atmosphere in such circumstances behaves in -an opposite manner, inasmuch as where a greater quantity of it lies -between the eye and the sphere of fire, it is seen much whiter. This -occurs towards the horizon. And the less the extent of atmosphere -between the eye and the sphere of fire, the deeper is the blue -colour, as may be seen even on low plains. Hence it follows, as I -say, that the atmosphere assumes this azure hue by reason of the -particles of moisture which catch the rays of the sun. Again, we may -note the difference in particles of dust, or particles of smoke, in -the sun beams admitted through holes into a dark chamber, when the -former will look ash grey and the thin smoke will appear of a most -beautiful blue; and it may be seen again in in the dark shadows of -distant mountains when the air between the eye and those shadows -will look very blue, though the brightest parts of those mountains -will not differ much from their true colour. But if any one wishes -for a final proof let him paint a board with various colours, among -them an intense black; and over all let him lay a very thin and -transparent [coating of] white. He will then see that this -transparent white will nowhere show a more beautiful blue than over -the black--but it must be very thin and finely ground. - -[Footnote 7: _reta_ here has the sense of _malanno_.] - -301. - -Experience shows us that the air must have darkness beyond it and -yet it appears blue. If you produce a small quantity of smoke from -dry wood and the rays of the sun fall on this smoke, and if you then -place behind the smoke a piece of black velvet on which the sun does -not shine, you will see that all the smoke which is between the eye -and the black stuff will appear of a beautiful blue colour. And if -instead of the velvet you place a white cloth smoke, that is too -thick smoke, hinders, and too thin smoke does not produce, the -perfection of this blue colour. Hence a moderate amount of smoke -produces the finest blue. Water violently ejected in a fine spray -and in a dark chamber where the sun beams are admitted produces -these blue rays and the more vividly if it is distilled water, and -thin smoke looks blue. This I mention in order to show that the -blueness of the atmosphere is caused by the darkness beyond it, and -these instances are given for those who cannot confirm my experience -on Monboso. - -302. - -When the smoke from dry wood is seen between the eye of the -spectator and some dark space [or object], it will look blue. Thus -the sky looks blue by reason of the darkness beyond it. And if you -look towards the horizon of the sky, you will see the atmosphere is -not blue, and this is caused by its density. And thus at each -degree, as you raise your eyes above the horizon up to the sky over -your head, you will see the atmosphere look darker [blue] and this -is because a smaller density of air lies between your eye and the -[outer] darkness. And if you go to the top of a high mountain the -sky will look proportionately darker above you as the atmosphere -becomes rarer between you and the [outer] darkness; and this will be -more visible at each degree of increasing height till at last we -should find darkness. - -That smoke will look bluest which rises from the driest wood and -which is nearest to the fire and is seen against the darkest -background, and with the sunlight upon it. - -303. - -A dark object will appear bluest in proportion as it has a greater -mass of luminous atmosphere between it and the eye. As may be seen -in the colour of the sky. - -304. - -The atmosphere is blue by reason of the darkness above it because -black and white make blue. - -305. - -In the morning the mist is denser above than below, because the sun -draws it upwards; hence tall buildings, even if the summit is at the -same distance as the base have the summit invisible. Therefore, -also, the sky looks darkest [in colour] overhead, and towards the -horizon it is not blue but rather between smoke and dust colour. - -The atmosphere, when full of mist, is quite devoid of blueness, and -only appears of the colour of clouds, which shine white when the -weather is fine. And the more you turn to the west the darker it -will be, and the brighter as you look to the east. And the verdure -of the fields is bluish in a thin mist, but grows grey in a dense -one. - -The buildings in the west will only show their illuminated side, -where the sun shines, and the mist hides the rest. When the sun -rises and chases away the haze, the hills on the side where it lifts -begin to grow clearer, and look blue, and seem to smoke with the -vanishing mists; and the buildings reveal their lights and shadows; -through the thinner vapour they show only their lights and through -the thicker air nothing at all. This is when the movement of the -mist makes it part horizontally, and then the edges of the mist will -be indistinct against the blue of the sky, and towards the earth it -will look almost like dust blown up. In proportion as the atmosphere -is dense the buildings of a city and the trees in a landscape will -look fewer, because only the tallest and largest will be seen. - -Darkness affects every thing with its hue, and the more an object -differs from darkness, the more we see its real and natural colour. -The mountains will look few, because only those will be seen which -are farthest apart; since, at such a distance, the density increases -to such a degree that it causes a brightness by which the darkness -of the hills becomes divided and vanishes indeed towards the top. -There is less [mist] between lower and nearer hills and yet little -is to be distinguished, and least towards the bottom. - -306. - -The surface of an object partakes of the colour of the light which -illuminates it; and of the colour of the atmosphere which lies -between the eye and that object, that is of the colour of the -transparent medium lying between the object and the eye; and among -colours of a similar character the second will be of the same tone -as the first, and this is caused by the increased thickness of the -colour of the medium lying between the object and the eye. - -307. OF PAINTING. - -Of various colours which are none of them blue that which at a great -distance will look bluest is the nearest to black; and so, -conversely, the colour which is least like black will at a great -distance best preserve its own colour. - -Hence the green of fields will assume a bluer hue than yellow or -white will, and conversely yellow or white will change less than -green, and red still less. - -_VII._ - -_On the Proportions and on the Movements of the Human Figure._ - -_Leonardo's researches on the proportions and movements of the human -figure must have been for the most part completed and written before -the year_ 1498; _for LUCA PACIOLO writes, in the dedication to -Ludovico il Moro, of his book_ Divina Proportione, _which was -published in that year:_ "Leonardo da venci ... hauedo gia co tutta -diligetia al degno libro de pictura e movimenti humani posto fine". - -_The selection of Leonardo's axioms contained in the Vatican copy -attributes these words to the author:_ "e il resto si dira nella -universale misura del huomo". (_MANZI, p. 147; LUDWIG, No. 264_). -_LOMAZZO, again, in his_ Idea del Tempio della Pittura Milano 1590, -cap. IV, _says:_ "Lionardo Vinci ... dimostro anco in figura tutte -le proporzioni dei membri del corpo umano". - -_The Vatican copy includes but very few sections of the_ "Universale -misura del huomo" _and until now nothing has been made known of the -original MSS. on the subject which have supplied the very extensive -materials for this portion of the work. The collection at Windsor, -belonging to her Majesty the Queen, includes by far the most -important part of Leonardo's investigations on this subject, -constituting about half of the whole of the materials here -published; and the large number of original drawings adds greatly to -the interest which the subject itself must command. Luca Paciolo -would seem to have had these MSS. (which I have distinguished by the -initials W. P.) in his mind when he wrote the passage quoted above. -Still, certain notes of a later date--such as Nos. 360, 362 and 363, -from MS. E, written in 1513--14, sufficiently prove that Leonardo did -not consider his earlier studies on the Proportions and Movements of -the Human Figure final and complete, as we might suppose from Luca -Paciolo's statement. Or else he took the subject up again at a -subsequent period, since his former researches had been carried on -at Milan between 1490 and 1500. Indeed it is highly probable that -the anatomical studies which he was pursuing zvith so much zeal -between 1510--16 should have led him to reconsider the subject of -Proportion. - -Preliminary observations (308. 309). - -308. - -Every man, at three years old is half the full height he will grow -to at last. - -309. - -If a man 2 braccia high is too small, one of four is too tall, the -medium being what is admirable. Between 2 and 4 comes 3; therefore -take a man of 3 braccia in height and measure him by the rule I will -give you. If you tell me that I may be mistaken, and judge a man to -be well proportioned who does not conform to this division, I answer -that you must look at many men of 3 braccia, and out of the larger -number who are alike in their limbs choose one of those who are most -graceful and take your measurements. The length of the hand is 1/3 -of a braccio [8 inches] and this is found 9 times in man. And the -face [Footnote 7: The account here given of the _braccio_ is of -importance in understanding some of the succeeding chapters. _Testa_ -must here be understood to mean the face. The statements in this -section are illustrated in part on Pl. XI.] is the same, and from -the pit of the throat to the shoulder, and from the shoulder to the -nipple, and from one nipple to the other, and from each nipple to -the pit of the throat. - -Proportions of the head and face (310-318). - -310. - -The space between the parting of the lips [the mouth] and the base -of the nose is one-seventh of the face. - -The space from the mouth to the bottom of the chin _c d_ is the -fourth part of the face and equal to the width of the mouth. - -The space from the chin to the base of the nose _e f_ is the third -part of the face and equal to the length of the nose and to the -forehead. - -The distance from the middle of the nose to the bottom of the chin -_g h_, is half the length of the face. - -The distance from the top of the nose, where the eyebrows begin, to -the bottom of the chin, _i k_, is two thirds of the face. - -The space from the parting of the lips to the top of the chin _l m_, -that is where the chin ends and passes into the lower lip of the -mouth, is the third of the distance from the parting of the lips to -the bottom of the chin and is the twelfth part of the face. From the -top to the bottom of the chin _m n_ is the sixth part of the face -and is the fifty fourth part of a man's height. - -From the farthest projection of the chin to the throat _o p_ is -equal to the space between the mouth and the bottom of the chin, and -a fourth of the face. - -The distance from the top of the throat to the pit of the throat -below _q r_ is half the length of the face and the eighteenth part -of a man's height. - -From the chin to the back of the neck _s t_, is the same distance as -between the mouth and the roots of the hair, that is three quarters -of the head. - -From the chin to the jaw bone _v x_ is half the head and equal to -the thickness of the neck in profile. - -The thickness of the head from the brow to the nape is once and 3/4 -that of the neck. - -[Footnote: The drawings to this text, lines 1-10 are on Pl. VII, No. -I. The two upper sketches of heads, Pl. VII, No. 2, belong to lines -11-14, and in the original are placed immediately below the sketches -reproduced on Pl. VII, No. 1.] - -311. - -The distance from the attachment of one ear to the other is equal to -that from the meeting of the eyebrows to the chin, and in a fine -face the width of the mouth is equal to the length from the parting -of the lips to the bottom of the chin. - -312. - -The cut or depression below the lower lip of the mouth is half way -between the bottom of the nose and the bottom of the chin. - -The face forms a square in itself; that is its width is from the -outer corner of one eye to the other, and its height is from the -very top of the nose to the bottom of the lower lip of the mouth; -then what remains above and below this square amounts to the height -of such another square, _a_ _b_ is equal to the space between _c_ -_d_; _d_ _n_ in the same way to _n_ _c_, and likewise _s_ _r_, _q_ -_p_, _h_ _k_ are equal to each other. - -It is as far between _m_ and _s_ as from the bottom of the nose to -the chin. The ear is exactly as long as the nose. It is as far from -_x_ to _j_ as from the nose to the chin. The parting of the mouth -seen in profile slopes to the angle of the jaw. The ear should be as -high as from the bottom of the nose to the top of the eye-lid. The -space between the eyes is equal to the width of an eye. The ear is -over the middle of the neck, when seen in profile. The distance from -4 to 5 is equal to that from s_ to _r_. - -[Footnote: See Pl. VIII, No. I, where the text of lines 3-13 is also -given in facsimile.] - -313. - -(_a_ _b_) is equal to (_c_ _d_). - -[Footnote: See Pl. VII, No. 3. Reference may also be made here to -two pen and ink drawings of heads in profile with figured -measurements, of which there is no description in the MS. These are -given on Pl. XVII, No. 2.--A head, to the left, with part of the -torso [W. P. 5a], No. 1 on the same plate is from MS. A 2b and in -the original occurs on a page with wholly irrelevant text on matters -of natural history. M. RAVAISSON in his edition of the Paris MS. A -has reproduced this head and discussed it fully [note on page 12]; -he has however somewhat altered the original measurements. The -complicated calculations which M. RAVAISSON has given appear to me -in no way justified. The sketch, as we see it, can hardly have been -intended for any thing more than an experimental attempt to -ascertain relative proportions. We do not find that Leonardo made -use of circular lines in any other study of the proportions of the -human head. At the same time we see that the proportions of this -sketch are not in accordance with the rules which he usually -observed (see for instance No. 310).] - -The head _a_ _f_ 1/6 larger than _n_ _f_. - -315. - -From the eyebrow to the junction of the lip with the chin, and the -angle of the jaw and the upper angle where the ear joins the temple -will be a perfect square. And each side by itself is half the head. - -The hollow of the cheek bone occurs half way between the tip of the -nose and the top of the jaw bone, which is the lower angle of the -setting on of the ear, in the frame here represented. - -From the angle of the eye-socket to the ear is as far as the length -of the ear, or the third of the face. - -[Footnote: See Pl. IX. The text, in the original is written behind -the head. The handwriting would seem to indicate a date earlier than -1480. On the same leaf there is a drawing in red chalk of two -horsemen of which only a portion of the upper figure is here -visible. The whole leaf measures 22 1/2 centimetres wide by 29 long, -and is numbered 127 in the top right-hand corner.] - -316. - -From _a_ to _b_--that is to say from the roots of the hair in front -to the top of the head--ought to be equal to _c_ _d_;--that is from -the bottom of the nose to the meeting of the lips in the middle of -the mouth. From the inner corner of the eye _m_ to the top of the -head _a_ is as far as from _m_ down to the chin _s_. _s_ _c_ _f_ _b_ -are all at equal distances from each other. - -[Footnote: The drawing in silver-point on bluish tinted paper--Pl. -X--which belongs to this chapter has been partly drawn over in ink -by Leonardo himself.] - -317. - -From the top of the head to the bottom of the chin is 1/9, and from -the roots of the hair to the chin is 1/9 of the distance from the -roots of the hair to the ground. The greatest width of the face is -equal to the space between the mouth and the roots of the hair and -is 1/12 of the whole height. From the top of the ear to the top of -the head is equal to the distance from the bottom of the chin to the -lachrymatory duct of the eye; and also equal to the distance from -the angle of the chin to that of the jaw; that is the 1/16 of the -whole. The small cartilage which projects over the opening of the -ear towards the nose is half-way between the nape and the eyebrow; -the thickness of the neck in profile is equal to the space between -the chin and the eyes, and to the space between the chin and the -jaw, and it is 1/18 of the height of the man. - -318. - -_a b_, _c d_, _e f_, _g h_, _i k_ are equal to each other in size -excepting that _d f_ is accidental. - -[Footnote: See Pl. XI.] - -Proportions of the head seen in front (319-321). - -319. - -_a n o f_ are equal to the mouth. - -_a c_ and _a f_ are equal to the space between one eye and the -other. - -_n m o f q r_ are equal to half the width of the eye lids, that is -from the inner [lachrymatory] corner of the eye to its outer corner; -and in like manner the division between the chin and the mouth; and -in the same way the narrowest part of the nose between the eyes. And -these spaces, each in itself, is the 19th part of the head, _n o_ is -equal to the length of the eye or of the space between the eyes. - -_m c_ is 1/3 of _n m_ measuring from the outer corner of the eyelids -to the letter _c_. _b s_ will be equal to the width of the nostril. - -[Footnote: See Pl. XII.] - -320. - -The distance between the centres of the pupils of the eyes is 1/3 of -the face. The space between the outer corners of the eyes, that is -where the eye ends in the eye socket which contains it, thus the -outer corners, is half the face. - -The greatest width of the face at the line of the eyes is equal to -the distance from the roots of the hair in front to the parting of -the lips. - -[Footnote: There are, with this section, two sketches of eyes, not -reproduced here.] - -321. - -The nose will make a double square; that is the width of the nose at -the nostrils goes twice into the length from the tip of the nose to -the eyebrows. And, in the same way, in profile the distance from the -extreme side of the nostril where it joins the cheek to the tip of -the nose is equal to the width of the nose in front from one nostril -to the other. If you divide the whole length of the nose--that is -from the tip to the insertion of the eyebrows, into 4 equal parts, -you will find that one of these parts extends from the tip of the -nostrils to the base of the nose, and the upper division lies -between the inner corner of the eye and the insertion of the -eyebrows; and the two middle parts [together] are equal to the -length of the eye from the inner to the outer corner. - -[Footnote: The two bottom sketches on Pl. VII, No. 4 face the six -lines of this section,--With regard to the proportions of the head -in profile see No. 312.] - -322. - -The great toe is the sixth part of the foot, taking the measure in -profile, on the inside of the foot, from where this toe springs from -the ball of the sole of the foot to its tip _a b_; and it is equal -to the distance from the mouth to the bottom of the chin. If you -draw the foot in profile from the outside, make the little toe begin -at three quarters of the length of the foot, and you will find the -same distance from the insertion of this toe as to the farthest -prominence of the great toe. - -323. - -For each man respectively the distance between _a b_ is equal to _c -d_. - -324. - -Relative proportion of the hand and foot. - -The foot is as much longer than the hand as the thickness of the arm -at the wrist where it is thinnest seen facing. - -Again, you will find that the foot is as much longer than the hand -as the space between the inner angle of the little toe to the last -projection of the big toe, if you measure along the length of the -foot. - -The palm of the hand without the fingers goes twice into the length -of the foot without the toes. - -If you hold your hand with the fingers straight out and close -together you will find it to be of the same width as the widest part -of the foot, that is where it is joined onto the toes. - -And if you measure from the prominence of the inner ancle to the end -of the great toe you will find this measure to be as long as the -whole hand. - -From the top angle of the foot to the insertion of the toes is equal -to the hand from wrist joint to the tip of the thumb. - -The smallest width of the hand is equal to the smallest width of the -foot between its joint into the leg and the insertion of the toes. - -The width of the heel at the lower part is equal to that of the arm -where it joins the hand; and also to the leg where it is thinnest -when viewed in front. - -The length of the longest toe, from its first division from the -great toe to its tip is the fourth of the foot from the centre of -the ancle bone to the tip, and it is equal to the width of the -mouth. The distance between the mouth and the chin is equal to that -of the knuckles and of the three middle fingers and to the length of -their first joints if the hand is spread, and equal to the distance -from the joint of the thumb to the outset of the nails, that is the -fourth part of the hand and of the face. - -The space between the extreme poles inside and outside the foot -called the ancle or ancle bone _a b_ is equal to the space between -the mouth and the inner corner of the eye. - -325. - -The foot, from where it is attached to the leg, to the tip of the -great toe is as long as the space between the upper part of the chin -and the roots of the hair _a b_; and equal to five sixths of the -face. - -326. - -_a d_ is a head's length, _c b_ is a head's length. The four smaller -toes are all equally thick from the nail at the top to the bottom, -and are 1/13 of the foot. - -[Footnote: See Pl. XIV, No. 1, a drawing of a foot with the text in -three lines below it.] - -327. - -The whole length of the foot will lie between the elbow and the -wrist and between the elbow and the inner angle of the arm towards -the breast when the arm is folded. The foot is as long as the whole -head of a man, that is from under the chin to the topmost part of -the head[Footnote 2: _nel modo che qui i figurato_. See Pl. VII, No. -4, the upper figure. The text breaks off at the end of line 2 and -the text given under No. 321 follows below. It may be here remarked -that the second sketch on W. P. 311 has in the original no -explanatory text.] in the way here figured. - -Proportions of the leg (328-331). - -328. - -The greatest thickness of the calf of the leg is at a third of its -height _a b_, and is a twentieth part thicker than the greatest -thickness of the foot. - -_a c_ is half of the head, and equal to _d b_ and to the insertion -of the five toes _e f_. _d k_ diminishes one sixth in the leg _g h_. -_g h_ is 1/3 of the head; _m n_ increases one sixth from _a e_ and -is 7/12 of the head, _o p_ is 1/10 less than _d k_ and is 6/17 of -the head. _a_ is at half the distance between _b q_, and is 1/4 of -the man. _r_ is half way between _s_ and _b_[Footnote 11: _b_ is -here and later on measured on the right side of the foot as seen by -the spectator.]. The concavity of the knee outside _r_ is higher -than that inside _a_. The half of the whole height of the leg from -the foot _r_, is half way between the prominence _s_ and the ground -_b_. _v_ is half way between _t_ and _b_. The thickness of the thigh -seen in front is equal to the greatest width of the face, that is -2/3 of the length from the chin to the top of the head; _z r_ is 5/6 -of 7 to _v_; _m n_ is equal to 7 _v_ and is 1/4 of _r b_, _x y_ goes -3 times into _r b_, and into _r s_. - -[Footnote 22-35: The sketch illustrating these lines is on Pl. XIII, -No. 2.] - -[Footnote 22: a b _entra in_ c f 6 _e_ 6 _in_ c n. Accurate -measurement however obliges us to read 7 for 6.] _a b_ goes six -times into _c f_ and six times into _c n_ and is equal to _g h_; _i -k l m_ goes 4 times into _d f_, and 4 times into _d n_ and is 3/7 of -the foot; _p q r s_ goes 3 times into _d f, and 3 times into _b n_; -[Footnote: 25. _y_ is not to be found on the diagram and _x_ occurs -twice; this makes the passage very obscure.] _x y_ is 1/8 of _x f_ -and is equal to _n q_. 3 7 is 1/9 of _n f_; 4 5 is 1/10 of _n f_ -[Footnote: 22-27. Compare with this lines 18-24 of No. 331, and the -sketch of a leg in profile Pl. XV.]. - -I want to know how much a man increases in height by standing on -tip-toe and how much _p g_ diminishes by stooping; and how much it -increases at _n q_ likewise in bending the foot. - -[Footnote 34: _e f_ 4 _dal cazo_. By reading _i_ for _e_ the sense -of this passage is made clear.] _e f_ is four times in the distance -between the genitals and the sole of the foot; [Footnote 35: 2 is -not to be found in the sketch which renders the passage obscure. The -two last lines are plainly legible in the facsimile.] 3 7 is six -times from 3 to 2 and is equal to _g h_ and _i k_. - -[Footnote: The drawing of a leg seen in front Pl. XIII, No. 1 -belongs to the text from lines 3-21. The measurements in this -section should be compared with the text No. 331, lines 1-13, and -the sketch of a leg seen in front on Pl. XV.] - -329. - -The length of the foot from the end of the toes to the heel goes -twice into that from the heel to the knee, that is where the leg -bone [fibula] joins the thigh bone [femur]. - -330. - -_a n b_ are equal; _c n d_ are equal; _n c_ makes two feet; _n d_ -makes 2 feet. - -[Footnote: See the lower sketch, Pl. XIV, No. 1.] - -331. - -_m n o_ are equal. The narrowest width of the leg seen in front goes -8 times from the sole of the foot to the joint of the knee, and is -the same width as the arm, seen in front at the wrist, and as the -longest measure of the ear, and as the three chief divisions into -which we divide the face; and this measurement goes 4 times from the -wrist joint of the hand to the point of the elbow. [14] The foot is -as long as the space from the knee between _a_ and _b_; and the -patella of the knee is as long as the leg between _r_ and _s_. - -[18] The least thickness of the leg in profile goes 6 times from the -sole of the foot to the knee joint and is the same width as the -space between the outer corner of the eye and the opening of the -ear, and as the thickest part of the arm seen in profile and between -the inner corner of the eye and the insertion of the hair. - -_a b c_ [_d_] are all relatively of equal length, _c d_ goes twice -from the sole of the foot to the centre of the knee and the same -from the knee to the hip. - -[28]_a b c_ are equal; _a_ to _b_ is 2 feet--that is to say -measuring from the heel to the tip of the great toe. - -[Footnote: See Pl. XV. The text of lines 2-17 is to the left of the -front view of the leg, to which it refers. Lines 18-27 are in the -middle column and refer to the leg seen in profile and turned to the -left, on the right hand side of the writing. Lines 20-30 are above, -to the left and apply to the sketch below them. - -Some farther remarks on the proportion of the leg will be found in -No. 336, lines 6, 7.] - -On the central point of the whole body. - -332. - -In kneeling down a man will lose the fourth part of his height. - -When a man kneels down with his hands folded on his breast the navel -will mark half his height and likewise the points of the elbows. - -Half the height of a man who sits--that is from the seat to the top -of the head--will be where the arms fold below the breast, and -below the shoulders. The seated portion--that is from the seat to -the top of the head--will be more than half the man's [whole height] -by the length of the scrotum. - -[Footnote: See Pl. VIII, No. 2.] - -The relative proportions of the torso and of the whole figure. - -333. - -The cubit is one fourth of the height of a man and is equal to the -greatest width of the shoulders. From the joint of one shoulder to -the other is two faces and is equal to the distance from the top of -the breast to the navel. [Footnote 9: _dalla detta somita_. It would -seem more accurate to read here _dal detto ombilico_.] From this -point to the genitals is a face's length. - -[Footnote: Compare with this the sketches on the other page of the -same leaf. Pl. VIII, No. 2.] - -The relative proportions of the head and of the torso. - -334. - -From the roots of the hair to the top of the breast _a b_ is the -sixth part of the height of a man and this measure is equal. - -From the outside part of one shoulder to the other is the same -distance as from the top of the breast to the navel and this measure -goes four times from the sole of the foot to the lower end of the -nose. - -The [thickness of] the arm where it springs from the shoulder in -front goes 6 times into the space between the two outside edges of -the shoulders and 3 times into the face, and four times into the -length of the foot and three into the hand, inside or outside. - -[Footnote: The three sketches Pl. XIV, No. 2 belong to this text.] - -The relative proportions of the torso and of the leg (335. 336). - -335. - -_a b c_ are equal to each other and to the space from the armpit of -the shoulder to the genitals and to the distance from the tip of the -fingers of the hand to the joint of the arm, and to the half of the -breast; and you must know that _c b_ is the third part of the height -of a man from the shoulders to the ground; _d e f_ are equal to each -other and equal to the greatest width of the shoulders. - -[Footnote: See Pl. XVI, No. 1.] - -336. - ---Top of the chin--hip--the insertion of the middle finger. The end -of the calf of the leg on the inside of the thigh.--The end of the -swelling of the shin bone of the leg. [6] The smallest thickness of -the leg goes 3 times into the thigh seen in front. - -[Footnote: See Pl. XVII, No. 2, middle sketch.] - -The relative proportions of the torso and of the foot. - -337. - -The torso _a b_ in its thinnest part measures a foot; and from _a_ -to _b_ is 2 feet, which makes two squares to the seat--its thinnest -part goes 3 times into the length, thus making 3 squares. - -[Footnote: See Pl, VII, No. 2, the lower sketch.] - -The proportions of the whole figure (338-341). - -338. - -A man when he lies down is reduced to 1/9 of his height. - -339. - -The opening of the ear, the joint of the shoulder, that of the hip -and the ancle are in perpendicular lines; _a n_ is equal to _m o_. - -[Footnote: See Pl. XVI, No. 2, the upper sketch.] - -340. - -From the chin to the roots of the hair is 1/10 of the whole figure. -From the joint of the palm of the hand to the tip of the longest -finger is 1/10. From the chin to the top of the head 1/8; and from -the pit of the stomach to the top of the breast is 1/6, and from the -pit below the breast bone to the top of the head 1/4. From the chin -to the nostrils 1/3 Part of the face, the same from the nostrils to -the brow and from the brow to the roots of the hair, and the foot is -1/6, the elbow 1/4, the width of the shoulders 1/4. - -341. - -The width of the shoulders is 1/4 of the whole. From the joint of -the shoulder to the hand is 1/3, from the parting of the lips to -below the shoulder-blade is one foot. - -The greatest thickness of a man from the breast to the spine is one -8th of his height and is equal to the space between the bottom of -the chin and the top of the head. - -The greatest width is at the shoulders and goes 4. - -The torso from the front and back. - -342. - -The width of a man under the arms is the same as at the hips. - -A man's width across the hips is equal to the distance from the top -of the hip to the bottom of the buttock, when a man stands equally -balanced on both feet; and there is the same distance from the top -of the hip to the armpit. The waist, or narrower part above the hips -will be half way between the arm pits and the bottom of the buttock. - -[Footnote: The lower sketch Pl. XVI, No. 2, is drawn by the side of -line 1.] - -Vitruvius' scheme of proportions. - -343. - -Vitruvius, the architect, says in his work on architecture that the -measurements of the human body are distributed by Nature as follows: -that is that 4 fingers make 1 palm, and 4 palms make 1 foot, 6 palms -make 1 cubit; 4 cubits make a man's height. And 4 cubits make one -pace and 24 palms make a man; and these measures he used in his -buildings. If you open your legs so much as to decrease your height -1/14 and spread and raise your arms till your middle fingers touch -the level of the top of your head you must know that the centre of -the outspread limbs will be in the navel and the space between the -legs will be an equilateral triangle. - -The length of a man's outspread arms is equal to his height. - -From the roots of the hair to the bottom of the chin is the tenth of -a man's height; from the bottom of the chin to the top of his head -is one eighth of his height; from the top of the breast to the top -of his head will be one sixth of a man. From the top of the breast -to the roots of the hair will be the seventh part of the whole man. -From the nipples to the top of the head will be the fourth part of a -man. The greatest width of the shoulders contains in itself the -fourth part of the man. From the elbow to the tip of the hand will -be the fifth part of a man; and from the elbow to the angle of the -armpit will be the eighth part of the man. The whole hand will be -the tenth part of the man; the beginning of the genitals marks the -middle of the man. The foot is the seventh part of the man. From the -sole of the foot to below the knee will be the fourth part of the -man. From below the knee to the beginning of the genitals will be -the fourth part of the man. The distance from the bottom of the chin -to the nose and from the roots of the hair to the eyebrows is, in -each case the same, and like the ear, a third of the face. - -[Footnote: See Pl. XVIII. The original leaf is 21 centimetres wide -and 33 1/2 long. At the ends of the scale below the figure are -written the words _diti_ (fingers) and _palmi_ (palms). The passage -quoted from Vitruvius is Book III, Cap. 1, and Leonardo's drawing is -given in the editions of Vitruvius by FRA GIOCONDO (Venezia 1511, -fol., Firenze 1513, 8vo.) and by CESARIANO (Como 1521).] - -The arm and head. - -344. - -From _b_ to _a_ is one head, as well as from _c_ to _a_ and this -happens when the elbow forms a right angle. - -[Footnote: See Pl. XLI, No. 1.] - -Proportions of the arm (345-349). - -345. - -From the tip of the longest finger of the hand to the shoulder joint -is four hands or, if you will, four faces. - -_a b c_ are equal and each interval is 2 heads. - -[Footnote: Lines 1-3 are given on Pl. XV below the front view of the -leg; lines 4 and 5 are below again, on the left side. The lettering -refers to the bent arm near the text.] - -346. - -The hand from the longest finger to the wrist joint goes 4 times -from the tip of the longest finger to the shoulder joint. - -347. - -_a b c_ are equal to each other and to the foot and to the space -between the nipple and the navel _d e_ will be the third part of the -whole man. - -_f g_ is the fourth part of a man and is equal to _g h_ and measures -a cubit. - -[Footnote: See Pl. XIX, No. 1. 1. _mamolino_ (=_bambino_, little -child) may mean here the navel.] - -348. - -_a b_ goes 4 times into _a c_ and 9 into _a m_. The greatest -thickness of the arm between the elbow and the hand goes 6 times -into _a m_ and is equal to _r f_. The greatest thickness of the arm -between the shoulder and the elbow goes 4 times into _c m_, and is -equal to _h n g_. The smallest thickness of the arm above the elbow -_x y_ is not the base of a square, but is equal to half the space -_h_ 3 which is found between the inner joint of the arm and the -wrist joint. - -[11]The width of the wrist goes 12 times into the whole arm; that is -from the tip of the fingers to the shoulder joint; that is 3 times -into the hand and 9 into the arm. - -The arm when bent is 4 heads. - -The arm from the shoulder to the elbow in bending increases in -length, that is in the length from the shoulder to the elbow, and -this increase is equal to the thickness of the arm at the wrist when -seen in profile. And the space between the bottom of the chin and -the parting of the lips, is equal to the thickness of the 2 middle -fingers, and to the width of the mouth and to the space between the -roots of the hair on the forehead and the top of the head [Footnote: -_Queste cose_. This passage seems to have been written on purpose to -rectify the foregoing lines. The error is explained by the -accompanying sketch of the bones of the arm.]. All these distances -are equal to each other, but they are not equal to the -above-mentioned increase in the arm. - -The arm between the elbow and wrist never increases by being bent or -extended. - -The arm, from the shoulder to the inner joint when extended. - -When the arm is extended, _p n_ is equal to _n a_. And when it is -bent _n a_ diminishes 1/6 of its length and _p n_ does the same. The -outer elbow joint increases 1/7 when bent; and thus by being bent it -increases to the length of 2 heads. And on the inner side, by -bending, it is found that whereas the arm from where it joins the -side to the wrist, was 2 heads and a half, in bending it loses the -half head and measures only two: one from the [shoulder] joint to -the end [by the elbow], and the other to the hand. - -The arm when folded will measure 2 faces up to the shoulder from the -elbow and 2 from the elbow to the insertion of the four fingers on -the palm of the hand. The length from the base of the fingers to the -elbow never alters in any position of the arm. - -If the arm is extended it decreases by 1/3 of the length between _b_ -and _h_; and if--being extended--it is bent, it will increase the -half of _o e_. [Footnote 59-61: The figure sketched in the margin is -however drawn to different proportions.] The length from the -shoulder to the elbow is the same as from the base of the thumb, -inside, to the elbow _a b c_. - -[Footnote 62-64: The arm sketch on the margin of the MS. is -identically the same as that given below on Pl. XX which may -therefore be referred to in this place. In line 62 we read therefore -_z c_ for _m n_.] The smallest thickness of the arm in profile _z c_ -goes 6 times between the knuckles of the hand and the dimple of the -elbow when extended and 14 times in the whole arm and 42 in the -whole man [64]. The greatest thickness of the arm in profile is -equal to the greatest thickness of the arm in front; but the first -is placed at a third of the arm from the shoulder joint to the elbow -and the other at a third from the elbow towards the hand. - -[Footnote: Compare Pl. XVII. Lines 1-10 and 11-15 are written in two -columns below the extended arm, and at the tips of the fingers we -find the words: _fine d'unghie_ (ends of the nails). Part of the -text--lines 22 to 25--is visible by the side of the sketches on Pl. -XXXV, No. 1.] - -349. - -From the top of the shoulder to the point of the elbow is as far as -from that point to the joints of the four fingers with the palm of -the hand, and each is 2 faces. - -[5]_a e_ is equal to the palm of the hand, _r f_ and _o g_ are equal -to half a head and each goes 4 times into _a b_ and _b c_. From _c_ -to _m_ is 1/2 a head; _m n_ is 1/3 of a head and goes 6 times into -_c b_ and into _b a_; _a b_ loses 1/7 of its length when the arm is -extended; _c b_ never alters; _o_ will always be the middle point -between _a_ and _s_. - -_y l_ is the fleshy part of the arm and measures one head; and when -the arm is bent this shrinks 2/5 of its length; _o a_ in bending -loses 1/6 and so does _o r_. - -_a b_ is 1/7 of _r c_. _f s_ will be 1/8 of _r c_, and each of those -2 measurements is the largest of the arm; _k h_ is the thinnest part -between the shoulder and the elbow and it is 1/8 of the whole arm _r -c_; _o p_ is 1/5 of _r l_; _c z_ goes 13 times into _r c_. - -[Footnote: See Pl. XX where the text is also seen from lines 5-23.] - -The movement of the arm (350-354). - -350. - -In the innermost bend of the joints of every limb the reliefs are -converted into a hollow, and likewise every hollow of the innermost -bends becomes a convexity when the limb is straightened to the -utmost. And in this very great mistakes are often made by those who -have insufficient knowledge and trust to their own invention and do -not have recourse to the imitation of nature; and these variations -occur more in the middle of the sides than in front, and more at the -back than at the sides. - -351. - -When the arm is bent at an angle at the elbow, it will produce some -angle; the more acute the angle is, the more will the muscles within -the bend be shortened; while the muscles outside will become of -greater length than before. As is shown in the example; _d c e_ will -shrink considerably; and _b n_ will be much extended. - -[Footnote: See Pl. XIX, No. 2.] - -352. - -OF PAINTING. - -The arm, as it turns, thrusts back its shoulder towards the middle -of the back. - -353. - -The principal movements of the hand are 10; that is forwards, -backwards, to right and to left, in a circular motion, up or down, -to close and to open, and to spread the fingers or to press them -together. - -354. - -OF THE MOTIONS OF THE FINGERS. - -The movements of the fingers principally consist in extending and -bending them. This extension and bending vary in manner; that is, -sometimes they bend altogether at the first joint; sometimes they -bend, or extend, half way, at the 2nd joint; and sometimes they bend -in their whole length and in all the three joints at once. If the 2 -first joints are hindered from bending, then the 3rd joint can be -bent with greater ease than before; it can never bend of itself, if -the other joints are free, unless all three joints are bent. Besides -all these movements there are 4 other principal motions of which 2 -are up and down, the two others from side to side; and each of these -is effected by a single tendon. From these there follow an infinite -number of other movements always effected by two tendons; one tendon -ceasing to act, the other takes up the movement. The tendons are -made thick inside the fingers and thin outside; and the tendons -inside are attached to every joint but outside they are not. - -[Footnote 26: This head line has, in the original, no text to -follow.] Of the strength [and effect] of the 3 tendons inside the -fingers at the 3 joints. - -The movement of the torso (355-361). - -355. - -Observe the altered position of the shoulder in all the movements of -the arm, going up and down, inwards and outwards, to the back and to -the front, and also in circular movements and any others. - -And do the same with reference to the neck, hands and feet and the -breast above the lips &c. - -356. - -Three are the principal muscles of the shoulder, that is _b c d_, -and two are the lateral muscles which move it forward and backward, -that is _a o_; _a_ moves it forward, and _o_ pulls it back; and bed -raises it; _a b c_ moves it upwards and forwards, and _c d o_ -upwards and backwards. Its own weight almost suffices to move it -downwards. - -The muscle _d_ acts with the muscle _c_ when the arm moves forward; -and in moving backward the muscle _b_ acts with the muscle _c_. - -[Footnote: See Pl. XXI. In the original the lettering has been -written in ink upon the red chalk drawing and the outlines of the -figures have in most places been inked over.] - -357. - -OF THE LOINS, WHEN BENT. - -The loins or backbone being bent. The breasts are are always lower -than the shoulderblades of the back. - -If the breast bone is arched the breasts are higher than the -shoulderblades. - -If the loins are upright the breast will always be found at the same -level as the shoulderblades. - -[Footnote: See Pl. XXII, No. 1.] - -358. - -_a b_ the tendon and ankle in raising the heel approach each other -by a finger's breadth; in lowering it they separate by a finger's -breadth. - -[Footnote: See Pl. XXII, No. 2. Compare this facsimile and text with -Pl. III, No. 2, and p. 152 of MANZI'S edition. Also with No. 274 of -LUDWIG'S edition of the Vatican Copy.] - -359. - -Just so much as the part _d a_ of the nude figure decreases in this -position so much does the opposite part increase; that is: in -proportion as the length of the part _d a_ diminishes the normal -size so does the opposite upper part increase beyond its [normal] -size. The navel does not change its position to the male organ; and -this shrinking arises because when a figure stands on one foot, that -foot becomes the centre [of gravity] of the superimposed weight. -This being so, the middle between the shoulders is thrust above it -out of it perpendicular line, and this line, which forms the central -line of the external parts of the body, becomes bent at its upper -extremity [so as to be] above the foot which supports the body; and -the transverse lines are forced into such angles that their ends are -lower on the side which is supported. As is shown at _a b c_. - -[Footnote: See Pl. XXII, No. 3.] - -360. - -OF PAINTING. - -Note in the motions and attitudes of figures how the limbs vary, and -their feeling, for the shoulderblades in the motions of the arms and -shoulders vary the [line of the] back bone very much. And you will -find all the causes of this in my book of Anatomy. - -361. - -OF [CHANGE OF] ATTITUDE. - -The pit of the throat is over the feet, and by throwing one arm -forward the pit of the throat is thrown off that foot. And if the -leg is thrown forward the pit of the throat is thrown forward; and. -so it varies in every attitude. - -362. - -OF PAINTING. - -Indicate which are the muscles, and which the tendons, which become -prominent or retreat in the different movements of each limb; or -which do neither [but are passive]. And remember that these -indications of action are of the first importance and necessity in -any painter or sculptor who professes to be a master &c. - -And indicate the same in a child, and from birth to decrepitude at -every stage of its life; as infancy, childhood, boyhood, youth &c. - -And in each express the alterations in the limbs and joints, which -swell and which grow thinner. - -363. - -O Anatomical Painter! beware lest the too strong indication of the -bones, sinews and muscles, be the cause of your becoming wooden in -your painting by your wish to make your nude figures display all -their feeling. Therefore, in endeavouring to remedy this, look in -what manner the muscles clothe or cover their bones in old or lean -persons; and besides this, observe the rule as to how these same -muscles fill up the spaces of the surface that extend between them, -which are the muscles which never lose their prominence in any -amount of fatness; and which too are the muscles of which the -attachments are lost to sight in the very least plumpness. And in -many cases several muscles look like one single muscle in the -increase of fat; and in many cases, in growing lean or old, one -single muscle divides into several muscles. And in this treatise, -each in its place, all their peculiarities will be explained--and -particularly as to the spaces between the joints of each limb &c. -Again, do not fail [to observe] the variations in the forms of the -above mentioned muscles, round and about the joints of the limbs of -any animal, as caused by the diversity of the motions of each limb; -for on some side of those joints the prominence of these muscles is -wholly lost in the increase or diminution of the flesh of which -these muscles are composed, &c. - -[Footnote: DE ROSSI remarks on this chapter, in the Roman edition of -the Trattato, p. 504: "_Non in questo luogo solo, ma in altri ancora -osservera il lettore, che Lionardo va fungendo quelli che fanno -abuso della loro dottrina anatomica, e sicuramente con cio ha in -mira il suo rivale Bonarroti, che di anatomia facea tanta pompa_." -Note, that Leonardo wrote this passage in Rome, probably under the -immediate impression of MICHAELANGELO'S paintings in the Sistine -Chapel and of RAPHAEL'S Isaiah in Sant' Agostino.] - -364. - -OF THE DIFFERENT MEASUREMENTS OF BOYS AND MEN. - -There is a great difference in the length between the joints in men -and boys for, in man, from the top of the shoulder [by the neck] to -the elbow, and from the elbow to the tip of the thumb and from one -shoulder to the other, is in each instance two heads, while in a boy -it is but one because Nature constructs in us the mass which is the -home of the intellect, before forming that which contains the vital -elements. - -365. - -OF PAINTING. - -Which are the muscles which subdivide in old age or in youth, when -becoming lean? Which are the parts of the limbs of the human frame -where no amount of fat makes the flesh thicker, nor any degree of -leanness ever diminishes it? - -The thing sought for in this question will be found in all the -external joints of the bones, as the shoulder, elbow, wrists, -finger-joints, hips, knees, ankle-bone and toes and the like; all of -which shall be told in its place. The greatest thickness acquired by -any limb is at the part of the muscles which is farthest from its -attachments. - -Flesh never increases on those portions of the limb where the bones -are near to the surface. - -At _b r d a c e f_ the increase or diminution of the flesh never -makes any considerable difference. Nature has placed in front of man -all those parts which feel most pain under a blow; and these are the -shin of the leg, the forehead, and the nose. And this was done for -the preservation of man, since, if such pain were not felt in these -parts, the number of blows to which they would be exposed must be -the cause of their destruction. - -Describe why the bones of the arm and leg are double near the hand -and foot [respectively]. - -And where the flesh is thicker or thinner in the bending of the -limbs. - -366. - -OF PAINTING. - -Every part of the whole must be in proportion to the whole. Thus, if -a man is of a stout short figure he will be the same in all his -parts: that is with short and thick arms, wide thick hands, with -short fingers with their joints of the same character, and so on -with the rest. I would have the same thing understood as applying to -all animals and plants; in diminishing, [the various parts] do so in -due proportion to the size, as also in enlarging. - -367. - -OF THE AGREEMENT OF THE PROPORTION OF THE LIMBS. - -And again, remember to be very careful in giving your figures limbs, -that they must appear to agree with the size of the body and -likewise to the age. Thus a youth has limbs that are not very -muscular not strongly veined, and the surface is delicate and round, -and tender in colour. In man the limbs are sinewy and muscular, -while in old men the surface is wrinkled, rugged and knotty, and the -sinews very prominent. - -HOW YOUNG BOYS HAVE THEIR JOINTS JUST THE REVERSE OF THOSE OF MEN, -AS TO SIZE. - -Little children have all the joints slender and the portions between -them are thick; and this happens because nothing but the skin covers -the joints without any other flesh and has the character of sinew, -connecting the bones like a ligature. And the fat fleshiness is laid -on between one joint and the next, and between the skin and the -bones. But, since the bones are thicker at the joints than between -them, as a mass grows up the flesh ceases to have that superfluity -which it had, between the skin and the bones; whence the skin clings -more closely to the bone and the limbs grow more slender. But since -there is nothing over the joints but the cartilaginous and sinewy -skin this cannot dry up, and, not drying up, cannot shrink. Thus, -and for this reason, children are slender at the joints and fat -between the joints; as may be seen in the joints of the fingers, -arms, and shoulders, which are slender and dimpled, while in man on -the contrary all the joints of the fingers, arms, and legs are -thick; and wherever children have hollows men have prominences. - -The movement of the human figure (368-375). - -368. - -Of the manner of representing the 18 actions of man. Repose, -movement, running, standing, supported, sitting, leaning, kneeling, -lying down, suspended. Carrying or being carried, thrusting, -pulling, striking, being struck, pressing down and lifting up. - -[As to how a figure should stand with a weight in its hand [Footnote -8: The original text ends here.] Remember]. - -369. - -A sitting man cannot raise himself if that part of his body which is -front of his axis [centre of gravity] does not weigh more than that -which is behind that axis [or centre] without using his arms. - -A man who is mounting any slope finds that he must involuntarily -throw the most weight forward, on the higher foot, rather than -behind--that is in front of the axis and not behind it. Hence a man -will always, involuntarily, throw the greater weight towards the -point whither he desires to move than in any other direction. - -The faster a man runs, the more he leans forward towards the point -he runs to and throws more weight in front of his axis than behind. -A man who runs down hill throws the axis onto his heels, and one who -runs up hill throws it into the points of his feet; and a man -running on level ground throws it first on his heels and then on the -points of his feet. - -This man cannot carry his own weight unless, by drawing his body -back he balances the weight in front, in such a way as that the foot -on which he stands is the centre of gravity. - -[Footnote: See Pl. XXII, No. 4.] - -370. - -How a man proceeds to raise himself to his feet, when he is sitting -on level ground. - -371. - -A man when walking has his head in advance of his feet. - -A man when walking across a long level plain first leans [rather] -backwards and then as much forwards. - -[Footnote 3-6: He strides forward with the air of a man going down -hill; when weary, on the contrary he walks like a man going up -hill.] - -372. - -A man when running throws less weight on his legs than when standing -still. And in the same way a horse which is running feels less the -weight of the man he carries. Hence many persons think it wonderful -that, in running, the horse can rest on one single foot. From this -it may be stated that when a weight is in progressive motion the -more rapid it is the less is the perpendicular weight towards the -centre. - -373. - -If a man, in taking a jump from firm ground, can leap 3 braccia, and -when he was taking his leap it were to recede 1/3 of a braccio, that -would be taken off his former leap; and so if it were thrust forward -1/3 of a braccio, by how much would his leap be increased? - -374. - -OF DRAWING. - -When a man who is running wants to neutralise the impetus that -carries him on he prepares a contrary impetus which is generated by -his hanging backwards. This can be proved, since, if the impetus -carries a moving body with a momentum equal to 4 and the moving body -wants to turn and fall back with a momentum of 4, then one momentum -neutralises the other contrary one, and the impetus is neutralised. - -Of walking up and down (375-379) - -375. - -When a man wants to stop running and check the impetus he is forced -to hang back and take short quick steps. [Footnote: Lines 5-31 refer -to the two upper figures, and the lower figure to the right is -explained by the last part of the chapter.] The centre of gravity of -a man who lifts one of his feet from the ground always rests on the -centre of the sole of the foot [he stands on]. - -A man, in going up stairs involuntarily throws so much weight -forward and on the side of the upper foot as to be a counterpoise to -the lower leg, so that the labour of this lower leg is limited to -moving itself. - -The first thing a man does in mounting steps is to relieve the leg -he is about to lift of the weight of the body which was resting on -that leg; and besides this, he gives to the opposite leg all the -rest of the bulk of the whole man, including [the weight of] the -other leg; he then raises the other leg and sets the foot upon the -step to which he wishes to raise himself. Having done this he -restores to the upper foot all the weight of the body and of the leg -itself, and places his hand on his thigh and throws his head forward -and repeats the movement towards the point of the upper foot, -quickly lifting the heel of the lower one; and with this impetus he -lifts himself up and at the same time extends the arm which rested -on his knee; and this extension of the arm carries up the body and -the head, and so straightens the spine which was curved. - -[32] The higher the step is which a man has to mount, the farther -forward will he place his head in advance of his upper foot, so as -to weigh more on _a_ than on _b_; this man will not be on the step -_m_. As is shown by the line _g f_. - -[Footnote: See Pl. XXIII, No. 1. The lower sketch to the left -belongs to the four first lines.] - -376. - -I ask the weight [pressure] of this man at every degree of motion on -these steps, what weight he gives to _b_ and to _c_. - -[Footnote 8: These lines are, in the original, written in ink] -Observe the perpendicular line below the centre of gravity of the -man. - -[Footnote: See Pl. XXIII, No. 2.] - -377. - -In going up stairs if you place your hands on your knees all the -labour taken by the arms is removed from the sinews at the back of -the knees. - -[Footnote: See Pl. XXIII, No. 3.] - -378. - -The sinew which guides the leg, and which is connected with the -patella of the knee, feels it a greater labour to carry the man -upwards, in proportion as the leg is more bent; and the muscle which -acts upon the angle made by the thigh where it joins the body has -less difficulty and has a less weight to lift, because it has not -the [additional] weight of the thigh itself. And besides this it has -stronger muscles, being those which form the buttock. - -379. - -A man coming down hill takes little steps, because the weight rests -upon the hinder foot, while a man mounting takes wide steps, because -his weight rests on the foremost foot. - -[Footnote: See Pl. XXIII, No. 4.] - -On the human body in action (380-388). - -380. - -OF THE HUMAN BODY IN ACTION. - -When you want to represent a man as moving some weight consider what -the movements are that are to be represented by different lines; -that is to say either from below upwards, with a simple movement, as -a man does who stoops forward to take up a weight which he will lift -as he straightens himself. Or as a man does who wants to squash -something backwards, or to force it forwards or to pull it downwards -with ropes passed through pullies [Footnote 10: Compare the sketch -on page 198 and on 201 (S. K. M. II.1 86b).]. And here remember that -the weight of a man pulls in proportion as his centre of gravity is -distant from his fulcrum, and to this is added the force given by -his legs and bent back as he raises himself. - -381. - -Again, a man has even a greater store of strength in his legs than -he needs for his own weight; and to see if this is true, make a man -stand on the shore-sand and then put another man on his back, and -you will see how much he will sink in. Then take the man from off -his back and make him jump straight up as high as he can, and you -will find that the print of his feet will be made deeper by the jump -than from having the man on his back. Hence, here, by 2 methods it -is proved that a man has double the strength he requires to support -his own body. - -382. - -OF PAINTING. - -If you have to draw a man who is in motion, or lifting or pulling, -or carrying a weight equal to his own, in what way must you set on -his legs below his body? - -[Footnote: In the MS. this question remains unanswered.] - -383. - -OF THE STRENGTH OF MAN. - -A man pulling a [dead] weight balanced against himself cannot pull -more than his own weight. And if he has to raise it he will [be able -to] raise as much more than his weight as his strength may be more -than that of other men. [Footnote 7: The stroke at the end of this -line finishes in the original in a sort of loop or flourish, and a -similar flourish occurs at the end of the previous passage written -on the same page. M. RAVAISSON regards these as numbers (compare the -photograph of page 30b in his edition of MS. A). He remarks: "_Ce -chiffre_ 8 _et, a la fin de l'alinea precedent, le chiffre_ 7 _sont, -dans le manuscrit, des renvois_."] The greatest force a man can -apply, with equal velocity and impetus, will be when he sets his -feet on one end of the balance [or lever] and then presses his -shoulders against some stable body. This will raise a weight at the -other end of the balance [lever], equal to his own weight and [added -to that] as much weight as he can carry on his shoulders. - -384. - -No animal can simply move [by its dead weight] a greater weight than -the sum of its own weight outside the centre of his fulcrum. - -385. - -A man who wants to send an arrow very far from the bow must be -standing entirely on one foot and raising the other so far from the -foot he stands on as to afford the requisite counterpoise to his -body which is thrown on the front foot. And he must not hold his arm -fully extended, and in order that he may be more able to bear the -strain he must hold a piece of wood which there is in all crossbows, -extending from the hand to the breast, and when he wishes to shoot -he suddenly leaps forward at the same instant and extends his arm -with the bow and releases the string. And if he dexterously does -every thing at once it will go a very long way. - -386. - -When two men are at the opposite ends of a plank that is balanced, -and if they are of equal weight, and if one of them wants to make a -leap into the air, then his leap will be made down from his end of -the plank and the man will never go up again but must remain in his -place till the man at the other end dashes up the board. - -[Footnote: See Pl. XXIV, No. 3.] - -387. - -Of delivering a blow to the right or left. - -[Footnote: Four sketches on Pl. XXIV, No. 1 belong to this passage. -The rest of the sketches and notes on that page are of a -miscellaneous nature.] - -388. - -Why an impetus is not spent at once [but diminishes] gradually in -some one direction? [Footnote 1: The paper has been damaged at the -end of line 1.] The impetus acquired in the line _a b c d_ is spent -in the line _d e_ but not so completely but that some of its force -remains in it and to this force is added the momentum in the line _d -e_ with the force of the motive power, and it must follow than the -impetus multiplied by the blow is greater that the simple impetus -produced by the momentum _d e_. - -[Footnote 8: The sketch No. 2 on Pl. XXIV stands, in the original, -between lines 7 and 8. Compare also the sketches on Pl. LIV.] A man -who has to deal a great blow with his weapon prepares himself with -all his force on the opposite side to that where the spot is which -he is to hit; and this is because a body as it gains in velocity -gains in force against the object which impedes its motion. - -On hair falling down in curls. - -389. - -Observe the motion of the surface of the water which resembles that -of hair, and has two motions, of which one goes on with the flow of -the surface, the other forms the lines of the eddies; thus the water -forms eddying whirlpools one part of which are due to the impetus of -the principal current and the other to the incidental motion and -return flow. - -[Footnote: See Pl. XXV. Where also the text of this passage is given -in facsimile.] - -On draperies (390--392). - -390. - -OF THE NATURE OF THE FOLDS IN DRAPERY. - -That part of a fold which is farthest from the ends where it is -confined will fall most nearly in its natural form. - -Every thing by nature tends to remain at rest. Drapery, being of -equal density and thickness on its wrong side and on its right, has -a tendency to lie flat; therefore when you give it a fold or plait -forcing it out of its flatness note well the result of the -constraint in the part where it is most confined; and the part which -is farthest from this constraint you will see relapses most into the -natural state; that is to say lies free and flowing. - -EXAMPLE. - -[Footnote 13: _a c sia_. In the original text _b_ is written instead -of _c_--an evident slip of the pen.] Let _a b c_ be the fold of the -drapery spoken of above, _a c_ will be the places where this folded -drapery is held fast. I maintain that the part of the drapery which -is farthest from the plaited ends will revert most to its natural -form. - -Therefore, _b_ being farthest from _a_ and _c_ in the fold _a b c_ -it will be wider there than anywhere else. - -[Footnote: See Pl. XXVIII, No. 6, and compare the drawing from -Windsor Pl. XXX for farther illustration of what is here stated.] - -391. - -OF SMALL FOLDS IN DRAPERIES. - -How figures dressed in a cloak should not show the shape so much as -that the cloak looks as if it were next the flesh; since you surely -cannot wish the cloak to be next the flesh, for you must suppose -that between the flesh and the cloak there are other garments which -prevent the forms of the limbs appearing distinctly through the -cloak. And those limbs which you allow to be seen you must make -thicker so that the other garments may appear to be under the cloak. -But only give something of the true thickness of the limbs to a -nymph [Footnote 9: _Una nifa_. Compare the beautiful drawing of a -Nymph, in black chalk from the Windsor collection, Pl. XXVI.] or an -angel, which are represented in thin draperies, pressed and clinging -to the limbs of the figures by the action of the wind. - -392. - -You ought not to give to drapery a great confusion of many folds, -but rather only introduce them where they are held by the hands or -the arms; the rest you may let fall simply where it is its nature to -flow; and do not let the nude forms be broken by too many details -and interrupted folds. How draperies should be drawn from nature: -that is to say if youwant to represent woollen cloth draw the folds -from that; and if it is to be silk, or fine cloth or coarse, or of -linen or of crape, vary the folds in each and do not represent -dresses, as many do, from models covered with paper or thin leather -which will deceive you greatly. - -[Footnote: The little pen and ink drawing from Windsor (W. 102), -given on Pl. XXVIII, No. 7, clearly illustrates the statement made -at the beginning of this passage; the writing of the cipher 19 on -the same page is in Leonardo's hand; the cipher 21 is certainly -not.] - -_VIII._ - -_Botany for Painters and Elements of Landscape Painting._ - -_The chapters composing this portion of the work consist of -observations on Form, Light and Shade in Plants, and particularly in -Trees summed up in certain general rules by which the author intends -to guide the artist in the pictorial representation of landscape._ - -_With these the first principles of a_ Theory of Landscape painting -_are laid down--a theory as profoundly thought out in its main -lines as it is lucidly worked out in its details. In reading these -chapters the conviction is irresistible that such a_ Botany for -painters _is or ought to be of similar importance in the practice of -painting as the principles of the Proportions and Movements of the -human figure_ i. e. Anatomy for painters. - -_There can be no doubt that Leonardo, in laying down these rules, -did not intend to write on Botany in the proper scientific -sense--his own researches on that subject have no place here; it -need only be observed that they are easily distinguished by their -character and contents from those which are here collected and -arranged under the title 'Botany for painters'. In some cases where -this division might appear doubtful,--as for instance in No._ -402--_the Painter is directly addressed and enjoined to take the -rule to heart as of special importance in his art._ - -_The original materials are principally derived from MS._ G, _in -which we often find this subject treated on several pages in -succession without any of that intermixture of other matters, which -is so frequent in Leonardo's writings. This MS., too, is one of the -latest; when it was written, the great painter was already more than -sixty years of age, so we can scarcely doubt that he regarded all he -wrote as his final views on the subject. And the same remark applies -to the chapters from MSS._ E _and_ M _which were also written -between_ 1513--15. - -_For the sake of clearness, however, it has been desirable to -sacrifice--with few exceptions--the original order of the passages -as written, though it was with much reluctance and only after long -hesitation that I resigned myself to this necessity. Nor do I mean -to impugn the logical connection of the author's ideas in his MS.; -but it will be easily understood that the sequence of disconnected -notes, as they occurred to Leonardo and were written down from time -to time, might be hardly satisfactory as a systematic arrangement of -his principles. The reader will find in the Appendix an exact -account of the order of the chapters in the original MS. and from -the data there given can restore them at will. As the materials are -here arranged, the structure of the tree as regards the growth of -the branches comes first_ (394-411) _and then the insertion of the -leaves on the stems_ (412-419). _Then follow the laws of Light and -Shade as applied, first, to the leaves (420-434), and, secondly, to -the whole tree and to groups of trees_ (435-457). _After the remarks -on the Light and Shade in landscapes generally_ (458-464), _we find -special observations on that of views of towns and buildings_ -(465-469). _To the theory of Landscape Painting belong also the -passages on the effect of Wind on Trees_ (470-473) _and on the Light -and Shade of Clouds_ (474-477), _since we find in these certain -comparisons with the effect of Light and Shade on Trees_ (e. g.: _in -No._ 476, 4. 5; _and No._ 477, 9. 12). _The chapters given in the -Appendix Nos._ 478 _and_ 481 _have hardly any connection with the -subjects previously treated._ - -Classification of trees. - -393. - -TREES. - -Small, lofty, straggling, thick, that is as to foliage, dark, light, -russet, branched at the top; some directed towards the eye, some -downwards; with white stems; this transparent in the air, that not; -some standing close together, some scattered. - -The relative thickness of the branches to the trunk (393--396). - -394. - -All the branches of a tree at every stage of its height when put -together are equal in thickness to the trunk [below them]. - -All the branches of a water [course] at every stage of its course, -if they are of equal rapidity, are equal to the body of the main -stream. - -395. - -Every year when the boughs of a plant [or tree] have made an end of -maturing their growth, they will have made, when put together, a -thickness equal to that of the main stem; and at every stage of its -ramification you will find the thickness of the said main stem; as: -_i k_, _g h_, _e f_, _c d_, _a b_, will always be equal to each -other; unless the tree is pollard--if so the rule does not hold -good. - -All the branches have a direction which tends to the centre of the -tree _m_. - -[Footnote: The two sketches of leafless trees one above another on -the left hand side of Pl. XXVII, No. 1, belong to this passage.] - -396. - -If the plant n grows to the thickness shown at m, its branches will -correspond [in thickness] to the junction a b in consequence of the -growth inside as well as outside. - -The branches of trees or plants have a twist wherever a minor branch -is given off; and this giving off the branch forms a fork; this said -fork occurs between two angles of which the largest will be that -which is on the side of the larger branch, and in proportion, unless -accident has spoilt it. - -[Footnote: The sketches illustrating this are on the right hand side -of PI. XXVII, No. I, and the text is also given there in facsimile.] - -397. - -There is no boss on branches which has not been produced by some -branch which has failed. - -The lower shoots on the branches of trees grow more than the upper -ones and this occurs only because the sap that nourishes them, being -heavy, tends downwards more than upwards; and again, because those -[branches] which grow downwards turn away from the shade which -exists towards the centre of the plant. The older the branches are, -the greater is the difference between their upper and their lower -shoots and in those dating from the same year or epoch. - -[Footnote: The sketch accompanying this in the MS. is so effaced -that an exact reproduction was impossible.] - -398. - -OF THE SCARS ON TREES. - -The scars on trees grow to a greater thickness than is required by -the sap of the limb which nourishes them. - -399. - -The plant which gives out the smallest ramifications will preserve -the straightest line in the course of its growth. - -[Footnote: This passage is illustrated by two partly effaced -sketches. One of these closely resembles the lower one given under -No. 408, the other also represents short closely set boughs on an -upright trunk.] - -400. - -OF THE RAMIFICATION. - -The beginning of the ramification [the shoot] always has the central -line [axis] of its thickness directed to the central line [axis] of -the plant itself. - -401. - -In starting from the main stem the branches always form a base with -a prominence as is shown at _a b c d_. - -402. - -WHY, VERY FREQUENTLY, TIMBER HAS VEINS THAT ARE NOT STRAIGHT. - -When the branches which grow the second year above the branch of the -preceding year, are not of equal thickness above the antecedent -branches, but are on one side, then the vigour of the lower branch -is diverted to nourish the one above it, although it may be somewhat -on one side. - -But if the ramifications are equal in their growth, the veins of the -main stem will be straight [parallel] and equidistant at every -degree of the height of the plant. - -Wherefore, O Painter! you, who do not know these laws! in order to -escape the blame of those who understand them, it will be well that -you should represent every thing from nature, and not despise such -study as those do who work [only] for money. - -The direction of growth (403-407). - -403. - -OF THE RAMIFICATIONS OF PLANTS. - -The plants which spread very much have the angles of the spaces -which divide their branches more obtuse in proportion as their point -of origin is lower down; that is nearer to the thickest and oldest -portion of the tree. Therefore in the youngest portions of the tree -the angles of ramification are more acute. [Footnote: Compare the -sketches on the lower portion of Pl. XXVII, No. 2.] - -404. - -The tips of the boughs of plants [and trees], unless they are borne -down by the weight of their fruits, turn towards the sky as much as -possible. - -The upper side of their leaves is turned towards the sky that it may -receive the nourishment of the dew which falls at night. - -The sun gives spirit and life to plants and the earth nourishes them -with moisture. [9] With regard to this I made the experiment of -leaving only one small root on a gourd and this I kept nourished -with water, and the gourd brought to perfection all the fruits it -could produce, which were about 60 gourds of the long kind, andi set -my mind diligently [to consider] this vitality and perceived that -the dews of night were what supplied it abundantly with moisture -through the insertion of its large leaves and gave nourishment to -the plant and its offspring--or the seeds which its offspring had -to produce--[21]. - -The rule of the leaves produced on the last shoot of the year will -be that they will grow in a contrary direction on the twin branches; -that is, that the insertion of the leaves turns round each branch in -such a way, as that the sixth leaf above is produced over the sixth -leaf below, and the way they turn is that if one turns towards its -companion to the right, the other turns to the left, the leaf -serving as the nourishing breast for the shoot or fruit which grows -the following year. - -[Footnote: A French translation of lines 9-12 was given by M. -RAVAISSON in the _Gazette des Beaux Arts_, Oct. 1877; his paper also -contains some valuable information as to botanical science in the -ancient classical writers and at the time of the Renaissance.] - -405. - -The lowest branches of those trees which have large leaves and heavy -fruits, such as nut-trees, fig-trees and the like, always droop -towards the ground. - -The branches always originate above [in the axis of] the leaves. - -406. - -The upper shoots of the lateral branches of plants lie closer to the -parent branch than the lower ones. - -407. - -The lowest branches, after they have formed the angle of their -separation from the parent stem, always bend downwards so as not to -crowd against the other branches which follow them on the same stem -and to be better able to take the air which nourishes them. As is -shown by the angle _b a c_; the branch _a c_ after it has made the -corner of the angle _a c_ bends downwards to _c d_ and the lesser -shoot _c_ dries up, being too thin. - -The main branch always goes below, as is shown by the branch _f n -m_, which does not go to _f n o_. - -The forms of trees (408--411). - -408. - -The elm always gives a greater length to the last branches of the -year's growth than to the lower ones; and Nature does this because -the highest branches are those which have to add to the size of the -tree; and those at the bottom must get dry because they grow in the -shade and their growth would be an impediment to the entrance of the -solar rays and the air among the main branches of the tree. - -The main branches of the lower part bend down more than those above, -so as to be more oblique than those upper ones, and also because -they are larger and older. - -409. - -In general almost all the upright portions of trees curve somewhat -turning the convexity towards the South; and their branches are -longer and thicker and more abundant towards the South than towards -the North. And this occurs because the sun draws the sap towards -that surface of the tree which is nearest to it. - -And this may be observed if the sun is not screened off by other -plants. - -410. - -The cherry-tree is of the character of the fir tree as regards its -ramification placed in stages round its main stem; and its branches -spring, 4 or five or 6 [together] opposite each other; and the tips -of the topmost shoots form a pyramid from the middle upwards; and -the walnut and oak form a hemisphere from the middle upwards. - -411. - -The bough of the walnut which is only hit and beaten when it has -brought to perfection... - -[Footnote: The end of the text and the sketch in red chalk belonging -to it, are entirely effaced.] - -The insertion of the leaves (412--419). - -412. - -OF THE INSERTION OF THE BRANCHES ON PLANTS. - -Such as the growth of the ramification of plants is on their -principal branches, so is that of the leaves on the shoots of the -same plant. These leaves have [Footnote 6: _Quattro modi_ (four -modes). Only three are described in the text, the fourth is only -suggested by a sketch. - -This passage occurs in MANZI'S edition of the Trattato, p. 399, but -without the sketches and the text is mutilated in an important part. -The whole passage has been commented on, from MANZI'S version, in -Part I of the _Nuovo Giornale Botanico Italiano_, by Prof. G. -UZIELLI (Florence 1869, Vol. I). He remarks as to the 'four modes': -"_Leonardo, come si vede nelle linie sententi da solo tre esempli. -Questa ed altre inessattezze fanno desiderare, sia esaminato di -nuovo il manoscritto Vaticano_". This has since been done by D. -KNAPP of Tubingen, and his accurate copy has been published by H. -LUDWIG, the painter. The passage in question occurs in his edition -as No. 833; and there also the drawings are wanting. The space for -them has been left vacant, but in the Vatican copy '_niente_' has -been written on the margin; and in it, as well as in LUDWIG'S and -MANZI'S edition, the text is mutilated.] four modes of growing one -above another. The first, which is the most general, is that the -sixth always originates over the sixth below [Footnote 8: _la sesta -di sotto. "Disposizione 2/5 o 1/5. Leonardo osservo probabilmente -soltanto la prima"_ (UZIELLl).]; the second is that two third ones -above are over the two third ones below [Footnote 10: _terze di -sotto: "Intende qui senza dubbio parlare di foglie decussate, in cui -il terzo verticello e nel piano del primo"_ (UZIELLI).]; and the -third way is that the third above is over the third below [Footnote -11: 3a _di sotto: "Disposizione 1/2"_ (UZIELLI).]. - -[Footnote: See the four sketches on the upper portion of the page -reproduced as fig. 2 on P1. XXVII.] - -413. - -A DESCRIPTION OF THE ELM. - -The ramification of the elm has the largest branch at the top. The -first and the last but one are smaller, when the main trunk is -straight. - -The space between the insertion of one leaf to the rest is half the -extreme length of the leaf or somewhat less, for the leaves are at -an interval which is about the 3rd of the width of the leaf. - -The elm has more leaves near the top of the boughs than at the base; -and the broad [surface] of the leaves varies little as to [angle -and] aspect. - -[Footnote: See Pl. XXVII, No. 3. Above the sketch and close under -the number of the page is the word '_olmo_' (elm).] - -414. - -In the walnut tree the leaves which are distributed on the shoots of -this year are further apart from each other and more numerous in -proportion as the branch from which this shoot springs is a young -one. And they are inserted more closely and less in number when the -shoot that bears them springs from an old branch. Its fruits are -borne at the ends of the shoots. And its largest boughs are the -lowest on the boughs they spring from. And this arises from the -weight of its sap which is more apt to descend than to rise, and -consequently the branches which spring from them and rise towards -the sky are small and slender [20]; and when the shoot turns towards -the sky its leaves spread out from it [at an angle] with an equal -distribution of their tips; and if the shoot turns to the horizon -the leaves lie flat; and this arises from the fact that leaves -without exception, turn their underside to the earth [29]. - -The shoots are smaller in proportion as they spring nearer to the -base of the bough they spring from. - -[Footnote: See the two sketches on Pl XXVII, No. 4. The second -refers to the passage lines 20-30.] - -415. - -OF THE INSERTION OF THE LEAVES ON THE BRANCHES. - -The thickness of a branch never diminishes within the space between -one leaf and the next excepting by so much as the thickness of the -bud which is above the leaf and this thickness is taken off from the -branch above [the node] as far as the next leaf. - -Nature has so placed the leaves of the latest shoots of many plants -that the sixth leaf is always above the first, and so on in -succession, if the rule is not [accidentally] interfered with; and -this occurs for two useful ends in the plant: First that as the -shoot and the fruit of the following year spring from the bud or eye -which lies above and in close contact with the insertion of the leaf -[in the axil], the water which falls upon the shoot can run down to -nourish the bud, by the drop being caught in the hollow [axil] at -the insertion of the leaf. And the second advantage is, that as -these shoots develop in the following year one will not cover the -next below, since the 5 come forth on five different sides; and the -sixth which is above the first is at some distance. - -416. - -OF THE RAMIFICATIONS OF TREES AND THEIR FOLIAGE. - -The ramifications of any tree, such as the elm, are wide and slender -after the manner of a hand with spread fingers, foreshortened. And -these are seen in the distribution [thus]: the lower portions are -seen from above; and those that are above are seen from below; and -those in the middle, some from below and some from above. The upper -part is the extreme [top] of this ramification and the middle -portion is more foreshortened than any other of those which are -turned with their tips towards you. And of those parts of the middle -of the height of the tree, the longest will be towards the top of -the tree and will produce a ramification like the foliage of the -common willow, which grows on the banks of rivers. - -Other ramifications are spherical, as those of such trees as put -forth their shoots and leaves in the order of the sixth being placed -above the first. Others are thin and light like the willow and -others. - -417. - -You will see in the lower branches of the elder, which puts forth -leaves two and two placed crosswise [at right angles] one above -another, that if the stem rises straight up towards the sky this -order never fails; and its largest leaves are on the thickest part -of the stem and the smallest on the slenderest part, that is towards -the top. But, to return to the lower branches, I say that the leaves -on these are placed on them crosswise like [those on] the upper -branches; and as, by the law of all leaves, they are compelled to -turn their upper surface towards the sky to catch the dew at night, -it is necessary that those so placed should twist round and no -longer form a cross. - -[Footnote: See Pl. XXVII, No. 5.] - -418. - -A leaf always turns its upper side towards the sky so that it may -the better receive, on all its surface, the dew which drops gently -from the atmosphere. And these leaves are so distributed on the -plant as that one shall cover the other as little as possible, but -shall lie alternately one above another as may be seen in the ivy -which covers the walls. And this alternation serves two ends; that -is, to leave intervals by which the air and sun may penetrate -between them. The 2nd reason is that the drops which fall from the -first leaf may fall onto the fourth or--in other trees--onto the -sixth. - -419. - -Every shoot and every fruit is produced above the insertion [in the -axil] of its leaf which serves it as a mother, giving it water from -the rain and moisture from the dew which falls at night from above, -and often it protects them against the too great heat of the rays of -the sun. - -LIGHT ON BRANCHES AND LEAVES (420--422). - -420. - -That part of the body will be most illuminated which is hit by the -luminous ray coming between right angles. - -[Footnote: See Pl. XXVIII, No. 1.] - -421. - -Young plants have more transparent leaves and a more lustrous bark -than old ones; and particularly the walnut is lighter coloured in -May than in September. - -422. - -OF THE ACCIDENTS OF COLOURING IN TREES. - -The accidents of colour in the foliage of trees are 4. That is: -shadow, light, lustre [reflected light] and transparency. - -OF THE VISIBILITY OF THESE ACCIDENTS. - -These accidents of colour in the foliage of trees become confused at -a great distance and that which has most breadth [whether light or -shade, &c.] will be most conspicuous. - -The proportions of light and shade in a leaf (423-426). - -423. - -OF THE SHADOWS OF A LEAF. - -Sometimes a leaf has three accidents [of light] that is: shade, -lustre [reflected light] and transparency [transmitted light]. Thus, -if the light were at _n_ as regards the leaf _s_, and the eye at -_m_, it would see _a_ in full light, _b_ in shadow and _c_ -transparent. - -424. - -A leaf with a concave surface seen from the under side and -up-side-down will sometimes show itself as half in shade, and half -transparent. Thus, if _o p_ is the leaf and the light _m_ and the -eye _n_, this will see _o_ in shadow because the light does not fall -upon it between equal angles, neither on the upper nor the under -side, and _p_ is lighted on the upper side and the light is -transmitted to its under side. [Footnote: See Pl. XXVIII, No. 2, the -upper sketch on the page. In the original they are drawn in red -chalk.] - -425. - -Although those leaves which have a polished surface are to a great -extent of the same colour on the right side and on the reverse, it -may happen that the side which is turned towards the atmosphere will -have something of the colour of the atmosphere; and it will seem to -have more of this colour of the atmosphere in proportion as the eye -is nearer to it and sees it more foreshortened. And, without -exception the shadows show as darker on the upper side than on the -lower, from the contrast offered by the high lights which limit the -shadows. - -The under side of the leaf, although its colour may be in itself the -same as that of the upper side, shows a still finer colour--a colour -that is green verging on yellow--and this happens when the leaf is -placed between - -426. - -the eye and the light which falls upon it from the opposite side. - -And its shadows are in the same positions as those were of the -opposite side. Therefore, O Painter! when you do trees close at -hand, remember that if the eye is almost under the tree you will see -its leaves [some] on the upper and [some] on the under side, and the -upper side will be bluer in proportion as they are seen more -foreshortened, and the same leaf sometimes shows part of the right -side and part of the under side, whence you must make it of two -colours. - -Of the transparency of leaves (427-429). - -427. - -The shadows in transparent leaves seen from the under side are the -same shadows as there are on the right side of this leaf, they will -show through to the underside together with lights, but the lustre -[reflected light] can never show through. - -428. - -When one green has another [green] behind it, the lustre on the -leaves and their transparent [lights] show more strongly than in -those which are [seen] against the brightness of the atmosphere. - -And if the sun illuminates the leaves without their coming between -it and the eye and without the eye facing the sun, then the -reflected lights and the transparent lights are very strong. - -It is very effective to show some branches which are low down and -dark and so set off the illuminated greens which are at some -distance from the dark greens seen below. That part is darkest which -is nearest to the eye or which is farthest from the luminous -atmosphere. - -429. - -Never paint leaves transparent to the sun, because they are -confused; and this is because on the transparency of one leaf will -be seen the shadow of another leaf which is above it. This shadow -has a distinct outline and a certain depth of shade and sometimes is -[as much as] half or a third of the leaf which is shaded; and -consequently such an arrangement is very confused and the imitation -of it should be avoided. - -The light shines least through a leaf when it falls upon it at an -acute angle. - -The gradations of shade and colour in leaves (430-434). - -430. - -The shadows of plants are never black, for where the atmosphere -penetrates there can never be utter darkness. - -431. - -If the light comes from _m_ and the eye is at _n_ the eye will see -the colour of the leaves _a b_ all affected by the colour of _m_ ---that is of the atmosphere; and _b c_ will be seen from the under -side as transparent, with a beautiful green colour verging on -yellow. - -If _m_ is the luminous body lighting up the leaf _s_ all the eyes -that see the under side of this leaf will see it of a beautiful -light green, being transparent. - -In very many cases the positions of the leaves will be without -shadow [or in full light], and their under side will be transparent -and the right side lustrous [reflecting light]. - -432. - -The willow and other similar trees, which have their boughs lopped -every 3 or 4 years, put forth very straight branches, and their -shadow is about the middle where these boughs spring; and towards -the extreme ends they cast but little shade from having small leaves -and few and slender branches. Hence the boughs which rise towards -the sky will have but little shade and little relief; and the -branches which are at an angle from the horizon, downwards, spring -from the dark part of the shadow and grow thinner by degrees up to -their ends, and these will be in strong relief, being in gradations -of light against a background of shadow. - -That tree will have the least shadow which has the fewest branches -and few leaves. - -433. - -OF DARK LEAVES IN FRONT OF TRANSPARENT ONES. - -When the leaves are interposed between the light and the eye, then -that which is nearest to the eye will be the darkest, and the most -distant will be the lightest, not being seen against the atmosphere; -and this is seen in the leaves which are away from the centre of the -tree, that is towards the light. - -[Footnote: See Pl. XXVIII, No. 2, the lower sketch.] - -434. - -OF THE LIGHTS ON DARK LEAVES. - -The lights on such leaves which are darkest, will be most near to -the colour of the atmosphere that is reflected in them. And the -cause of this is that the light on the illuminated portion mingles -with the dark hue to compose a blue colour; and this light is -produced by the blueness of the atmosphere which is reflected in the -smooth surface of these leaves and adds to the blue hue which this -light usually produces when it falls on dark objects. - -OF THE LIGHTS ON LEAVES OF A YELLOWISH GREEN. - -But leaves of a green verging on yellow when they reflect the -atmosphere do not produce a reflection verging on blue, inasmuch as -every thing which appears in a mirror takes some colour from that -mirror, hence the blue of the atmosphere being reflected in the -yellow of the leaf appears green, because blue and yellow mixed -together make a very fine green colour, therefore the lustre of -light leaves verging on yellow will be greenish yellow. - -A classification of trees according to their colours. - -435. - -The trees in a landscape are of various kinds of green, inasmuch as -some verge towards blackness, as firs, pines, cypresses, laurels, -box and the like. Some tend to yellow such as walnuts, and pears, -vines and verdure. Some are both yellowish and dark as chesnuts, -holm-oak. Some turn red in autumn as the service-tree, pomegranate, -vine, and cherry; and some are whitish as the willow, olive, reeds -and the like. Trees are of various forms ... - -The proportions of light and shade in trees (436-440). - -436. - -OF A GENERALLY DISTRIBUTED LIGHT AS LIGHTING UP TREES. - -That part of the trees will be seen to lie in the least dark shadow -which is farthest from the earth. - -To prove it let _a p_ be the tree, _n b c_ the illuminated -hemisphere [the sky], the under portion of the tree faces the earth -_p c_, that is on the side _o_, and it faces a small part of the -hemisphere at _c d_. But the highest part of the convexity a faces -the greatest part of the hemisphere, that is _b c_. For this -reason--and because it does not face the darkness of the earth--it -is in fuller light. But if the tree has dense foliage, as the -laurel, arbutus, box or holm oak, it will be different; because, -although _a_ does not face the earth, it faces the dark [green] of -the leaves cut up by many shadows, and this darkness is reflected -onto the under sides of the leaves immediately above. Thus these -trees have their darkest shadows nearest to the middle of the tree. - -437. - -OF THE SHADOWS OF VERDURE. - -The shadows of verdure are always somewhat blue, and so is every -shadow of every object; and they assume this hue more in proportion -as they are remote from the eye, and less in proportion as they are -nearer. The leaves which reflect the blue of the atmosphere always -present themselves to the eye edgewise. - -OF THE ILLUMINATED PART OF VERDURE AND OF MOUNTAINS. - -The illuminated portion, at a great distance, will appear most -nearly of its natural colour where the strongest light falls upon -it. - -438. - -OF TREES THAT ARE LIGHTED BY THE SUN AND BY THE ATMOSPHERE. - -In trees that are illuminated [both] by the sun and the atmosphere -and that have leaves of a dark colour, one side will be illuminated -by the atmosphere [only] and in consequence of this light will tend -to blueness, while on the other side they will be illuminated by the -atmosphere and the sun; and the side which the eye sees illuminated -by the sun will reflect light. - -439. - -OF DEPICTING A FOREST SCENE. - -The trees and plants which are most thickly branched with slender -branches ought to have less dark shadow than those trees and plants -which, having broader leaves, will cast more shadow. - -440. - -ON PAINTING. - -In the position of the eye which sees that portion of a tree -illuminated which turns towards the light, one tree will never be -seen to be illuminated equally with the other. To prove this, let -the eye be _c_ which sees the two trees _b d_ which are illuminated -by the sun _a_; I say that this eye _c_ will not see the light in -the same proportion to the shade, in one tree as in the other. -Because, the tree which is nearest to the sun will display so much -the stronger shadow than the more distant one, in proportion as one -tree is nearer to the rays of the sun that converge to the eye than -the other; &c. - -You see that the eye _c_ sees nothing of the tree _d_ but shadow, -while the same eye _c_ sees the tree _b_ half in light and half in -shade. - -When a tree is seen from below, the eye sees the top of it as placed -within the circle made by its boughs[23]. - -Remember, O Painter! that the variety of depth of shade in any one -particular species of tree is in proportion to the rarity or density -of their branches. - -[Footnote: The two lower sketches on the left of Pl XXVIII, No. 3, -refer to lines 21-23. The upper sketch has apparently been effaced -by Leonardo himself.] - -The distribution of light and shade with reference to the position -of the spectator (441-443). - -441. - -The shadows of trees placed in a landscape do not display themselves -in the same position in the trees on the right hand and those on the -left; still more so if the sun is to the right or left. As is proved -by the 4th which says: Opaque bodies placed between the light and -the eye display themselves entirely in shadow; and by the 5th: The -eye when placed between the opaque body and the light sees the -opaque body entirely illuminated. And by the 6th: When the eye and -the opaque body are placed between darkness and light, it will be -seen half in shadow and half in light. - -[Footnote: See the figure on the right hand side of Pl. XXVIII, No. -3. The first five lines of the text are written below the diagram -and above it are the last eight lines of the text, given as No. -461.] - -442. - -OF THE HERBS OF THE FIELD. - -Of the plants which take a shadow from the plants which spring among -them, those which are on this side [in front] of the shadow have the -stems lighted up on a background of shadow, and the plants on which -the shadows fall have their stems dark on a light background; that -is on the background beyond the shadow. - -OF TREES WHICH ARE BETWEEN THE EYE AND THE LIGHT. - -Of the trees which are between the eye and the light the part in -front will be light; but this light will be broken by the -ramifications of transparent leaves--being seen from the under -side--and lustrous leaves--being seen from the upper side; and the -background below and behind will be dark green, being in shadow from -the front portion of the said tree. This occurs in trees placed -above the eye. - -443. - -FROM WHENCE TO DEPICT A LANDSCAPE - -Landscapes should be represented so that the trees may be half in -light and half in shadow; but it is better to do them when the sun -is covered with clouds, for then the trees are lighted by the -general light of the sky, and the general darkness of the earth. And -then they are darkest in certain parts in proportion as those parts -are nearest to the middle of the tree and to the earth. - -The effects of morning light (444-448). - -444. - -OF TREES TO THE SOUTH. - -When the sun is in the east the trees to the South and to the North -have almost as much light as shadow. But a greater share of light in -proportion as they lie to the West and a greater share of shadow in -proportion as they lie to the East. - -OF MEADOWS. - -If the sun is in the East the verdure of the meadows and of other -small plants is of a most beautiful green from being transparent to -the sun; this does not occur in the meadows to the West, and in -those to the South and North the grass is of a moderately brilliant -green. - -445. - -OF THE 4 POINTS OF THE COMPASS [IN LANDSCAPES]. - -When the sun is in the East all the portions of plants lighted by it -are of a most lively verdure, and this happens because the leaves -lighted by the sun within the half of the horizon that is the -Eastern half, are transparent; and within the Western semicircle the -verdure is of a dull hue and the moist air is turbid and of the -colour of grey ashes, not being transparent like that in the East, -which is quite clear and all the more so in proportion as it is -moister. - -The shadows of the trees to the East cover a large portion of them -and are darker in proportion as the foliage of the trees is thicker. - -446. - -OF TREES IN THE EAST. - -When the sun is in the East the trees seen towards the East will -have the light which surrounds them all round their shadows, -excepting on the side towards the earth; unless the tree has been -pruned [below] in the past year. And the trees to the South and -North will be half in shade and half in light, and more or less in -shade or in light in proportion as they are more or less to the East -or to the West. - -The [position of] the eye above or below varies the shadows and -lights in trees, inasmuch as the eye placed above sees the tree with -the little shadow, and the eye placed below with a great deal of -shadow. - -The colour of the green in plants varies as much as their species. - -447. - -OF THE SHADOWS IN TREES. - -The sun being in the East [to the right], the trees to the West [or -left] of the eye will show in small relief and almost imperceptible -gradations, because the atmosphere which lies between the eye and -those trees is very dense [Footnote 7: _per la 7a di questo_. This -possibly referred to something written on the seventh page of this -note book marked _G_. Unfortunately it has been cut out and lost.], -see the 7th of this--and they have no shade; for though a shadow -exists in every detail of the ramification, it results that the -images of the shade and light that reach the eye are confused and -mingled together and cannot be perceived on account of their -minuteness. And the principal lights are in the middle of the trees, -and the shadows to wards the edges; and their separation is shown by -the shadows of the intervals between the trees; but when the forests -are thick with trees the thin edges are but little seen. - -448. - -OF TREES TO THE EAST. - -When the sun is in the East the trees are darker towards the middle -while their edges are light. - -The effects of midday light. - -449. - -OBJECTS IN HIGH LIGHT SHOW BUT LITTLE, BUT BETWEEN LIGHT AND SHADOW -THEY STAND OUT WELL. - -To represent a landscape choose that the sun shall be at noon and -look towards the West or East and then draw. And if you turn towards -the North, every object placed on that side will have no shadow, -particularly those which are nearest to the [direction of the] -shadow of your head. And if you turn towards the South every object -on that side will be wholly in shadow. All the trees which are -towards the sun and have the atmosphere for their background are -dark, and the other trees which lie against that darkness will be -black [very dark] in the middle and lighter towards the edges. - -The appearance of trees in the distance (450. 451). - -450. - -OF THE SPACES [SHOWING THE SKY] IN TREES THEMSELVES. - -The spaces between the parts in the mass of trees, and the spaces -between the trees in the air, are, at great distances, invisible to -the eye; for, where it is an effort [even] to see the whole it is -most difficult to discern the parts.--But a confused mixture is the -result, partaking chiefly of the [hue] which predominates. The -spaces between the leaves consist of particles of illuminated air -which are very much smaller than the tree and are lost sight of -sooner than the tree; but it does not therefore follow that they are -not there. Hence, necessarily, a compounded [effect] is produced of -the sky and of the shadows of the tree in shade, which both together -strike the eye which sees them. - -OF TREES WHICH CONCEAL THESE SPACES IN ONE ANOTHER. - -That part of a tree will show the fewest spaces, behind which a -large number of trees are standing between the tree and the air -[sky]; thus in the tree _a_ the spaces are not concealed nor in _b_, -as there is no tree behind. But in _c_ only half shows the spaces -filled up by the tree _d_, and part of the tree _d_ is filled up by -the tree _e_ and a little farther on all the spaces in the mass of -the trees are lost, and only that at the side remains. - -451. - -OF TREES. - -What outlines are seen in trees at a distance against the sky which -serves as their background? - -The outlines of the ramification of trees, where they lie against -the illuminated sky, display a form which more nearly approaches the -spherical on proportion as they are remote, and the nearer they are -the less they appear in this spherical form; as in the first tree -_a_ which, being near to the eye, displays the true form of its -ramification; but this shows less in _b_ and is altogether lost in -_c_, where not merely the branches of the tree cannot be seen but -the whole tree is distinguished with difficulty. Every object in -shadow, of whatever form it may be, at a great distance appears to -be spherical. And this occurs because, if it is a square body, at a -very short distance it loses its angles, and a little farther off it -loses still more of its smaller sides which remain. And thus before -the whole is lost [to sight] the parts are lost, being smaller than -the whole; as a man, who in such a distant position loses his legs, -arms and head before [the mass of] his body, then the outlines of -length are lost before those of breadth, and where they have become -equal it would be a square if the angles remained; but as they are -lost it is round. - -[Footnote: The sketch No. 4, Pl. XXVIII, belongs to this passage.] - -The cast shadow of trees (452. 453). - -452. - -The image of the shadow of any object of uniform breadth can never -be [exactly] the same as that of the body which casts it. - -[Footnote: See Pl. XXVIII, No. 5.] - -Light and shade on groups of trees (453-457). - -453. - -All trees seen against the sun are dark towards the middle and this -shadow will be of the shape of the tree when apart from others. - -The shadows cast by trees on which the sun shines are as dark as -those of the middle of the tree. - -The shadow cast by a tree is never less than the mass of the tree -but becomes taller in proportion as the spot on which it falls, -slopes towards the centre of the world. - -The shadow will be densest in the middle of the tree when the tree -has the fewest branches. - -[Footnote: The three diagrams which accompany this text are placed, -in the original, before lines 7-11. At the spots marked _B_ Leonardo -wrote _Albero_ (tree). At _A_ is the word _Sole_ (sun), at _C Monte_ -(mountain) at _D piano_ (plain) and at _E cima_ (summit).] - -Every branch participates of the central shadow of every other -branch and consequently [of that] of the whole tree. - -The form of any shadow from a branch or tree is circumscribed by the -light which falls from the side whence the light comes; and this -illumination gives the shape of the shadow, and this may be of the -distance of a mile from the side where the sun is. - -If it happens that a cloud should anywhere overshadow some part of a -hill the [shadow of the] trees there will change less than in the -plains; for these trees on the hills have their branches thicker, -because they grow less high each year than in the plains. Therefore -as these branches are dark by nature and being so full of shade, the -shadow of the clouds cannot darken them any more; but the open -spaces between the trees, which have no strong shadow change very -much in tone and particularly those which vary from green; that is -ploughed lands or fallen mountains or barren lands or rocks. Where -the trees are against the atmosphere they appear all the same -colour--if indeed they are not very close together or very thickly -covered with leaves like the fir and similar trees. When you see the -trees from the side from which the sun lights them, you will see -them almost all of the same tone, and the shadows in them will be -hidden by the leaves in the light, which come between your eye and -those shadows. - -TREES AT A SHORT DISTANCE. - -[Footnote 29: The heading _alberi vicini_ (trees at a short -distance) is in the original manuscript written in the margin.] When -the trees are situated between the sun and the eye, beyond the -shadow which spreads from their centre, the green of their leaves -will be seen transparent; but this transparency will be broken in -many places by the leaves and boughs in shadow which will come -between you and them, or, in their upper portions, they will be -accompanied by many lights reflected from the leaves. - -454. - -The trees of the landscape stand out but little from each other; -because their illuminated portions come against the illuminated -portions of those beyond and differ little from them in light and -shade. - -455. - -Of trees seen from below and against the light, one beyond the other -and near together. The topmost part of the first will be in great -part transparent and light, and will stand out against the dark -portion of the second tree. And thus it will be with all in -succession that are placed under the same conditions. - -Let _s_ be the light, and _r_ the eye, _c d n_ the first tree, _a b -c_ the second. Then I say that _r_, the eye, will see the portion _c -f_ in great part transparent and lighted by the light _s_ which -falls upon it from the opposite side, and it will see it, on a dark -ground _b c_ because that is the dark part and shadow of the tree _a -b c_. - -But if the eye is placed at _t_ it will see _o p_ dark on the light -background _n g_. - -Of the transparent and shadowy parts of trees, that which is nearest -to you is the darkest. - -456. - -That part of a tree which has shadow for background, is all of one -tone, and wherever the trees or branches are thickest they will be -darkest, because there are no little intervals of air. But where the -boughs lie against a background of other boughs, the brighter parts -are seen lightest and the leaves lustrous from the sunlight falling -on them. - -457. - -In the composition of leafy trees be careful not to repeat too often -the same colour of one tree against the same colour of another -[behind it]; but vary it with a lighter, or a darker, or a stronger -green. - -On the treatment of light for landscapes (458-464). - -458. - -The landscape has a finer azure [tone] when, in fine weather the sun -is at noon than at any other time of the day, because the air is -purified of moisture; and looking at it under that aspect you will -see the trees of a beautiful green at the outside and the shadows -dark towards the middle; and in the remoter distance the atmosphere -which comes between you and them looks more beautiful when there is -something dark beyond. And still the azure is most beautiful. The -objects seen from the side on which the sun shines will not show you -their shadows. But, if you are lower than the sun, you can see what -is not seen by the sun and that will be all in shade. The leaves of -the trees, which come between you and the sun are of two principal -colours which are a splendid lustre of green, and the reflection of -the atmosphere which lights up the objects which cannot be seen by -the sun, and the shaded portions which only face the earth, and the -darkest which are surrounded by something that is not dark. The -trees in the landscape which are between you and the sun are far -more beautiful than those you see when you are between the sun and -them; and this is so because those which face the sun show their -leaves as transparent towards the ends of their branches, and those -that are not transparent--that is at the ends--reflect the light; -and the shadows are dark because they are not concealed by any -thing. - -The trees, when you place yourself between them and the sun, will -only display to you their light and natural colour, which, in -itself, is not very strong, and besides this some reflected lights -which, being against a background which does not differ very much -from themselves in tone, are not conspicuous; and if you are lower -down than they are situated, they may also show those portions on -which the light of the sun does not fall and these will be dark. - -In the Wind. - -But, if you are on the side whence the wind blows, you will see the -trees look very much lighter than on the other sides, and this -happens because the wind turns up the under side of the leaves, -which, in all trees, is much whiter than the upper sides; and, more -especially, will they be very light indeed if the wind blows from -the quarter where the sun is, and if you have your back turned to -it. - -[Footnote: At _S_, in the original is the word _Sole_ (sun) and at -_N parte di nuvolo_ (the side of the clouds).] - -459. - -When the sun is covered by clouds, objects are less conspicuous, -because there is little difference between the light and shade of -the trees and of the buildings being illuminated by the brightness -of the atmosphere which surrounds the objects in such a way that the -shadows are few, and these few fade away so that their outline is -lost in haze. - -460. - -OF TREES AND LIGHTS ON THEM. - -The best method of practice in representing country scenes, or I -should say landscapes with their trees, is to choose them so that -the sun is covered with clouds so that the landscape receives an -universal light and not the direct light of the sun, which makes the -shadows sharp and too strongly different from the lights. - -461. - -OF PAINTING. - -In landscapes which represent [a scene in] winter. The mountains -should not be shown blue, as we see in the mountains in the summer. -And this is proved [Footnote 5. 6.: _Per la_ 4_a di questo_. It is -impossible to ascertain what this quotation refers to. _Questo_ -certainly does not mean the MS. in hand, nor any other now known to -us. The same remark applies to the phrase in line 15: _per la_ 2_a -di questo_.] in the 4th of this which says: Among mountains seen -from a great distance those will look of the bluest colour which are -in themselves the darkest; hence, when the trees are stripped of -their leaves, they will show a bluer tinge which will be in itself -darker; therefore, when the trees have lost their leaves they will -look of a gray colour, while, with their leaves, they are green, and -in proportion as the green is darker than the grey hue the green -will be of a bluer tinge than the gray. Also by the 2nd of this: The -shadows of trees covered with leaves are darker than the shadows of -those trees which have lost their leaves in proportion as the trees -covered with leaves are denser than those without leaves--and thus -my meaning is proved. - -The definition of the blue colour of the atmosphere explains why the -landscape is bluer in the summer than in the winter. - -462. - -OF PAINTING IN A LANDSCAPE. - -If the slope of a hill comes between the eye and the horizon, -sloping towards the eye, while the eye is opposite the middle of the -height of this slope, then that hill will increase in darkness -throughout its length. This is proved by the 7th of this which says -that a tree looks darkest when it is seen from below; the -proposition is verified, since this hill will, on its upper half -show all its trees as much from the side which is lighted by the -light of the sky, as from that which is in shade from the darkness -of the earth; whence it must result that these trees are of a medium -darkness. And from this [middle] spot towards the base of the hill, -these trees will be lighter by degrees by the converse of the 7th -and by the said 7th: For trees so placed, the nearer they are to the -summit of the hill the darker they necessarily become. But this -darkness is not in proportion to the distance, by the 8th of this -which says: That object shows darkest which is [seen] in the -clearest atmosphere; and by the 10th: That shows darkest which -stands out against a lighter background. - -[Footnote: The quotation in this passage again cannot be verified.] - -463. - -OF LANDSCAPES. - -The colours of the shadows in mountains at a great distance take a -most lovely blue, much purer than their illuminated portions. And -from this it follows that when the rock of a mountain is reddish the -illuminated portions are violet (?) and the more they are lighted -the more they display their proper colour. - -464. - -A place is most luminous when it is most remote from mountains. - -On the treatment of light for views of towns (465-469). - -465. - -OF LIGHT AND SHADOW IN A TOWN. - -When the sun is in the East and the eye is above the centre of a -town, the eye will see the Southern part of the town with its roofs -half in shade and half in light, and the same towards the North; the -Eastern side will be all in shadow and the Western will be all in -light. - -466. - -Of the houses of a town, in which the divisions between the houses -may be distinguished by the light which fall on the mist at the -bottom. If the eye is above the houses the light seen in the space -that is between one house and the next sinks by degrees into thicker -mist; and yet, being less transparent, it appears whiter; and if the -houses are some higher than the others, since the true [colour] is -always more discernible through the thinner atmosphere, the houses -will look darker in proportion as they are higher up. Let _n o p q_ -represent the various density of the atmosphere thick with moisture, -_a_ being the eye, the house _b c_ will look lightest at the bottom, -because it is in a thicker atmosphere; the lines _c d f_ will appear -equally light, for although _f_ is more distant than _c_, it is -raised into a thinner atmosphere, if the houses _b e_ are of the -same height, because they cross a brightness which is varied by -mist, but this is only because the line of the eye which starts from -above ends by piercing a lower and denser atmosphere at _d_ than at -_b_. Thus the line a _f_ is lower at _f_ than at _c_; and the house -_f_ will be seen darker at _e_ from the line _e k_ as far as _m_, -than the tops of the houses standing in front of it. - -467. - -OF TOWNS OR OTHER BUILDINGS SEEN IN THE EVENING OR THE MORNING -THROUGH THE MIST. - -Of buildings seen at a great distance in the evening or the morning, -as in mist or dense atmosphere, only those portions are seen in -brightness which are lighted up by the sun which is near the -horizon; and those portions which are not lighted up by the sun -remain almost of the same colour and medium tone as the mist. - -WHY OBJECTS WHICH ARE HIGH UP AND AT A DISTANCE ARE DARKER THAN THE -LOWER ONES, EVEN IF THE MIST IS UNIFORMLY DENSE. - -Of objects standing in a mist or other dense atmosphere, whether -from vapour or smoke or distance, those will be most visible which -are the highest. And among objects of equal height that will be the -darkest [strongest] which has for background the deepest mist. Thus -the eye _h_ looking at _a b c_, towers of equal height, one with -another, sees _c_ the top of the first tower at _r_, at two degrees -of depth in the mist; and sees the height of the middle tower _b_ -through one single degree of mist. Therefore the top of the tower -_c_ appears stronger than the top of the tower _b_, &c. - -468. - -OF THE SMOKE OF A TOWN. - -Smoke is seen better and more distinctly on the Eastern side than on -the Western when the sun is in the East; and this arises from two -causes; the first is that the sun, with its rays, shines through the -particles of the smoke and lights them up and makes them visible. -The second is that the roofs of the houses seen in the East at this -time are in shadow, because their obliquity does not allow of their -being illuminated by the sun. And the same thing occurs with dust; -and both one and the other look the lighter in proportion as they -are denser, and they are densest towards the middle. - -469. - -OF SMOKE AND DUST. - -If the sun is in the East the smoke of cities will not be visible in -the West, because on that side it is not seen penetrated by the -solar rays, nor on a dark background; since the roofs of the houses -turn the same side to the eye as they turn towards the sun, and on -this light background the smoke is not very visible. - -But dust, under the same aspect, will look darker than smoke being -of denser material than smoke which is moist. - -The effect of wind on trees (470-473). - -470. - -OF REPRESENTING WIND. - -In representing wind, besides the bending of the boughs and the -reversing of their leaves towards the quarter whence the wind comes, -you should also represent them amid clouds of fine dust mingled with -the troubled air. - -471. - -Describe landscapes with the wind, and the water, and the setting -and rising of the sun. - -THE WIND. - -All the leaves which hung towards the earth by the bending of the -shoots with their branches, are turned up side down by the gusts of -wind, and here their perspective is reversed; for, if the tree is -between you and the quarter of the wind, the leaves which are -towards you remain in their natural aspect, while those on the -opposite side which ought to have their points in a contrary -direction have, by being turned over, their points turned towards -you. - -472. - -Trees struck by the force of the wind bend to the side towards which -the wind is blowing; and the wind being past they bend in the -contrary direction, that is in reverse motion. - -473. - -That portion of a tree which is farthest from the force which -strikes it is the most injured by the blow because it bears most -strain; thus nature has foreseen this case by thickening them in -that part where they can be most hurt; and most in such trees as -grow to great heights, as pines and the like. [Footnote: Compare the -sketch drawn with a pen and washed with Indian ink on Pl. XL, No. 1. -In the Vatican copy we find, under a section entitled '_del fumo_', -the following remark: _Era sotto di questo capitulo un rompimento di -montagna, per dentro delle quali roture scherzaua fiame di fuoco, -disegnate di penna et ombrate d'acquarella, da uedere cosa mirabile -et uiua (Ed. MANZI, p. 235. Ed. LUDWIG, Vol. I, 460). This appears -to refer to the left hand portion of the drawing here given from the -Windsor collection, and from this it must be inferred, that the leaf -as it now exists in the library of the Queen of England, was already -separated from the original MS. at the time when the Vatican copy -was made.] - -Light and shade on clouds (474-477). - -474. - -Describe how the clouds are formed and how they dissolve, and what -cause raises vapour. - -475. - -The shadows in clouds are lighter in proportion as they are nearer -to the horizon. - -[Footnote: The drawing belonging to this was in black chalk and is -totally effaced.] - -476. - -When clouds come between the sun and the eye all the upper edges of -their round forms are light, and towards the middle they are dark, -and this happens because towards the top these edges have the sun -above them while you are below them; and the same thing happens with -the position of the branches of trees; and again the clouds, like -the trees, being somewhat transparent, are lighted up in part, and -at the edges they show thinner. - -But, when the eye is between the cloud and the sun, the cloud has -the contrary effect to the former, for the edges of its mass are -dark and it is light towards the middle; and this happens because -you see the same side as faces the sun, and because the edges have -some transparency and reveal to the eye that portion which is hidden -beyond them, and which, as it does not catch the sunlight like that -portion turned towards it, is necessarily somewhat darker. Again, it -may be that you see the details of these rounded masses from the -lower side, while the sun shines on the upper side and as they are -not so situated as to reflect the light of the sun, as in the first -instance they remain dark. - -The black clouds which are often seen higher up than those which are -illuminated by the sun are shaded by other clouds, lying between -them and the sun. - -Again, the rounded forms of the clouds that face the sun, show their -edges dark because they lie against the light background; and to see -that this is true, you may look at the top of any cloud that is -wholly light because it lies against the blue of the atmosphere, -which is darker than the cloud. - -[Footnote: A drawing in red chalk from the Windsor collection (see -Pl. XXIX), representing a landscape with storm-clouds, may serve to -illustrate this section as well as the following one.] - -477. - -OF CLOUDS, SMOKE AND DUST AND THE FLAMES OF A FURNACE OR OF A -BURNING KILN. - -The clouds do not show their rounded forms excepting on the sides -which face the sun; on the others the roundness is imperceptible -because they are in the shade. [Footnote: The text of this chapter -is given in facsimile on Pls. XXXVI and XXXVII. The two halves of -the leaf form but one in the original. On the margin close to lines -4 and 5 is the note: _rossore d'aria inverso l'orizonte_--(of the -redness of the atmosphere near the horizon). The sketches on the -lower portion of the page will be spoken of in No. 668.] - -If the sun is in the East and the clouds in the West, the eye placed -between the sun and the clouds sees the edges of the rounded forms -composing these clouds as dark, and the portions which are -surrounded by this dark [edge] are light. And this occurs because -the edges of the rounded forms of these clouds are turned towards -the upper or lateral sky, which is reflected in them. - -Both the cloud and the tree display no roundness at all on their -shaded side. - -On images reflected in water. - -478. - -Painters often deceive themselves, by representing water in which -they make the water reflect the objects seen by the man. But the -water reflects the object from one side and the man sees it from the -other; and it often happens that the painter sees an object from -below, and thus one and the same object is seen from hind part -before and upside down, because the water shows the image of the -object in one way, and the eye sees it in another. - -Of rainbows and rain (479. 480). - -479. - -The colours in the middle of the rainbow mingle together. - -The bow in itself is not in the rain nor in the eye that sees it; -though it is generated by the rain, the sun, and the eye. The -rainbow is always seen by the eye that is between the rain and the -body of the sun; hence if the sun is in the East and the rain is in -the West it will appear on the rain in the West. - -480. - -When the air is condensed into rain it would produce a vacuum if the -rest of the air did not prevent this by filling its place, as it -does with a violent rush; and this is the wind which rises in the -summer time, accompanied by heavy rain. - -Of flower seeds. - -481. - -All the flowers which turn towards the sun perfect their seeds; but -not the others; that is to say those which get only the reflection -of the sun. - -IX. - -_The Practice of Painting._ - -_It is hardly necessary to offer any excuses for the division -carried out in the arrangement of the text into practical -suggestions and theoretical enquiries. It was evidently intended by -Leonardo himself as we conclude from incidental remarks in the MSS. -(for instance No_ 110_). The fact that this arrangement was never -carried out either in the old MS. copies or in any edition since, is -easily accounted for by the general disorder which results from the -provisional distribution of the various chapters in the old copies. -We have every reason to believe that the earliest copyists, in -distributing the materials collected by them, did not in the least -consider the order in which the original MS.lay before them._ - -_It is evident that almost all the chapters which refer to the -calling and life of the painter--and which are here brought together -in the first section (Nos._ 482-508_)--may be referred to two -distinct periods in Leonardo's life; most of them can be dated as -belonging to the year_ 1492 _or to_ 1515. _At about this later time -Leonardo may have formed the project of completing his Libro della -Pittura, after an interval of some years, as it would seem, during -which his interest in the subject had fallen somewhat into the -background._ - -_In the second section, which treats first of the artist's studio, -the construction of a suitable window forms the object of careful -investigations; the special importance attached to this by Leonardo -is sufficiently obvious. His theory of the incidence of light which -was fully discussed in a former part of this work, was to him by no -means of mere abstract value, but, being deduced, as he says, from -experience (or experiment) was required to prove its utility in -practice. Connected with this we find suggestions for the choice of -a light with practical hints as to sketching a picture and some -other precepts of a practical character which must come under -consideration in the course of completing the painting. In all this -I have followed the same principle of arrangement in the text as was -carried out in the Theory of Painting, thus the suggestions for the -Perspective of a picture, (Nos._ 536-569_), are followed by the -theory of light and shade for the practical method of optics (Nos._ -548--566_) and this by the practical precepts or the treatment of -aerial perspective (_567--570_)._ - -_In the passage on Portrait and Figure Painting the principles of -painting as applied to a bust and head are separated and placed -first, since the advice to figure painters must have some connection -with the principles of the treatment of composition by which they -are followed._ - -_But this arrangement of the text made it seem advisable not to pick -out the practical precepts as to the representation of trees and -landscape from the close connection in which they were originally -placed--unlike the rest of the practical precepts--with the theory -of this branch of the subject. They must therefore be sought under -the section entitled Botany for Painters._ - -_As a supplement to the_ Libro di Pittura _I have here added those -texts which treat of the Painter's materials,--as chalk, drawing -paper, colours and their preparation, of the management of oils and -varnishes; in the appendix are some notes on chemical substances. -Possibly some of these, if not all, may have stood in connection -with the preparation of colours. It is in the very nature of things -that Leonardo's incidental indications as to colours and the like -should be now-a-days extremely obscure and could only be explained -by professional experts--by them even in but few instances. It might -therefore have seemed advisable to reproduce exactly the original -text without offering any translation. The rendering here given is -merely an attempt to suggest what Leonardo's meaning may have been._ - -_LOMAZZO tells us in his_ Trattato dell'arte della Pittura, Scultura -ed Architettura (Milano 1584, libro II, Cap. XIV): "Va discorrendo -ed argomentando Leonardo Vinci in un suo libro letto da me (?) -questi anni passati, ch'egli scrisse di mano stanca ai prieghi di -LUDOVICO SFORZA duca di Milano, in determinazione di questa -questione, se e piu nobile la pittura o la scultura; dicendo che -quanto piu un'arte porta seco fatica di corpo, e sudore, tanto piu e -vile, e men pregiata". _But the existence of any book specially -written for Lodovico il Moro on the superiority of Painting over -sculpture is perhaps mythical. The various passages in praise of -Painting as compared not merely with Sculpture but with Poetry, are -scattered among MSS. of very different dates._ - -_Besides, the way, in which the subject is discussed appears not to -support the supposition, that these texts were prepared at a special -request of the Duke._ - -I. - -MORAL PRECEPTS FOR THE STUDENT OF PAINTING. - -How to ascertain the dispositions for an artistic career. - -482. - -A WARNING CONCERNING YOUTHS WISHING TO BE PAINTERS. - -Many are they who have a taste and love for drawing, but no talent; -and this will be discernible in boys who are not diligent and never -finish their drawings with shading. - -The course of instruction for an artist (483-485). - -483. - -The youth should first learn perspective, then the proportions of -objects. Then he may copy from some good master, to accustom himself -to fine forms. Then from nature, to confirm by practice the rules he -has learnt. Then see for a time the works of various masters. Then -get the habit of putting his art into practice and work. - -[Footnote: The Vatican copy and numerous abridgements all place this -chapter at the beginning of the _Trattato_, and in consequence -DUFRESNE and all subsequent editors have done the same. In the -Vatican copy however all the general considerations on the relation -of painting to the other arts are placed first, as introductory.] - -484. - -OF THE ORDER OF LEARNING TO DRAW. - -First draw from drawings by good masters done from works of art and -from nature, and not from memory; then from plastic work, with the -guidance of the drawing done from it; and then from good natural -models and this you must put into practice. - -485. - -PRECEPTS FOR DRAWING. - -The artist ought first to exercise his hand by copying drawings from -the hand of a good master. And having acquired that practice, under -the criticism of his master, he should next practise drawing objects -in relief of a good style, following the rules which will presently -be given. - -The study of the antique (486. 487). - -486. - -OF DRAWING. - -Which is best, to draw from nature or from the antique? and which is -more difficult to do outlines or light and shade? - -487. - -It is better to imitate [copy] the antique than modern work. - -[Footnote 486, 487: These are the only two passages in which -Leonardo alludes to the importance of antique art in the training of -an artist. The question asked in No. 486 remains unanswered by him -and it seems to me very doubtful whether the opinion stated in No. -487 is to be regarded as a reply to it. This opinion stands in the -MS. in a connection--as will be explained later on--which seems to -require us to limit its application to a single special case. At any -rate we may suspect that when Leonardo put the question, he felt -some hesitation as to the answer. Among his very numerous drawings I -have not been able to find a single study from the antique, though a -drawing in black chalk, at Windsor, of a man on horseback (PI. -LXXIII) may perhaps be a reminiscence of the statue of Marcus -Aurelius at Rome. It seems to me that the drapery in a pen and ink -drawing of a bust, also at Windsor, has been borrowed from an -antique model (Pl. XXX). G. G. Rossi has, I believe, correctly -interpreted Leonardo's feeling towards the antique in the following -note on this passage in manzi's edition, p. 501: "Sappiamo dalla -storia, che i valorosi artisti Toscani dell'eta dell'oro dell'arte -studiarono sugli antichi marmi raccolti dal Magnifico LORENZO DE' -MEDICI. Pare che il Vinci a tali monumenti non si accostasse. Quest' -uomo sempre riconosce per maestra la natura, e questo principio lo -stringeva alla sola imitazione di essa"--Compare No. 10, 26--28 -footnote.] - -The necessity of anatomical knowledge (488. 489). - -488. - -OF PAINTING. - -It is indispensable to a Painter who would be thoroughly familiar -with the limbs in all the positions and actions of which they are -capable, in the nude, to know the anatomy of the sinews, bones, -muscles and tendons so that, in their various movements and -exertions, he may know which nerve or muscle is the cause of each -movement and show those only as prominent and thickened, and not the -others all over [the limb], as many do who, to seem great -draughtsmen, draw their nude figures looking like wood, devoid of -grace; so that you would think you were looking at a sack of walnuts -rather than the human form, or a bundle of radishes rather than the -muscles of figures. - -489. - -HOW IT IS NECESSARY TO A PAINTER THAT HE SHOULD KNOW THE INTRINSIC -FORMS [STRUCTURE] OF MAN. - -The painter who is familiar with the nature of the sinews, muscles, -and tendons, will know very well, in giving movement to a limb, how -many and which sinews cause it; and which muscle, by swelling, -causes the contraction of that sinew; and which sinews, expanded -into the thinnest cartilage, surround and support the said muscle. -Thus he will variously and constantly demonstrate the different -muscles by means of the various attitudes of his figures, and will -not do, as many who, in a variety of movements, still display the -very same things [modelling] in the arms, back, breast and legs. And -these things are not to be regarded as minor faults. - -How to acquire practice. - -490. - -OF STUDY AND THE ORDER OF STUDY. - -I say that first you ought to learn the limbs and their mechanism, -and having this knowledge, their actions should come next, according -to the circumstances in which they occur in man. And thirdly to -compose subjects, the studies for which should be taken from natural -actions and made from time to time, as circumstances allow; and pay -attention to them in the streets and _piazze_ and fields, and note -them down with a brief indication of the forms; [Footnote 5: Lines -5-7 explained by the lower portion of the sketch No. 1 on Pl. XXXI.] -thus for a head make an o, and for an arm a straight or a bent line, -and the same for the legs and the body, [Footnote 7: Lines 5-7 -explained by the lower portion of the sketch No. 1 on Pl. XXXI.] and -when you return home work out these notes in a complete form. The -Adversary says that to acquire practice and do a great deal of work -it is better that the first period of study should be employed in -drawing various compositions done on paper or on walls by divers -masters, and that in this way practice is rapidly gained, and good -methods; to which I reply that the method will be good, if it is -based on works of good composition and by skilled masters. But since -such masters are so rare that there are but few of them to be found, -it is a surer way to go to natural objects, than to those which are -imitated from nature with great deterioration, and so form bad -methods; for he who can go to the fountain does not go to the -water-jar. - -[Footnote: This passage has been published by Dr. M. JORDAN, _Das -Malerbuck des L. da Vinci_, p. 89; his reading however varies -slightly from mine.] - -Industry and thoroughness the first conditions (491-493.) - -491. - -WHAT RULES SHOULD BE GIVEN TO BOYS LEARNING TO PAINT. - -We know for certain that sight is one of the most rapid actions we -can perform. In an instant we see an infinite number of forms, still -we only take in thoroughly one object at a time. Supposing that you, -Reader, were to glance rapidly at the whole of this written page, -you would instantly perceive that it was covered with various -letters; but you could not, in the time, recognise what the letters -were, nor what they were meant to tell. Hence you would need to see -them word by word, line by line to be able to understand the -letters. Again, if you wish to go to the top of a building you must -go up step by step; otherwise it will be impossible that you should -reach the top. Thus I say to you, whom nature prompts to pursue this -art, if you wish to have a sound knowledge of the forms of objects -begin with the details of them, and do not go on to the second -[step] till you have the first well fixed in memory and in practice. -And if you do otherwise you will throw away your time, or certainly -greatly prolong your studies. And remember to acquire diligence -rather than rapidity. - -492. - -HOW THAT DILIGENCE [ACCURACY] SHOULD FIRST BE LEARNT RATHER THAN -RAPID EXECUTION. - -If you, who draw, desire to study well and to good purpose, always -go slowly to work in your drawing; and discriminate in. the lights, -which have the highest degree of brightness, and to what extent and -likewise in the shadows, which are those that are darker than the -others and in what way they intermingle; then their masses and the -relative proportions of one to the other. And note in their -outlines, which way they tend; and which part of the lines is curved -to one side or the other, and where they are more or less -conspicuous and consequently broad or fine; and finally, that your -light and shade blend without strokes and borders [but] looking like -smoke. And when you have thus schooled your hand and your judgment -by such diligence, you will acquire rapidity before you are aware. - -The artist's private life and choice of company (493-494). - -493. - -OF THE LIFE OF THE PAINTER IN THE COUNTRY. - -A painter needs such mathematics as belong to painting. And the -absence of all companions who are alienated from his studies; his -brain must be easily impressed by the variety of objects, which -successively come before him, and also free from other cares -[Footnote 6: Leonardo here seems to be speaking of his own method of -work as displayed in his MSS. and this passage explains, at least in -part, the peculiarities in their arrangement.]. And if, when -considering and defining one subject, a second subject -intervenes--as happens when an object occupies the mind, then he -must decide which of these cases is the more difficult to work out, -and follow that up until it becomes quite clear, and then work out -the explanation of the other [Footnote 11: Leonardo here seems to be -speaking of his own method of work as displayed in his MSS. and this -passage explains, at least in part, the peculiarities in their -arrangement.]. And above all he must keep his mind as clear as the -surface of a mirror, which assumes colours as various as those of -the different objects. And his companions should be like him as to -their studies, and if such cannot be found he should keep his -speculations to himself alone, so that at last he will find no more -useful company [than his own]. - -[Footnote: In the title line Leonardo had originally written _del -pictore filosofo_ (the philosophical painter), but he himself struck -out_filosofo_. Compare in No. 363 _pictora notomista_ (anatomical -painter). The original text is partly reproduced on Pl. CI.] - -494. - -OF THE LIFE OF THE PAINTER IN HIS STUDIO. - -To the end that well-being of the body may not injure that of the -mind, the painter or draughtsman must remain solitary, and -particularly when intent on those studies and reflections which will -constantly rise up before his eye, giving materials to be well -stored in the memory. While you are alone you are entirely your own -[master] and if you have one companion you are but half your own, -and the less so in proportion to the indiscretion of his behaviour. -And if you have many companions you will fall deeper into the same -trouble. If you should say: "I will go my own way and withdraw -apart, the better to study the forms of natural objects", I tell -you, you will not be able to help often listening to their chatter. -And so, since one cannot serve two masters, you will badly fill the -part of a companion, and carry out your studies of art even worse. -And if you say: "I will withdraw so far that their words cannot -reach me and they cannot disturb me", I can tell you that you will -be thought mad. But, you see, you will at any rate be alone. And if -you must have companions ship find it in your studio. This may -assist you to have the advantages which arise from various -speculations. All other company may be highly mischievous. - -The distribution of time for studying (495-497). - -495. - -OF WHETHER IT IS BETTER TO DRAW WITH COMPANIONS OR NOT. - -I say and insist that drawing in company is much better than alone, -for many reasons. The first is that you would be ashamed to be seen -behindhand among the students, and such shame will lead you to -careful study. Secondly, a wholesome emulation will stimulate you to -be among those who are more praised than yourself, and this praise -of others will spur you on. Another is that you can learn from the -drawings of others who do better than yourself; and if you are -better than they, you can profit by your contempt for their defects, -while the praise of others will incite you to farther merits. - -[Footnote: The contradiction by this passage of the foregoing -chapter is only apparent. It is quite clear, from the nature of the -reasoning which is here used to prove that it is more improving to -work with others than to work alone, that the studies of pupils only -are under consideration here.] - -496. - -OF STUDYING, IN THE DARK, WHEN YOU WAKE, OR IN BED BEFORE YOU GO TO -SLEEP. - -I myself have proved it to be of no small use, when in bed in the -dark, to recall in fancy the external details of forms previously -studied, or other noteworthy things conceived by subtle speculation; -and this is certainly an admirable exercise, and useful for -impressing things on the memory. - -497. - -OF THE TIME FOR STUDYING SELECTION OF SUBJECTS. - -Winter evenings ought to be employed by young students in looking -over the things prepared during the summer; that is, all the -drawings from the nude done in the summer should be brought together -and a choice made of the best [studies of] limbs and bodies among -them, to apply in practice and commit to memory. - -OF POSITIONS. - -After this in the following summer you should select some one who is -well grown and who has not been brought up in doublets, and so may -not be of stiff carriage, and make him go through a number of agile -and graceful actions; and if his muscles do not show plainly within -the outlines of his limbs that does not matter at all. It is enough -that you can see good attitudes and you can correct [the drawing of] -the limbs by those you studied in the winter. - -[Footnote: An injunction to study in the evening occurs also in No. -524.] - -On the productive power of minor artists (498-501). - -498. - -He is a poor disciple who does not excel his master. - -499. - -Nor is the painter praiseworthy who does but one thing well, as the -nude figure, heads, draperies, animals, landscapes or other such -details, irrespective of other work; for there can be no mind so -inept, that after devoting itself to one single thing and doing it -constantly, it should fail to do it well. - -[Footnote: In MANZI'S edition (p. 502) the painter G. G. Bossi -indignantly remarks on this passage. "_Parla il Vince in questo -luogo come se tutti gli artisti avessero quella sublimita d'ingegno -capace di abbracciare tutte le cose, di cui era egli dotato"_ And he -then mentions the case of CLAUDE LORRAIN. But he overlooks the fact -that in Leonardo's time landscape painting made no pretensions to -independence but was reckoned among the details (_particulari_, -lines 3, 4).] - -500. - -THAT A PAINTER IS NOT ADMIRABLE UNLESS HE IS UNIVERSAL. - -Some may distinctly assert that those persons are under a delusion -who call that painter a good master who can do nothing well but a -head or a figure. Certainly this is no great achievement; after -studying one single thing for a life-time who would not have -attained some perfection in it? But, since we know that painting -embraces and includes in itself every object produced by nature or -resulting from the fortuitous actions of men, in short, all that the -eye can see, he seems to me but a poor master who can only do a -figure well. For do you not perceive how many and various actions -are performed by men only; how many different animals there are, as -well as trees, plants, flowers, with many mountainous regions and -plains, springs and rivers, cities with public and private -buildings, machines, too, fit for the purposes of men, divers -costumes, decorations and arts? And all these things ought to be -regarded as of equal importance and value, by the man who can be -termed a good painter. - -501. - -OF THE MISERABLE PRETENCES MADE BY THOSE WHO FALSELY AND UNWORTHILY -ACQUIRE THE NAME OF PAINTERS. - -Now there is a certain race of painters who, having studied but -little, must need take as their standard of beauty mere gold and -azure, and these, with supreme conceit, declare that they will not -give good work for miserable payment, and that they could do as well -as any other if they were well paid. But, ye foolish folks! cannot -such artists keep some good work, and then say: this is a costly -work and this more moderate and this is average work and show that -they can work at all prices? - -A caution against one-sided study. - -502. - -HOW, IN IMPORTANT WORKS, A MAN SHOULD NOT TRUST ENTIRELY TO HIS -MEMORY WITHOUT CONDESCENDING TO DRAW FROM NATURE. - -Any master who should venture to boast that he could remember all -the forms and effects of nature would certainly appear to me to be -graced with extreme ignorance, inasmuch as these effects are -infinite and our memory is not extensive enough to retain them. -Hence, O! painter, beware lest the lust of gain should supplant in -you the dignity of art; for the acquisition of glory is a much -greater thing than the glory of riches. Hence, for these and other -reasons which might be given, first strive in drawing to represent -your intention to the eye by expressive forms, and the idea -originally formed in your imagination; then go on taking out or -putting in, until you have satisfied yourself. Then have living men, -draped or nude, as you may have purposed in your work, and take care -that in dimensions and size, as determined by perspective, nothing -is left in the work which is not in harmony with reason and the -effects in nature. And this will be the way to win honour in your -art. - -How to acquire universality (503-506). - -503. - -OF VARIETY IN THE FIGURES. - -The painter should aim at universality, because there is a great -want of self-respect in doing one thing well and another badly, as -many do who study only the [rules of] measure and proportion in the -nude figure and do not seek after variety; for a man may be well -proportioned, or he may be fat and short, or tall and thin, or -medium. And a painter who takes no account of these varieties always -makes his figures on one pattern so that they might all be taken for -brothers; and this is a defect that demands stern reprehension. - -504. - -HOW SOMETHING MAY BE LEARNT EVERYWHERE. - -Nature has beneficently provided that throughout the world you may -find something to imitate. - -505. - -OF THE MEANS OF ACQUIRING UNIVERSALITY. - -It is an easy matter to men to acquire universality, for all -terrestrial animals resemble each other as to their limbs, that is -in their muscles, sinews and bones; and they do not vary excepting -in length or in thickness, as will be shown under Anatomy. But then -there are aquatic animals which are of great variety; I will not try -to convince the painter that there is any rule for them for they are -of infinite variety, and so is the insect tribe. - -506. - -PAINTING. - -The mind of the painter must resemble a mirror, which always takes -the colour of the object it reflects and is completely occupied by -the images of as many objects as are in front of it. Therefore you -must know, Oh Painter! that you cannot be a good one if you are not -the universal master of representing by your art every kind of form -produced by nature. And this you will not know how to do if you do -not see them, and retain them in your mind. Hence as you go through -the fields, turn your attention to various objects, and, in turn -look now at this thing and now at that, collecting a store of divers -facts selected and chosen from those of less value. But do not do -like some painters who, when they are wearied with exercising their -fancy dismiss their work from their thoughts and take exercise in -walking for relaxation, but still keep fatigue in their mind which, -though they see various objects [around them], does not apprehend -them; but, even when they meet friends or relations and are saluted -by them, although they see and hear them, take no more cognisance of -them than if they had met so much empty air. - -Useful games and exercises (507. 508). - -507. - -OF GAMES TO BE PLAYED BY THOSE WHO DRAW. - -When, Oh draughtsmen, you desire to find relaxation in games you -should always practise such things as may be of use in your -profession, by giving your eye good practice in judging accurately -of the breadth and length of objects. Thus, to accustom your mind to -such things, let one of you draw a straight line at random on a -wall, and each of you, taking a blade of grass or of straw in his -hand, try to cut it to the length that the line drawn appears to him -to be, standing at a distance of 10 braccia; then each one may go up -to the line to measure the length he has judged it to be. And he who -has come nearest with his measure to the length of the pattern is -the best man, and the winner, and shall receive the prize you have -settled beforehand. Again you should take forshortened measures: -that is take a spear, or any other cane or reed, and fix on a point -at a certain distance; and let each one estimate how many times he -judges that its length will go into that distance. Again, who will -draw best a line one braccio long, which shall be tested by a -thread. And such games give occasion to good practice for the eye, -which is of the first importance in painting. - -508. - -A WAY OF DEVELOPING AND AROUSING THE MIND TO VARIOUS INVENTIONS. - -I cannot forbear to mention among these precepts a new device for -study which, although it may seem but trivial and almost ludicrous, -is nevertheless extremely useful in arousing the mind to various -inventions. And this is, when you look at a wall spotted with -stains, or with a mixture of stones, if you have to devise some -scene, you may discover a resemblance to various landscapes, -beautified with mountains, rivers, rocks, trees, plains, wide -valleys and hills in varied arrangement; or again you may see -battles and figures in action; or strange faces and costumes, and an -endless variety of objects, which you could reduce to complete and -well drawn forms. And these appear on such walls confusedly, like -the sound of bells in whose jangle you may find any name or word you -choose to imagine. - -II. - -THE ARTIST'S STUDIO.--INSTRUMENTS AND HELPS FOR THE APPLICATION OF -PERSPECTIVE.--ON JUDGING OF A PICTURE. - -On the size of the studio. - -509. - -Small rooms or dwellings discipline the mind, large ones weaken it. - -On the construction of windows (510-512). - -510. - -The larger the wall the less the light will be. - -511. - -The different kinds of light afforded in cellars by various forms of -windows. The least useful and the coldest is the window at _a_. The -most useful, the lightest and warmest and most open to the sky is -the window at _b_. The window at _c_ is of medium utility. - -[Footnote: From a reference to the notes on the right light for -painting it becomes evident that the observations made on -cellar-windows have a direct bearing on the construction of the -studio-window. In the diagram _b_ as well as in that under No. 510 -the window-opening is reduced to a minimum, but only, it would seem, -in order to emphasize the advantage of walls constructed on the plan -there shown.] - -512. - -OF THE PAINTER'S WINDOW AND ITS ADVANTAGE. - -The painter who works from nature should have a window, which he can -raise and lower. The reason is that sometimes you will want to -finish a thing you are drawing, close to the light. - -Let _a b c d_ be the chest on which the work may be raised or -lowered, so that the work moves up and down and not the painter. And -every evening you can let down the work and shut it up above so that -in the evening it may be in the fashion of a chest which, when shut -up, may serve the purpose of a bench. - -[Footnote: See Pl. XXXI, No. 2. In this plate the lines have -unfortunately lost their sharpness, for the accidental loss of the -negative has necessitated a reproduction from a positive. But having -formerly published this sketch by another process, in VON LUTZOW'S -_Zeitschrift fur bildende Kunst_ (Vol. XVII, pg. 13) I have -reproduced it here in the text. The sharpness of the outline in the -original sketch is here preserved but it gives it from the reversed -side.] - -On the best light for painting (513-520). - -513. - -Which light is best for drawing from nature; whether high or low, or -large or small, or strong and broad, or strong and small, or broad -and weak or small and weak? - -[Footnote: The question here put is unanswered in the original MS.] - -514. - -OF THE QUALITY OF THE LIGHT. - -A broad light high up and not too strong will render the details of -objects very agreeable. - -515. - -THAT THE LIGHT FOR DRAWING FROM NATURE SHOULD BE HIGH UP. - -The light for drawing from nature should come from the North in -order that it may not vary. And if you have it from the South, keep -the window screened with cloth, so that with the sun shining the -whole day the light may not vary. The height of the light should be -so arranged as that every object shall cast a shadow on the ground -of the same length as itself. - -516. - -THE KIND OF LIGHT REQUISITE FOR PAINTING LIGHT AND SHADE. - -An object will display the greatest difference of light and shade -when it is seen in the strongest light, as by sunlight, or, at -night, by the light of a fire. But this should not be much used in -painting because the works remain crude and ungraceful. - -An object seen in a moderate light displays little difference in the -light and shade; and this is the case towards evening or when the -day is cloudy, and works then painted are tender and every kind of -face becomes graceful. Thus, in every thing extremes are to be -avoided: Too much light gives crudeness; too little prevents our -seeing. The medium is best. - -OF SMALL LIGHTS. - -Again, lights cast from a small window give strong differences of -light and shade, all the more if the room lighted by it be large, -and this is not good for painting. - -517. - -PAINTING. - -The luminous air which enters by passing through orifices in walls -into dark rooms will render the place less dark in proportion as the -opening cuts into the walls which surround and cover in the -pavement. - -518. - -OF THE QUALITY OF LIGHT. - -In proportion to the number of times that _a b_ goes into _c d_ will -it be more luminous than _c d_. And similarly, in proportion as the -point _e_ goes into _c d_ will it be more luminous than _c d;_ and -this light is useful for carvers of delicate work. [Footnote 5: For -the same reason a window thus constructed would be convenient for an -illuminator or a miniature painter.] - -[Footnote: M. RAVAISSON in his edition of the Paris MS. A remarks on -this passage: _"La figure porte les lettres_ f _et_ g, _auxquelles -rien ne renvoie dans l'explication; par consequent, cette -explication est incomplete. La figure semblerait, d'ailleurs, se -rapporter a l'effet de la reflexion par un miroir concave."_ So far -as I can see the text is not imperfect, nor is the sense obscure. It -is hardly necessary to observe that _c d_ here indicate the wall of -the room opposite to the window _e_ and the semicircle described by -_f g_ stands for the arch of the sky; this occurs in various -diagrams, for example under 511. A similar semicircle, Pl III, No. 2 -(and compare No. 149) is expressly called '_orizonte_' in writing.] - -519. - -That the light should fall upon a picture from one window only. This -may be seen in the case of objects in this form. If you want to -represent a round ball at a certain height you must make it oval in -this shape, and stand so far off as that by foreshortening it -appears round. - -520. - -OF SELECTING THE LIGHT WHICH GIVES MOST GRACE TO FACES. - -If you should have a court yard that you can at pleasure cover with -a linen awning that light will be good. Or when you want to take a -portrait do it in dull weather, or as evening falls, making the -sitter stand with his back to one of the walls of the court yard. -Note in the streets, as evening falls, the faces of the men and -women, and when the weather is dull, what softness and delicacy you -may perceive in them. Hence, Oh Painter! have a court arranged with -the walls tinted black and a narrow roof projecting within the -walls. It should be 10 braccia wide and 20 braccia long and 10 -braccia high and covered with a linen awning; or else paint a work -towards evening or when it is cloudy or misty, and this is a perfect -light. - -On various helps in preparing a picture (521-530). - -521. - -To draw a nude figure from nature, or any thing else, hold in your -hand a plumb-line to enable you to judge of the relative position -of objects. - -522. - -OF DRAWING AN OBJECT. - -When you draw take care to set up a principal line which you must -observe all throughout the object you are drawing; every thing -should bear relation to the direction of this principal line. - -523. - -OF A MODE OF DRAWING A PLACE ACCURATELY. - -Have a piece of glass as large as a half sheet of royal folio paper -and set thus firmly in front of your eyes that is, between your eye -and the thing you want to draw; then place yourself at a distance of -2/3 of a braccia from the glass fixing your head with a machine in -such a way that you cannot move it at all. Then shut or entirely -cover one eye and with a brush or red chalk draw upon the glass that -which you see beyond it; then trace it on paper from the glass, -afterwards transfer it onto good paper, and paint it if you like, -carefully attending to the arial perspective. - -HOW TO LEARN TO PLACE YOUR FIGURES CORRECTLY. - -If you want to acquire a practice of good and correct attitudes for -your figures, make a square frame or net, and square it out with -thread; place this between your eye and the nude model you are -drawing, and draw these same squares on the paper on which you mean -to draw the figure, but very delicately. Then place a pellet of wax -on a spot of the net which will serve as a fixed point, which, -whenever you look at your model, must cover the pit of the throat; -or, if his back is turned, it may cover one of the vertebrae of the -neck. Thus these threads will guide you as to each part of the body -which, in any given attitude will be found below the pit of the -throat, or the angles of the shoulders, or the nipples, or hips and -other parts of the body; and the transverse lines of the net will -show you how much the figure is higher over the leg on which it is -posed than over the other, and the same with the hips, and the knees -and the feet. But always fix the net perpendicularly so that all the -divisions that you see the model divided into by the net work -correspond with your drawing of the model on the net work you have -sketched. The squares you draw may be as much smaller than those of -the net as you wish that your figure should be smaller than nature. -Afterwards remember when drawing figures, to use the rule of the -corresponding proportions of the limbs as you have learnt it from -the frame and net. This should be 3 braccia and a half high and 3 -braccia wide; 7 braccia distant from you and 1 braccio from the -model. - -[Footnote: Leonardo is commonly credited with the invention of the -arrangement of a plate of glass commonly known as the "vertical -plane." Professor E. VON BRUCKE in his _"Bruchstucke aus der Theorie -der bildenden Kunste,"_ Leipzig 1877, pg. 3, writes on this -contrivance. _"Unsere Glastafel ist die sogenannte Glastafel des -Leonardo da Vinci, die in Gestalt einer Glastafel vorgestellte -Bildflache."_] - -524. - -A METHOD OF DRAWING AN OBJECT IN RELIEF AT NIGHT. - -Place a sheet of not too transparent paper between the relievo and -the light and you can draw thus very well. - -[Footnote: Bodies thus illuminated will show on the surface of the -paper how the copyist has to distribute light and shade.] - -525. - -If you want to represent a figure on a wall, the wall being -foreshortened, while the figure is to appear in its proper form, and -as standing free from the wall, you must proceed thus: have a thin -plate of iron and make a small hole in the centre; this hole must be -round. Set a light close to it in such a position as that it shines -through the central hole, then place any object or figure you please -so close to the wall that it touches it and draw the outline of the -shadow on the wall; then fill in the shade and add the lights; place -the person who is to see it so that he looks through that same hole -where at first the light was; and you will never be able to persuade -yourself that the image is not detached from the wall. - -[Footnote: _uno piccolo spiracelo nel mezzo_. M. RAVAISSON, in his -edition of MS. A (Paris), p. 52, reads _nel muro_--evidently a -mistake for _nel mezzo_ which is quite plainly written; and he -translates it _"fait lui une petite ouverture dans le mur,"_ adding -in a note: _"les mots 'dans le mur' paraissent etre de trop. -Leonardo a du les ecrire par distraction"_ But _'nel mezzo'_ is -clearly legible even on the photograph facsimile given by Ravaisson -himself, and the objection he raises disappears at once. It is not -always wise or safe to try to prove our author's absence of mind or -inadvertence by apparent difficulties in the sense or connection of -the text.] - -526. - -TO DRAW A FIGURE ON A WALL 12 BRACCIA HIGH WHICH SHALL LOOK 24 -BRACCIA HIGH. - -If you wish to draw a figure or any other object to look 24 braccia -high you must do it in this way. First, on the surface _m r_ draw -half the man you wish to represent; then the other half; then put on -the vault _m n_ [the rest of] the figure spoken of above; first set -out the vertical plane on the floor of a room of the same shape as -the wall with the coved part on which you are to paint your figure. -Then, behind it, draw a figure set out in profile of whatever size -you please, and draw lines from it to the point _f_ and, as these -lines cut _m n_ on the vertical plane, so will the figure come on -the wall, of which the vertical plane gives a likeness, and you will -have all the [relative] heights and prominences of the figure. And -the breadth or thickness which are on the upright wall _m n_ are to -be drawn in their proper form, since, as the wall recedes the figure -will be foreshortened by itself; but [that part of] the figure which -goes into the cove you must foreshorten, as if it were standing -upright; this diminution you must set out on a flat floor and there -must stand the figure which is to be transferred from the vertical -plane _r n_[Footnote 17: _che leverai dalla pariete r n_. The -letters refer to the larger sketch, No. 3 on Pl. XXXI.] in its real -size and reduce it once more on a vertical plane; and this will be a -good method [Footnote 18: Leonardo here says nothing as to how the -image foreshortened by perspective and thus produced on the vertical -plane is to be transferred to the wall; but from what is said in -Nos. 525 and 523 we may conclude that he was familiar with the -process of casting the enlarged shadow of a squaring net on the -surface of a wall to guide him in drawing the figure. - -_Pariete di rilieuo; "sur une parai en relief"_ (RAVAISSON). _"Auf -einer Schnittlinie zum Aufrichten"_ (LUDWIG). The explanation of -this puzzling expression must be sought in No. 545, lines 15-17.]. - -[Footnote: See Pl. XXXI. 3. The second sketch, which in the plate is -incomplete, is here reproduced and completed from the original to -illustrate the text. In the original the larger diagram is placed -between lines 5 and 6. - -1. 2. C. A. 157a; 463a has the similar heading: '_del cressciere -della figura_', and the text begins: "_Se voli fare 1a figura -grande_ b c" but here it breaks off. The translation here given -renders the meaning of the passage as I think it must be understood. -The MS. is perfectly legible and the construction of the sentence is -simple and clear; difficulties can only arise from the very fullness -of the meaning, particularly towards the end of the passage.] - -527. - -If you would to draw a cube in an angle of a wall, first draw the -object in its own proper shape and raise it onto a vertical plane -until it resembles the angle in which the said object is to be -represented. - -528. - -Why are paintings seen more correctly in a mirror than out of it? - -529. - -HOW THE MIRROR IS THE MASTER [AND GUIDE] OF PAINTERS. - -When you want to see if your picture corresponds throughout with the -objects you have drawn from nature, take a mirror and look in that -at the reflection of the real things, and compare the reflected -image with your picture, and consider whether the subject of the two -images duly corresponds in both, particularly studying the mirror. -You should take the mirror for your guide--that is to say a flat -mirror--because on its surface the objects appear in many respects -as in a painting. Thus you see, in a painting done on a flat -surface, objects which appear in relief, and in the mirror--also a -flat surface--they look the same. The picture has one plane surface -and the same with the mirror. The picture is intangible, in so far -as that which appears round and prominent cannot be grasped in the -hands; and it is the same with the mirror. And since you can see -that the mirror, by means of outlines, shadows and lights, makes -objects appear in relief, you, who have in your colours far stronger -lights and shades than those in the mirror, can certainly, if you -compose your picture well, make that also look like a natural scene -reflected in a large mirror. - -[Footnote: I understand the concluding lines of this passage as -follows: If you draw the upper half a figure on a large sheet of -paper laid out on the floor of a room (_sala be piana_) to the same -scale (_con le sue vere grosseze_) as the lower half, already drawn -upon the wall (lines 10, 11)you must then reduce them on a '_pariete -di rilievo_,' a curved vertical plane which serves as a model to -reproduce the form of the vault.] - -530. - -OF JUDGING YOUR OWN PICTURES. - -We know very well that errors are better recognised in the works of -others than in our own; and that often, while reproving little -faults in others, you may ignore great ones in yourself. To avoid -such ignorance, in the first place make yourself a master of -perspective, then acquire perfect knowledge of the proportions of -men and other animals, and also, study good architecture, that is so -far as concerns the forms of buildings and other objects which are -on the face of the earth; these forms are infinite, and the better -you know them the more admirable will your work be. And in cases -where you lack experience do not shrink from drawing them from -nature. But, to carry out my promise above [in the title]--I say -that when you paint you should have a flat mirror and often look at -your work as reflected in it, when you will see it reversed, and it -will appear to you like some other painter's work, so you will be -better able to judge of its faults than in any other way. Again, it -is well that you should often leave off work and take a little -relaxation, because, when you come back to it you are a better -judge; for sitting too close at work may greatly deceive you. Again, -it is good to retire to a distance because the work looks smaller -and your eye takes in more of it at a glance and sees more easily -the discords or disproportion in the limbs and colours of the -objects. - -On the management of works (531. 532). - -531. - -OF A METHOD OF LEARNING WELL BY HEART. - -When you want to know a thing you have studied in your memory -proceed in this way: When you have drawn the same thing so many -times that you think you know it by heart, test it by drawing it -without the model; but have the model traced on flat thin glass and -lay this on the drawing you have made without the model, and note -carefully where the tracing does not coincide with your drawing, and -where you find you have gone wrong; and bear in mind not to repeat -the same mistakes. Then return to the model, and draw the part in -which you were wrong again and again till you have it well in your -mind. If you have no flat glass for tracing on, take some very thin -kidts-kin parchment, well oiled and dried. And when you have used it -for one drawing you can wash it clean with a sponge and make a -second. - -532. - -THAT A PAINTER OUGHT TO BE CURIOUS TO HEAR THE OPINIONS OF EVERY ONE -ON HIS WORK. - -Certainly while a man is painting he ought not to shrink from -hearing every opinion. For we know very well that a man, though he -may not be a painter, is familiar with the forms of other men and -very capable of judging whether they are hump backed, or have one -shoulder higher or lower than the other, or too big a mouth or nose, -and other defects; and, as we know that men are competent to judge -of the works of nature, how much more ought we to admit that they -can judge of our errors; since you know how much a man may be -deceived in his own work. And if you are not conscious of this in -yourself study it in others and profit by their faults. Therefore be -curious to hear with patience the opinions of others, consider and -weigh well whether those who find fault have ground or not for -blame, and, if so amend; but, if not make as though you had not -heard, or if he should be a man you esteem show him by argument the -cause of his mistake. - -On the limitations of painting (533-535) - -533. - -HOW IN SMALL OBJECTS ERRORS ARE LESS EVIDENT THAN IN LARGE ONES. - -In objects of minute size the extent of error is not so perceptible -as in large ones; and the reason is that if this small object is a -representation of a man or of some other animal, from the immense -diminution the details cannot be worked out by the artist with the -finish that is requisite. Hence it is not actually complete; and, -not being complete, its faults cannot be determined. For instance: -Look at a man at a distance of 300 braccia and judge attentively -whether he be handsome or ugly, or very remarkable or of ordinary -appearance. You will find that with the utmost effort you cannot -persuade yourself to decide. And the reason is that at such a -distance the man is so much diminished that the character of the -details cannot be determined. And if you wish to see how much this -man is diminished [by distance] hold one of your fingers at a span's -distance from your eye, and raise or lower it till the top joint -touches the feet of the figure you are looking at, and you will see -an incredible reduction. For this reason we often doubt as to the -person of a friend at a distance. - -534. - -WHY A PAINTING CAN NEVER APPEAR DETACHED AS NATURAL OBJECTS DO. - -Painters often fall into despair of imitating nature when they see -their pictures fail in that relief and vividness which objects have -that are seen in a mirror; while they allege that they have colours -which for brightness or depth far exceed the strength of light and -shade in the reflections in the mirror, thus displaying their own -ignorance rather than the real cause, because they do not know it. -It is impossible that painted objects should appear in such relief -as to resemble those reflected in the mirror, although both are seen -on a flat surface, unless they are seen with only one eye; and the -reason is that two eyes see one object behind another as _a_ and _b_ -see _m_ and _n_. _m_ cannot exactly occupy [the space of] _n_ -because the base of the visual lines is so broad that the second -body is seen beyond the first. But if you close one eye, as at _s_ -the body _f_ will conceal _r_, because the line of sight proceeds -from a single point and makes its base in the first body, whence the -second, of the same size, can never be seen. - -[Footnote: This passage contains the solution of the problem -proposed in No. 29, lines 10-14. Leonardo was evidently familiar -with the law of optics on which the construction of the stereoscope -depends. Compare E. VON BRUCKE, _Bruchstucke aus der Theorie der -bildenden Kunste_, pg. 69: "_Schon Leonardo da Vinci wusste, dass -ein noch so gut gemaltes Bild nie den vollen Eindruck der -Korperlichkeit geben kann, wie ihn die Natur selbst giebt. Er -erklart dies auch in Kap. LIII und Kap. CCCXLI_ (ed. DU FRESNE) -_des_ 'Trattato' _in sachgemasser Weise aus dem Sehen mit beiden -Augen_." - -Chap. 53 of DU FRESNE'S edition corresponds to No. 534 of this -work.] - -535. - -WHY OF TWO OBJECTS OF EQUAL SIZE A PAINTED ONE WILL LOOK LARGER THAN -A SOLID ONE. - -The reason of this is not so easy to demonstrate as many others. -Still I will endeavour to accomplish it, if not wholly, at any rate -in part. The perspective of diminution demonstrates by reason, that -objects diminish in proportion as they are farther from the eye, and -this reasoning is confirmed by experience. Hence, the lines of sight -that extend between the object and the eye, when they are directed -to the surface of a painting are all intersected at uniform limits, -while those lines which are directed towards a piece of sculpture -are intersected at various limits and are of various lengths. The -lines which are longest extend to a more remote limb than the others -and therefore that limb looks smaller. As there are numerous lines -each longer than the others--since there are numerous parts, each -more remote than the others and these, being farther off, -necessarily appear smaller, and by appearing smaller it follows that -their diminution makes the whole mass of the object look smaller. -But this does not occur in painting; since the lines of sight all -end at the same distance there can be no diminution, hence the parts -not being diminished the whole object is undiminished, and for this -reason painting does not diminish, as a piece of sculpture does. - -On the choice of a position (536-537) - -536. - -HOW HIGH THE POINT OF SIGHT SHOULD BE PLACED. - -The point of sight must be at the level of the eye of an ordinary -man, and the farthest limit of the plain where it touches the sky -must be placed at the level of that line where the earth and sky -meet; excepting mountains, which are independent of it. - -537. - -OF THE WAY TO DRAW FIGURES FOR HISTORICAL PICTURES. - -The painter must always study on the wall on which he is to picture -a story the height of the position where he wishes to arrange his -figures; and when drawing his studies for them from nature he must -place himself with his eye as much below the object he is drawing -as, in the picture, it will have to be above the eye of the -spectator. Otherwise the work will look wrong. - -The apparent size of figures in a picture (538-539) - -538. - -OF PLACING A FIGURE IN THE FOREGROUND OF A HISTORICAL PICTURE. - -You must make the foremost figure in the picture less than the size -of nature in proportion to the number of braccia at which you place -it from the front line, and make the others in proportion by the -above rule. - -539. - -PERSPECTIVE. - -You are asked, O Painter, why the figures you draw on a small scale -according to the laws of perspective do not appear--notwithstanding -the demonstration of distance--as large as real ones--their height -being the same as in those painted on the wall. - -And why [painted] objects seen at a small distance appear larger -than the real ones? - -The right position of the artist, when painting, and of the -spectator (540-547) - -540. - -OF PAINTING. - -When you draw from nature stand at a distance of 3 times the height -of the object you wish to draw. - -541. - -OF DRAWING FROM RELIEF. - -In drawing from the round the draughtsman should so place himself -that the eye of the figure he is drawing is on a level with his own. -This should be done with any head he may have to represent from -nature because, without exception, the figures or persons you meet -in the streets have their eyes on the same level as your own; and if -you place them higher or lower you will see that your drawing will -not be true. - -542. - -WHY GROUPS OF FIGURES ONE ABOVE ANOTHER ARE TO BE AVOIDED. - -The universal practice which painters adopt on the walls of chapels -is greatly and reasonably to be condemned. Inasmuch as they -represent one historical subject on one level with a landscape and -buildings, and then go up a step and paint another, varying the -point [of sight], and then a third and a fourth, in such a way as -that on one wall there are 4 points of sight, which is supreme folly -in such painters. We know that the point of sight is opposite the -eye of the spectator of the scene; and if you would [have me] tell -you how to represent the life of a saint divided into several -pictures on one and the same wall, I answer that you must set out -the foreground with its point of sight on a level with the eye of -the spectator of the scene, and upon this plane represent the more -important part of the story large and then, diminishing by degrees -the figures, and the buildings on various hills and open spaces, you -can represent all the events of the history. And on the remainder of -the wall up to the top put trees, large as compared with the -figures, or angels if they are appropriate to the story, or birds or -clouds or similar objects; otherwise do not trouble yourself with it -for your whole work will be wrong. - -543. - -A PICTURE OF OBJECTS IN PERSPECTIVE WILL LOOK MORE LIFELIKE WHEN -SEEN FROM THE POINT FROM WHICH THE OBJECTS WERE DRAWN. - -If you want to represent an object near to you which is to have the -effect of nature, it is impossible that your perspective should not -look wrong, with every false relation and disagreement of proportion -that can be imagined in a wretched work, unless the spectator, when -he looks at it, has his eye at the very distance and height and -direction where the eye or the point of sight was placed in doing -this perspective. Hence it would be necessary to make a window, or -rather a hole, of the size of your face through which you can look -at the work; and if you do this, beyond all doubt your work, if it -is correct as to light and shade, will have the effect of nature; -nay you will hardly persuade yourself that those objects are -painted; otherwise do not trouble yourself about it, unless indeed -you make your view at least 20 times as far off as the greatest -width or height of the objects represented, and this will satisfy -any spectator placed anywhere opposite to the picture. - -If you want the proof briefly shown, take a piece of wood in the -form of a little column, eight times as high as it is thick, like a -column without any plinth or capital; then mark off on a flat wall -40 equal spaces, equal to its width so that between them they make -40 columns resembling your little column; you then must fix, -opposite the centre space, and at 4 braccia from the wall, a thin -strip of iron with a small round hole in the middle about as large -as a big pearl. Close to this hole place a light touching it. Then -place your column against each mark on the wall and draw the outline -of its shadow; afterwards shade it and look through the hole in the -iron plate. - -[Footnote: In the original there is a wide space between lines 3 and -4 in which we find two sketches not belonging to the text. It is -unnecessary to give prominence to the points in which my reading -differs from that of M. RAVAISSON or to justify myself, since they -are all of secondary importance and can also be immediately verified -from the photograph facsimile in his edition.] - -544. - -A diminished object should be seen from the same distance, height -and direction as the point of sight of your eye, or else your -knowledge will produce no good effect. - -And if you will not, or cannot, act on this principle--because as -the plane on which you paint is to be seen by several persons you -would need several points of sight which would make it look -discordant and wrong--place yourself at a distance of at least 10 -times the size of the objects. - -The lesser fault you can fall into then, will be that of -representing all the objects in the foreground of their proper size, -and on whichever side you are standing the objects thus seen will -diminish themselves while the spaces between them will have no -definite ratio. For, if you place yourself in the middle of a -straight row [of objects], and look at several columns arranged in a -line you will see, beyond a few columns separated by intervals, that -the columns touch; and beyond where they touch they cover each -other, till the last column projects but very little beyond the last -but one. Thus the spaces between the columns are by degrees entirely -lost. So, if your method of perspective is good, it will produce the -same effect; this effect results from standing near the line in -which the columns are placed. This method is not satisfactory unless -the objects seen are viewed from a small hole, in the middle of -which is your point of sight; but if you proceed thus your work will -be perfect and will deceive the beholder, who will see the columns -as they are here figured. - -Here the eye is in the middle, at the point _a_ and near to the -columns. - -[Footnote: The diagram which stands above this chapter in the -original with the note belonging to it: "a b _e la ripruova_" (_a b_ -is the proof) has obviously no connection with the text. The second -sketch alone is reproduced and stands in the original between lines -22 and 23.] - -545. - -If you cannot arrange that those who look at your work should stand -at one particular point, when constructing your work, stand back -until your eye is at least 20 times as far off as the greatest -height and width of your work. This will make so little difference -when the eye of the spectator moves, that it will be hardly -appreciable, and it will look very good. - -If the point of sight is at _t_ you would make the figures on the -circle _d b e_ all of one size, as each of them bears the same -relation to the point _t_. But consider the diagram given below and -you will see that this is wrong, and why I shall make _b_ smaller -than _d e_ [Footnote 8: The second diagram of this chapter stands in -the original between lines 8 and 9.]. - -It is easy to understand that if 2 objects equal to each other are -placed side by side the one at 3 braccia distance looks smaller than -that placed at 2 braccia. This however is rather theoretical than -for practice, because you stand close by [Footnote 11: Instead of -'_se preso_' (=_sie presso_) M. RAVAISSON reads '_sempre se_' which -gives rise to the unmeaning rendering: '_parceque toujours_ ...']. - -All the objects in the foreground, whether large or small, are to be -drawn of their proper size, and if you see them from a distance they -will appear just as they ought, and if you see them close they will -diminish of themselves. - -[Footnote 15: Compare No. 526 line 18.] Take care that the vertical -plan on which you work out the perspective of the objects seen is of -the same form as the wall on which the work is to be executed. - -546. - -OF PAINTING. - -The size of the figures represented ought to show you the distance -they are seen from. If you see a figure as large as nature you know -it appears to be close to the eye. - -547. - -WHERE A SPECTATOR SHOULD STAND TO LOOK AT A PICTURE. - -Supposing _a b_ to be the picture and _d_ to be the light, I say -that if you place yourself between _c_ and _e_ you will not -understand the picture well and particularly if it is done in oils, -or still more if it is varnished, because it will be lustrous and -somewhat of the nature of a mirror. And for this reason the nearer -you go towards the point _c_, the less you will see, because the -rays of light falling from the window on the picture are reflected -to that point. But if you place yourself between _e_ and _d_ you -will get a good view of it, and the more so as you approach the -point _d_, because that spot is least exposed to these reflected -rays of light. - -III. - -THE PRACTICAL METHODS OF LIGHT AND SHADE AND AERIAL PERSPECTIVE. - -Gradations of light and shade. - -548. - -OF PAINTING: OF THE DARKNESS OF THE SHADOWS, OR I MAY SAY, THE -BRIGHTNESS OF THE LIGHTS. - -Although practical painters attribute to all shaded objects--trees, -fields, hair, beards and skin--four degrees of darkness in each -colour they use: that is to say first a dark foundation, secondly a -spot of colour somewhat resembling the form of the details, thirdly -a somewhat brighter and more defined portion, fourthly the lights -which are more conspicuous than other parts of the figure; still to -me it appears that these gradations are infinite upon a continuous -surface which is in itself infinitely divisible, and I prove it -thus:--[Footnote 7: See Pl. XXXI, No. 1; the two upper sketches.] -Let _a g_ be a continuous surface and let _d_ be the light which -illuminates it; I say--by the 4th [proposition] which says that that -side of an illuminated body is most highly lighted which is nearest -to the source of light--that therefore _g_ must be darker than _c_ -in proportion as the line _d g_ is longer than the line _d c_, and -consequently that these gradations of light--or rather of shadow, -are not 4 only, but may be conceived of as infinite, because _c d_ -is a continuous surface and every continuous surface is infinitely -divisible; hence the varieties in the length of lines extending -between the light and the illuminated object are infinite, and the -proportion of the light will be the same as that of the length of -the lines between them; extending from the centre of the luminous -body to the surface of the illuminated object. - -On the choice of light for a picture (549-554). - -549. - -HOW THE PAINTER MUST PLACE HIMSELF WITH REFERENCE TO THE LIGHT, TO -GIVE THE EFFECT OF RELIEF. - -Let _a b_ be the window, _m_ the point of light. I say that on -whichever side the painter places himself he will be well placed if -only his eye is between the shaded and the illuminated portions of -the object he is drawing; and this place you will find by putting -yourself between the point _m_ and the division between the shadow -and the light on the object to be drawn. - -550. - -THAT SHADOWS CAST BY A PARTICULAR LIGHT SHOULD BE AVOIDED, BECAUSE -THEY ARE EQUALLY STRONG AT THE ENDS AND AT THE BEGINNING. - -The shadows cast by the sun or any other particular light have not a -pleasing effect on the body to which they belong, because the parts -remain confuse, being divided by distinct outlines of light and -shade. And the shadows are of equal strength at the end and at the -beginning. - -551. - -HOW LIGHT SHOULD BE THROWN UPON FIGURES. - -The light must be arranged in accordance with the natural conditions -under which you wish to represent your figures: that is, if you -represent them in the sunshine make the shadows dark with large -spaces of light, and mark their shadows and those of all the -surrounding objects strongly on the ground. And if you represent -them as in dull weather give little difference of light and shade, -without any shadows at their feet. If you represent them as within -doors, make a strong difference between the lights and shadows, with -shadows on the ground. If the window is screened and the walls -white, there will be little difference of light. If it is lighted by -firelight make the high lights ruddy and strong, and the shadows -dark, and those cast on the walls and on the floor will be clearly -defined and the farther they are from the body the broader and -longer will they be. If the light is partly from the fire and partly -from the outer day, that of day will be the stronger and that of the -fire almost as red as fire itself. Above all see that the figures -you paint are broadly lighted and from above, that is to say all -living persons that you paint; for you will see that all the people -you meet out in the street are lighted from above, and you must know -that if you saw your most intimate friend with a light [on his face] -from below you would find it difficult to recognise him. - -552. - -OF HELPING THE APPARENT RELIEF OF A PICTURE BY GIVING IT ARTIFICIAL -LIGHT AND SHADE. - -To increase relief of a picture you may place, between your figure -and the solid object on which its shadow falls, a line of bright -light, dividing the figure from the object in shadow. And on the -same object you shall represent two light parts which will surround -the shadow cast upon the wall by the figure placed opposite [6]; and -do this frequently with the limbs which you wish should stand out -somewhat from the body they belong to; particularly when the arms -cross the front of the breast show, between the shadow cast by the -arms on the breast and the shadow on the arms themselves, a little -light seeming to fall through a space between the breast and the -arms; and the more you wish the arm to look detached from the breast -the broader you must make the light; always contrive also to arrange -the figures against the background in such a way as that the parts -in shadow are against a light background and the illuminated -portions against a dark background. - -[Footnote 6: Compare the two diagrams under No. 565.] - -553. - -OF SITUATION. - -Remember [to note] the situation of your figures; for the light and -shade will be one thing if the object is in a dark place with a -particular light, and another thing if it is in a light place with -direct sunlight; one thing in a dark place with a diffused evening -light or a cloudy sky, and another in the diffused light of the -atmosphere lighted by the sun. - -554. - -OF THE JUDGMENT TO BE MADE OF A PAINTER'S WORK. - -First you must consider whether the figures have the relief required -by their situation and the light which illuminates them; for the -shadows should not be the same at the extreme ends of the -composition as in the middle, because it is one thing when figures -are surrounded by shadows and another when they have shadows only on -one side. Those which are in the middle of the picture are -surrounded by shadows, because they are shaded by the figures which -stand between them and the light. And those are lighted on one side -only which stand between the principal group and the light, because -where they do not look towards the light they face the group and the -darkness of the group is thrown on them: and where they do not face -the group they face the brilliant light and it is their own darkness -shadowing them, which appears there. - -In the second place observe the distribution or arrangement of -figures, and whether they are distributed appropriately to the -circumstances of the story. Thirdly, whether the figures are -actively intent on their particular business. - -555. - -OF THE TREATMENT OF THE LIGHTS. - -First give a general shadow to the whole of that extended part which -is away from the light. Then put in the half shadows and the strong -shadows, comparing them with each other and, in the same way give -the extended light in half tint, afterwards adding the half lights -and the high lights, likewise comparing them together. - -The distribution of light and shade (556-559) - -556. - -OF SHADOWS ON BODIES. - -When you represent the dark shadows in bodies in light and shade, -always show the cause of the shadow, and the same with reflections; -because the dark shadows are produced by dark objects and the -reflections by objects only moderately lighted, that is with -diminished light. And there is the same proportion between the -highly lighted part of a body and the part lighted by a reflection -as between the origin of the lights on the body and the origin of -the reflections. - -557. - -OF LIGHTS AND SHADOWS. - -I must remind you to take care that every portion of a body, and -every smallest detail which is ever so little in relief, must be -given its proper importance as to light and shade. - -558. - -OF THE WAY TO MAKE THE SHADOW ON FIGURES CORRESPOND TO THE LIGHT AND -TO [THE COLOUR] OF THE BODY. - -When you draw a figure and you wish to see whether the shadow is the -proper complement to the light, and neither redder nor yellower than -is the nature of the colour you wish to represent in shade, proceed -thus. Cast a shadow with your finger on the illuminated portion, and -if the accidental shadow that you have made is like the natural -shadow cast by your finger on your work, well and good; and by -putting your finger nearer or farther off, you can make darker or -lighter shadows, which you must compare with your own. - -559. - -OF SURROUNDING BODIES BY VARIOUS FORMS OF SHADOW. - -Take care that the shadows cast upon the surface of the bodies by -different objects must undulate according to the various curves of -the limbs which cast the shadows, and of the objects on which they -are cast. - -The juxtaposition of light and shade (560, 561). - -560. - -ON PAINTING. - -The comparison of the various qualities of shadows and lights not -infrequently seems ambiguous and confused to the painter who desires -to imitate and copy the objects he sees. The reason is this: If you -see a white drapery side by side with a black one, that part of the -white drapery which lies against the black one will certainly look -much whiter than the part which lies against something whiter than -itself. [Footnote: It is evident from this that so early as in 1492 -Leonardo's writing in perspective was so far advanced that he could -quote his own statements.--As bearing on this subject compare what -is said in No. 280.] And the reason of this is shown in my [book on] -perspective. - -561. - -OF SHADOWS. - -Where a shadow ends in the light, note carefully where it is paler -or deeper and where it is more or less indistinct towards the light; -and, above all, in [painting] youthful figures I remind you not to -make the shadow end like a stone, because flesh has a certain -transparency, as may be seen by looking at a hand held between the -eye and the sun, which shines through it ruddy and bright. Place the -most highly coloured part between the light and shadow. And to see -what shadow tint is needed on the flesh, cast a shadow on it with -your finger, and according as you wish to see it lighter or darker -hold your finger nearer to or farther from your picture, and copy -that [shadow]. - -On the lighting of the background (562-565). - -562. - -OF THE BACKGROUNDS FOR PAINTED FIGURES. - -The ground which surrounds the forms of any object you paint should -be darker than the high lights of those figures, and lighter than -their shadowed part: &c. - -563. - -OF THE BACKGROUND THAT THE PAINTER SHOULD ADOPT IN HIS WORKS. - -Since experience shows us that all bodies are surrounded by light -and shade it is necessary that you, O Painter, should so arrange -that the side which is in light shall terminate against a dark body -and likewise that the shadow side shall terminate against a light -body. And by [following] this rule you will add greatly to the -relief of your figures. - -564. - -A most important part of painting consists in the backgrounds of the -objects represented; against these backgrounds the outlines of -those natural objects which are convex are always visible, and also -the forms of these bodies against the background, even though the -colours of the bodies should be the same as that of the background. -This is caused by the convex edges of the objects not being -illuminated in the same way as, by the same light, the background is -illuminated, since these edges will often be lighter or darker than -the background. But if the edge is of the same colour as the -background, beyond a doubt it will in that part of the picture -interfere with your perception of the outline, and such a choice in -a picture ought to be rejected by the judgment of good painters, -inasmuch as the purpose of the painter is to make his figures appear -detached from the background; while in the case here described the -contrary occurs, not only in the picture, but in the objects -themselves. - -565. - -That you ought, when representing objects above the eye and on one -side--if you wish them to look detached from the wall--to show, -between the shadow on the object and the shadow it casts a middle -light, so that the body will appear to stand away from the wall. - -On the lighting of white objects. - -566. - -HOW WHITE BODIES SHOULD BE REPRESENTED. - -If you are representing a white body let it be surrounded by ample -space, because as white has no colour of its own, it is tinged and -altered in some degree by the colour of the objects surrounding it. -If you see a woman dressed in white in the midst of a landscape, -that side which is towards the sun is bright in colour, so much so -that in some portions it will dazzle the eyes like the sun itself; -and the side which is towards the atmosphere,--luminous through -being interwoven with the sun's rays and penetrated by them--since -the atmosphere itself is blue, that side of the woman's figure will -appear steeped in blue. If the surface of the ground about her be -meadows and if she be standing between a field lighted up by the sun -and the sun itself, you will see every portion of those folds which -are towards the meadow tinged by the reflected rays with the colour -of that meadow. Thus the white is transmuted into the colours of the -luminous and of the non-luminous objects near it. - -The methods of aerial (567--570). - -567. - -WHY FACES [SEEN] AT A DISTANCE LOOK DARK. - -We see quite plainly that all the images of visible objects that lie -before us, whether large or small, reach our sense by the minute -aperture of the eye; and if, through so small a passage the image -can pass of the vast extent of sky and earth, the face of a -man--being by comparison with such large images almost nothing by -reason of the distance which diminishes it,--fills up so little of -the eye that it is indistinguishable. Having, also, to be -transmitted from the surface to the sense through a dark medium, -that is to say the crystalline lens which looks dark, this image, -not being strong in colour becomes affected by this darkness on its -passage, and on reaching the sense it appears dark; no other reason -can in any way be assigned. If the point in the eye is black, it is -because it is full of a transparent humour as clear as air and acts -like a perforation in a board; on looking into it it appears dark -and the objects seen through the bright air and a dark one become -confused in this darkness. - -WHY A MAN SEEN AT A CERTAIN DISTANCE IS NOT RECOGNISABLE. - -The perspective of diminution shows us that the farther away an -object is the smaller it looks. If you look at a man at a distance -from you of an arrow's flight, and hold the eye of a small needle -close to your own eye, you can see through it several men whose -images are transmitted to the eye and will all be comprised within -the size of the needle's eye; hence, if the man who is at the -distance of an arrow's flight can send his whole image to your eye, -occupying only a small space in the needle's eye how can you -[expect] in so small a figure to distinguish or see the nose or -mouth or any detail of his person? and, not seeing these you cannot -recognise the man, since these features, which he does not show, are -what give men different aspects. - -568. - -THE REASON WHY SMALL FIGURES SHOULD NOT BE MADE FINISHED. - -I say that the reason that objects appear diminished in size is -because they are remote from the eye; this being the case it is -evident that there must be a great extent of atmosphere between the -eye and the objects, and this air interferes with the distinctness -of the forms of the object. Hence the minute details of these -objects will be indistinguishable and unrecognisable. Therefore, O -Painter, make your smaller figures merely indicated and not highly -finished, otherwise you will produce effects the opposite to nature, -your supreme guide. The object is small by reason of the great -distance between it and the eye, this great distance is filled with -air, that mass of air forms a dense body which intervenes and -prevents the eye seeing the minute details of objects. - -569. - -Whenever a figure is placed at a considerable distance you lose -first the distinctness of the smallest parts; while the larger parts -are left to the last, losing all distinctness of detail and outline; -and what remains is an oval or spherical figure with confused edges. - -570. - -OF PAINTING. - -The density of a body of smoke looks white below the horizon while -above the horizon it is dark, even if the smoke is in itself of a -uniform colour, this uniformity will vary according to the variety -in the ground on which it is seen. - -IV. - -OF PORTRAIT AND FIGURE PAINTING. - -Of sketching figures and portraits (571-572). - -571. - -OF THE WAY TO LEARN TO COMPOSE FIGURES [IN GROUPS] IN HISTORICAL -PICTURES. - -When you have well learnt perspective and have by heart the parts -and forms of objects, you must go about, and constantly, as you go, -observe, note and consider the circumstances and behaviour of men in -talking, quarrelling or laughing or fighting together: the action of -the men themselves and the actions of the bystanders, who separate -them or who look on. And take a note of them with slight strokes -thus, in a little book which you should always carry with you. And -it should be of tinted paper, that it may not be rubbed out, but -change the old [when full] for a new one; since these things should -not be rubbed out but preserved with great care; for the forms, and -positions of objects are so infinite that the memory is incapable of -retaining them, wherefore keep these [sketches] as your guides and -masters. - -[Footnote: Among Leonardo's numerous note books of pocket size not -one has coloured paper, so no sketches answering to this description -can be pointed out. The fact that most of the notes are written in -ink, militates against the supposition that they were made in the -open air.] - -572. - -OF A METHOD OF KEEPING IN MIND THE FORM OF A FACE. - -If you want to acquire facility for bearing in mind the expression -of a face, first make yourself familiar with a variety of [forms of] -several heads, eyes, noses, mouths, chins and cheeks and necks and -shoulders: And to put a case: Noses are of 10 types: straight, -bulbous, hollow, prominent above or below the middle, aquiline, -regular, flat, round or pointed. These hold good as to profile. In -full face they are of 11 types; these are equal thick in the middle, -thin in the middle, with the tip thick and the root narrow, or -narrow at the tip and wide at the root; with the nostrils wide or -narrow, high or low, and the openings wide or hidden by the point; -and you will find an equal variety in the other details; which -things you must draw from nature and fix them in your mind. Or else, -when you have to draw a face by heart, carry with you a little book -in which you have noted such features; and when you have cast a -glance at the face of the person you wish to draw, you can look, in -private, which nose or mouth is most like, or there make a little -mark to recognise it again at home. Of grotesque faces I need say -nothing, because they are kept in mind without difficulty. - -The position of the head. - -573. - -HOW YOU SHOULD SET TO WORK TO DRAW A HEAD OF WHICH ALL THE PARTS -SHALL AGREE WITH THE POSITION GIVEN TO IT. - -To draw a head in which the features shall agree with the turn and -bend of the head, pursue this method. You know that the eyes, -eyebrows, nostrils, corners of the mouth, and sides of the chin, the -jaws, cheeks, ears and all the parts of a face are squarely and -straightly set upon the face. - -[Footnote: Compare the drawings and the text belonging to them on -Pl. IX. (No. 315), Pl. X (No. 316), Pl. XL (No. 318) and Pl. XII. -(No. 319).] - -Therefore when you have sketched the face draw lines passing from -one corner of the eye to the other; and so for the placing of each -feature; and after having drawn the ends of the lines beyond the two -sides of the face, look if the spaces inside the same parallel lines -on the right and on the left are equal [12]. But be sure to remember -to make these lines tend to the point of sight. - -[Footnote: See Pl. XXXI, No. 4, the slight sketch on the left hand -side. The text of this passage is written by the side of it. In this -sketch the lines seem intentionally incorrect and converging to the -right (compare I. 12) instead of parallel. Compare too with this -text the drawing in red chalk from Windsor Castle which is -reproduced on Pl. XL, No. 2.] - -Of the light on the face (574-576). - -574. - -HOW TO KNOW WHICH SIDE OF AN OBJECT IS TO BE MORE OR LESS LUMINOUS -THAN THE OTHER. - -Let _f_ be the light, the head will be the object illuminated by it -and that side of the head on which the rays fall most directly will -be the most highly lighted, and those parts on which the rays fall -most aslant will be less lighted. The light falls as a blow might, -since a blow which falls perpendicularly falls with the greatest -force, and when it falls obliquely it is less forcible than the -former in proportion to the width of the angle. _Exempli gratia_ if -you throw a ball at a wall of which the extremities are equally far -from you the blow will fall straight, and if you throw the ball at -the wall when standing at one end of it the ball will hit it -obliquely and the blow will not tell. - -[Footnote: See Pl. XXXI. No. 4; the sketch on the right hand side.] - -575. - -THE PROOF AND REASON WHY AMONG THE ILLUMINATED PARTS CERTAIN -PORTIONS ARE IN HIGHER LIGHT THAN OTHERS. - -Since it is proved that every definite light is, or seems to be, -derived from one single point the side illuminated by it will have -its highest light on the portion where the line of radiance falls -perpendicularly; as is shown above in the lines _a g_, and also in -_a h_ and in _l a_; and that portion of the illuminated side will be -least luminous, where the line of incidence strikes it between two -more dissimilar angles, as is seen at _b c d_. And by this means you -may also know which parts are deprived of light as is seen at _m k_. - -Where the angles made by the lines of incidence are most equal there -will be the highest light, and where they are most unequal it will -be darkest. - -I will make further mention of the reason of reflections. - -[Footnote: See Pl. XXXII. The text, here given complete, is on the -right hand side. The small circles above the beginning of lines 5 -and 11 as well as the circle above the text on Pl. XXXI, are in a -paler ink and evidently added by a later hand in order to -distinguish the text as belonging to the _Libro di Pittura_ (see -Prolegomena. No. 12, p. 3). The text on the left hand side of this -page is given as Nos. 577 and 137.] - -576. - -Where the shadow should be on the face. - -General suggestions for historical pictures (577-581). - -577. - -When you compose a historical picture take two points, one the point -of sight, and the other the source of light; and make this as -distant as possible. - -578. - -Historical pictures ought not to be crowded and confused with too -many figures. - -579. - -PRECEPTS IN PAINTING. - -Let you sketches of historical pictures be swift and the working out -of the limbs not be carried too far, but limited to the position of -the limbs, which you can afterwards finish as you please and at your -leisure. - -[Footnote: See Pl. XXXVIII, No. 2. The pen and ink drawing given -there as No. 3 may also be compared with this passage. It is in the -Windsor collection where it is numbered 101.] - -580. - -The sorest misfortune is when your views are in advance of your -work. - -581. - -Of composing historical pictures. Of not considering the limbs in -the figures in historical pictures; as many do who, in the wish to -represent the whole of a figure, spoil their compositions. And when -you place one figure behind another take care to draw the whole of -it so that the limbs which come in front of the nearer figures may -stand out in their natural size and place. - -How to represent the differences of age and sex (582-583). - -582. - -How the ages of man should be depicted: that is, Infancy, Childhood, -Youth, Manhood, Old age, Decrepitude. - -[Footnote: No answer is here given to this question, in the original -MS.] - -583. - -Old men ought to be represented with slow and heavy movements, their -legs bent at the knees, when they stand still, and their feet placed -parallel and apart; bending low with the head leaning forward, and -their arms but little extended. - -Women must be represented in modest attitudes, their legs close -together, their arms closely folded, their heads inclined and -somewhat on one side. - -Old women should be represented with eager, swift and furious -gestures, like infernal furies; but the action should be more -violent in their arms and head than in their legs. - -Little children, with lively and contorted movements when sitting, -and, when standing still, in shy and timid attitudes. - -[Footnote: _bracci raccolte_. Compare Pl. XXXIII. This drawing, in -silver point on yellowish tinted paper, the lights heightened with -white, represents two female hands laid together in a lap. Above is -a third finished study of a right hand, apparently holding a veil -from the head across the bosom. This drawing evidently dates from -before 1500 and was very probably done at Florence, perhaps as a -preparatory study for some picture. The type of hand with its -slender thin forms is more like the style of the _Vierge aux -Rochers_ in the Louvre than any later works--as the Mona Lisa for -instance.] - -Of representing the emotions. - -584. - -THAT A FIGURE IS NOT ADMIRABLE UNLESS IT EXPRESSES BY ITS ACTION THE -PASSION OF ITS SENTIMENT. - -That figure is most admirable which by its actions best expresses -the passion that animates it. - -HOW AN ANGRY MAN IS TO BE FIGURED. - -You must make an angry person holding someone by the hair, wrenching -his head against the ground, and with one knee on his ribs; his -right arm and fist raised on high. His hair must be thrown up, his -brow downcast and knit, his teeth clenched and the two corners of -his mouth grimly set; his neck swelled and bent forward as he leans -over his foe, and full of furrows. - -HOW TO REPRESENT A MAN IN DESPAIR. - -You must show a man in despair with a knife, having already torn -open his garments, and with one hand tearing open the wound. And -make him standing on his feet and his legs somewhat bent and his -whole person leaning towards the earth; his hair flying in disorder. - -Of representing imaginary animals. - -585. - -HOW YOU SHOULD MAKE AN IMAGINARY ANIMAL LOOK NATURAL. - -You know that you cannot invent animals without limbs, each of -which, in itself, must resemble those of some other animal. Hence if -you wish to make an animal, imagined by you, appear natural--let us -say a Dragon, take for its head that of a mastiff or hound, with the -eyes of a cat, the ears of a porcupine, the nose of a greyhound, the -brow of a lion, the temples of an old cock, the neck of a water -tortoise. - -[Footnote: The sketch here inserted of two men on horseback fighting -a dragon is the facsimile of a pen and ink drawing belonging to -BARON EDMOND DE ROTHSCHILD of Paris.] - -The selection of forms. - -586. - -OF THE DELUSIONS WHICH ARISE IN JUDGING OF THE LIMBS. - -A painter who has clumsy hands will paint similar hands in his -works, and the same will occur with any limb, unless long study has -taught him to avoid it. Therefore, O Painter, look carefully what -part is most ill-favoured in your own person and take particular -pains to correct it in your studies. For if you are coarse, your -figures will seem the same and devoid of charm; and it is the same -with any part that may be good or poor in yourself; it will be shown -in some degree in your figures. - -587. - -OF THE SELECTION OF BEAUTIFUL FACES. - -It seems to me to be no small charm in a painter when he gives his -figures a pleasing air, and this grace, if he have it not by nature, -he may acquire by incidental study in this way: Look about you and -take the best parts of many beautiful faces, of which the beauty is -confirmed rather by public fame than by your own judgment; for you -might be mistaken and choose faces which have some resemblance to -your own. For it would seem that such resemblances often please us; -and if you should be ugly, you would select faces that were not -beautiful and you would then make ugly faces, as many painters do. -For often a master's work resembles himself. So select beauties as I -tell you, and fix them in your mind. - -588. - -Of the limbs, which ought to be carefully selected, and of all the -other parts with regard to painting. - -589. - -When selecting figures you should choose slender ones rather than -lean and wooden ones. - -590. - -OF THE MUSCLES OF ANIMALS. - -The hollow spaces interposed between the muscles must not be of such -a character as that the skin should seem to cover two sticks laid -side by side like _c_, nor should they seem like two sticks somewhat -remote from such contact so that the skin hangs in an empty loose -curve as at _f_; but it should be like _i_, laid over the spongy fat -that lies in the angles as the angle _n m o_; which angle is formed -by the contact of the ends of the muscles and as the skin cannot -fold down into such an angle, nature has filled up such angles with -a small quantity of spongy and, as I may say, vesicular fat, with -minute bladders [in it] full of air, which is condensed or rarefied -in them according to the increase or the diminution of the substance -of the muscles; in which latter case the concavity _i_ always has a -larger curve than the muscle. - -591. - -OF UNDULATING MOVEMENTS AND EQUIPOISE IN FIGURES AND OTHER ANIMALS. - -When representing a human figure or some graceful animal, be careful -to avoid a wooden stiffness; that is to say make them move with -equipoise and balance so as not to look like a piece of wood; but -those you want to represent as strong you must not make so, -excepting in the turn of the head. - -How to pose figures. - -592. - -OF GRACE IN THE LIMBS. - -The limbs should be adapted to the body with grace and with -reference to the effect that you wish the figure to produce. And if -you wish to produce a figure that shall of itself look light and -graceful you must make the limbs elegant and extended, and without -too much display of the muscles; and those few that are needed for -your purpose you must indicate softly, that is, not very prominent -and without strong shadows; the limbs, and particularly the arms -easy; that is, none of the limbs should be in a straight line with -the adjoining parts. And if the hips, which are the pole of a man, -are by reason of his position, placed so, that the right is higher -than the left, make the point of the higher shoulder in a -perpendicular line above the highest prominence of the hip, and let -this right shoulder be lower than the left. Let the pit of the -throat always be over the centre of the joint of the foot on which -the man is leaning. The leg which is free should have the knee lower -than the other, and near the other leg. The positions of the head -and arms are endless and I shall therefore not enlarge on any rules -for them. Still, let them be easy and pleasing, with various turns -and twists, and the joints gracefully bent, that they may not look -like pieces of wood. - -Of appropriate gestures (593-600). - -593. - -A picture or representation of human figures, ought to be done in -such a way as that the spectator may easily recognise, by means of -their attitudes, the purpose in their minds. Thus, if you have to -represent a man of noble character in the act of speaking, let his -gestures be such as naturally accompany good words; and, in the same -way, if you wish to depict a man of a brutal nature, give him fierce -movements; as with his arms flung out towards the listener, and his -head and breast thrust forward beyond his feet, as if following the -speaker's hands. Thus it is with a deaf and dumb person who, when he -sees two men in conversation--although he is deprived of -hearing--can nevertheless understand, from the attitudes and -gestures of the speakers, the nature of their discussion. I once saw -in Florence a man who had become deaf who, when you spoke very loud -did not understand you, but if you spoke gently and without making -any sound, understood merely from the movement of the lips. Now -perhaps you will say that the lips of a man who speaks loudly do not -move like those of one speaking softly, and that if they were to -move them alike they would be alike understood. As to this argument, -I leave the decision to experiment; make a man speak to you gently -and note [the motion of] his lips. - -[Footnote: The first ten lines of this text have already been -published, but with a slightly different reading by Dr. M. JORDAN: -_Das Malerbuch Leonardo da Vinci's_ p. 86.] - -594. - -OF REPRESENTING A MAN SPEAKING TO A MULTITUDE. - -When you wish to represent a man speaking to a number of people, -consider the matter of which he has to treat and adapt his action to -the subject. Thus, if he speaks persuasively, let his action be -appropriate to it. If the matter in hand be to set forth an -argument, let the speaker, with the fingers of the right hand hold -one finger of the left hand, having the two smaller ones closed; and -his face alert, and turned towards the people with mouth a little -open, to look as though he spoke; and if he is sitting let him -appear as though about to rise, with his head forward. If you -represent him standing make him leaning slightly forward with body -and head towards the people. These you must represent as silent and -attentive, all looking at the orator's face with gestures of -admiration; and make some old men in astonishment at the things they -hear, with the corners of their mouths pulled down and drawn in, -their cheeks full of furrows, and their eyebrows raised, and -wrinkling the forehead where they meet. Again, some sitting with -their fingers clasped holding their weary knees. Again, some bent -old man, with one knee crossed over the other; on which let him hold -his hand with his other elbow resting in it and the hand supporting -his bearded chin. - -[Footnote: The sketches introduced here are a facsimile of a pen and -ink drawing in the Louvre which Herr CARL BRUN considers as studies -for the Last Supper in the church of _Santa Maria delle Grazie_ (see -Leonardo da Vinci, LXI, pp. 21, 27 and 28 in DOHME'S _Kunst und -Kunstler_, Leipzig, Seemann). I shall not here enter into any -discussion of this suggestion; but as a justification for -introducing the drawing in this place, I may point out that some of -the figures illustrate this passage as perfectly as though they had -been drawn for that express purpose. I have discussed the -probability of a connection between this sketch and the picture of -the Last Supper on p. 335. The original drawing is 27 3/4 -centimetres wide by 21 high.--The drawing in silver point on reddish -paper given on Pl. LII. No. 1--the original at Windsor Castle--may -also serve to illustrate the subject of appropriate gestures, -treated in Nos. 593 and 594.] - -595. - -OF THE DISPOSITION OF LIMBS. - -As regards the disposition of limbs in movement you will have to -consider that when you wish to represent a man who, by some chance, -has to turn backwards or to one side, you must not make him move his -feet and all his limbs towards the side to which he turns his head. -Rather must you make the action proceed by degrees and through the -different joints; that is, those of the foot, the knee and the hip -and the neck. And if you set him on the right leg, you must make the -left knee bend inwards, and let his foot be slightly raised on the -outside, and the left shoulder be somewhat lower than the right, -while the nape of the neck is in a line directly over the outer -ancle of the left foot. And the left shoulder will be in a -perpendicular line above the toes of the right foot. And always set -your figures so that the side to which the head turns is not the -side to which the breast faces, since nature for our convenience has -made us with a neck which bends with ease in many directions, the -eye wishing to turn to various points, the different joints. And if -at any time you make a man sitting with his arms at work on -something which is sideways to him, make the upper part of his body -turn upon the hips. - -[Footnote: Compare Pl. VII, No. 5. The original drawing at Windsor -Castle is numbered 104.] - -596. - -When you draw the nude always sketch the whole figure and then -finish those limbs which seem to you the best, but make them act -with the other limbs; otherwise you will get a habit of never -putting the limbs well together on the body. - -Never make the head turn the same way as the torso, nor the arm and -leg move together on the same side. And if the face is turned to the -right shoulder, make all the parts lower on the left side than on -the right; and when you turn the body with the breast outwards, if -the head turns to the left side make the parts on the right side -higher than those on the left. - -[Footnote: In the original MS. a much defaced sketch is to be seen -by the side of the second part of this chapter; its faded condition -has rendered reproduction impossible. In M. RAVAISSON'S facsimile -the outlines of the head have probably been touched up. This passage -however is fitly illustrated by the drawings on Pl. XXI.] - -597. - -OF PAINTING. - -Of the nature of movements in man. Do not repeat the same gestures -in the limbs of men unless you are compelled by the necessity of -their action, as is shown in _a b_. - -[Footnote: See Pl. V, where part of the text is also reproduced. The -effaced figure to the extreme left has evidently been cancelled by -Leonardo himself as unsatisfactory.] - -598. - -The motions of men must be such as suggest their dignity or their -baseness. - -599. - -OF PAINTING. - -Make your work carry out your purpose and meaning. That is when you -draw a figure consider well who it is and what you wish it to be -doing. - -OF PAINTING. - -With regard to any action which you give in a picture to an old man -or to a young one, you must make it more energetic in the young man -in proportion as he is stronger than the old one; and in the same -way with a young man and an infant. - -600. - -OF SETTING ON THE LIMBS. - -The limbs which are used for labour must be muscular and those which -are not much used you must make without muscles and softly rounded. - -OF THE ACTION OF THE FIGURES. - -Represent your figures in such action as may be fitted to express -what purpose is in the mind of each; otherwise your art will not be -admirable. - -V. - -SUGGESTIONS FOR COMPOSITIONS. - -Of painting battle pieces (601-603). - -601. - -OF THE WAY OF REPRESENTING A BATTLE. - -First you must represent the smoke of artillery mingling in the air -with the dust and tossed up by the movement of horses and the -combatants. And this mixture you must express thus: The dust, being -a thing of earth, has weight; and although from its fineness it is -easily tossed up and mingles with the air, it nevertheless readily -falls again. It is the finest part that rises highest; hence that -part will be least seen and will look almost of the same colour as -the air. The higher the smoke mixed with the dust-laden air rises -towards a certain level, the more it will look like a dark cloud; -and it will be seen that at the top, where the smoke is more -separate from the dust, the smoke will assume a bluish tinge and the -dust will tend to its colour. This mixture of air, smoke and dust -will look much lighter on the side whence the light comes than on -the opposite side. The more the combatants are in this turmoil the -less will they be seen, and the less contrast will there be in their -lights and shadows. Their faces and figures and their appearance, -and the musketeers as well as those near them you must make of a -glowing red. And this glow will diminish in proportion as it is -remote from its cause. - -The figures which are between you and the light, if they be at a -distance, will appear dark on a light background, and the lower part -of their legs near the ground will be least visible, because there -the dust is coarsest and densest [19]. And if you introduce horses -galloping outside the crowd, make the little clouds of dust distant -from each other in proportion to the strides made by the horses; and -the clouds which are furthest removed from the horses, should be -least visible; make them high and spreading and thin, and the nearer -ones will be more conspicuous and smaller and denser [23]. The air -must be full of arrows in every direction, some shooting upwards, -some falling, some flying level. The balls from the guns must have a -train of smoke following their flight. The figures in the foreground -you must make with dust on the hair and eyebrows and on other flat -places likely to retain it. The conquerors you will make rushing -onwards with their hair and other light things flying on the wind, -with their brows bent down, - -[Footnote: 19--23. Compare 608. 57--75.] - -602. - -and with the opposite limbs thrust forward; that is where a man puts -forward the right foot the left arm must be advanced. And if you -make any one fallen, you must show the place where he has slipped -and been dragged along the dust into blood stained mire; and in the -half-liquid earth arround show the print of the tramping of men and -horses who have passed that way. Make also a horse dragging the dead -body of his master, and leaving behind him, in the dust and mud, the -track where the body was dragged along. You must make the conquered -and beaten pale, their brows raised and knit, and the skin above -their brows furrowed with pain, the sides of the nose with wrinkles -going in an arch from the nostrils to the eyes, and make the -nostrils drawn up--which is the cause of the lines of which I -speak--, and the lips arched upwards and discovering the upper -teeth; and the teeth apart as with crying out and lamentation. And -make some one shielding his terrified eyes with one hand, the palm -towards the enemy, while the other rests on the ground to support -his half raised body. Others represent shouting with their mouths -open, and running away. You must scatter arms of all sorts among the -feet of the combatants, as broken shields, lances, broken swords and -other such objects. And you must make the dead partly or entirely -covered with dust, which is changed into crimson mire where it has -mingled with the flowing blood whose colour shows it issuing in a -sinuous stream from the corpse. Others must be represented in the -agonies of death grinding their teeth, rolling their eyes, with -their fists clenched against their bodies and their legs contorted. -Some might be shown disarmed and beaten down by the enemy, turning -upon the foe, with teeth and nails, to take an inhuman and bitter -revenge. You might see some riderless horse rushing among the enemy, -with his mane flying in the wind, and doing no little mischief with -his heels. Some maimed warrior may be seen fallen to the earth, -covering himself with his shield, while the enemy, bending over him, -tries to deal him a deathstroke. There again might be seen a number -of men fallen in a heap over a dead horse. You would see some of the -victors leaving the fight and issuing from the crowd, rubbing their -eyes and cheeks with both hands to clean them of the dirt made by -their watering eyes smarting from the dust and smoke. The reserves -may be seen standing, hopeful but cautious; with watchful eyes, -shading them with their hands and gazing through the dense and murky -confusion, attentive to the commands of their captain. The captain -himself, his staff raised, hurries towards these auxiliaries, -pointing to the spot where they are most needed. And there may be a -river into which horses are galloping, churning up the water all -round them into turbulent waves of foam and water, tossed into the -air and among the legs and bodies of the horses. And there must not -be a level spot that is not trampled with gore. - -603. - -OF LIGHTING THE LOWER PARTS OF BODIES CLOSE TOGETHER, AS OF MEN IN -BATTLE. - -As to men and horses represented in battle, their different parts -will be dark in proportion as they are nearer to the ground on which -they stand. And this is proved by the sides of wells which grow -darker in proportion to their depth, the reason of which is that the -deepest part of the well sees and receives a smaller amount of the -luminous atmosphere than any other part. - -And the pavement, if it be of the same colour as the legs of these -said men and horses, will always be more lighted and at a more -direct angle than the said legs &c. - -604. - -OF THE WAY TO REPRESENT A NIGHT [SCENE]. - -That which is entirely bereft of light is all darkness; given a -night under these conditions and that you want to represent a night -scene,--arrange that there shall be a great fire, then the objects -which are nearest to this fire will be most tinged with its colour; -for those objects which are nearest to a coloured light participate -most in its nature; as therefore you give the fire a red colour, you -must make all the objects illuminated by it ruddy; while those which -are farther from the fire are more tinted by the black hue of night. -The figures which are seen against the fire look dark in the glare -of the firelight because that side of the objects which you see is -tinged by the darkness of the night and not by the fire; and those -who stand at the side are half dark and half red; while those who -are visible beyond the edges of the flame will be fully lighted by -the ruddy glow against a black background. As to their gestures, -make those which are near it screen themselves with their hands and -cloaks as a defence against the intense heat, and with their faces -turned away as if about to retire. Of those farther off represent -several as raising their hands to screen their eyes, hurt by the -intolerable glare. - -Of depicting a tempest (605. 606). - -605. - -Describe a wind on land and at sea. Describe a storm of rain. - -606. - -HOW TO REPRESENT A TEMPEST. - -If you wish to represent a tempest consider and arrange well its -effects as seen, when the wind, blowing over the face of the sea and -earth, removes and carries with it such things as are not fixed to -the general mass. And to represent the storm accurately you must -first show the clouds scattered and torn, and flying with the wind, -accompanied by clouds of sand blown up from the sea shore, and -boughs and leaves swept along by the strength and fury of the blast -and scattered with other light objects through the air. Trees and -plants must be bent to the ground, almost as if they would follow -the course of the gale, with their branches twisted out of their -natural growth and their leaves tossed and turned about [Footnote -11: See Pl. XL, No. 2.]. Of the men who are there some must have -fallen to the ground and be entangled in their garments, and hardly -to be recognized for the dust, while those who remain standing may -be behind some tree, with their arms round it that the wind may not -tear them away; others with their hands over their eyes for the -dust, bending to the ground with their clothes and hair streaming in -the wind. [Footnote 15: See Pl. XXXIV, the right hand lower sketch.] -Let the sea be rough and tempestuous and full of foam whirled among -the lofty waves, while the wind flings the lighter spray through the -stormy air, till it resembles a dense and swathing mist. Of the -ships that are therein some should be shown with rent sails and the -tatters fluttering through the air, with ropes broken and masts -split and fallen. And the ship itself lying in the trough of the sea -and wrecked by the fury of the waves with the men shrieking and -clinging to the fragments of the vessel. Make the clouds driven by -the impetuosity of the wind and flung against the lofty mountain -tops, and wreathed and torn like waves beating upon rocks; the air -itself terrible from the deep darkness caused by the dust and fog -and heavy clouds. - -Of representing the deluge (607-609). - -607. - -TO REPRESENT THE DELUGE. - -The air was darkened by the heavy rain whose oblique descent driven -aslant by the rush of the winds, flew in drifts through the air not -otherwise than as we see dust, varied only by the straight lines of -the heavy drops of falling water. But it was tinged with the colour -of the fire kindled by the thunder-bolts by which the clouds were -rent and shattered; and whose flashes revealed the broad waters of -the inundated valleys, above which was seen the verdure of the -bending tree tops. Neptune will be seen in the midst of the water -with his trident, and [15] let AEolus with his winds be shown -entangling the trees floating uprooted, and whirling in the huge -waves. The horizon and the whole hemisphere were obscure, but lurid -from the flashes of the incessant lightning. Men and birds might be -seen crowded on the tall trees which remained uncovered by the -swelling waters, originators of the mountains which surround the -great abysses [Footnote 23: Compare Vol. II. No. 979.]. - -608. - -OF THE DELUGE AND HOW TO REPRESENT IT IN A PICTURE. - -Let the dark and gloomy air be seen buffeted by the rush of contrary -winds and dense from the continued rain mingled with hail and -bearing hither and thither an infinite number of branches torn from -the trees and mixed with numberless leaves. All round may be seen -venerable trees, uprooted and stripped by the fury of the winds; and -fragments of mountains, already scoured bare by the torrents, -falling into those torrents and choking their valleys till the -swollen rivers overflow and submerge the wide lowlands and their -inhabitants. Again, you might have seen on many of the hill-tops -terrified animals of different kinds, collected together and subdued -to tameness, in company with men and women who had fled there with -their children. The waters which covered the fields, with their -waves were in great part strewn with tables, bedsteads, boats and -various other contrivances made from necessity and the fear of -death, on which were men and women with their children amid sounds -of lamentation and weeping, terrified by the fury of the winds which -with their tempestuous violence rolled the waters under and over and -about the bodies of the drowned. Nor was there any object lighter -than the water which was not covered with a variety of animals -which, having come to a truce, stood together in a frightened -crowd--among them wolves, foxes, snakes and others--fleing from -death. And all the waters dashing on their shores seemed to be -battling them with the blows of drowned bodies, blows which killed -those in whom any life remained [19]. You might have seen -assemblages of men who, with weapons in their hands, defended the -small spots that remained to them against lions, wolves and beasts -of prey who sought safety there. Ah! what dreadful noises were heard -in the air rent by the fury of the thunder and the lightnings it -flashed forth, which darted from the clouds dealing ruin and -striking all that opposed its course. Ah! how many you might have -seen closing their ears with their hands to shut out the tremendous -sounds made in the darkened air by the raging of the winds mingling -with the rain, the thunders of heaven and the fury of the -thunder-bolts. Others were not content with shutting their eyes, but -laid their hands one over the other to cover them the closer that -they might not see the cruel slaughter of the human race by the -wrath of God. Ah! how many laments! and how many in their terror -flung themselves from the rocks! Huge branches of great oaks loaded -with men were seen borne through the air by the impetuous fury of -the winds. How many were the boats upset, some entire, and some -broken in pieces, on the top of people labouring to escape with -gestures and actions of grief foretelling a fearful death. Others, -with desperate act, took their own lives, hopeless of being able to -endure such suffering; and of these, some flung themselves from -lofty rocks, others strangled themselves with their own hands, other -seized their own children and violently slew them at a blow; some -wounded and killed themselves with their own weapons; others, -falling on their knees recommended themselves to God. Ah! how many -mothers wept over their drowned sons, holding them upon their knees, -with arms raised spread out towards heaven and with words and -various threatening gestures, upbraiding the wrath of the gods. -Others with clasped hands and fingers clenched gnawed them and -devoured them till they bled, crouching with their breast down on -their knees in their intense and unbearable anguish. Herds of -animals were to be seen, such as horses, oxen, goats and swine -already environed by the waters and left isolated on the high peaks -of the mountains, huddled together, those in the middle climbing to -the top and treading on the others, and fighting fiercely -themselves; and many would die for lack of food. Already had the -birds begun to settle on men and on other animals, finding no land -uncovered which was not occupied by living beings, and already had -famine, the minister of death, taken the lives of the greater number -of the animals, when the dead bodies, now fermented, where leaving -the depth of the waters and were rising to the top. Among the -buffeting waves, where they were beating one against the other, and, -like as balls full of air, rebounded from the point of concussion, -these found a resting place on the bodies of the dead. And above -these judgements, the air was seen covered with dark clouds, riven -by the forked flashes of the raging bolts of heaven, lighting up on -all sides the depth of the gloom. - -The motion of the air is seen by the motion of the dust thrown up by -the horse's running and this motion is as swift in again filling up -the vacuum left in the air which enclosed the horse, as he is rapid -in passing away from the air. - -Perhaps it will seem to you that you may reproach me with having -represented the currents made through the air by the motion of the -wind notwithstanding that the wind itself is not visible in the air. -To this I must answer that it is not the motion of the wind but only -the motion of the things carried along by it which is seen in the -air. - -THE DIVISIONS. [Footnote 76: These observations, added at the bottom -of the page containing the full description of the doluge seem to -indicate that it was Leonardo's intention to elaborate the subject -still farther in a separate treatise.] - -Darkness, wind, tempest at sea, floods of water, forests on fire, -rain, bolts from heaven, earthquakes and ruins of mountains, -overthrow of cities [Footnote 81: _Spianamenti di citta_ (overthrow -of cities). A considerable number of drawings in black chalk, at -Windsor, illustrate this catastrophe. Most of them are much rubbed; -one of the least injured is reproduced at Pl. XXXIX. Compare also -the pen and ink sketch Pl. XXXVI.]. - -Whirlwinds which carry water [spouts] branches of trees, and men -through the air. - -Boughs stripped off by the winds, mingling by the meeting of the -winds, with people upon them. - -Broken trees loaded with people. - -Ships broken to pieces, beaten on rocks. - -Flocks of sheep. Hail stones, thunderbolts, whirlwinds. - -People on trees which are unable to to support them; trees and -rocks, towers and hills covered with people, boats, tables, troughs, -and other means of floating. Hills covered with men, women and -animals; and lightning from the clouds illuminating every thing. - -[Footnote: This chapter, which, with the next one, is written on a -loose sheet, seems to be the passage to which one of the compilers -of the Vatican copy alluded when he wrote on the margin of fol. 36: -"_Qua mi ricordo della mirabile discritione del Diluuio dello -autore._" It is scarcely necessary to point out that these chapters -are among those which have never before been published. The -description in No. 607 may be regarded as a preliminary sketch for -this one. As the MS. G. (in which it is to be found) must be -attributed to the period of about 1515 we may deduce from it the -approximate date of the drawings on Pl. XXXIV, XXXV, Nos. 2 and 3, -XXXVI and XXXVII, since they obviously belong to this text. The -drawings No. 2 on Pl. XXXV are, in the original, side by side with -the text of No. 608; lines 57 to 76 are shown in the facsimile. In -the drawing in Indian ink given on Pl. XXXIV we see Wind-gods in the -sky, corresponding to the allusion to Aeolus in No. 607 1. -15.-Plates XXXVI and XXXVII form one sheet in the original. The -texts reproduced on these Plates have however no connection with the -sketches, excepting the sketches of clouds on the right hand side. -These texts are given as No. 477. The group of small figures on Pl. -XXXVII, to the left, seems to be intended for a '_congregatione -d'uomini._' See No. 608, 1. 19.] - -609. - -DESCRIPTION OF THE DELUGE. - -Let there be first represented the summit of a rugged mountain with -valleys surrounding its base, and on its sides let the surface of -the soil be seen to slide, together with the small roots of the -bushes, denuding great portions of the surrounding rocks. And -descending ruinous from these precipices in its boisterous course, -let it dash along and lay bare the twisted and gnarled roots of -large trees overthrowing their roots upwards; and let the mountains, -as they are scoured bare, discover the profound fissures made in -them by ancient earthquakes. The base of the mountains may be in -great part clothed and covered with ruins of shrubs, hurled down -from the sides of their lofty peaks, which will be mixed with mud, -roots, boughs of trees, with all sorts of leaves thrust in with the -mud and earth and stones. And into the depth of some valley may have -fallen the fragments of a mountain forming a shore to the swollen -waters of its river; which, having already burst its banks, will -rush on in monstrous waves; and the greatest will strike upon and -destroy the walls of the cities and farmhouses in the valley [14]. -Then the ruins of the high buildings in these cities will throw up a -great dust, rising up in shape like smoke or wreathed clouds against -the falling rain; But the swollen waters will sweep round the pool -which contains them striking in eddying whirlpools against the -different obstacles, and leaping into the air in muddy foam; then, -falling back, the beaten water will again be dashed into the air. -And the whirling waves which fly from the place of concussion, and -whose impetus moves them across other eddies going in a contrary -direction, after their recoil will be tossed up into the air but -without dashing off from the surface. Where the water issues from -the pool the spent waves will be seen spreading out towards the -outlet; and there falling or pouring through the air and gaining -weight and impetus they will strike on the water below piercing it -and rushing furiously to reach its depth; from which being thrown -back it returns to the surface of the lake, carrying up the air that -was submerged with it; and this remains at the outlet in foam -mingled with logs of wood and other matters lighter than water. -Round these again are formed the beginnings of waves which increase -the more in circumference as they acquire more movement; and this -movement rises less high in proportion as they acquire a broader -base and thus they are less conspicuous as they die away. But if -these waves rebound from various objects they then return in direct -opposition to the others following them, observing the same law of -increase in their curve as they have already acquired in the -movement they started with. The rain, as it falls from the clouds is -of the same colour as those clouds, that is in its shaded side; -unless indeed the sun's rays should break through them; in that case -the rain will appear less dark than the clouds. And if the heavy -masses of ruin of large mountains or of other grand buildings fall -into the vast pools of water, a great quantity will be flung into -the air and its movement will be in a contrary direction to that of -the object which struck the water; that is to say: The angle of -reflection will be equal to the angle of incidence. Of the objects -carried down by the current, those which are heaviest or rather -largest in mass will keep farthest from the two opposite shores. The -water in the eddies revolves more swiftly in proportion as it is -nearer to their centre. The crests of the waves of the sea tumble to -their bases falling with friction on the bubbles of their sides; and -this friction grinds the falling water into minute particles and -this being converted into a dense mist, mingles with the gale in the -manner of curling smoke and wreathing clouds, and at last it, rises -into the air and is converted into clouds. But the rain which falls -through the atmosphere being driven and tossed by the winds becomes -rarer or denser according to the rarity or density of the winds that -buffet it, and thus there is generated in the atmosphere a moisture -formed of the transparent particles of the rain which is near to the -eye of the spectator. The waves of the sea which break on the slope -of the mountains which bound it, will foam from the velocity with -which they fall against these hills; in rushing back they will meet -the next wave as it comes and and after a loud noise return in a -great flood to the sea whence they came. Let great numbers of -inhabitants--men and animals of all kinds--be seen driven [54] by -the rising of the deluge to the peaks of the mountains in the midst -of the waters aforesaid. - -The wave of the sea at Piombino is all foaming water. [Footnote 55. -56: These two lines are written below the bottom sketch on Pl. XXXV, -3. The MS. Leic. being written about the year 1510 or later, it does -not seem to me to follow that the sketches must have been made at -Piombino, where Leonardo was in the year 1502 and possibly returned -there subsequently (see Vol. II. Topographical notes).] - -Of the water which leaps up from the spot where great masses fall on -its surface. Of the winds of Piombino at Piombino. Eddies of wind -and rain with boughs and shrubs mixed in the air. Emptying the boats -of the rain water. - -[Footnote: The sketches on Pl. XXXV 3 stand by the side of lines 14 -to 54.] - -Of depicting natural phenomena (610. 611). - -610. - -The tremendous fury of the wind driven by the falling in of the -hills on the caves within--by the falling of the hills which served -as roofs to these caverns. - -A stone flung through the air leaves on the eye which sees it the -impression of its motion, and the same effect is produced by the -drops of water which fall from the clouds when it [16] rains. - -[17] A mountain falling on a town, will fling up dust in the form of -clouds; but the colour of this dust will differ from that of the -clouds. Where the rain is thickest let the colour of the dust be -less conspicuous and where the dust is thickest let the rain be less -conspicuous. And where the rain is mingled with the wind and with -the dust the clouds created by the rain must be more transparent -than those of dust [alone]. And when flames of fire are mingled with -clouds of smoke and water very opaque and dark clouds will be formed -[Footnote 26-28: Compare Pl. XL, 1--the drawing in Indian ink on the -left hand side, which seems to be a reminiscence of his observations -of an eruption (see his remarks on Mount Etna in Vol II).]. And the -rest of this subject will be treated in detail in the book on -painting. - -[Footnote: See the sketches and text on Pl. XXXVIII, No. 1. Lines -1-16 are there given on the left hand side, 17-30 on the right. The -four lines at the bottom on the right are given as No. 472. Above -these texts, which are written backwards, there are in the original -sixteen lines in a larger writing from left to right, but only half -of this is here visible. They treat of the physical laws of motion -of air and water. It does not seem to me that there is any reason -for concluding that this writing from left to right is spurious. -Compare with it the facsimile of the rough copy of Leonardo's letter -to Ludovico il Moro in Vol. II.] - -611. - -People were to be seen eagerly embarking victuals on various kinds -of hastily made barks. But little of the waves were visible in those -places where the dark clouds and rain were reflected. - -But where the flashes caused by the bolts of heaven were reflected, -there were seen as many bright spots, caused by the image of the -flashes, as there were waves to reflect them to the eye of the -spectator. - -The number of the images produced by the flash of lightning on the -waves of the water were multiplied in proportion to the distance of -the spectator's eye. - -So also the number of the images was diminished in proportion as -they were nearer the eye which saw them [Footnote 22. 23: _Com'e -provato_. See Vol. II, Nos. 874-878 and 892-901], as it has been -proved in the definition of the luminosity of the moon, and of our -marine horizon when the sun's rays are reflected in it and the eye -which receives the reflection is remote from the sea. - -VI. - -THE ARTIST'S MATERIALS. - -Of chalk and paper (612--617). - -612. - -To make points [crayons] for colouring dry. Temper with a little wax -and do not dry it; which wax you must dissolve with water: so that -when the white lead is thus tempered, the water being distilled, may -go off in vapour and the wax may remain; you will thus make good -crayons; but you must know that the colours must be ground with a -hot stone. - -613. - -Chalk dissolves in wine and in vinegar or in aqua fortis and can be -recombined with gum. - -614. - -PAPER FOR DRAWING UPON IN BLACK BY THE AID OF YOUR SPITTLE. - -Take powdered gall nuts and vitriol, powder them and spread them on -paper like a varnish, then write on it with a pen wetted with -spittle and it will turn as black as ink. - -615. - -If you want to make foreshortened letters stretch the paper in a -drawing frame and then draw your letters and cut them out, and make -the sunbeams pass through the holes on to another stretched paper, -and then fill up the angles that are wanting. - -616. - -This paper should be painted over with candle soot tempered with -thin glue, then smear the leaf thinly with white lead in oil as is -done to the letters in printing, and then print in the ordinary way. -Thus the leaf will appear shaded in the hollows and lighted on the -parts in relief; which however comes out here just the contrary. - -[Footnote: This text, which accompanies a facsimile impression of a -leaf of sage, has already been published in the _Saggio delle Opere -di L. da Vinci_, Milano 1872, p. 11. G. GOVI observes on this -passage: "_Forse aveva egli pensato ancora a farsi un erbario, od -almeno a riprodurre facilmente su carta le forme e i particolari -delle foglie di diverse piante; poiche (modificando un metodo che -probabilmente gli eia stato insegnato da altri, e che piu tardi si -legge ripetuto in molti ricettarii e libri di segreti), accanto a -una foglia di Salvia impressa in nero su carta bianca, lascio -scritto: Questa carta ... - -Erano i primi tentativi di quella riproduzione immediata delle parti -vegetali, che poi sotto il nome d'Impressione Naturale, fu condotta -a tanta perfezione in questi ultimi tempi dal signor de Hauer e da -altri_."] - -617. - -Very excellent will be a stiff white paper, made of the usual -mixture and filtered milk of an herb called calves foot; and when -this paper is prepared and damped and folded and wrapped up it may -be mixed with the mixture and thus left to dry; but if you break it -before it is moistened it becomes somewhat like the thin paste -called _lasagne_ and you may then damp it and wrap it up and put it -in the mixture and leave it to dry; or again this paper may be -covered with stiff transparent white and _sardonio_ and then damped -so that it may not form angles and then covered up with strong -transparent size and as soon as it is firm cut it two fingers, and -leave it to dry; again you may make stiff cardboard of _sardonio_ -and dry it and then place it between two sheets of papyrus and break -it inside with a wooden mallet with a handle and then open it with -care holding the lower sheet of paper flat and firm so that the -broken pieces be not separated; then have a sheet of paper covered -with hot glue and apply it on the top of all these pieces and let -them stick fast; then turn it upside down and apply transparent size -several times in the spaces between the pieces, each time pouring in -first some black and then some stiff white and each time leaving it -to dry; then smooth it and polish it. - -On the preparation and use of colours (618-627). - -618. - -To make a fine green take green and mix it with bitumen and you will -make the shadows darker. Then, for lighter [shades] green with -yellow ochre, and for still lighter green with yellow, and for the -high lights pure yellow; then mix green and turmeric together and -glaze every thing with it. To make a fine red take cinnabar or red -chalk or burnt ochre for the dark shadows and for the lighter ones -red chalk and vermilion and for the lights pure vermilion and then -glaze with fine lake. To make good oil for painting. One part of -oil, one of the first refining and one of the second. - -619. - -Use black in the shadow, and in the lights white, yellow, green, -vermilion and lake. Medium shadows; take the shadow as above and mix -it with the flesh tints just alluded to, adding to it a little -yellow and a little green and occasionally some lake; for the -shadows take green and lake for the middle shades. - -[Footnote 618 and 619: If we may judge from the flourishes with -which the writing is ornamented these passages must have been -written in Leonardo's youth.] - -620. - -You can make a fine ochre by the same method as you use to make -white. - -621. - -A FINE YELLOW. - -Dissolve realgar with one part of orpiment, with aqua fortis. - -WHITE. - -Put the white into an earthen pot, and lay it no thicker than a -string, and let it stand in the sun undisturbed for 2 days; and in -the morning when the sun has dried off the night dews. - -622. - -To make reddish black for flesh tints take red rock crystals from -Rocca Nova or garnets and mix them a little; again armenian bole is -good in part. - -623. - -The shadow will be burnt ,terra-verte'. - -624. - -THE PROPORTIONS OF COLOURS. - -If one ounce of black mixed with one ounce of white gives a certain -shade of darkness, what shade of darkness will be produced by 2 -ounces of black to 1 ounce of white? - -625. - -Remix black, greenish yellow and at the end blue. - -626. - -Verdigris with aloes, or gall or turmeric makes a fine green and so -it does with saffron or burnt orpiment; but I doubt whether in a -short time they will not turn black. Ultramarine blue and glass -yellow mixed together make a beautiful green for fresco, that is -wall-painting. Lac and verdigris make a good shadow for blue in oil -painting. - -627. - -Grind verdigris many times coloured with lemon juice and keep it -away from yellow (?). - -Of preparing the panel. - -628. - -TO PREPARE A PANEL FOR PAINTING ON. - -The panel should be cypress or pear or service-tree or walnut. You -must coat it over with mastic and turpentine twice distilled and -white or, if you like, lime, and put it in a frame so that it may -expand and shrink according to its moisture and dryness. Then give -it [a coat] of aqua vitae in which you have dissolved arsenic or -[corrosive] sublimate, 2 or 3 times. Then apply boiled linseed oil -in such a way as that it may penetrate every part, and before it is -cold rub it well with a cloth to dry it. Over this apply liquid -varnish and white with a stick, then wash it with urine when it is -dry, and dry it again. Then pounce and outline your drawing finely -and over it lay a priming of 30 parts of verdigris with one of -verdigris with two of yellow. - -[Footnote: M. RAVAISSON'S reading varies from mine in the following -passages: - -1._opero allor [?] bo [alloro?]_ = "_ou bien de [laurier]_." - -6. _fregalo bene con un panno_. He reads _pane_ for _panno_ and -renders it. "_Frotte le bien avec un pain de facon [jusqu'a ce] -qu'il_" etc. - -7. _colla stecca po laua_. He reads "_polacca_" = "_avec le couteau -de bois [?] polonais [?]_."] - -The preparation of oils (629--634). - -629. - -OIL. - -Make some oil of mustard seed; and if you wish to make it with -greater ease mix the ground seeds with linseed oil and put it all -under the press. - -630. - -TO REMOVE THE SMELL OF OIL. - -Take the rank oil and put ten pints into a jar and make a mark on -the jar at the height of the oil; then add to it a pint of vinegar -and make it boil till the oil has sunk to the level of the mark and -thus you will be certain that the oil is returned to its original -quantity and the vinegar will have gone off in vapour, carrying with -it the evil smell; and I believe you may do the same with nut oil or -any other oil that smells badly. - -631. - -Since walnuts are enveloped in a thin rind, which partakes of the -nature of ..., if you do not remove it when you make the oil from -them, this skin tinges the oil, and when you work with it this skin -separates from the oil and rises to the surface of the painting, and -this is what makes it change. - -632. - -TO RESTORE OIL COLOURS THAT HAVE BECOME DRY. - -If you want to restore oil colours that have become dry keep them -soaking in soft soap for a night and, with your finger, mix them up -with the soft soap; then pour them into a cup and wash them with -water, and in this way you can restore colours that have got dry. -But take care that each colour has its own vessel to itself adding -the colour by degrees as you restore it and mind that they are -thoroughly softened, and when you wish to use them for tempera wash -them five and six times with spring water, and leave them to settle; -if the soft soap should be thick with any of the colours pass it -through a filter. [Footnote: The same remark applies to these -sections as to No. 618 and 619.] - -633. - -OIL. - -Mustard seed pounded with linseed oil. - -634. - -... outside the bowl 2 fingers lower than the level of the oil, and -pass it into the neck of a bottle and let it stand and thus all the -oil will separate from this milky liquid; it will enter the bottle -and be as clear as crystal; and grind your colours with this, and -every coarse or viscid part will remain in the liquid. You must know -that all the oils that have been created in seads or fruits are -quite clear by nature, and the yellow colour you see in them only -comes of your not knowing how to draw it out. Fire or heat by its -nature has the power to make them acquire colour. See for example -the exudation or gums of trees which partake of the nature of rosin; -in a short time they harden because there is more heat in them than -in oil; and after some time they acquire a certain yellow hue -tending to black. But oil, not having so much heat does not do so; -although it hardens to some extent into sediment it becomes finer. -The change in oil which occurs in painting proceeds from a certain -fungus of the nature of a husk which exists in the skin which covers -the nut, and this being crushed along with the nuts and being of a -nature much resembling oil mixes with it; it is of so subtle a -nature that it combines with all colours and then comes to the -surface, and this it is which makes them change. And if you want the -oil to be good and not to thicken, put into it a little camphor -melted over a slow fire and mix it well with the oil and it will -never harden. - -[Footnote: The same remark applies to these sections as to No. 618 -and 619.] - -On varnishes [or powders] (635-637). - -635. - -VARNISH [OR POWDER]. - -Take cypress [oil] and distil it and have a large pitcher, and put -in the extract with so much water as may make it appear like amber, -and cover it tightly so that none may evaporate. And when it is -dissolved you may add in your pitcher as much of the said solution, -as shall make it liquid to your taste. And you must know that amber -is the gum of the cypress-tree. - -VARNISH [OR POWDER]. - -And since varnish [powder] is the resin of juniper, if you distil -juniper you can dissolve the said varnish [powder] in the essence, -as explained above. - -636. - -VARNISH [OR POWDER]. - -Notch a juniper tree and give it water at the roots, mix the liquor -which exudes with nut-oil and you will have a perfect varnish -[powder], made like amber varnish [powder], fine and of the best -quality make it in May or April. - -637. - -VARNISH [OR POWDER]. - -Mercury with Jupiter and Venus,--a paste made of these must be -corrected by the mould (?) continuously, until Mercury separates -itself entirely from Jupiter and Venus. [Footnote: Here, and in No. -641 _Mercurio_ seems to mean quicksilver, _Giove_ stands for iron, -_Venere_ for copper and _Saturno_ for lead.] - -On chemical materials (638-650). - -638. - -Note how aqua vitae absorbs into itself all the colours and smells -of flowers. If you want to make blue put iris flowers into it and -for red solanum berries (?) - -639. - -Salt may be made from human excrement burnt and calcined and made -into lees, and dried by a slow fire, and all dung in like manner -yields salt, and these salts when distilled are very pungent. - -640. - -Sea water filtered through mud or clay, leaves all its saltness in -it. Woollen stuffs placed on board ship absorb fresh water. If sea -water is distilled under a retort it becomes of the first excellence -and any one who has a little stove in his kitchen can, with the same -wood as he cooks with, distil a great quantity of water if the -retort is a large one. - -641. - -MOULD(?). - -The mould (?) may be of Venus, or of Jupiter and Saturn and placed -frequently in the fire. And it should be worked with fine emery and -the mould (?) should be of Venus and Jupiter impasted over (?) -Venus. But first you will test Venus and Mercury mixed with Jove, -and take means to cause Mercury to disperse; and then fold them well -together so that Venus or Jupiter be connected as thinly as -possible. - -[Footnote: See the note to 637.] - -642. - -Nitre, vitriol, cinnabar, alum, salt ammoniac, sublimated mercury, -rock salt, alcali salt, common salt, rock alum, alum schist (?), -arsenic, sublimate, realgar, tartar, orpiment, verdegris. - -643. - -Pitch four ounces virgin wax, four ounces incense, two ounces oil of -roses one ounce. - -644. - -Four ounces virgin wax, four ounces Greek pitch, two ounces incense, -one ounce oil of roses, first melt the wax and oil then the Greek -pitch then the other things in powder. - -645. - -Very thin glass may be cut with scissors and when placed over inlaid -work of bone, gilt, or stained of other colours you can saw it -through together with the bone and then put it together and it will -retain a lustre that will not be scratched nor worn away by rubbing -with the hand. - -646. - -TO DILUTE WHITE WINE AND MAKE IT PURPLE. - -Powder gall nuts and let this stand 8 days in the white wine; and in -the same way dissolve vitriol in water, and let the water stand and -settle very clear, and the wine likewise, each by itself, and strain -them well; and when you dilute the white wine with the water the -wine will become red. - -647. - -Put marcasite into aqua fortis and if it turns green, know that it -has copper in it. Take it out with saltpetre and soft soap. - -648. - -A white horse may have the spots removed with the Spanish haematite -or with aqua fortis or with ... Removes the black hair on a white -horse with the singeing iron. Force him to the ground. - -649. - -FIRE. - -If you want to make a fire which will set a hall in a blaze without -injury do this: first perfume the hall with a dense smoke of incense -or some other odoriferous substance: It is a good trick to play. Or -boil ten pounds of brandy to evaporate, but see that the hall is -completely closed and throw up some powdered varnish among the fumes -and this powder will be supported by the smoke; then go into the -room suddenly with a lighted torch and at once it will be in a -blaze. - -650. - -FIRE. - -Take away that yellow surface which covers oranges and distill them -in an alembic, until the distillation may be said to be perfect. - -FIRE. - -Close a room tightly and have a brasier of brass or iron with fire -in it and sprinkle on it two pints of aqua vitae, a little at a -time, so that it may be converted into smoke. Then make some one -come in with a light and suddenly you will see the room in a blaze -like a flash of lightning, and it will do no harm to any one. - -VII. - -PHILOSOPHY AND HISTORY OF THE ART OF PAINTING. - -The relation of art and nature (651. 652). - -651. - -What is fair in men, passes away, but not so in art. - -652. - -HE WHO DESPISES PAINTING LOVES NEITHER PHILOSOPHY NOR NATURE. - -If you condemn painting, which is the only imitator of all visible -works of nature, you will certainly despise a subtle invention which -brings philosophy and subtle speculation to the consideration of the -nature of all forms--seas and plains, trees, animals, plants and -flowers--which are surrounded by shade and light. And this is true -knowledge and the legitimate issue of nature; for painting is born -of nature--or, to speak more correctly, we will say it is the -grandchild of nature; for all visible things are produced by nature, -and these her children have given birth to painting. Hence we may -justly call it the grandchild of nature and related to God. - -Painting is superior to poetry (653. 654). - -653. - -THAT PAINTING SURPASSES ALL HUMAN WORKS BY THE SUBTLE CONSIDERATIONS -BELONGING TO IT. - -The eye, which is called the window of the soul, is the principal -means by which the central sense can most completely and abundantly -appreciate the infinite works of nature; and the ear is the second, -which acquires dignity by hearing of the things the eye has seen. If -you, historians, or poets, or mathematicians had not seen things -with your eyes you could not report of them in writing. And if you, -0 poet, tell a story with your pen, the painter with his brush can -tell it more easily, with simpler completeness and less tedious to -be understood. And if you call painting dumb poetry, the painter may -call poetry blind painting. Now which is the worse defect? to be -blind or dumb? Though the poet is as free as the painter in the -invention of his fictions they are not so satisfactory to men as -paintings; for, though poetry is able to describe forms, actions and -places in words, the painter deals with the actual similitude of the -forms, in order to represent them. Now tell me which is the nearer -to the actual man: the name of man or the image of the man. The name -of man differs in different countries, but his form is never changed -but by death. - -654. - -And if the poet gratifies the sense by means of the ear, the painter -does so by the eye--the worthier sense; but I will say no more of -this but that, if a good painter represents the fury of a battle, -and if a poet describes one, and they are both together put before -the public, you will see where most of the spectators will stop, to -which they will pay most attention, on which they will bestow most -praise, and which will satisfy them best. Undoubtedly painting being -by a long way the more intelligible and beautiful, will please most. -Write up the name of God [Christ] in some spot and setup His image -opposite and you will see which will be most reverenced. Painting -comprehends in itself all the forms of nature, while you have -nothing but words, which are not universal as form is, and if you -have the effects of the representation, we have the representation -of the effects. Take a poet who describes the beauty of a lady to -her lover and a painter who represents her and you will see to which -nature guides the enamoured critic. Certainly the proof should be -allowed to rest on the verdict of experience. You have ranked -painting among the mechanical arts but, in truth, if painters were -as apt at praising their own works in writing as you are, it would -not lie under the stigma of so base a name. If you call it -mechanical because it is, in the first place, manual, and that it is -the hand which produces what is to be found in the imagination, you -too writers, who set down manually with the pen what is devised in -your mind. And if you say it is mechanical because it is done for -money, who falls into this error--if error it can be called--more -than you? If you lecture in the schools do you not go to whoever -pays you most? Do you do any work without pay? Still, I do not say -this as blaming such views, for every form of labour looks for its -reward. And if a poet should say: "I will invent a fiction with a -great purpose," the painter can do the same, as Apelles painted -Calumny. If you were to say that poetry is more eternal, I say the -works of a coppersmith are more eternal still, for time preserves -them longer than your works or ours; nevertheless they have not much -imagination [29]. And a picture, if painted on copper with enamel -colours may be yet more permanent. We, by our arts may be called the -grandsons of God. If poetry deals with moral philosophy, painting -deals with natural philosophy. Poetry describes the action of the -mind, painting considers what the mind may effect by the motions [of -the body]. If poetry can terrify people by hideous fictions, -painting can do as much by depicting the same things in action. -Supposing that a poet applies himself to represent beauty, ferocity, -or a base, a foul or a monstrous thing, as against a painter, he may -in his ways bring forth a variety of forms; but will the painter not -satisfy more? are there not pictures to be seen, so like the actual -things, that they deceive men and animals? - -Painting is superior to sculpture (655. 656). - -655. - -THAT SCULPTURE IS LESS INTELLECTUAL THAN PAINTING, AND LACKS MANY -CHARACTERISTICS OF NATURE. - -I myself, having exercised myself no less in sculpture than in -painting and doing both one and the other in the same degree, it -seems to me that I can, without invidiousness, pronounce an opinion -as to which of the two is of the greatest merit and difficulty and -perfection. In the first place sculpture requires a certain light, -that is from above, a picture carries everywhere with it its own -light and shade. Thus sculpture owes its importance to light and -shade, and the sculptor is aided in this by the nature, of the -relief which is inherent in it, while the painter whose art -expresses the accidental aspects of nature, places his effects in -the spots where nature must necessarily produce them. The sculptor -cannot diversify his work by the various natural colours of objects; -painting is not defective in any particular. The sculptor when he -uses perspective cannot make it in any way appear true; that of the -painter can appear like a hundred miles beyond the picture itself. -Their works have no aerial perspective whatever, they cannot -represent transparent bodies, they cannot represent luminous bodies, -nor reflected lights, nor lustrous bodies--as mirrors and the like -polished surfaces, nor mists, nor dark skies, nor an infinite number -of things which need not be told for fear of tedium. As regards the -power of resisting time, though they have this resistance [Footnote -19: From what is here said as to painting on copper it is very -evident that Leonardo was not acquainted with the method of painting -in oil on thin copper plates, introduced by the Flemish painters of -the XVIIth century. J. LERMOLIEFF has already pointed out that in -the various collections containing pictures by the great masters of -the Italian Renaissance, those painted on copper (for instance the -famous reading Magdalen in the Dresden Gallery) are the works of a -much later date (see _Zeitschrift fur bildende Kunst_. Vol. X pg. -333, and: _Werke italienischer Master in den Galerien von Munchen, -Dresden und Berlin_. Leipzig 1880, pg. 158 and 159.)--Compare No. -654, 29.], a picture painted on thick copper covered with white -enamel on which it is painted with enamel colours and then put into -the fire again and baked, far exceeds sculpture in permanence. It -may be said that if a mistake is made it is not easy to remedy it; -it is but a poor argument to try to prove that a work be the nobler -because oversights are irremediable; I should rather say that it -will be more difficult to improve the mind of the master who makes -such mistakes than to repair the work he has spoilt. - -656. - -We know very well that a really experienced and good painter will -not make such mistakes; on the contrary, with sound rules he will -remove so little at a time that he will bring his work to a good -issue. Again the sculptor if working in clay or wax, can add or -reduce, and when his model is finished it can easily be cast in -bronze, and this is the last operation and is the most permanent -form of sculpture. Inasmuch as that which is merely of marble is -liable to ruin, but not bronze. Hence a painting done on copper -which as I said of painting may be added to or altered, resembles -sculpture in bronze, which, having first been made in wax could then -be altered or added to; and if sculpture in bronze is durable, this -work in copper and enamel is absolutely imperishable. Bronze is but -dark and rough after all, but this latter is covered with various -and lovely colours in infinite variety, as has been said above; or -if you will have me only speak of painting on panel, I am content to -pronounce between it and sculpture; saying that painting is the more -beautiful and the more imaginative and the more copious, while -sculpture is the more durable but it has nothing else. Sculpture -shows with little labour what in painting appears a miraculous thing -to do; to make what is impalpable appear palpable, flat objects -appear in relief, distant objects seem close. In fact painting is -adorned with infinite possibilities which sculpture cannot command. - -Aphorisms (657-659). - -657. - -OF PAINTING. - -Men and words are ready made, and you, O Painter, if you do not know -how to make your figures move, are like an orator who knows not how -to use his words. - -658. - -As soon as the poet ceases to represent in words what exists in -nature, he in fact ceases to resemble the painter; for if the poet, -leaving such representation, proceeds to describe the flowery and -flattering speech of the figure, which he wishes to make the -speaker, he then is an orator and no longer a poet nor a painter. -And if he speaks of the heavens he becomes an astrologer, and -philosopher; and a theologian, if he discourses of nature or God. -But, if he restricts himself to the description of objects, he would -enter the lists against the painter, if with words he could satisfy -the eye as the painter does. - -659. - -Though you may be able to tell or write the exact description of -forms, the painter can so depict them that they will appear alive, -with the shadow and light which show the expression of a face; which -you cannot accomplish with the pen though it can be achieved by the -brush. - -On the history of painting (660. 661). - -660. - -THAT PAINTING DECLINES AND DETERIORATES FROM AGE TO AGE, WHEN -PAINTERS HAVE NO OTHER STANDARD THAN PAINTING ALREADY DONE. - -Hence the painter will produce pictures of small merit if he takes -for his standard the pictures of others. But if he will study from -natural objects he will bear good fruit; as was seen in the painters -after the Romans who always imitated each other and so their art -constantly declined from age to age. After these came Giotto the -Florentine who--not content with imitating the works of Cimabue his -master--being born in the mountains and in a solitude inhabited only -by goats and such beasts, and being guided by nature to his art, -began by drawing on the rocks the movements of the goats of which he -was keeper. And thus he began to draw all the animals which were to -be found in the country, and in such wise that after much study he -excelled not only all the masters of his time but all those of many -bygone ages. Afterwards this art declined again, because everyone -imitated the pictures that were already done; thus it went on from -century to century until Tomaso, of Florence, nicknamed Masaccio, -showed by his perfect works how those who take for their standard -any one but nature--the mistress of all masters--weary themselves in -vain. And, I would say about these mathematical studies that those -who only study the authorities and not the works of nature are -descendants but not sons of nature the mistress of all good authors. -Oh! how great is the folly of those who blame those who learn from -nature [Footnote 22: _lasciando stare li autori_. In this -observation we may detect an indirect evidence that Leonardo -regarded his knowledge of natural history as derived from his own -investigations, as well as his theories of perspective and optics. -Compare what he says in praise of experience (Vol II; _XIX_).], -setting aside those authorities who themselves were the disciples of -nature. - -661. - -That the first drawing was a simple line drawn round the shadow of a -man cast by the sun on a wall. - -The painter's scope. - -662. - -The painter strives and competes with nature. - -_X. - -Studies and Sketches for Pictures and Decorations. - -An artist's manuscript notes can hardly be expected to contain any -thing more than incidental references to those masterpieces of his -work of which the fame, sounded in the writings of his -contemporaries, has left a glorious echo to posterity. We need not -therefore be surprised to find that the texts here reproduced do not -afford us such comprehensive information as we could wish. On the -other hand, the sketches and studies prepared by Leonardo for the -two grandest compositions he ever executed: The Fresco of the Last -Supper in the Refectory of Santa Maria delle Grazie at Milan, and -the Cartoon of the Battle of Anghiari, for the Palazzo della -Signoria at Florence--have been preserved; and, though far from -complete, are so much more numerous than the manuscript notes, that -we are justified in asserting that in value and interest they amply -compensate for the meagerness of the written suggestions. - -The notes for the composition of the Last Supper, which are given -under nos._ 665 _and_ 666 _occur in a MS. at South Kensington, II2, -written in the years_ 1494-1495. _This MS. sketch was noted down not -more than three or four years before the painting was executed, -which justifies the inference that at the time when it was written -the painter had not made up his mind definitely even as to the -general scheme of the work; and from this we may also conclude that -the drawings of apostles' heads at Windsor, in red chalk, must be -ascribed to a later date. They are studies for the head of St. -Matthew, the fourth figure on Christ's left hand--see Pl. XL VII, -the sketch (in black chalk) for the head of St. Philip, the third -figure on the left hand--see Pl. XL VIII, for St. Peter's right -arm--see Pl. XLIX, and for the expressive head of Judas which has -unfortunately somewhat suffered by subsequent restoration of -outlines,--see Pl. L. According to a tradition, as unfounded as it -is improbable, Leonardo made use of the head of Padre Bandelli, the -prior of the convent, as the prototype of his Judas; this however -has already been contradicted by Amoretti "Memorie storiche" cap. -XIV. The study of the head of a criminal on Pl. LI has, it seems to -me, a better claim to be regarded as one of the preparatory sketches -for the head of Judas. The Windsor collection contains two old -copies of the head of St. Simon, the figure to the extreme left of -Christ, both of about equal merit (they are marked as Nos._ 21 _and_ -36_)--the second was reproduced on Pl. VIII of the Grosvenor -Gallery Publication in_ 1878. _There is also at Windsor a drawing in -black chalk of folded hands (marked with the old No._ 212; _No. LXI -of the Grosvenor Gallery Publication) which I believe to be a copy -of the hands of St. John, by some unknown pupil. A reproduction of -the excellent drawings of heads of Apostles in the possession of H. -R. H. the Grand Duchess of Weimar would have been out of my province -in this work, and, with regard to them, I must confine myself to -pointing out that the difference in style does not allow of our -placing the Weimar drawings in the same category as those here -reproduced. The mode of grouping in the Weimar drawings is of itself -sufficient to indicate that they were not executed before the -picture was painted, but, on the contrary, afterwards, and it is, on -the face of it, incredible that so great a master should thus have -copied from his own work. - -The drawing of Christ's head, in the Brera palace at Milan was -perhaps originally the work of Leonardo's hand; it has unfortunately -been entirely retouched and re-drawn, so that no decisive opinion -can be formed as to its genuineness. - -The red chalk drawing reproduced on Pl. XLVI is in the Accademia at -Venice; it was probably made before the text, Nos._ 664 _and_ 665, -_was written. - -The two pen and ink sketches on Pl. XLV seem to belong to an even -earlier date; the more finished drawing of the two, on the right -hand, represents Christ with only St. John and Judas and a third -disciple whose action is precisely that described in No._ 666, -_Pl._ 4. _It is hardly necessary to observe that the other sketches -on this page and the lines of text below the circle (containing the -solution of a geometrical problem) have no reference to the picture -of the Last Supper. With this figure of Christ may be compared a -similar pen and ink drawing reproduced on page_ 297 _below on the -left hand; the original is in the Louvre. On this page again the -rest of the sketches have no direct bearing on the composition of -the Last Supper, not even, as it seems to me, the group of four men -at the bottom to the right hand--who are listening to a fifth, in -their midst addressing them. Moreover the writing on this page (an -explanation of a disk shaped instrument) is certainly not in the -same style as we find constantly used by Leonardo after the year_ -1489. - -_It may be incidentally remarked that no sketches are known for the -portrait of "Mona Lisa", nor do the MS. notes ever allude to it, -though according to Vasari the master had it in hand for fully four -years. - -Leonardo's cartoon for the picture of the battle of Anghiari has -shared the fate of the rival work, Michaelangelo's "Bathers summoned -to Battle". Both have been lost in some wholly inexplicable manner. -I cannot here enter into the remarkable history of this work; I can -only give an account of what has been preserved to us of Leonardo's -scheme and preparations for executing it. The extent of the material -in studies and drawings was till now quite unknown. Their -publication here may give some adequate idea of the grandeur of this -famous work. The text given as No._ 669 _contains a description of -the particulars of the battle, but for the reasons given in the note -to this text, I must abandon the idea of taking this passage as the -basis of my attempt to reconstruct the picture as the artist -conceived and executed it. - -I may here remind the reader that Leonardo prepared the cartoon in -the Sala del Papa of Santa Maria Novella at Florence and worked -there from the end of October 1503 till February 1504, and then was -busied with the painting in the Sala del Consiglio in the Palazzo -della Signoria, till the work was interrupted at the end of May -1506. (See Milanesi's note to Vasari pp. 43--45 Vol. IV ed. 1880.) -Vasari, as is well known, describes only one scene or episode of the -cartoon--the Battle for the Standard in the foreground of the -composition, as it would seem; and this only was ever finished as a -mural decoration in the Sala del Consiglio. This portion of the -composition is familiar to all from the disfigured copy engraved by -Edelinck. Mariette had already very acutely observed that Edelinck -must surely have worked from a Flemish copy of the picture. There is -in the Louvre a drawing by Rubens (No. 565) which also represents -four horsemen fighting round a standard and which agrees with -Edelinck's engraving, but the engraving reverses the drawing. An -earlier Flemish drawing, such as may have served as the model for -both Rubens and Edelinck, is in the Uffizi collection (see -Philpots's Photograph, No. 732). It seems to be a work of the second -half of the XVIth century, a time when both the picture and the -cartoon had already been destroyed. It is apparently the production -of a not very skilled hand. Raphael Trichet du Fresne, 1651, -mentions that a small picture by Leonardo himself of the Battle of -the Standard was then extant in the Tuileries; by this he probably -means the painting on panel which is now in the possession of Madame -Timbal in Paris, and which has lately been engraved by Haussoullier -as a work by Leonardo. The picture, which is very carefully painted, -seems to me however to be the work of some unknown Florentine -painter, and probably executed within the first ten years of the -XVIth century. At the same time, it would seem to be a copy not from -Leonardo's cartoon, but from his picture in the Palazzo della -Signoria; at any rate this little picture, and the small Flemish -drawing in Florence are the oldest finished copies of this episode -in the great composition of the Battle of Anghiari. - -In his Life of Raphael, Vasari tells us that Raphael copied certain -works of Leonardo's during his stay in Florence. Raphael's first -visit to Florence lasted from the middle of October 1504 till July -1505, and he revisited it in the summer of 1506. The hasty sketch, -now in the possession of the University of Oxford and reproduced on -page 337 also represents the Battle of the Standard and seems to -have been made during his first stay, and therefore not from the -fresco but from the cartoon; for, on the same sheet we also find, -besides an old man's head drawn in Leonardo's style, some studies -for the figure of St. John the Martyr which Raphael used in 1505 in -his great fresco in the Church of San Severo at Perugia. - -Of Leonardo's studies for the Battle of Anghiari I must in the first -place point to five, on three of which--Pl. LII 2, Pl. LIII, Pl. -LVI--we find studies for the episode of the Standard. The standard -bearer, who, in the above named copies is seen stooping, holding on -to the staff across his shoulder, is immediately recognisable as the -left-hand figure in Raphael's sketch, and we find it in a similar -attitude in Leonardo's pen and ink drawing in the British -Museum--Pl. LII, 2--the lower figure to the right. It is not -difficult to identify the same figure in two more complicated groups -in the pen and ink drawings, now in the Accademia at Venice--Pl. -LIII, and Pl. LIV--where we also find some studies of foot soldiers -fighting. On the sheet in the British Museum--Pl. LII, 2--we find, -among others, one group of three horses galloping forwards: one -horseman is thrown and protects himself with his buckler against the -lance thrusts of two others on horseback, who try to pierce him as -they ride past. The same action is repeated, with some variation, in -two sketches in pen and ink on a third sheet, in the Accademia at -Venice, Pl. LV; a coincidence which suggests the probability of such -an incident having actually been represented on the cartoon. We are -not, it is true, in a position to declare with any certainty which -of these three dissimilar sketches may have been the nearest to the -group finally adopted in executing the cartoon. - -With regard, however, to one of the groups of horsemen it is -possible to determine with perfect certainty not only which -arrangement was preferred, but the position it occupied in the -composition. The group of horsemen on Pl. LVII is a drawing in black -chalk at Windsor, which is there attributed to Leonardo, but which -appears to me to be the work of Cesare da Sesto, and the -Commendatore Giov. Morelli supports me in this view. It can hardly -be doubted that da Sesto, as a pupil of Leonardo's, made this -drawing from his master's cartoon, if we compare it with the copy -made by Raphael--here reproduced, for just above the fighting -horseman in Raphael's copy it is possible to detect a horse which is -seen from behind, going at a slower pace, with his tail flying out -to the right and the same horse may be seen in the very same -attitude carrying a dimly sketched rider, in the foreground of -Cesare da Sesto's drawing._ - -_If a very much rubbed drawing in black chalk at Windsor--Pl. -LVI--is, as it appears to be, the reversed impression of an original -drawing, it is not difficult to supplement from it the portions -drawn by Cesare da Sesto. Nay, it may prove possible to reconstruct -the whole of the lost cartoon from the mass of materials we now have -at hand which we may regard as the nucleus of the composition. A -large pen and ink drawing by Raphael in the Dresden collection, -representing three horsemen fighting, and another, by Cesare da -Sesto, in the Uffizi, of light horsemen fighting are a further -contribution which will help us to reconstruct it._ - -_The sketch reproduced on Pl. LV gives a suggestive example of the -way in which foot-soldiers may have been introduced into the cartoon -as fighting among the groups of horsemen; and I may here take the -opportunity of mentioning that, for reasons which it would be out of -place to enlarge upon here, I believe the two genuine drawings by -Raphael's hand in his "Venetian sketch-book" as it is called--one of -a standard bearer marching towards the left, and one of two -foot-soldiers armed with spears and fighting with a horseman--to be -undoubtedly copies from the cartoon of the Battle of Anghiari._ - -_Leonardo's two drawings, preserved in the museum at Buda-Pesth and -reproduced on pages 338 and 339 are preliminary studies for the -heads of fighting warriors. The two heads drawn in black chalk (pg. -338) and the one seen in profile, turned to the left, drawn in red -chalk (pg. 339), correspond exactly with those of two horsemen in -the scene of the fight round the standard as we see them in Madame -Timbal's picture and in the other finished copies. An old copy of -the last named drawing by a pupil of Leonardo is in MS. C. A. 187b; -561b (See Saggio, Tav. XXII). Leonardo used to make such finished -studies of heads as those, drawn on detached sheets, before -beginning his pictures from his drawings--compare the preparatory -studies for the fresco of the Last Supper, given on Pl. XLVII and -Pl. L. Other drawings of heads, all characterised by the expression -of vehement excitement that is appropriate to men fighting, are to -be seen at Windsor (No. 44) and at the Accademia at Venice (IV, 13); -at the back of one of the drawings at Buda-Pesth there is the bust -of a warrior carrying a spear on his left shoulder, holding up the -left arm (See Csatakepek a XVI--lk Szazadbol osszeallitotta Pvlszky -Karoly). These drawings may have been made for other portions of the -cartoon, of which no copies exist, and thus we are unable to -identify these preparatory drawings. Finally I may add that a sketch -of fighting horse and foot soldiers, formerly in the possession of -M. Thiers and published by Charles Blanc in his "Vies des Peintres" -can hardly be accepted as genuine. It is not to be found, as I am -informed, among the late President's property, and no one appears to -know where it now is._ - -_An attempted reconstruction of the Cartoon, which is not only -unsuccessful but perfectly unfounded, is to be seen in the -lithograph by Bergeret, published in Charles Blanc's "Vies des -peintres" and reprinted in "The great Artists. L. da Vinci", p. 80. -This misleading pasticcio may now be rejected without hesitation._ - -_There are yet a few original drawings by Leonardo which might be -mentioned here as possibly belonging to the cartoon of the Battle; -such as the pen and ink sketches on Pl. XXI and on Pl. XXXVIII, No. -3, but we should risk too wide a departure from the domain of -ascertained fact._ - -_With regard to the colours and other materials used by Leonardo the -reader may be referred to the quotations from the accounts for the -picture in question given by Milanesi in his edition of Vasari (Vol. -IV, p. 44, note) where we find entries of a similar character to -those in Leonardo's note books for the year 1505; S. K. M. 12 (see -No. 636)._ - -_That Leonardo was employed in designing decorations and other -preparations for high festivals, particularly for the court of -Milan, we learn not only from the writings of his contemporaries but -from his own incidental allusions; for instance in MS. C. l5b (1), -l. 9. In the arrangement of the texts referring to this I have -placed those first, in which historical personages are named--Nos. -670-674. Among the descriptions of Allegorical subjects two texts -lately found at Oxford have been included, Nos. 676 and 677. They -are particularly interesting because they are accompanied by large -sketches which render the meaning of the texts perfectly clear. It -is very intelligible that in other cases, where there are no -illustrative sketches, the notes must necessarily remain obscure or -admit of various interpretations. The literature of the time affords -ample evidence of the use of such allegorical representations, -particularly during the Carnival and in Leonardo's notes we find the -Carnival expressly mentioned--Nos. 685 and 704. Vasari in his Life -of Pontormo, particularly describes that artist's various -undertakings for Carnival festivities. These very graphic -descriptions appear to me to throw great light in more ways than one -on the meaning of Leonardo's various notes as to allegorical -representations and also on mottoes and emblems--Nos. 681-702. In -passing judgment on the allegorical sketches and emblems it must not -be overlooked that even as pictures they were always accompanied by -explanations in words. Several finished drawings of allegorical -compositions or figures have been preserved, but as they have no -corresponding explanation in the MSS. they had no claim to be -reproduced here. The female figure on Pl. XXVI may perhaps be -regarded as a study for such an allegorical painting, of which the -purport would have been explained by an inscription._ - -On Madonna pictures. - -663. - -[In the autumn of] 1478 I began the two Madonna [pictures]. - -[Footnote: Photographs of this page have been published by BRAUN, -No. 439, and PHILPOT, No. 718. - -1. _Incominciai_. We have no other information as to the two -pictures of the Madonna here spoken of. As Leonardo here tells us -that he had begun two Madonnas at the same time, the word -'_incominciai_' may be understood to mean that he had begun at the -same time preparatory studies for two pictures to be painted later. -If this is so, the non-existence of the pictures may be explained by -supposing that they were only planned and never executed. I may here -mention a few studies for pictures of the Madonna which probably -belong to this early time; particularly a drawing in silver-point on -bluish tinted paper at Windsor--see Pl. XL, No. 3--, a drawing of -which the details have almost disappeared in the original but have -been rendered quite distinct in the reproduction; secondly a slight -pen and ink sketch in, the Codex VALLARDI, in the Louvre, fol. 64, -No. 2316; again a silver point drawing of a Virgin and child drawn -over again with the pen in the His de la Salle collection also in -the Louvre, No. 101. (See Vicomte BOTH DE TAUZIA, _Notice des -dessins de la collection His de la Salle, exposes au Louvre_. Paris -1881, pp. 80, 81.) This drawing is, it is true, traditionally -ascribed to Raphael, but the author of the catalogue very justly -points out its great resemblance with the sketches for Madonnas in -the British Museum which are indisputably Leonardo's. Some of these -have been published by Mr. HENRY WALLIS in the Art Journal, New Ser. -No. 14, Feb. 1882. If the non-existence of the two pictures here -alluded to justifies my hypothesis that only studies for such -pictures are meant by the text, it may also be supposed that the -drawings were made for some comrade in VERROCCHIO'S atelier. (See -VASARI, Sansoni's ed. Florence 1880. Vol. IV, p. 564): "_E perche a -Lerenzo piaceva fuor di modo la maniera di Lionardo, la seppe cosi -bene imitare, che niuno fu che nella pulitezza e nel finir l'opere -con diligenza l'imitasse piu di lui_." Leonardo's notes give me no -opportunity of discussing the pictures executed by him in Florence, -before he moved to Milan. So the studies for the unfinished picture -of the Adoration of the Magi--in the Uffizi, Florence--cannot be -described here, nor would any discussion about the picture in the -Louvre "_La Vierge aux Rochers_" be appropriate in the absence of -all allusion to it in the MSS. Therefore, when I presently add a few -remarks on this painting in explanation of the Master's drawings for -it, it will be not merely with a view to facilitate critical -researches about the picture now in the National Gallery, London, -which by some critics has been pronounced to be a replica of the -Louvre picture, but also because I take this opportunity of -publishing several finished studies of the Master's which, even if -they were not made in Florence but later in Milan, must have been -prior to the painting of the Last Supper. The original picture in -Paris is at present so disfigured by dust and varnish that the -current reproductions in photography actually give evidence more of -the injuries to which the picture has been exposed than of the -original work itself. The wood-cut given on p. 344, is only intended -to give a general notion of the composition. It must be understood -that the outline and expression of the heads, which in the picture -is obscured but not destroyed, is here altogether missed. The -facsimiles which follow are from drawings which appear to me to be -studies for "_La Vierge aux Rochers_." - -1. A drawing in silver point on brown toned paper of a woman's head -looking to the left. In the Royal Library at Turin, apparently a -study from nature for the Angel's head (Pl. XLII). - -2. A study of drapery for the left leg of the same figure, done with -the brush, Indian ink on greenish paper, the lights heightened with -white. - -The original is at Windsor, No. 223. The reproduction Pl. XLIII is -defective in the shadow on the upper part of the thigh, which is not -so deep as in the original; it should also be observed that the -folds of the drapery near the hips are somewhat altered in the -finished work in the Louvre, while the London copy shows a greater -resemblance to this study in that particular. - -3. A study in red chalk for the bust of the Infant Christ--No. 3 in -the Windsor collection (Pl. XLIV). The well-known silver-point -drawing on pale green paper, in the Louvre, of a boy's head (No. 363 -in REISET, _Notice des dessins, Ecoles d'Italie_) seems to me to be -a slightly altered copy, either from the original picture or from -this red chalk study. - -4. A silver-point study on greenish paper, for the head of John the -Baptist, reproduced on p. 342. This was formerly in the Codex -Vallardi and is now exhibited among the drawings in the Louvre. The -lights are, in the original, heightened with white; the outlines, -particularly round the head and ear, are visibly restored. - -There is a study of an outstretched hand--No. 288 in the Windsor -collection--which was published in the Grosvenor Gallery -Publication, 1878, simply under the title of: "No. 72 Study of a -hand, pointing" which, on the other hand, I regard as a copy by a -pupil. The action occurs in the kneeling angel of the Paris picture -and not in the London copy. - -These four genuine studies form, I believe, a valuable substitute in -the absence of any MS. notes referring to the celebrated Paris -picture.] - -Bernardo di Bandino's Portrait. - -664. - -A tan-coloured small cap, A doublet of black serge, A black jerkin -lined A blue coat lined, with fur of foxes' breasts, and the collar -of the jerkin covered with black and white stippled velvet Bernardo -di Bandino Baroncelli; black hose. - -[Footnote: These eleven lines of text are by the side of the pen and -ink drawing of a man hanged--Pl. LXII, No. 1. This drawing was -exhibited in 1879 at the _Ecole des Beaux-Arts_ in Paris and the -compilers of the catalogue amused themselves by giving the victim's -name as follows: "_Un pendu, vetu d'une longue robe, les mains liees -sur le dos ... Bernardo di Bendino Barontigni, marchand de -pantalons_" (see _Catalogue descriptif des Dessins de Mailres -anciens exposes a l'Ecole des Beaux Arts_, Paris 1879; No. 83, pp. -9-10). Now, the criminal represented here, is none other than -Bernardino di Bandino Baroncelli the murderer of Giuliano de'Medici, -whose name as a coadjutor in the conspiracy of the Pazzi has gained -a melancholy notoriety by the tragedy of the 26th April 1478. -Bernardo was descended from an ancient family and the son of the man -who, under King Ferrante, was President of the High Court of Justice -in Naples. His ruined fortunes, it would seem, induced him to join -the Pazzi; he and Francesco Pazzi were entrusted with the task of -murdering Giuliano de'Medici on the fixed day. Their victim not -appearing in the cathedral at the hour when they expected him, the -two conspirators ran to the palace of the Medici and induced him to -accompany them. Giuliano then took his place in the chancel of the -Cathedral, and as the officiating priest raised the Host--the sign -agreed upon--Bernardo stabbed the unsuspecting Giuliano in the -breast with a short sword; Giuliano stepped backwards and fell dead. -The attempt on Lorenzo's life however, by the other conspirators at -the same moment, failed of success. Bernardo no sooner saw that -Lorenzo tried to make his escape towards the sacristy, than he -rushed upon him, and struck down Francesco Nori who endeavoured to -protect Lorenzo. How Lorenzo then took refuge behind the brazen -doors of the sacristy, and how, as soon as Giuliano's death was made -known, the further plans of the conspirators were defeated, while a -terrible vengeance overtook all the perpetrators and accomplices, -this is no place to tell. Bernardo Bandini alone seemed to be -favoured by fortune; he hid first in the tower of the Cathedral, and -then escaped undiscovered from Florence. Poliziano, who was with -Lorenzo in the Cathedral, says in his 'Conjurationis Pactianae -Commentarium': "_Bandinus fugitans in Tiphernatem incidit, a quo in -aciem receptus Senas pervenit_." And Gino Capponi in summing up the -reports of the numerous contemporary narrators of the event, says: -"_Bernardo Bandini ricoverato in Costantinopoli, fu per ordine del -Sultano preso e consegnato a un Antonio di Bernardino dei Medici, -che Lorenzo aveva mandato apposta in Turchia: cosi era grande la -potenza di quest' uomo e grande la voglia di farne mostra e che non -restasse in vita chi aveagli ucciso il fratello, fu egli applicato -appena giunto_" (_Storia della Republica di Firenze II_, 377, 378). -Details about the dates may be found in the _Chronichetta di -Belfredello Strinati Alfieri_: "_Bernardo di Bandino Bandini -sopradetto ne venne preso da Gostantinopoti a di 14. Dicembre 1479 e -disaminato, che fu al Bargello, fu impiccato alle finestre di detto -Bargello allato alla Doana a di 29. Dicembre MCCCCLXXIX che pochi di -stette_." It may however be mentioned with reference to the mode of -writing the name of the assassin that, though most of his -contemporaries wrote Bernardo Bandini, in the _Breve Chronicon -Caroli Petri de Joanninis_ he is called Bernardo di Bandini -Baroncelli; and, in the _Sententiae Domini Matthaei de Toscana_, -Bernardus Joannis Bandini de Baroncellis, as is written on -Leonardo's drawing of him when hanged. Now VASARI, in the life of -_Andrea del Castagno_ (Vol. II, 680; ed. Milanesi 1878), tells us -that in 1478 this painter was commissioned by order of the Signoria -to represent the members of the Pazzi conspiracy as traitors, on the -facade of the Palazzo del Podesta--the Bargello. This statement is -obviously founded on a mistake, for Andrea del Castagno was already -dead in 1457. He had however been commissioned to paint Rinaldo -degli Albizzi, when declared a rebel and exiled in 1434, and his -adherents, as hanging head downwards; and in consequence he had -acquired the nickname of Andrea degl' Impiccati. On the 21st July -1478 the Council of Eight came to the following resolution: "_item -servatis etc. deliberaverunt et santiaverunt Sandro Botticelli pro -ejus labore in pingendo proditores flor. quadraginta largos_" (see -G. MILANESI, _Arch. star. VI_ (1862) p. 5 note.) - -As has been told, Giuliano de' Medici was murdered on the 26th April -1478, and we see by this that only three months later Botticelli was -paid for his painting of the "_proditores_". We can however hardly -suppose that all the members of the conspiracy were depicted by him -in fresco on the facade of the palace, since no fewer than eighty -had been condemned to death. We have no means of knowing whether, -besides Botticelli, any other painters, perhaps Leonardo, was -commissioned, when the criminals had been hanged in person out of -the windows of the Palazzo del Podesta to represent them there -afterwards in effigy in memory of their disgrace. Nor do we know -whether the assassin who had escaped may at first not have been -provisionally represented as hanged in effigy. Now, when we try to -connect the historical facts with this drawing by Leonardo -reproduced on Pl. LXII, No. I, and the full description of the -conspirator's dress and its colour on the same sheet, there seems to -be no reasonable doubt that Bernardo Bandini is here represented as -he was actually hanged on December 29th, 1479, after his capture at -Constantinople. The dress is certainly not that in which he -committed the murder. A long furred coat might very well be worn at -Constantinople or at Florence in December, but hardly in April. The -doubt remains whether Leonardo described Bernardo's dress so fully -because it struck him as remarkable, or whether we may not rather -suppose that this sketch was actually made from nature with the -intention of using it as a study for a wall painting to be executed. -It cannot be denied that the drawing has all the appearance of -having been made for this purpose. Be this as it may, the sketch -under discussion proves, at any rate, that Leonardo was in Florence -in December 1479, and the note that accompanies it is valuable as -adding one more characteristic specimen to the very small number of -his MSS. that can be proved to have been written between 1470 and -1480.] - -Notes on the Last Supper (665-668). - -665. - -One who was drinking and has left the glass in its position and -turned his head towards the speaker. - -Another, twisting the fingers of his hands together turns with stern -brows to his companion [6]. Another with his hands spread open shows -the palms, and shrugs his shoulders up his ears making a mouth of -astonishment [8]. - -[9] Another speaks into his neighbour's ear and he, as he listens to -him, turns towards him to lend an ear [10], while he holds a knife -in one hand, and in the other the loaf half cut through by the -knife. [13] Another who has turned, holding a knife in his hand, -upsets with his hand a glass on the table [14]. - -[Footnote 665, 666: In the original MS. there is no sketch to -accompany these passages, and if we compare them with those drawings -made by Leonardo in preparation for the composition of the -picture--Pl. XLV, XLVI--, (compare also Pl. LII, 1 and the drawings -on p. 297) it is impossible to recognise in them a faithful -interpretation of the whole of this text; but, if we compare these -passages with the finished picture (see p. 334) we shall see that in -many places they coincide. For instance, compare No. 665, 1. 6--8, -with the fourth figure on the right hand of Christ. The various -actions described in lines 9--10, 13--14 are to be seen in the group -of Peter, John and Judas; in the finished picture however it is not -a glass but a salt cellar that Judas is upsetting.] - -666. - -Another lays his hand on the table and is looking. Another blows his -mouthful. [3] Another leans forward to see the speaker shading his -eyes with his hand. [5] Another draws back behind the one who leans -forward, and sees the speaker between the wall and the man who is -leaning [Footnote: 6. _chinato_. I have to express my regret for -having misread this word, written _cinato_ in the original, and -having altered it to _"ciclo"_ when I first published this text, in -'The Academy' for Nov. 8, 1879 immediately after I had discovered -it, and subsequently in the small biography of Leonardo da Vinci -(Great Artists) p. 29.]. - -[Footnote: In No. 666. Line I must refer to the furthest figure on -the left; 3, 5 and 6 describe actions which are given to the group -of disciples on the left hand of Christ.] - -667. - -CHRIST. - -Count Giovanni, the one with the Cardinal of Mortaro. - -[Footnote: As this note is in the same small Manuscript as the -passage here immediately preceding it, I may be justified in -assuming that Leonardo meant to use the features of the person here -named as a suitable model for the figure of Christ. The celebrated -drawing of the head of Christ, now hanging in the Brera Gallery at -Milan, has obviously been so much restored that it is now impossible -to say, whether it was ever genuine. We have only to compare it with -the undoubtedly genuine drawings of heads of the disciples in PI. -XLVII, XLVIII and L, to admit that not a single line of the Milan -drawing in its present state can be by the same hand.] - -668. - -Philip, Simon, Matthew, Thomas, James the Greater, Peter, Philip, -Andrew, Bartholomew. - -[Footnote: See PI. XLVI. The names of the disciples are given in the -order in which they are written in the original, from right to left, -above each head. The original drawing is here slightly reduced in -scale; it measures 39 centimetres in length by 26 in breadth.] - -669. - - On the battle of Anghiari. - Florentine - Neri di Gino Capponi - Bernardetto de' Medici - Micheletto, - Niccolo da Pisa - Conte Francesco - Pietro Gian Paolo - Guelfo Orsino, - Messer Rinaldo degli - Albizzi - -Begin with the address of Niccolo Piccinino to the soldiers and the -banished Florentines among whom are Messer Rinaldo degli Albizzi and -other Florentines. Then let it be shown how he first mounted on -horseback in armour; and the whole army came after him--40 squadrons -of cavalry, and 2000 foot soldiers went with him. Very early in the -morning the Patriarch went up a hill to reconnoitre the country, -that is the hills, fields and the valley watered by a river; and -from thence he beheld Niccolo Picinino coming from Borgo San -Sepolcro with his people, and with a great dust; and perceiving them -he returned to the camp of his own people and addressed them. Having -spoken he prayed to God with clasped hands, when there appeared a -cloud in which Saint Peter appeared and spoke to the Patriarch.--500 -cavalry were sent forward by the Patriarch to hinder or check the -rush of the enemy. In the foremost troop Francesco the son of -Niccolo Piccinino [24] was the first to attack the bridge which was -held by the Patriarch and the Florentines. Beyond the bridge to his -left he sent forward some infantry to engage ours, who drove them -back, among whom was their captain Micheletto [29] whose lot it was -to be that day at the head of the army. Here, at this bridge there -is a severe struggle; our men conquer and the enemy is repulsed. -Here Guido and Astorre, his brother, the Lord of Faenza with a great -number of men, re-formed and renewed the fight, and rushed upon the -Florentines with such force that they recovered the bridge and -pushed forward as far as the tents. But Simonetto advanced with 600 -horse, and fell upon the enemy and drove them back once more from -the place, and recaptured the bridge; and behind him came more men -with 2000 horse soldiers. And thus for a long time they fought with -varying fortune. But then the Patriarch, in order to divert the -enemy, sent forward Niccolo da Pisa [44] and Napoleone Orsino, a -beardless lad, followed by a great multitude of men, and then was -done another great feat of arms. At the same time Niccolo Piccinino -urged forward the remnant of his men, who once more made ours give -way; and if it had not been that the Patriarch set himself at their -head and, by his words and deeds controlled the captains, our -soldiers would have taken to flight. The Patriarch had some -artillery placed on the hill and with these he dispersed the enemy's -infantry; and the disorder was so complete that Niccolo began to -call back his son and all his men, and they took to flight towards -Borgo. And then began a great slaughter of men; none escaped but the -foremost of those who had fled or who hid themselves. The battle -continued until sunset, when the Patriarch gave his mind to -recalling his men and burying the dead, and afterwards a trophy was -erected. - -[Footnote: 669. This passage does not seem to me to be in Leonardo's -hand, though it has hitherto been generally accepted as genuine. Not -only is the writing unlike his, but the spelling also is quite -different. I would suggest that this passage is a description of the -events of the battle drawn up for the Painter by order of the -Signoria, perhaps by some historian commissioned by them, to serve -as a scheme or programme of the work. The whole tenor of the style -seems to me to argue in favour of this theory; and besides, it would -be in no way surprising that such a document should have been -preserved among Leonardo's autographs.] - -Allegorical representations referring to the duke of Milan -(670-673). - -670. - -Ermine with blood Galeazzo, between calm weather and a -representation of a tempest. - -[Footnote: 670. Only the beginning of this text is legible; the -writing is much effaced and the sense is consequently obscure. It -seems to refer like the following passage to an allegorical -picture.] - -671. - -Il Moro with spectacles, and Envy depicted with False Report and -Justice black for il Moro. - -Labour as having a branch of vine [_or_ a screw] in her hand. - -672. - -Il Moro as representing Good Fortune, with hair, and robes, and his -hands in front, and Messer Gualtieri taking him by the robes with a -respectful air from below, having come in from the front [5]. - -Again, Poverty in a hideous form running behind a youth. Il Moro -covers him with the skirt of his robe, and with his gilt sceptre he -threatens the monster. - -A plant with its roots in the air to represent one who is at his -last;--a robe and Favour. - -Of tricks [_or_ of magpies] and of burlesque poems [_or_ of -starlings]. - -Those who trust themselves to live near him, and who will be a large -crowd, these shall all die cruel deaths; and fathers and mothers -together with their families will be devoured and killed by cruel -creatures. - -[Footnote: 1--10 have already been published by _Amoretti_ in -_Memorie Storiche_ cap. XII. He adds this note with regard to -Gualtieri: "_A questo M. Gualtieri come ad uomo generoso e benefico -scrive il Bellincioni un Sonetto (pag, 174) per chiedergli un -piacere; e 'l Tantio rendendo ragione a Lodovico il Moro, perche -pubblicasse le Rime del Bellincioni; cio hammi imposto, gli dice: -l'humano fidele, prudente e sollicito executore delli tuoi -comandamenti Gualtero, che fa in tutte le cose ove tu possi far -utile, ogni studio vi metti._" A somewhat mysterious and evidently -allegorical composition--a pen and ink drawing--at Windsor, see PL -LVIII, contains a group of figures in which perhaps the idea is -worked out which is spoken of in the text, lines 1-5.] - -673. - -He was blacker than a hornet, his eyes were as red as a burning fire -and he rode on a tall horse six spans across and more than 20 long -with six giants tied up to his saddle-bow and one in his hand which -he gnawed with his teeth. And behind him came boars with tusks -sticking out of their mouths, perhaps ten spans. - -Allegorical representations (674--678). - -674. - -Above the helmet place a half globe, which is to signify our -hemisphere, in the form of a world; on which let there be a peacock, -richly decorated, and with his tail spread over the group; and every -ornament belonging to the horse should be of peacock's feathers on a -gold ground, to signify the beauty which comes of the grace bestowed -on him who is a good servant. - -On the shield a large mirror to signify that he who truly desires -favour must be mirrored in his virtues. - -On the opposite side will be represented Fortitude, in like manner -in her place with her pillar in her hand, robed in white, to signify -... And all crowned; and Prudence with 3 eyes. The housing of the -horse should be of plain cloth of gold closely sprinkled with -peacock's eyes, and this holds good for all the housings of the -horse, and the man's dress. And the man's crest and his neck-chain -are of peacock's feathers on golden ground. - -On the left side will be a wheel, the centre of which should be -attached to the centre of the horse's hinder thigh piece, and in the -centre Prudence is seen robed in red, Charity sitting in a fiery -chariot and with a branch of laurel in her hand, to signify the hope -which comes of good service. - -[21] Messer Antonio Grimani of Venice companion of Antonio Maria -[23]. - -[Footnote: _Messer Antonio Gri_. His name thus abbreviated is, there -can be no doubt, Grimani. Antonio Grimani was the famous Doge who in -1499 commanded the Venetian fleet in battle against the Turks. But -after the abortive conclusion of the expedition--Ludovico being the -ally of the Turks who took possession of Friuli--, Grimani was driven -into exile; he went to live at Rome with his son Cardinal Domenico -Grimani. On being recalled to Venice he filled the office of Doge -from 1521 to 1523. _Antonio Maria_ probably means Antonio Maria -Grimani, the Patriarch of Aquileia.] - -675. - -Fame should be depicted as covered all over with tongues instead of -feathers, and in the figure of a bird. - -676. - -Pleasure and Pain represent as twins, since there never is one -without the other; and as if they were united back to back, since -they are contrary to each other. - -[6] Clay, gold. - -[Footnote: 7. _oro. fango_: gold, clay. These words stand below the -allegorical figure.] - -If you take Pleasure know that he has behind him one who will deal -you Tribulation and Repentance. - -[9] This represents Pleasure together with Pain, and show them as -twins because one is never apart from the other. They are back to -back because they are opposed to each other; and they exist as -contraries in the same body, because they have the same basis, -inasmuch as the origin of pleasure is labour and pain, and the -various forms of evil pleasure are the origin of pain. Therefore it -is here represented with a reed in his right hand which is useless -and without strength, and the wounds it inflicts are poisoned. In -Tuscany they are put to support beds, to signify that it is here -that vain dreams come, and here a great part of life is consumed. It -is here that much precious time is wasted, that is, in the morning, -when the mind is composed and rested, and the body is made fit to -begin new labours; there again many vain pleasures are enjoyed; both -by the mind in imagining impossible things, and by the body in -taking those pleasures that are often the cause of the failing of -life. And for these reasons the reed is held as their support. - -[Footnote: 676. The pen and ink drawing on PI. LIX belongs to this -passage.] - -[Footnote: 8. _tribolatione_. In the drawing caltrops may be seen -lying in the old man's right hand, others are falling and others -again are shewn on the ground. Similar caltrops are drawn in MS. -Tri. p. 98 and underneath them, as well as on page 96 the words -_triboli di ferro_ are written. From the accompanying text it -appears that they were intended to be scattered on the ground at the -bottom of ditches to hinder the advance of the enemy. Count Giulio -Porro who published a short account of the Trivulzio MS. in the -"_Archivio Storico Lombardo_", Anno VIII part IV (Dec. 31, 1881) has -this note on the passages treating of "_triboli_": "_E qui -aggiungero che anni sono quando venne fabbricata la nuova -cavallerizza presso il castello di Milano, ne furono trovati due che -io ho veduto ed erano precisamente quali si trovano descritti e -disegnati da Leonardo in questo codice_". - -There can therefore be no doubt that this means of defence was in -general use, whether it were originally Leonardo's invention or not. -The play on the word "_tribolatione_", as it occurs in the drawing -at Oxford, must then have been quite intelligible.] - -[Footnote: 9--22. These lines, in the original, are written on the -left side of the page and refer to the figure shown on PI. LXI. Next -to it is placed the group of three figures given in PI. LX No. I. -Lines 21 and 22, which are written under it, are the only -explanation given.] - -Evil-thinking is either Envy or Ingratitude. - -677. - -Envy must be represented with a contemptuous motion of the hand -towards heaven, because if she could she would use her strength -against God; make her with her face covered by a mask of fair -seeming; show her as wounded in the eye by a palm branch and by an -olive-branch, and wounded in the ear by laurel and myrtle, to -signify that victory and truth are odious to her. Many thunderbolts -should proceed from her to signify her evil speaking. Let her be -lean and haggard because she is in perpetual torment. Make her heart -gnawed by a swelling serpent, and make her with a quiver with -tongues serving as arrows, because she often offends with it. Give -her a leopard's skin, because this creature kills the lion out of -envy and by deceit. Give her too a vase in her hand full of flowers -and scorpions and toads and other venomous creatures; make her ride -upon death, because Envy, never dying, never tires of ruling. Make -her bridle, and load her with divers kinds of arms because all her -weapons are deadly. - -Toleration. - -Intolerable. - -No sooner is Virtue born than Envy comes into the world to attack -it; and sooner will there be a body without a shadow than Virtue -without Envy. - -[Footnote: The larger of the two drawings on PI. LXI is explained by -the first 21 lines of this passage. L. 22 and 23, which are written -above the space between the two drawings, do not seem to have any -reference to either. L. 24-27 are below the allegorical twin figure -which they serve to explain.] - -678. - -When Pluto's Paradise is opened, then there may be devils placed in -twelve pots like openings into hell. Here will be Death, the Furies, -ashes, many naked children weeping; living fires made of various -colours.... - -679. - - John the Baptist - Saint Augustin - Saint Peter - Paul - Elisabeth - Saint Clara. - Bernardino - Our Lady Louis - Bonaventura - Anthony of Padua. - Saint Francis. - Francis, - Anthony, a lily and book; - Bernardino with the [monogram of] Jesus, - Louis with 3 fleur de lys on his breast and - the crown at his feet, - Bonaventura with Seraphim, - Saint Clara with the tabernacle, - Elisabeth with a Queen's crown. - -[Footnote: 679. The text of the first six lines is written within a -square space of the same size as the copy here given. The names are -written in the margin following the order in which they are here -printed. In lines 7--12 the names of those saints are repeated of -whom it seemed necessary to point out the emblems.] - -List of drawings. - -680. - - A head, full face, of a young man - with fine flowing hair, - Many flowers drawn from nature, - A head, full face, with curly hair, - Certain figures of Saint Jerome, - [6] The measurements of a figure, - Drawings of furnaces. - A head of the Duke, - [9] many designs for knots, - 4 studies for the panel of Saint Angelo - A small composition of Girolamo da Fegline, - A head of Christ done with the pen, - [13] 8 Saint Sebastians, - Several compositions of Angels, - A chalcedony, - A head in profile with fine hair, - Some pitchers seen in(?) perspective, - Some machines for ships, - Some machines for waterworks, - A head, a portrait of Atalanta raising her - face; - The head of Geronimo da Fegline, - The head of Gian Francisco Borso, - Several throats of old women, - Several heads of old men, - Several nude figures, complete, - Several arms, eyes, feet, and positions, - A Madonna, finished, - Another, nearly in profile, - Head of Our Lady ascending into Heaven, - A head of an old man with long chin, - A head of a gypsy girl, - A head with a hat on, - A representation of the Passion, a cast, - A head of a girl with her hair gathered in a knot, - A head, with the brown hair dressed. - -[Footnote: 680. This has already been published by AMORETTI _Memorie -storiche_ cap. XVI. His reading varies somewhat from that here -given, _e. g._ l. 5 and 6. _Certi Sangirolami in su d'una figura_; -and instead of I. 13. _Un San Bastiano_.] - -[Footnote: 680. 9. _Molti disegni di gruppi_. VASARI in his life of -Leonardo (IV, 21, ed. MILANESI 1880) says: "_Oltreche perse tempo -fino a disegnare_ gruppi _di corde fatti con ordine, e che da un -capo seguissi tutto il resto fino all' altro, tanto che s'empiessi -un tondo; che se ne vede in istampa uno difficilissimo e molto -bello, e nel mezzo vi sono queste parole: Leonardus Vinci -Accademia_". _Gruppi_ must here be understood as a technical -expression for those twisted ornaments which are well known through -wood cuts. AMORETTI mentions six different ones in the Ambrosian -Library. I am indebted to M. DELABORDE for kindly informing me that -the original blocks of these are preserved in his department in the -Bibliotheque Nationale in Paris. On the cover of these volumes is a -copy from one of them. The size of the original is 23 1/2 -centimetres by 26 1/4. The centre portion of another is given on p. -361. G. Govi remarks on these ornaments (_Saggio_ p. 22): "_Codesti -gruppi eran probabilmente destinati a servir di modello a ferri da -rilegatori per adornar le cartelle degli scolari (?). Fregi -somigliantissimi a questi troviamo infatti impressi in oro sui -cartoni di vari volumi contemporanei, e li vediam pur figurare nelle -lettere iniziali di alcune edizioni del tempo._" - -Durer who copied them, omitting the inscription, added to the second -impressions his own monogram. In his diary he designates them simply -as "_Die sechs Knoten_" (see THAUSING, Life of A. Durer I, 362, -363). In Leonardo's MSS. we find here and there little sketches or -suggestions for similar ornaments. Compare too G. MONGERI, _L'Arte -in Milano_, p. 315 where an ornament of the same character is given -from the old decorations of the vaulted ceiling of the Sacristy of -S. Maria delle Grazie.] - -[Footnote: 680, 17. The meaning in which the word _coppi_, literally -pitchers, is here used I am unable to determine; but a change to -_copie_ seems to me too doubtful to be risked.] - -681. - - Stubborn rigour. - Doomed rigour. - -[Footnote: See PI. LXII, No. 2, the two upper pen and ink drawings. -The originals, in the Windsor collection are slightly washed with -colour. The background is blue sky; the plough and the instrument -with the compass are reddish brown, the sun is tinted yellow]. - -682. - - Obstacles cannot crush me - Every obstacle yields to stern resolve - He who is fixed to a star does not change - his mind. - -[Footnote: This text is written to elucidate two sketches which were -obviously the first sketches for the drawings reproduced on PL LXII, -No. 2.] - -683. - -Ivy is [a type] of longevity. - -[Footnote: In the original there is, near this text, a sketch of a -coat wreathed above the waist with ivy.] - -684. - - Truth the sun. - falsehood a mask. - innocence, - malignity. - - Fire destroys falsehood, - that is sophistry, and - restores truth, driving out - darkness. - - Fire may be represented as the destroy of - all sophistry, and as the - image and demonstration of truth; - because it is light and drives - out darkness which conceals - all essences [or subtle things]. - -[Footnote: See PI. LXIII. L. 1-8 are in the middle of the page; 1. -9-14 to the right below; 1. 15-22 below in the middle column. The -rest of the text is below the sketches on the left. There are some -other passages on this page relating to geometry.] - -TRUTH. - - Fire destroys all sophistry, that is deceit; - and maintains truth alone, that is gold. - - Truth at last cannot be hidden. - Dissimulation is of no avail. Dissimulation is - to no purpose before - so great a judge. - Falsehood puts on a mask. - Nothing is hidden under the sun. - - Fire is to represent truth because it - destroys all sophistry and lies; and the - mask is for lying and falsehood - which conceal truth. - -685. - - Movement will cease before we are - weary - of being useful. - - Movement will fail sooner than usefulness. - Death sooner than I am never weary of - weariness. being useful, - In serving others I is a motto for carnval. - cannot do enough. Without fatigue. - - No labour is - sufficient to tire me. - - Hands into which - ducats and precious - stones fall like snow; they - never become tired by serving, - but this service is only for its - utility and not for our I am never weary - own benefit. of being useful. - - Naturally - nature has so disposed me. - -686. - - This shall be placed in the - hand of Ingratitude. - Wood nourishes the fire that - consumes it. - -687. - -TO REPRESENT INGRATITUDE. - - When the sun appears - which dispels darkness in - general, you put out the - light which dispelled it - for you in particular - for your need and convenience. - -688. - - On this side Adam and Eve on the other; - O misery of mankind, of how many things do - you make yourself the slave for money! - -[Footnote: See PI. LXIV. The figures of Adam and Eve in the clouds -here alluded to would seem to symbolise their superiority to all -earthly needs.] - -689. - -Thus are base unions sundered. - -[Footnote: A much blurred sketch is on the page by this text. It -seems to represent an unravelled plait or tissue.] - -690. - - Constancy does not begin, but is that - which perseveres. - -[Footnote: A drawing in red chalk, also rubbed, which stands in the -original in the middle of this text, seems to me to be intended for -a sword hilt, held in a fist.] - -691. - - Love, Fear, and Esteem,-- - Write these on three stones. Of servants. - -692. - -Prudence Strength. - -693. - - Fame alone raises herself to Heaven, - because virtuous things are in favour with God. - - Disgrace should be represented upside - down, because all her deeds are contrary to - God and tend to hell. - -694. - -Short liberty. - -695. - - Nothing is so much to be feared as Evil - Report. - This Evil Report is born of life. - -696. - -Not to disobey. - -697. - - A felled tree which is shooting - again. - - I am still hopeful. - A falcon, - Time. - -[Footnote: I. _Albero tagliato_. This emblem was displayed during -the Carnival at Florence in 1513. See VASARI VI, 251, ed. MILANESI -1881. But the coincidence is probably accidental.] - -698. - - Truth here makes Falsehood torment - lying tongues. - -699. - - Such as harm is when it hurts me not, - is good which avails me not. - -[Footnote: See PI. LX, No. 2. Compare this sketch with that on PI. -LXII, No. 2. Below the two lines of the text there are two more -lines: _li guchi (giunchi) che ritego le paglucole (pagliucole) -chelli (che li) anniegano_.] - -700. - -He who offends others, does not secure himself. - -[Footnote: See PI. LX, No. 3.] - -701. - -Ingratitude. - -[Footnote: See PI. LX, No. 4. Below the bottom sketches are the -unintelligible words "_sta stilli_." For "_Ingratitudo_" compare -also Nos. 686 and 687.] - -702. - -One's thoughts turn towards Hope. - -[Footnote: 702. By the side of this passage is a sketch of -a cage with a bird sitting in it.] - -Ornaments and Decorations for feasts (703-705). - -703. - -A bird, for a comedy. - -[Footnote: The biographies say so much, and the author's notes say -so little of the invention attributed to Leonardo of making -artificial birds fly through the air, that the text here given is of -exceptional interest from being accompanied by a sketch. It is a -very slight drawing of a bird with outspread wings, which appears to -be sliding down a stretched string. Leonardo's flying machines and -his studies of the flight of birds will be referred to later.] - -704. - -A DRESS FOR THE CARNIVAL. - -To make a beautiful dress cut it in thin cloth and give it an -odoriferous varnish, made of oil of turpentine and of varnish in -grain, with a pierced stencil, which must be wetted, that it may not -stick to the cloth; and this stencil may be made in a pattern of -knots which afterwards may be filled up with black and the ground -with white millet.[Footnote 7: The grains of black and white millet -would stick to the varnish and look like embroidery.] - -[Footnote: Ser Giuliano, da Vinci the painter's brother, had been -commissioned, with some others, to order and to execute the garments -of the Allegorical figures for the Carnival at Florence in 1515--16; -VASARI however is incorrect in saying of the Florentine Carnival of -1513: "_equelli che feciono ed ordinarono gli abiti delle figure -furono Ser Piero da Vinci, padre di Lonardo, e Bernardino di -Giordano, bellissimi ingegni_" (See MILANESI'S ed. Voi. VI, pg. -251.)] - -705. - -Snow taken from the high peaks of mountains might be carried to hot -places and let to fall at festivals in open places at summer time. - - - -*** End of Volume 1 - - -The Notebooks of Leonardo Da Vinci - -Volume 2 - -Translated by Jean Paul Richter - -1888 - - - - - - - -XI. - -The notes on Sculpture. - -Compared with the mass of manuscript treating of Painting, a very -small number of passages bearing on the practice and methods of -Sculpture are to be found scattered through the note books; these -are here given at the beginning of this section (Nos. 706-709). -There is less cause for surprise at finding that the equestrian -statue of Francesco Sforza is only incidentally spoken of; for, -although Leonardo must have worked at it for a long succession of -years, it is not in the nature of the case that it could have given -rise to much writing. We may therefore regard it as particularly -fortunate that no fewer than thirteen notes in the master's -handwriting can be brought together, which seem to throw light on -the mysterious history of this famous work. Until now writers on -Leonardo were acquainted only with the passages numbered 712, 719, -720, 722 and 723. - -In arranging these notes on sculpture I have given the precedence to -those which treat of the casting of the monument, not merely because -they are the fullest, but more especially with a view to -reconstructing the monument, an achievement which really almost lies -within our reach by combining and comparing the whole of the -materials now brought to light, alike in notes and in sketches. - -A good deal of the first two passages, Nos. 710 and 711, which refer -to this subject seems obscure and incomprehensible; still, they -supplement each other and one contributes in no small degree to the -comprehension of the other. A very interesting and instructive -commentary on these passages may be found in the fourth chapter of -Vasari's Introduzione della Scultura under the title "Come si fanno -i modelli per fare di bronzo le figure grandi e picciole, e come le -forme per buttarle; come si armino di ferri, e come si gettino di -metallo," &c. Among the drawings of models of the moulds for casting -we find only one which seems to represent the horse in the act of -galloping--No. 713. All the other designs show the horse as pacing -quietly and as these studies of the horse are accompanied by copious -notes as to the method of casting, the question as to the position -of the horse in the model finally selected, seems to be decided by -preponderating evidence. "Il cavallo dello Sforza"--C. Boito remarks -very appositely in the Saggio on page 26, "doveva sembrare fratello -al cavallo del Colleoni. E si direbbe che questo fosse figlio del -cavallo del Gattamelata, il quale pare figlio di uno dei quattro -cavalli che stavano forse sull' Arco di Nerone in Roma" (now at -Venice). The publication of the Saggio also contains the -reproduction of a drawing in red chalk, representing a horse walking -to the left and supported by a scaffolding, given here on Pl. LXXVI, -No. 1. It must remain uncertain whether this represents the model as -it stood during the preparations for casting it, or whether--as -seems to me highly improbable--this sketch shows the model as it was -exhibited in 1493 on the Piazza del Castello in Milan under a -triumphal arch, on the occasion of the marriage of the Emperor -Maximilian to Bianca Maria Sforza. The only important point here is -to prove that strong evidence seems to show that, of the numerous -studies for the equestrian statue, only those which represent the -horse pacing agree with the schemes of the final plans. - -The second group of preparatory sketches, representing the horse as -galloping, must therefore be considered separately, a distinction -which, in recapitulating the history of the origin of the monument -seems justified by the note given under No. 720. - -Galeazza Maria Sforza was assassinated in 1476 before his scheme for -erecting a monument to his father Francesco Sforza could be carried -into effect. In the following year Ludovico il Moro the young -aspirant to the throne was exiled to Pisa, and only returned to -Milan in 1479 when he was Lord (Governatore) of the State of Milan, -in 1480 after the minister Cecco Simonetta had been murdered. It may -have been soon after this that Ludovico il Moro announced a -competition for an equestrian statue, and it is tolerably certain -that Antonio del Pollajuolo took part in it, from this passage in -Vasari's Life of this artist: "E si trovo, dopo la morte sua, il -disegno e modello che a Lodovico Sforza egli aveva fatto per la -statua a cavallo di Francesco Sforza, duca di Milano; il quale -disegno e nel nostro Libro, in due modi: in uno egli ha sotto -Verona; nell'altro, egli tutto armato, e sopra un basamento pieno di -battaglie, fa saltare il cavallo addosso a un armato; ma la cagione -perche non mettesse questi disegni in opera, non ho gia potuto -sapere." One of Pollajuolo's drawings, as here described, has lately -been discovered by Senatore Giovanni Morelli in the Munich -Pinacothek. Here the profile of the horseman is a portrait of -Francesco Duke of Milan, and under the horse, who is galloping to -the left, we see a warrior thrown and lying on the ground; precisely -the same idea as we find in some of Leonardo's designs for the -monument, as on Pl. LXVI, LXVII, LXVIII, LXIX and LXXII No. 1; and, -as it is impossible to explain this remarkable coincidence by -supposing that either artist borrowed it from the other, we can only -conclude that in the terms of the competition the subject proposed -was the Duke on a horse in full gallop, with a fallen foe under its -hoofs. - -Leonardo may have been in the competition there and then, but the -means for executing the monument do not seem to have been at once -forthcoming. It was not perhaps until some years later that Leonardo -in a letter to the Duke (No. 719) reminded him of the project for -the monument. Then, after he had obeyed a summons to Milan, the plan -seems to have been so far modified, perhaps in consequence of a -remonstrance on the part of the artist, that a pacing horse was -substituted for one galloping, and it may have been at the same time -that the colossal dimensions of the statue were first decided on. -The designs given on Pl. LXX, LXXI, LXXII, 2 and 3, LXXIII and LXXIV -and on pp. 4 and 24, as well as three sketches on Pl. LXIX may be -studied with reference to the project in its new form, though it is -hardly possible to believe that in either of these we see the design -as it was actually carried out. It is probable that in Milan -Leonardo worked less on drawings, than in making small models of wax -and clay as preparatory to his larger model. Among the drawings -enumerated above, one in black chalk, Pl. LXXIII--the upper sketch -on the right hand side, reminds us strongly of the antique statue of -Marcus Aurelius. If, as it would seem, Leonardo had not until then -visited Rome, he might easily have known this statue from drawings -by his former master and friend Verrocchio, for Verrocchio had been -in Rome for a long time between 1470 and 1480. In 1473 Pope Sixtus -IV had this antique equestrian statue restored and placed on a new -pedestal in front of the church of San Giovanni in Luterano. -Leonardo, although he was painting independently as early as in 1472 -is still spoken of as working in Verrocchio's studio in 1477. Two -years later the Venetian senate decided on erecting an equestrian -statue to Colleoni; and as Verrocchio, to whom the work was -entrusted, did not at once move from Florence to Venice--where he -died in 1488 before the casting was completed--but on the contrary -remained in Florence for some years, perhaps even till 1485, -Leonardo probably had the opportunity of seeing all his designs for -the equestrian statue at Venice and the red chalk drawing on Pl. -LXXIV may be a reminiscence of it. - -The pen and ink drawing on Pl. LXXII, No. 3, reminds us of -Donatello's statue of Gattamelata at Padua. However it does not -appear that Leonardo was ever at Padua before 1499, but we may -conclude that he took a special interest in this early bronze statue -and the reports he could procure of it, form an incidental remark -which is to be found in C. A. 145a; 432a, and which will be given in -Vol. II under Ricordi or Memoranda. Among the studies--in the widest -sense of the word--made in preparation statue we may include the -Anatomy of the Horse which Lomazzo and Vas mention; the most -important parts of this work still exist in the Queen's Li Windsor. -It was beyond a doubt compiled by Leonardo when at Milan; only -interesting records to be found among these designs are reproduced -in Nos. 716a but it must be pointed out that out of 40 sheets of -studies of the movements of the belonging to that treatise, a horse -in full gallop occurs but once. - -If we may trust the account given by Paulus Jovius--about l527-- -Leonardo's horse was represented as "vehementer incitatus et -anhelatus". Jovius had probably seen the model exhibited at Milan; -but, need we, in fact, infer from this description that the horse -was galloping? Compare Vasari's description of the Gattamelata -monument at Padua: "Egli [Donatello] vi ando ben volentieri, e fece -il cavallo di bronzo, che e in sulla piazza di Sant Antonio, nel -quale si dimostra lo sbuffamento ed il fremito del cavallo, ed il -grande animo e la fierezza vivacissimamente espressa dall'arte nella -figura che lo cavalca". - -These descriptions, it seems to me, would only serve to mark the -difference between the work of the middle ages and that of the -renaissance. - -We learn from a statement of Sabba da Castiglione that, when Milan -was taken by the French in 1499, the model sustained some injury; -and this informant, who, however is not invariably trustworthy, adds -that Leonardo had devoted fully sixteen years to this work (la forma -del cavallo, intorno a cui Leonardo avea sedici anni continui -consumati). This often-quoted passage has given ground for an -assumption, which has no other evidence to support it, that Leonardo -had lived in Milan ever since 1483. But I believe it is nearer the -truth to suppose that this author's statement alludes to the fact -that about sixteen years must have past since the competition in -which Leonardo had taken part. - -I must in these remarks confine myself strictly to the task in hand -and give no more of the history of the Sforza monument than is -needed to explain the texts and drawings I have been able to -reproduce. In the first place, with regard to the drawings, I may -observe that they are all, with the following two exceptions, in the -Queen's Library at Windsor Castle; the red chalk drawing on Pl. -LXXVI No. 1 is in the MS. C. A. (see No. 7l2) and the fragmentary -pen and ink drawing on page 4 is in the Ambrosian Library. The -drawings from Windsor on Pl. LXVI have undergone a trifling -reduction from the size of the originals. - -There can no longer be the slightest doubt that the well-known -engraving of several horsemen (Passavant, Le Peintre-Graveur, Vol. -V, p. 181, No. 3) is only a copy after original drawings by -Leonardo, executed by some unknown engraver; we have only to compare -the engraving with the facsimiles of drawings on Pl. LXV, No. 2, Pl. -LXVII, LXVIII and LXIX which, it is quite evident, have served as -models for the engraver. - -On Pl. LXV No. 1, in the larger sketch to the right hand, only the -base is distinctly visible, the figure of the horseman is effaced. -Leonardo evidently found it unsatisfactory and therefore rubbed it -out. - -The base of the monument--the pedestal for the equestrian statue--is -repeatedly sketched on a magnificent plan. In the sketch just -mentioned it has the character of a shrine or aedicula to contain a -sarcophagus. Captives in chains are here represented on the -entablature with their backs turned to that portion of the monument -which more - -strictly constitutes the pedestal of the horse. The lower portion of -the aedicula is surrounded by columns. In the pen and ink drawing -Pl. LXVI--the lower drawing on the right hand side--the sarcophagus -is shown between the columns, and above the entablature is a plinth -on which the horse stands. But this arrangement perhaps seemed to -Leonardo to lack solidity, and in the little sketch on the left -hand, below, the sarcophagus is shown as lying under an arched -canopy. In this the trophies and the captive warriors are detached -from the angles. In the first of these two sketches the place for -the trophies is merely indicated by a few strokes; in the third -sketch on the left the base is altogether broader, buttresses and -pinnacles having been added so as to form three niches. The black -chalk drawing on Pl. LXVIII shows a base in which the angles are -formed by niches with pilasters. In the little sketch to the extreme -left on Pl. LXV, No. 1, the equestrian statue serves to crown a -circular temple somewhat resembling Bramante's tempietto of San -Pietro in Montario at Rome, while the sketch above to the right -displays an arrangement faintly reminding us of the tomb of the -Scaligers in Verona. The base is thus constructed of two platforms -or slabs, the upper one considerably smaller than the lower one -which is supported on flying buttresses with pinnacles. - -On looking over the numerous studies in which the horse is not -galloping but merely walking forward, we find only one drawing for -the pedestal, and this, to accord with the altered character of the -statue, is quieter and simpler in style (Pl. LXXIV). It rises almost -vertically from the ground and is exactly as long as the pacing -horse. The whole base is here arranged either as an independent -baldaquin or else as a projecting canopy over a recess in which the -figure of the deceased Duke is seen lying on his sarcophagus; in the -latter case it was probably intended as a tomb inside a church. -Here, too, it was intended to fill the angles with trophies or -captive warriors. Probably only No. 724 in the text refers to the -work for the base of the monument. - -If we compare the last mentioned sketch with the description of a -plan for an equestrian monument to Gian Giacomo Trivulzio (No. 725) -it seems by no means impossible that this drawing is a preparatory -study for the very monument concerning which the manuscript gives us -detailed information. We have no historical record regarding this -sketch nor do the archives in the Trivulzio Palace give us any -information. The simple monument to the great general in San Nazaro -Maggiore in Milan consists merely of a sarcophagus placed in recess -high on the wall of an octagonal chapel. The figure of the warrior -is lying on the sarcophagus, on which his name is inscribed; a piece -of sculpture which is certainly not Leonardo's work. Gian Giacomo -Trivulzio died at Chartres in 1518, only five months before -Leonardo, and it seems to me highly improbable that this should have -been the date of this sketch; under these circumstances it would -have been done under the auspices of Francis I, but the Italian -general was certainly not in favour with the French monarch at the -time. Gian Giacomo Trivulzio was a sworn foe to Ludovico il Moro, -whom he strove for years to overthrow. On the 6th September 1499 he -marched victorious into Milan at the head of a French army. In a -short time, however, he was forced to quit Milan again when Ludovico -il Moro bore down upon the city with a force of Swiss troops. On the -15th of April following, after defeating Lodovico at Novara, -Trivulzio once more entered Milan as a Conqueror, but his hopes of -becoming _Governatore_ of the place were soon wrecked by intrigue. -This victory and triumph, historians tell us, were signalised by -acts of vengeance against the dethroned Sforza, and it might have -been particularly flattering to him that the casting and -construction of the Sforza monument were suspended for the time. - -It must have been at this moment--as it seems to me--that he -commissioned the artist to prepare designs for his own monument, -which he probably intended should find a place in the Cathedral or -in some other church. He, the husband of Margherita di Nicolino -Colleoni, would have thought that he had a claim to the same -distinction and public homage as his less illustrious connection had -received at the hands of the Venetian republic. It was at this very -time that Trivulzio had a medal struck with a bust portrait of -himself and the following remarkable inscription on the reverse:_ -DEO FAVENTE--1499--DICTVS--10--IA--EXPVLIT--LVDOVICV--SF-- -(Sfortiam) DVC-- (ducem) MLI (Mediolani)--NOIE -(nomine)--REGIS--FRANCORVM--EODEM--ANN --(anno) RED'T (redit)--LVS -(Ludovicus)--SVPERATVS ET CAPTVS--EST--AB--EO. _In the Library of -the Palazzo Trivulzio there is a MS. of Callimachus Siculus written -at the end of the XVth or beginning of the XVIth century. At the -beginning of this MS. there is an exquisite illuminated miniature of -an equestrian statue with the name of the general on the base; it is -however very doubtful whether this has any connection with -Leonardo's design. - -Nos. 731-740, which treat of casting bronze, have probably a very -indirect bearing on the arrangements made for casting the equestrian -statue of Francesco Sforza. Some portions evidently relate to the -casting of cannon. Still, in our researches about Leonardo's work on -the monument, we may refer to them as giving us some clue to the -process of bronze casting at that period. - -Some practical hints (706-709). - -7O6. - -OF A STATUE. - -If you wish to make a figure in marble, first make one of clay, and -when you have finished it, let it dry and place it in a case which -should be large enough, after the figure is taken out of it, to -receive also the marble, from which you intend to reveal the figure -in imitation of the one in clay. After you have put the clay figure -into this said case, have little rods which will exactly slip in to -the holes in it, and thrust them so far in at each hole that each -white rod may touch the figure in different parts of it. And colour -the portion of the rod that remains outside black, and mark each rod -and each hole with a countersign so that each may fit into its -place. Then take the clay figure out of this case and put in your -piece of marble, taking off so much of the marble that all your rods -may be hidden in the holes as far as their marks; and to be the -better able to do this, make the case so that it can be lifted up; -but the bottom of it will always remain under the marble and in this -way it can be lifted with tools with great ease. - -707. - -Some have erred in teaching sculptors to measure the limbs of their -figures with threads as if they thought that these limbs were -equally round in every part where these threads were wound about -them. - -708. - -MEASUREMENT AND DIVISION OF A STATUE. - -Divide the head into 12 degrees, and each degree divide into 12 -points, and each point into 12 minutes, and the minutes into minims -and the minims into semi minims. - -Degree--point--minute--minim. - -709. - -Sculptured figures which appear in motion, will, in their standing -position, actually look as if they were falling forward. - -[Footnote: _figure di rilievo_. Leonardo applies this term -exclusively to wholly detached figures, especially to those standing -free. This note apparently refers to some particular case, though we -have no knowledge of what that may have been. If we suppose it to -refer to the first model of the equestrian statue of Francesco -Sforza (see the introduction to the notes on Sculpture) this -observation may be regarded as one of his arguments for abandoning -the first scheme of the Sforza Monument, in which the horse was to -be galloping (see page 2). It is also in favour of this theory that -the note is written in a manuscript volume already completed in -1492. Leonardo's opinions as to the shortcomings of plastic works -when compared with paintings are given under No. 655 and 656.] - -Notes on the casting of the Sforza monument (710-715). - -710. - -Three braces which bind the mould. - -[If you want to make simple casts quickly, make them in a box of -river sand wetted with vinegar.] - -[When you shall have made the mould upon the horse you must make the -thickness of the metal in clay.] - -Observe in alloying how many hours are wanted for each -hundredweight. [In casting each one keep the furnace and its fire -well stopped up.] [Let the inside of all the moulds be wetted with -linseed oil or oil of turpentine, and then take a handful of -powdered borax and Greek pitch with aqua vitae, and pitch the mould -over outside so that being under ground the damp may not [damage -it?] - -[To manage the large mould make a model of the small mould, make a -small room in proportion.] - -[Make the vents in the mould while it is on the horse.] - -Hold the hoofs in the tongs, and cast them with fish glue. Weigh the -parts of the mould and the quantity of metal it will take to fill -them, and give so much to the furnace that it may afford to each -part its amount of metal; and this you may know by weighing the clay -of each part of the mould to which the quantity in the furnace must -correspond. And this is done in order that the furnace for the legs -when filled may not have to furnish metal from the legs to help out -the head, which would be impossible. [Cast at the same casting as -the horse the little door] - -[Footnote: The importance of the notes included under this number is -not diminished by the fact that they have been lightly crossed out -with red chalk. Possibly they were the first scheme for some fuller -observations which no longer exist; or perhaps they were crossed out -when Leonardo found himself obliged to give up the idea of casting -the equestrian statue. In the original the first two sketches are -above l. 1, and the third below l. 9.] - -711. - -THE MOULD FOR THE HORSE. - -Make the horse on legs of iron, strong and well set on a good -foundation; then grease it and cover it with a coating, leaving each -coat to dry thoroughly layer by layer; and this will thicken it by -the breadth of three fingers. Now fix and bind it with iron as may -be necessary. Moreover take off the mould and then make the -thickness. Then fill the mould by degrees and make it good -throughout; encircle and bind it with its irons and bake it inside -where it has to touch the bronze. - -OF MAKING THE MOULD IN PIECES. - -Draw upon the horse, when finished, all the pieces of the mould with -which you wish to cover the horse, and in laying on the clay cut it -in every piece, so that when the mould is finished you can take it -off, and then recompose it in its former position with its joins, by -the countersigns. - -The square blocks _a b_ will be between the cover and the core, that -is in the hollow where the melted bronze is to be; and these square -blocks of bronze will support the intervals between the mould and -the cover at an equal distance, and for this reason these squares -are of great importance. - -The clay should be mixed with sand. - -Take wax, to return [what is not used] and to pay for what is used. - -Dry it in layers. - -Make the outside mould of plaster, to save time in drying and the -expense in wood; and with this plaster enclose the irons [props] -both outside and inside to a thickness of two fingers; make terra -cotta. And this mould can be made in one day; half a boat load of -plaster will serve you. - -Good. - -Dam it up again with glue and clay, or white of egg, and bricks and -rubbish. - -[Footnote: See Pl. LXXV. The figure "40," close to the sketch in the -middle of the page between lines 16 and 17 has been added by a -collector's hand. - -In the original, below line 21, a square piece of the page has been -cut out about 9 centimetres by 7 and a blank piece has been gummed -into the place. - -Lines 22-24 are written on the margin. l. 27 and 28 are close to the -second marginal sketch. l. 42 is a note written above the third -marginal sketch and on the back of this sheet is the text given as -No. 642. Compare also No. 802.] - -712. - -All the heads of the large nails. - -[Footnote: See Pl. LXXVI, No. i. This drawing has already been -published in the "_Saggio delle Opere di L. da Vinci_." Milano 1872, -Pl. XXIV, No. i. But, for various reasons I cannot regard the -editor's suggestions as satisfactory. He says: "_Veggonsi le -armature di legname colle quali forse venne sostenuto il modello, -quando per le nozze di Bianca Maria Sforza con Massimiliano -imperatore, esso fu collocato sotto un arco trionfale davanti al -Castello_." - -713. - -These bindings go inside. - -714. - -Salt may be made from human excrements, burnt and calcined, made -into lees and dried slowly at a fire, and all the excrements produce -salt in a similar way and these salts when distilled, are very -strong. - -[Footnote: VASARI repeatedly states, in the fourth chapter of his -_Introduzione della Scultura_, that in preparing to cast bronze -statues horse-dung was frequently used by sculptors. If, -notwithstanding this, it remains doubtful whether I am justified in -having introduced here this text of but little interest, no such -doubt can be attached to the sketch which accompanies it.] - -715. - -METHOD OF FOUNDING AGAIN. - -This may be done when the furnace is made [Footnote: this note is -written below the sketches.] strong and bruised. - -Models for the horse of the Sforza monument (716-718). - -7l6. - -Messer Galeazzo's big genet - -717. - -Messer Galeazzo's Sicilian horse. - -[Footnote: These notes are by the side of a drawing of a horse with -figured measurements.] - -718. - -Measurement of the Sicilian horse the leg from behind, seen in -front, lifted and extended. - -[Footnote: There is no sketch belonging to this passage. Galeazze -here probably means Galeazze di San Severino, the famous captain who -married Bianca the daughter of Ludovico il Moro.] - -Occasional references to the Sforza monument (719-724). - -719. - -Again, the bronze horse may be taken in hand, which is to be to the -immortal glory and eternal honour of the happy memory of the prince -your father, and of the illustrious house of Sforza. - -[Footnote: The letter from which this passage is here extracted will -be found complete in section XXI. (see the explanation of it, on -page 2).] - -720. - -On the 23rd of April 1490 I began this book, and recommenced the -horse. - -721. - -There is to be seen, in the mountains of Parma and Piacenza, a -multitude of shells and corals full of holes, still sticking to the -rocks, and when I was at work on the great horse for Milan, a large -sackful of them, which were found thereabout, was brought to me into -my workshop, by certain peasants. - -722. - -Believe me, Leonardo the Florentine, who has to do the equestrian -bronze statue of the Duke Francesco that he does not need to care -about it, because he has work for all his life time, and, being so -great a work, I doubt whether he can ever finish it. [Footnote: This -passage is quoted from a letter to a committee at Piacenza for whom -Leonardo seems to have undertaken to execute some work. The letter -is given entire in section XXL; in it Leonardo remonstrates as to -some unreasonable demands.] - -723. - -Of the horse I will say nothing because I know the times. [Footnote: -This passage occurs in a rough copy of a letter to Ludovico il Moro, -without date (see below among the letters).] - -724. - -During ten years the works on the marbles have been going on I will -not wait for my payment beyond the time, when my works are finished. -[Footnote: This possibly refers to the works for the pedestal of the -equestrian statue concerning which we have no farther information in -the MSS. See p. 6.] - -The project of the Trivulzio monument. - -725. - -THE MONUMENT TO MESSER GIOVANNI JACOMO DA TREVULZO. - -[2] Cost of the making and materials for the horse [5]. - -[Footnote: In the original, lines 2-5, 12-14, 33-35, are written on -the margin. This passage has been recently published by G. Govi in -Vol. V, Ser. 3a, of _Transunti, Reale Accademia dei Linea, sed. del -5 Giugno, 1881,_ with the following introductory note: _"Desidero -intanto che siano stampati questi pochi frammenti perche so che sono -stati trascritti ultimamente, e verranno messi in luce tra poco -fuori d'Italia. Li ripubblichi pure chi vuole, ma si sappia almeno -che anche tra noi si conoscevano, e s'eran raccolti da anni per -comporne, quando che fosse, una edizione ordinata degli scritti di -Leonardo."_ - -The learned editor has left out line 22 and has written 3 _pie_ for -8 _piedi_ in line 25. There are other deviations of less importance -from the original.] - -A courser, as large as life, with the rider requires for the cost of -the metal, duc. 500. - -And for cost of the iron work which is inside the model, and -charcoal, and wood, and the pit to cast it in, and for binding the -mould, and including the furnace where it is to be cast ... duc. -200. - -To make the model in clay and then in wax......... duc. 432. - -To the labourers for polishing it when it is cast. ....... duc. 450. - -in all. . duc. 1582. - -[12] Cost of the marble of the monument [14]. - -Cost of the marble according to the drawing. The piece of marble -under the horse which is 4 braccia long, 2 braccia and 2 inches wide -and 9 inches thick 58 hundredweight, at 4 Lire and 10 Soldi per -hundredweight.. duc. 58. - -And for 13 braccia and 6 inches of cornice, 7 in. wide and 4 in. -thick, 24 hundredweight....... duc. 24. - -And for the frieze and architrave, which is 4 br. and 6 in. long, 2 -br. wide and 6 in. thick, 29 hundredweight., duc. 20. - -And for the capitals made of metal, which are 8, 5 inches in. square -and 2 in. thick, at the price of 15 ducats each, will come to...... -duc. 122. - -And for 8 columns of 2 br. 7 in., 4 1/2 in. thick, 20 hundredweight -duc. 20. - -And for 8 bases which are 5 1/2 in. square and 2 in. high 5 hund'.. -duc. 5. - -And for the slab of the tombstone 4 br. io in. long, 2 br. 4 1/2 in. -wide 36 hundredweight....... duc. 36. - -And for 8 pedestal feet each 8 br. long and 6 1/2 in. wide and 6 1/2 -in. thick, 20 hundredweight come to... duc. 20. - -And for the cornice below which is 4 br. and 10 in. long, and 2 br. -and 5 in. wide, and 4 in. thick, 32 hund'.. duc. 32. - -And for the stone of which the figure of the deceased is to be made -which is 3 br. and 8 in. long, and 1 br. and 6 in. wide, and 9 in. -thick, 30 hund'.. duc. 30. - -And for the stone on which the figure lies which is 3 br. and 4 in. -long and 1 br. and 2 in., wide and 4 1/2 in. thick duc. 16. - -And for the squares of marble placed between the pedestals which are -8 and are 9 br. long and 9 in. wide, and 3 in. thick, 8 -hundredweight . . . duc. 8. in all. . duc. 389. - -[33]Cost of the work in marble[35]. - -Round the base on which the horse stands there are 8 figures at 25 -ducats each ............ duc. 200. - -And on the same base there are 8 festoons with some other ornaments, -and of these there are 4 at the price of 15 ducats each, and 4 at -the price of 8 ducats each ....... duc. 92. - -And for squaring the stones duc. 6. - -Again, for the large cornice which goes below the base on which the -horse stands, which is 13 br. and 6 in., at 2 due. per br. ...... -duc. 27. - -And for 12 br. of frieze at 5 due. per br. ........... duc. 60. - -And for 12 br. of architrave at 1 1/2 duc. per br. ....... duc. 18. - -And for 3 rosettes which will be the soffit of the monument, at 20 -ducats each .......... duc. 60. - -And for 8 fluted columns at 8 ducats each ......... duc. 64. - -And for 8 bases at 1 ducat each, duc. 8. - -And for 8 pedestals, of which 4 are at 10 duc. each, which go above -the angles; and 4 at 6 duc. each .. duc. 64. - -And for squaring and carving the moulding of the pedestals at 2 duc. -each, and there are 8 .... duc. 16. - -And for 6 square blocks with figures and trophies, at 25 duc. each -.. duc. 150. - -And for carving the moulding of the stone under the figure of the -deceased .......... duc. 40. - -For the statue of the deceased, to do it well .......... duc. 100. - -For 6 harpies with candelabra, at 25 ducats each ......... duc. 150. - -For squaring the stone on which the statue lies, and carving the -moulding ............ duc. 20. - -in all .. duc. 1075. - -The sum total of every thing added together amount to ...... duc. -3046. - -726. - -MINT AT ROME. - -It can also be made without a spring. But the screw above must -always be joined to the part of the movable sheath: [Margin note: -The mint of Rome.] [Footnote: See Pl. LXXVI. This passage is taken -from a note book which can be proved to have been used in Rome.] - -All coins which do not have the rim complete, are not to be accepted -as good; and to secure the perfection of their rim it is requisite -that, in the first place, all the coins should be a perfect circle; -and to do this a coin must before all be made perfect in weight, and -size, and thickness. Therefore have several plates of metal made of -the same size and thickness, all drawn through the same gauge so as -to come out in strips. And out of [24] these strips you will stamp -the coins, quite round, as sieves are made for sorting chestnuts -[27]; and these coins can then be stamped in the way indicated -above; &c. - -[31] The hollow of the die must be uniformly wider than the lower, -but imperceptibly [35]. - -This cuts the coins perfectly round and of the exact thickness, and -weight; and saves the man who cuts and weighs, and the man who makes -the coins round. Hence it passes only through the hands of the -gauger and of the stamper, and the coins are very superior. -[Footnote: See Pl. LXXVI No. 2. The text of lines 31-35 stands -parallel 1. 24-27. - -Farther evidence of Leonardo's occupations and engagements at Rome -under Pope Leo X. may be gathered from some rough copies of letters -which will be found in this volume. Hitherto nothing has been known -of his work in Rome beyond some doubtful, and perhaps mythical, -statements in Vasari.] - -727. - -POWDER FOR MEDALS. - -The incombustible growth of soot on wicks reduced to powder, burnt -tin and all the metals, alum, isinglass, smoke from a brass forge, -each ingredient to be moistened, with aqua vitae or malmsey or -strong malt vinegar, white wine or distilled extract of turpentine, -or oil; but there should be little moisture, and cast in moulds. -[Margin note: On the coining of medals (727. 728).] [Footnote: The -meaning of _scagliuolo_ in this passage is doubtful.] - -728. - -OF TAKING CASTS OF MEDALS. - -A paste of emery mixed with aqua vitae, or iron filings with -vinegar, or ashes of walnut leaves, or ashes of straw very finely -powdered. - -[Footnote: The meaning of _scagliuolo_ in this passage is doubtful.] - -The diameter is given in the lead enclosed; it is beaten with a -hammer and several times extended; the lead is folded and kept -wrapped up in parchment so that the powder may not be spilt; then -melt the lead, and the powder will be on the top of the melted lead, -which must then be rubbed between two plates of steel till it is -thoroughly pulverised; then wash it with aqua fortis, and the -blackness of the iron will be dissolved leaving the powder clean. - -Emery in large grains may be broken by putting it on a cloth many -times doubled, and hit it sideways with the hammer, when it will -break up; then mix it little by little and it can be founded with -ease; but if you hold it on the anvil you will never break it, when -it is large. - -Any one who grinds smalt should do it on plates of tempered steel -with a cone shaped grinder; then put it in aqua fortis, which melts -away the steel that may have been worked up and mixed with the -smalt, and which makes it black; it then remains purified and clean; -and if you grind it on porphyry the porphyry will work up and mix -with the smalt and spoil it, and aqua fortis will never remove it -because it cannot dissolve the porphyry. - -If you want a fine blue colour dissolve the smalt made with tartar, -and then remove the salt. - -Vitrified brass makes a fine red. - -729. - -STUCCO. - -Place stucco over the prominence of the..... which may be composed -of Venus and Mercury, and lay it well over that prominence of the -thickness of the side of a knife, made with the ruler and cover this -with the bell of a still, and you will have again the moisture with -which you applied the paste. The rest you may dry [Margin note: On -stucco (729. 730).] [Footnote: In this passage a few words have been -written in a sort of cipher--that is to say backwards; as in l. 3 -_erenev_ for _Venere_, l. 4 _oirucrem_ for Mercurio, l. 12 _il -orreve co ecarob_ for _il everro (?) co borace_. The meaning of the -word before _"di giesso"_ in l. 1 is unknown; and the sense, in -which _sagoma_ is used here and in other passages is obscure.-- -_Venere_ and _Mercurio_ may mean 'marble' and 'lime', of which -stucco is composed. - -12. The meaning of _orreve_ is unknown.] - -well; afterwards fire it, and beat it or burnish it with a good -burnisher, and make it thick towards the side. - -STUCCO. - -Powder ... with borax and water to a paste, and make stucco of it, -and then heat it so that it may dry, and then varnish it, with fire, -so that it shines well. - -730. - -STUCCO FOR MOULDING. - -Take of butter 6 parts, of wax 2 parts, and as much fine flour as -when put with these 2 things melted, will make them as firm as wax -or modelling clay. - -GLUE. - -Take mastic, distilled turpentine and white lead. - -On bronze casting generally (731-740). - -731. - -TO CAST. - -Tartar burnt and powdered with plaster and cast cause the plaster to -hold together when it is mixed up again; and then it will dissolve -in water. - -732. - -TO CAST BRONZE IN PLASTER. - -Take to every 2 cups of plaster 1 of ox-horns burnt, mix them -together and make your cast with it. - -733. - -When you want to take a cast in wax, burn the scum with a candle, -and the cast will come out without bubbles. - -734. - -2 ounces of plaster to a pound of metal;-- walnut, which makes it -like the curve. - -[Footnote: The second part of this is quite obscure.] - -735. - -[Dried earth 16 pounds, 100 pounds of metal wet clay 20,--of wet -100,-half,- which increases 4 Ibs. of water,--1 of wax, 1 Ib. of -metal, a little less,-the scrapings of linen with earth, measure for -measure.] [Footnote: The translation is given literally, but the -meaning is quite obscure.] - -736. - -Such as the mould is, so will the cast be. - -737. - -HOW CASTS OUGHT TO BE POLISHED. - -Make a bunch of iron wire as thick as thread, and scrub them with -[this and] water; hold a bowl underneath that it may not make a mud -below. - -HOW TO REMOVE THE ROUGH EDGES FROM BRONZE. - -Make an iron rod, after the manner of a large chisel, and with this -rub over those seams on the bronze which remain on the casts of the -guns, and which are caused by the joins in the mould; but make the -tool heavy enough, and let the strokes be long and broad. - -TO FACILITATE MELTING. - -First alloy part of the metal in the crucible, then put it in the -furnace, and this being in a molten state will assist in beginning -to melt the copper. - -TO PREVENT THE COPPER COOLING IN THE FURNACE. - -When the copper cools in the furnace, be ready, as soon as you -perceive it, to cut it with a long stick while it is still in a -paste; or if it is quite cold cut it as lead is cut with broad and -large chisels. - -IF YOU HAVE TO MAKE A LARGE CAST. - -If you have to make a cast of a hundred thousand pounds do it with -two furnaces and with 2000 pounds in each, or as much as 3000 pounds -at most. - -738. - -HOW TO PROCEED TO BREAK A LARGE MASS OF BRONZE. - -If you want to break up a large mass of bronze, first suspend it, -and then make round it a wall on the four sides, like a trough of -bricks, and make a great fire therein. When it is quite red hot give -it a blow with a heavy weight raised above it, and with great force. - -739. - -TO COMBINE LEAD WITH OTHER METAL. - -If you wish for economy in combining lead with the metal in order to -lessen the amount of tin which is necessary in the metal, first -alloy the lead with the tin and then add the molten copper. - -How TO MELT [METAL] IN A FURNACE. - -The furnace should be between four well founded pillars. - -OF THE THICKNESS OF THE COATING. - -The coating should not be more than two fingers thick, it should be -laid on in four thicknesses over fine clay and then well fixed, and -it should be fired only on the inside and then carefully covered -with ashes and cow's dung. - -OF THE THICKNESS OF THE GUN. - -The gun being made to carry 600 Ibs. of ball and more, by this rule -you will take the measure of the diameter of the ball and divide it -into 6 parts and one of these parts will be its thickness at the -muzzle; but at the breech it must always be half. And if the ball is -to be 700 lbs., 1/7th of the diameter of the ball must be its -thickness in front; and if the ball is to be 800, the eighth of its -diameter in front; and if 900, 1/8th and 1/2 [3/16], and if 1000, -1/9th. - -OF THE LENGTH OF THE BODY OF THE GUN. - -If you want it to throw a ball of stone, make the length of the gun -to be 6, or as much as 7 diameters of the ball; and if the ball is -to be of iron make it as much as 12 balls, and if the ball is to be -of lead, make it as much as 18 balls. I mean when the gun is to have -the mouth fitted to receive 600 lbs. of stone ball, and more. - -OF THE THICKNESS OF SMALL GUNS. - -The thickness at the muzzle of small guns should be from a half to -one third of the diameter of the ball, and the length from 30 to 36 -balls. - -740. - -OF LUTING THE FURNACE WITHIN. - -The furnace must be luted before you put the metal in it, with earth -from Valenza, and over that with ashes. - -[Footnote 1. 2.: _Terra di Valenza_.--Valenza is north of -Alessandria on the Po.] - -OF RESTORING THE METAL WHEN IT IS BECOMING COOL. - -When you see that the bronze is congealing take some willow-wood cut -in small chips and make up the fire with it. - -THE CAUSE OF ITS CURDLING. - -I say that the cause of this congealing often proceeds from too much -fire, or from ill-dried wood. - -TO KNOW THE CONDITION OF THE FIRE. - -You may know when the fire is good and fit for your purpose by a -clear flame, and if you see the tips of the flames dull and ending -in much smoke do not trust it, and particularly when the flux metal -is almost fluid. - -OF ALLOYING THE METAL. - -Metal for guns must invariably be made with 6 or even 8 per cent, -that is 6 of tin to one hundred of copper, for the less you put in, -the stronger will the gun be. - -WHEN THE TIN SHOULD BE ADDED TO THE COPPER. - -The tin should be put in with the copper when the copper is reduced -to a fluid. - -HOW TO HASTEN THE MELTING. - -You can hasten the melting when 2/3ds of the copper is fluid; you -can then, with a stick of chestnut-wood, repeatedly stir what of -copper remains entire amidst what is melted. - -_Introductory Observations on the Architectural Designs (XII), and -Writings on Architecture (XIII)._ - -_Until now very little has been known regarding Leonardo's labours -in the domain of Architecture. No building is known to have been -planned and executed by him, though by some contemporary writers -incidental allusion is made to his occupying himself with -architecture, and his famous letter to Lodovico il Moro,--which has -long been a well-known document,--in which he offers his service as -an architect to that prince, tends to confirm the belief that he was -something more than an amateur of the art. This hypothesis has -lately been confirmed by the publication of certain documents, -preserved at Milan, showing that Leonardo was not only employed in -preparing plans but that he took an active part, with much credit, -as member of a commission on public buildings; his name remains -linked with the history of the building of the Cathedral at Pavia -and that of the Cathedral at Milan._ - -_Leonardo's writings on Architecture are dispersed among a large -number of MSS., and it would be scarcely possible to master their -contents without the opportunity of arranging, sorting and comparing -the whole mass of materials, so as to have some comprehensive idea -of the whole. The sketches, when isolated and considered by -themselves, might appear to be of but little value; it is not till -we understand their general purport, from comparing them with each -other, that we can form any just estimate of their true worth._ - -_Leonardo seems to have had a project for writing a complete and -separate treatise on Architecture, such as his predecessors and -contemporaries had composed--Leon Battista Alberti, Filarete, -Francesco di Giorgio and perhaps also Bramante. But, on the other -hand, it cannot be denied that possibly no such scheme was connected -with the isolated notes and researches, treating on special -questions, which are given in this work; that he was merely working -at problems in which, for some reason or other he took a special -interest._ - -_A great number of important buildings were constructed in Lombardy -during the period between 1472 and 1499, and among them there are -several by unknown architects, of so high an artistic merit, that it -is certainly not improbable that either Bramante or Leonardo da -Vinci may have been, directly or indirectly, concerned in their -erection._ - -_Having been engaged, for now nearly twenty years, in a thorough -study of Bramante's life and labours, I have taken a particular -interest in detecting the distinguishing marks of his style as -compared with Leonardo's. In 1869 I made researches about the -architectural drawings of the latter in the Codex Atlanticus at -Milan, for the purpose of finding out, if possible the original -plans and sketches of the churches of Santa Maria delle Grazie at -Milan, and of the Cathedral at Pavia, which buildings have been -supposed to be the work both of Bramante and of Leonardo. Since 1876 -I have repeatedly examined Leonardo's architectural studies in the -collection of his manuscripts in the Institut de France, and some of -these I have already given to the public in my work on_ "Les Projets -Primitifs pour la Basilique de St. Pierre de Rome", _P1. 43. In 1879 -I had the opportunity of examining the manuscript in the Palazzo -Trivulzio at Milan, and in 1880 Dr Richter showed me in London the -manuscripts in the possession of Lord Ashburnham, and those in the -British Museum. I have thus had opportunities of seeing most of -Leonardo's architectural drawings in the original, but of the -manuscripts tliemselves I have deciphered only the notes which -accompany the sketches. It is to Dr Richter's exertions that we owe -the collected texts on Architecture which are now published, and -while he has undertaken to be responsible for the correct reading of -the original texts, he has also made it his task to extract the -whole of the materials from the various MSS. It has been my task to -arrange and elucidate the texts under the heads which have been -adopted in this work. MS. B. at Paris and the Codex Atlanticus at -Milan are the chief sources of our knowledge of Leonardo as an -architect, and I have recently subjected these to a thorough -re-investigation expressly with a view to this work._ - -_A complete reproduction of all Leonardo's architectural sketches -has not, indeed, been possible, but as far as the necessarily -restricted limits of the work have allowed, the utmost completeness -has been aimed at, and no efforts have been spared to include every -thing that can contribute to a knowledge of Leonardo's style. It -would have been very interesting, if it had been possible, to give -some general account at least of Leonardo's work and studies in -engineering, fortification, canal-making and the like, and it is -only on mature reflection that we have reluctantly abandoned this -idea. Leonardo's occupations in these departments have by no means -so close a relation to literary work, in the strict sense of the -word as we are fairly justified in attributing to his numerous notes -on Architecture._ - -_Leonardo's architectural studies fall naturally under two heads:_ - -_I. Those drawings and sketches, often accompanied by short remarks -and explanations, which may be regarded as designs for buildings or -monuments intended to be built. With these there are occasionally -explanatory texts._ - -_II. Theoretical investigations and treatises. A special interest -attaches to these because they discuss a variety of questions which -are of practical importance to this day. Leonardo's theory as to the -origin and progress of cracks in buildings is perhaps to be -considered as unique in its way in the literature of Architecture._ - -_HENRY DE GEYMULLER_ - -_XII._ - -_Architectural Designs._ - -_I. Plans for towns._ - -_A. Sketches for laying out a new town with a double system of high- -level and low-level road-ways._ - -_Pl. LXXVII, No. 1 (MS. B, 15b). A general view of a town, with the -roads outside it sloping up to the high-level ways within._ - -_Pl. LXXVII, No. 3 (MS. B, 16b. see No. 741; and MS. B. 15b, see No. -742) gives a partial view of the town, with its streets and houses, -with explanatory references._ - -_Pl. LXXVII, No. 2 (MS. B, 15b; see No. 743). View of a double -staircaise with two opposite flights of steps._ - -_Pl. LXXVIII, Nos. 2 and 3 (MS. B, 37a). Sketches illustrating the -connection of the two levels of roads by means of steps. The lower -galleries are lighted by openings in the upper roadway._ - -_B. Notes on removing houses (MS. Br. M., 270b, see No. 744)._ - -741. - -The roads _m_ are 6 braccia higher than the roads _p s_, and each -road must be 20 braccia wide and have 1/2 braccio slope from the -sides towards the middle; and in the middle let there be at every -braccio an opening, one braccio long and one finger wide, where the -rain water may run off into hollows made on the same level as _p s_. -And on each side at the extremity of the width of the said road let -there be an arcade, 6 braccia broad, on columns; and understand that -he who would go through the whole place by the high level streets -can use them for this purpose, and he who would go by the low level -can do the same. By the high streets no vehicles and similar objects -should circulate, but they are exclusively for the use of gentlemen. -The carts and burdens for the use and convenience of the inhabitants -have to go by the low ones. One house must turn its back to the -other, leaving the lower streets between them. Provisions, such as -wood, wine and such things are carried in by the doors _n_, and -privies, stables and other fetid matter must be emptied away -underground. From one arch to the next - -742. - -must be 300 braccia, each street receiving its light through the -openings of the upper streets, and at each arch must be a winding -stair on a circular plan because the corners of square ones are -always fouled; they must be wide, and at the first vault there must -be a door entering into public privies and the said stairs lead from -the upper to the lower streets and the high level streets begin -outside the city gates and slope up till at these gates they have -attained the height of 6 braccia. Let such a city be built near the -sea or a large river in order that the dirt of the city may be -carried off by the water. - -743. - -The construction of the stairs: The stairs _c d_ go down to _f g_, -and in the same way _f g_ goes down to _h k_. - -744. - -ON MOVING HOUSES. - -Let the houses be moved and arranged in order; and this will be done -with facility because such houses are at first made in pieces on the -open places, and can then be fitted together with their timbers in -the site where they are to be permanent. - -[9] Let the men of the country [or the village] partly inhabit the -new houses when the court is absent [12]. - -[Footnote: On the same page we find notes referring to Romolontino -and Villafranca with a sketch-map of the course of the "Sodro" and -the "(Lo)cra" (both are given in the text farther on). There can -hardly be a doubt that the last sentence of the passage given above, -refers to the court of Francis I. King of France.--L.9-13 are -written inside the larger sketch, which, in the original, is on the -right hand side of the page by the side of lines 1-8. The three -smaller sketches are below. J. P. R.] - -_II. Plans for canals and streets in a town. - -Pl. LXXIX, 1. and 2, (MS. B, 37b, see No. 745, and MS. B. 36a, see -No. 746). A Plan for streets and canals inside a town, by which the -cellars of the houses are made accessible in boats. - -The third text given under No. 747 refers to works executed by -Leonardo in France._ - -745. - -The front _a m_ will give light to the rooms; _a e_ will be 6 -braccia--_a b_ 8 braccia --_b e_ 30 braccia, in order that the rooms -under the porticoes may be lighted; _c d f_ is the place where the -boats come to the houses to be unloaded. In order to render this -arrangement practicable, and in order that the inundation of the -rivers may not penetrate into the cellars, it is necessary to chose -an appropriate situation, such as a spot near a river which can be -diverted into canals in which the level of the water will not vary -either by inundations or drought. The construction is shown below; -and make choice of a fine river, which the rains do not render -muddy, such as the Ticino, the Adda and many others. [Footnote 12: -_Tesino, Adda e molti altri, i.e._ rivers coming from the mountains -and flowing through lakes.] The construction to oblige the waters to -keep constantly at the same level will be a sort of dock, as shown -below, situated at the entrance of the town; or better still, some -way within, in order that the enemy may not destroy it [14]. - -[Footnote: L. 1-4 are on the left hand side and within the sketch -given on Pl. LXXIX, No. I. Then follows after line 14, the drawing -of a sluicegate--_conca_--of which the use is explained in the text -below it. On the page 38a, which comes next in the original MS. is -the sketch of an oval plan of a town over which is written "_modo di -canali per la citta_" and through the longer axis of it "_canale -magior_" is written with "_Tesino_" on the prolongation of the -canal. J. P. R.] - -746. - -Let the width of the streets be equal to the average height of the -houses. - -747. - -The main underground channel does not receive turbid water, but that -water runs in the ditches outside the town with four mills at the -entrance and four at the outlet; and this may be done by damming the -water above Romorantin. - -[11]There should be fountains made in each piazza[13]. - -[Footnote: In the original this text comes immediately after the -passage given as No. 744. The remainder of the writing on the same -page refers to the construction of canals and is given later, in the -"Topographical Notes". - -Lines 1-11 are written to the right of the plan lines 11-13 -underneath it. J. P. R.] - -[Footnote 10: _Romolontino_ is Romorantin, South of Orleans in -France.] - -_III. Castles and Villas. - -A. Castles. - -Pl. LXXX, No. 1 (P. V. fol. 39b; No. d'ordre 2282). The fortified -place here represented is said by Vallardi to be the_ "castello" _at -Milan, but without any satisfactory reason. The high tower behind -the_ "rivellino" _ravelin--seems to be intended as a watch-tower. - -Pl. LXXX, No. 2 (MS. B, 23b). A similarly constructed tower probably -intended for the same use. - -Pl. LXXX, No. 3 (MS. B). Sketches for corner towers with steps for a -citadel. - -Pl. LXXX, No. 4 (W. XVI). A cupola crowning a corner tower; an -interesting example of decorative fortification. In this -reproduction of the original pen and ink drawing it appears -reversed. - -B. Projects for Palaces. - -Pl. LXXXI, No. 2 (MS. C. A, 75b; 221a, see No. 748). Project for a -royal residence at Amboise in France. - -Pl. LXXXII, No. 1 (C. A 308a; 939a). A plan for a somewhat extensive -residence, and various details; but there is no text to elucidate -it; in courts are written the three names: - -Sam cosi giova - _(St. Mark)_ _(Cosmo)_ _(John)_, -arch mo nino - -C. Plans for small castles or Villas. - -The three following sketches greatly resemble each other. Pl. -LXXXII, No. 2 (MS. K3 36b; see No. 749)._ - -_Pl. LXXXII, No. 3 (MS. B 60a; See No. 750). - -Pl. LXXXIII (W. XVII). The text on this sheet refers to Cyprus (see -Topographical Notes No. 1103), but seems to have no direct -connection with the sketches inserted between. - -Pl. LXXXVIII, Nos. 6 and 7 (MS. B, 12a; see No. 751). A section of a -circular pavilion with the plan of a similar building by the side of -it. These two drawings have a special historical interest because -the text written below mentions the Duke and Duchess of Milan. - -The sketch of a villa on a terrace at the end of a garden occurs in -C. A. 150; and in C. A. 77b; 225b is another sketch of a villa -somewhat resembling the_ Belvedere _of Pope Innocent VIII, at Rome. -In C. A. 62b; 193b there is a Loggia. - -Pl. LXXXII, No. 4 (C. A. 387a; 1198a) is a tower-shaped_ Loggia -_above a fountain. The machinery is very ingeniously screened from -view._ - -748. - -The Palace of the prince must have a piazza in front of it. - -Houses intended for dancing or any kind of jumping or any other -movements with a multitude of people, must be on the ground- floor; -for I have already witnessed the destruction of some, causing death -to many persons, and above all let every wall, be it ever so thin, -rest on the ground or on arches with a good foundation. - -Let the mezzanines of the dwellings be divided by walls made of very -thin bricks, and without wood on account of fire. - -Let all the privies have ventilation [by shafts] in the thickness of -the walls, so as to exhale by the roofs. - -The mezzanines should be vaulted, and the vaults will be stronger in -proportion as they are of small size. - -The ties of oak must be enclosed in the walls in order to be -protected from fire. - -[Footnote: The remarks accompanying the plan reproduced on Pl. -LXXXI, No. 2 are as follows: Above, to the left: "_in_ a _angholo -stia la guardia de la sstalla_" (in the angle _a_ may be the keeper -of the stable). Below are the words "_strada dabosa_" (road to -Amboise), parallel with this "_fossa br 40_" (the moat 40 braccia) -fixing the width of the moat. In the large court surrounded by a -portico "_in terre No.--Largha br.80 e lugha br 120_." To the right -of the castle is a large basin for aquatic sports with the words -"_Giostre colle nave cioe li giostra li stieno sopra le na_" -(Jousting in boats that is the men are to be in boats). J. P. R.] - -The privies must be numerous and going one into the other in order -that the stench may not penetrate into the dwellings., and all their -doors must shut off themselves with counterpoises. - -The main division of the facade of this palace is into two portions; -that is to say the width of the court-yard must be half the whole -facade; the 2nd ... - -749. - -30 braccia wide on each side; the lower entrance leads into a hall -10 braccia wide and 30 braccia long with 4 recesses each with a -chimney. - -[Footnote: On each side of the castle, Pl. LXXXII. No. 2 there are -drawings of details, to the left "_Camino_" a chimney, to the right -the central lantern, sketched in red "_8 lati_" _i.e._ an octagon.] - -750. - -The firststorey [or terrace] must be entirely solid. - -751. - -The pavilion in the garden of the Duchess of Milan. - -The plan of the pavilion which is in the middle of the labyrinth of -the Duke of Milan. - -[Footnote: This passage was first published by AMORETTI in _Memorie -Storiche_ Cap. X: Una sua opera da riportarsi a quest' anno fu il -bagno fatto per la duchessa Beatrice nel parco o giardino del -Castello. Lionardo non solo ne disegno il piccolo edifizio a foggia -di padiglione, nel cod. segnato Q. 3, dandone anche separatamente la -pianta; ma sotto vi scrisse: Padiglione del giardino della duchessa; -e sotto la pianta: Fondamento del padiglione ch'e nel mezzo del -labirinto del duca di Milano; nessuna data e presso il padiglione, -disegnato nella pagina 12, ma poco sopra fra molti circoli -intrecciati vedesi = 10 Luglio 1492 = e nella pagina 2 presso ad -alcuni disegni di legumi qualcheduno ha letto Settembre 1482 in vece -di 1492, come dovea scriverevi, e probabilmente scrisse Lionardo. - -The original text however hardly bears the interpretation put upon -it by AMORETTI. He is mistaken as to the mark on the MS. as well as -in his statements as to the date, for the MS. in question has no -date; the date he gives occurs, on the contrary, in another -note-book. Finally, it appears to me quite an open question whether -Leonardo was the architect who carried out the construction of the -dome-like Pavilion here shown in section, or of the ground plan of -the Pavilion drawn by the side of it. Must we, in fact, suppose that -"_il duca di Milano_" here mentioned was, as has been generally -assumed, Ludovico il Moro? He did not hold this title from the -Emperor before 1494; till that date he was only called _Governatore_ -and Leonardo in speaking of him, mentions him generally as "_il -Moro_" even after 1494. On January 18, 1491, he married Beatrice -d'Este the daughter of Ercole I, Duke of Ferrara. She died on the -2nd January 1497, and for the reasons I have given it seems -improbable that it should be this princess who is here spoken of as -the "_Duchessa di Milano_". From the style of the handwriting it -appears to me to be beyond all doubt that the MS. B, from which this -passage is taken, is older than the dated MSS. of 1492 and 1493. In -that case the Duke of Milan here mentioned would be Gian Galeazzo -(1469-1494) and the Duchess would be his wife Isabella of Aragon, to -whom he was married on the second February 1489. J. P. R.] - -752. - -The earth that is dug out from the cellars must be raised on one -side so high as to make a terrace garden as high as the level of the -hall; but between the earth of the terrace and the wall of the -house, leave an interval in order that the damp may not spoil the -principal walls. - -_IV. Ecclesiastical Architecture. - -A. General Observations._ - -753. - -A building should always be detached on all sides so that its form -may be seen. - -[Footnote: The original text is reproduced on Pl. XCII, No. 1 to the -left hand at the bottom.] - -754. - -Here there cannot and ought not to be any _campanile_; on the -contrary it must stand apart like that of the Cathedral and of San -Giovanni at Florence, and of the Cathedral at Pisa, where the -campanile is quite detached as well as the dome. Thus each can -display its own perfection. If however you wish to join it to the -church, make the lantern serve for the campanile as in the church at -Chiaravalle. - -[Footnote: This text is written by the side of the plan given on Pl. -XCI. No. 2.] - -[Footnote 12: The Abbey of Chiaravalle, a few miles from Milan, has -a central tower on the intersection of the cross in the style of -that of the Certosa of Pavia, but the style is mediaeval (A. D. -1330). Leonardo seems here to mean, that in a building, in which the -circular form is strongly conspicuous, the campanile must either be -separated, or rise from the centre of the building and therefore -take the form of a lantern.] - -755. - -It never looks well to see the roofs of a church; they should rather -be flat and the water should run off by gutters made in the frieze. - -[Footnote: This text is to the left of the domed church reproduced -on Pl. LXXXVII, No. 2.] - -_B. The theory of Dome Architecture. - -This subject has been more extensively treated by Leonardo in -drawings than in writing. Still we may fairly assume that it was his -purpose, ultimately to embody the results of his investigation in a_ -"Trattato delle Cupole." _The amount of materials is remarkably -extensive. MS. B is particularly rich in plans and elevations of -churches with one or more domes--from the simplest form to the most -complicated that can be imagined. Considering the evident connexion -between a great number of these sketches, as well as the -impossibility of seeing in them designs or preparatory sketches for -any building intended to be erected, the conclusion is obvious that -they were not designed for any particular monument, but were -theoretical and ideal researches, made in order to obtain a clear -understanding of the laws which must govern the construction of a -great central dome, with smaller ones grouped round it; and with or -without the addition of spires, so that each of these parts by -itself and in its juxtaposition to the other parts should produce -the grandest possible effect. - -In these sketches Leonardo seems to have exhausted every imaginable -combination. [Footnote 1: In MS. B, 32b (see Pl. C III, No. 2) we -find eight geometrical patterns, each drawn in a square; and in MS. -C.A., fol. 87 to 98 form a whole series of patterns done with the -same intention.] The results of some of these problems are perhaps -not quite satisfactory; still they cannot be considered to give -evidence of a want of taste or of any other defect in Leonardo s -architectural capacity. They were no doubt intended exclusively for -his own instruction, and, before all, as it seems, to illustrate the -features or consequences resulting from a given principle._ - -_I have already, in another place,_ [Footnote 1: Les Projets -Primitifs pour la Basilique de St. Pierre de Rome, par Bramante, -Raphael etc.,Vol. I, p. 2.] _pointed out the law of construction for -buildings crowned by a large dome: namely, that such a dome, to -produce the greatest effect possible, should rise either from the -centre of a Greek cross, or from the centre of a structure of which -the plan has some symmetrical affinity to a circle, this circle -being at the same time the centre of the whole plan of the building. - -Leonardo's sketches show that he was fully aware, as was to be -expected, of this truth. Few of them exhibit the form of a Latin -cross, and when this is met with, it generally gives evidence of the -determination to assign as prominent a part as possible to the dome -in the general effect of the building. - -While it is evident, on the one hand, that the greater number of -these domes had no particular purpose, not being designed for -execution, on the other hand several reasons may be found for -Leonardo's perseverance in his studies of the subject. - -Besides the theoretical interest of the question for Leonardo and -his_ Trattato _and besides the taste for domes prevailing at that -time, it seems likely that the intended erection of some building of -the first importance like the Duomos of Pavia and Como, the church -of Sta. Maria delle Grazie at Milan, and the construction of a Dome -or central Tower_ (Tiburio) _on the cathedral of Milan, may have -stimulated Leonardo to undertake a general and thorough -investigation of the subject; whilst Leonardo's intercourse with -Bramante for ten years or more, can hardly have remained without -influence in this matter. In fact now that some of this great -Architect's studies for S. Peter's at Rome have at last become -known, he must be considered henceforth as the greatest master of -Dome-Architecture that ever existed. His influence, direct or -indirect even on a genius like Leonardo seems the more likely, since -Leonardo's sketches reveal a style most similar to that of Bramante, -whose name indeed, occurs twice in Leonardo's manuscript notes. It -must not be forgotten that Leonardo was a Florentine; the -characteristic form of the two principal domes of Florence, Sta. -Maria del Fiore and the Battisterio, constantly appear as leading -features in his sketches. - -The church of San Lorenzo at Milan, was at that time still intact. -The dome is to this day one of the most wonderful cupolas ever -constructed, and with its two smaller domes might well attract the -attention and study of a never resting genius such as Leonardo. A -whole class of these sketches betray in fact the direct influence of -the church of S. Lorenzo, and this also seems to have suggested the -plan of Bramante's dome of St. Peter's at Rome. - -In the following pages the various sketches for the construction of -domes have been classified and discussed from a general point of -view. On two sheets: Pl. LXXXIV (C.A. 354b; 118a) and Pl. LXXXV, -Nos. 1-11 (Ash. II, 6b) we see various dissimilar types, grouped -together; thus these two sheets may be regarded as a sort of -nomenclature of the different types, on which we shall now have to -treat._ - -_1. Churches formed on the plan of a Greek cross. - -Group I. - -Domes rising from a circular base. - -The simplest type of central building is a circular edifice. - -Pl. LXXXIV, No. 9. Plan of a circular building surrounded by a -colonnade. - -Pl. LXXXIV, No. 8. Elevation of the former, with a conical roof. - -Pl. XC. No. 5. A dodecagon, as most nearly approaching the circle. - -Pl. LXXXVI, No. 1, 2, 3. Four round chapels are added at the -extremities of the two principal axes;--compare this plan with fig. -1 on p. 44 and fig. 3 on p. 47 (W. P. 5b) where the outer wall is -octagonal. - -Group II. - -Domes rising from a square base. - -The plan is a square surrounded by a colonnade, and the dome seems -to be octagonal. - -Pl. LXXXIV. The square plan below the circular building No. 8, and -its elevation to the left, above the plan: here the ground-plan is -square, the upper storey octagonal. A further development of this -type is shown in two sketches C. A. 3a (not reproduced here), and in - -Pl. LXXXVI, No. 5 (which possibly belongs to No. 7 on Pl. LXXXIV). - -Pl, LXXXV, No. 4, and p. 45, Fig. 3, a Greek cross, repeated p. 45, -Fig. 3, is another development of the square central plan. - -The remainder of these studies show two different systems; in the -first the dome rises from a square plan,--in the second from an -octagonal base._ - -_Group III. - -Domes rising from a square base and four pillars. [Footnote 1: The -ancient chapel San Satiro, via del Falcone, Milan, is a specimen of -this type.]_ - -a) First type. _A Dome resting on four pillars in the centre of a -square edifice, with an apse in the middle, of each of the four -sides. We have eleven variations of this type. - -aa) Pl. LXXXVIII, No. 3. - -bb) Pl. LXXX, No. 5. - -cc) Pl. LXXXV, Nos. 2, 3, 5. - -dd) Pl. LXXXIV, No. 1 and 4 beneath. - -ee) Pl. LXXXV, Nos. 1, 7, 10, 11._ - -b) Second type. _This consists in adding aisles to the whole plan of -the first type; columns are placed between the apses and the aisles; -the plan thus obtained is very nearly identical with that of S. -Lorenzo at Milan. - -Fig. 1 on p. 56. (MS. B, 75a) shows the result of this treatment -adapted to a peculiar purpose about which we shall have to say a few -words later on. - -Pl. XCV, No. 1, shows the same plan but with the addition of a short -nave. This plan seems to have been suggested by the general -arrangement of S. Sepolcro at Milan. - -MS. B. 57b (see the sketch reproduced on p.51). By adding towers in -the four outer angles to the last named plan, we obtain a plan which -bears the general features of Bramante's plans for S. Peter's at -Rome. [Footnote 2: See_ Les projets primitifs _etc., Pl. 9-12.] (See -p. 51 Fig. 1.) - -Group IV. - -Domes rising from an octagonal base. - -This system, developed according to two different schemes, has given -rise to two classes with many varieties. - -In a) On each side of the octagon chapels of equal form are added. - -In b) The chapels are dissimilar; those which terminate the -principal axes being different in form from those which are added on -the diagonal sides of the octagon. - -a. First Class. - -The Chapel_ "degli Angeli," _at Florence, built only to a height of -about 20 feet by Brunellesco, may be considered as the prototype of -this group; and, indeed it probably suggested it. The fact that we -see in MS. B. 11b (Pl. XCIV, No. 3) by the side of Brunellesco's -plan for the Basilica of Sto. Spirito at Florence, a plan almost -identical with that of the_ Capella degli Angeli, _confirms this -supposition. Only two small differences, or we may say improvements, -have been introduced by Leonardo. Firstly the back of the chapels -contains a third niche, and each angle of the Octagon a folded -pilaster like those in Bramante's_ Sagrestia di S. M. presso San -Satiro _at Milan, instead of an interval between the two pilasters -as seen in the Battistero at Florence and in the Sacristy of Sto. -Spirito in the same town and also in the above named chapel by -Brunellesco. - -The first set of sketches which come under consideration have at -first sight the appearance of mere geometrical studies. They seem to -have been suggested by the plan given on page 44 Fig. 2 (MS. B, 55a) -in the centre of which is written_ "Santa Maria in perticha da -Pavia", _at the place marked A on the reproduction. - -a) (MS. B, 34b, page 44 Fig. 3). In the middle of each side a column -is added, and in the axes of the intercolumnar spaces a second row -of columns forms an aisle round the octagon. These are placed at the -intersection of a system of semicircles, of which the sixteen -columns on the sides of the octagon are the centres. - -b) The preceding diagram is completed and becomes more monumental in -style in the sketch next to it (MS. B, 35a, see p. 45 Fig. 1). An -outer aisle is added by circles, having for radius the distance -between the columns in the middle sides of the octagon. - -c) (MS. B. 96b, see p. 45 Fig. 2). Octagon with an aisle round it; -the angles of both are formed by columns. The outer sides are formed -by 8 niches forming chapels. The exterior is likewise octagonal, -with the angles corresponding to the centre of each of the interior -chapels. - -Pl. XCII, No. 2 (MS. B. 96b). Detail and modification of the -preceding plan--half columns against piers--an arrangement by which -the chapels of the aisle have the same width of opening as the inner -arches between the half columns. Underneath this sketch the -following note occurs:_ questo vole - avere 12 facce - co 12 -tabernaculi - come - _a_ - _b_. _(This will have twelve sides with -twelve tabernacles as_ a b._) In the remaining sketches of this -class the octagon is not formed by columns at the angles. - -The simplest type shows a niche in the middle of each side and is -repeated on several sheets, viz: MS. B 3; MS. C.A. 354b (see Pl. -LXXXIV, No. 11) and MS. Ash II 6b; (see Pl. LXXXV, No. 9 and the -elevations No. 8; Pl. XCII, No. 3; MS. B. 4b [not reproduced here] -and Pl. LXXXIV, No. 2)._ - -_Pl. XCII, 3 (MS. B, 56b) corresponds to a plan like the one in MS. -B 35a, in which the niches would be visible outside or, as in the -following sketch, with the addition of a niche in the middle of each -chapel. - -Pl. XC, No. 6. The niches themselves are surrounded by smaller -niches (see also No. 1 on the same plate). - -Octagon expanded on each side. - -A. by a square chapel: - -MS. B. 34b (not reproduced here). - -B. by a square with 3 niches: - -MS. B. 11b (see Pl. XCIV, No. 3). - -C. by octagonal chapels: - -a) MS. B, 21a; Pl. LXXXVIII, No. 4. - -b) No. 2 on the same plate. Underneath there is the remark:_ -"quest'e come le 8 cappele ano a essere facte" _(this is how the -eight chapels are to be executed). - -c) Pl. LXXXVIII, No. 5. Elevation to the plans on the same sheet, it -is accompanied by the note:_ "ciasscuno de' 9 tiburi no'uole - -passare l'alteza - di - 2 - quadri" _(neither of the 9 domes must -exceed the height of two squares). - -d) Pl. LXXXVIII, No. 1. Inside of the same octagon. MS. B, 30a, and -34b; these are three repetitions of parts of the same plan with very -slight variations. - -D. by a circular chapel: - -MS. B, 18a (see Fig. 1 on page 47) gives the plan of this -arrangement in which the exterior is square on the ground floor with -only four of the chapels projecting, as is explained in the next -sketch. - -Pl. LXXXIX, MS. B, 17b. Elevation to the preceding plan sketched on -the opposite side of the sheet, and also marked A. It is accompanied -by the following remark, indicating the theoretical character of -these studies:_ questo - edifitio - anchora - starebbe - bene -affarlo dalla linja - _a_ - _b_ - _c_ - _d_ - insu. _("This edifice -would also produce a good effect if only the part above the lines_ a -b, c d, _were executed"). - -Pl. LXXXIV, No. 11. The exterior has the form of an octagon, but the -chapels project partly beyond it. On the left side of the sketch -they appear larger than on the right side. - -Pl. XC, No. 1, (MS. B, 25b); Repetition of Pl. LXXXIV, No. 11. - -Pl. XC, No. 2. Elevation to the plan No. 1, and also to No. 6 of the -same sheet._ - -_E. By chapels formed by four niches: - -Pl. LXXXIV, No. 7 (the circular plan on the left below) shows this -arrangement in which the central dome has become circular inside and -might therefore be classed after this group. [Footnote 1: This plan -and some others of this class remind us of the plan of the Mausoleum -of Augustus as it is represented for instance by Durand. See_ Cab. -des Estampes, Bibliotheque Nationale, Paris, Topographie de Rome, V, -6, 82._] - -The sketch on the right hand side gives most likely the elevation -for the last named plan. - -F. By chapels of still richer combinations, which necessitate an -octagon of larger dimensions: - -Pl. XCI, No. 2 (MS. Ash. 11. 8b) [Footnote 2: The note accompanying -this plan is given under No. 754.]; on this plan the chapels -themselves appear to be central buildings formed like the first type -of the third group. Pl. LXXXVIII, No. 3. - -Pl. XCI, No. 2 above; the exterior of the preceding figure, -particularly interesting on account of the alternation of apses and -niches, the latter containing statues of a gigantic size, in -proportion to the dimension of the niches. - -b. Second Class. - -Composite plans of this class are generally obtained by combining -two types of the first class--the one worked out on the principal -axes, the other on the diagonal ones. - -MS. B. 22 shows an elementary combination, without any additions on -the diagonal axes, but with the dimensions of the squares on the two -principal axes exceeding those of the sides of the octagon. - -In the drawing W. P. 5b (see page 44 Fig. 1) the exterior only of -the edifice is octagonal, the interior being formed by a circular -colonnade; round chapels are placed against the four sides of the -principal axes. - -The elevation, drawn on the same sheet (see page 47 Fig. 3), shows -the whole arrangement which is closely related with the one on Pl. -LXXXVI No. 1, 2. - -MS. B. 21a shows: - -a) four sides with rectangular chapels crowned by pediments Pl. -LXXXVII No. 3 (plan and elevation); - -b) four sides with square chapels crowned by octagonal domes. Pl. -LXXXVII No. 4; the plan underneath. - -MS. B. 18a shows a variation obtained by replacing the round chapels -in the principal axes of the sketch MS. B. l8a by square ones, with -an apse. Leonardo repeated both ideas for better comparison side by -side, see page 47. Fig. 2. - -Pl. LXXXIX (MS. B. 17b). Elevation for the preceding figure. The -comparison of the drawing marked M with the plan on page 47 Fig. 2, -bearing the same mark, and of the elevation on Pl. LXXXIX below -(marked A) with the corresponding plan on page 47 is highly -instructive, as illustrating the spirit in which Leonardo pursued -these studies. - -Pl. LXXXIV No. 12 shows the design Pl. LXXXVII No. 3 combined with -apses, with the addition of round chapels on the diagonal sides. - -Pl. LXXXIV No. 13 is a variation of the preceding sketch. - -Pl. XC No. 3. MS. B. 25b. The round chapels of the preceding sketch -are replaced by octagonal chapels, above which rise campaniles. - -Pl. XC No. 4 is the elevation for the preceding plan. - -Pl. XCII No. 1. (MS. B. 39b.); the plan below. On the principal as -well as on the diagonal axes are diagonal chapels, but the latter -are separated from the dome by semicircular recesses. The -communication between these eight chapels forms a square aisle round -the central dome. - -Above this figure is the elevation, showing four campaniles on the -angles. [Footnote 1: The note accompanying this drawing is -reproduced under No. 753.] - -Pl. LXXXIV No. 3. On the principal axes are square chapels with -three niches; on the diagonals octagonal chapels with niches. Cod. -Atl. 340b gives a somewhat similar arrangement. - -MS. B. 30. The principal development is thrown on the diagonal axes -by square chapels with three niches; on the principal axes are inner -recesses communicating with outer ones. - -The plan Pl. XCIII No. 2 (MS. B. 22) differs from this only in so -far as the outer semicircles have become circular chapels, -projecting from the external square as apses; one of them serves as -the entrance by a semicircular portico. - -The elevation is drawn on the left side of the plan. - -MS. B. 19. A further development of MS. B. 18, by employing for the -four principal chapels the type Pl. LXXXVIII No. 3, as we have -already seen in Pl. XCI No. 2; the exterior presents two varieties. - -a) The outer contour follows the inner. [Footnote 2: These chapels -are here sketched in two different sizes; it is the smaller type -which is thus formed.] - -b) It is semicircular. - -Pl. LXXXVII No. 2 (MS. B. 18b) Elevation to the first variation MS. -B. 19. If we were not certain that this sketch was by Leonardo, we -might feel tempted to take it as a study by Bramante for St. Peter's -at Rome. [Footnote 3: See_ Les projets primitifs Pl. 43._]_ - -_MS. P. V. 39b. In the principal axes the chapels of MS. B. 19, and -semicircular niches on the diagonals. The exterior of the whole -edifice is also an octagon, concealing the form of the interior -chapels, but with its angles on their axes. - -Group V. - -Suggested by San Lorenzo at Milan. - -In MS. C. A. 266 IIb, 8l2b there is a plan almost identical with -that of San Lorenzo. The diagonal sides of the irregular octagon are -not indicated. - -If it could be proved that the arches which, in the actual church, -exist on these sides in the first story, were added in 1574 by -Martimo Bassi, then this plan and the following section would be -still nearer the original state of San Lorenzo than at present. A -reproduction of this slightly sketched plan has not been possible. -It may however be understood from Pl. LXXXVIII No. 3, by suppressing -the four pillars corresponding to the apses. - -Pl. LXXXVII No. 1 shows the section in elevation corresponding with -the above-named plan. The recessed chapels are decorated with large -shells in the halfdomes like the arrangement in San Lorenzo, but -with proportions like those of Bramante's Sacristy of Santa Maria -presso S. Satiro. - -MS. C. A. 266; a sheet containing three views of exteriors of Domes. -On the same sheet there is a plan similar to the one above-named but -with uninterrupted aisles and with the addition of round chapels in -the axes (compare Pl. XCVII No. 3 and page 44 Fig. 1), perhaps a -reminiscence of the two chapels annexed to San Lorenzo.--Leonardo -has here sketched the way of transforming this plan into a Latin -cross by means of a nave with side aisles. - -Pl. XCI No. 1. Plan showing a type deprived of aisles and comprised -in a square building which is surrounded by a portico. It is -accompanied by the following text:_ - -756. - -This edifice is inhabited [accessible] below and above, like San -Sepolcro, and it is the same above as below, except that the upper -story has the dome _c d_; and the [Footnote: The church of San -Sepolcro at Milan, founded in 1030 and repeatedly rebuilt after the -middle of the XVIth century, still stands over the crypt of the -original structure.] lower has the dome _a b_, and when you enter -into the crypt, you descend 10 steps, and when you mount into the -upper you ascend 20 steps, which, with 1/3 braccio for each, make 10 -braccia, and this is the height between one floor of the church and -the other. - -_Above the plan on the same sheet is a view of the exterior. By the -aid of these two figures and the description, sections of the -edifice may easily be reconstructed. But the section drawn on the -left side of the building seems not to be in keeping with the same -plan, notwithstanding the explanatory note written underneath it: -"dentro il difitio di sopra" (interior of the edifice -above)[Footnote 1: _The small inner dome corresponds to_ a b _on the -plan--it rises from the lower church into the upper-- above, and -larger, rises the dome_ c d. _The aisles above and below thus -correspond_ (e di sopra come di sotto, salvoche etc.). _The only -difference is, that in the section Leonardo has not taken the -trouble to make the form octagonal, but has merely sketched circular -lines in perspective._ J. P. R._]. - -_Before leaving this group, it is well to remark that the germ of it -seems already indicated by the diagonal lines in the plans Pl. LXXXV -No. 11 and No. 7. We shall find another application of the same type -to the Latin cross in Pl. XCVII No. 3. - -_2. Churches formed on the plan of a Latin cross. - -We find among Leonardo's studies several sketches for churches on -the plan of the Latin cross; we shall begin by describing them, and -shall add a few observations. - -A. Studies after existing Monuments. - -Pl. XCIV No. 2. (MS. B. 11b.) Plan of Santo Spirito at Florence, a -basilica built after the designs of Brunellesco.--Leonardo has added -the indication of a portico in front, either his own invention or -the reproduction of a now lost design. - -Pl. XCV No. 2. Plan accompanied by the words: "A_ e santo sepolcro -di milano di sopra"(A _is the upper church of S. Sepolcro at Milan); -although since Leonardo's time considerably spoilt, it is still the -same in plan. - -The second plan with its note: "B_ e la sua parte socto tera" (B _is -its subterranean part [the crypt]) still corresponds with the -present state of this part of the church as I have ascertained by -visiting the crypt with this plan. Excepting the addition of a few -insignificant walls, the state of this interesting part of the -church still conforms to Leonardo's sketch; but in the Vestibolo the -two columns near the entrance of the winding stairs are absent. - -B. Designs or Studies. - -PL. XCV No. 1. Plan of a church evidently suggested by that of San -Sepolcro at Milan. The central part has been added to on the -principle of the second type of Group III. Leonardo has placed the_ -"coro" _(choir) in the centre._ - -_Pl. XCVI No. 2. In the plan the dome, as regards its interior, -belongs to the First Class of Group IV, and may be grouped with the -one in MS. B. 35a. The nave seems to be a development of the type -represented in Pl. XCV No. 2, B. by adding towers and two lateral -porticos[Footnote 1: Already published in Les projets primitifs Pl. -XLIII.]. - -On the left is a view of the exterior of the preceding plan. It is -accompanied by the following note:_ - -757. - -This building is inhabited below and above; the way up is by the -campaniles, and in going up one has to use the platform, where the -drums of the four domes are, and this platform has a parapet in -front, and none of these domes communicate with the church, but they -are quite separate. - -_Pl. XCVI No. 1 (MS. C. A. 16b; 65a). Perspective view of a church -seen from behind; this recalls the Duomo at Florence, but with two -campaniles[Footnote 2: Already published in the Saggio Pl. IX.]. - -Pl. XCVII No. 3 (MS. B. 52a). The central part is a development of -S. Lorenzo at Milan, such as was executed at the Duomo of Pavia. -There is sufficient analogy between the building actually executed -and this sketch to suggest a direct connection between them. -Leonardo accompanied Francesco di Giorgio[Footnote 3: See MALASPINA, -il Duomo di Pavia. Documents.] when the latter was consulted on June -21st, 1490 as to this church; the fact that the only word -accompanying the plan is:_ "sagrestia", _seems to confirm our -supposition, for the sacristies were added only in 1492, i. e. four -years after the beginning of the Cathedral, which at that time was -most likely still sufficiently unfinished to be capable of receiving -the form of the present sketch. - -Pl. XCVII No. 2 shows the exterior of this design. Below is the -note:_ edifitio al proposito del fodameto figurato di socto -_(edifice proper for the ground plan figured below). - -Here we may also mention the plan of a Latin cross drawn in MS. C. -A. fol. 266 (see p. 50). - -Pl. XCIV No. 1 (MS. L. 15b). External side view of Brunellesco's -Florentine basilica San Lorenzo, seen from the North. - -Pl. XCIV No. 4 (V. A. V, 1). Principal front of a nave, most likely -of a church on the plan of a Latin cross. We notice here not only -the principal features which were employed afterwards in Alberti's -front of S. Maria Novella, but even details of a more advanced -style, such as we are accustomed to meet with only after the year -1520. - -In the background of Leonardo's unfinished picture of St. Jerome -(Vatican Gallery) a somewhat similar church front is indicated (see -the accompanying sketch). - -[Illustration with caption: The view of the front of a temple, -apparently a dome in the centre of four corinthian porticos bearing -pediments (published by Amoretti Tav. II. B as being by Leonardo), -is taken from a drawing, now at the Ambrosian Gallery. We cannot -consider this to be by the hand of the master.]_ - -_C. Studies for a form of a Church most proper for preaching. - -The problem as to what form of church might answer the requirements -of acoustics seems to have engaged Leonardo's very particular -attention. The designation of_ "teatro" _given to some of these -sketches, clearly shows which plan seemed to him most favourable for -hearing the preacher's voice. - -Pl. XCVII, No. 1 (MS. B, 52). Rectangular edifice divided into three -naves with an apse on either side, terminated by a semicircular -theatre with rising seats, as in antique buildings. The pulpit is in -the centre. Leonardo has written on the left side of the sketch_: -"teatro da predicare" _(Theatre for preaching). - -MS. B, 55a (see page 56, Fig. 1). A domed church after the type of -Pl. XCV, No. 1, shows four theatres occupying the apses and facing -the square_ "coro" _(choir), which is in the centre between the four -pillars of the dome.[Footnote 1: The note_ teatro de predicar, _on -the right side is, I believe, in the handwriting of Pompeo Leoni. J. -P. R.] The rising arrangement of the seats is shown in the sketch -above. At the place marked_ B _Leonardo wrote_ teatri per uldire -messa _(rows of seats to hear mass), at_ T teatri,_ and at_ C coro -_(choir). - -In MS. C.A. 260, are slight sketches of two plans for rectangular -choirs and two elevations of the altar and pulpit which seem to be -in connection with these plans. - -In MS. Ash II, 8a (see p. 56 and 57. Fig. 2 and 3)._ "Locho dove si -predica" _(Place for preaching). A most singular plan for a -building. The interior is a portion of a sphere, the centre of which -is the summit of a column destined to serve as the preacher's -pulpit. The inside is somewhat like a modern theatre, whilst the -exterior and the galleries and stairs recall the ancient -amphitheatres. - -[Illustration with caption: Page 57, Fig. 4. A plan accompanying the -two preceding drawings. If this gives the complete form Leonardo -intended for the edifice, it would have comprised only about two -thirds of the circle. Leonardo wrote in the centre_ "fondamento", _a -word he often employed for plans, and on the left side of the view -of the exterior:_ locho dove si predicha _(a place for preaching -in)._] - -_D. Design for a Mausoleum. - -Pl. XCVIII (P. V., 182._ No. d'ordre 2386). In the midst of a hilly -landscape rises an artificial mountain in the form of a gigantic -cone, crowned by an imposing temple. At two thirds of the height a -terrace is cut out with six doorways forming entrances to galleries, -each leading to three sepulchral halls, so constructed as to contain -about five hundred funeral urns, disposed in the customary antique -style. From two opposite sides steps ascend to the terrace in a -single flight and beyond it to the temple above. A large circular -opening, like that in the Pantheon, is in the dome above what may be -the altar, or perhaps the central monument on the level of the -terrace below. - -The section of a gallery given in the sketch to the right below -shows the roof to be constructed on the principle of superimposed -horizontal layers, projecting one beyond the other, and each -furnished with a sort of heel, which appears to be undercut, so as -to give the appearance of a beam from within. Granite alone would be -adequate to the dimensions here given to the key stone, as the -thickness of the layers can hardly be considered to be less than a -foot. In taking this as the basis of our calculation for the -dimensions of the whole construction, the width of the chamber would -be about 25 feet but, judging from the number of urns it -contains--and there is no reason to suppose that these urns were -larger than usual--it would seem to be no more than about 8 or 10 -feet. - -The construction of the vaults resembles those in the galleries of -some etruscan tumuli, for instance the Regulini Galeassi tomb at -Cervetri (lately discovered) and also that of the chamber and -passages of the pyramid of Cheops and of the treasury of Atreus at -Mycenae. - -The upper cone displays not only analogies with the monuments -mentioned in the note, but also with Etruscan tumuli, such as the -Cocumella tomb at Vulci, and the Regulini Galeassi tomb_[Footnote 1: -_See_ FERSGUSON, _Handbook of Architecture, I,_ 291.]. _The whole -scheme is one of the most magnificent in the history of -Architecture. - -It would be difficult to decide as to whether any monument he had -seen suggested this idea to Leonardo, but it is worth while to -enquire, if any monument, or group of monuments of an earlier date -may be supposed to have done so._[Footnote 2: _There are, in -Algiers, two Monuments, commonly called_ "Le Madracen" _and_ "Le -tombeau de la Chretienne," _which somewhat resemble Leonardo's -design. They are known to have served as the Mausolea of the Kings -of Mauritania. Pomponius Mela, the geographer of the time of the -Emperor Claudius, describes them as having been_ "Monumentum commune -regiae gentis." _See_ Le Madracen, Rapport fait par M. le Grand -Rabbin AB. CAHEN, Constantine 1873--Memoire sur les fouilles -executees au Madras'en .. par le Colonel BRUNON, Constantine -l873.--Deux Mausolees Africains, le Madracen et le tombeau de la -Chretienne par M. J. DE LAURIERE, Tours l874.--Le tombeau de la -Chretienne, Mausolee des rois Mauritaniens par M. BERBRUGGER, Alger -1867.--_I am indebted to M. LE BLANC, of the Institut, and M. LUD, -LALANNE, Bibliothecaire of the Institut for having first pointed out -to me the resemblance between these monuments; while M. ANT. HERON -DE VlLLEFOSSE of the Louvre was kind enough to place the -abovementioned rare works at my disposal. Leonardo's observations on -the coast of Africa are given later in this work. The Herodium near -Bethlehem in Palestine_ (Jebel el Fureidis, _the Frank Mountain) -was, according to the latest researches, constructed on a very -similar plan. See_ Der Frankenberg, von Baurath C. SCHICK in -Jerusalem, Zeitschrift des Deutschen Palastina-Vereins, _Leipzag_ -1880, _Vol. III, pages_ 88-99 _and Plates IV and V._ J. P. R.] - -_E. Studies for the Central Tower, or Tiburio of Milan Cathedral. - -Towards the end of the fifteenth century the Fabbricceria del Duomo -had to settle on the choice of a model for the crowning and central -part of this vast building. We learn from a notice published by G. -L. Calvi [Footnote: G. L. CALVI, Notizie sulla vita e sulle opere -dei principali architetti scultori e pittori che fiorirono in -Milano, Part III, 20. See also: H. DE GEYMULLER, Les projets -primitifs etc. I, 37 and 116-119.--The Fabbricceria of the Duomo has -lately begun the publication of the archives, which may possibly -tell us more about the part taken by Leonardo, than has hitherto -been known.] that among the artists who presented models in the year -1488 were: Bramante, Pietro da Gorgonzola, Luca Paperio (Fancelli), -and Leonardo da Vinci.-- - -Several sketches by Leonardo refer to this important project: - -Pl. XCIX, No. 2 (MS. S. K. III, No. 36a) a small plan of the whole -edifice.--The projecting chapels in the middle of the transept are -wanting here. The nave appears to be shortened and seems to be -approached by an inner "vestibolo".-- - -Pl. C, No. 2 (Tr. 21). Plan of the octagon tower, giving the -disposition of the buttresses; starting from the eight pillars -adjoining the four principal piers and intended to support the eight -angles of the Tiburio. These buttresses correspond exactly with -those described by Bramante as existing in the model presented by -Omodeo. [Footnote: Bramante's opinion was first published by G. -MONGERl, Arch. stor. Lomb. V, fasc. 3 and afterwards by me in the -publication mentioned in the preceding note.] - -Pl. C, 3 (MS. Tr. 16). Two plans showing different arrangements of -the buttresses, which seem to be formed partly by the intersection -of a system of pointed arches such as that seen in ** - -Pl. C, No. 5 (MS. B, 27a) destined to give a broader base to the -drum. The text underneath is given under No. 788. - -MS. B, 3--three slight sketches of plans in connexion with the -preceding ones._ - -_Pl. XCIX, No.1 (MS. Tr. 15) contains several small sketches of -sections and exterior views of the Dome; some of them show -buttress-walls shaped as inverted arches. Respecting these Leonardo -notes:_ - -758. - -L'arco rivescio e migliore per fare spalla che l'ordinario, perche -il rovescio trova sotto se muro resistete alla sua debolezza, e -l'ordinario no trova nel suo debole se non aria - -The inverted arch is better for giving a shoulder than the ordinary -one, because the former finds below it a wall resisting its -weakness, whilst the latter finds in its weak part nothing but air. - -[Footnote: _Three slight sketches of sections on the same -leaf--above those reproduced here--are more closely connected with -the large drawing in the centre of Pl. C, No. 4 (M.S, Tr. 41) which -shows a section of a very elevated dome, with double vaults, -connected by ribs and buttresses ingeniously disposed, so as to -bring the weight of the lantern to bear on the base of the dome. - -A sketch underneath it shows a round pillar on which is indicated -which part of its summit is to bear the weight: "il pilastro sara -charicho in . a . b." (The column will bear the weight at a b.) -Another note is above on the right side:_ Larcho regiera tanto sotto -asse chome di sopra se _(The arch supports as much below it [i. e. a -hanging weight] as above it). - -Pl. C, No. 1 (C. A. 303a). Larger sketch of half section of the -Dome, with a very complicated system of arches, and a double vault. -Each stone is shaped so as to be knit or dovetailed to its -neighbours. Thus the inside of the Dome cannot be seen from below. - -MS. C. A. 303b. A repetition of the preceding sketch with very -slight modifications._] - -[Figs. 1. and Fig. 2. two sketeches of the dome] - -MS. Tr. 9 (see Fig. 1 and 2). Section of the Dome with reverted -buttresses between the windows, above which iron anchors or chains -seem to be intended. Below is the sketch of the outside._ - -_PI. XCIX, No. 3 (C. A., 262a) four sketches of the exterior of the -Dome. - -C. A. 12. Section, showing the points of rupture of a gothic vault, -in evident connection with the sketches described above. - -It deserves to be noticed how easily and apparently without effort, -Leonardo manages to combine gothic details and structure with the -more modern shape of the Dome. - -The following notes are on the same leaf,_ oni cosa poderosa, _and_ -oni cosa poderosa desidera de(scendere); _farther below, several -multiplications most likely intended to calculate the weight of some -parts of the Dome, thus 16 x 47 = 720; 720 x 800 = 176000, next to -which is written:_ peso del pilastro di 9 teste _(weight of the -pillar 9 diameters high). - -Below:_ 176000 x 8 = 1408000; _and below:_ - -Semjlio e se ce 80 (?) il peso del tiburio _(six millions six -hundred (?) 80 the weight of the Dome). - -Bossi hazarded the theory that Leonardo might have been the -architect who built the church of Sta. Maria delle Grazie, but there -is no evidence to support this, either in documents or in the -materials supplied by Leonardos manuscripts and drawings. The sketch -given at the side shows the arrangement of the second and third -socle on the apses of the choir of that church; and it is remarkable -that those sketches, in MS. S. K. M. II2, 2a and Ib, occur with the -passage given in Volume I as No. 665 and 666 referring to the -composition of the Last Supper in the Refectory of that church._] - -_F. The Project for lifting up the Battistero of Florence and -setting it on a basement._ - -_Among the very few details Vasari gives as to the architectural -studies of Leonardo, we read: "And among these models and designs -there was one by way of which he showed several times to many -ingenious citizens who then governed Florence, his readiness to lift -up without ruining it, the church of San Giovanni in Florence (the -Battistero, opposite the Duomo) in order to place under it the -missing basement with steps; he supported his assertions with -reasons so persuasive, that while he spoke the undertaking seemed -feasable, although every one of his hearers, when he had departed, -could see by himself the impossibility of so vast an undertaking."_ - -[Footnote: _This latter statement of Vasari's must be considered to -be exaggerated. I may refer here to some data given by_ LIBRI, -Histoire des sciences mathematiques en Italie (II, 216, 217): "On a -cru dans ces derniers temps faire un miracle en mecanique en -effectuant ce transport, et cependant des l'annee 1455, Gaspard Nadi -et Aristote de Fioravantio avaient transporte, a une distance -considerable, la tour de la Magione de Bologne, avec ses fondements, -qui avait presque quatre-vingts pieds de haut. Le continuateur de la -chronique de Pugliola dit que le trajet fut de 35 pieds et que -durant le transport auquel le chroniqueur affirme avoir assiste, il -arriva un accident grave qui fit pencher de trois pieds la tour -pendant qu'elle etait suspendue, mais que cet accident fut -promptement repare (Muratori, Scriptores rer. ital. Tom. XVIII, col. -717, 718). Alidosi a rapporte une note ou Nadi rend compte de ce -transport avec une rare simplicite. D'apres cette note, on voit que -les operations de ce genre n'etaient pas nouvelles. Celle-ci ne -couta que 150 livres (monnaie d'alors) y compris le cadeau que le -Legat fit aux deux mecaniciens. Dans la meme annee, Aristote -redressa le clocher de Cento, qui penchait de plus de cinq pieds -(Alidosi, instruttione p. 188-- Muratori, Scriptores rer. ital., -tom. XXIII, col. 888.--Bossii, chronica Mediol., 1492, in-fol. ad -ann. 1455). On ne concoit pas comment les historiens des beaux-arts -ont pu negliger de tels hommes." J. P. R.] - -_In the MS. C. A. fol. 293, there are two sketches which possibly -might have a bearing on this bold enterprise. We find there a plan -of a circular or polygonal edifice surrounded by semicircular arches -in an oblique position. These may be taken for the foundation of the -steps and of the new platform. In the perspective elevation the same -edifice, forming a polygon, is shown as lifted up and resting on a -circle of inverted arches which rest on an other circle of arches in -the ordinary position, but so placed that the inverted arches above -rest on the spandrels of the lower range._ - -_What seems to confirm the supposition that the lifting up of a -building is here in question, is the indication of engines for -winding up, such as jacks, and a rack and wheel. As the lifting -apparatus represented on this sheet does not seem particularly -applicable to an undertaking of such magnitude, we may consider it -to be a first sketch or scheme for the engines to be used._ - -_G. Description of an unknown Temple._ - -759. - -Twelve flights of steps led up to the great temple, which was eight -hundred braccia in circumference and built on an octagonal plan. At -the eight corners were eight large plinths, one braccia and a half -high, and three wide, and six long at the bottom, with an angle in -the middle; on these were eight great pillars, standing on the -plinths as a foundation, and twenty four braccia high. And on the -top of these were eight capitals three braccia long and six wide, -above which were the architrave frieze and cornice, four braccia and -a half high, and this was carried on in a straight line from one -pillar to the next and so, continuing for eight hundred braccia, -surrounded the whole temple, from pillar to pillar. To support this -entablature there were ten large columns of the same height as the -pillars, three braccia thick above their bases which were one -braccia and a half high. - -The ascent to this temple was by twelve flights of steps, and the -temple was on the twelfth, of an octagonal form, and at each angle -rose a large pillar; and between the pillars were placed ten columns -of the same height as the pillars, rising at once from the pavement -to a height of twenty eight braccia and a half; and at this height -the architrave, frieze and cornice were placed which surrounded the -temple having a length of eight hundred braccia. At the same height, -and within the temple at the same level, and all round the centre of -the temple at a distance of 24 braccia farther in, are pillars -corresponding to the eight pillars in the angles, and columns -corresponding to those placed in the outer spaces. These rise to the -same height as the former ones, and over these the continuous -architrave returns towards the outer row of pillars and columns. - -[Footnote: Either this description is incomplete, or, as seems to me -highly probable, it refers to some ruin. The enormous dimensions -forbid our supposing this to be any temple in Italy or Greece. Syria -was the native land of colossal octagonal buildings, in the early -centuries A. D. The Temple of Baalbek, and others are even larger -than that here described. J. P. R.] - -_V. Palace architecture. - -But a small number of Leonardo's drawings refer to the architecture -of palaces, and our knowledge is small as to what style Leonardo -might have adopted for such buildings. - -Pl. CII No. 1 (W. XVIII). A small portion of a facade of a palace -in two stories, somewhat resembling Alberti's Palazzo -Rucellai.--Compare with this Bramante's painted front of the Casa -Silvestri, and a painting by Montorfano in San Pietro in Gessate at -Milan, third chapel on the left hand side and also with Bramante's -palaces at Rome. The pilasters with arabesques, the rustica between -them, and the figures over the window may be painted or in -sgraffito. The original is drawn in red chalk. - -Pl. LXXXI No. 1 (MS. Tr. 42). Sketch of a palace with battlements -and decorations, most likely graffiti; the details remind us of -those in the Castello at Vigevano._ [Footnote 1: _Count GIULIO -PORRO, in his valuable contribution to the_ Archivio Storico -Lombardo, Anno VIII, Fasc. IV (31 Dec. 1881): Leonardo da Vinci, -Libro di Annotazioni e Memorie, _refers to this in the following -note:_ "Alla pag. 41 vi e uno schizzo di volta ed accanto scrisse: -'il pilastro sara charicho in su 6' e potrebbe darsi che si -riferisse alla cupola della chiesa delle Grazie tanto piu che a -pag. 42 vi e un disegno che rassomiglia assai al basamento che oggi -si vede nella parte esterna del coro di quella chiesa." _This may -however be doubted. The drawing, here referred to, on page 41 of the -same manuscript, is reproduced on Pl. C No. 4 and described on page -61 as being a study for the cupola of the Duomo of Milan._ J. P. R.] - -_MS. Mz. 0", contains a design for a palace or house with a loggia -in the middle of the first story, over which rises an attic with a -Pediment reproduced on page 67. The details drawn close by on the -left seem to indicate an arrangement of coupled columns against the -wall of a first story. - -Pl. LXXXV No. 14 (MS. S. K. M. Ill 79a) contains a very slight -sketch in red chalk, which most probably is intended to represent -the facade of a palace. Inside is the short note 7 he 7 (7 and 7)._ - -_MS. J2 8a (see pages 68 Fig. 1 and 2) contains a view of an unknown -palace. Its plan is indicated at the side._ - -_In MS. Br. M. 126a(see Fig. 3 on page 68) there is a sketch of a -house, on which Leonardo notes; casa con tre terrazi (house with -three terraces)._ - -_Pl. CX, No. 4 (MS. L. 36b) represents the front of a fortified -building drawn at Cesena in 1502 (see No. 1040)._ - -_Here we may also mention the singular building in the allegorical -composition represented on Pl. LVIII in Vol. I. In front of it -appears the head of a sphinx or of a dragon which seems to be -carrying the palace away._ - -_The following texts refer to the construction of palaces and other -buildings destined for private use:_ - -760. - -In the courtyard the walls must be half the height of its width, -that is if the court be 40 braccia, the house must be 20 high as -regards the walls of the said courtyard; and this courtyard must be -half as wide as the whole front. - -[Footnote: See Pl. CI, no. 1, and compare the dimensions here given, -with No. 748 lines 26-29; and the drawing belonging to it Pl. LXXXI, -no. 2.] - -On the dispositions of a stable. - -761. - -FOR MAKING A CLEAN STABLE. - -The manner in which one must arrange a stable. You must first divide -its width in 3 parts, its depth matters not; and let these 3 -divisions be equal and 6 braccia broad for each part and 10 high, -and the middle part shall be for the use of the stablemasters; the 2 -side ones for the horses, each of which must be 6 braccia in width -and 6 in length, and be half a braccio higher at the head than -behind. Let the manger be at 2 braccia from the ground, to the -bottom of the rack, 3 braccia, and the top of it 4 braccia. Now, in -order to attain to what I promise, that is to make this place, -contrary to the general custom, clean and neat: as to the upper part -of the stable, i. e. where the hay is, that part must have at its -outer end a window 6 braccia high and 6 broad, through which by -simple means the hay is brought up to the loft, as is shown by the -machine _E_; and let this be erected in a place 6 braccia wide, and -as long as the stable, as seen at _k p_. The other two parts, which -are on either side of this, are again divided; those nearest to the -hay-loft are 4 braccia, _p s_, and only for the use and circulation -of the servants belonging to the stable; the other two which reach -to the outer walls are 2 braccia, as seen at _s k_, and these are -made for the purpose of giving hay to the mangers, by means of -funnels, narrow at the top and wide over the manger, in order that -the hay should not choke them. They must be well plastered and clean -and are represented at 4 _f s_. As to the giving the horses water, -the troughs must be of stone and above them [cisterns of] water. The -mangers may be opened as boxes are uncovered by raising the lids. -[Footnote: See Pl. LXXVIII, No.1.] - -Decorations for feasts. - -762. - -THE WAY TO CONSTRUCT A FRAME-WORK FOR DECORATING BUILDINGS. - -The way in which the poles ought to be placed for tying bunches of -juniper on to them. These poles must lie close to the framework of -the vaulting and tie the bunches on with osier withes, so as to clip -them even afterwards with shears. - -Let the distance from one circle to another be half a braccia; and -the juniper [sprigs] must lie top downwards, beginning from below. - -Round this column tie four poles to which willows about as thick as -a finger must be nailed and then begin from the bottom and work -upwards with bunches of juniper sprigs, the tops downwards, that is -upside down. [Footnote: See Pl. CII, No. 3. The words here given as -the title line, lines 1--4, are the last in the original MS.--Lines -5--16 are written under fig. 4.] - -763. - -The water should be allowed to fall from the whole circle _a b_. -[Footnote: Other drawings of fountains are given on Pl. CI (W. XX); -the original is a pen and ink drawing on blue paper; on Pl. CIII -(MS. B.) and Pl. LXXXII.] - -_VI. Studies of architectural details._ - -_Several of Leonardo's drawings of architectural details prove that, -like other great masters of that period, he had devoted his -attention to the study of the proportion of such details. As every -organic being in nature has its law of construction and growth, -these masters endeavoured, each in his way, to discover and prove a -law of proportion in architecture. The following notes in Leonardo's -manuscripts refer to this subject._ - -_MS. S. K. M. Ill, 47b (see Fig. 1). A diagram, indicating the rules -as given by Vitruvius and by Leon Battista Alberti for the -proportions of the Attic base of a column._ - -_MS. S. K. M. Ill 55a (see Fig. 2). Diagram showing the same rules._ - -764. - -B toro superiore . . . . . toro superiore -2B nestroli . . . . . . astragali quadre -3B orbiculo . . . . . . . . troclea -4B nestroli . . . . . . astragali quadre -5B toro iferiore . . . . . . toro iferiore -6B latastro . . . . . . . . plintho - -[Footnote: No explanation can be offered of the meaning of the -letter B, which precedes each name. It may be meant for _basa_ -(base). Perhaps it refers to some author on architecture or an -architect (Bramante?) who employed the designations, thus marked for -the mouldings. 3. _troclea._ Philander: _Trochlea sive trochalia aut -rechanum._ 6. _Laterculus_ or _latastrum_ is the Latin name for -_Plinthus_ (pi lambda Xiv) but Vitruvius adopted this Greek name -and "latastro" seems to have been little in use. It is to be found -besides the text given above, as far as I am aware, only two -drawings of the Uffizi Collection, where in one instance, it -indicates the _abacus_ of a Doric capital.] - -765. - -STEPS OF URRBINO. - -The plinth must be as broad as the thickness of the wall against -which the plinth is built. [Footnote: See Pl. CX No. 3. The hasty -sketch on the right hand side illustrates the unsatisfactory effect -produced when the plinth is narrower than the wall.] - -766. - -The ancient architects ...... beginning with the Egyptians (?) who, -as Diodorus Siculus writes, were the first to build and construct -large cities and castles, public and private buildings of fine form, -large and well proportioned ..... - -The column, which has its thickness at the third part .... The one -which would be thinnest in the middle, would break ...; the one -which is of equal thickness and of equal strength, is better for the -edifice. The second best as to the usefulness will be the one whose -greatest thickness is where it joins with the base. - -[Footnote: See Pl. CIII, No. 3, where the sketches belonging to -lines 10--16 are reproduced, but reversed. The sketch of columns, -here reproduced by a wood cut, stands in the original close to lines -5--8.] - -The capital must be formed in this way. Divide its thickness at the -top into 8; at the foot make it 5/7, and let it be 5/7 high and you -will have a square; afterwards divide the height into 8 parts as you -did for the column, and then take 1/8 for the echinus and another -eighth for the thickness of the abacus on the top of the capital. -The horns of the abacus of the capital have to project beyond the -greatest width of the bell 2/7, i. e. sevenths of the top of the -bell, so 1/7 falls to the projection of each horn. The truncated -part of the horns must be as broad as it is high. I leave the rest, -that is the ornaments, to the taste of the sculptors. But to return -to the columns and in order to prove the reason of their strength or -weakness according to their shape, I say that when the lines -starting from the summit of the column and ending at its base and -their direction and length ..., their distance apart or width may be -equal; I say that this column ... - -767. - -The cylinder of a body columnar in shape and its two opposite ends -are two circles enclosed between parallel lines, and through the -centre of the cylinder is a straight line, ending at the centre of -these circles, and called by the ancients the axis. - -[Footnote: Leonardo wrote these lines on the margin of a page of the -Trattato di Francesco di Giorgio, where there are several drawings -of columns, as well as a head drawn in profile inside an outline -sketch of a capital.] - -768. - -_a b_ is 1/3 of _n m_; _m o_ is 1/6 of _r o_. The ovolo projects 1/6 -of _r o_; _s_ 7 1/5 of _r o_, _a b_ is divided into 9 1/2; the -abacus is 3/9 the ovolo 4/9, the bead-moulding and the fillet 2/9 -and 1/2. - -[Footnote: See Pl. LXXXV, No. 16. In the original the drawing and -writing are both in red chalk.] - -_Pl. LXXXV No. 6 (MS. Ash. II 6b) contains a small sketch of a -capital with the following note, written in three lines:_ I chorni -del capitelo deono essere la quarta parte d'uno quadro _(The horns -of a capital must measure the fourth part of a square)._ - -_MS. S. K. M. III 72b contains two sketches of ornamentations of -windows._ - -_In MS. C. A. 308a; 938a (see Pl. LXXXII No. 1) there are several -sketches of columns. One of the two columns on the right is similar -to those employed by Bramante at the Canonica di S. Ambrogio. The -same columns appear in the sketch underneath the plan of a castle. -There they appear coupled, and in two stories one above the other. -The archivolls which seem to spring out of the columns, are shaped -like twisted cords, meant perhaps to be twisted branches. The walls -between the columns seem to be formed out of blocks of wood, the -pedestals are ornamented with a reticulated pattern. From all this -we may suppose that Leonardo here had in mind either some festive -decoration, or perhaps a pavilion for some hunting place or park. -The sketch of columns marked "35" gives an example of columns shaped -like candelabra, a form often employed at that time, particularly in -Milan, and the surrounding districts for instance in the Cortile di -Casa Castiglione now Silvestre, in the cathedral of Como, at Porta -della Rana &c._ - -769. - -CONCERNING ARCHITRAVES OF ONE OR SEVERAL PIECES. - -An architrave of several pieces is stronger than that of one single -piece, if those pieces are placed with their length in the direction -of the centre of the world. This is proved because stones have their -grain or fibre generated in the contrary direction i. e. in the -direction of the opposite horizons of the hemisphere, and this is -contrary to fibres of the plants which have ... - -[Footnote: The text is incomplete in the original.] - -_The Proportions of the stories of a building are indicated by a -sketch in MS. S. K. M. II2 11b (see Pl. LXXXV No. 15). The measures -are written on the left side, as follows: br 1 1/2--6 3/4--br -1/12--2 br--9 e 1/2--1 1/2--br 5--o 9--o 3 [br=braccia; o=oncie]. - -Pl. LXXXV No. 13 (MS. B. 62a) and Pl. XCIII No. 1. (MS. B. 15a) give -a few examples of arches supported on piers._ - -_XIII. - -Theoretical writings on Architecture. - -Leonardo's original writings on the theory of Architecture have come -down to us only in a fragmentary state; still, there seems to be no -doubt that he himself did not complete them. It would seem that -Leonardo entertained the idea of writing a large and connected book -on Architecture; and it is quite evident that the materials we -possess, which can be proved to have been written at different -periods, were noted down with a more or less definite aim and -purpose. They might all be collected under the one title: "Studies -on the Strength of Materials". Among them the investigations on the -subject of fissures in walls are particularly thorough, and very -fully reported; these passages are also especially interesting, -because Leonardo was certainly the first writer on architecture who -ever treated the subject at all. Here, as in all other cases -Leonardo carefully avoids all abstract argument. His data are not -derived from the principles of algebra, but from the laws of -mechanics, and his method throughout is strictly experimental. - -Though the conclusions drawn from his investigations may not have -that precision which we are accustomed to find in Leonardo's -scientific labours, their interest is not lessened. They prove at -any rate his deep sagacity and wonderfully clear mind. No one -perhaps, who has studied these questions since Leonardo, has -combined with a scientific mind anything like the artistic delicacy -of perception which gives interest and lucidity to his observations. - -I do not assert that the arrangement here adopted for the passages -in question is that originally intended by Leonardo; but their -distribution into five groups was suggested by the titles, or -headings, which Leonardo himself prefixed to most of these notes. -Some of the longer sections perhaps should not, to be in strict -agreement with this division, have been reproduced in their entirety -in the place where they occur. But the comparatively small amount of -the materials we possess will render them, even so, sufficiently -intelligible to the reader; it did not therefore seem necessary or -desirable to subdivide the passages merely for the sake of strict -classification._ - -_The small number of chapters given under the fifth class, treating -on the centre of gravity in roof-beams, bears no proportion to the -number of drawings and studies which refer to the same subject. Only -a small selection of these are reproduced in this work since the -majority have no explanatory text._ - -I. - -ON FISSURES IN WALLS. - -770. - -First write the treatise on the causes of the giving way of walls -and then, separately, treat of the remedies. - -Parallel fissures constantly occur in buildings which are erected on -a hill side, when the hill is composed of stratified rocks with an -oblique stratification, because water and other moisture often -penetrates these oblique seams carrying in greasy and slippery soil; -and as the strata are not continuous down to the bottom of the -valley, the rocks slide in the direction of the slope, and the -motion does not cease till they have reached the bottom of the -valley, carrying with them, as though in a boat, that portion of the -building which is separated by them from the rest. The remedy for -this is always to build thick piers under the wall which is -slipping, with arches from one to another, and with a good scarp and -let the piers have a firm foundation in the strata so that they may -not break away from them. - -In order to find the solid part of these strata, it is necessary to -make a shaft at the foot of the wall of great depth through the -strata; and in this shaft, on the side from which the hill slopes, -smooth and flatten a space one palm wide from the top to the bottom; -and after some time this smooth portion made on the side of the -shaft, will show plainly which part of the hill is moving. - -[Footnote: See Pl. CIV.] - -771. - -The cracks in walls will never be parallel unless the part of the -wall that separates from the remainder does not slip down. - -WHAT IS THE LAW BY WHICH BUILDINGS HAVE STABILITY. - -The stability of buildings is the result of the contrary law to the -two former cases. That is to say that the walls must be all built up -equally, and by degrees, to equal heights all round the building, -and the whole thickness at once, whatever kind of walls they may be. -And although a thin wall dries more quickly than a thick one it will -not necessarily give way under the added weight day by day and thus, -[16] although a thin wall dries more quickly than a thick one, it -will not give way under the weight which the latter may acquire from -day to day. Because if double the amount of it dries in one day, one -of double the thickness will dry in two days or thereabouts; thus -the small addition of weight will be balanced by the smaller -difference of time [18]. - -The adversary says that _a_ which projects, slips down. - -And here the adversary says that _r_ slips and not _c_. - -HOW TO PROGNOSTICATE THE CAUSES OF CRACKS IN ANY SORT OF WALL. - -The part of the wall which does not slip is that in which the -obliquity projects and overhangs the portion which has parted from -it and slipped down. - -ON THE SITUATION OF FOUNDATIONS AND IN WHAT PLACES THEY ARE A CAUSE -OF RUIN. - -When the crevice in the wall is wider at the top than at the bottom, -it is a manifest sign, that the cause of the fissure in the wall is -remote from the perpendicular line through the crevice. - -[Footnote: Lines 1-5 refer to Pl. CV, No. 2. Line 9 _alle due -anteciedete_, see on the same page. - -Lines 16-18. The translation of this is doubtful, and the meaning in -any case very obscure. - -Lines 19-23 are on the right hand margin close to the two sketches -on Pl. CII, No. 3.] - -772. - -OF CRACKS IN WALLS, WHICH ARE WIDE AT THE BOTTOM AND NARROW AT THE -TOP AND OF THEIR CAUSES. - -That wall which does not dry uniformly in an equal time, always -cracks. - -A wall though of equal thickness will not dry with equal quickness -if it is not everywhere in contact with the same medium. Thus, if -one side of a wall were in contact with a damp slope and the other -were in contact with the air, then this latter side would remain of -the same size as before; that side which dries in the air will -shrink or diminish and the side which is kept damp will not dry. And -the dry portion will break away readily from the damp portion -because the damp part not shrinking in the same proportion does not -cohere and follow the movement of the part which dries continuously. - -OF ARCHED CRACKS, WIDE AT THE TOP, AND NARROW BELOW. - -Arched cracks, wide at the top and narrow below are found in -walled-up doors, which shrink more in their height than in their -breadth, and in proportion as their height is greater than their -width, and as the joints of the mortar are more numerous in the -height than in the width. - -The crack diminishes less in _r o_ than in _m n_, in proportion as -there is less material between _r_ and _o_ than between _n_ and _m_. - -Any crack made in a concave wall is wide below and narrow at the -top; and this originates, as is here shown at _b c d_, in the side -figure. - -1. That which gets wet increases in proportion to the moisture it -imbibes. - -2. And a wet object shrinks, while drying, in proportion to the -amount of moisture which evaporates from it. - -[Footnote: The text of this passage is reproduced in facsimile on -Pl. CVI to the left. L. 36-40 are written inside the sketch No. 2. -L. 41-46 are partly written over the sketch No. 3 to which they -refer.] - -773. - -OF THE CAUSES OF FISSURES IN [THE WALLS OF] PUBLIC AND PRIVATE -BUILDINGS. - -The walls give way in cracks, some of which are more or less -vertical and others are oblique. The cracks which are in a vertical -direction are caused by the joining of new walls, with old walls, -whether straight or with indentations fitting on to those of the old -wall; for, as these indentations cannot bear the too great weight of -the wall added on to them, it is inevitable that they should break, -and give way to the settling of the new wall, which will shrink one -braccia in every ten, more or less, according to the greater or -smaller quantity of mortar used between the stones of the masonry, -and whether this mortar is more or less liquid. And observe, that -the walls should always be built first and then faced with the -stones intended to face them. For, if you do not proceed thus, since -the wall settles more than the stone facing, the projections left on -the sides of the wall must inevitably give way; because the stones -used for facing the wall being larger than those over which they are -laid, they will necessarily have less mortar laid between the -joints, and consequently they settle less; and this cannot happen if -the facing is added after the wall is dry. - -_a b_ the new wall, _c_ the old wall, which has already settled; and -the part _a b_ settles afterwards, although _a_, being founded on -_c_, the old wall, cannot possibly break, having a stable foundation -on the old wall. But only the remainder _b_ of the new wall will -break away, because it is built from top to bottom of the building; -and the remainder of the new wall will overhang the gap above the -wall that has sunk. - -774. - -A new tower founded partly on old masonry. - -775. - -OF STONES WHICH DISJOIN THEMSELVES FROM THEIR MORTAR. - -Stones laid in regular courses from bottom to top and built up with -an equal quantity of mortar settle equally throughout, when the -moisture that made the mortar soft evaporates. - -By what is said above it is proved that the small extent of the new -wall between _A_ and _n_ will settle but little, in proportion to -the extent of the same wall between _c_ and _d_. The proportion will -in fact be that of the thinness of the mortar in relation to the -number of courses or to the quantity of mortar laid between the -stones above the different levels of the old wall. - -[Footnote: See Pl. CV, No. 1. The top of the tower is wanting in -this reproduction, and with it the letter _n_ which, in the -original, stands above the letter _A_ over the top of the tower, -while _c_ stands perpendicularly over _d_.] - -776. - -This wall will break under the arch _e f_, because the seven whole -square bricks are not sufficient to sustain the spring of the arch -placed on them. And these seven bricks will give way in their middle -exactly as appears in _a b_. The reason is, that the brick _a_ has -above it only the weight _a k_, whilst the last brick under the arch -has above it the weight _c d x a_. - -_c d_ seems to press on the arch towards the abutment at the point -_p_ but the weight _p o_ opposes resistence to it, whence the whole -pressure is transmitted to the root of the arch. Therefore the foot -of the arch acts like 7 6, which is more than double of _x z_. - -II. - -ON FISSURES IN NICHES. - -777. - -ON FISSURES IN NICHES. - -An arch constructed on a semicircle and bearing weights on the two -opposite thirds of its curve will give way at five points of the -curve. To prove this let the weights be at _n m_ which will break -the arch _a_, _b_, _f_. I say that, by the foregoing, as the -extremities _c_ and _a_ are equally pressed upon by the thrust _n_, -it follows, by the 5th, that the arch will give way at the point -which is furthest from the two forces acting on them and that is the -middle _e_. The same is to be understood of the opposite curve, _d g -b_; hence the weights _n m_ must sink, but they cannot sink by the -7th, without coming closer together, and they cannot come together -unless the extremities of the arch between them come closer, and if -these draw together the crown of the arch must break; and thus the -arch will give way in two places as was at first said &c. - -I ask, given a weight at _a_ what counteracts it in the direction -_n_ _f_ and by what weight must the weight at _f_ be counteracted. - -778. - -ON THE SHRINKING OF DAMP BODIES OF DIFFERENT THICKNESS AND WIDTH. - -The window _a_ is the cause of the crack at _b_; and this crack is -increased by the pressure of _n_ and _m_ which sink or penetrate -into the soil in which foundations are built more than the lighter -portion at _b_. Besides, the old foundation under _b_ has already -settled, and this the piers _n_ and _m_ have not yet done. Hence the -part _b_ does not settle down perpendicularly; on the contrary, it -is thrown outwards obliquely, and it cannot on the contrary be -thrown inwards, because a portion like this, separated from the main -wall, is larger outside than inside and the main wall, where it is -broken, is of the same shape and is also larger outside than inside; -therefore, if this separate portion were to fall inwards the larger -would have to pass through the smaller--which is impossible. Hence -it is evident that the portion of the semicircular wall when -disunited from the main wall will be thrust outwards, and not -inwards as the adversary says. - -When a dome or a half-dome is crushed from above by an excess of -weight the vault will give way, forming a crack which diminishes -towards the top and is wide below, narrow on the inner side and wide -outside; as is the case with the outer husk of a pomegranate, -divided into many parts lengthwise; for the more it is pressed in -the direction of its length, that part of the joints will open most, -which is most distant from the cause of the pressure; and for that -reason the arches of the vaults of any apse should never be more -loaded than the arches of the principal building. Because that which -weighs most, presses most on the parts below, and they sink into the -foundations; but this cannot happen to lighter structures like the -said apses. - -[Footnote: The figure on Pl. CV, No. 4 belongs to the first -paragraph of this passage, lines 1-14; fig. 5 is sketched by the -side of lines l5--and following. The sketch below of a pomegranate -refers to line 22. The drawing fig. 6 is, in the original, over line -37 and fig. 7 over line 54.] - -Which of these two cubes will shrink the more uniformly: the cube -_A_ resting on the pavement, or the cube _b_ suspended in the air, -when both cubes are equal in weight and bulk, and of clay mixed with -equal quantities of water? - -The cube placed on the pavement diminishes more in height than in -breadth, which the cube above, hanging in the air, cannot do. Thus -it is proved. The cube shown above is better shown here below. - -The final result of the two cylinders of damp clay that is _a_ and -_b_ will be the pyramidal figures below _c_ and _d_. This is proved -thus: The cylinder _a_ resting on block of stone being made of clay -mixed with a great deal of water will sink by its weight, which -presses on its base, and in proportion as it settles and spreads all -the parts will be somewhat nearer to the base because that is -charged with the whole weight. - -III. - -ON THE NATURE OF THE ARCH. - -779. - -WHAT IS AN ARCH? - -The arch is nothing else than a force originated by two weaknesses, -for the arch in buildings is composed of two segments of a circle, -each of which being very weak in itself tends to fall; but as each -opposes this tendency in the other, the two weaknesses combine to -form one strength. - -OF THE KIND OF PRESSURE IN ARCHES. - -As the arch is a composite force it remains in equilibrium because -the thrust is equal from both sides; and if one of the segments -weighs more than the other the stability is lost, because the -greater pressure will outweigh the lesser. - -OF DISTRIBUTING THE PRESSURE ABOVE AN ARCH. - -Next to giving the segments of the circle equal weight it is -necessary to load them equally, or you will fall into the same -defect as before. - -WHERE AN ARCH BREAKS. - -An arch breaks at the part which lies below half way from the -centre. - -SECOND RUPTURE OF THE ARCH. - -If the excess of weight be placed in the middle of the arch at the -point _a_, that weight tends to fall towards _b_, and the arch -breaks at 2/3 of its height at _c e_; and _g e_ is as many times -stronger than _e a_, as _m o_ goes into _m n_. - -ON ANOTHER CAUSE OF RUIN. - -The arch will likewise give way under a transversal thrust, for when -the charge is not thrown directly on the foot of the arch, the arch -lasts but a short time. - -780. - -ON THE STRENGTH OF THE ARCH. - -The way to give stability to the arch is to fill the spandrils with -good masonry up to the level of its summit. - -ON THE LOADING OF ROUND ARCHES. - -ON THE PROPER MANNER OF LOADING THE POINTED ARCH. - -ON THE EVIL EFFECTS OF LOADING THE POINTED ARCH DIRECTLY ABOVE ITS -CROWN. - -ON THE DAMAGE DONE TO THE POINTED ARCH BY THROWING THE PRESSURE ON -THE FLANKS. - -An arch of small curve is safe in itself, but if it be heavily -charged, it is necessary to strengthen the flanks well. An arch of a -very large curve is weak in itself, and stronger if it be charged, -and will do little harm to its abutments, and its places of giving -way are _o p_. - -[Footnote: Inside the large figure on the righi is the note: _Da -pesare la forza dell' archo_.] - -781. - -ON THE REMEDY FOR EARTHQUAKES. - -The arch which throws its pressure perpendicularly on the abutments -will fulfil its function whatever be its direction, upside down, -sideways or upright. - -The arch will not break if the chord of the outer arch does not -touch the inner arch. This is manifest by experience, because -whenever the chord _a o n_ of the outer arch _n r a_ approaches the -inner arch _x b y_ the arch will be weak, and it will be weaker in -proportion as the inner arch passes beyond that chord. When an arch -is loaded only on one side the thrust will press on the top of the -other side and be transmitted to the spring of the arch on that -side; and it will break at a point half way between its two -extremes, where it is farthest from the chord. - -782. - -A continuous body which has been forcibly bent into an arch, thrusts -in the direction of the straight line, which it tends to recover. - -783. - -In an arch judiciously weighted the thrust is oblique, so that the -triangle _c n b_ has no weight upon it. - -784. - -I here ask what weight will be needed to counterpoise and resist the -tendency of each of these arches to give way? - -[Footnote: The two lower sketches are taken from the MS. S. K. M. -III, 10a; they have there no explanatory text.] - -785. - -ON THE STRENGTH OF THE ARCH IN ARCHITECTURE. - -The stability of the arch built by an architect resides in the tie -and in the flanks. - -ON THE POSITION OF THE TIE IN THE ABOVE NAMED ARCH. - -The position of the tie is of the same importance at the beginning -of the arch and at the top of the perpendicular pier on which it -rests. This is proved by the 2nd "of supports" which says: that part -of a support has least resistance which is farthest from its solid -attachment; hence, as the top of the pier is farthest from the -middle of its true foundation and the same being the case at the -opposite extremities of the arch which are the points farthest from -the middle, which is really its [upper] attachment, we have -concluded that the tie _a b_ requires to be in such a position as -that its opposite ends are between the four above-mentioned -extremes. - -The adversary says that this arch must be more than half a circle, -and that then it will not need a tie, because then the ends will not -thrust outwards but inwards, as is seen in the excess at _a c_, _b -d_. To this it must be answered that this would be a very poor -device, for three reasons. The first refers to the strength of the -arch, since it is proved that the circular parallel being composed -of two semicircles will only break where these semicircles cross -each other, as is seen in the figure _n m;_ besides this it follows -that there is a wider space between the extremes of the semicircle -than between the plane of the walls; the third reason is that the -weight placed to counterbalance the strength of the arch diminishes -in proportion as the piers of the arch are wider than the space -between the piers. Fourthly in proportion as the parts at _c a b d_ -turn outwards, the piers are weaker to support the arch above them. -The 5th is that all the material and weight of the arch which are in -excess of the semicircle are useless and indeed mischievous; and -here it is to be noted that the weight placed above the arch will be -more likely to break the arch at _a b_, where the curve of the -excess begins that is added to the semicircle, than if the pier were -straight up to its junction with the semicircle [spring of the -arch]. - -AN ARCH LOADED OVER THE CROWN WILL GIVE WAY AT THE LEFT HAND AND -RIGHT HAND QUARTERS. - -This is proved by the 7th of this which says: The opposite ends of -the support are equally pressed upon by the weight suspended to -them; hence the weight shown at _f_ is felt at _b c_, that is half -at each extremity; and by the third which says: in a support of -equal strength [throughout] that portion will give way soonest which -is farthest from its attachment; whence it follows that _d_ being -equally distant from _f, e_ ..... - -If the centering of the arch does not settle as the arch settles, -the mortar, as it dries, will shrink and detach itself from the -bricks between which it was laid to keep them together; and as it -thus leaves them disjoined the vault will remain loosely built, and -the rains will soon destroy it. - -786. - -ON THE STRENGTH AND NATURE OF ARCHES, AND WHERE THEY ARE STRONG OR -WEAK; AND THE SAME AS TO COLUMNS. - -That part of the arch which is nearer to the horizontal offers least -resistance to the weight placed on it. - -When the triangle _a z n_, by settling, drives backwards the 2/3 of -each 1/2 circle that is _a s_ and in the same way _z m_, the reason -is that _a_ is perpendicularly over _b_ and so likewise _z_ is above -_f_. - -Either half of an arch, if overweighted, will break at 2/3 of its -height, the point which corresponds to the perpendicular line above -the middle of its bases, as is seen at _a b_; and this happens -because the weight tends to fall past the point _r_.--And if, -against its nature it should tend to fall towards the point _s_ the -arch _n s_ would break precisely in its middle. If the arch _n s_ -were of a single piece of timber, if the weight placed at _n_ should -tend to fall in the line _n m_, the arch would break in the middle -of the arch _e m_, otherwise it will break at one third from the top -at the point a because from _a_ to _n_ the arch is nearer to the -horizontal than from _a_ to _o_ and from _o_ to _s_, in proportion -as _p t_ is greater than _t n_, _a o_ will be stronger than _a n_ -and likewise in proportion as _s o_ is stronger than _o a_, _r p_ -will be greater than _p t_. - -The arch which is doubled to four times of its thickness will bear -four times the weight that the single arch could carry, and more in -proportion as the diameter of its thickness goes a smaller number of -times into its length. That is to say that if the thickness of the -single arch goes ten times into its length, the thickness of the -doubled arch will go five times into its length. Hence as the -thickness of the double arch goes only half as many times into its -length as that of the single arch does, it is reasonable that it -should carry half as much more weight as it would have to carry if -it were in direct proportion to the single arch. Hence as this -double arch has 4 times the thickness of the single arch, it would -seem that it ought to bear 4 times the weight; but by the above rule -it is shown that it will bear exactly 8 times as much. - -THAT PIER, WHICH is CHARGED MOST UNEQUALLY, WILL SOONEST GIVE WAY. - -The column _c b_, being charged with an equal weight, [on each side] -will be most durable, and the other two outward columns require on -the part outside of their centre as much pressure as there is inside -of their centre, that is, from the centre of the column, towards the -middle of the arch. - -Arches which depend on chains for their support will not be very -durable. - -THAT ARCH WILL BE OF LONGER DURATION WHICH HAS A GOOD ABUTMENT -OPPOSED TO ITS THRUST. - -The arch itself tends to fall. If the arch be 30 braccia and the -interval between the walls which carry it be 20, we know that 30 -cannot pass through the 20 unless 20 becomes likewise 30. Hence the -arch being crushed by the excess of weight, and the walls offering -insufficient resistance, part, and afford room between them, for the -fall of the arch. - -But if you do not wish to strengthen the arch with an iron tie you -must give it such abutments as can resist the thrust; and you can do -this thus: fill up the spandrels _m n_ with stones, and direct the -lines of the joints between them to the centre of the circle of the -arch, and the reason why this makes the arch durable is this. We -know very well that if the arch is loaded with an excess of weight -above its quarter as _a b_, the wall _f g_ will be thrust outwards -because the arch would yield in that direction; if the other quarter -_b c_ were loaded, the wall _f g_ would be thrust inwards, if it -were not for the line of stones _x y_ which resists this. - -787. - -PLAN. - -Here it is shown how the arches made in the side of the octagon -thrust the piers of the angles outwards, as is shown by the line _h -c_ and by the line _t d_ which thrust out the pier _m_; that is they -tend to force it away from the centre of such an octagon. - -788. - -An Experiment to show that a weight placed on an arch does not -discharge itself entirely on its columns; on the contrary the -greater the weight placed on the arches, the less the arch transmits -the weight to the columns. The experiment is the following. Let a -man be placed on a steel yard in the middle of the shaft of a well, -then let him spread out his hands and feet between the walls of the -well, and you will see him weigh much less on the steel yard; give -him a weight on the shoulders, you will see by experiment, that the -greater the weight you give him the greater effort he will make in -spreading his arms and legs, and in pressing against the wall and -the less weight will be thrown on the steel yard. - -IV. - -ON FOUNDATIONS, THE NATURE OF THE GROUND AND SUPPORTS. - -789. - -The first and most important thing is stability. - -As to the foundations of the component parts of temples and other -public buildings, the depths of the foundations must bear the same -proportions to each other as the weight of material which is to be -placed upon them. - -Every part of the depth of earth in a given space is composed of -layers, and each layer is composed of heavier or lighter materials, -the lowest being the heaviest. And this can be proved, because these -layers have been formed by the sediment from water carried down to -the sea, by the current of rivers which flow into it. The heaviest -part of this sediment was that which was first thrown down, and so -on by degrees; and this is the action of water when it becomes -stagnant, having first brought down the mud whence it first flowed. -And such layers of soil are seen in the banks of rivers, where their -constant flow has cut through them and divided one slope from the -other to a great depth; where in gravelly strata the waters have run -off, the materials have, in consequence, dried and been converted -into hard stone, and this happened most in what was the finest mud; -whence we conclude that every portion of the surface of the earth -was once at the centre of the earth, and _vice_versa_ &c. - -790. - -The heaviest part of the foundations of buildings settles most, and -leaves the lighter part above it separated from it. - -And the soil which is most pressed, if it be porous yields most. - -You should always make the foundations project equally beyond the -weight of the walls and piers, as shown at _m a b_. If you do as -many do, that is to say if you make a foundation of equal width from -the bottom up to the surface of the ground, and charge it above with -unequal weights, as shown at _b e_ and at _e o_, at the part of the -foundation at _b e_, the pier of the angle will weigh most and -thrust its foundation downwards, which the wall at _e o_ will not -do; since it does not cover the whole of its foundation, and -therefore thrusts less heavily and settles less. Hence, the pier _b -e_ in settling cracks and parts from the wall _e o_. This may be -seen in most buildings which are cracked round the piers. - -791. - -The window _a_ is well placed under the window _c_, and the window -_b_ is badly placed under the pier _d_, because this latter is -without support and foundation; mind therefore never to make a break -under the piers between the windows. - -792. - -OF THE SUPPORTS. - -A pillar of which the thickness is increased will gain more than its -due strength, in direct proportion to what its loses in relative -height. - -EXAMPLE. - -If a pillar should be nine times as high as it is broad--that is to -say, if it is one braccio thick, according to rule it should be nine -braccia high--then, if you place 100 such pillars together in a mass -this will be ten braccia broad and 9 high; and if the first pillar -could carry 10000 pounds the second being only about as high as it -is wide, and thus lacking 8 parts of its proper length, it, that is -to say, each pillar thus united, will bear eight times more than -when disconnected; that is to say, that if at first it would carry -ten thousand pounds, it would now carry 90 thousand. - -V. - -ON THE RESISTANCE OF BEAMS. - -793. - -That angle will offer the greatest resistance which is most acute, -and the most obtuse will be the weakest. - -[Footnote: The three smaller sketches accompany the text in the -original, but the larger one is not directly connected with it. It -is to be found on fol. 89a of the same Manuscript and there we read -in a note, written underneath, _coverchio della perdicha del -castello_ (roof of the flagstaff of the castle),--Compare also Pl. -XCIII, No. 1.] - -794. - -If the beams and the weight _o_ are 100 pounds, how much weight will -be wanted at _ae_ to resist such a weight, that it may not fall -down? - -795. - -ON THE LENGTH OF BEAMS. - -That beam which is more than 20 times as long as its greatest -thickness will be of brief duration and will break in half; and -remember, that the part built into the wall should be steeped in hot -pitch and filleted with oak boards likewise so steeped. Each beam -must pass through its walls and be secured beyond the walls with -sufficient chaining, because in consequence of earthquakes the beams -are often seen to come out of the walls and bring down the walls and -floors; whilst if they are chained they will hold the walls strongly -together and the walls will hold the floors. Again I remind you -never to put plaster over timber. Since by expansion and shrinking -of the timber produced by damp and dryness such floors often crack, -and once cracked their divisions gradually produce dust and an ugly -effect. Again remember not to lay a floor on beams supported on -arches; for, in time the floor which is made on beams settles -somewhat in the middle while that part of the floor which rests on -the arches remains in its place; hence, floors laid over two kinds -of supports look, in time, as if they were made in hills [Footnote: -19 M. RAVAISSON, in his edition of MS. A gives a very different -rendering of this passage translating it thus: _Les planchers qui -sont soutenus par deux differentes natures de supports paraissent -avec le temps faits en voute a cholli_.] - -Remarks on the style of Leonardo's architecture. - -A few remarks may here be added on the style of Leonardo's -architectural studies. However incomplete, however small in scale, -they allow us to establish a certain number of facts and -probabilities, well worthy of consideration. - -When Leonardo began his studies the great name of Brunellesco was -still the inspiration of all Florence, and we cannot doubt that -Leonardo was open to it, since we find among his sketches the plan -of the church of Santo Spirito[Footnote 1: See Pl. XCIV, No. 2. Then -only in course of erection after the designs of Brunellesco, though -he was already dead; finished in 1481.] and a lateral view of San -Lorenzo (Pl. XCIV No. 1), a plan almost identical with the chapel -Degli Angeli, only begun by him (Pl. XCIV, No. 3) while among -Leonardo's designs for domes several clearly betray the influence of -Brunellesco's Cupola and the lantern of Santa Maria del -Fiore[Footnote 2: A small sketch of the tower of the Palazzo della -Signoria (MS. C.A. 309) proves that he also studied mediaeval -monuments.] - -The beginning of the second period of modern Italian architecture -falls during the first twenty years of Leonardo's life. However the -new impetus given by Leon Battista Alberti either was not generally -understood by his contemporaries, or those who appreciated it, had -no opportunity of showing that they did so. It was only when taken -up by Bramante and developed by him to the highest rank of modern -architecture that this new influence was generally felt. Now the -peculiar feature of Leonardo's sketches is that, like the works of -Bramante, they appear to be the development and continuation of -Alberti's. - -_But a question here occurs which is difficult to answer. Did -Leonardo, till he quitted Florence, follow the direction given by -the dominant school of Brunellesco, which would then have given rise -to his "First manner", or had he, even before he left Florence, felt -Alberti's influence--either through his works (Palazzo Ruccellai, -and the front of Santa Maria Novella) or through personal -intercourse? Or was it not till he went to Milan that Alberti's work -began to impress him through Bramante, who probably had known -Alberti at Mantua about 1470 and who not only carried out Alberti's -views and ideas, but, by his designs for St. Peter's at Rome, proved -himself the greatest of modern architects. When Leonardo went to -Milan Bramante had already been living there for many years. One of -his earliest works in Milan was the church of Santa Maria presso San -Satiro, Via del Falcone[Footnote 1: Evidence of this I intend to -give later on in a Life of Bramante, which I have in preparation.]. - -Now we find among Leonardos studies of Cupolas on Plates LXXXIV and -LXXXV and in Pl. LXXX several sketches which seem to me to have been -suggested by Bramante's dome of this church. - -The MSS. B and Ash. II contain the plans of S. Sepolcro, the -pavilion in the garden of the duke of Milan, and two churches, -evidently inspired by the church of San Lorenzo at Milan. - -MS. B. contains besides two notes relating to Pavia, one of them a -design for the sacristy of the Cathedral at Pavia, which cannot be -supposed to be dated later than 1492, and it has probably some -relation to Leonardo's call to Pavia June 21, 1490[Footnote 2: The -sketch of the plan of Brunellesco's church of Santo Spirito at -Florence, which occurs in the same Manuscript, may have been done -from memory.]. These and other considerations justify us in -concluding, that Leonardo made his studies of cupolas at Milan, -probably between the years 1487 and 1492 in anticipation of the -erection of one of the grandest churches of Italy, the Cathedral of -Pavia. This may explain the decidedly Lombardo-Bramantesque tendency -in the style of these studies, among which only a few remind us of -the forms of the cupolas of S. Maria del Fiore and of the Baptistery -of Florence. Thus, although when compared with Bramante's work, -several of these sketches plainly reveal that master's influence, we -find, among the sketches of domes, some, which show already -Bramante's classic style, of which the Tempietto of San Pietro in -Montorio, his first building executed at Rome, is the foremost -example[Footnote 3: It may be mentioned here, that in 1494 Bramante -made a similar design for the lantern of the Cupola of the Church of -Santa Maria delle Grazie.]. - -On Plate LXXXIV is a sketch of the plan of a similar circular -building; and the Mausoleum on Pl. XCVIII, no less than one of the -pedestals for the statue of Francesco Sforza (Pl. LXV), is of the -same type. - -The drawings Pl. LXXXIV No. 2, Pl. LXXXVI No. 1 and 2 and the ground -flour ("flour" sic but should be "floor" ?) of the building in the -drawing Pl. XCI No. 2, with the interesting decoration by gigantic -statues in large niches, are also, I believe, more in the style -Bramante adopted at Rome, than in the Lombard style. Are we to -conclude from this that Leonardo on his part influenced Bramante in -the sense of simplifying his style and rendering it more congenial -to antique art? The answer to this important question seems at first -difficult to give, for we are here in presence of Bramante, the -greatest of modern architects, and with Leonardo, the man comparable -with no other. We have no knowledge of any buildings erected by -Leonardo, and unless we admit personal intercourse--which seems -probable, but of which there is no proof--, it would be difficult to -understand how Leonardo could have affected Bramante's style. The -converse is more easily to be admitted, since Bramante, as we have -proved elsewhere, drew and built simultaneously in different -manners, and though in Lombardy there is no building by him in his -classic style, the use of brick for building, in that part of Italy, -may easily account for it._ - -_Bramante's name is incidentally mentioned in Leonardo's manuscripts -in two passages (Nos. 1414 and 1448). On each occasion it is only a -slight passing allusion, and the nature of the context gives us no -due information as to any close connection between the two artists._ - -_It might be supposed, on the ground of Leonardo's relations with -the East given in sections XVII and XXI of this volume, that some -evidence of oriental influence might be detected in his -architectural drawings. I do not however think that any such traces -can be pointed out with certainty unless perhaps the drawing for a -Mausoleum, Pl. XC VIII._ - -_Among several studies for the construction of cupolas above a Greek -cross there are some in which the forms are decidedly monotonous. -These, it is clear, were not designed as models of taste; they must -be regarded as the results of certain investigations into the laws -of proportion, harmony and contrast._ - -_The designs for churches, on the plan of a Latin cross are -evidently intended to depart as little as possible from the form of -a Greek cross; and they also show a preference for a nave surrounded -with outer porticos._ - -_The architectural forms preferred by Leonardo are pilasters coupled -(Pl. LXXXII No. 1; or grouped (Pl. LXXX No. 5 and XCIV No. 4), often -combined with niches. We often meet with orders superposed, one in -each story, or two small orders on one story, in combination with -one great order (Pl. XCVI No. 2)._ - -The drum (tamburo) of these cupolas is generally octagonal, as in -the cathedral of Florence, and with similar round windows in its -sides. In Pl. LXXXVII No. 2 it is circular like the model actually -carried out by Michael Angelo at St. Peter's. - -The cupola itself is either hidden under a pyramidal roof, as in the -Baptistery of Florence, San Lorenzo of Milan and most of the Lombard -churches (Pl. XCI No. 1 and Pl. XCII No. 1); but it more generally -suggests the curve of Sta Maria del Fiore (Pl. LXXXVIII No. 5; Pl. -XC No. 2; Pl. LXXXIX, M; Pl XC No. 4, Pl. XCVI No. 2). In other -cases (Pl. LXXX No. 4; Pl. LXXXIX; Pl. XC No. 2) it shows the sides -of the octagon crowned by semicircular pediments, as in -Brunellesco's lantern of the Cathedral and in the model for the -Cathedral of Pavia. - -Finally, in some sketches the cupola is either semicircular, or as -in Pl. LXXXVII No. 2, shows the beautiful line, adopted sixty years -later by Michael Angelo for the existing dome of St. Peter's. - -It is worth noticing that for all these domes Leonardo is not -satisfied to decorate the exterior merely with ascending ribs or -mouldings, but employs also a system of horizontal parallels to -complete the architectural system. Not the least interesting are the -designs for the tiburio (cupola) of the Milan Cathedral. They show -some of the forms, just mentioned, adapted to the peculiar gothic -style of that monument. - -The few examples of interiors of churches recall the style employed -in Lombardy by Bramante, for instance in S. Maria di Canepanuova at -Pavia, or by Dolcebuono in the Monastero Maggiore at Milan (see Pl. -CI No. 1 [C. A. 181b; 546b]; Pl. LXXXIV No. 10). - -The few indications concerning palaces seem to prove that Leonardo -followed Alberti's example of decorating the walls with pilasters -and a flat rustica, either in stone or by graffitti (Pl. CII No. 1 -and Pl. LXXXV No. 14). - -By pointing out the analogies between Leonardo's architecture and -that of other masters we in no way pretend to depreciate his -individual and original inventive power. These are at all events -beyond dispute. The project for the Mausoleum (Pl. XCVIII) would -alone suffice to rank him among the greatest architects who ever -lived. The peculiar shape of the tower (Pl. LXXX), of the churches -for preaching (Pl. XCVII No. 1 and pages 56 and 57, Fig. 1-4), his -curious plan for a city with high and low level streets (Pl. LXXVII -and LXXVIII No. 2 and No. 3), his Loggia with fountains (Pl. LXXXII -No. 4) reveal an originality, a power and facility of invention for -almost any given problem, which are quite wonderful. - -_In addition to all these qualities he propably stood alone in his -day in one department of architectural study,--his investigations, -namely, as to the resistance of vaults, foundations, walls and -arches._ - -_As an application of these studies the plan of a semicircular vault -(Pl. CIII No. 2) may be mentioned here, disposed so as to produce no -thrust on the columns on which it rests:_ volta i botte e non -ispignie ifori le colone. _Above the geometrical patterns on the -same sheet, close to a circle inscribed in a square is the note:_ la -ragio d'una volta cioe il terzo del diamitro della sua ... del -tedesco in domo. - -_There are few data by which to judge of Leonardo's style in the -treatment of detail. On Pl. LXXXV No. 10 and Pl. CIII No. 3, we find -some details of pillars; on Pl. CI No. 3 slender pillars designed -for a fountain and on Pl. CIII No. 1 MS. B, is a pen and ink drawing -of a vase which also seems intended for a fountain. Three handles -seem to have been intended to connect the upper parts with the base. -There can be no doubt that Leonardo, like Bramante, but unlike -Michael Angelo, brought infinite delicacy of motive and execution to -bear on the details of his work._ - -_XIV._ - -_Anatomy, Zoology and Physiology._ - -_Leonardo's eminent place in the history of medicine, as a pioneer -in the sciences of Anatomy and Physiology, will never be appreciated -till it is possible to publish the mass of manuscripts in which he -largely treated of these two branches of learning. In the present -work I must necessarily limit myself to giving the reader a general -view of these labours, by publishing his introductory notes to the -various books on anatomical subjects. I have added some extracts, -and such observations as are scattered incidentally through these -treatises, as serving to throw a light on Leonardo's scientific -attitude, besides having an interest for a wider circle than that of -specialists only._ - -_VASARI expressly mentions Leonardo's anatomical studies, having had -occasion to examine the manuscript books which refer to them. -According to him Leonardo studied Anatomy in the companionship of -Marc Antonio della Torre_ "aiutato e scambievolmente -aiutando."_--This learned Anatomist taught the science in the -universities first of Padua and then of Pavia, and at Pavia he and -Leonardo may have worked and studied together. We have no clue to -any exact dates, but in the year 1506 Marc Antonio della Torre seems -to have not yet left Padua. He was scarcely thirty years old when he -died in 1512, and his writings on anatomy have not only never been -published, but no manuscript copy of them is known to exist._ - -_This is not the place to enlarge on the connection between Leonardo -and Marc Antonio della Torre. I may however observe that I have not -been able to discover in Leonardo's manuscripts on anatomy any -mention of his younger contemporary. The few quotations which occur -from writers on medicine--either of antiquity or of the middle ages -are printed in Section XXII. Here and there in the manuscripts -mention is made of an anonymous "adversary"_ (avversario) _whose -views are opposed and refuted by Leonardo, but there is no ground -for supposing that Marc Antonio della Torre should have been this -"adversary"._ - -_Only a very small selection from the mass of anatomical drawings -left by Leonardo have been published here in facsimile, but to form -any adequate idea of their scientific merit they should be compared -with the coarse and inadequate figures given in the published books -of the early part of the XVI. century. - -William Hunter, the great surgeon--a competent judge--who had an -opportunity in the time of George III. of seeing the originals in -the King's Library, has thus recorded his opinion: "I expected to -see little more than such designs in Anatomy as might be useful to a -painter in his own profession. But I saw, and indeed with -astonishment, that Leonardo had been a general and deep student. -When I consider what pains he has taken upon every part of the body, -the superiority of his universal genius, his particular excellence -in mechanics and hydraulics, and the attention with which such a man -would examine and see objects which he has to draw, I am fully -persuaded that Leonardo was the best Anatomist, at that time, in the -world ... Leonardo was certainly the first man, we know of, who -introduced the practice of making anatomical drawings" (Two -introductory letters. London 1784, pages 37 and 39). - -The illustrious German Naturalist Johan Friedrich Blumenback -esteemed them no less highly; he was one of the privileged few who, -after Hunter, had the chance of seeing these Manuscripts. He writes: -_Der Scharfblick dieses grossen Forschers und Darstellers der Natur -hat schon auf Dinge geachtet, die noch Jahrhunderte nachher -unbemerkt geblieben sind_" (see _Blumenbach's medicinische -Bibliothek_, Vol. 3, St. 4, 1795. page 728). - -These opinions were founded on the drawings alone. Up to the present -day hardly anything has been made known of the text, and, for the -reasons I have given, it is my intention to reproduce here no more -than a selection of extracts which I have made from the originals at -Windsor Castle and elsewhere. In the Bibliography of the -Manuscripts, at the end of this volume a short review is given of -the valuable contents of these Anatomical note books which are at -present almost all in the possession of her Majesty the Queen of -England. It is, I believe, possible to assign the date with -approximate accuracy to almost all the fragments, and I am thus led -to conclude that the greater part of Leonardo's anatomical -investigations were carried out after the death of della Torre. - -Merely in reading the introductory notes to his various books on -Anatomy which are here printed it is impossible to resist the -impression that the Master's anatomical studies bear to a very great -extent the stamp of originality and independent thought. - -I. - -ANATOMY. - -796. - -A general introduction - -I wish to work miracles;--it may be that I shall possess less than -other men of more peaceful lives, or than those who want to grow -rich in a day. I may live for a long time in great poverty, as -always happens, and to all eternity will happen, to alchemists, the -would-be creators of gold and silver, and to engineers who would -have dead water stir itself into life and perpetual motion, and to -those supreme fools, the necromancer and the enchanter. - -[Footnote 23: The following seems to be directed against students of -painting and young artists rather than against medical men and -anatomists.] - -And you, who say that it would be better to watch an anatomist at -work than to see these drawings, you would be right, if it were -possible to observe all the things which are demonstrated in such -drawings in a single figure, in which you, with all your cleverness, -will not see nor obtain knowledge of more than some few veins, to -obtain a true and perfect knowledge of which I have dissected more -than ten human bodies, destroying all the other members, and -removing the very minutest particles of the flesh by which these -veins are surrounded, without causing them to bleed, excepting the -insensible bleeding of the capillary veins; and as one single body -would not last so long, since it was necessary to proceed with -several bodies by degrees, until I came to an end and had a complete -knowledge; this I repeated twice, to learn the differences [59]. - -[Footnote: Lines 1-59 and 60-89 are written in two parallel columns. -When we here find Leonardo putting himself in the same category as -the Alchemists and Necromancers, whom he elsewhere mocks at so -bitterly, it is evidently meant ironically. In the same way -Leonardo, in the introduction to the Books on Perspective sets -himself with transparent satire on a level with other writers on the -subject.] - -And if you should have a love for such things you might be prevented -by loathing, and if that did not prevent you, you might be deterred -by the fear of living in the night hours in the company of those -corpses, quartered and flayed and horrible to see. And if this did -not prevent you, perhaps you might not be able to draw so well as is -necessary for such a demonstration; or, if you had the skill in -drawing, it might not be combined with knowledge of perspective; and -if it were so, you might not understand the methods of geometrical -demonstration and the method of the calculation of forces and of the -strength of the muscles; patience also may be wanting, so that you -lack perseverance. As to whether all these things were found in me -or not [Footnote 84: Leonardo frequently, and perhaps habitually, -wrote in note books of a very small size and only moderately thick; -in most of those which have been preserved undivided, each contains -less than fifty leaves. Thus a considerable number of such volumes -must have gone to make up a volume of the bulk of the '_Codex -Atlanticus_' which now contains nearly 1200 detached leaves. In the -passage under consideration, which was evidently written at a late -period of his life, Leonardo speaks of his Manuscript note-books as -numbering 12O; but we should hardly be justified in concluding from -this passage that the greater part of his Manuscripts were now -missing (see _Prolegomena_, Vol. I, pp. 5-7).], the hundred and -twenty books composed by me will give verdict Yes or No. In these I -have been hindered neither by avarice nor negligence, but simply by -want of time. Farewell [89]. - -Plans and suggestions for the arrangement of materials (797-802). - -797. - -OF THE ORDER OF THE BOOK. - -This work must begin with the conception of man, and describe the -nature of the womb and how the foetus lives in it, up to what stage -it resides there, and in what way it quickens into life and feeds. -Also its growth and what interval there is between one stage of -growth and another. What it is that forces it out from the body of -the mother, and for what reasons it sometimes comes out of the -mother's womb before the due time. - -Then I will describe which are the members, which, after the boy is -born, grow more than the others, and determine the proportions of a -boy of one year. - -Then describe the fully grown man and woman, with their proportions, -and the nature of their complexions, colour, and physiognomy. - -Then how they are composed of veins, tendons, muscles and bones. -This I shall do at the end of the book. Then, in four drawings, -represent four universal conditions of men. That is, Mirth, with -various acts of laughter, and describe the cause of laughter. -Weeping in various aspects with its causes. Contention, with various -acts of killing; flight, fear, ferocity, boldness, murder and every -thing pertaining to such cases. Then represent Labour, with pulling, -thrusting, carrying, stopping, supporting and such like things. - -Further I would describe attitudes and movements. Then perspective, -concerning the functions and effects of the eye; and of -hearing--here I will speak of music--, and treat of the other -senses. - -And then describe the nature of the senses. - -This mechanism of man we will demonstrate in ... figures; of which -the three first will show the ramification of the bones; that is: -first one to show their height and position and shape: the second -will be seen in profile and will show the depth of the whole and of -the parts, and their position. The third figure will be a -demonstration of the bones of the backparts. Then I will make three -other figures from the same point of view, with the bones sawn -across, in which will be shown their thickness and hollowness. Three -other figures of the bones complete, and of the nerves which rise -from the nape of the neck, and in what limbs they ramify. And three -others of the bones and veins, and where they ramify. Then three -figures with the muscles and three with the skin, and their proper -proportions; and three of woman, to illustrate the womb and the -menstrual veins which go to the breasts. - -[Footnote: The meaning of the word _nervo_ varies in different -passages, being sometimes used for _muscolo_ (muscle).] - -798. - -THE ORDER OF THE BOOK. - -This depicting of mine of the human body will be as clear to you as -if you had the natural man before you; and the reason is that if you -wish thoroughly to know the parts of man, anatomically, you--or your -eye--require to see it from different aspects, considering it from -below and from above and from its sides, turning it about and -seeking the origin of each member; and in this way the natural -anatomy is sufficient for your comprehension. But you must -understand that this amount of knowledge will not continue to -satisfy you; seeing the very great confusion that must result from -the combination of tissues, with veins, arteries, nerves, sinews, -muscles, bones, and blood which, of itself, tinges every part the -same colour. And the veins, which discharge this blood, are not -discerned by reason of their smallness. Moreover integrity of the -tissues, in the process of the investigating the parts within them, -is inevitably destroyed, and their transparent substance being -tinged with blood does not allow you to recognise the parts covered -by them, from the similarity of their blood-stained hue; and you -cannot know everything of the one without confusing and destroying -the other. Hence, some further anatomy drawings become necessary. Of -which you want three to give full knowledge of the veins and -arteries, everything else being destroyed with the greatest care. -And three others to display the tissues; and three for the sinews -and muscles and ligaments; and three for the bones and cartilages; -and three for the anatomy of the bones, which have to be sawn to -show which are hollow and which are not, which have marrow and which -are spongy, and which are thick from the outside inwards, and which -are thin. And some are extremely thin in some parts and thick in -others, and in some parts hollow or filled up with bone, or full of -marrow, or spongy. And all these conditions are sometimes found in -one and the same bone, and in some bones none of them. And three you -must have for the woman, in which there is much that is mysterious -by reason of the womb and the foetus. Therefore by my drawings every -part will be known to you, and all by means of demonstrations from -three different points of view of each part; for when you have seen -a limb from the front, with any muscles, sinews, or veins which take -their rise from the opposite side, the same limb will be shown to -you in a side view or from behind, exactly as if you had that same -limb in your hand and were turning it from side to side until you -had acquired a full comprehension of all you wished to know. In the -same way there will be put before you three or four demonstrations -of each limb, from various points of view, so that you will be left -with a true and complete knowledge of all you wish to learn of the -human figure[Footnote 35: Compare Pl. CVII. The original drawing at -Windsor is 28 1/2 X 19 1/2 centimetres. The upper figures are -slightly washed with Indian ink. On the back of this drawing is the -text No. 1140.]. - -Thus, in twelve entire figures, you will have set before you the -cosmography of this lesser world on the same plan as, before me, was -adopted by Ptolemy in his cosmography; and so I will afterwards -divide them into limbs as he divided the whole world into provinces; -then I will speak of the function of each part in every direction, -putting before your eyes a description of the whole form and -substance of man, as regards his movements from place to place, by -means of his different parts. And thus, if it please our great -Author, I may demonstrate the nature of men, and their customs in -the way I describe his figure. - -And remember that the anatomy of the nerves will not give the -position of their ramifications, nor show you which muscles they -branch into, by means of bodies dissected in running water or in -lime water; though indeed their origin and starting point may be -seen without such water as well as with it. But their ramifications, -when under running water, cling and unite--just like flat or hemp -carded for spinning--all into a skein, in a way which makes it -impossible to trace in which muscles or by what ramification the -nerves are distributed among those muscles. - -799. - -THE ARRANGEMENT OF ANATOMY - -First draw the bones, let us say, of the arm, and put in the motor -muscle from the shoulder to the elbow with all its lines. Then -proceed in the same way from the elbow to the wrist. Then from the -wrist to the hand and from the hand to the fingers. - -And in the arm you will put the motors of the fingers which open, -and these you will show separately in their demonstration. In the -second demonstration you will clothe these muscles with the -secondary motors of the fingers and so proceed by degrees to avoid -confusion. But first lay on the bones those muscles which lie close -to the said bones, without confusion of other muscles; and with -these you may put the nerves and veins which supply their -nourishment, after having first drawn the tree of veins and nerves -over the simple bones. - -800. - -Begin the anatomy at the head and finish at the sole of the foot. - -801. - -3 men complete, 3 with bones and nerves, 3 with the bones only. Here -we have 12 demonstrations of entire figures. - -802. - -When you have finished building up the man, you will make the statue -with all its superficial measurements. - -[Footnote: _Cresciere l'omo_. The meaning of this expression appears -to be different here and in the passage C.A. 157a, 468a (see No. -526, Note 1. 2). Here it can hardly mean anything else than -modelling, since the sculptor forms the figure by degrees, by adding -wet clay and the figure consequently increases or grows. _Tu farai -la statua_ would then mean, you must work out the figure in marble. -If this interpretation is the correct one, this passage would have -no right to find a place in the series on anatomical studies. I may -say that it was originally inserted in this connection under the -impression that _di cresciere_ should be read _descrivere_.] - -Plans for the representation of muscles by drawings (803-809). - -803. - -You must show all the motions of the bones with their joints to -follow the demonstration of the first three figures of the bones, -and this should be done in the first book. - -804. - -Remember that to be certain of the point of origin of any muscle, -you must pull the sinew from which the muscle springs in such a way -as to see that muscle move, and where it is attached to the -ligaments of the bones. - -NOTE. - -You will never get any thing but confusion in demonstrating the -muscles and their positions, origin, and termination, unless you -first make a demonstration of thin muscles after the manner of linen -threads; and thus you can represent them, one over another as nature -has placed them; and thus, too, you can name them according to the -limb they serve; for instance the motor of the point of the great -toe, of its middle bone, of its first bone, &c. And when you have -the knowledge you will draw, by the side of this, the true form and -size and position of each muscle. But remember to give the threads -which explain the situation of the muscles in the position which -corresponds to the central line of each muscle; and so these threads -will demonstrate the form of the leg and their distance in a plain -and clear manner. - -I have removed the skin from a man who was so shrunk by illness that -the muscles were worn down and remained in a state like thin -membrane, in such a way that the sinews instead of merging in -muscles ended in wide membrane; and where the bones were covered by -the skin they had very little over their natural size. - -[Footnote: The photograph No. 41 of Grosvenor Gallery Publications: -a drawing of the muscles of the foot, includes a complete facsimile -of the text of this passage.] - -805. - -Which nerve causes the motion of the eye so that the motion of one -eye moves the other? - -Of frowning the brows, of raising the brows, of lowering the -brows,--of closing the eyes, of opening the eyes,--of raising the -nostrils, of opening the lips, with the teeth shut, of pouting with -the lips, of smiling, of astonishment.-- - -Describe the beginning of man when it is caused in the womb and why -an eight months child does not live. What sneezing is. What yawning -is. Falling sickness, spasms, paralysis, shivering with cold, -sweating, fatigue, hunger, sleepiness, thirst, lust. - -Of the nerve which is the cause of movement from the shoulder to the -elbow, of the movement from the elbow to the hand, from the joint of -the hand to the springing of the fingers. From the springing of the -fingers to the middle joints, and from the middle joints to the -last. - -Of the nerve which causes the movement of the thigh, and from the -knee to the foot, and from the joint of the foot to the toes, and -then to the middle of the toes and of the rotary motion of the leg. - -806. - -ANATOMY. - -Which nerves or sinews of the hand are those which close and part -the fingers and toes latteraly? - -807. - -Remove by degrees all the parts of the front of a man in making your -dissection, till you come to the bones. Description of the parts of -the bust and of their motions. - -808. - -Give the anatomy of the leg up to the hip, in all views and in every -action and in every state; veins, arteries, nerves, sinews and -muscles, skin and bones; then the bones in sections to show the -thickness of the bones. - -[Footnote: A straightened leg in profile is sketched by the side of -this text.] - -On corpulency and leanness (809-811). - -809. - -Make the rule and give the measurement of each muscle, and give the -reasons of all their functions, and in which way they work and what -makes them work &c. - -[4] First draw the spine of the back; then clothe it by degrees, one -after the other, with each of its muscles and put in the nerves and -arteries and veins to each muscle by itself; and besides these note -the vertebrae to which they are attached; which of the intestines -come in contact with them; and which bones and other organs &c. - -The most prominent parts of lean people are most prominent in the -muscular, and equally so in fat persons. But concerning the -difference in the forms of the muscles in fat persons as compared -with muscular persons, it shall be described below. - -[Footnote: The two drawings given on Pl. CVIII no. 1 come between -lines 3 and 4. A good and very early copy of this drawing without -the written text exists in the collection of drawings belonging to -Christ's College Oxford, where it is attributed to Leonardo.] - -810. - -Describe which muscles disappear in growing fat, and which become -visible in growing lean. - -And observe that that part which on the surface of a fat person is -most concave, when he grows lean becomes more prominent. - -Where the muscles separate one from another you must give profiles -and where they coalesce ... - -811. - -OF THE HUMAN FIGURE. - -Which is the part in man, which, as he grows fatter, never gains -flesh? - -Or what part which as a man grows lean never falls away with a too -perceptible diminution? And among the parts which grow fat which is -that which grows fattest? - -Among those which grow lean which is that which grows leanest? - -In very strong men which are the muscles which are thickest and most -prominent? - -In your anatomy you must represent all the stages of the limbs from -man's creation to his death, and then till the death of the bone; -and which part of him is first decayed and which is preserved the -longest. - -And in the same way of extreme leanness and extreme fatness. - -The divisions of the head (812. 813). - -812. - -ANATOMY. - -There are eleven elementary tissues:-- Cartilage, bones, nerves, -veins, arteries, fascia, ligament and sinews, skin, muscle and fat. - -OF THE HEAD. - -The divisions of the head are 10, viz. 5 external and 5 internal, -the external are the hair, skin, muscle, fascia and the skull; the -internal are the dura mater, the pia mater, [which enclose] the -brain. The pia mater and the dura mater come again underneath and -enclose the brain; then the rete mirabile, and the occipital bone, -which supports the brain from which the nerves spring. - -813. - -_a_. hair - -_n_. skin - -_c_. muscle - -_m_. fascia - -_o_. skull _i.e._ bone - -_b_. dura mater - -_d_. pia mater - -_f_. brain - -_r_. pia mater, below - -_t_. dura mater - -_l_. rete mirablile - -_s_. the occipitul bone. - -[Footnote: See Pl. CVIII, No. 3.] - -Physiological problems (814. 815). - -814. - -Of the cause of breathing, of the cause of the motion of the heart, -of the cause of vomiting, of the cause of the descent of food from -the stomach, of the cause of emptying the intestines. - -Of the cause of the movement of the superfluous matter through the -intestines. - -Of the cause of swallowing, of the cause of coughing, of the cause -of yawning, of the cause of sneezing, of the cause of limbs getting -asleep. - -Of the cause of losing sensibility in any limb. - -Of the cause of tickling. - -Of the cause of lust and other appetites of the body, of the cause -of urine and also of all the natural excretions of the body. - -[Footnote: By the side of this text stands the pen and ink drawing -reproduced on Pl. CVIII, No. 4; a skull with indications of the -veins in the fleshy covering.] - -815. - -The tears come from the heart and not from the brain. - -Define all the parts, of which the body is composed, beginning with -the skin with its outer cuticle which is often chapped by the -influence of the sun. - -II. - -ZOOLOGY AND COMPARATIVE ANATOMY. - -The divisions of the animal kingdom (816. 817). - -816. - -_Man_. The description of man, which includes that of such creatures -as are of almost the same species, as Apes, Monkeys and the like, -which are many, - -_The Lion_ and its kindred, as Panthers. [Footnote 3: _Leonza_--wild -cat? "_Secondo alcuni, lo stesso che Leonessa; e secondo altri con -piu certezza, lo stesso che Pantera_" FANFANI, _Vocabolario_ page -858.] Wildcats (?) Tigers, Leopards, Wolfs, Lynxes, Spanish cats, -common cats and the like. - -_The Horse_ and its kindred, as Mule, Ass and the like, with incisor -teeth above and below. - -_The Bull_ and its allies with horns and without upper incisors as -the Buffalo, Stag Fallow Deer, Wild Goat, Swine, Goat, wild Goats -Muskdeers, Chamois, Giraffe. - -817. - -Describe the various forms of the intestines of the human species, -of apes and such like. Then, in what way the leonine species differ, -and then the bovine, and finally birds; and arrange this description -after the manner of a disquisition. - -Miscellaneous notes on the study of Zoology (818-821). - -818. - -Procure the placenta of a calf when it is born and observe the form -of the cotyledons, if their cotyledons are male or female. - -819. - -Describe the tongue of the woodpecker and the jaw of the crocodile. - -820. - -Of the flight of the 4th kind of butterflies that consume winged -ants. Of the three principal positions of the wings of birds in -downward flight. - -[Footnote: A passing allusion is all I can here permit myself to -Leonardo's elaborate researches into the flight of birds. Compare -the observations on this subject in the Introduction to section -XVIII and in the Bibliography of Manuscripts at the end of the -work.] - -821. - -Of the way in which the tail of a fish acts in propelling the fish; -as in the eel, snake and leech. - -[Footnote: A sketch of a fish, swimming upwards is in the original, -inserted above this text.--Compare No. 1114.] - -Comparative study of the structure of bones and of the action of -muscles (822-826). - -822. - -OF THE PALM OF THE HAND. - -Then I will discourse of the hands of each animal to show in what -they vary; as in the bear, which has the ligatures of the sinews of -the toes joined above the instep. - -823. - -A second demonstration inserted between anatomy and [the treatise -on] the living being. - -You will represent here for a comparison, the legs of a frog, which -have a great resemblance to the legs of man, both in the bones and -in the muscles. Then, in continuation, the hind legs of the hare, -which are very muscular, with strong active muscles, because they -are not encumbered with fat. - -[Footnote: This text is written by the side of a drawing in black -chalk of a nude male figure, but there is no connection between the -sketch and the text.] - -824. - -Here I make a note to demonstrate the difference there is between -man and the horse and in the same way with other animals. And first -I will begin with the bones, and then will go on to all the muscles -which spring from the bones without tendons and end in them in the -same way, and then go on to those which start with a single tendon -at one end. - -[Footnote: See Pl. CVIII, No. 2.] - -825. - -Note on the bendings of joints and in what way the flesh grows upon -them in their flexions or extensions; and of this most important -study write a separate treatise: in the description of the movements -of animals with four feet; among which is man, who likewise in his -infancy crawls on all fours. - -826. - -OF THE WAY OF WALKING IN MAN. - -The walking of man is always after the universal manner of walking -in animals with 4 legs, inasmuch as just as they move their feet -crosswise after the manner of a horse in trotting, so man moves his -4 limbs crosswise; that is, if he puts forward his right foot in -walking he puts forward, with it, his left arm and vice versa, -invariably. - -III. - -PHYSIOLOGY. - -Comparative study of the organs of sense in men and animals. - -827. - -I have found that in the composition of the human body as compared -with the bodies of animals the organs of sense are duller and -coarser. Thus it is composed of less ingenious instruments, and of -spaces less capacious for receiving the faculties of sense. I have -seen in the Lion tribe that the sense of smell is connected with -part of the substance of the brain which comes down the nostrils, -which form a spacious receptacle for the sense of smell, which -enters by a great number of cartilaginous vesicles with several -passages leading up to where the brain, as before said, comes down. - -The eyes in the Lion tribe have a large part of the head for their -sockets and the optic nerves communicate at once with the brain; but -the contrary is to be seen in man, for the sockets of the eyes are -but a small part of the head, and the optic nerves are very fine and -long and weak, and by the weakness of their action we see by day but -badly at night, while these animals can see as well at night as by -day. The proof that they can see is that they prowl for prey at -night and sleep by day, as nocturnal birds do also. - -Advantages in the structure of the eye in certain animals (828-831). - -828. - -Every object we see will appear larger at midnight than at midday, -and larger in the morning than at midday. - -This happens because the pupil of the eye is much smaller at midday -than at any other time. - -In proportion as the eye or the pupil of the owl is larger in -proportion to the animal than that of man, so much the more light -can it see at night than man can; hence at midday it can see nothing -if its pupil does not diminish; and, in the same way, at night -things look larger to it than by day. - -829. - -OF THE EYES IN ANIMALS. - -The eyes of all animals have their pupils adapted to dilate and -diminish of their own accord in proportion to the greater or less -light of the sun or other luminary. But in birds the variation is -much greater; and particularly in nocturnal birds, such as horned -owls, and in the eyes of one species of owl; in these the pupil -dilates in such away as to occupy nearly the whole eye, or -diminishes to the size of a grain of millet, and always preserves -the circular form. But in the Lion tribe, as panthers, pards, -ounces, tigers, lynxes, Spanish cats and other similar animals the -pupil diminishes from the perfect circle to the figure of a pointed -oval such as is shown in the margin. But man having a weaker sight -than any other animal is less hurt by a very strong light and his -pupil increases but little in dark places; but in the eyes of these -nocturnal animals, the horned owl--a bird which is the largest of -all nocturnal birds--the power of vision increases so much that in -the faintest nocturnal light (which we call darkness) it sees with -much more distinctness than we do in the splendour of noon day, at -which time these birds remain hidden in dark holes; or if indeed -they are compelled to come out into the open air lighted up by the -sun, they contract their pupils so much that their power of sight -diminishes together with the quantity of light admitted. - -Study the anatomy of various eyes and see which are the muscles -which open and close the said pupils of the eyes of animals. - -[Footnote: Compare No. 24, lines 8 and fol.] - -830. - -_a b n_ is the membrane which closes the eye from below, upwards, -with an opaque film, _c n b_ encloses the eye in front and behind -with a transparent membrane. - -It closes from below, upwards, because it [the eye] comes downwards. - -When the eye of a bird closes with its two lids, the first to close -is the nictitating membrane which closes from the lacrymal duct over -to the outer corner of the eye; and the outer lid closes from below -upwards, and these two intersecting motions begin first from the -lacrymatory duct, because we have already seen that in front and -below birds are protected and use only the upper portion of the eye -from fear of birds of prey which come down from above and behind; -and they uncover first the membrane from the outer corner, because -if the enemy comes from behind, they have the power of escaping to -the front; and again the muscle called the nictitating membrane is -transparent, because, if the eye had not such a screen, they could -not keep it open against the wind which strikes against the eye in -the rush of their rapid flight. And the pupil of the eye dilates and -contracts as it sees a less or greater light, that is to say intense -brilliancy. - -831. - -If at night your eye is placed between the light and the eye of a -cat, it will see the eye look like fire. - -Remarks on the organs of speech - -(832. 833). - -832. - -_a e i o u -ba be bi bo bu -ca ce ci co cu -da de di do du -fa fe fi fo fu -ga ge gi go gu -la le li lo lu -ma me mi mo mu -na ne ni no nu -pa pe pi po pu -qa qe qi qo qu -ra re ri ro ru -sa se si so su -ta te ti to tu_ - -The tongue is found to have 24 muscles which correspond to the six -muscles which compose the portion of the tongue which moves in the -mouth. - -And when _a o u_ are spoken with a clear and rapid pronunciation, it -is necessary, in order to pronounce continuously, without any pause -between, that the opening of the lips should close by degrees; that -is, they are wide apart in saying _a_, closer in saying _o_, and -much closer still to pronounce _u_. - -It may be shown how all the vowels are pronounced with the farthest -portion of the false palate which is above the epiglottis. - -833. - -If you draw in breath by the nose and send it out by the mouth you -will hear the sound made by the division that is the membrane in -[Footnote 5: The text here breaks off.]... - -On the conditions of sight (834. 835). - -834. - -OF THE NATURE OF SIGHT. - -I say that sight is exercised by all animals, by the medium of -light; and if any one adduces, as against this, the sight of -nocturnal animals, I must say that this in the same way is subject -to the very same natural laws. For it will easily be understood that -the senses which receive the images of things do not project from -themselves any visual virtue [Footnote 4: Compare No. 68.]. On the -contrary the atmospheric medium which exists between the object and -the sense incorporates in itself the figure of things, and by its -contact with the sense transmits the object to it. If the -object--whether by sound or by odour--presents its spiritual force -to the ear or the nose, then light is not required and does not act. -The forms of objects do not send their images into the air if they -are not illuminated [8]; and the eye being thus constituted cannot -receive that from the air, which the air does not possess, although -it touches its surface. If you choose to say that there are many -animals that prey at night, I answer that when the little light -which suffices the nature of their eyes is wanting, they direct -themselves by their strong sense of hearing and of smell, which are -not impeded by the darkness, and in which they are very far superior -to man. If you make a cat leap, by daylight, among a quantity of -jars and crocks you will see them remain unbroken, but if you do the -same at night, many will be broken. Night birds do not fly about -unless the moon shines full or in part; rather do they feed between -sun-down and the total darkness of the night. - -[Footnote 8: See No. 58-67.] - -No body can be apprehended without light and shade, and light and -shade are caused by light. - -835. - -WHY MEN ADVANCED IN AGE SEE BETTER AT A DISTANCE. - -Sight is better from a distance than near in those men who are -advancing in age, because the same object transmits a smaller -impression of itself to the eye when it is distant than when it is -near. - -The seat of the common sense. - -836. - -The Common Sense, is that which judges of things offered to it by -the other senses. The ancient speculators have concluded that that -part of man which constitutes his judgment is caused by a central -organ to which the other five senses refer everything by means of -impressibility; and to this centre they have given the name Common -Sense. And they say that this Sense is situated in the centre of the -head between Sensation and Memory. And this name of Common Sense is -given to it solely because it is the common judge of all the other -five senses _i.e._ Seeing, Hearing, Touch, Taste and Smell. This -Common Sense is acted upon by means of Sensation which is placed as -a medium between it and the senses. Sensation is acted upon by means -of the images of things presented to it by the external instruments, -that is to say the senses which are the medium between external -things and Sensation. In the same way the senses are acted upon by -objects. Surrounding things transmit their images to the senses and -the senses transfer them to the Sensation. Sensation sends them to -the Common Sense, and by it they are stamped upon the memory and are -there more or less retained according to the importance or force of -the impression. That sense is most rapid in its function which is -nearest to the sensitive medium and the eye, being the highest is -the chief of the others. Of this then only we will speak, and the -others we will leave in order not to make our matter too long. -Experience tells us that the eye apprehends ten different natures of -things, that is: Light and Darkness, one being the cause of the -perception of the nine others, and the other its absence:-- Colour -and substance, form and place, distance and nearness, motion and -stillness [Footnote 15: Compare No. 23.]. - -On the origin of the soul. - -837. - -Though human ingenuity may make various inventions which, by the -help of various machines answering the same end, it will never -devise any inventions more beautiful, nor more simple, nor more to -the purpose than Nature does; because in her inventions nothing is -wanting, and nothing is superfluous, and she needs no counterpoise -when she makes limbs proper for motion in the bodies of animals. But -she puts into them the soul of the body, which forms them that is -the soul of the mother which first constructs in the womb the form -of the man and in due time awakens the soul that is to inhabit it. -And this at first lies dormant and under the tutelage of the soul of -the mother, who nourishes and vivifies it by the umbilical vein, -with all its spiritual parts, and this happens because this -umbilicus is joined to the placenta and the cotyledons, by which the -child is attached to the mother. And these are the reason why a -wish, a strong craving or a fright or any other mental suffering in -the mother, has more influence on the child than on the mother; for -there are many cases when the child loses its life from them, &c. - -This discourse is not in its place here, but will be wanted for the -one on the composition of animated bodies--and the rest of the -definition of the soul I leave to the imaginations of friars, those -fathers of the people who know all secrets by inspiration. - -[Footnote 57: _lettere incoronate_. By this term Leonardo probably -understands not the Bible only, but the works of the early Fathers, -and all the books recognised as sacred by the Roman Church.] I leave -alone the sacred books; for they are supreme truth. - -On the relations of the soul to the organs of sense. - -838. - -HOW THE FIVE SENSES ARE THE MINISTERS OF THE SOUL. - -The soul seems to reside in the judgment, and the judgment would -seem to be seated in that part where all the senses meet; and this -is called the Common Sense and is not all-pervading throughout the -body, as many have thought. Rather is it entirely in one part. -Because, if it were all-pervading and the same in every part, there -would have been no need to make the instruments of the senses meet -in one centre and in one single spot; on the contrary it would have -sufficed that the eye should fulfil the function of its sensation on -its surface only, and not transmit the image of the things seen, to -the sense, by means of the optic nerves, so that the soul--for the -reason given above-- may perceive it in the surface of the eye. In -the same way as to the sense of hearing, it would have sufficed if -the voice had merely sounded in the porous cavity of the indurated -portion of the temporal bone which lies within the ear, without -making any farther transit from this bone to the common sense, where -the voice confers with and discourses to the common judgment. The -sense of smell, again, is compelled by necessity to refer itself to -that same judgment. Feeling passes through the perforated cords and -is conveyed to this common sense. These cords diverge with infinite -ramifications into the skin which encloses the members of the body -and the viscera. The perforated cords convey volition and sensation -to the subordinate limbs. These cords and the nerves direct the -motions of the muscles and sinews, between which they are placed; -these obey, and this obedience takes effect by reducing their -thickness; for in swelling, their length is reduced, and the nerves -shrink which are interwoven among the particles of the limbs; being -extended to the tips of the fingers, they transmit to the sense the -object which they touch. - -The nerves with their muscles obey the tendons as soldiers obey the -officers, and the tendons obey the Common [central] Sense as the -officers obey the general. [27] Thus the joint of the bones obeys -the nerve, and the nerve the muscle, and the muscle the tendon and -the tendon the Common Sense. And the Common Sense is the seat of the -soul [28], and memory is its ammunition, and the impressibility is -its referendary since the sense waits on the soul and not the soul -on the sense. And where the sense that ministers to the soul is not -at the service of the soul, all the functions of that sense are also -wanting in that man's life, as is seen in those born mute and blind. - -[Footnote: The peculiar use of the words _nervo_, _muscolo_, -_corda_, _senso comune_, which are here literally rendered by nerve, -muscle cord or tendon and Common Sense may be understood from lines -27 and 28.] - -On involuntary muscular action. - -839. - -HOW THE NERVES SOMETIMES ACT OF THEMSELVES WITHOUT ANY COMMANDS FROM -THE OTHER FUNCTIONS OF THE SOUL. - -This is most plainly seen; for you will see palsied and shivering -persons move, and their trembling limbs, as their head and hands, -quake without leave from their soul and their soul with all its -power cannot prevent their members from trembling. The same thing -happens in falling sickness, or in parts that have been cut off, as -in the tails of lizards. The idea or imagination is the helm and -guiding-rein of the senses, because the thing conceived of moves the -sense. Pre-imagining, is imagining the things that are to be. -Post-imagining, is imagining the things that are past. - -Miscellaneous physiological observations (840-842). - -840. - -There are four Powers: memory and intellect, desire and -covetousness. The two first are mental and the others sensual. The -three senses: sight, hearing and smell cannot well be prevented; -touch and taste not at all. Smell is connected with taste in dogs -and other gluttonous animals. - -841. - -I reveal to men the origin of the first, or perhaps second cause of -their existence. - -842. - -Lust is the cause of generation. - -Appetite is the support of life. Fear or timidity is the -prolongation of life and preservation of its instruments. - -The laws of nutrition and the support of life (843-848). - -843. - -HOW THE BODY OF ANIMALS IS CONSTANTLY DYING AND BEING RENEWED. - -The body of any thing whatever that takes nourishment constantly -dies and is constantly renewed; because nourishment can only enter -into places where the former nourishment has expired, and if it has -expired it no longer has life. And if you do not supply nourishment -equal to the nourishment which is gone, life will fail in vigour, -and if you take away this nourishment, the life is entirely -destroyed. But if you restore as much is destroyed day by day, then -as much of the life is renewed as is consumed, just as the flame of -the candle is fed by the nourishment afforded by the liquid of this -candle, which flame continually with a rapid supply restores to it -from below as much as is consumed in dying above: and from a -brilliant light is converted in dying into murky smoke; and this -death is continuous, as the smoke is continuous; and the continuance -of the smoke is equal to the continuance of the nourishment, and in -the same instant all the flame is dead and all regenerated, -simultaneously with the movement of its own nourishment. - -844. - -King of the animals--as thou hast described him--I should rather say -king of the beasts, thou being the greatest--because thou hast -spared slaying them, in order that they may give thee their children -for the benefit of the gullet, of which thou hast attempted to make -a sepulchre for all animals; and I would say still more, if it were -allowed me to speak the entire truth [5]. But we do not go outside -human matters in telling of one supreme wickedness, which does not -happen among the animals of the earth, inasmuch as among them are -found none who eat their own kind, unless through want of sense (few -indeed among them, and those being mothers, as with men, albeit they -be not many in number); and this happens only among the rapacious -animals, as with the leonine species, and leopards, panthers lynxes, -cats and the like, who sometimes eat their children; but thou, -besides thy children devourest father, mother, brothers and friends; -nor is this enough for thee, but thou goest to the chase on the -islands of others, taking other men and these half-naked, the ... -and the ... thou fattenest, and chasest them down thy own -throat[18]; now does not nature produce enough simples, for thee to -satisfy thyself? and if thou art not content with simples, canst -thou not by the mixture of them make infinite compounds, as Platina -wrote[Footnote 21: _Come scrisse il Platina_ (Bartolomeo Sacchi, a -famous humanist). The Italian edition of his treatise _De arte -coquinaria_, was published under the title _De la honestra -voluptate, e valetudine, Venezia_ 1487.], and other authors on -feeding? - -[Footnote: We are led to believe that Leonardo himself was a -vegetarian from the following interesting passage in the first of -Andrea Corsali's letters to Giuliano de'Medici: _Alcuni gentili -chiamati Guzzarati non si cibano di cosa, alcuna che tenga sangue, -ne fra essi loro consentono che si noccia ad alcuna cosa animata, -come il nostro Leonardo da Vinci_. - -5-18. Amerigo Vespucci, with whom Leonardo was personally -acquainted, writes in his second letter to Pietro Soderini, about -the inhabitants of the Canary Islands after having stayed there in -1503: "_Hanno una scelerata liberta di viuere; ... si cibano di -carne humana, di maniera che il padre magia il figliuolo, et -all'incontro il figliuolo il padre secondo che a caso e per sorte -auiene. Io viddi un certo huomo sceleratissimo che si vantaua, et si -teneua a non piccola gloria di hauer mangiato piu di trecento -huomini. Viddi anche vna certa citta, nella quale io dimorai forse -ventisette giorni, doue le carni humane, hauendole salate, eran -appicate alli traui, si come noi alli traui di cucina_ _appicchiamo -le carni di cinghali secche al sole o al fumo, et massimamente -salsiccie, et altre simil cose: anzi si marauigliauano gradem ete -che noi non magiaissimo della carne de nemici, le quali dicono -muouere appetito, et essere di marauiglioso sapore, et le lodano -come cibi soaui et delicati (Lettere due di Amerigo Vespucci -Fiorentino drizzate al magnifico Pietro Soderini, Gonfaloniere della -eccelsa Republica di Firenze_; various editions).] - -845. - -Our life is made by the death of others. - -In dead matter insensible life remains, which, reunited to the -stomachs of living beings, resumes life, both sensual and -intellectual. - -846. - -Here nature appears with many animals to have been rather a cruel -stepmother than a mother, and with others not a stepmother, but a -most tender mother. - -847. - -Man and animals are really the passage and the conduit of food, the -sepulchre of animals and resting place of the dead, one causing the -death of the other, making themselves the covering for the -corruption of other dead [bodies]. - -On the circulation of the blood (848-850). - -848. - -Death in old men, when not from fever, is caused by the veins which -go from the spleen to the valve of the liver, and which thicken so -much in the walls that they become closed up and leave no passage -for the blood that nourishes it. - -[6]The incessant current of the blood through the veins makes these -veins thicken and become callous, so that at last they close up and -prevent the passage of the blood. - -849. - -The waters return with constant motion from the lowest depths of the -sea to the utmost height of the mountains, not obeying the nature of -heavier bodies; and in this they resemble the blood of animated -beings which always moves from the sea of the heart and flows -towards the top of the head; and here it may burst a vein, as may be -seen when a vein bursts in the nose; all the blood rises from below -to the level of the burst vein. When the water rushes out from the -burst vein in the earth, it obeys the law of other bodies that are -heavier than the air since it always seeks low places. - -[Footnote: From this passage it is quite plain that Leonardo had not -merely a general suspicion of the circulation of the blood but a -very clear conception of it. Leonardo's studies on the muscles of -the heart are to be found in the MS. W. An. III. but no information -about them has hitherto been made public. The limits of my plan in -this work exclude all purely anatomical writings, therefore only a -very brief excerpt from this note book can be given here. WILLIAM -HARVEY (born 1578 and Professor of Anatomy at Cambridge from 1615) -is always considered to have been the discoverer of the circulation -of the blood. He studied medicine at Padua in 1598, and in 1628 -brought out his memorable and important work: _De motu cordis et -sanguinis_.] - -850. - -That the blood which returns when the heart opens again is not the -same as that which closes the valves of the heart. - -Some notes on medicine (851-855). - -851. - -Make them give you the definition and remedies for the case ... and -you will see that men are selected to be doctors for diseases they -do not know. - -852. - -A remedy for scratches taught me by the Herald to the King of -France. 4 ounces of virgin wax, 4 ounces of colophony, 2 ounces of -incense. Keep each thing separate; and melt the wax, and then put in -the incense and then the colophony, make a mixture of it and put it -on the sore place. - -853. - -Medicine is the restoration of discordant elements; sickness is the -discord of the elements infused into the living body. - -854. - -Those who are annoyed by sickness at sea should drink extract of -wormwood. - -855. - -To keep in health, this rule is wise: Eat only when you want and -relish food. Chew thoroughly that it may do you good. Have it well -cooked, unspiced and undisguised. He who takes medicine is ill -advised. - -[Footnote: This appears to be a sketch for a poem.] - -856. - -I teach you to preserve your health; and in this you will succed -better in proportion as you shun physicians, because their medicines -are the work of alchemists. - -[Footnote: This passage is written on the back of the drawing Pl. -CVIII. Compare also No. 1184.] - -_XV_. - -_Astronomy_. - -_Ever since the publication by Venturi in_ 1797 _and Libri in_ 1840 -_of some few passages of Leonardo's astronomical notes, scientific -astronomers have frequently expressed the opinion, that they must -have been based on very important discoveries, and that the great -painter also deserved a conspicuous place in the history of this -science. In the passages here printed, a connected view is given of -his astronomical studies as they lie scattered through the -manuscripts, which have come down to us. Unlike his other purely -scientific labours, Leonardo devotes here a good deal of attention -to the opinions of the ancients, though he does not follow the -practice universal in his day of relying on them as authorities; he -only quotes them, as we shall see, in order to refute their -arguments. His researches throughout have the stamp of independent -thought. There is nothing in these writings to lead us to suppose -that they were merely an epitome of the general learning common to -the astronomers of the period. As early as in the XIVth century -there were chairs of astronomy in the universities of Padua and -Bologna, but so late as during the entire XVIth century Astronomy -and Astrology were still closely allied._ - -_It is impossible now to decide whether Leonardo, when living in -Florence, became acquainted in his youth with the doctrines of Paolo -Toscanelli the great astronomer and mathematician (died_ 1482_), of -whose influence and teaching but little is now known, beyond the -fact that he advised and encouraged Columbus to carry out his -project of sailing round the world. His name is nowhere mentioned by -Leonardo, and from the dates of the manuscripts from which the texts -on astronomy are taken, it seems highly probable that Leonardo -devoted his attention to astronomical studies less in his youth than -in his later years. It was evidently his purpose to treat of -Astronomy in a connected form and in a separate work (see the -beginning of Nos._ 866 _and_ 892_; compare also No._ 1167_). It is -quite in accordance with his general scientific thoroughness that he -should propose to write a special treatise on Optics as an -introduction to Astronomy (see Nos._ 867 _and_ 877_). Some of the -chapters belonging to this Section bear the title "Prospettiva" -_(see Nos._ 869 _and_ 870_), this being the term universally applied -at the time to Optics as well as Perspective (see Vol. I, p._ 10, -_note to No._ 13, _l._ 10_)_. - -_At the beginning of the XVIth century the Ptolemaic theory of the -universe was still universally accepted as the true one, and -Leonardo conceives of the earth as fixed, with the moon and sun -revolving round it, as they are represented in the diagram to No._ -897. _He does not go into any theory of the motions of the planets; -with regard to these and the fixed stars he only investigates the -phenomena of their luminosity. The spherical form of the earth he -takes for granted as an axiom from the first, and he anticipates -Newton by pointing out the universality of Gravitation not merely in -the earth, but even in the moon. Although his acute research into -the nature of the moon's light and the spots on the moon did not -bring to light many results of lasting importance beyond making it -evident that they were a refutation of the errors of his -contemporaries, they contain various explanations of facts which -modern science need not modify in any essential point, and -discoveries which history has hitherto assigned to a very much later -date_. - -_The ingenious theory by which he tries to explain the nature of -what is known as earth shine, the reflection of the sun's rays by -the earth towards the moon, saying that it is a peculiar refraction, -originating in the innumerable curved surfaces of the waves of the -sea may be regarded as absurd; but it must not be forgotten that he -had no means of detecting the fundamental error on which he based -it, namely: the assumption that the moon was at a relatively short -distance from the earth. So long as the motion of the earth round -the sun remained unknown, it was of course impossible to form any -estimate of the moon's distance from the earth by a calculation of -its parallax_. - -_Before the discovery of the telescope accurate astronomical -observations were only possible to a very limited extent. It would -appear however from certain passages in the notes here printed for -the first time, that Leonardo was in a position to study the spots -in the moon more closely than he could have done with the unaided -eye. So far as can be gathered from the mysterious language in which -the description of his instrument is wrapped, he made use of -magnifying glasses; these do not however seem to have been -constructed like a telescope--telescopes were first made about_ -1600. _As LIBRI pointed out_ (Histoire des Sciences mathematiques -III, 101) _Fracastoro of Verona_ (1473-1553) _succeeded in -magnifying the moon's face by an arrangement of lenses (compare No._ -910, _note), and this gives probability to Leonardo's invention at a -not much earlier date._ - -I. - -THE EARTH AS A PLANET. - -The earth's place in the universe (857. 858). - -857. - -The equator, the line of the horizon, the ecliptic, the meridian: - -These lines are those which in all their parts are equidistant from -the centre of the globe. - -858. - -The earth is not in the centre of the Sun's orbit nor at the centre -of the universe, but in the centre of its companion elements, and -united with them. And any one standing on the moon, when it and the -sun are both beneath us, would see this our earth and the element of -water upon it just as we see the moon, and the earth would light it -as it lights us. - -The fundamental laws of the solar system (859-864). - -859. - -Force arises from dearth or abundance; it is the child of physical -motion, and the grand-child of spiritual motion, and the mother and -origin of gravity. Gravity is limited to the elements of water and -earth; but this force is unlimited, and by it infinite worlds might -be moved if instruments could be made by which the force could be -generated. - -Force, with physical motion, and gravity, with resistance are the -four external powers on which all actions of mortals depend. - -Force has its origin in spiritual motion; and this motion, flowing -through the limbs of sentient animals, enlarges their muscles. Being -enlarged by this current the muscles are shrunk in length and -contract the tendons which are connected with them, and this is the -cause of the force of the limbs in man. - -The quality and quantity of the force of a man are able to give -birth to other forces, which will be proportionally greater as the -motions produced by them last longer. - -[Footnote: Only part of this passage belongs, strictly speaking, to -this section. The principle laid down in the second paragraph is -more directly connected with the notes given in the preceding -section on Physiology.] - -860. - -Why does not the weight _o_ remain in its place? It does not remain -because it has no resistance. Where will it move to? It will move -towards the centre [of gravity]. And why by no other line? Because a -weight which has no support falls by the shortest road to the lowest -point which is the centre of the world. And why does the weight know -how to find it by so short a line? Because it is not independant and -does not move about in various directions. - -[Footnote: This text and the sketch belonging to it, are reproduced -on Pl. CXXI.] - -861. - -Let the earth turn on which side it may the surface of the waters -will never move from its spherical form, but will always remain -equidistant from the centre of the globe. - -Granting that the earth might be removed from the centre of the -globe, what would happen to the water? - -It would remain in a sphere round that centre equally thick, but the -sphere would have a smaller diameter than when it enclosed the -earth. - -[Footnote: Compare No. 896, lines 48-64; and No. 936.] - -862. - -Supposing the earth at our antipodes which supports the ocean were -to rise and stand uncovered, far out of the sea, but remaining -almost level, by what means afterwards, in the course of time, would -mountains and vallies be formed? - -And the rocks with their various strata? - -863. - -Each man is always in the middle of the surface of the earth and -under the zenith of his own hemisphere, and over the centre of the -earth. - -864. - -Mem.: That I must first show the distance of the sun from the earth; -and, by means of a ray passing through a small hole into a dark -chamber, detect its real size; and besides this, by means of the -aqueous sphere calculate the size of the globe ... - -Here it will be shown, that when the sun is in the meridian of our -hemisphere [Footnote 10: _Antipodi orientali cogli occidentali_. The -word _Antipodes_ does not here bear its literal sense, but--as we -may infer from the simultaneous reference to inhabitants of the -North and South-- is used as meaning men living at a distance of 90 -degrees from the zenith of the rational horizon of each observer.], -the antipodes to the East and to the West, alike, and at the same -time, see the sun mirrored in their waters; and the same is equally -true of the arctic and antarctic poles, if indeed they are -inhabited. - -How to prove that the earth is a planet (865-867). - -865. - -That the earth is a star. - -866. - -In your discourse you must prove that the earth is a star much like -the moon, and the glory of our universe; and then you must treat of -the size of various stars, according to the authors. - -867. - -THE METHOD OF PROVING THAT THE EARTH IS A STAR. - -First describe the eye; then show how the twinkling of a star is -really in the eye and why one star should twinkle more than another, -and how the rays from the stars originate in the eye; and add, that -if the twinkling of the stars were really in the stars --as it seems -to be--that this twinkling appears to be an extension as great as -the diameter of the body of the star; therefore, the star being -larger than the earth, this motion effected in an instant would be a -rapid doubling of the size of the star. Then prove that the surface -of the air where it lies contiguous to fire, and the surface of the -fire where it ends are those into which the solar rays penetrate, -and transmit the images of the heavenly bodies, large when they -rise, and small, when they are on the meridian. Let _a_ be the earth -and _n d m_ the surface of the air in contact with the sphere of -fire; _h f g_ is the orbit of the moon or, if you please, of the -sun; then I say that when the sun appears on the horizon _g_, its -rays are seen passing through the surface of the air at a slanting -angle, that is _o m_; this is not the case at _d k_. And so it -passes through a greater mass of air; all of _e m_ is a denser -atmosphere. - -868. - -Beyond the sun and us there is darkness and so the air appears blue. - -[Footnote: Compare Vol. I, No. 301.] - -869. - -PERSPECTIVE. - -It is possible to find means by which the eye shall not see remote -objects as much diminished as in natural perspective, which -diminishes them by reason of the convexity of the eye which -necessarily intersects, at its surface, the pyramid of every image -conveyed to the eye at a right angle on its spherical surface. But -by the method I here teach in the margin [9] these pyramids are -intersected at right angles close to the surface of the pupil. The -convex pupil of the eye can take in the whole of our hemisphere, -while this will show only a single star; but where many small stars -transmit their images to the surface of the pupil those stars are -extremely small; here only one star is seen but it will be large. -And so the moon will be seen larger and its spots of a more defined -form [Footnote 20 and fol.: Telescopes were not in use till a century -later. Compare No. 910 and page 136.]. You must place close to the -eye a glass filled with the water of which mention is made in number -4 of Book 113 "On natural substances" [Footnote 23: _libro_ 113. -This is perhaps the number of a book in some library catalogue. But -it may refer, on the other hand, to one of the 120 Books mentioned -in No. 796. l. 84.]; for this water makes objects which are enclosed -in balls of crystalline glass appear free from the glass. - -OF THE EYE. - -Among the smaller objects presented to the pupil of the eye, that -which is closest to it, will be least appreciable to the eye. And at -the same time, the experiments here made with the power of sight, -show that it is not reduced to speck if the &c. [32][Footnote 32: -Compare with this the passage in Vol. I, No. 52, written about -twenty years earlier.]. - -Read in the margin. - -[34]Those objects are seen largest which come to the eye at the -largest angles. - -But the images of the objects conveyed to the pupil of the eye are -distributed to the pupil exactly as they are distributed in the air: -and the proof of this is in what follows; that when we look at the -starry sky, without gazing more fixedly at one star than another, -the sky appears all strewn with stars; and their proportions to the -eye are the same as in the sky and likewise the spaces between them -[61]. - -[Footnote: 9. 32. _in margine:_ lines 34-61 are, in the original, -written on the margin and above them is the diagram to which -Leonardo seems to refer here.] - -870. - -PERSPECTIVE. - -Among objects moved from the eye at equal distance, that undergoes -least diminution which at first was most remote. - -When various objects are removed at equal distances farther from -their original position, that which was at first the farthest from -the eye will diminish least. And the proportion of the diminution -will be in proportion to the relative distance of the objects from -the eye before they were removed. - -That is to say in the object _t_ and the object _e_ the proportion -of their distances from the eye _a_ is quintuple. I remove each from -its place and set it farther from the eye by one of the 5 parts into -which the proposition is divided. Hence it happens that the nearest -to the eye has doubled the distance and according to the last -proposition but one of this, is diminished by the half of its whole -size; and the body _e_, by the same motion, is diminished 1/5 of its -whole size. Therefore, by that same last proposition but one, that -which is said in this last proposition is true; and this I say of -the motions of the celestial bodies which are more distant by 3500 -miles when setting than when overhead, and yet do not increase or -diminish in any sensible degree. - -871. - -_a b_ is the aperture through which the sun passes, and if you could -measure the size of the solar rays at _n m_, you could accurately -trace the real lines of the convergence of the solar rays, the -mirror being at _a b_, and then show the reflected rays at equal -angles to _n m_; but, as you want to have them at _n m_, take them -at the. inner side of the aperture at cd, where they maybe measured -at the spot where the solar rays fall. Then place your mirror at the -distance _a b_, making the rays _d b_, _c a_ fall and then be -reflected at equal angles towards _c d_; and this is the best -method, but you must use this mirror always in the same month, and -the same day, and hour and instant, and this will be better than at -no fixed time because when the sun is at a certain distance it -produces a certain pyramid of rays. - -872. - -_a_, the side of the body in light and shade _b_, faces the whole -portion of the hemisphere bed _e f_, and does not face any part of -the darkness of the earth. And the same occurs at the point _o_; -therefore the space a _o_ is throughout of one and the same -brightness, and s faces only four degrees of the hemisphere _d e f g -h_, and also the whole of the earth _s h_, which will render it -darker; and how much must be demonstrated by calculation. [Footnote: -This passage, which has perhaps a doubtful right to its place in -this connection, stands in the Manuscript between those given in -Vol. I as No. 117 and No. 427.] - -873. - -THE REASON OF THE INCREASED SIZE OF THE SUN IN THE WEST. - -Some mathematicians explain that the sun looks larger as it sets, -because the eye always sees it through a denser atmosphere, alleging -that objects seen through mist or through water appear larger. To -these I reply: No; because objects seen through a mist are similar -in colour to those at a distance; but not being similarly diminished -they appear larger. Again, nothing increases in size in smooth -water; and the proof of this may be seen by throwing a light on a -board placed half under water. But the reason why the sun looks -larger is that every luminous body appears larger in proportion as -it is more remote. [Footnote: Lines 5 and 6 are thus rendered by M. -RAVAISSON in his edition of MS. A. "_De meme, aucune chose ne croit -dans l'eau plane, et tu en feras l'experience_ en calquant un ais -sous l'eau."--Compare the diagrams in Vol. I, p. 114.] - -On the luminosity of the Earth in the universal space (874-878). - -874. - -In my book I propose to show, how the ocean and the other seas must, -by means of the sun, make our world shine with the appearance of a -moon, and to the remoter worlds it looks like a star; and this I -shall prove. - -Show, first that every light at a distance from the eye throws out -rays which appear to increase the size of the luminous body; and -from this it follows that 2 ...[Footnote 10: Here the text breaks -off; lines 11 and fol. are written in the margin.]. - -[11]The moon is cold and moist. Water is cold and moist. Thus our -seas must appear to the moon as the moon does to us. - -875. - -The waves in water magnify the image of an object reflected in it. - -Let _a_ be the sun, and _n m_ the ruffled water, _b_ the image of -the sun when the water is smooth. Let _f_ be the eye which sees the -image in all the waves included within the base of the triangle _c e -f_. Now the sun reflected in the unruffled surface occupied the -space _c d_, while in the ruffled surface it covers all the watery -space _c e_ (as is proved in the 4th of my "Perspective") [Footnote -9: _Nel quarto della mia prospettiva_. If this reference is to the -diagrams accompanying the text--as is usual with Leonardo--and not -to some particular work, the largest of the diagrams here given must -be meant. It is the lowest and actually the fifth, but he would have -called it the fourth, for the text here given is preceded on the -same page of the manuscript by a passage on whirlpools, with the -diagram belonging to it also reproduced here. The words _della mia -prospettiva_ may therefore indicate that the diagram to the -preceding chapter treating on a heterogeneal subject is to be -excluded. It is a further difficulty that this diagram belongs -properly to lines 9-10 and not to the preceding sentence. The -reflection of the sun in water is also discussed in the Theoretical -part of the Book on Painting; see Vol. I, No. 206, 207.] and it will -cover more of the water in proportion as the reflected image is -remote from the eye [10]. - -[Footnote: In the original sketch, inside the circle in the first -diagram, is written _Sole_ (sun), and to the right of it _luna_ -(moon). Thus either of these heavenly bodies may be supposed to fill -that space. Within the lower circle is written _simulacro_ (image). -In the two next diagrams at the spot here marked _L_ the word _Luna_ -is written, and in the last _sole_ is written in the top circle at -_a_.] - -The image of the sun will be more brightly shown in small waves than -in large ones--and this is because the reflections or images of the -sun are more numerous in the small waves than in large ones, and the -more numerous reflections of its radiance give a larger light than -the fewer. - -Waves which intersect like the scales of a fir cone reflect the -image of the sun with the greatest splendour; and this is the case -because the images are as many as the ridges of the waves on which -the sun shines, and the shadows between these waves are small and -not very dark; and the radiance of so many reflections together -becomes united in the image which is transmitted to the eye, so that -these shadows are imperceptible. - -That reflection of the sun will cover most space on the surface of -the water which is most remote from the eye which sees it. - -Let _a_ be the sun, _p q_ the reflection of the sun; _a b_ is the -surface of the water, in which the sun is mirrored, and _r_ the eye -which sees this reflection on the surface of the water occupying the -space _o m_. _c_ is the eye at a greater distance from the surface -of the water and also from the reflection; hence this reflection -covers a larger space of water, by the distance between _n_ and _o_. - -876. - -It is impossible that the side of a spherical mirror, illuminated by -the sun, should reflect its radiance unless this mirror were -undulating or filled with bubbles. - -You see here the sun which lights up the moon, a spherical mirror, -and all of its surface, which faces the sun is rendered radiant. - -Whence it may be concluded that what shines in the moon is water -like that of our seas, and in waves as that is; and that portion -which does not shine consists of islands and terra firma. - -This diagram, of several spherical bodies interposed between the eye -and the sun, is given to show that, just as the reflection of the -sun is seen in each of these bodies, in the same way that image may -be seen in each curve of the waves of the sea; and as in these many -spheres many reflections of the sun are seen, so in many waves there -are many images, each of which at a great distance is much magnified -to the eye. And, as this happens with each wave, the spaces -interposed between the waves are concealed; and, for this reason, it -looks as though the many suns mirrored in the many waves were but -one continuous sun; and the shadows,, mixed up with the luminous -images, render this radiance less brilliant than that of the sun -mirrored in these waves. - -[Footnote: In the original, at letter _A_ in the diagram "_Sole_" -(the sun) is written, and at _o_ "_occhio_" (the eye).] - -877. - -This will have before it the treatise on light and shade. - -The edges in the moon will be most strongly lighted and reflect most -light, because, there, nothing will be visible but the tops of the -waves of the water [Footnote 5: I have thought it unnecessary to -reproduce the detailed explanation of the theory of reflection on -waves contained in the passage which follows this.]. - -878. - -The sun will appear larger in moving water or on waves than in still -water; an example is the light reflected on the strings of a -monochord. - -II. - -THE SUN. - -The question of the true and of the apparent size of the sun -(879-884). - -879. - -IN PRAISE OF THE SUN. - -If you look at the stars, cutting off the rays (as may be done by -looking through a very small hole made with the extreme point of a -very fine needle, placed so as almost to touch the eye), you will -see those stars so minute that it would seem as though nothing could -be smaller; it is in fact their great distance which is the reason -of their diminution, for many of them are very many times larger -than the star which is the earth with water. Now reflect what this -our star must look like at such a distance, and then consider how -many stars might be added--both in longitude and latitude--between -those stars which are scattered over the darkened sky. But I cannot -forbear to condemn many of the ancients, who said that the sun was -no larger than it appears; among these was Epicurus, and I believe -that he founded his reason on the effects of a light placed in our -atmosphere equidistant from the centre of the earth. Any one looking -at it never sees it diminished in size at whatever distance; and the -rea- - -[Footnote 879-882: What Leonardo says of Epicurus-- who according to -LEWIS, _The Astronomy of the ancients_, and MADLER, _Geschichte der -Himmelskunde_, did not devote much attention to the study of -celestial phenomena--, he probably derived from Book X of Diogenes -Laertius, whose _Vitae Philosophorum_ was not printed in Greek till -1533, but the Latin translation appeared in 1475.] - -880. - -sons of its size and power I shall reserve for Book 4. But I wonder -greatly that Socrates - -[Footnote 2: _Socrates;_ I have little light to throw on this -reference. Plato's Socrates himself declares on more than one -occasion that in his youth he had turned his mind to the study of -celestial phenomena (METEWPA) but not in his later years (see G. C. -LEWIS, _The Astronomy of the ancients_, page 109; MADLER, -_Geschichte der Himmelskunde_, page 41). Here and there in Plato's -writings we find incidental notes on the sun and other heavenly -bodies. Leonardo may very well have known of these, since the Latin -version by Ficinus was printed as early as 1491; indeed an undated -edition exists which may very likely have appeared between 1480--90. - -There is but one passage in Plato, Epinomis (p. 983) where he speaks -of the physical properties of the sun and says that it is larger -than the earth. - -Aristotle who goes very fully into the subject says the same. A -complete edition of Aristotele's works was first printed in Venice -1495-98, but a Latin version of the Books _De Coelo et Mundo_ and -_De Physica_ had been printed in Venice as early as in 1483 (H. -MULLER-STRUBING).] - -should have depreciated that solar body, saying that it was of the -nature of incandescent stone, and the one who opposed him as to that -error was not far wrong. But I only wish I had words to serve me to -blame those who are fain to extol the worship of men more than that -of the sun; for in the whole universe there is nowhere to be seen a -body of greater magnitude and power than the sun. Its light gives -light to all the celestial bodies which are distributed throughout -the universe; and from it descends all vital force, for the heat -that is in living beings comes from the soul [vital spark]; and -there is no other centre of heat and light in the universe as will -be shown in Book 4; and certainly those who have chosen to worship -men as gods--as Jove, Saturn, Mars and the like--have fallen into -the gravest error, seeing that even if a man were as large as our -earth, he would look no bigger than a little star which appears but -as a speck in the universe; and seeing again that these men are -mortal, and putrid and corrupt in their sepulchres. - -Marcellus [Footnote 23: I have no means of identifying _Marcello_ -who is named in the margin. It may be Nonius Marcellus, an obscure -Roman Grammarian of uncertain date (between the IInd and Vth -centuries A. C.) the author of the treatise _De compendiosa doctrina -per litteras ad filium_ in which he treats _de rebus omnibus et -quibusdam aliis_. This was much read in the middle ages. The _editto -princeps_ is dated 1470 (H. MULLER-STRUBING).] and many others -praise the sun. - -881. - -Epicurus perhaps saw the shadows cast by columns on the walls in -front of them equal in diameter to the columns from which the -shadows were cast; and the breadth of the shadows being parallel -from beginning to end, he thought he might infer that the sun also -was directly opposite to this parallel and that consequently its -breadth was not greater than that of the column; not perceiving that -the diminution in the shadow was insensibly slight by reason of the -remoteness of the sun. If the sun were smaller than the earth, the -stars on a great portion of our hemisphere would have no light, -which is evidence against Epicurus who says the sun is only as large -as it appears. - -[Footnote: In the original the writing is across the diagram.] - -882. - -Epicurus says the sun is the size it looks. Hence as it looks about -a foot across we must consider that to be its size; it would follow -that when the moon eclipses the sun, the sun ought not to appear the -larger, as it does. Then, the moon being smaller than the sun, the -moon must be less than a foot, and consequently when our world -eclipses the moon, it must be less than a foot by a finger's -breadth; inasmuch as if the sun is a foot across, and our earth -casts a conical shadow on the moon, it is inevitable that the -luminous cause of the cone of shadow must be larger than the opaque -body which casts the cone of shadow. - -883. - -To measure how many times the diameter of the sun will go into its -course in 24 hours. - -Make a circle and place it to face the south, after the manner of a -sundial, and place a rod in the middle in such a way as that its -length points to the centre of this circle, and mark the shadow cast -in the sunshine by this rod on the circumference of the circle, and -this shadow will be--let us say-- as broad as from _a_ to _n_. Now -measure how many times this shadow will go into this circumference -of a circle, and that will give you the number of times that the -solar body will go into its orbit in 24 hours. Thus you may see -whether Epicurus was [right in] saying that the sun was only as -large as it looked; for, as the apparent diameter of the sun is -about a foot, and as that sun would go a thousand times into the -length of its course in 24 hours, it would have gone a thousand -feet, that is 300 braccia, which is the sixth of a mile. Whence it -would follow that the course of the sun during the day would be the -sixth part of a mile and that this venerable snail, the sun will -have travelled 25 braccia an hour. - -884. - -Posidonius composed books on the size of the sun. [Footnote: -Poseidonius of Apamea, commonly called the Rhodian, because he -taught in Rhodes, was a Stoic philosopher, a contemporary and friend -of Cicero's, and the author of numerous works on natural science, -among them. - -Strabo quotes no doubt from one of his works, when he says that -Poseidonius explained how it was that the sun looked larger when it -was rising or setting than during the rest of its course (III, p. -135). Kleomedes, a later Greek Naturalist also mentions this -observation of Poseidonius' without naming the title of his work; -however, as Kleomedes' Cyclia Theorica was not printed till 1535, -Leonardo must have derived his quotation from Strabo. He probably -wrote this note in 1508, and as the original Greek was first printed -in Venice in 1516, we must suppose him to quote here from the -translation by Guarinus Veronensis, which was printed as early as -1471, also at Venice (H. MULLER-STRUBING).] - -Of the nature of Sunlight. - -885. - -OF THE PROOF THAT THE SUN IS HOT BY NATURE AND NOT BY VIRTUE. - -Of the nature of Sunlight. - -That the heat of the sun resides in its nature and not in its virtue -[or mode of action] is abundantly proved by the radiance of the -solar body on which the human eye cannot dwell and besides this no -less manifestly by the rays reflected from a concave mirror, -which--when they strike the eye with such splendour that the eye -cannot bear them--have a brilliancy equal to the sun in its own -place. And that this is true I prove by the fact that if the mirror -has its concavity formed exactly as is requisite for the collecting -and reflecting of these rays, no created being could endure the -heat that strikes from the reflected rays of such a mirror. And if -you argue that the mirror itself is cold and yet send forth hot -rays, I should reply that those rays come really from the sun and -that it is the ray of the concave mirror after having passed through -the window. - -Considerations as to the size of the sun (886-891). - -886. - -The sun does not move. [Footnote: This sentence occurs incidentally -among mathematical notes, and is written in unusually large -letters.] - -887. - -PROOF THAT THE NEARER YOU ARE TO THE SOURCE OF THE SOLAR RAYS, THE -LARGER WILL THE REFLECTION OF THE SUN FROM THE SEA APPEAR TO YOU. - -[Footnote: Lines 4 and fol. Compare Vol. I, Nos. 130, 131.] If it is -from the centre that the sun employs its radiance to intensify the -power of its whole mass, it is evident that the farther its rays -extend, the more widely they will be divided; and this being so, -you, whose eye is near the water that mirrors the sun, see but a -small portion of the rays of the sun strike the surface of the -water, and reflecting the form of the sun. But if you were near to -the sun--as would be the case when the sun is on the meridian and -the sea to the westward--you would see the sun, mirrored in the sea, -of a very great size; because, as you are nearer to the sun, your -eye taking in the rays nearer to the point of radiation takes more -of them in, and a great splendour is the result. And in this way it -can be proved that the moon must have seas which reflect the sun, -and that the parts which do not shine are land. - -888. - -Take the measure of the sun at the solstice in mid-June. - -889. - -WHY THE SUN APPEARS LARGER WHEN SETTING THAN AT NOON, WHEN IT IS -NEAR TO US. - -Every object seen through a curved medium seems to be of larger size -than it is. - -[Footnote: At A is written _sole_ (the sun), at B _terra_ (the -earth).] - -890. - -Because the eye is small it can only see the image of the sun as of -a small size. If the eye were as large as the sun it would see the -image of the sun in water of the same size as the real body of the -sun, so long as the water is smooth. - -891. - -A METHOD OF SEEING THE SUN ECLIPSED WITHOUT PAIN TO THE EYE. - -Take a piece of paper and pierce holes in it with a needle, and look -at the sun through these holes. - -III. - -THE MOON. - -On the luminousity of the moon (892-901). - -892. - -OF THE MOON. - -As I propose to treat of the nature of the moon, it is necessary -that first I should describe the perspective of mirrors, whether -plane, concave or convex; and first what is meant by a luminous ray, -and how it is refracted by various kinds of media; then, when a -reflected ray is most powerful, whether when the angle of incidence -is acute, right, or obtuse, or from a convex, a plane, or a concave -surface; or from an opaque or a transparent body. Besides this, how -it is that the solar rays which fall on the waves of the sea, are -seen by the eye of the same width at the angle nearest to the eye, -as at the highest line of the waves on the horizon; but -notwithstanding this the solar rays reflected from the waves of the -sea assume the pyramidal form and consequently, at each degree of -distance increase proportionally in size, although to our sight, -they appear as parallel. - -1st. Nothing that has very little weight is opaque. - -2dly. Nothing that is excessively weighty can remain beneath that -which is heavier. - -3dly. As to whether the moon is situated in the centre of its -elements or not. - -And, if it has no proper place of its own, like the earth, in the -midst of its elements, why does it not fall to the centre of our -elements? [Footnote 26: The problem here propounded by Leonardo was -not satisfactorily answered till Newton in 1682 formulated the law -of universal attraction and gravitation. Compare No. 902, lines -5-15.] - -And, if the moon is not in the centre of its own elements and yet -does not fall, it must then be lighter than any other element. - -And, if the moon is lighter than the other elements why is it opaque -and not transparent? - -When objects of various sizes, being placed at various distances, -look of equal size, there must be the same relative proportion in -the distances as in the magnitudes of the objects. - -[Footnote: In the diagram Leonardo wrote _sole_ at the place marked -_A_.] - -893. - -OF THE MOON AND WHETHER IT IS POLISHED AND SPHERICAL. - -The image of the sun in the moon is powerfully luminous, and is only -on a small portion of its surface. And the proof may be seen by -taking a ball of burnished gold and placing it in the dark with a -light at some distance from it; and then, although it will -illuminate about half of the ball, the eye will perceive its -reflection only in a small part of its surface, and all the rest of -the surface reflects the darkness which surrounds it; so that it is -only in that spot that the image of the light is seen, and all the -rest remains invisible, the eye being at a distance from the ball. -The same thing would happen on the surface of the moon if it were -polished, lustrous and opaque, like all bodies with a reflecting -surface. - -Show how, if you were standing on the moon or on a star, our earth -would seem to reflect the sun as the moon does. - -And show that the image of the sun in the sea cannot appear one and -undivided, as it appears in a perfectly plane mirror. - -894. - -How shadows are lost at great distances, as is shown by the shadow -side of the moon which is never seen. [Footnote: Compare also Vol. -I, Nos. 175-179.] - -895. - -Either the moon has intrinsic luminosity or not. If it has, why does -it not shine without the aid of the sun? But if it has not any light -in itself it must of necessity be a spherical mirror; and if it is a -mirror, is it not proved in Perspective that the image of a luminous -object will never be equal to the extent of surface of the -reflecting body that it illuminates? And if it be thus [Footnote 13: -At A, in the diagram, Leonardo wrote "_sole_" (the sun), and at B -"_luna o noi terra_" (the moon or our earth). Compare also the text -of No. 876.], as is here shown at _r s_ in the figure, whence comes -so great an extent of radiance as that of the full moon as we see -it, at the fifteenth day of the moon? - -896. - -OF THE MOON. - -The moon has no light in itself; but so much of it as faces the sun -is illuminated, and of that illumined portion we see so much as -faces the earth. And the moon's night receives just as much light as -is lent it by our waters as they reflect the image of the sun, which -is mirrored in all those waters which are on the side towards the -sun. The outside or surface of the waters forming the seas of the -moon and of the seas of our globe is always ruffled little or much, -or more or less--and this roughness causes an extension of the -numberless images of the sun which are repeated in the ridges and -hollows, the sides and fronts of the innumerable waves; that is to -say in as many different spots on each wave as our eyes find -different positions to view them from. This could not happen, if the -aqueous sphere which covers a great part of the moon were uniformly -spherical, for then the images of the sun would be one to each -spectator, and its reflections would be separate and independent and -its radiance would always appear circular; as is plainly to be seen -in the gilt balls placed on the tops of high buildings. But if those -gilt balls were rugged or composed of several little balls, like -mulberries, which are a black fruit composed of minute round -globules, then each portion of these little balls, when seen in the -sun, would display to the eye the lustre resulting from the -reflection of the sun, and thus, in one and the same body many tiny -suns would be seen; and these often combine at a long distance and -appear as one. The lustre of the new moon is brighter and stronger, -than when the moon is full; and the reason of this is that the angle -of incidence is more obtuse in the new than in the full moon, in -which the angles [of incidence and reflection] are highly acute. The -waves of the moon therefore mirror the sun in the hollows of the -waves as well as on the ridges, and the sides remain in shadow. But -at the sides of the moon the hollows of the waves do not catch the -sunlight, but only their crests; and thus the images are fewer and -more mixed up with the shadows in the hollows; and this -intermingling of the shaded and illuminated spots comes to the eye -with a mitigated splendour, so that the edges will be darker, -because the curves of the sides of the waves are insufficient to -reflect to the eye the rays that fall upon them. Now the new moon -naturally reflects the solar rays more directly towards the eye from -the crests of the waves than from any other part, as is shown by the -form of the moon, whose rays a strike the waves _b_ and are -reflected in the line _b d_, the eye being situated at _d_. This -cannot happen at the full moon, when the solar rays, being in the -west, fall on the extreme waters of the moon to the East from _n_ to -_m_, and are not reflected to the eye in the West, but are thrown -back eastwards, with but slight deflection from the straight course -of the solar ray; and thus the angle of incidence is very wide -indeed. - -The moon is an opaque and solid body and if, on the contrary, it -were transparent, it would not receive the light of the sun. - -The yellow or yolk of an egg remains in the middle of the albumen, -without moving on either side; now it is either lighter or heavier -than this albumen, or equal to it; if it is lighter, it ought to -rise above all the albumen and stop in contact with the shell of the -egg; and if it is heavier, it ought to sink, and if it is equal, it -might just as well be at one of the ends, as in the middle or below -[54]. - -[Footnote 48-64: Compare No. 861.] - -The innumerable images of the solar rays reflected from the -innumerable waves of the sea, as they fall upon those waves, are -what cause us to see the very broad and continuous radiance on the -surface of the sea. - -897. - -That the sun could not be mirrored in the body of the moon, which is -a convex mirror, in such a way as that so much of its surface as is -illuminated by the sun, should reflect the sun unless the moon had a -surface adapted to reflect it--in waves and ridges, like the surface -of the sea when its surface is moved by the wind. - -[Footnote: In the original diagrams _sole_ is written at the place -marked _A; luna_ at _C,_ and _terra_ at the two spots marked _B_.] - -The waves in water multiply the image of the object reflected in it. - -These waves reflect light, each by its own line, as the surface of -the fir cone does [Footnote 14: See the diagram p. 145.] - -These are 2 figures one different from the other; one with -undulating water and the other with smooth water. - -It is impossible that at any distance the image of the sun cast on -the surface of a spherical body should occupy the half of the -sphere. - -Here you must prove that the earth produces all the same effects -with regard to the moon, as the moon with regard to the earth. - -The moon, with its reflected light, does not shine like the sun, -because the light of the moon is not a continuous reflection of that -of the sun on its whole surface, but only on the crests and hollows -of the waves of its waters; and thus the sun being confusedly -reflected, from the admixture of the shadows that lie between the -lustrous waves, its light is not pure and clear as the sun is. - -[Footnote 38: This refers to the small diagram placed between _B_ -and _B_.--]. The earth between the moon on the fifteenth day and the -sun. [Footnote 39: See the diagram below the one referred to in the -preceding note.] Here the sun is in the East and the moon on the -fifteenth day in the West. [Footnote 40.41: Refers to the diagram -below the others.] The moon on the fifteenth [day] between the earth -and the sun. [41]Here it is the moon which has the sun to the West -and the earth to the East. - -898. - -WHAT SORT OF THING THE MOON IS. - -The moon is not of itself luminous, but is highly fitted to -assimilate the character of light after the manner of a mirror, or -of water, or of any other reflecting body; and it grows larger in -the East and in the West, like the sun and the other planets. And -the reason is that every luminous body looks larger in proportion as -it is remote. It is easy to understand that every planet and star is -farther from us when in the West than when it is overhead, by about -3500 miles, as is proved on the margin [Footnote 7: refers to the -first diagram.--A = _sole_ (the sun), B = _terra_ (the earth), C = -_luna_ (the moon).], and if you see the sun or moon mirrored in the -water near to you, it looks to you of the same size in the water as -in the sky. But if you recede to the distance of a mile, it will -look 100 times larger; and if you see the sun reflected in the sea -at sunset, its image would look to you more than 10 miles long; -because that reflected image extends over more than 10 miles of sea. -And if you could stand where the moon is, the sun would look to you, -as if it were reflected from all the sea that it illuminates by day; -and the land amid the water would appear just like the dark spots -that are on the moon, which, when looked at from our earth, appears -to men the same as our earth would appear to any men who might dwell -in the moon. - -[Footnote: This text has already been published by LIBRI: _Histoire -des Sciences,_ III, pp. 224, 225.] - -OF THE NATURE OF THE MOON. - -When the moon is entirely lighted up to our sight, we see its full -daylight; and at that time, owing to the reflection of the solar -rays which fall on it and are thrown off towards us, its ocean casts -off less moisture towards us; and the less light it gives the more -injurious it is. - -899. - -OF THE MOON. - -I say that as the moon has no light in itself and yet is luminous, -it is inevitable but that its light is caused by some other body. - -900. - -OF THE MOON. - -All my opponent's arguments to say that there is no water in the -moon. [Footnote: The objections are very minutely noted down in the -manuscript, but they hardly seem to have a place here.] - -901. - -Answer to Maestro Andrea da Imola, who said that the solar rays -reflected from a convex mirror are mingled and lost at a short -distance; whereby it is altogether denied that the luminous side of -the moon is of the nature of a mirror, and that consequently the -light is not produced by the innumerable multitude of the waves of -that sea, which I declared to be the portion of the moon which is -illuminated by the solar rays. - -Let _o p_ be the body of the sun, _c n s_ the moon, and _b_ the eye -which, above the base _c n_ of the cathetus _c n m_, sees the body -of the sun reflected at equal angles _c n_; and the same again on -moving the eye from _b_ to _a_. [Footnote: The large diagram on the -margin of page 161 belongs to this chapter.] - -Explanation of the lumen cinereum in the moon. - -902. - -OF THE MOON. - -No solid body is less heavy than the atmosphere. - -[Footnote: 1. On the margin are the words _tola romantina, -tola--ferro stagnato_ (tinned iron); _romantina_ is some special -kind of sheet-iron no longer known by that name.] - -Having proved that the part of the moon that shines consists of -water, which mirrors the body of the sun and reflects the radiance -it receives from it; and that, if these waters were devoid of waves, -it would appear small, but of a radiance almost like the sun; --[5] -It must now be shown whether the moon is a heavy or a light body: -for, if it were a heavy body--admitting that at every grade of -distance from the earth greater levity must prevail, so that water -is lighter than the earth, and air than water, and fire than air and -so on successively--it would seem that if the moon had density as it -really has, it would have weight, and having weight, that it could -not be sustained in the space where it is, and consequently that it -would fall towards the centre of the universe and become united to -the earth; or if not the moon itself, at least its waters would fall -away and be lost from it, and descend towards the centre, leaving -the moon without any and so devoid of lustre. But as this does not -happen, as might in reason be expected, it is a manifest sign that -the moon is surrounded by its own elements: that is to say water, -air and fire; and thus is, of itself and by itself, suspended in -that part of space, as our earth with its element is in this part of -space; and that heavy bodies act in the midst of its elements just -as other heavy bodies do in ours [Footnote 15: This passage would -certainly seem to establish Leonardo's claim to be regarded as the -original discoverer of the cause of the ashy colour of the new moon -(_lumen cinereum_). His observations however, having hitherto -remained unknown to astronomers, Moestlin and Kepler have been -credited with the discoveries which they made independently a -century later. - -Some disconnected notes treat of the same subject in MS. C. A. 239b; -718b and 719b; "_Perche la luna cinta della parte alluminata dal -sole in ponente, tra maggior splendore in mezzo a tal cerchio, che -quando essa eclissava il sole. Questo accade perche nell' eclissare -il sole ella ombrava il nostro oceano, il qual caso non accade -essendo in ponente, quando il sole alluma esso oceano_." The editors -of the "_Saggio_" who first published this passage (page 12) add -another short one about the seasons in the moon which I confess not -to have seen in the original manuscript: "_La luna ha ogni mese un -verno e una state, e ha maggiori freddi e maggiori caldi, e i suoi -equinozii son piu freddi de' nostri._"] - -When the eye is in the East and sees the moon in the West near to -the setting sun, it sees it with its shaded portion surrounded by -luminous portions; and the lateral and upper portion of this light -is derived from the sun, and the lower portion from the ocean in the -West, which receives the solar rays and reflects them on the lower -waters of the moon, and indeed affords the part of the moon that is -in shadow as much radiance as the moon gives the earth at midnight. -Therefore it is not totally dark, and hence some have believed that -the moon must in parts have a light of its own besides that which is -given it by the sun; and this light is due, as has been said, to the -above- mentioned cause,--that our seas are illuminated by the sun. - -Again, it might be said that the circle of radiance shown by the -moon when it and the sun are both in the West is wholly borrowed -from the sun, when it, and the sun, and the eye are situated as is -shown above. - -[Footnote 23. 24: The larger of the two diagrams reproduced above -stands between these two lines, and the smaller one is sketched in -the margin. At the spot marked _A_ Leonardo wrote _corpo solare_ -(solar body) in the larger diagram and _Sole_ (sun) in the smaller -one. At _C luna_ (moon) is written and at _B terra_ (the earth).] - -Some might say that the air surrounding the moon as an element, -catches the light of the sun as our atmosphere does, and that it is -this which completes the luminous circle on the body of the moon. - -Some have thought that the moon has a light of its own, but this -opinion is false, because they have founded it on that dim light -seen between the hornes of the new moon, which looks dark where it -is close to the bright part, while against the darkness of the -background it looks so light that many have taken it to be a ring of -new radiance completing the circle where the tips of the horns -illuminated by the sun cease to shine [Footnote 34: See Pl. CVIII, -No. 5.]. And this difference of background arises from the fact that -the portion of that background which is conterminous with the bright -part of the moon, by comparison with that brightness looks darker -than it is; while at the upper part, where a portion of the luminous -circle is to be seen of uniform width, the result is that the moon, -being brighter there than the medium or background on which it is -seen by comparison with that darkness it looks more luminous at that -edge than it is. And that brightness at such a time itself is -derived from our ocean and other inland-seas. These are, at that -time, illuminated by the sun which is already setting in such a way -as that the sea then fulfils the same function to the dark side of -the moon as the moon at its fifteenth day does to us when the sun is -set. And the small amount of light which the dark side of the moon -receives bears the same proportion to the light of that side which -is illuminated, as that... [Footnote 42: Here the text breaks off; -lines 43-52 are written on the margin.]. - -If you want to see how much brighter the shaded portion of the moon -is than the background on which it is seen, conceal the luminous -portion of the moon with your hand or with some other more distant -object. - -On the spots in the moon (903-907). - -903. - -THE SPOTS ON THE MOON. - -Some have said that vapours rise from the moon, after the manner of -clouds and are interposed between the moon and our eyes. But, if -this were the case, these spots would never be permanent, either as -to position or form; and, seeing the moon from various aspects, even -if these spots did not move they would change in form, as objects do -which are seen from different sides. - -904. - -OF THE SPOTS ON THE MOON. - -Others say that the moon is composed of more or less transparent -parts; as though one part were something like alabaster and others -like crystal or glass. It would follow from this that the sun -casting its rays on the less transparent portions, the light would -remain on the surface, and so the denser part would be illuminated, -and the transparent portions would display the shadow of their -darker depths; and this is their account of the structure and nature -of the moon. And this opinion has found favour with many -philosophers, and particularly with Aristotle, and yet it is a false -view--for, in the various phases and frequent changes of the moon -and sun to our eyes, we should see these spots vary, at one time -looking dark and at another light: they would be dark when the sun -is in the West and the moon in the middle of the sky; for then the -transparent hollows would be in shadow as far as the tops of the -edges of those transparent hollows, because the sun could not then -fling his rays into the mouth of the hollows, which however, at full -moon, would be seen in bright light, at which time the moon is in -the East and faces the sun in the West; then the sun would -illuminate even the lowest depths of these transparent places and -thus, as there would be no shadows cast, the moon at these times -would not show us the spots in question; and so it would be, now -more and now less, according to the changes in the position of the -sun to the moon, and of the moon to our eyes, as I have said above. - -905. - -OF THE SPOTS ON THE MOON. - -It has been asserted, that the spots on the moon result from the -moon being of varying thinness or density; but if this were so, when -there is an eclipse of the moon the solar rays would pierce through -the portions which were thin as is alleged [Footnote 3-5: _Eclissi_. -This word, as it seems to me, here means eclipses of the sun; and -the sense of the passage, as I understand it, is that by the -foregoing hypothesis the moon, when it comes between the sun and the -earth must appear as if pierced,--we may say like a sieve.]. But as -we do not see this effect the opinion must be false. - -Others say that the surface of the moon is smooth and polished and -that, like a mirror, it reflects in itself the image of our earth. -This view is also false, inasmuch as the land, where it is not -covered with water, presents various aspects and forms. Hence when -the moon is in the East it would reflect different spots from those -it would show when it is above us or in the West; now the spots on -the moon, as they are seen at full moon, never vary in the course of -its motion over our hemisphere. A second reason is that an object -reflected in a convex body takes up but a small portion of that -body, as is proved in perspective [Footnote 18: _come e provato_. -This alludes to the accompanying diagram.]. The third reason is that -when the moon is full, it only faces half the hemisphere of the -illuminated earth, on which only the ocean and other waters reflect -bright light, while the land makes spots on that brightness; thus -half of our earth would be seen girt round with the brightness of -the sea lighted up by the sun, and in the moon this reflection would -be the smallest part of that moon. Fourthly, a radiant body cannot -be reflected from another equally radiant; therefore the sea, since -it borrows its brightness from the sun,--as the moon does--, could -not cause the earth to be reflected in it, nor indeed could the body -of the sun be seen reflected in it, nor indeed any star opposite to -it. - -906. - -If you keep the details of the spots of the moon under observation -you will often find great variation in them, and this I myself have -proved by drawing them. And this is caused by the clouds that rise -from the waters in the moon, which come between the sun and those -waters, and by their shadow deprive these waters of the sun's rays. -Thus those waters remain dark, not being able to reflect the solar -body. - -907. - -How the spots on the moon must have varied from what they formerly -were, by reason of the course of its waters. - -On the moon's halo. - -908. - -OF HALOS ROUND THE MOON. - -I have found, that the circles which at night seem to surround the -moon, of various sizes, and degrees of density are caused by various -gradations in the densities of the vapours which exist at different -altitudes between the moon and our eyes. And of these halos the -largest and least red is caused by the lowest of these vapours; the -second, smaller one, is higher up, and looks redder because it is -seen through two vapours. And so on, as they are higher they will -appear smaller and redder, because, between the eye and them, there -is thicker vapour. Whence it is proved that where they are seen to -be reddest, the vapours are most dense. - -On instruments for observing the moon (909. 910). - -909. - -If you want to prove why the moon appears larger than it is, when it -reaches the horizon; take a lens which is highly convex on one -surface and concave on the opposite, and place the concave side next -the eye, and look at the object beyond the convex surface; by this -means you will have produced an exact imitation of the atmosphere -included beneath the sphere of fire and outside that of water; for -this atmosphere is concave on the side next the earth, and convex -towards the fire. - -910. - -Construct glasses to see the moon magnified. - -[Footnote: See the Introduction, p. 136, Fracastoro says in his work -Homocentres: "_Per dua specilla ocularla si quis perspiciat, alteri -altero superposito, majora multo et propinquiora videbit -omnia.--Quin imo quaedam specilla ocularia fiunt tantae densitatis, -ut si per ea quis aut lunam, aut aliud siderum spectet, adeo -propinqua illa iudicet, ut ne turres ipsas excedant_" (sect. II c. 8 -and sect. III, c. 23).] - -I. -THE STARS. -On the light of the stars (911-913). -911. -The stars are visible by night and not by day, because we are -eneath the dense atmosphere, which is full of innumerable -articles of moisture, each of which independently, when the -ays of the sun fall upon it, reflects a radiance, and so these -umberless bright particles conceal the stars; and if it were not -or this atmosphere the sky would always display the stars against -ts darkness. -[Footnote: See No. 296, which also refers to starlight.] -912. -Whether the stars have their light from the sun or in themselves. -Some say that they shine of themselves, alledging that if Venus -nd Mercury had not a light of their own, when they come between -ur eye and the sun they would darken so much of the sun as they -ould cover from our eye. But this is false, for it is proved that - dark object against a luminous body is enveloped and entirely -oncealed by the lateral rays of the rest of that luminous body -nd so remains invisible. As may be seen when the sun is seen -hrough the boughs of trees bare of their leaves, at some distance -he branches do not conceal any portion of the sun from our eye. -he same thing happens with the above mentioned planets which, -hough they have no light of their own, do not--as has been said-- -onceal any part of the sun from our eye -[18]. - -SECOND ARGUMENT. - -Some say that the stars appear most brilliant at night in proportion -as they are higher up; and that if they had no light of their own, -the shadow of the earth which comes between them and the sun, would -darken them, since they would not face nor be faced by the solar -body. But those persons have not considered that the conical shadow -of the earth cannot reach many of the stars; and even as to those it -does reach, the cone is so much diminished that it covers very -little of the star's mass, and all the rest is illuminated by the -sun. - -Footnote: From this and other remarks (see No. 902) it is clear -hat Leonardo was familiar with the phenomena of Irradiation.] - -13. - -Why the planets appear larger in the East than they do overhead, -whereas the contrary should be the case, as they are 3500 miles -nearer to us when in mid sky than when on the horizon. - -All the degrees of the elements, through which the images of the -celestial bodies pass to reach the eye, are equal curves and the -angles by which the central line of those images passes through -them, are unequal angles [Footnote 13: _inequali_, here and -elsewhere does not mean unequal in the sense of not being equal to -each other, but angles which are not right angles.]; and the -distance is greater, as is shown by the excess of _a b_ beyond _a -d_; and the enlargement of these celestial bodies on the horizon is -shown by the 9th of the 7th. - -Observations on the stars. - -914. - -To see the real nature of the planets open the covering and note at -the base [Footnote 4: _basa_. This probably alludes to some -instrument, perhaps the Camera obscura.] one single planet, and the -reflected movement of this base will show the nature of the said -planet; but arrange that the base may face only one at the time. - -On history of astronomy. - -915. - -Cicero says in [his book] De Divinatione that Astrology has been -practised five hundred seventy thousand years before the Trojan war. - -57000. - -[Footnote: The statement that CICERO, _De Divin._ ascribes the -discovery of astrology to a period 57000 years before the Trojan war -I believe to be quite erroneous. According to ERNESTI, _Clavis -Ciceroniana,_ CH. G. SCHULZ (_Lexic. Cicer._) and the edition of _De -Divin._ by GIESE the word Astrologia occurs only twice in CICERO: -_De Divin. II_, 42. _Ad Chaldaeorum monstra veniamus, de quibus -Eudoxus, Platonis auditor, in astrologia judicio doctissimorum -hominum facile princeps, sic opinatur (id quod scriptum reliquit): -Chaldaeis in praedictione et in notatione cujusque vitae ex natali -die minime esse credendum._" He then quotes the condemnatory verdict -of other philosophers as to the teaching of the Chaldaeans but says -nothing as to the antiquity and origin of astronomy. CICERO further -notes _De oratore_ I, 16 that Aratus was "_ignarus astrologiae_" but -that is all. So far as I know the word occurs nowhere else in -CICERO; and the word _Astronomia_ he does not seem to have used at -all. (H. MULLER-STRUBING.)] - -Of time and its divisions (916-918). - -916. - -Although time is included in the class of Continuous Quantities, -being indivisible and immaterial, it does not come entirely under -the head of Geometry, which represents its divisions by means of -figures and bodies of infinite variety, such as are seen to be -continuous in their visible and material properties. But only with -its first principles does it agree, that is with the Point and the -Line; the point may be compared to an instant of time, and the line -may be likened to the length of a certain quantity of time, and just -as a line begins and terminates in a point, so such a space of time. -begins and terminates in an instant. And whereas a line is -infinitely divisible, the divisibility of a space of time is of the -same nature; and as the divisions of the line may bear a certain -proportion to each other, so may the divisions of time. - -[Footnote: This passage is repeated word for word on page 190b of -the same manuscript and this is accounted for by the text in Vol. I, -No. 4. Compare also No. 1216.] - -917. - -Describe the nature of Time as distinguished from the Geometrical -definitions. - -918. - -Divide an hour into 3000 parts, and this you can do with a clock by -making the pendulum lighter or heavier. - -_XVI. - -Physical Geography. - -Leonardo's researches as to the structure of the earth and sea were -made at a time, when the extended voyages of the Spaniards and -Portuguese had also excited a special interest in geographical -questions in Italy, and particularly in Tuscany. Still, it need -scarcely surprise us to find that in deeper questions, as to the -structure of the globe, the primitive state of the earth's surface, -and the like, he was far in advance of his time. - -The number of passages which treat of such matters is relatively -considerable; like almost all Leonardo's scientific notes they deal -partly with theoretical and partly with practical questions. Some of -his theoretical views of the motion of water were collected in a -copied manuscript volume by an early transcriber, but without any -acknowledgment of the source whence they were derived. This copy is -now in the Library of the Barberini palace at Rome and was published -under the title: "De moto e misura dell'acqua," by FRANCESCO -CARDINALI, Bologna_ 1828. _In this work the texts are arranged under -the following titles:_ Libr. I. Della spera dell'acqua; Libr. II. -Del moto dell'acqua; Libr. III. Dell'onda dell'acqua; Libr. IV. Dei -retrosi d'acqua; Libr. V. Dell'acqua cadente; Libr. VI. Delle -rotture fatte dall'acqua; Libr. VII Delle cose portate dall'acqua; -Libr. VIII. Dell'oncia dell'acqua e delle canne; Libr. IX. De molini -e d'altri ordigni d'acqua. - -_The large number of isolated observations scattered through the -manuscripts, accounts for our so frequently finding notes of new -schemes for the arrangement of those relating to water and its -motions, particularly in the Codex Atlanticus: I have printed -several of these plans as an introduction to the Physical Geography, -and I have actually arranged the texts in accordance with the clue -afforded by one of them which is undoubtedly one of the latest notes -referring to the subject (No._ 920_). The text given as No._ 930 -_which is also taken from a late note-book of Leonardo's, served as -a basis for the arrangement of the first of the seven books--or -sections--, bearing the title: Of the Nature of Water_ (Dell'acque -in se). - -_As I have not made it any part of this undertaking to print the -passages which refer to purely physical principles, it has also been -necessary to exclude those practical researches which, in accordance -with indications given in_ 920, _ought to come in as Books_ 13, 14 -_and_ 15. _I can only incidentally mention here that Leonardo--as it -seems to me, especially in his youth--devoted a great deal of -attention to the construction of mills. This is proved by a number -of drawings of very careful and minute execution, which are to be -found in the Codex Atlanticus. Nor was it possible to include his -considerations on the regulation of rivers, the making of canals and -so forth (No._ 920, _Books_ 10, 11 _and_ 12_); but those passages in -which the structure of a canal is directly connected with notices of -particular places will be found duly inserted under section XVII -(Topographical notes). In Vol. I, No._ 5 _the text refers to -canal-making in general._ - -_On one point only can the collection of passages included under the -general heading of Physical Geography claim to be complete. When -comparing and sorting the materials for this work I took particular -care not to exclude or omit any text in which a geographical name -was mentioned even incidentally, since in all such researches the -chief interest, as it appeared to me, attached to the question -whether these acute observations on the various local -characteristics of mountains, rivers or seas, had been made by -Leonardo himself, and on the spot. It is self-evident that the few -general and somewhat superficial observations on the Rhine and the -Danube, on England and Flanders, must have been obtained from maps -or from some informants, and in the case of Flanders Leonardo -himself acknowledges this (see No._ 1008_). But that most of the -other and more exact observations were made, on the spot, by -Leonardo himself, may be safely assumed from their method and the -style in which he writes of them; and we should bear it in mind that -in all investigations, of whatever kind, experience is always spoken -of as the only basis on which he relies. Incidentally, as in No._ -984, _he thinks it necessary to allude to the total absence of all -recorded observations._ - -I. - -INTRODUCTION. - -Schemes for the arrangement of the materials (919-928). - -919. - -These books contain in the beginning: Of the nature of water itself -in its motions; the others treat of the effects of its currents, -which change the world in its centre and its shape. - -920. - -DIVISIONS OF THE BOOK. - -Book 1 of water in itself. - -Book 2 of the sea. - -Book 3 of subterranean rivers. - -Book 4 of rivers. - -Book 5 of the nature of the abyss. - -Book 6 of the obstacles. - -Book 7 of gravels. - -Book 8 of the surface of water. - -Book 9 of the things placed therein. - -Book 10 of the repairing of rivers. - -Book 11 of conduits. - -Book 12 of canals. - -Book 13 of machines turned by water. - -Book 14 of raising water. - -Book 15 of matters worn away by water. - -921. - -First you shall make a book treating of places occupied by fresh -waters, and the second by salt waters, and the third, how by the -disappearance of these, our parts of the world were made lighter and -in consequence more remote from the centre of the world. - -922. - -First write of all water, in each of its motions; then describe all -its bottoms and their various materials, always referring to the -propositions concerning the said waters; and let the order be good, -for otherwise the work will be confused. - -Describe all the forms taken by water from its greatest to its -smallest wave, and their causes. - -923. - -Book 9, of accidental risings of water. - -924. - -THE ORDER OF THE BOOK. - -Place at the beginning what a river can effect. - -925. - -A book of driving back armies by the force of a flood made by -releasing waters. - -A book showing how the waters safely bring down timber cut in the -mountains. - -A book of boats driven against the impetus of rivers. - -A book of raising large bridges higher. Simply by the swelling of -the waters. - -A book of guarding against the impetus of rivers so that towns may -not be damaged by them. - -926. - -A book of the ordering of rivers so as to preserve their banks. - -A book of the mountains, which would stand forth and become land, if -our hemisphere were to be uncovered by the water. - -A book of the earth carried down by the waters to fill up the great -abyss of the seas. - -A book of the ways in which a tempest may of itself clear out filled -up sea-ports. - -A book of the shores of rivers and of their permanency. - -A book of how to deal with rivers, so that they may keep their -bottom scoured by their own flow near the cities they pass. - -A book of how to make or to repair the foundations for bridges over -the rivers. - -A book of the repairs which ought to be made in walls and banks of -rivers where the water strikes them. - -A book of the formation of hills of sand or gravel at great depths -in water. - -927. - -Water gives the first impetus to its motion. - -A book of the levelling of waters by various means, - -A book of diverting rivers from places where they do mischief. - -A book of guiding rivers which occupy too much ground. - -A book of parting rivers into several branches and making them -fordable. - -A book of the waters which with various currents pass through seas. - -A book of deepening the beds of rivers by means of currents of -water. - -A book of controlling rivers so that the little beginnings of -mischief, caused by them, may not increase. - -A book of the various movements of waters passing through channels -of different forms. - -A book of preventing small rivers from diverting the larger one into -which their waters run. - -A book of the lowest level which can be found in the current of the -surface of rivers. - -A book of the origin of rivers which flow from the high tops of -mountains. - -A book of the various motions of waters in their rivers. - -928. - -[1] Of inequality in the concavity of a ship. [Footnote 1: The first -line of this passage was added subsequently, evidently as a -correction of the following line.] - -[1] A book of the inequality in the curve of the sides of ships. - -[1] A book of the inequality in the position of the tiller. - -[1] A book of the inequality in the keel of ships. - -[2] A book of various forms of apertures by which water flows out. - -[3] A book of water contained in vessels with air, and of its -movements. - -[4] A book of the motion of water through a syphon. [Footnote 7: -_cicognole_, see No. 966, 11, 17.] - -[5] A book of the meetings and union of waters coming from different -directions. - -[6] A book of the various forms of the banks through which rivers -pass. - -[7] A book of the various forms of shoals formed under the sluices -of rivers. - -[8] A book of the windings and meanderings of the currents of -rivers. - -[9] A book of the various places whence the waters of rivers are -derived. - -[10] A book of the configuration of the shores of rivers and of -their permanency. - -[11] A book of the perpendicular fall of water on various objects. - -[12] Abook of the course of water when it is impeded in various -places. - -[12] A book of the various forms of the obstacles which impede the -course of waters. - -[13] A book of the concavity and globosity formed round various -objects at the bottom. - -[14] Abook of conducting navigable canals above or beneath the -rivers which intersect them. - -[15] A book of the soils which absorb water in canals and of -repairing them. - -[16] Abook of creating currents for rivers, which quit their beds, -[and] for rivers choked with soil. - -General introduction. - -929. - -THE BEGINNING OF THE TREATISE ON WATER. - -By the ancients man has been called the world in miniature; and -certainly this name is well bestowed, because, inasmuch as man is -composed of earth, water, air and fire, his body resembles that of -the earth; and as man has in him bones the supports and framework of -his flesh, the world has its rocks the supports of the earth; as man -has in him a pool of blood in which the lungs rise and fall in -breathing, so the body of the earth has its ocean tide which -likewise rises and falls every six hours, as if the world breathed; -as in that pool of blood veins have their origin, which ramify all -over the human body, so likewise the ocean sea fills the body of the -earth with infinite springs of water. The body of the earth lacks -sinews and this is, because the sinews are made expressely for -movements and, the world being perpetually stable, no movement takes -place, and no movement taking place, muscles are not necessary. ---But in all other points they are much alike. - -I. - -OF THE NATURE OF WATER. - -The arrangement of Book I. - -930. - -THE ORDER OF THE FIRST BOOK ON WATER. - -Define first what is meant by height and depth; also how the -elements are situated one inside another. Then, what is meant by -solid weight and by liquid weight; but first what weight and -lightness are in themselves. Then describe why water moves, and why -its motion ceases; then why it becomes slower or more rapid; besides -this, how it always falls, being in contact with the air but lower -than the air. And how water rises in the air by means of the heat of -the sun, and then falls again in rain; again, why water springs -forth from the tops of mountains; and if the water of any spring -higher than the ocean can pour forth water higher than the surface -of that ocean. And how all the water that returns to the ocean is -higher than the sphere of waters. And how the waters of the -equatorial seas are higher than the waters of the North, and higher -beneath the body of the sun than in any part of the equatorial -circle; for experiment shows that under the heat of a burning brand -the water near the brand boils, and the water surrounding this -ebullition always sinks with a circular eddy. And how the waters of -the North are lower than the other seas, and more so as they become -colder, until they are converted into ice. - -Definitions (931. 932). - -931. - -OF WHAT IS WATER. - -Among the four elements water is the second both in weight and in -instability. - -932. - -THE BEGINNING OF THE BOOK ON WATER. - -Sea is the name given to that water which is wide and deep, in which -the waters have not much motion. - -[Footnote: Only the beginning of this passage is here given, the -remainder consists of definitions which have no direct bearing on -the subject.] - -Of the surface of the water in relation to the globe (933-936). - -933. - -The centres of the sphere of water are two, one universal and common -to all water, the other particular. The universal one is that which -is common to all waters not in motion, which exist in great -quantities. As canals, ditches, ponds, fountains, wells, dead -rivers, lakes, stagnant pools and seas, which, although they are at -various levels, have each in itself the limits of their superficies -equally distant from the centre of the earth, such as lakes placed -at the tops of high mountains; as the lake near Pietra Pana and the -lake of the Sybil near Norcia; and all the lakes that give rise to -great rivers, as the Ticino from Lago Maggiore, the Adda from the -lake of Como, the Mincio from the lake of Garda, the Rhine from the -lakes of Constance and of Chur, and from the lake of Lucerne, like -the Tigris which passes through Asia Minor carrying with it the -waters of three lakes, one above the other at different heights of -which the highest is Munace, the middle one Pallas, and the lowest -Triton; the Nile again flows from three very high lakes in Ethiopia. - -[Footnote 5: _Pietra Pana_, a mountain near Florence. If for Norcia, -we may read Norchia, the remains of the Etruscan city near Viterbo, -there can be no doubt that by '_Lago della Sibilla_'--a name not -known elsewhere, so far as I can learn--Leonardo meant _Lago di -Vico_ (Lacus Ciminus, Aen. 7).] - -934. - -OF THE CENTRE OF THE OCEAN. - -The centre of the sphere of waters is the true centre of the globe -of our world, which is composed of water and earth, having the shape -of a sphere. But, if you want to find the centre of the element of -the earth, this is placed at a point equidistant from the surface of -the ocean, and not equidistant from the surface of the earth; for it -is evident that this globe of earth has nowhere any perfect -rotundity, excepting in places where the sea is, or marshes or other -still waters. And every part of the earth that rises above the water -is farther from the centre. - -935. - -OF THE SEA WHICH CHANGES THE WEIGHT OF THE EARTH. - -The shells, oysters, and other similar animals, which originate in -sea-mud, bear witness to the changes of the earth round the centre -of our elements. This is proved thus: Great rivers always run -turbid, being coloured by the earth, which is stirred by the -friction of their waters at the bottom and on their shores; and this -wearing disturbs the face of the strata made by the layers of -shells, which lie on the surface of the marine mud, and which were -produced there when the salt waters covered them; and these strata -were covered over again from time to time, with mud of various -thickness, or carried down to the sea by the rivers and floods of -more or less extent; and thus these layers of mud became raised to -such a height, that they came up from the bottom to the air. At the -present time these bottoms are so high that they form hills or high -mountains, and the rivers, which wear away the sides of these -mountains, uncover the strata of these shells, and thus the softened -side of the earth continually rises and the antipodes sink closer to -the centre of the earth, and the ancient bottoms of the seas have -become mountain ridges. - -936. - -Let the earth make whatever changes it may in its weight, the -surface of the sphere of waters can never vary in its equal distance -from the centre of the world. - -Of the proportion of the mass of water to that of the earth (937. -938). - -937. - -WHETHER THE EARTH IS LESS THAN THE WATER. - -Some assert that it is true that the earth, which is not covered by -water is much less than that covered by water. But considering the -size of 7000 miles in diameter which is that of this earth, we may -conclude the water to be of small depth. - -938. - -OF THE EARTH. - -The great elevations of the peaks of the mountains above the sphere -of the water may have resulted from this that: a very large portion -of the earth which was filled with water that is to say the vast -cavern inside the earth may have fallen in a vast part of its vault -towards the centre of the earth, being pierced by means of the -course of the springs which continually wear away the place where -they pass. - -Sinking in of countries like the Dead Sea in Syria, that is Sodom -and Gomorrah. - -It is of necessity that there should be more water than land, and -the visible portion of the sea does not show this; so that there -must be a great deal of water inside the earth, besides that which -rises into the lower air and which flows through rivers and springs. - -[Footnote: The small sketch below on the left, is placed in the -original close to the text referring to the Dead Sea.] - -The theory of Plato. - -939. - -THE FIGURES OF THE ELEMENTS. - -Of the figures of the elements; and first as against those who deny -the opinions of Plato, and who say that if the elements include one -another in the forms attributed to them by Plato they would cause a -vacuum one within the other. I say it is not true, and I here prove -it, but first I desire to propound some conclusions. It is not -necessary that the elements which include each other should be of -corresponding magnitude in all the parts, of that which includes and -of that which is included. We see that the sphere of the waters -varies conspicuously in mass from the surface to the bottom, and -that, far from investing the earth when that was in the form of a -cube that is of 8 angles as Plato will have it, that it invests the -earth which has innumerable angles of rock covered by the water and -various prominences and concavities, and yet no vacuum is generated -between the earth and water; again, the air invests the sphere of -waters together with the mountains and valleys, which rise above -that sphere, and no vacuum remains between the earth and the air, so -that any one who says a vacuum is generated, speaks foolishly. - -But to Plato I would reply that the surface of the figures which -according to him the elements would have, could not exist. - -That the flow of rivers proves the slope of the land. - -940. - -PROVES HOW THE EARTH IS NOT GLOBULAR AND NOT BEING GLOBULAR CANNOT -HAVE A COMMON CENTRE. - -We see the Nile come from Southern regions and traverse various -provinces, running towards the North for a distance of 3000 miles -and flow into the Mediterranean by the shores of Egypt; and if we -will give to this a fall of ten braccia a mile, as is usually -allowed to the course of rivers in general, we shall find that the -Nile must have its mouth ten miles lower than its source. Again, we -see the Rhine, the Rhone and the Danube starting from the German -parts, almost the centre of Europe, and having a course one to the -East, the other to the North, and the last to Southern seas. And if -you consider all this you will see that the plains of Europe in -their aggregate are much higher than the high peaks of the maritime -mountains; think then how much their tops must be above the sea -shores. - -Theory of the elevation of water within the mountains. - -941. - -OF THE HEAT THAT IS IN THE WORLD. - -Where there is life there is heat, and where vital heat is, there is -movement of vapour. This is proved, inasmuch as we see that the -element of fire by its heat always draws to itself damp vapours and -thick mists as opaque clouds, which it raises from seas as well as -lakes and rivers and damp valleys; and these being drawn by degrees -as far as the cold region, the first portion stops, because heat and -moisture cannot exist with cold and dryness; and where the first -portion stops the rest settle, and thus one portion after another -being added, thick and dark clouds are formed. They are often wafted -about and borne by the winds from one region to another, where by -their density they become so heavy that they fall in thick rain; and -if the heat of the sun is added to the power of the element of fire, -the clouds are drawn up higher still and find a greater degree of -cold, in which they form ice and fall in storms of hail. Now the -same heat which holds up so great a weight of water as is seen to -rain from the clouds, draws them from below upwards, from the foot -of the mountains, and leads and holds them within the summits of the -mountains, and these, finding some fissure, issue continuously and -cause rivers. - -The relative height of the surface of the sea to that of the land -(942-945). - -942. - -OF THE SEA, WHICH TO MANY FOOLS APPEARS TO BE HIGHER THAN THE EARTH -WHICH FORMS ITS SHORE. - -_b d_ is a plain through which a river flows to the sea; this plain -ends at the sea, and since in fact the dry land that is uncovered is -not perfectly level--for, if it were, the river would have no -motion--as the river does move, this place is a slope rather than a -plain; hence this plain _d b_ so ends where the sphere of water -begins that if it were extended in a continuous line to _b a_ it -would go down beneath the sea, whence it follows that the sea _a c -b_ looks higher than the dry land. - -Obviously no portions of dry land left uncovered by water can ever -be lower than the surface of the watery sphere. - -943. - -OF CERTAIN PERSONS WHO SAY THE WATERS WERE HIGHER THAN THE DRY LAND. - -Certainly I wonder not a little at the common opinion which is -contrary to truth, but held by the universal consent of the judgment -of men. And this is that all are agreed that the surface of the sea -is higher than the highest peaks of the mountains; and they allege -many vain and childish reasons, against which I will allege only one -simple and short reason; We see plainly that if we could remove the -shores of the sea, it would invest the whole earth and make it a -perfect sphere. Now, consider how much earth would be carried away -to enable the waves of the sea to cover the world; therefore that -which would be carried away must be higher than the sea-shore. - -944. - -THE OPINION OF SOME PERSONS WHO SAY THAT THE WATER OF SOME SEAS IS -HIGHER THAN THE HIGHEST SUMMITS OF MOUNTAINS; AND NEVERTHELESS THE -WATER WAS FORCED UP TO THESE SUMMITS. - -Water would not move from place to place if it were not that it -seeks the lowest level and by a natural consequence it never can -return to a height like that of the place where it first on issuing -from the mountain came to light. And that portion of the sea which, -in your vain imagining, you say was so high that it flowed over the -summits of the high mountains, for so many centuries would be -swallowed up and poured out again through the issue from these -mountains. You can well imagine that all the time that Tigris and -Euphrates - -945. - -have flowed from the summits of the mountains of Armenia, it must be -believed that all the water of the ocean has passed very many times -through these mouths. And do you not believe that the Nile must have -sent more water into the sea than at present exists of all the -element of water? Undoubtedly, yes. And if all this water had fallen -away from this body of the earth, this terrestrial machine would -long since have been without water. Whence we may conclude that the -water goes from the rivers to the sea, and from the sea to the -rivers, thus constantly circulating and returning, and that all the -sea and the rivers have passed through the mouth of the Nile an -infinite number of times [Footnote: _Moti Armeni, Ermini_ in the -original, in M. RAVAISSON'S transcript _"monti ernini [le loro -ruine?]"_. He renders this _"Le Tigre et l'Euphrate se sont deverses -par les sommets des montagnes [avec leurs eaux destructives?] on -pent cro're" &c. Leonardo always writes _Ermini, Erminia_, for -_Armeni, Armenia_ (Arabic: _Irminiah_). M. RAVAISSON also deviates -from the original in his translation of the following passage: "_Or -tu ne crois pas que le Nil ait mis plus d'eau dans la mer qu'il n'y -en a a present dans tout l'element de l'eau. Il est certain que si -cette eau etait tombee_" &c.] - -II. - -ON THE OCEAN. - -Refutation of Pliny's theory as to the saltness of the sea (946. -947). - -946. - -WHY WATER IS SALT. - -Pliny says in his second book, chapter 103, that the water of the -sea is salt because the heat of the sun dries up the moisture and -drinks it up; and this gives to the wide stretching sea the savour -of salt. But this cannot be admitted, because if the saltness of the -sea were caused by the heat of the sun, there can be no doubt that -lakes, pools and marshes would be so much the more salt, as their -waters have less motion and are of less depth; but experience shows -us, on the contrary, that these lakes have their waters quite free -from salt. Again it is stated by Pliny in the same chapter that this -saltness might originate, because all the sweet and subtle portions -which the heat attracts easily being taken away, the more bitter and -coarser part will remain, and thus the water on the surface is -fresher than at the bottom [Footnote 22: Compare No. 948.]; but this -is contradicted by the same reason given above, which is, that the -same thing would happen in marshes and other waters, which are dried -up by the heat. Again, it has been said that the saltness of the sea -is the sweat of the earth; to this it may be answered that all the -springs of water which penetrate through the earth, would then be -salt. But the conclusion is, that the saltness of the sea must -proceed from the many springs of water which, as they penetrate into -the earth, find mines of salt and these they dissolve in part, and -carry with them to the ocean and the other seas, whence the clouds, -the begetters of rivers, never carry it up. And the sea would be -salter in our times than ever it was at any time; and if the -adversary were to say that in infinite time the sea would dry up or -congeal into salt, to this I answer that this salt is restored to -the earth by the setting free of that part of the earth which rises -out of the sea with the salt it has acquired, and the rivers return -it to the earth under the sea. - -[Footnote: See PLINY, Hist. Nat. II, CIII [C]. _Itaque Solis ardore -siccatur liquor: et hoc esse masculum sidus accepimus, torrens -cuncta sorbensque._ (cp. CIV.) _Sic mari late patenti saporem -incoqui salis, aut quia exhausto inde dulci tenuique, quod facillime -trahat vis ignea, omne asperius crassiusque linquatur: ideo summa -aequorum aqua dulciorem profundam; hanc esse veriorem causam, quam -quod mare terrae sudor sit aeternus: aut quia plurimum ex arido -misceatur illi vapore: aut quia terrae natura sicut medicatas aquas -inficiat_ ... (cp. CV): _altissimum mare XV. stadiorum Fabianus -tradit. Alii n Ponto coadverso Coraxorum gentis (vocant B Ponti) -trecentis fere a continenti stadiis immensam altitudinem maris -tradunt, vadis nunquam repertis._ (cp. CVI [CIII]) _Mirabilius id -faciunt aquae dulces, juxta mare, ut fistulis emicantes. Nam nec -aquarum natura a miraculis cessat. Dulces mari invehuntur, leviores -haud dubie. Ideo et marinae, quarum natura gravior, magis invecta -sustinent. Quaedam vero et dulces inter se supermeant alias._] - -947. - -For the third and last reason we will say that salt is in all -created things; and this we learn from water passed over the ashes -and cinders of burnt things; and the urine of every animal, and the -superfluities issuing from their bodies, and the earth into which -all things are converted by corruption. - -But,--to put it better,--given that the world is everlasting, it -must be admitted that its population will also be eternal; hence the -human species has eternally been and would be consumers of salt; and -if all the mass of the earth were to be turned into salt, it would -not suffice for all human food [Footnote 27: That is, on the -supposition that salt, once consumed, disappears for ever.]; whence -we are forced to admit, either that the species of salt must be -everlasting like the world, or that it dies and is born again like -the men who devour it. But as experience teaches us that it does not -die, as is evident by fire, which does not consume it, and by water -which becomes salt in proportion to the quantity dissolved in -it,--and when it is evaporated the salt always remains in the -original quantity--it must pass through the bodies of men either in -the urine or the sweat or other excretions where it is found again; -and as much salt is thus got rid of as is carried every year into -towns; therefore salt is dug in places where there is urine.-- Sea -hogs and sea winds are salt. - -We will say that the rains which penetrate the earth are what is -under the foundations of cities with their inhabitants, and are what -restore through the internal passages of the earth the saltness -taken from the sea; and that the change in the place of the sea, -which has been over all the mountains, caused it to be left there in -the mines found in those mountains, &c. - -The characteristics of sea water (948. 949). - -948. - -The waters of the salt sea are fresh at the greatest depths. - -949. - -THAT THE OCEAN DOES NOT PENETRATE UNDER THE EARTH. - -The ocean does not penetrate under the earth, and this we learn from -the many and various springs of fresh water which, in many parts of -the ocean make their way up from the bottom to the surface. The same -thing is farther proved by wells dug beyond the distance of a mile -from the said ocean, which fill with fresh water; and this happens -because the fresh water is lighter than salt water and consequently -more penetrating. - -Which weighs most, water when frozen or when not frozen? - -FRESH WATER PENETRATES MORE AGAINST SALT WATER THAN SALT WATER -AGAINST FRESH WATER. - -That fresh water penetrates more against salt water, than salt water -against fresh is proved by a thin cloth dry and old, hanging with -the two opposite ends equally low in the two different waters, the -surfaces of which are at an equal level; and it will then be seen -how much higher the fresh water will rise in this piece of linen -than the salt; by so much is the fresh lighter than the salt. - -On the formation of Gulfs (950. 951). - -950. - -All inland seas and the gulfs of those seas, are made by rivers -which flow into the sea. - -951. - -HERE THE REASON IS GIVEN OF THE EFFECTS PRODUCED BY THE WATERS IN -THE ABOVE MENTIONED PLACE. - -All the lakes and all the gulfs of the sea and all inland seas are -due to rivers which distribute their waters into them, and from -impediments in their downfall into the Mediterranean --which divides -Africa from Europe and Europe from Asia by means of the Nile and the -Don which pour their waters into it. It is asked what impediment is -great enough to stop the course of the waters which do not reach the -ocean. - -On the encroachments of the sea on the land and vice versa -(952-954). - -952. - -OF WAVES. - -A wave of the sea always breaks in front of its base, and that -portion of the crest will then be lowest which before was highest. - -[Footnote: The page of FRANCESCO DI GIORGIO'S _Trattato_, on which -Leonardo has written this remark, contains some notes on the -construction of dams, harbours &c.] - -953. - -That the shores of the sea constantly acquire more soil towards the -middle of the sea; that the rocks and promontories of the sea are -constantly being ruined and worn away; that the Mediterranean seas -will in time discover their bottom to the air, and all that will be -left will be the channel of the greatest river that enters it; and -this will run to the ocean and pour its waters into that with those -of all the rivers that are its tributaries. - -954. - -How the river Po, in a short time might dry up the Adriatic sea in -the same way as it has dried up a large part of Lombardy. - -The ebb and flow of the tide (955-960). - -955. - -Where there is a larger quantity of water, there is a greater flow -and ebb, but the contrary in narrow waters. - -Look whether the sea is at its greatest flow when the moon is half -way over our hemisphere [on the meridian]. - -956. - -Whether the flow and ebb are caused by the moon or the sun, or are -the breathing of this terrestrial machine. That the flow and ebb are -different in different countries and seas. - -[Footnote: 1. Allusion may here be made to the mythological -explanation of the ebb and flow given in the Edda. Utgardloki says -to Thor (Gylfaginning 48): "When thou wert drinking out of the horn, -and it seemed to thee that it was slow in emptying a wonder befell, -which I should not have believed possible: the other end of the horn -lay in the sea, which thou sawest not; but when thou shalt go to the -sea, thou shalt see how much thou hast drunk out of it. And that men -now call the ebb tide." - -Several passages in various manuscripts treat of the ebb and flow. -In collecting them I have been guided by the rule only to transcribe -those which named some particular spot.] - -957. - -Book 9 of the meeting of rivers and their flow and ebb. The cause is -the same in the sea, where it is caused by the straits of Gibraltar. -And again it is caused by whirlpools. - -958. - -OF THE FLOW AND EBB. - -All seas have their flow and ebb in the same period, but they seem -to vary because the days do not begin at the same time throughout -the universe; in such wise as that when it is midday in our -hemisphere, it is midnight in the opposite hemisphere; and at the -Eastern boundary of the two hemispheres the night begins which -follows on the day, and at the Western boundary of these hemispheres -begins the day, which follows the night from the opposite side. -Hence it is to be inferred that the above mentioned swelling and -diminution in the height of the seas, although they take place in -one and the same space of time, are seen to vary from the above -mentioned causes. The waters are then withdrawn into the fissures -which start from the depths of the sea and which ramify inside the -body of the earth, corresponding to the sources of rivers, which are -constantly taking from the bottom of the sea the water which has -flowed into it. A sea of water is incessantly being drawn off from -the surface of the sea. And if you should think that the moon, -rising at the Eastern end of the Mediterranean sea must there begin -to attract to herself the waters of the sea, it would follow that we -must at once see the effect of it at the Eastern end of that sea. -Again, as the Mediterranean sea is about the eighth part of the -circumference of the aqueous sphere, being 3000 miles long, while -the flow and ebb only occur 4 times in 24 hours, these results would -not agree with the time of 24 hours, unless this Mediterranean sea -were six thousand miles in length; because if such a superabundance -of water had to pass through the straits of Gibraltar in running -behind the moon, the rush of the water through that strait would be -so great, and would rise to such a height, that beyond the straits -it would for many miles rush so violently into the ocean as to cause -floods and tremendous seething, so that it would be impossible to -pass through. This agitated ocean would afterwards return the waters -it had received with equal fury to the place they had come from, so -that no one ever could pass through those straits. Now experience -shows that at every hour they are passed in safety, but when the -wind sets in the same direction as the current, the strong ebb -increases [Footnote 23: In attempting to get out of the -Mediterranean, vessels are sometimes detained for a considerable -time; not merely by the causes mentioned by Leonardo but by the -constant current flowing eastwards through the middle of the straits -of Gibraltar.]. The sea does not raise the water that has issued -from the straits, but it checks them and this retards the tide; then -it makes up with furious haste for the time it has lost until the -end of the ebb movement. - -959. - -That the flow and ebb are not general; for on the shore at Genoa -there is none, at Venice two braccia, between England and Flanders -18 braccia. That in the straits of Sicily the current is very strong -because all the waters from the rivers that flow into the Adriatic -pass there. - -[Footnote: A few more recent data may be given here to facilitate -comparison. In the Adriatic the tide rises 2 and 1/2 feet, at -Terracina 1 1/4. In the English channel between Calais and Kent it -rises from 18 to 20 feet. In the straits of Messina it rises no more -than 2 1/2 feet, and that only in stormy weather, but the current is -all the stronger. When Leonardo accounts for this by the southward -flow of all the Italian rivers along the coasts, the explanation is -at least based on a correct observation; namely that a steady -current flows southwards along the coast of Calabria and another -northwards, along the shores of Sicily; he seems to infer, from the -direction of the fust, that the tide in the Adriatic is caused by -it.] - -960. - -In the West, near to Flanders, the sea rises and decreases every 6 -hours about 20 braccia, and 22 when the moon is in its favour; but -20 braccia is the general rule, and this rule, as it is evident, -cannot have the moon for its cause. This variation in the increase -and decrease of the sea every 6 hours may arise from the damming up -of the waters, which are poured into the Mediterranean by the -quantity of rivers from Africa, Asia and Europe, which flow into -that sea, and the waters which are given to it by those rivers; it -pours them to the ocean through the straits of Gibraltar, between -Abila and Calpe [Footnote 5: _Abila_, Lat. _Abyla_, Gr. , now -Sierra _Ximiera_ near Ceuta; _Calpe_, Lat. _Calpe_. Gr., now -Gibraltar. Leonardo here uses the ancient names of the rocks, which -were known as the Pillars of Hercules.]. That ocean extends to the -island of England and others farther North, and it becomes dammed up -and kept high in various gulfs. These, being seas of which the -surface is remote from the centre of the earth, have acquired a -weight, which as it is greater than the force of the incoming waters -which cause it, gives this water an impetus in the contrary -direction to that in which it came and it is borne back to meet the -waters coming out of the straits; and this it does most against the -straits of Gibraltar; these, so long as this goes on, remain dammed -up and all the water which is poured out meanwhile by the -aforementioned rivers, is pent up [in the Mediterranean]; and this -might be assigned as the cause of its flow and ebb, as is shown in -the 21st of the 4th of my theory. - -III. - -SUBTERRANEAN WATER COURSES. - -Theory of the circulation of the waters (961. 962). - -961. - -Very large rivers flow under ground. - -962. - -This is meant to represent the earth cut through in the middle, -showing the depths of the sea and of the earth; the waters start -from the bottom of the seas, and ramifying through the earth they -rise to the summits of the mountains, flowing back by the rivers and -returning to the sea. - -Observations in support of the hypothesis (963-969). - -963. - -The waters circulate with constant motion from the utmost depths of -the sea to the highest summits of the mountains, not obeying the -nature of heavy matter; and in this case it acts as does the blood -of animals which is always moving from the sea of the heart and -flows to the top of their heads; and here it is that veins burst--as -one may see when a vein bursts in the nose, that all the blood from -below rises to the level of the burst vein. When the water rushes -out of a burst vein in the earth it obeys the nature of other things -heavier than the air, whence it always seeks the lowest places. [7] -These waters traverse the body of the earth with infinite -ramifications. - -[Footnote: The greater part of this passage has been given as No. -849 in the section on Anatomy.] - -964. - -The same cause which stirs the humours in every species of animal -body and by which every injury is repaired, also moves the waters -from the utmost depth of the sea to the greatest heights. - -965. - -It is the property of water that it constitutes the vital human of -this arid earth; and the cause which moves it through its ramified -veins, against the natural course of heavy matters, is the same -property which moves the humours in every species of animal body. -But that which crowns our wonder in contemplating it is, that it -rises from the utmost depths of the sea to the highest tops of the -mountains, and flowing from the opened veins returns to the low -seas; then once more, and with extreme swiftness, it mounts again -and returns by the same descent, thus rising from the inside to the -outside, and going round from the lowest to the highest, from whence -it rushes down in a natural course. Thus by these two movements -combined in a constant circulation, it travels through the veins of -the earth. - -966. - -WHETHER WATER RISES FROM THE SEA TO THE TOPS OF MOUNTAINS. - -The water of the ocean cannot make its way from the bases to the -tops of the mountains which bound it, but only so much rises as the -dryness of the mountain attracts. And if, on the contrary, the rain, -which penetrates from the summit of the mountain to the base, which -is the boundary of the sea, descends and softens the slope opposite -to the said mountain and constantly draws the water, like a syphon -[Footnote 11: Cicognola, Syphon. See Vol. I, Pl. XXIV, No. 1.] which -pours through its longest side, it must be this which draws up the -water of the sea; thus if _s n_ were the surface of the sea, and the -rain descends from the top of the mountain _a_ to _n_ on one side, -and on the other sides it descends from _a_ to _m_, without a doubt -this would occur after the manner of distilling through felt, or as -happens through the tubes called syphons [Footnote 17: Cicognola, -Syphon. See Vol. I, Pl. XXIV, No. 1.]. And at all times the water -which has softened the mountain, by the great rain which runs down -the two opposite sides, would constantly attract the rain _a n_, on -its longest side together with the water from the sea, if that side -of the mountain _a m_ were longer than the other _a n_; but this -cannot be, because no part of the earth which is not submerged by -the ocean can be lower than that ocean. - -967. - -OF SPRINGS OF WATER ON THE TOPS OF MOUNTAINS. - -It is quite evident that the whole surface of the ocean--when there -is no storm--is at an equal distance from the centre of the earth, -and that the tops of the mountains are farther from this centre in -proportion as they rise above the surface of that sea; therefore if -the body of the earth were not like that of man, it would be -impossible that the waters of the sea--being so much lower than the -mountains--could by their nature rise up to the summits of these -mountains. Hence it is to be believed that the same cause which -keeps the blood at the top of the head in man keeps the water at the -summits of the mountains. - -[Footnote: This conception of the rising of the blood, which has -given rise to the comparison, was recognised as erroneous by -Leonardo himself at a later period. It must be remembered that the -MS. A, from which these passages are taken, was written about twenty -years earlier than the MS. Leic. (Nos. 963 and 849) and twenty-five -years before the MS. W. An. IV. - -There is, in the original a sketch with No. 968 which is not -reproduced. It represents a hill of the same shape as that shown at -No. 982. There are veins, or branched streams, on the side of the -hill, like those on the skull Pl. CVIII, No. 4] - -968. - -IN CONFIRMATION OF WHY THE WATER GOES TO THE TOPS OF MOUNTAINS. - -I say that just as the natural heat of the blood in the veins keeps -it in the head of man,--for when the man is dead the cold blood -sinks to the lower parts--and when the sun is hot on the head of a -man the blood increases and rises so much, with other humours, that -by pressure in the veins pains in the head are often caused; in the -same way veins ramify through the body of the earth, and by the -natural heat which is distributed throughout the containing body, -the water is raised through the veins to the tops of mountains. And -this water, which passes through a closed conduit inside the body of -the mountain like a dead thing, cannot come forth from its low place -unless it is warmed by the vital heat of the spring time. Again, the -heat of the element of fire and, by day, the heat of the sun, have -power to draw forth the moisture of the low parts of the mountains -and to draw them up, in the same way as it draws the clouds and -collects their moisture from the bed of the sea. - -969. - -That many springs of salt water are found at great distances from -the sea; this might happen because such springs pass through some -mine of salt, like that in Hungary where salt is hewn out of vast -caverns, just as stone is hewn. - -[Footnote: The great mine of Wieliczka in Galicia, out of which a -million cwt. of rock-salt are annually dug out, extends for 3000 -metres from West to East, and 1150 metres from North to South.] - -IV. - -OF RIVERS. - -On the way in which the sources of rivers are fed. - -970. - -OF THE ORIGIN OF RIVERS. - -The body of the earth, like the bodies of animals, is intersected -with ramifications of waters which are all in connection and are -constituted to give nutriment and life to the earth and to its -creatures. These come from the depth of the sea and, after many -revolutions, have to return to it by the rivers created by the -bursting of these springs; and if you chose to say that the rains of -the winter or the melting of the snows in summer were the cause of -the birth of rivers, I could mention the rivers which originate in -the torrid countries of Africa, where it never rains--and still less -snows--because the intense heat always melts into air all the clouds -which are borne thither by the winds. And if you chose to say that -such rivers, as increase in July and August, come from the snows -which melt in May and June from the sun's approach to the snows on -the mountains of Scythia [Footnote 9: Scythia means here, as in -Ancient Geography, the whole of the Northern part of Asia as far as -India.], and that such meltings come down into certain valleys and -form lakes, into which they enter by springs and subterranean caves -to issue forth again at the sources of the Nile, this is false; -because Scythia is lower than the sources of the Nile, and, besides, -Scythia is only 400 miles from the Black sea and the sources of the -Nile are 3000 miles distant from the sea of Egypt into which its -waters flow. - -The tide in estuaries. - -971. - -Book 9, of the meeting of rivers and of their ebb and flow. The -cause is the same in the sea, where it is caused by the straits of -Gibraltar; and again it is caused by whirlpools. - -[3] If two rivers meet together to form a straight line, and then -below two right angles take their course together, the flow and ebb -will happen now in one river and now in the other above their -confluence, and principally if the outlet for their united volume is -no swifter than when they were separate. Here occur 4 instances. - -[Footnote: The first two lines of this passage have already been -given as No. 957. In the margin, near line 3 of this passage, the -text given as No. 919 is written.] - -On the alterations, caused in the courses of rivers by their -confluence (972-974). - -972. - -When a smaller river pours its waters into a larger one, and that -larger one flows from the opposite direction, the course of the -smaller river will bend up against the approach of the larger river; -and this happens because, when the larger river fills up all its bed -with water, it makes an eddy in front of the mouth of the other -river, and so carries the water poured in by the smaller river with -its own. When the smaller river pours its waters into the larger -one, which runs across the current at the mouth of the smaller -river, its waters will bend with the downward movement of the larger -river. [Footnote: In the original sketches the word _Arno_ is -written at the spot here marked _A_, at _R. Rifredi_, and at _M. -Mugnone_.] - -973. - -When the fulness of rivers is diminished, then the acute angles -formed at the junction of their branches become shorter at the sides -and wider at the point; like the current _a n_ and the current _d -n_, which unite in _n_ when the river is at its greatest fulness. I -say, that when it is in this condition if, before the fullest time, -_d n_ was lower than _a n_, at the time of fulness _d n_ will be -full of sand and mud. When the water _d n_ falls, it will carry away -the mud and remain with a lower bottom, and the channel _a n_ -finding itself the higher, will fling its waters into the lower, _d -n_, and will wash away all the point of the sand-spit _b n c_, and -thus the angle _a c d_ will remain larger than the angle _a n d_ and -the sides shorter, as I said before. - -[Footnote: Above the first sketch we find, in the original, this -note: "_Sopra il pote rubaconte alla torricella_"; and by the -second, which represents a pier of a bridge, "_Sotto l'ospedal del -ceppo._"] - -974. - -WATER. - -OF THE MOVEMENT OF A SUDDEN RUSH MADE BY A RIVER IN ITS BED -PREVIOUSLY DRY. - -In proportion as the current of the water given forth by the -draining of the lake is slow or rapid in the dry river bed, so will -this river be wider or narrower, or shallower or deeper in one place -than another, according to this proposition: the flow and ebb of the -sea which enters the Mediterranean from the ocean, and of the rivers -which meet and struggle with it, will raise their waters more or -less in proportion as the sea is wider or narrower. - -[Footnote: In the margin is a sketch of a river which winds so as to -form islands.] - -Whirlpools. - -975. - -Whirlpools, that is to say caverns; that is to say places left by -precipitated waters. - -On the alterations in the channels of rivers. - -976. - -OF THE VIBRATION OF THE EARTH. - -The subterranean channels of waters, like those which exist between -the air and the earth, are those which unceasingly wear away and -deepen the beds of their currents. - -The origin of the sand in rivers (977. 978). - -977. - -A river that flows from mountains deposits a great quantity of large -stones in its bed, which still have some of their angles and sides, -and in the course of its flow it carries down smaller stones with -the angles more worn; that is to say the large stones become -smaller. And farther on it deposits coarse gravel and then smaller, -and as it proceeds this becomes coarse sand and then finer, and -going on thus the water, turbid with sand and gravel, joins the sea; -and the sand settles on the sea-shores, being cast up by the salt -waves; and there results the sand of so fine a nature as to seem -almost like water, and it will not stop on the shores of the sea but -returns by reason of its lightness, because it was originally formed -of rotten leaves and other very light things. Still, being -almost--as was said--of the nature of water itself, it afterwards, -when the weather is calm, settles and becomes solid at the bottom of -the sea, where by its fineness it becomes compact and by its -smoothness resists the waves which glide over it; and in this shells -are found; and this is white earth, fit for pottery. - -978. - -All the torrents of water flowing from the mountains to the sea -carry with them the stones from the hills to the sea, and by the -influx of the sea-water towards the mountains; these stones were -thrown back towards the mountains, and as the waters rose and -retired, the stones were tossed about by it and in rolling, their -angles hit together; then as the parts, which least resisted the -blows, were worn off, the stones ceased to be angular and became -round in form, as may be seen on the banks of the Elsa. And those -remained larger which were less removed from their native spot; and -they became smaller, the farther they were carried from that place, -so that in the process they were converted into small pebbles and -then into sand and at last into mud. After the sea had receded from -the mountains the brine left by the sea with other humours of the -earth made a concretion of these pebbles and this sand, so that the -pebbles were converted into rock and the sand into tufa. And of this -we see an example in the Adda where it issues from the mountains of -Como and in the Ticino, the Adige and the Oglio coming from the -German Alps, and in the Arno at Monte Albano [Footnote 13: At the -foot of _Monte Albano_ lies Vinci, the birth place of Leonardo. -Opposite, on the other bank of the Arno, is _Monte Lupo_.], near -Monte Lupo and Capraia where the rocks, which are very large, are -all of conglomerated pebbles of various kinds and colours. - -V. - -ON MOUNTAINS. - -The formation of mountains (979-983). - -979. - -Mountains are made by the currents of rivers. - -Mountains are destroyed by the currents of rivers. - -[Footnote: Compare 789.] - -980. - -That the Northern bases of some Alps are not yet petrified. And this -is plainly to be seen where the rivers, which cut through them, flow -towards the North; where they cut through the strata in the living -stone in the higher parts of the mountains; and, where they join the -plains, these strata are all of potter's clay; as is to be seen in -the valley of Lamona where the river Lamona, as it issues from the -Appenines, does these things on its banks. - -That the rivers have all cut and divided the mountains of the great -Alps one from the other. This is visible in the order of the -stratified rocks, because from the summits of the banks, down to the -river the correspondence of the strata in the rocks is visible on -either side of the river. That the stratified stones of the -mountains are all layers of clay, deposited one above the other by -the various floods of the rivers. That the different size of the -strata is caused by the difference in the floods--that is to say -greater or lesser floods. - -981. - -The summits of mountains for a long time rise constantly. - -The opposite sides of the mountains always approach each other -below; the depths of the valleys which are above the sphere of the -waters are in the course of time constantly getting nearer to the -centre of the world. - -In an equal period, the valleys sink much more than the mountains -rise. - -The bases of the mountains always come closer together. - -In proportion as the valleys become deeper, the more quickly are -their sides worn away. - -982. - -In every concavity at the summit of the mountains we shall always -find the divisions of the strata in the rocks. - -983. - -OF THE SEA WHICH ENCIRCLES THE EARTH. - -I find that of old, the state of the earth was that its plains were -all covered up and hidden by salt water. [Footnote: This passage has -already been published by Dr. M. JORDAN: _Das Malerbuch des L. da -Vinci, Leipzig_ 1873, p. 86. However, his reading of the text -differs from mine.] - -The authorities for the study of the structure of the earth. - -984. - -Since things are much more ancient than letters, it is no marvel if, -in our day, no records exist of these seas having covered so many -countries; and if, moreover, some records had existed, war and -conflagrations, the deluge of waters, the changes of languages and -of laws have consumed every thing ancient. But sufficient for us is -the testimony of things created in the salt waters, and found again -in high mountains far from the seas. - -VI. - -GEOLOGICAL PROBLEMS. - -985. - -In this work you have first to prove that the shells at a thousand -braccia of elevation were not carried there by the deluge, because -they are seen to be all at one level, and many mountains are seen to -be above that level; and to inquire whether the deluge was caused by -rain or by the swelling of the sea; and then you must show how, -neither by rain nor by swelling of the rivers, nor by the overflow -of this sea, could the shells--being heavy objects--be floated up -the mountains by the sea, nor have carried there by the rivers -against the course of their waters. - -Doubts about the deluge. - -986. - -A DOUBTFUL POINT. - -Here a doubt arises, and that is: whether the deluge, which happened -at the time of Noah, was universal or not. And it would seem not, -for the reasons now to be given: We have it in the Bible that this -deluge lasted 40 days and 40 nights of incessant and universal rain, -and that this rain rose to ten cubits above the highest mountains in -the world. And if it had been that the rain was universal, it would -have covered our globe which is spherical in form. And this -spherical surface is equally distant in every part, from the centre -of its sphere; hence the sphere of the waters being under the same -conditions, it is impossible that the water upon it should move, -because water, in itself, does not move unless it falls; therefore -how could the waters of such a deluge depart, if it is proved that -it has no motion? and if it departed how could it move unless it -went upwards? Here, then, natural reasons are wanting; hence to -remove this doubt it is necessary to call in a miracle to aid us, or -else to say that all this water was evaporated by the heat of the -sun. - -[Footnote: The passages, here given from the MS. Leic., have -hitherto remained unknown. Some preliminary notes on the subject are -to be found in MS. F 8oa and 8ob; but as compared with the fuller -treatment here given, they are, it seems to me, of secondary -interest. They contain nothing that is not repeated here more -clearly and fully. LIBRI, _Histoire des Sciences mathematiques III_, -pages 218--221, has printed the text of F 80a and 80b, therefore it -seemed desirable to give my reasons for not inserting it in this -work.] - -That marine shells could not go up the mountains. - -987. - -OF THE DELUGE AND OF MARINE SHELLS. - -If you were to say that the shells which are to be seen within the -confines of Italy now, in our days, far from the sea and at such -heights, had been brought there by the deluge which left them there, -I should answer that if you believe that this deluge rose 7 cubits -above the highest mountains-- as he who measured it has -written--these shells, which always live near the sea-shore, should -have been left on the mountains; and not such a little way from the -foot of the mountains; nor all at one level, nor in layers upon -layers. And if you were to say that these shells are desirous of -remaining near to the margin of the sea, and that, as it rose in -height, the shells quitted their first home, and followed the -increase of the waters up to their highest level; to this I answer, -that the cockle is an animal of not more rapid movement than the -snail is out of water, or even somewhat slower; because it does not -swim, on the contrary it makes a furrow in the sand by means of its -sides, and in this furrow it will travel each day from 3 to 4 -braccia; therefore this creature, with so slow a motion, could not -have travelled from the Adriatic sea as far as Monferrato in -Lombardy [Footnote: _Monferrato di Lombardia_. The range of hills of -Monferrato is in Piedmont, and Casale di Monferrato belonged, in -Leonardo's time, to the Marchese di Mantova.], which is 250 miles -distance, in 40 days; which he has said who took account of the -time. And if you say that the waves carried them there, by their -gravity they could not move, excepting at the bottom. And if you -will not grant me this, confess at least that they would have to -stay at the summits of the highest mountains, in the lakes which are -enclosed among the mountains, like the lakes of Lario, or of Como -and il Maggiore [Footnote: _Lago di Lario._ Lacus Larius was the -name given by the Romans to the lake of Como. It is evident that it -is here a slip of the pen since the the words in the MS. are: _"Come -Lago di Lario o'l Magare e di Como,"_ In the MS. after line 16 we -come upon a digression treating of the weight of water; this has -here been omitted. It is 11 lines long.] and of Fiesole, and of -Perugia, and others. - -And if you should say that the shells were carried by the waves, -being empty and dead, I say that where the dead went they were not -far removed from the living; for in these mountains living ones are -found, which are recognisable by the shells being in pairs; and they -are in a layer where there are no dead ones; and a little higher up -they are found, where they were thrown by the waves, all the dead -ones with their shells separated, near to where the rivers fell into -the sea, to a great depth; like the Arno which fell from the -Gonfolina near to Monte Lupo [Footnote: _Monte Lupo_, compare 970, -13; it is between Empoli and Florence.], where it left a deposit of -gravel which may still be seen, and which has agglomerated; and of -stones of various districts, natures, and colours and hardness, -making one single conglomerate. And a little beyond the sandstone -conglomerate a tufa has been formed, where it turned towards Castel -Florentino; farther on, the mud was deposited in which the shells -lived, and which rose in layers according to the levels at which the -turbid Arno flowed into that sea. And from time to time the bottom -of the sea was raised, depositing these shells in layers, as may be -seen in the cutting at Colle Gonzoli, laid open by the Arno which is -wearing away the base of it; in which cutting the said layers of -shells are very plainly to be seen in clay of a bluish colour, and -various marine objects are found there. And if the earth of our -hemisphere is indeed raised by so much higher than it used to be, it -must have become by so much lighter by the waters which it lost -through the rift between Gibraltar and Ceuta; and all the more the -higher it rose, because the weight of the waters which were thus -lost would be added to the earth in the other hemisphere. And if the -shells had been carried by the muddy deluge they would have been -mixed up, and separated from each other amidst the mud, and not in -regular steps and layers-- as we see them now in our time. - -The marine shells were not produced away from the sea. - -988. - -As to those who say that shells existed for a long time and were -born at a distance from the sea, from the nature of the place and of -the cycles, which can influence a place to produce such -creatures--to them it may be answered: such an influence could not -place the animals all on one line, except those of the same sort and -age; and not the old with the young, nor some with an operculum and -others without their operculum, nor some broken and others whole, -nor some filled with sea-sand and large and small fragments of other -shells inside the whole shells which remained open; nor the claws of -crabs without the rest of their bodies; nor the shells of other -species stuck on to them like animals which have moved about on -them; since the traces of their track still remain, on the outside, -after the manner of worms in the wood which they ate into. Nor would -there be found among them the bones and teeth of fish which some -call arrows and others serpents' tongues, nor would so many -[Footnote: I. Scilla argued against this hypothesis, which was still -accepted in his days; see: _La vana Speculazione, Napoli_ 1670.] -portions of various animals be found all together if they had not -been thrown on the sea shore. And the deluge cannot have carried -them there, because things that are heavier than water do not float -on the water. But these things could not be at so great a height if -they had not been carried there by the water, such a thing being -impossible from their weight. In places where the valleys have not -been filled with salt sea water shells are never to be seen; as is -plainly visible in the great valley of the Arno above Gonfolina; a -rock formerly united to Monte Albano, in the form of a very high -bank which kept the river pent up, in such a way that before it -could flow into the sea, which was afterwards at its foot, it formed -two great lakes; of which the first was where we now see the city of -Florence together with Prato and Pistoia, and Monte Albano. It -followed the rest of its bank as far as where Serravalle now stands. ->From the Val d'Arno upwards, as far as Arezzo, another lake was -formed, which discharged its waters into the former lake. It was -closed at about the spot where now we see Girone, and occupied the -whole of that valley above for a distance of 40 miles in length. -This valley received on its bottom all the soil brought down by the -turbid waters. And this is still to be seen at the foot of Prato -Magno; it there lies very high where the rivers have not worn it -away. Across this land are to be seen the deep cuts of the rivers -that have passed there, falling from the great mountain of Prato -Magno; in these cuts there are no vestiges of any shells or of -marine soil. This lake was joined with that of Perugia [Footnote: -See PI. CXIII.] - -A great quantity of shells are to be seen where the rivers flow into -the sea, because on such shores the waters are not so salt owing to -the admixture of the fresh water, which is poured into it. Evidence -of this is to be seen where, of old, the Appenines poured their -rivers into the Adriatic sea; for there in most places great -quantities of shells are to be found, among the mountains, together -with bluish marine clay; and all the rocks which are torn off in -such places are full of shells. The same may be observed to have -been done by the Arno when it fell from the rock of Gonfolina into -the sea, which was not so very far below; for at that time it was -higher than the top of San Miniato al Tedesco, since at the highest -summit of this the shores may be seen full of shells and oysters -within its flanks. The shells did not extend towards Val di Nievole, -because the fresh waters of the Arno did not extend so far. - -That the shells were not carried away from the sea by the deluge, -because the waters which came from the earth although they drew the -sea towards the earth, were those which struck its depths; because -the water which goes down from the earth, has a stronger current -than that of the sea, and in consequence is more powerful, and it -enters beneath the sea water and stirs the depths and carries with -it all sorts of movable objects which are to be found in the earth, -such as the above-mentioned shells and other similar things. And in -proportion as the water which comes from the land is muddier than -sea water it is stronger and heavier than this; therefore I see no -way of getting the said shells so far in land, unless they had been -born there. If you were to tell me that the river Loire [Footnote: -Leonardo has written Era instead of Loera or Loira--perhaps under -the mistaken idea that _Lo_ was an article.],which traverses France -covers when the sea rises more than eighty miles of country, because -it is a district of vast plains, and the sea rises about 20 braccia, -and shells are found in this plain at the distance of 80 miles from -the sea; here I answer that the flow and ebb in our Mediterranean -Sea does not vary so much; for at Genoa it does not rise at all, and -at Venice but little, and very little in Africa; and where it varies -little it covers but little of the country. - -The course of the water of a river always rises higher in a place -where the current is impeded; it behaves as it does where it is -reduced in width to pass under the arches of a bridge. - -Further researches (989-991). - -989. - -A CONFUTATION OF THOSE WHO SAY THAT SHELLS MAY HAVE BEEN CARRIED TO -A DISTANCE OF MANY DAYS' JOURNEY FROM THE SEA BY THE DELUGE, WHICH -WAS SO HIGH AS TO BE ABOVE THOSE HEIGHTS. - -I say that the deluge could not carry objects, native to the sea, up -to the mountains, unless the sea had already increased so as to -create inundations as high up as those places; and this increase -could not have occurred because it would cause a vacuum; and if you -were to say that the air would rush in there, we have already -concluded that what is heavy cannot remain above what is light, -whence of necessity we must conclude that this deluge was caused by -rain water, so that all these waters ran to the sea, and the sea did -not run up the mountains; and as they ran to the sea, they thrust -the shells from the shore of the sea and did not draw them to wards -themselves. And if you were then to say that the sea, raised by the -rain water, had carried these shells to such a height, we have -already said that things heavier than water cannot rise upon it, but -remain at the bottom of it, and do not move unless by the impact of -the waves. And if you were to say that the waves had carried them to -such high spots, we have proved that the waves in a great depth move -in a contrary direction at the bottom to the motion at the top, and -this is shown by the turbidity of the sea from the earth washed down -near its shores. Anything which is lighter than the water moves with -the waves, and is left on the highest level of the highest margin of -the waves. Anything which is heavier than the water moves, suspended -in it, between the surface and the bottom; and from these two -conclusions, which will be amply proved in their place, we infer -that the waves of the surface cannot convey shells, since they are -heavier than water. - -If the deluge had to carry shells three hundred and four hundred -miles from the sea, it would have carried them mixed with various -other natural objects heaped together; and we see at such distances -oysters all together, and sea-snails, and cuttlefish, and all the -other shells which congregate together, all to be found together and -dead; and the solitary shells are found wide apart from each other, -as we may see them on sea-shores every day. And if we find oysters -of very large shells joined together and among them very many which -still have the covering attached, indicating that they were left -here by the sea, and still living when the strait of Gibraltar was -cut through; there are to be seen, in the mountains of Parma and -Piacenza, a multitude of shells and corals, full of holes, and still -sticking to the rocks there. When I was making the great horse for -Milan, a large sack full was brought to me in my workshop by certain -peasants; these were found in that place and among them were many -preserved in their first freshness. - -Under ground, and under the foundations of buildings, timbers are -found of wrought beams and already black. Such were found in my time -in those diggings at Castel Fiorentino. And these had been in that -deep place before the sand carried by the Arno into the sea, then -covering the plain, had heen raised to such a height; and before the -plains of Casentino had been so much lowered, by the earth being -constantly carried down from them. - -[Footnote: These lines are written in the margin.] - -And if you were to say that these shells were created, and were -continually being created in such places by the nature of the spot, -and of the heavens which might have some influence there, such an -opinion cannot exist in a brain of much reason; because here are the -years of their growth, numbered on their shells, and there are large -and small ones to be seen which could not have grown without food, -and could not have fed without motion--and here they could not move -[Footnote: These lines are written in the margin.] - -990. - -That in the drifts, among one and another, there are still to be -found the traces of the worms which crawled upon them when they were -not yet dry. And all marine clays still contain shells, and the -shells are petrified together with the clay. From their firmness and -unity some persons will have it that these animals were carried up -to places remote from the sea by the deluge. Another sect of -ignorant persons declare that Nature or Heaven created them in these -places by celestial influences, as if in these places we did not -also find the bones of fishes which have taken a long time to grow; -and as if, we could not count, in the shells of cockles and snails, -the years and months of their life, as we do in the horns of bulls -and oxen, and in the branches of plants that have never been cut in -any part. Besides, having proved by these signs the length of their -lives, it is evident, and it must be admitted, that these animals -could not live without moving to fetch their food; and we find in -them no instrument for penetrating the earth or the rock where we -find them enclosed. But how could we find in a large snail shell the -fragments and portions of many other sorts of shells, of various -sorts, if they had not been thrown there, when dead, by the waves of -the sea like the other light objects which it throws on the earth? -Why do we find so many fragments and whole shells between layer and -layer of stone, if this had not formerly been covered on the shore -by a layer of earth thrown up by the sea, and which was afterwards -petrified? And if the deluge before mentioned had carried them to -these parts of the sea, you might find these shells at the boundary -of one drift but not at the boundary between many drifts. We must -also account for the winters of the years during which the sea -multiplied the drifts of sand and mud brought down by the -neighbouring rivers, by washing down the shores; and if you chose to -say that there were several deluges to produce these rifts and the -shells among them, you would also have to affirm that such a deluge -took place every year. Again, among the fragments of these shells, -it must be presumed that in those places there were sea coasts, -where all the shells were thrown up, broken, and divided, and never -in pairs, since they are found alive in the sea, with two valves, -each serving as a lid to the other; and in the drifts of rivers and -on the shores of the sea they are found in fragments. And within the -limits of the separate strata of rocks they are found, few in number -and in pairs like those which were left by the sea, buried alive in -the mud, which subsequently dried up and, in time, was petrified. - -991. - -And if you choose to say that it was the deluge which carried these -shells away from the sea for hundreds of miles, this cannot have -happened, since that deluge was caused by rain; because rain -naturally forces the rivers to rush towards the sea with all the -things they carry with them, and not to bear the dead things of the -sea shores to the mountains. And if you choose to say that the -deluge afterwards rose with its waters above the mountains, the -movement of the sea must have been so sluggish in its rise against -the currents of the rivers, that it could not have carried, floating -upon it, things heavier than itself; and even if it had supported -them, in its receding it would have left them strewn about, in -various spots. But how are we to account for the corals which are -found every day towards Monte Ferrato in Lombardy, with the holes of -the worms in them, sticking to rocks left uncovered by the currents -of rivers? These rocks are all covered with stocks and families of -oysters, which as we know, never move, but always remain with one of -their halves stuck to a rock, and the other they open to feed -themselves on the animalcules that swim in the water, which, hoping -to find good feeding ground, become the food of these shells. We do -not find that the sand mixed with seaweed has been petrified, -because the weed which was mingled with it has shrunk away, and this -the Po shows us every day in the debris of its banks. - -Other problems (992-994). - -992. - -Why do we find the bones of great fishes and oysters and corals and -various other shells and sea-snails on the high summits of mountains -by the sea, just as we find them in low seas? - -993. - -You now have to prove that the shells cannot have originated if not -in salt water, almost all being of that sort; and that the shells in -Lombardy are at four levels, and thus it is everywhere, having been -made at various times. And they all occur in valleys that open -towards the seas. - -994. - ->From the two lines of shells we are forced to say that the earth -indignantly submerged under the sea and so the first layer was made; -and then the deluge made the second. - -[Footnote: This note is in the early writing of about 1470--1480. On -the same sheet are the passages No. 1217 and 1219. Compare also No. -1339. All the foregoing chapters are from Manuscripts of about 1510. -This explains the want of connection and the contradiction between -this and the foregoing texts.] - -VII. - -ON THE ATMOSPHERE. - -Constituents of the atmosphere. - -995. - -That the brightness of the air is occasioned by the water which has -dissolved itself in it into imperceptible molecules. These, being -lighted by the sun from the opposite side, reflect the brightness -which is visible in the air; and the azure which is seen in it is -caused by the darkness that is hidden beyond the air. [Footnote: -Compare Vol. I, No. 300.] - -On the motion of air (996--999). - -996. - -That the return eddies of wind at the mouth of certain valleys -strike upon the waters and scoop them out in a great hollow, whirl -the water into the air in the form of a column, and of the colour of -a cloud. And I saw this thing happen on a sand bank in the Arno, -where the sand was hollowed out to a greater depth than the stature -of a man; and with it the gravel was whirled round and flung about -for a great space; it appeared in the air in the form of a great -bell-tower; and the top spread like the branches of a pine tree, and -then it bent at the contact of the direct wind, which passed over -from the mountains. - -997. - -The element of fire acts upon a wave of air in the same way as the -air does on water, or as water does on a mass of sand --that is -earth; and their motions are in the same proportions as those of the -motors acting upon them. - -998. - -OF MOTION. - -I ask whether the true motion of the clouds can be known by the -motion of their shadows; and in like manner of the motion of the -sun. - -999. - -To know better the direction of the winds. [Footnote: In connection -with this text I may here mention a hygrometer, drawn and probably -invented by Leonardo. A facsimile of this is given in Vol. I, p. 297 -with the note: _'Modi di pesare l'arie eddi sapere quando s'a -arrompere il tepo'_ (Mode of weighing the air and of knowing when -the weather will change); by the sponge _"Spugnea"_ is written.] - -The globe an organism. - -1000. - -Nothing originates in a spot where there is no sentient, vegetable -and rational life; feathers grow upon birds and are changed every -year; hairs grow upon animals and are changed every year, excepting -some parts, like the hairs of the beard in lions, cats and their -like. The grass grows in the fields, and the leaves on the trees, -and every year they are, in great part, renewed. So that we might -say that the earth has a spirit of growth; that its flesh is the -soil, its bones the arrangement and connection of the rocks of which -the mountains are composed, its cartilage the tufa, and its blood -the springs of water. The pool of blood which lies round the heart -is the ocean, and its breathing, and the increase and decrease of -the blood in the pulses, is represented in the earth by the flow and -ebb of the sea; and the heat of the spirit of the world is the fire -which pervades the earth, and the seat of the vegetative soul is in -the fires, which in many parts of the earth find vent in baths and -mines of sulphur, and in volcanoes, as at Mount Aetna in Sicily, and -in many other places. - -[Footnote: Compare No. 929.] - -_XVII._ - -_Topographical Notes._ - -_A large part of the texts published in this section might perhaps -have found their proper place in connection with the foregoing -chapters on Physical Geography. But these observations on Physical -Geography, of whatever kind they may be, as soon as they are -localised acquire a special interest and importance and particularly -as bearing on the question whether Leonardo himself made the -observations recorded at the places mentioned or merely noted the -statements from hearsay. In a few instances he himself tells us that -he writes at second hand. In some cases again, although the style -and expressions used make it seem highly probable that he has -derived his information from others-- though, as it seems to me, -these cases are not very numerous--we find, on the other hand, among -these topographical notes a great number of observations, about -which it is extremely difficult to form a decided opinion. Of what -the Master's life and travels may have been throughout his -sixty-seven years of life we know comparatively little; for a long -course of time, and particularly from about 1482 to 1486, we do not -even know with certainty that he was living in Italy. Thus, from a -biographical point of view a very great interest attaches to some of -the topographical notes, and for this reason it seemed that it would -add to their value to arrange them in a group by themselves. -Leonardo's intimate knowledge with places, some of which were -certainly remote from his native home, are of importance as -contributing to decide the still open question as to the extent of -Leonardo's travels. We shall find in these notes a confirmation of -the view, that the MSS. in which the Topographical Notes occur are -in only a very few instances such diaries as may have been in use -during a journey. These notes are mostly found in the MSS. books of -his later and quieter years, and it is certainly remarkable that -Leonardo is very reticent as to the authorities from whom he quotes -his facts and observations: For instance, as to the Straits of -Gibraltar, the Nile, the Taurus Mountains and the Tigris and -Euphrates. Is it likely that he, who declared that in all scientific -research, his own experience should be the foundation of his -statements (see XIX Philosophy No. 987--991,) should here have made -an exception to this rule without mentioning it?_ - -_As for instance in the discussion as to the equilibrium of the mass -of water in the Mediterranean Sea--a subject which, it may be -observed, had at that time attracted the interest and study of -hardly any other observer. The acute remarks, in Nos. 985--993, on -the presence of shells at the tops of mountains, suffice to -prove--as it seems to me--that it was not in his nature to allow -himself to be betrayed into wide generalisations, extending beyond -the limits of his own investigations, even by such brilliant results -of personal study._ - -_Most of these Topographical Notes, though suggesting very careful -and thorough research, do not however, as has been said, afford -necessarily indisputable evidence that that research was Leonardo's -own. But it must be granted that in more than one instance -probability is in favour of this idea._ - -_Among the passages which treat somewhat fully of the topography of -Eastern places by far the most interesting is a description of the -Taurus Mountains; but as this text is written in the style of a -formal report and, in the original, is associated with certain -letters which give us the history of its origin, I have thought it -best not to sever it from that connection. It will be found under -No. XXI (Letters)._ - -_That Florence, and its neighbourhood, where Leonardo spent his -early years, should be nowhere mentioned except in connection with -the projects for canals, which occupied his attention for some short -time during the first ten years of the XVIth century, need not -surprise us. The various passages relating to the construction of -canals in Tuscany, which are put together at the beginning, are -immediately followed by those which deal with schemes for canals in -Lombardy; and after these come notes on the city and vicinity of -Milan as well as on the lakes of North Italy._ - -_The notes on some towns of Central Italy which Leonardo visited in -1502, when in the service of Cesare Borgia, are reproduced here in -the same order as in the note book used during these travels (MS. -L., Institut de France). These notes have but little interest in -themselves excepting as suggesting his itinerary. The maps of the -districts drawn by Leonardo at the time are more valuable (see No. -1054 note). The names on these maps are not written from right to -left, but in the usual manner, and we are permitted to infer that -they were made in obedience to some command, possibly for the use of -Cesare Borgia himself; the fact that they remained nevertheless in -Leonardo's hands is not surprising when we remember the sudden -political changes and warlike events of the period. There can be no -doubt that these maps, which are here published for the first time, -are original in the strictest sense of the word, that is to say -drawn from observations of the places themselves; this is proved by -the fact--among others--that we find among his manuscripts not only -the finished maps themselves but the rough sketches and studies for -them. And it would perhaps be difficult to point out among the -abundant contributions to geographical knowledge published during -the XVIth century, any maps at all approaching these in accuracy and -finish._ - -_The interesting map of the world, so far as it was then known, -which is among the Leonardo MSS. at Windsor (published in the_ -'Archaeologia' _Vol. XI) cannot be attributed to the Master, as the -Marchese Girolamo d'Adda has sufficiently proved; it has not -therefore been reproduced here._ - -_Such of Leonardo's observations on places in Italy as were made -before or after his official travels as military engineer to Cesare -Borgia, have been arranged in alphabetical order, under Nos. -1034-1054. The most interesting are those which relate to the Alps -and the Appenines, Nos. 1057-1068._ - -_Most of the passages in which France is mentioned have hitherto -remained unknown, as well as those which treat of the countries -bordering on the Mediterranean, which come at the end of this -section. Though these may be regarded as of a more questionable -importance in their bearing on the biography of the Master than -those which mention places in France, it must be allowed that they -are interesting as showing the prominent place which the countries -of the East held in his geographical studies. He never once alludes -to the discovery of America._ - -I. - -ITALY. - -Canals in connection with the Arno (1001-1008). - -1001. - -CANAL OF FLORENCE. - -Sluices should be made in the valley of la Chiana at Arezzo, so that -when, in the summer, the Arno lacks water, the canal may not remain -dry: and let this canal be 20 braccia wide at the bottom, and at the -top 30, and 2 braccia deep, or 4, so that two of these braccia may -flow to the mills and the meadows, which will benefit the country; -and Prato, Pistoia and Pisa, as well as Florence, will gain two -hundred thousand ducats a year, and will lend a hand and money to -this useful work; and the Lucchese the same, for the lake of Sesto -will be navigable; I shall direct it to Prato and Pistoia, and cut -through Serravalle and make an issue into the lake; for there will -be no need of locks or supports, which are not lasting and so will -always be giving trouble in working at them and keeping them up. - -And know that in digging this canal where it is 4 braccia deep, it -will cost 4 dinari the square braccio; for twice the depth 6 dinari, -if you are making 4 braccia [Footnote: This passage is illustrated -by a slightly sketched map, on which these places are indicated from -West to East: Pisa, Luccha, Lago, Seravalle, Pistoja, Prato, -Firenze.] and there are but 2 banks; that is to say one from the -bottom of the trench to the surface of the edges of it, and the -other from these edges to the top of the ridge of earth which will -be raised on the margin of the bank. And if this bank were of double -the depth only the first bank will be increased, that is 4 braccia -increased by half the first cost; that is to say that if at first 4 -dinari were paid for 2 banks, for 3 it would come to 6, at 2 dinari -the bank, if the trench measured 16 braccia at the bottom; again, if -the trench were 16 braccia wide and 4 deep, coming to 4 lire for the -work, 4 Milan dinari the square braccio; a trench which was 32 -braccia at the bottom would come to 8 dinari the square braccio. - -1002. - ->From the wall of the Arno at [the gate of] la Giustizia to the bank -of the Arno at Sardigna where the walls are, to the mills, is 7400 -braccia, that is 2 miles and 1400 braccia and beyond the Arno is -5500 braccia. - -[Footnote: 2. _Giustizia_. By this the Porta della Giustizia seems -to be meant; from the XVth to the XVIth centuries it was also -commonly known as Porta Guelfa, Porta San Francesco del Renaio, -Porta Nuova, and Porta Reale. It was close to the Arno opposite to -the Porta San Niccolo, which still exists.] - -1003. - -By guiding the Arno above and below a treasure will be found in each -acre of ground by whomsoever will. - -1004. - -The wall of the old houses runs towards the gate of San Nicolo. - -[Footnote: By the side of this text there is an indistinct sketch, -resembling that given under No.973. On the bank is written the word -_Casace_. There then follows in the original a passage of 12 lines -in which the consequences of the windings of the river are -discussed. A larger but equally hasty diagram on the same page -represents the shores of the Arno inside Florence as in two parallel -lines. Four horizontal lines indicate the bridges. By the side these -measures are stated in figures: I. (at the Ponte alla Carraja): -_230--largho br. 12 e 2 di spoda e 14 di pile e a 4 pilastri;_ 2. -(at the Ponte S. Trinita); _l88--largho br. 15 e 2 di spode he 28 -di pilastri for delle spode e pilastri so 2;_ 3. (at the Ponte -vecchio); _pote lung br. 152 e largo;_ 4. (at the Ponte alle -Grazie): _290 ellargo 12 e 2 di spode e 6 di pili._ - -There is, in MS. W. L. 2l2b, a sketched plan of Florence, with the -following names of gates: -_Nicholo--Saminiato--Giorgo--Ghanolini--Porta San Fredian ---Prato--Faenza--Ghallo--Pinti--Giustitia_.] - -1005. - -The ruined wall is 640 braccia; 130 is the wall remaining with the -mill; 300 braccia were broken in 4 years by Bisarno. - -1006. - -They do not know why the Arno will never remain in a channel. It is -because the rivers which flow into it deposit earth where they -enter, and wear it away on the opposite side, bending the river in -that direction. The Arno flows for 6 miles between la Caprona and -Leghorn; and for 12 through the marshes, which extend 32 miles, and -16 from La Caprona up the river, which makes 48; by the Arno from -Florence beyond 16 miles; to Vico 16 miles, and the canal is 5; from -Florence to Fucechio it is 40 miles by the river Arno. - -56 miles by the Arno from Florence to Vico; by the Pistoia canal it -is 44 miles. Thus it is 12 miles shorter by the canal than by the -Arno. - -[Footnote: This passage is written by the side of a map washed in -Indian ink, of the course of the Arno; it is evidently a sketch for -a completer map. - -These investigations may possibly be connected with the following -documents. _Francesco Guiducci alla Balia di Firenze. Dal Campo -contro Pisa_ 24 _Luglio_ 1503 (_Archivio di Stato, Firenze, Lettere -alla Balia_; published by J. GAYE, _Carteggio inedito d'Artisti, -Firenze_ 1840, _Tom. II_, p. 62): _Ex Castris, Franciscus -Ghuiduccius,_ 24. _Jul._ 1503. _Appresso fu qui hieri con una di V. -Signoria Alexandro degli Albizi insieme con Leonardo da Vinci et -certi altri, et veduto el disegno insieme con el ghovernatore, doppo -molte discussioni et dubii conclusesi che l'opera fussi molto al -proposito, o si veramente Arno volgersi qui, o restarvi con un -canale, che almeno vieterebbe che le colline da nemici non -potrebbono essere offese; come tucto referiranno loro a bocha V. S._ - -And, _Archivio di Stato, Firenze, Libro d'Entrata e Uscita di cassa -de' Magnifici Signori di luglio e agosto_ - -1503 _a_ 51 _T.: Andata di Leonardo al Campo sotto Pisa. Spese -extraordinarie dieno dare a di XXVI di luglio L. LVI sol. XII per -loro a Giovanni Piffero; e sono per tanti, asegnia avere spexi in -vetture di sei chavalli a spese di vitto per andare chon Lionardo da -Vinci a livellare Arno in quello di Pisa per levallo del lilo suo._ -(Published by MILANESI, _Archivio Storico Italiano, Serie III, Tom. -XVI._} VASARI asserts: _(Leonardo) fu il primo ancora, che -giovanetto discorresse sopra il fiume d'Arno per metterlo in canale -da Pisa a Fiorenza_ (ed. SANSONI, IV, 20). - -The passage above is in some degree illustrated by the map on Pl. -CXII, where the course of the Arno westward from Empoli is shown.] - -1007. - -The eddy made by the Mensola, when the Arno is low and the Mensola -full. - -[Footnote: _Mensola_ is a mountain stream which falls into the Arno -about a mile and a half above Florence. - -A=Arno, I=Isola, M=Mvgone, P=Pesa, N=Mesola.] - -1008. - -That the river which is to be turned from one place to another must -be coaxed and not treated roughly or with violence; and to do this a -sort of floodgate should be made in the river, and then lower down -one in front of it and in like manner a third, fourth and fifth, so -that the river may discharge itself into the channel given to it, or -that by this means it may be diverted from the place it has damaged, -as was done in Flanders--as I was told by Niccolo di Forsore. - -How to protect and repair the banks washed by the water, as below -the island of Cocomeri. - -Ponte Rubaconte (Fig. 1); below [the palaces] Bisticci and Canigiani -(Fig. 2). Above the flood gate of la Giustizia (Fig. 3); _a b_ is a -sand bank opposite the end of the island of the Cocomeri in the -middle of the Arno (Fig. 4). [Footnote: The course of the river Arno -is also discussed in Nos. 987 and 988.] - -Canals in the Milanese (1009-1013). - -1009. - -The canal of San Cristofano at Milan made May 3rd 1509. [Footnote: -This observation is written above a washed pen and ink drawing which -has been published as Tav. VI in the _,,Saggio."_ The editors of -that work explain the drawing as _"uno Studio di bocche per -estrazione d'acqua."_] - -1010. - -OF THE CANAL OF MARTESANA. - -By making the canal of Martesana the water of the Adda is greatly -diminished by its distribution over many districts for the -irrigation of the fields. A remedy for this would be to make several -little channels, since the water drunk up by the earth is of no more -use to any one, nor mischief neither, because it is taken from no -one; and by making these channels the water which before was lost -returns again and is once more serviceable and useful to men. - -[Footnote: _"el navilio di Martagano"_ is also mentioned in a note -written in red chalk, MS. H2 17a Leonardo has, as it seems, little -to do with Lodovico il Moro's scheme to render this canal navigable. -The canal had been made in 1460 by Bertonino da Novara. Il Moro -issued his degree in 1493, but Leonardo's notes about this canal -were, with the exception of one (No. 1343), written about sixteen -years later.] - -1011. - -No canal which is fed by a river can be permanent if the river -whence it originates is not wholly closed up, like the canal of -Martesana which is fed by the Ticino. - -1012. - ->From the beginning of the canal to the mill. - ->From the beginning of the canal of Brivio to the mill of Travaglia -is 2794 trabochi, that is 11176 braccia, which is more than 3 miles -and two thirds; and here the canal is 57 braccia higher than the -surface of the water of the Adda, giving a fall of two inches in -every hundred trabochi; and at that spot we propose to take the -opening of our canal. - -[Footnote: The following are written on the sketches: At the place -marked _N: navilio da dacquiue_ (canal of running water); at _M: -molin del Travaglia_ (Mill of Travaglia); at _R: rochetta ssanta -maria_ (small rock of Santa Maria); at _A: Adda;_ at _L: Lagho di -Lecho ringorgato alli 3 corni in Adda,--Concha perpetua_ (lake of -Lecco overflowing at Tre Corni, in Adda,-- a permanent sluice). Near -the second sketch, referring to the sluice near _Q: qui la chatena -ttalie d'u peso_ (here the chain is in one piece). At _M_ in the -lower sketch: _mol del travaglia, nel cavare la concha il tereno -ara chotrapero co cassa d'acqua._ (Mill of Travaglia, in digging -out the sluice the soil will have as a counterpoise a vessel of -water).] - -1013. - -If it be not reported there that this is to be a public canal, it -will be necessary to pay for the land; [Footnote 3: _il re_. Louis -XII or Francis I of France. It is hardly possible to doubt that the -canals here spoken of were intended to be in the Milanese. Compare -with this passage the rough copy of a letter by Leonardo, to the -_"Presidente dell' Ufficio regolatore dell' acqua"_ on No. 1350. See -also the note to No. 745, 1. 12.] and the king will pay it by -remitting the taxes for a year. - -Estimates and preparatory studies for canals (1014. 1015). - -1014. - -CANAL. - -The canal which may be 16 braccia wide at the bottom and 20 at the -top, we may say is on the average 18 braccia wide, and if it is 4 -braccia deep, at 4 dinari the square braccia; it will only cost 900 -ducats, to excavate by the mile, if the square braccio is calculated -in ordinary braccia; but if the braccia are those used in measuring -land, of which every 4 are equal to 4 1/2 and if by the mile we -understand three thousand ordinary braccia; turned into land -braccia, these 3000 braccia will lack 1/4; there remain 2250 -braccia, which at 4 dinari the braccio will amount to 675 ducats a -mile. At 3 dinari the square braccio, the mile will amount to 506 -1/4 ducats so that the excavation of 30 miles of the canal will -amount to 15187 1/2 ducats. - -1015. - -To make the great canal, first make the smaller one and conduct into -it the waters which by a wheel will help to fill the great one. - -Notes on buildings in Milan (1016-1019) - -1016. - -Indicate the centre of Milan. - -Moforte--porta resa--porta nova--strada nova--navilio--porta -cumana--barco--porta giovia--porta vercellina--porta sco -Anbrogio--porta Tesinese--torre dell' Imperatore-- porta -Lodovica--acqua. - -[Footnote: See Pl. CIX. The original sketch is here reduced to about -half its size. The gates of the town are here named, beginning at -the right hand and following the curved line. In the bird's eye view -of Milan below, the cathedral is plainly recognisable in the middle; -to the right is the tower of San Gottardo. The square, above the -number 9147, is the Lazzaretto, which was begun in 1488. On the left -the group of buildings of the _'Castello'_ will be noticed. On the -sketched Plan of Florence (see No. 1004 note) Leonardo has written -on the margin the following names of gates of Milan: Vercellina ---Ticinese--Ludovica--Romana--Orientale-- -Nova--Beatrice--Cumana--Compare too No. 1448, 11. 5, 12.] - -1017. - -The moat of Milan. - -Canal 2 braccia wide. - -The castle with the moats full. - -The filling of the moats of the Castle of Milan. - -1018. - -THE BATH. - -To heat the water for the stove of the Duchess take four parts of -cold water to three parts of hot water. - -[Footnote: _Duchessa di Milano_, Beatrice d'Este, wife of Ludovico -il Moro to whom she was married, in 1491. She died in June 1497.] - -1019. - -In the Cathedral at the pulley of the nail of the cross. - -Item. - -To place the mass _v r_ in the... - -[Footnote: On this passage AMORETTI remarks _(Memorie Storiche_ -chap. IX): _Nell'anno stesso lo veggiamo formare un congegno di -carucole e di corde, con cui trasportare in piu venerabile e piu -sicuro luogo, cioe nell'ultima arcata della nave di mezzo della -metropolitana, la sacra reliquia del Santo Chiodo, che ivi ancor si -venera. Al fol. 15 del codice segnato Q. R. in 16, egli ci ha -lasciata di tal congegno una doppia figura, cioe una di quattro -carucole, e una di tre colle rispettive corde, soggiugnandovi: in -Domo alla carucola del Chiodo della Croce._ - -AMORETTI'S views as to the mark on the MS, and the date when it was -written are, it may be observed, wholly unfounded. The MS. L, in -which it occurs, is of the year 1502, and it is very unlikely that -Leonardo was in Milan at that time; this however would not prevent -the remark, which is somewhat obscure, from applying to the -Cathedral at Milan.] - -1020. - -OF THE FORCE OF THE VACUUM FORMED IN A MOMENT. - -I saw, at Milan, a thunderbolt fall on the tower della Credenza on -its Northern side, and it descended with a slow motion down that -side, and then at once parted from that tower and carried with it -and tore away from that wall a space of 3 braccia wide and two deep; -and this wall was 4 braccia thick and was built of thin and small -old bricks; and this was dragged out by the vacuum which the flame -of the thunderbolt had caused, &c. - -[Footnote: With reference to buildings at Milan see also Nos. 751 -and 756, and Pl. XCV, No. 2 (explained on p. 52), Pl. C (explained -on pages 60-62). See also pages 25, 39 and 40.] - -Remarks on natural phenomena in and near Milan (1021. 1022). - -1021. - -I have already been to see a great variety (of atmospheric effects). -And lately over Milan towards Lago Maggiore I saw a cloud in the -form of an immense mountain full of rifts of glowing light, because -the rays of the sun, which was already close to the horizon and red, -tinged the cloud with its own hue. And this cloud attracted to it -all the little clouds that were near while the large one did not -move from its place; thus it retained on its summit the reflection -of the sunlight till an hour and a half after sunset, so immensely -large was it; and about two hours after sunset such a violent wind -arose, that it was really tremendous and unheard of. - -[Footnote: _di arie_ is wanting in the original but may safely be -inserted in the context, as the formation of clouds is under -discussion before this text.] - -1022. - -On the 10th day of December at 9 o'clock a. m. fire was set to the -place. - -On the l8th day of December 1511 at 9 o'clock a. m. this second fire -was kindled by the Swiss at Milan at the place called DCXC. -[Footnote: With these two texts, (l. 1--2 and l. 3--5 are in the -original side by side) there are sketches of smoke wreaths in red -chalk.] - -Note on Pavia. - -1023. - -The chimneys of the castle of Pavia have 6 rows of openings and from -each to the other is one braccio. - -[Footnote: Other notes relating to Pavia occur on p. 43 and p. 53 -(Pl. XCVIII, No. 3). Compare No. 1448, 26.] - -Notes on the Sforzesca near Vigevano (1024-1028). - -1024. - -On the 2nd day of February 1494. At Sforzesca I drew twenty five -steps, 2/3 braccia to each, and 8 braccia wide. - -[Footnote: See Pl. CX, No. 2. The rest of the notes on this page -refer to the motion of water. On the lower sketch we read: 4 _br._ -(four braccia) and _giara_ (for _ghiaja_, sand, gravel).] - -1025. - -The vineyards of Vigevano on the 20th day of March 1494. - -[Footnote: On one side there is an effaced sketch in red chalk.] - -1026. - -To lock up a butteris at Vigevano. - -1027. - -Again if the lowest part of the bank which lies across the current -of the waters is made in deep and wide steps, after the manner of -stairs, the waters which, in their course usually fall -perpendicularly from the top of such a place to the bottom, and wear -away the foundations of this bank can no longer descend with a blow -of too great a force; and I find the example of this in the stairs -down which the water falls in the fields at Sforzesca at Vigevano -over which the running water falls for a height of 50 braccia. - -1028. - -Stair of Vigevano below La Sforzesca, 130 steps, 1/4 braccio high -and 1/2 braccio wide, down which the water falls, so as not to wear -away anything at the end of its fall; by these steps so much soil -has come down that it has dried up a pool; that is to say it has -filled it up and a pool of great depth has been turned into meadows. - -Notes on the North Italian lake. (1029-1033) - -1029. - -In many places there are streams of water which swell for six hours -and ebb for six hours; and I, for my part, have seen one above the -lake of Como called Fonte Pliniana, which increases and ebbs, as I -have said, in such a way as to turn the stones of two mills; and -when it fails it falls so low that it is like looking at water in a -deep pit. - -[Footnote: The fountain is known by this name to this day: it is -near Torno, on the Eastern shore of Como. The waters still rise and -fall with the flow and ebb of the tide as Pliny described it (Epist. -IV, 30; Hist. Nat. II, 206).] - -1030. - -LAKE OF COMO. VALLEY OF CHIAVENNA. - -Above the lake of Como towards Germany is the valley of Chiavenna -where the river Mera flows into this lake. Here are barren and very -high mountains, with huge rocks. Among these mountains are to be -found the water-birds called gulls. Here grow fir trees, larches and -pines. Deer, wildgoats, chamois, and terrible bears. It is -impossible to climb them without using hands and feet. The peasants -go there at the time of the snows with great snares to make the -bears fall down these rocks. These mountains which very closely -approach each other are parted by the river. They are to the right -and left for the distance of 20 miles throughout of the same nature. ->From mile to mile there are good inns. Above on the said river there -are waterfalls of 400 braccia in height, which are fine to see; and -there is good living at 4 soldi the reckoning. This river brings -down a great deal of timber. - -VAL SASINA. - -Val Sasina runs down towards Italy; this is almost the same form and -character. There grow here many _mappello_ and there are great ruins -and falls of water [Footnote 14: The meaning of _mappello_ is -unknown.]. - -VALLEY OF INTROZZO. - -This valley produces a great quantity of firs, pines and larches; -and from here Ambrogio Fereri has his timber brought down; at the -head of the Valtellina are the mountains of Bormio, terrible and -always covered with snow; marmots (?) are found there. - -BELLAGGIO. - -Opposite the castle Bellaggio there is the river Latte, which falls -from a height of more than 100 braccia from the source whence it -springs, perpendicularly, into the lake with an inconceivable roar -and noise. This spring flows only in August and September. - -VALTELLINA. - -Valtellina, as it is called, is a valley enclosed in high and -terrible mountains; it produces much strong wine, and there is so -much cattle that the natives conclude that more milk than wine grows -there. This is the valley through which the Adda passes, which first -runs more than 40 miles through Germany; this river breeds the fish -_temolo_ which live on silver, of which much is to be found in its -sands. In this country every one can sell bread and wine, and the -wine is worth at most one soldo the bottle and a pound of veal one -soldo, and salt ten dinari and butter the same and their pound is 30 -ounces, and eggs are one soldo the lot. - -1031. - -At BORMIO. - -At Bormio are the baths;--About eight miles above Como is the -Pliniana, which increases and ebbs every six hours, and its swell -supplies water for two mills; and its ebbing makes the spring dry -up; two miles higher up there is Nesso, a place where a river falls -with great violence into a vast rift in the mountain. These -excursions are to be made in the month of May. And the largest bare -rocks that are to be found in this part of the country are the -mountains of Mandello near to those of Lecco, and of Gravidona -towards Bellinzona, 30 miles from Lecco, and those of the valley of -Chiavenna; but the greatest of all is that of Mandello, which has at -its base an opening towards the lake, which goes down 200 steps, and -there at all times is ice and wind. - -IN VAL SASINA. - -In Val Sasina, between Vimognio and Introbbio, to the right hand, -going in by the road to Lecco, is the river Troggia which falls from -a very high rock, and as it falls it goes underground and the river -ends there. 3 miles farther we find the buildings of the mines of -copper and silver near a place called Pra' Santo Pietro, and mines -of iron and curious things. La Grigna is the highest mountain there -is in this part, and it is quite bare. - -[Footnote: 1030 and 1031. From the character of the handwriting we -may conclude that these observations were made in Leonardo's youth; -and I should infer from their contents, that they were notes made in -anticipation of a visit to the places here described, and derived -from some person (unknown to us) who had given him an account of -them.] - -1032. - -The lake of Pusiano flows into the lake of Segrino [Footnote 3: The -statement about the lake Segrino is incorrect; it is situated in the -Valle Assina, above the lake of Pusiano.] and of Annone and of Sala. -The lake of Annone is 22 braccia higher at the surface of its water -than the surface of the water of the lake of Lecco, and the lake of -Pusiano is 20 braccia higher than the lake of Annone, which added to -the afore said 22 braccia make 42 braccia and this is the greatest -height of the surface of the lake of Pusiano above the surface of -the lake of Lecco. - -[Footnote: This text has in the original a slight sketch to -illustrate it.] - -1033. - -At Santa Maria in the Valley of Ravagnate [Footnote 2: _Ravagnate_ -(Leonardo writes _Ravagna_) in the Brianza is between Oggiono and -Brivio, South of the lake of Como. M. Ravaisson avails himself of -this note to prove his hypothesis that Leonardo paid two visits to -France. See Gazette des Beaux Arts, 1881 pag. 528: - -_Au recto du meme feuillet, on lit encore une note relative a une -vallee "nemonti brigatia"; il me semble qu'il s'agit bien des monts -de Briancon, le Brigantio des anciens. Briancon est sur la route de -Lyon en Italie. Ce fut par le mont Viso que passerent, en aout 1515, -les troupes francaises qui allaient remporter la victoire de -Marignan. - -Leonard de Vinci, ingenieur de Francois Ier, comme il l'avait ete de -Louis XII, aurait-il ete pour quelque chose dans le plan du celebre -passage des Alpes, qui eut lieu en aout 1515, et a la suite duquel -on le vit accompagner partout le chevaleresque vainqueur? Auraitil -ete appele par le jeune roi, de Rome ou l'artiste etait alors, des -son avenement au trone?_] in the mountains of Brianza are the rods -of chestnuts of 9 braccia and one out of an average of 100 will be -14 braccia. - -At Varallo di Ponbia near to Sesto on the Ticino the quinces are -white, large and hard. - -[Footnote 5: Varallo di Ponbia, about ten miles South of Arona is -distinct from Varallo the chief town in the Val di Sesia.] - -Notes on places in Central Italy, visited in 1502 (1034-1054). - -1034. - -Pigeon-house at Urbino, the 30th day of July 1502. [Footnote: An -indistinct sketch is introduced with this text, in the original, in -which the word _Scolatoro_ (conduit) is written.] - -1035. - -Made by the sea at Piombino. [Footnote: Below the sketch there are -eleven lines of text referring to the motion of waves.] - -1036. - -Acquapendente is near Orvieto. [Footnote: _Acquapendente_ is about -10 miles West of Orvieto, and is to the right in the map on Pl. -CXIII, near the lake of Bolsena.] - -1037. - -The rock of Cesena. [Footnote: See Pl. XCIV No. 1, the lower sketch. -The explanation of the upper sketch is given on p. 29.] - -1038. - -Siena, _a b_ 4 braccia, _a c_ 10 braccia. Steps at [the castle of] -Urbino. [Footnote: See Pl. CX No. 3; compare also No. 765.] - -1039. - -The bell of Siena, that is the manner of its movement, and the place -of the attachment of the clapper. [Footnote: The text is accompanied -by an indistinct sketch.] - -1040. - -On St. Mary's day in the middle of August, at Cesena, 1502. -[Footnote: See Pl. CX, No. 4.] - -1041. - -Stairs of the [palace of the] Count of Urbino,--rough. [Footnote: -The text is accompanied by a slight sketch.] - -1042. - -At the fair of San Lorenzo at Cesena. 1502. - -1043. - -Windows at Cesena. [Footnote: There are four more lines of text -which refer to a slightly sketched diagram.] - -1044. - -At Porto Cesenatico, on the 6th of September 1502 at 9 o'clock a. m. - -The way in which bastions ought to project beyond the walls of the -towers to defend the outer talus; so that they may not be taken by -artillery. - -[Footnote: An indistinct sketch, accompanies this passage.] - -1045. - -The rock of the harbour of Cesena is four points towards the South -West from Cesena. - -1046. - -In Romagna, the realm of all stupidity, vehicles with four wheels -are used, of which O the two in front are small and two high ones -are behind; an arrangement which is very unfavourable to the motion, -because on the fore wheels more weight is laid than on those behind, -as I showed in the first of the 5th on "Elements". - -1047. - -Thus grapes are carried at Cesena. The number of the diggers of the -ditches is [arranged] pyramidically. [Footnote: A sketch, -representing a hook to which two bunches of grapes are hanging, -refers to these first two lines. Cesena is mentioned again Fol. 82a: -_Carro da Cesena_ (a cart from Cesena).] - -1048. - -There might be a harmony of the different falls of water as you saw -them at the fountain of Rimini on the 8th day of August, 1502. - -1049. - -The fortress at Urbino. [Footnote: 1049. In the original the text is -written inside the sketch in the place here marked _n_.] - -1050. - -Imola, as regards Bologna, is five points from the West, towards the -North West, at a distance of 20 miles. - -Castel San Piero is seen from Imola at four points from the West -towards the North West, at a distance of 7 miles. - -Faenza stands with regard to Imola between East and South East at a -distance of ten miles. Forli stands with regard to Faenza between -South East and East at a distance of 20 miles from Imola and ten -from Faenza. - -Forlimpopoli lies in the same direction at 25 miles from Imola. - -Bertinoro, as regards Imola, is five points from the East to wards -the South East, at 27 miles. - -1051. - -Imola as regards Bologna is five points from the West towards the -North West at a distance of 20 miles. - -Castel San Pietro lies exactly North West of Imola, at a distance of -7 miles. - -Faenza, as regards Imola lies exactly half way between the East and -South East at a distance of 10 miles; and Forli lies in the same -direction from Imola at a distance of 20 miles; and Forlimpopolo -lies in the same direction from Forli at a distance of 25 miles. - -Bertinoro is seen from Imola two points from the East towards the -South East at a distance of 27 miles. - -[Footnote: Leonardo inserted this passage on the margin of the -circular plan, in water colour, of Imola--see Pl. CXI No. 1.--In the -original the fields surrounding the town are light green; the moat, -which surrounds the fortifications and the windings of the river -Santerno, are light blue. The parts, which have come out blackish -close to the river are yellow ochre in the original. The dark groups -of houses inside the town are red. At the four points of the compass -drawn in the middle of the town Leonardo has written (from right to -left): _Mezzodi_ (South) at the top; to the left _Scirocho_ (South -east), _levante_ (East), _Greco_ (North East), _Septantrione_ -(North), _Maesstro_ (North West), _ponente_ (West) _Libecco_ (South -West). The arch in which the plan is drawn is, in the original, 42 -centimetres across. - -At the beginning of October 1502 Cesare Borgia was shut up in Imola -by a sudden revolt of the Condottieri, and it was some weeks before -he could release himself from this state of siege (see Gregorovius, -_Geschichte der Stadt Rom im Mittelalter_, Vol. VII, Book XIII, 5, -5). - -Besides this incident Imola plays no important part in the history -of the time. I therefore think myself fully justified in connecting -this map, which is at Windsor, with the siege of 1502 and with -Leonardo's engagements in the service of Cesare Borgia, because a -comparison of these texts, Nos. 1050 and 1051, raise, I believe, the -hypothesis to a certainty.] - -1052. - ->From Bonconventi to Casa Nova are 10 miles, from Casa Nova to Chiusi -9 miles, from Chiusi to Perugia, from, Perugia to Santa Maria degli -Angeli, and then to Fuligno. [Footnote: Most of the places here -described lie within the district shown in the maps on Pl. CXIII.] - -1053. - -On the first of August 1502, the library at Pesaro. - -1054. - -OF PAINTING. - -On the tops and sides of hills foreshorten the shape of the ground -and its divisions, but give its proper shape to what is turned -towards you. [Footnote: This passage evidently refers to the making -of maps, such as Pl. CXII, CXIII, and CXIV. There is no mention of -such works, it is true, excepting in this one passage of MS. L. But -this can scarcely be taken as evidence against my view that Leonardo -busied himself very extensively at that time in the construction of -maps; and all the less since the foregoing chapters clearly prove -that at a time so full of events Leonardo would only now and then -commit his observations to paper, in the MS. L. - -By the side of this text we find, in the original, a very indistinct -sketch, perhaps a plan of a position. Instead of this drawing I have -here inserted a much clearer sketch of a position from the same MS., -L. 82b and 83a. They are the only drawings of landscape, it may be -noted, which occur at all in that MS.] - -Alessandria in Piedmont (1055. 1056). - -1055. - -At Candia in Lombardy, near Alessandria della Paglia, in making a -well for Messer Gualtieri [Footnote 2: Messer Gualtieri, the same -probably as is mentioned in Nos. 672 and 1344.] of Candia, the -skeleton of a very large boat was found about 10 braccia -underground; and as the timber was black and fine, it seemed good to -the said Messer Gualtieri to have the mouth of the well lengthened -in such a way as that the ends of the boat should be uncovered. - -1056. - -At Alessandria della Paglia in Lombardy there are no stones for -making lime of, but such as are mixed up with an infinite variety of -things native to the sea, which is now more than 200 miles away. - -The Alps (1057-1062). - -1057. - -At Monbracco, above Saluzzo,--a mile above the Certosa, at the foot -of Monte Viso, there is a quarry of flakey stone, which is as white -as Carrara marble, without a spot, and as hard as porphyry or even -harder; of which my worthy gossip, Master Benedetto the sculptor, -has promised to give me a small slab, for the colours, the second -day of January 1511. - -[Footnote: Saluzzo at the foot of the Alps South of Turin.] - -[Footnote 9. 10.: _Maestro Benedetto scultore_; probably some native -of Northern Italy acquainted with the place here described. Hardly -the Florentine sculptor Benedetto da Majano. Amoretti had published -this passage, and M. Ravaisson who gave a French translation of it -in the _Gazette des Beaux Arts_ (1881, pag. 528), remarks as -follows: _Le maitre sculpteur que Leonard appelle son "compare" ne -serait-il pas Benedetto da Majano, un de ceux qui jugerent avec lui -de la place a donner au David de Michel-Ange, et de qui le Louvre a -acquis recemment un buste d'apres Philippe Strozzi?_ To this it may -be objected that Benedetto da Majano had already lain in his grave -fourteen years, in the year 1511, when he is supposed to have given -the promise to Leonardo. The colours may have been given to the -sculptor Benedetto and the stone may have been in payment for them. ->From the description of the stone here given we may conclude that it -is repeated from hearsay of the sculptor's account of it. I do not -understand how, from this observation, it is possible to conclude -that Leonardo was on the spot.] - -1058. - -That there are springs which suddenly break forth in earthquakes or -other convulsions and suddenly fail; and this happened in a mountain -in Savoy where certain forests sank in and left a very deep gap, and -about four miles from here the earth opened itself like a gulf in -the mountain, and threw out a sudden and immense flood of water -which scoured the whole of a little valley of the tilled soil, -vineyards and houses, and did the greatest mischief, wherever it -overflowed. - -1059. - -The river Arve, a quarter of a mile from Geneva in Savoy, where the -fair is held on midsummerday in the village of Saint Gervais. - -[Footnote: An indistinct sketch is to be seen by the text.] - -1060. - -And this may be seen, as I saw it, by any one going up Monbroso -[Footnote: I have vainly enquired of every available authority for a -solution of the mystery as to what mountain is intended by the name -Monboso (Comp. Vol. I Nos. 300 and 301). It seems most obvious to -refer it to Monte Rosa. ROSA derived from the Keltic ROS which -survives in Breton and in Gaelic, meaning, in its first sense, a -mountain spur, but which also--like HORN--means a very high peak; -thus Monte Rosa would mean literally the High Peak.], a peak of the -Alps which divide France from Italy. The base of this mountain gives -birth to the 4 rivers which flow in four different directions -through the whole of Europe. And no mountain has its base at so -great a height as this, which lifts itself above almost all the -clouds; and snow seldom falls there, but only hail in the summer, -when the clouds are highest. And this hail lies [unmelted] there, so -that if it were not for the absorption of the rising and falling -clouds, which does not happen more than twice in an age, an enormous -mass of ice would be piled up there by the layers of hail, and in -the middle of July I found it very considerable; and I saw the sky -above me quite dark, and the sun as it fell on the mountain was far -brighter here than in the plains below, because a smaller extent of -atmosphere lay between the summit of the mountain and the sun. -[Footnote 6: _in una eta._ This is perhaps a slip of the pen on -Leonardo's part and should be read _estate_ (summer).] - -Leic. 9b] - -1061. - -In the mountains of Verona the red marble is found all mixed with -cockle shells turned into stone; some of them have been filled at -the mouth with the cement which is the substance of the stone; and -in some parts they have remained separate from the mass of the rock -which enclosed them, because the outer covering of the shell had -interposed and had not allowed them to unite with it; while in other -places this cement had petrified those which were old and almost -stripped the outer skin. - -1062. - -Bridge of Goertz-Wilbach (?). - -[Footnote: There is a slight sketch with this text, Leonardo seems -to have intended to suggest, with a few pen-strokes, the course of -the Isonzo and of the Wipbach in the vicinity of Gorizia (Goerz). He -himself says in another place that he had been in Friuli (see No. -1077 1. 19).] - -The Appenins (1063-1068). - -1063. - -That part of the earth which was lightest remained farthest from the -centre of the world; and that part of the earth became the lightest -over which the greatest quantity of water flowed. And therefore that -part became lightest where the greatest number of rivers flow; like -the Alps which divide Germany and France from Italy; whence issue -the Rhone flowing Southwards, and the Rhine to the North. The Danube -or Tanoia towards the North East, and the Po to the East, with -innumerable rivers which join them, and which always run turbid with -the soil carried by them to the sea. - -The shores of the sea are constantly moving towards the middle of -the sea and displace it from its original position. The lowest -portion of the Mediterranean will be reserved for the bed and -current of the Nile, the largest river that flows into that sea. And -with it are grouped all its tributaries, which at first fell into -the sea; as may be seen with the Po and its tributaries, which first -fell into that sea, which between the Appenines and the German Alps -was united to the Adriatic sea. - -That the Gallic Alps are the highest part of Europe. - -1064. - -And of these I found some in the rocks of the high Appenines and -mostly at the rock of La Vernia. [Footnote 6: _Sasso della Vernia._ -The frowning rock between the sources of the Arno and the Tiber, as -Dante describes this mountain, which is 1269 metres in height. - -This note is written by the side of that given as No. 1020; but -their connection does not make it clear what Leonardo's purpose was -in writing it.] - -1065. - -At Parma, at 'La Campana' on the twenty-fifth of October 1514. -[Footnote 2: _Capano_, an Inn.] - -A note on the petrifactions, or fossils near Parma will be found -under No. 989.] - -1066. - -A method for drying the marsh of Piombino. [Footnote: There is a -slight sketch with this text in the original.--Piombino is also -mentioned in Nos. 609, l. 55-58 (compare Pl. XXXV, 3, below). Also -in No. 1035.] - -1067. - -The shepherds in the Romagna at the foot of the Apennines make -peculiar large cavities in the mountains in the form of a horn, and -on one side they fasten a horn. This little horn becomes one and the -same with the said cavity and thus they produce by blowing into it a -very loud noise. [Footnote: As to the Romagna see also No. 1046.] - -1068. - -A spring may be seen to rise in Sicily which at certain times of the -year throws out chesnut leaves in quantities; but in Sicily chesnuts -do not grow, hence it is evident that that spring must issue from -some abyss in Italy and then flow beneath the sea to break forth in -Sicily. [Footnote: The chesnut tree is very common in Sicily. In -writing _cicilia_ Leonardo meant perhaps Cilicia.] - -II. - -FRANCE. - -1069. - - GERMANY. FRANCE. - -a. Austria, a. Picardy. -b. Saxony. b. Normandy. -c. Nuremberg. c. Dauphine. -d. Flanders. - - SPAIN. - - a. Biscay. - b. Castille. - c. Galicia. - d. Portugal. - e. Taragona. - f. Granada. - -[Footnote: Two slightly sketched maps, one of Europe the other of -Spain, are at the side of these notes.] - -1070. - -Perpignan. Roanne. Lyons. Paris. Ghent. Bruges. Holland. - -[Footnote: _Roana_ does not seem to mean here Rouen in Normandy, but -is probably Roanne (Rodumna) on the upper Loire, Lyonnais (Dep. du -Loire). This town is now unimportant, but in Leonardo's time was -still a place of some consequence.] - -1071. - -At Bordeaux in Gascony the sea rises about 40 braccia before its -ebb, and the river there is filled with salt water for more than a -hundred and fifty miles; and the vessels which are repaired there -rest high and dry on a high hill above the sea at low tide. -[Footnote 2: This is obviously an exaggeration founded on inaccurate -information. Half of 150 miles would be nearer the mark.] - -1072. - -The Rhone issues from the lake of Geneva and flows first to the West -and then to the South, with a course of 400 miles and pours its -waters into the Mediterranean. - -1073. - -_c d_ is the garden at Blois; _a b_ is the conduit of Blois, made in -France by Fra Giocondo, _b c_ is what is wanting in the height of -that conduit, _c d_ is the height of the garden at Blois, _e f_ is -the siphon of the conduit, _b c_, _e f_, _f g_ is where the siphon -discharges into the river. [Footnote: The tenor of this note (see -lines 2 and 3) seems to me to indicate that this passage was not -written in France, but was written from oral information. We have no -evidence as to when this note may have been written beyond the -circumstance that Fra Giocondo the Veronese Architect left France -not before the year 1505. The greater part of the magnificent -Chateau of Blois has now disappeared. Whether this note was made for -a special purpose is uncertain. The original form and extent of the -Chateau is shown in Androvet, _Les plus excellents Bastiments de -France, Paris MDCVII,_ and it may be observed that there is in the -middle of the garden a Pavilion somewhat similar to that shown on -Pl. LXXXVIII No. 7. - -See S. DE LA SAUSSAYE, _Histoire du Chateau de Blois 4eme edition -Blois et Paris_ p. 175: _En mariant sa fille ainee a Francois, comte -d'Angouleme, Louis XII lui avait constitue en dot les comtes de -Blois, d'Asti, de Coucy, de Montfort, d'Etampes et de Vertus. Une -ordonnance de Francois I. lui laissa en_ 1516 _l'administration du -comte de Blois. - -Le roi fit commencer, dans la meme annee, les travaux de celle belle -partie du chateau, connue sous le nom d'aile de Francois I, et dont -nous avons donne la description au commencement de ce livre. Nous -trouvons en effet, dans les archives du Baron de Foursanvault, une -piece qui en fixe parfaitement la date. On y lit: "Je, Baymon -Philippeaux, commis par le Roy a tenir le compte et fair le payement -des bastiments, ediffices et reparacions que le dit seigneur fait -faire en son chastu de Blois, confesse avoir eu et receu ... la -somme de trois mille livres tournois ... le cinquieme jour de -juillet, l'an mil cinq cent et seize._ P. 24: _Les jardins avaient -ete decores avec beaucoup de luxe par les differents possesseurs du -chateau. Il ne reste de tous les batiments qu'ils y eleverent que -ceux des officiers charges de l'ad_ministration et de la culture des -jardins, et un pavilion carre en pierre et en brique flanque de -terrasses a chacun de ses angles. Quoique defigure par des mesures -elevees sur les terrasses, cet edifice est tris-digne d'interet par -l'originalite du plan, la decoration architecturale et le souvenir -d'Anne de Bretagne qui le fit construire._ Felibien describes the -garden as follows: _Le jardin haut etait fort bien dresse par grands -compartimens de toutes sortes de figures, avec des allees de -meuriers blancs et des palissades de coudriers. Deux grands berceaux -de charpenterie separoient toute la longueur et la largeur du -jardin, et dans les quatres angles des allees, ou ces berceaux se -croissent, il y auoit 4 cabinets, de mesme charpenterie ... Il y a -pas longtemps qu'il y auoit dans ce mesme jardin, a l'endroit ou se -croissent les allees du milieu, un edifice de figure octogone, de -plus de 7 thoises de diametre et de plus de neuf thoises de haut; -avec 4 enfoncements en forme de niches dans les 4 angles des allies. -Ce bastiment.... esloit de charpente mais d'un extraordinairement -bien travaille. On y voyait particulierement la cordiliere qui -regnati tout autour en forme de cordon. Car la Reyne affectait de la -mettre nonseulement a ses armes et a ses chiffres mais de la faire -representer en divers manieres dans tous les ouvrages qu'on lui -faisait pour elle ... le bastiment estati couvert en forme de dome -qui dans son milieu avait encore un plus petit dome, ou lanterne -vitree au-dessus de laquelle estait une figure doree representant -Saint Michel. Les deux domes estoient proprement couvert d'ardoise -et de plomb dore par dehors; par dedans ils esloient lambrissez -d'une menuiserie tres delicate. Au milieu de ce Salon il y avait un -grand bassin octogone de marbre blanc, dont toutes les faces -estoient enrichies de differentes sculptures, avec les armes et les -chiffres du Roy Louis XII et de la Reine Anne, Dans ce bassin il y -en avait un autre pose sur un piedestal lequel auoit sept piedz de -diametre. Il estait de figure ronde a godrons, avec des masques et -d'autres ornements tres scauamment taillez. Du milieu de ce -deuxiesme bassin s'y levoit un autre petit piedestal qui portait un -troisiesme bassin de trois pieds de diametre, aussy parfaitement -bien taille; c'estoit de ce dernier bassin que jallissoit l'eau qui -se rependoit en suitte dans les deux autres bassins. Les beaux -ouvrages faits d'un marbre esgalement blanc et poli, furent brisez -par la pesanteur de tout l'edifice, que les injures de l'air -renverserent de fond en comble.] - -1074. - -The river Loire at Amboise. - -The river is higher within the bank _b d_ than outside that bank. - -The island where there is a part of Amboise. - -This is the river that passes through Amboise; it passes at _a b c -d_, and when it has passed the bridge it turns back, against the -original current, by the channel _d e_, _b f_ in contact with the -bank which lies between the two contrary currents of the said river, -_a b_, _c d_, and _d e_, _b f_. It then turns down again by the -channel _f l_, _g h_, _n m_, and reunites with the river from which -it was at first separated, which passes by _k n_, which makes _k m_, -_r t_. But when the river is very full it flows all in one channel -passing over the bank _b d_. [Footnote: See Pl. CXV. Lines 1-7 are -above, lines 8-10 in the middle of the large island and the word -_Isola_ is written above _d_ in the smaller island; _a_ is written -on the margin on the bank of the river above 1. I; in the -reproduction it is not visible. As may be seen from the last -sentence, the observation was made after long study of the river's -course, when Leonardo had resided for some time at, or near, -Amboise.] - -1075. - -The water may be dammed up above the level of Romorantin to such a -height, that in its fall it may be used for numerous mills. - -1075. - -The river at Villefranche may be conducted to Romorantin which may -be done by the inhabitants; and the timber of which their houses are -built may be carried in boats to Romorantin [Footnote: Compare No. -744.]. The river may be dammed up at such a height that the waters -may be brought back to Romorantin with a convenient fall. - -1076. - -As to whether it is better that the water should all be raised in a -single turn or in two? - -The answer is that in one single turn the wheel could not support -all the water that it can raise in two turns, because at the half -turn of the wheel it would be raising 100 pounds and no more; and if -it had to raise the whole, 200 pounds in one turn, it could not -raise them unless the wheel were of double the diameter and if the -diameter were doubled, the time of its revolution would be doubled; -therefore it is better and a greater advantage in expense to make -such a wheel of half the size (?) the land which it would water and -would render the country fertile to supply food to the inhabitants, -and would make navigable canals for mercantile purposes. - -The way in which the river in its flow should scour its own channel. - -By the ninth of the third; the more rapid it is, the more it wears -away its channel; and, by the converse proposition, the slower the -water the more it deposits that which renders it turbid. - -And let the sluice be movable like the one I arranged in Friuli -[Footnote 19: This passage reveals to us the fact that Leonardo had -visited the country of Friuli and that he had stayed there for some -time. Nothing whatever was known of this previously.], where when -one sluice was opened the water which passed through it dug out the -bottom. Therefore when the rivers are flooded, the sluices of the -mills ought to be opened in order that the whole course of the river -may pass through falls to each mill; there should be many in order -to give a greater impetus, and so all the river will be scoured. And -below the site of each of the two mills there may be one of the said -sluice falls; one of them may be placed below each mill. - -1078. - -A trabocco is four braccia, and one mile is three thousand of the -said braccia. Each braccio is divided into 12 inches; and the water -in the canals has a fall in every hundred trabocchi of two of these -inches; therefore 14 inches of fall are necessary in two thousand -eight hundred braccia of flow in these canals; it follows that 15 -inches of fall give the required momentum to the currents of the -waters in the said canals, that is one braccio and a half in the -mile. And from this it may be concluded that the water taken from -the river of Ville-franche and lent to the river of Romorantin -will..... Where one river by reason of its low level cannot flow -into the other, it will be necessary to dam it up, so that it may -acquire a fall into the other, which was previously the higher. - -The eve of Saint Antony I returned from Romorantin to Amboise, and -the King went away two days before from Romorantin. - ->From Romorantin as far as the bridge at Saudre it is called the -Saudre, and from that bridge as far as Tours it is called the Cher. - -I would test the level of that channel which is to lead from the -Loire to Romorantin, with a channel one braccio wide and one braccio -deep. - -[Footnote: Lines 6-18 are partly reproduced in the facsimile on p. -254, and the whole of lines 19-25. - -The following names are written along the rivers on the larger -sketch, _era f_ (the Loire) _scier f_ (the Cher) three times. _Pote -Sodro_ (bridge of the Soudre). _Villa francha_ (Villefranche) -_banco_ (sandbank) _Sodro_ (Soudre). The circle below shows the -position of Romorantin. The words '_orologio del sole_' written -below do not belong to the map of the rivers. The following names -are written by the side of the smaller sketch-map:--_tors_ (Tours), -_Abosa_ (Amboise) _bres_--for Bles (Blois) _mo rica_ (Montrichard). -_Lione_ (Lyons). This map was also published in the 'Saggio' -(Milano, 1872) Pl. XXII, and the editors remark: _Forse la linia -retta che va da Amboise a Romorantin segna l'andamento proposto d'un -Canale, che poi rembra prolungarsi in giu fin dove sta scritto -Lione._ - -M. Ravaisson has enlarged on this idea in the Gazette des Beaux Arts -(1881 p. 530): _Les traces de Leonard permettent d'entrevoir que le -canal commencant soit aupres de Tours, soit aupres de Blois et -passant par Romorantin, avec port d'embarquement a Villefranche, -devait, au dela de Bourges, traverser l'Allier au-dessous des -affluents de la Dore et de la Sioule, aller par Moulins jusqu' a -Digoin; enfin, sur l'autre rive de la Loire, depasser les monts du -Charolais et rejoindre la Saone aupres de Macon._ It seems to me -rash, however, to found so elaborate an hypothesis on these sketches -of rivers. The slight stroke going to _Lione_ is perhaps only an -indication of the direction.--With regard to the Loire compare also -No. 988. l. 38.] - -1079. - -THE ROAD TO ORLEANS - -At 1/4 from the South to the South East. At 1/3 from the South to -the South East. At 1/4 from the South to the South East. At 1/5 from -the South to the South East. Between the South West and South, to -the East bearing to the South; from the South towards the East 1/8; -thence to the West, between the South and South West; at the South. - -[Footnote: The meaning is obscure; a more important passage -referring to France is to be found under No. 744] - -On the Germans (1080. 1081). - -1080. - -The way in which the Germans closing up together cross and -interweave their broad leather shields against the enemy, stooping -down and putting one of the ends on the ground while they hold the -rest in their hand. [Footnote: Above the text is a sketch of a few -lines crossing each other and the words _de ponderibus_. The meaning -of the passage is obscure.] - -1081. - -The Germans are wont to annoy a garrison with the smoke of feathers, -sulphur and realgar, and they make this smoke last 7 or 8 hours. -Likewise the husks of wheat make a great and lasting smoke; and also -dry dung; but this must be mixed with olive husks, that is olives -pressed for oil and from which the oil has been extracted. -[Footnote: There is with this passage a sketch of a round tower -shrouded in smoke.] - -The Danube. - -1082. - -That the valleys were formerly in great part covered by lakes the -soil of which always forms the banks of rivers,--and by seas, which -afterwards, by the persistent wearing of the rivers, cut through the -mountains and the wandering courses of the rivers carried away the -other plains enclosed by the mountains; and the cutting away of the -mountains is evident from the strata in the rocks, which correspond -in their sections as made by the courses of the rivers [Footnote 4: -_Emus_, the Balkan; _Dardania_, now Servia.], The Haemus mountains -which go along Thrace and Dardania and join the Sardonius mountains -which, going on to the westward change their name from Sardus to -Rebi, as they come near Dalmatia; then turning to the West cross -Illyria, now called Sclavonia, changing the name of Rebi to Albanus, -and going on still to the West, they change to Mount Ocra in the -North; and to the South above Istria they are named Caruancas; and -to the West above Italy they join the Adula, where the Danube rises -[8], which stretches to the East and has a course of 1500 miles; its -shortest line is about l000 miles, and the same or about the same is -that branch of the Adula mountains changed as to their name, as -before mentioned. To the North are the Carpathians, closing in the -breadth of the valley of the Danube, which, as I have said extends -eastward, a length of about 1000 miles, and is sometimes 200 and in -some places 300 miles wide; and in the midst flows the Danube, the -principal river of Europe as to size. The said Danube runs through -the middle of Austria and Albania and northwards through Bavaria, -Poland, Hungary, Wallachia and Bosnia and then the Danube or Donau -flows into the Black Sea, which formerly extended almost to Austria -and occupied the plains through which the Danube now courses; and -the evidence of this is in the oysters and cockle shells and -scollops and bones of great fishes which are still to be found in -many places on the sides of those mountains; and this sea was formed -by the filling up of the spurs of the Adula mountains which then -extended to the East joining the spurs of the Taurus which extend to -the West. And near Bithynia the waters of this Black Sea poured into -the Propontis [Marmora] falling into the Aegean Sea, that is the -Mediterranean, where, after a long course, the spurs of the Adula -mountains became separated from those of the Taurus. The Black Sea -sank lower and laid bare the valley of the Danube with the above -named countries, and the whole of Asia Minor beyond the Taurus range -to the North, and the plains from mount Caucasus to the Black Sea to -the West, and the plains of the Don this side--that is to say, at -the foot of the Ural mountains. And thus the Black Sea must have -sunk about 1000 braccia to uncover such vast plains. - -[Footnote 8: _Danubio_, in the original _Reno_; evidently a mistake -as we may infer from _come dissi_ l. 10 &c.] - -III. - -THE COUNTRIES OF THE WESTERN END OF THE MEDITERRANEAN. - -The straits of Gibraltar (1083-1085). - -1083. - -WHY THE SEA MAKES A STRONGER CURRENT IN THE STRAITS OF SPAIN THAN -ELSEWHERE. - -A river of equal depth runs with greater speed in a narrow space -than in a wide one, in proportion to the difference between the -wider and the narrower one. - -This proposition is clearly proved by reason confirmed by -experiment. Supposing that through a channel one mile wide there -flows one mile in length of water; where the river is five miles -wide each of the 5 square miles will require 1/5 of itself to be -equal to the square mile of water required in the sea, and where the -river is 3 miles wide each of these square miles will require the -third of its volume to make up the amount of the square mile of the -narrow part; as is demonstrated in _f g h_ at the mile marked _n_. - -[Footnote: In the place marked A in the diagram _Mare Mediterano_ -(Mediterranean Sea) is written in the original. And at B, _stretto -di Spugna_ (straits of Spain, _i.e._ Gibraltar). Compare No. 960.] - -1084. - -WHY THE CURRENT OF GIBRALTAR IS ALWAYS GREATER TO THE WEST THAN TO -THE EAST. - -The reason is that if you put together the mouths of the rivers -which discharge into the Mediterranean sea, you would find the sum -of water to be larger than that which this sea pours through the -straits into the ocean. You see Africa discharging its rivers that -run northwards into this sea, and among them the Nile which runs -through 3000 miles of Africa; there is also the Bagrada river and -the Schelif and others. [Footnote 5: _Bagrada_ (Leonardo writes -Bragada) in Tunis, now Medscherda; _Mavretano_, now Schelif.] -Likewise Europe pours into it the Don and the Danube, the Po, the -Rhone, the Arno, and the Tiber, so that evidently these rivers, with -an infinite number of others of less fame, make its great breadth -and depth and current; and the sea is not wider than 18 miles at the -most westerly point of land where it divides Europe from Africa. - -1085. - -The gulf of the Mediterranean, as an inland sea, received the -principal waters of Africa, Asia and Europe that flowed towards it; -and its waters came up to the foot of the mountains that surrounded -it and made its shores. And the summits of the Apennines stood up -out of this sea like islands, surrounded by salt water. Africa -again, behind its Atlas mountains did not expose uncovered to the -sky the surface of its vast plains about 3000 miles in length, and -Memphis [Footnote 6: _Mefi._ Leonardo can only mean here the citadel -of Cairo on the Mokattam hills.] was on the shores of this sea, and -above the plains of Italy, where now birds fly in flocks, fish were -wont to wander in large shoals. - -1086. - -Tunis. - -The greatest ebb made anywhere by the Mediterranean is above Tunis, -being about two and a half braccia and at Venice it falls two -braccia. In all the rest of the Mediterranean sea the fall is little -or none. - -1087. - -Libya. - -Describe the mountains of shifting deserts; that is to say the -formation of waves of sand borne by the wind, and of its mountains -and hills, such as occur in Libya. Examples may be seen on the wide -sands of the Po and the Ticino, and other large rivers. - -1088. - -Majorca. - -Circumfulgore is a naval machine. It was an invention of the men of -Majorca. [Footnote: The machine is fully described in the MS. and -shown in a sketch.] - -1089. - -The Tyrrhene Sea. - -Some at the Tyrrhene sea employ this method; that is to say they -fastened an anchor to one end of the yard, and to the other a cord, -of which the lower end was fastened to an anchor; and in battle they -flung this anchor on to the oars of the opponent's boat and by the -use of a capstan drew it to the side; and threw soft soap and tow, -daubed with pitch and set ablaze, on to that side where the anchor -hung; so that in order to escape that fire, the defenders of that -ship had to fly to the opposite side; and in doing this they aided -to the attack, because the galley was more easily drawn to the side -by reason of the counterpoise. [Footnote: This text is illustrated -in the original by a pen and ink sketch.] - -IV. - -THE LEVANT. - -The Levantine Sea. - -1090. - -On the shores of the Mediterranean 300 rivers flow, and 40, 200 -ports. And this sea is 3000 miles long. Many times has the increase -of its waters, heaped up by their backward flow and the blowing of -the West winds, caused the overflow of the Nile and of the rivers -which flow out through the Black Sea, and have so much raised the -seas that they have spread with vast floods over many countries. And -these floods take place at the time when the sun melts the snows on -the high mountains of Ethiopia that rise up into the cold regions of -the air; and in the same way the approach of the sun acts on the -mountains of Sarmatia in Asia and on those in Europe; so that the -gathering together of these three things are, and always have been, -the cause of tremendous floods: that is, the return flow of the sea -with the West wind and the melting of the snows. So every river will -overflow in Syria, in Samaria, in Judea between Sinai and the -Lebanon, and in the rest of Syria between the Lebanon and the Taurus -mountains, and in Cilicia, in the Armenian mountains, and in -Pamphilia and in Lycia within the hills, and in Egypt as far as the -Atlas mountains. The gulf of Persia which was formerly a vast lake -of the Tigris and discharged into the Indian Sea, has now worn away -the mountains which formed its banks and laid them even with the -level of the Indian ocean. And if the Mediterranean had continued -its flow through the gulf of Arabia, it would have done the same, -that is to say, would have reduced the level of the Mediterranean to -that of the Indian Sea. - -The Red Sea. (1091. 1092). - -1091. - -For a long time the water of the Mediterranean flowed out through -the Red Sea, which is 100 miles wide and 1500 long, and full of -reefs; and it has worn away the sides of Mount Sinai, a fact which -testifies, not to an inundation from the Indian sea beating on these -coasts, but to a deluge of water which carried with it all the -rivers which abound round the Mediterranean, and besides this there -is the reflux of the sea; and then, a cutting being made to the West -3000 miles away from this place, Gibraltar was separated from Ceuta, -which had been joined to it. And this passage was cut very low down, -in the plains between Gibraltar and the ocean at the foot of the -mountain, in the low part, aided by the hollowing out of some -valleys made by certain rivers, which might have flowed here. -Hercules [Footnote 9: Leonardo seems here to mention Hercules half -jestingly and only in order to suggest to the reader an allusion to -the legend of the pillars of Hercules.] came to open the sea to the -westward and then the sea waters began to pour into the Western -Ocean; and in consequence of this great fall, the Red Sea remained -the higher; whence the water, abandoning its course here, ever after -poured away through the Straits of Spain. - -1092. - -The surface of the Red Sea is on a level with the ocean. - -A mountain may have fallen and closed the mouth of the Red Sea and -prevented the outlet of the Mediterranean, and the Mediterranean Sea -thus overfilled had for outlet the passage below the mountains of -Gades; for, in our own times a similar thing has been seen [Footnote -6: Compare also No. 1336, ll. 30, 35 and 36.-- Paolo Giovio, the -celebrated historian (born at Como in 1483) reports that in 1513 at -the foot of the Alps, above Bellinzona, on the road to Switzerland, -a mountain fell with a very great noise, in consequence of an -earthquake, and that the mass of rocks, which fell on the left -(Western) side blocked the river Breno (T. I p. 218 and 345 of D. -Sauvage's French edition, quoted in ALEXIS PERCY, _Memoire des -tremblements de terre de la peninsule italique; Academie Royale de -Belgique._ T. XXII).--]; a mountain fell seven miles across a valley -and closed it up and made a lake. And thus most lakes have been made -by mountains, as the lake of Garda, the lakes of Como and Lugano, -and the Lago Maggiore. The Mediterranean fell but little on the -confines of Syria, in consequence of the Gaditanean passage, but a -great deal in this passage, because before this cutting was made the -Mediterranean sea flowed to the South East, and then the fall had to -be made by its run through the Straits of Gades. - -At _a_ the water of the Mediterranean fell into the ocean. - -All the plains which lie between the sea and mountains were formerly -covered with salt water. - -Every valley has been made by its own river; and the proportion -between valleys is the same as that between river and river. - -The greatest river in our world is the Mediterranean river, which -moves from the sources of the Nile to the Western ocean. - -And its greatest height is in Outer Mauritania and it has a course -of ten thousand miles before it reunites with its ocean, the father -of the waters. - -That is 3000 miles for the Mediterranean, 3000 for the Nile, as far -as discovered and 3000 for the Nile which flows to the East, &c. - -[Footnote: See Pl. CXI 2, a sketch of the shores of the -Mediterranean Sea, where lines 11 to 16 may be seen. The large -figures 158 are not in Leonardo's writing. The character of the -writing leads us to conclude that this text was written later than -the foregoing. A slight sketch of the Mediterranean is also to be -found in MS. I', 47a.] - -The Nile (1093-1098). - -1093. - -Therefore we must conclude those mountains to be of the greatest -height, above which the clouds falling in snow give rise to the -Nile. - -1094. - -The Egyptians, the Ethiopians, and the Arabs, in crossing the Nile -with camels, are accustomed to attach two bags on the sides of the -camel's bodies that is skins in the form shown underneath. - -In these four meshes of the net the camels for baggage place their -feet. - -[Footnote: Unfortunately both the sketches which accompany this -passage are too much effaced to be reproduced. The upper represents -the two sacks joined by ropes, as here described, the other shows -four camels with riders swimming through a river.] - -1095. - -The Tigris passes through Asia Minor and brings with it the water of -three lakes, one after the other of various elevations; the first -being Munace and the middle Pallas and the lowest Triton. And the -Nile again springs from three very high lakes in Ethiopia, and runs -northwards towards the sea of Egypt with a course of 4000 miles, and -by the shortest and straightest line it is 3000 miles. It is said -that it issues from the Mountains of the Moon, and has various -unknown sources. The said lakes are about 4000 braccia above the -surface of the sphere of water, that is 1 mile and 1/3, giving to -the Nile a fall of 1 braccia in every mile. - -[Footnote 5: _Incogniti principio._ The affluents of the lakes are -probably here intended. Compare, as to the Nile, Nos. 970, 1063 and -1084.] - -1096. - -Very many times the Nile and other very large rivers have poured out -their whole element of water and restored it to the sea. - -1097. - -Why does the inundation of the Nile occur in the summer, coming from -torrid countries? - -1098. - -It is not denied that the Nile is constantly muddy in entering the -Egyptian sea and that its turbidity is caused by soil that this -river is continually bringing from the places it passes; which soil -never returns in the sea which receives it, unless it throws it on -its shores. You see the sandy desert beyond Mount Atlas where -formerly it was covered with salt water. - -Customs of Asiatic Nations (1099. 1100). - -1099. - -The Assyrians and the people of Euboea accustom their horses to -carry sacks which they can at pleasure fill with air, and which in -case of need they carry instead of the girth of the saddle above and -at the side, and they are well covered with plates of cuir bouilli, -in order that they may not be perforated by flights of arrows. Thus -they have not on their minds their security in flight, when the -victory is uncertain; a horse thus equipped enables four or five men -to cross over at need. - -1100. - -SMALL BOATS. - -The small boats used by the Assyrians were made of thin laths of -willow plaited over rods also of willow, and bent into the form of a -boat. They were daubed with fine mud soaked with oil or with -turpentine, and reduced to a kind of mud which resisted the water -and because pine would split; and always remained fresh; and they -covered this sort of boats with the skins of oxen in safely crossing -the river Sicuris of Spain, as is reported by Lucant; [Footnote 7: -See Lucan's Pharsalia IV, 130: _Utque habuit ripas Sicoris camposque -reliquit, Primum cana salix madefacto vimine parvam Texitur in -puppim, calsoque inducto juvenco Vectoris patiens tumidum supernatat -amnem. Sic Venetus stagnante Pado, fusoque Britannus Navigat oceano, -sic cum tenet omnia Nilus, Conseritur bibula Memphitis cymbo papyro. -His ratibus transjecta manus festinat utrimque Succisam cavare nemus -] - -The Spaniards, the Scythians and the Arabs, when they want to make a -bridge in haste, fix hurdlework made of willows on bags of ox-hide, -and so cross in safety. - -Rhodes (1101. 1102). - -1101. - -In [fourteen hundred and] eighty nine there was an earthquake in the -sea of Atalia near Rhodes, which opened the sea--that is its -bottom--and into this opening such a torrent of water poured that -for more than three hours the bottom of the sea was uncovered by -reason of the water which was lost in it, and then it closed to the -former level. - -[Footnote: _Nello ottanto_ 9. It is scarcely likely that Leonardo -should here mean 89 AD. Dr. H. MULLER- STRUBING writes to me as -follows on this subject: "With reference to Rhodes Ross says (_Reise -auf den Griechischen Inseln, III_ 70 _ff_. 1840), that ancient -history affords instances of severe earthquakes at Rhodes, among -others one in the second year of the 138th Olympiad=270 B. C.; a -remarkably violent one under Antoninus Pius (A. D. 138-161) and -again under Constantine and later. But Leonardo expressly speaks of -an earthquake "_nel mar di Atalia presso a Rodi_", which is -singular. The town of Attalia, founded by Attalus, which is what he -no doubt means, was in Pamphylia and more than 150 English miles -East of Rhodes in a straight line. Leake and most other geographers -identify it with the present town of Adalia. Attalia is rarely -mentioned by the ancients, indeed only by Strabo and Pliny and no -earthquake is spoken of. I think therefore you are justified in -assuming that Leonardo means 1489". In the elaborate catalogue of -earthquakes in the East by Sciale Dshelal eddin Sayouthy (an -unpublished Arabic MS. in the possession of Prof. SCHEFER, (Membre -de l'Institut, Paris) mention is made of a terrible earthquake in -the year 867 of the Mohamedan Era corresponding to the year 1489, -and it is there stated that a hundred persons were killed by it in -the fortress of Kerak. There are three places of this name. Kerak on -the sea of Tiberias, Kerak near Tahle on the Libanon, which I -visited in the summer of l876--but neither of these is the place -alluded to. Possibly it may be the strongly fortified town of -Kerak=Kir Moab, to the West of the Dead Sea. There is no notice -about this in ALEXIS PERCY, _Memoire sur les tremblements de terres -ressentis dans la peninsule turco- hellenique et en Syrie (Memoires -couronnes et memoires des savants etrangers, Academie Royale de -Belgique, Tome XXIII)._] - -1102. - -Rhodes has in it 5000 houses. - -Cyprus (1103. 1104). - -1103. - -SITE FOR [A TEMPLE OF] VENUS. - -You must make steps on four sides, by which to mount to a meadow -formed by nature at the top of a rock which may be hollowed out and -supported in front by pilasters and open underneath in a large -portico, - -[Footnote: See Pl. LXXXIII. Compare also p. 33 of this Vol. The -standing male figure at the side is evidently suggested by Michael -Angelo's David. On the same place a slight sketch of horses seems to -have been drawn first; there is no reason for assuming that the text -and this sketch, which have no connection with each other, are of -the same date. - -_Sito di Venere._ By this heading Leonardo appears to mean Cyprus, -which was always considered by the ancients to be the home and birth -place of Aphrodite (Kirpic in Homer).] - -in which the water may fall into various vases of granite, -porphyryand serpentine, within semi-circular recesses; and the water -may overflow from these. And round this portico towards the North -there should be a lake with a little island in the midst of which -should be a thick and shady wood; the waters at the top of the -pilasters should pour into vases at their base, from whence they -should flow in little channels. - -Starting from the shore of Cilicia towards the South you discover -the beauties of the island of Cyprus. - -The Caspian Sea (1105. 1106). - -1104. - ->From the shore of the Southern coast of Cilicia may be seen to the -South the beautiful island of Cyprus, which was the realm of the -goddess Venus, and many navigators being attracted by her beauty, -had their ships and rigging broken amidst the reefs, surrounded by -the whirling waters. Here the beauty of delightful hills tempts -wandering mariners to refresh themselves amidst their flowery -verdure, where the winds are tempered and fill the island and the -surrounding seas with fragrant odours. Ah! how many a ship has here -been sunk. Ah! how many a vessel broken on these rocks. Here might -be seen barks without number, some wrecked and half covered by the -sand; others showing the poop and another the prow, here a keel and -there the ribs; and it seems like a day of judgment when there -should be a resurrection of dead ships, so great is the number of -them covering all the Northern shore; and while the North gale makes -various and fearful noises there. - -1105. - -Write to Bartolomeo the Turk as to the flow and ebb of the Black -sea, and whether he is aware if there be such a flow and ebb in the -Hyrcanean or Caspian sea. [Footnote: The handwriting of this note -points to a late date.] - -1106. - -WHY WATER IS FOUND AT THE TOP OF MOUNTAINS. - ->From the straits of Gibraltar to the Don is 3500 miles, that is one -mile and 1/6, giving a fall of one braccio in a mile to any water -that moves gently. The Caspian sea is a great deal higher; and none -of the mountains of Europe rise a mile above the surface of our -seas; therefore it might be said that the water which is on the -summits of our mountains might come from the height of those seas, -and of the rivers which flow into them, and which are still higher. - -The sea of Azov. - -1107. - -Hence it follows that the sea of Azov is the highest part of the -Mediterranean sea, being at a distance of 3500 miles from the -Straits of Gibraltar, as is shown by the map for navigation; and it -has 3500 braccia of descent, that is, one mile and 1/6; therefore it -is higher than any mountains which exist in the West. - -[Footnote: The passage before this, in the original, treats of the -exit of the waters from Lakes in general.] - -The Dardanelles. - -1108. - -In the Bosphorus the Black Sea flows always into the Egean sea, and -the Egean sea never flows into it. And this is because the Caspian, -which is 400 miles to the East, with the rivers which pour into it, -always flows through subterranean caves into this sea of Pontus; and -the Don does the same as well as the Danube, so that the waters of -Pontus are always higher than those of the Egean; for the higher -always fall towards the lower, and never the lower towards the -higher. - -Constantinople. - -1109. - -The bridge of Pera at Constantinople, 40 braccia wide, 70 braccia -high above the water, 600 braccia long; that is 400 over the sea and -200 on the land, thus making its own abutments. - -[Footnote: See Pl. CX No. 1. In 1453 by order of Sultan Mohamed II. -the Golden Horn was crossed by a pontoon bridge laid on barrels (see -Joh. Dukas' History of the Byzantine Empire XXXVIII p. 279). --The -biographers of Michelangelo, Vasari as well as Condivi, relate that -at the time when Michelangelo suddenly left Rome, in 1506, he -entertained some intention of going to Constantinople, there to -serve the Sultan, who sought to engage him, by means of certain -Franciscan Monks, for the purpose of constructing a bridge to -connect Constantinople with Pera. See VASARI, _Vite_ (ed. Sansoni -VII, 168): _Michelangelo, veduto questa furia del papa, dubitando di -lui, ebbe, secondo che si dice, voglia di andarsene in -Gostantinopoli a servire il Turco, per mezzo di certi frati di San -Francesco, che desiderava averlo per fare un ponte che passassi da -Gostantinopoli a Pera._ And CONDIVI, _Vita di M. Buonaroti chap._ -30_; Michelangelo allora vedendosi condotto a questo, temendo -dell'ira del papa, penso d'andarsene in Levante; massimamente -essendo stato dal Turco ricercato con grandissime promesse per mezzo -di certi frati di San Francesco, per volersene servire in fare un -ponte da Costantinopoli a Pera ed in altri affari._ Leonardo's plan -for this bridge was made in 1502. We may therefore conclude that at -about that time the Sultan Bajazet II. had either announced a -competition in this matter, or that through his agents Leonardo had -first been called upon to carry out the scheme.] - -The Euphrates. - -1110. - -If the river will turn to the rift farther on it will never return -to its bed, as the Euphrates does, and this may do at Bologna the -one who is disappointed for his rivers. - -Centrae Asia. - -1111. - -Mounts Caucasus, Comedorum, and Paropemisidae are joined together -between Bactria and India, and give birth to the river Oxus which -takes its rise in these mountains and flows 500 miles towards the -North and as many towards the West, and discharges its waters into -the Caspian sea; and is accompanied by the Oxus, Dargados, Arthamis, -Xariaspes, Dargamaim, Ocus and Margus, all very large rivers. From -the opposite side towards the South rises the great river Indus -which sends its waters for 600 miles Southwards and receives as -tributaries in this course the rivers Xaradrus, Hyphasis, Vadris, -Vandabal Bislaspus to the East, Suastes and Coe to the West, uniting -with these rivers, and with their waters it flows 800 miles to the -West; then, turning back by the Arbiti mountains makes an elbow and -turns Southwards, where after a course of about 100 miles it finds -the Indian Sea, in which it pours itself by seven branches. On the -side of the same mountains rises the great Ganges, which river flows -Southwards for 500 miles and to the Southwest a thousand ... and -Sarabas, Diarnuna, Soas and Scilo, Condranunda are its tributaries. -It flows into the Indian sea by many mouths. - -On the natives of hot countries. - -1112. - -Men born in hot countries love the night because it refreshes them -and have a horror of light because it burns them; and therefore they -are of the colour of night, that is black. And in cold countries it -is just the contrary. - -[Footnote: The sketch here inserted is in MS. H3 55b.] - -_XVIII._ - -_Naval Warfare.--Mechanical Appliances.--Music._ - -_Such theoretical questions, as have been laid before the reader in -Sections XVI and XVII, though they were the chief subjects of -Leonardo's studies of the sea, did not exclusively claim his -attention. A few passages have been collected at the beginning of -this section, which prove that he had turned his mind to the -practical problems of navigation, and more especially of naval -warfare. What we know for certain of his life gives us no data, it -is true, as to when or where these matters came under his -consideration; but the fact remains certain both from these notes in -his manuscripts, and from the well known letter to Ludovico il Moro -(No._ 1340_), in which he expressly states that he is as capable as -any man, in this very department._ - -_The numerous notes as to the laws and rationale of the flight of -birds, are scattered through several note-books. An account of these -is given in the Bibliography of the manuscripts at the end of this -work. It seems probable that the idea which led him to these -investigations was his desire to construct a flying or aerial -machine for man. At the same time it must be admitted that the notes -on the two subjects are quite unconnected in the manuscripts, and -that those on the flight of birds are by far the most numerous and -extensive. The two most important passages that treat of the -construction of a flying machine are those already published as Tav. -XVI, No._ 1 _and Tav. XVIII in the_ "Saggio delle opere di Leonardo -da Vinci" _(Milan_ 1872_). The passages--Nos._ 1120-1125--_here -printed for the first time and hitherto unknown--refer to the same -subject and, with the exception of one already published in the -Saggio-- No._ 1126--_they are, so far as I know, the only notes, -among the numerous observations on the flight of birds, in which the -phenomena are incidentally and expressly connected with the idea of -a flying machine._ - -_The notes on machines of war, the construction of fortifications, -and similar matters which fall within the department of the -Engineer, have not been included in this work, for the reasons given -on page_ 26 _of this Vol. An exception has been made in favour of -the passages Nos._ 1127 _and_ 1128, _because they have a more -general interest, as bearing on the important question: whence the -Master derived his knowledge of these matters. Though it would be -rash to assert that Leonardo was the first to introduce the science -of mining into Italy, it may be confidently said that he is one of -the earliest writers who can be proved to have known and understood -it; while, on the other hand, it is almost beyond doubt that in the -East at that time, the whole science of besieging towns and mining -in particular, was far more advanced than in Europe. This gives a -peculiar value to the expressions used in No._ 1127. - -_I have been unable to find in the manuscripts any passage whatever -which throws any light on Leonardo's great reputation as a musician. -Nothing therein illustrates VASARPS well-known statement:_ Avvenne -che morto Giovan Galeazze duca di Milano, e creato Lodovico Sforza -nel grado medesimo anno 1494, fu condotto a Milano con gran -riputazione Lionardo al duca, il quale molto si dilettava del suono -della lira, perche sonasse; e Lionardo porto quello strumento -ch'egli aveva di sua mano fabbricato d'argento gran parte, in forma -d'un teschio di cavallo, cosa bizzarra e nuova, acciocche l'armonia -fosse con maggior tuba e piu sonora di voce; laonde supero tutti i -musici che quivi erano concorsi a sonare. - -_The only notes on musical matters are those given as Nos._ 1129 -_and_ 1130, _which explain certain arrangements in instruments._ - -The ship's logs of Vitruvius, of Alberti and of Leonardo - -1113. - -ON MOVEMENTS;--TO KNOW HOW MUCH A SHIP ADVANCES IN AN HOUR. - -The ancients used various devices to ascertain the distance gone by -a ship each hour, among which Vitruvius [Footnote 6: See VITRUVIUS, -_De Architectura lib. X._ C. 14 (p. 264 in the edition of Rose and -Muller- Strubing). The German edition published at Bale in 1543 has, -on fol. 596, an illustration of the contrivance, as described by -Vitruvius.] gives one in his work on Architecture which is just as -fallacious as all the others; and this is a mill wheel which touches -the waves of the sea at one end and in each complete revolution -describes a straight line which represents the circumference of the -wheel extended to a straightness. But this invention is of no worth -excepting on the smooth and motionless surface of lakes. But if the -water moves together with the ship at an equal rate, then the wheel -remains motionless; and if the motion of the water is more or less -rapid than that of the ship, then neither has the wheel the same -motion as the ship so that this invention is of but little use. -There is another method tried by experiment with a known distance -between one island and another; and this is done by a board or under -the pressure of wind which strikes on it with more or less -swiftness. This is in Battista Alberti [Footnote 25: LEON BATTISTA -ALBERTI, _De Architectura lib. V._, c. 12 treats '_de le navi e -parti loro_', but there is no reference to the machine, mentioned by -Leonardo. Alberti says here: _Noi abbiamo trattato lungamente in -altro luogo de' modi de le navi, ma in questo luogo ne abbiamo detto -quel tanto che si bisogna_. To this the following note is added in -the most recent Italian edition: _Questo libro e tuttora inedito e -porta il titolo, secondo Gesnero di_ '_Liber navis_'.]. - -Battista Alberti's method which is made by experiment on a known -distance between one island and another. But such an invention does -not succeed excepting on a ship like the one on which the experiment -was made, and it must be of the same burden and have the same sails, -and the sails in the same places, and the size of the waves must be -the same. But my method will serve for any ship, whether with oars -or sails; and whether it be small or large, broad or long, or high -or low, it always serves [Footnote 52: Leonardo does not reveal the -method invented by him.]. - -Methods of staying and moving in water - -1114. - -How an army ought to cross rivers by swimming with air-bags ... How -fishes swim [Footnote 2: Compare No. 821.]; of the way in which they -jump out of the water, as may be seen with dolphins; and it seems a -wonderful thing to make a leap from a thing which does not resist -but slips away. Of the swimming of animals of a long form, such as -eels and the like. Of the mode of swimming against currents and in -the rapid falls of rivers. Of the mode of swimming of fishes of a -round form. How it is that animals which have not long hind quartres -cannot swim. How it is that all other animals which have feet with -toes, know by nature how to swim, excepting man. In what way man -ought to learn to swim. Of the way in which man may rest on the -water. How man may protect himself against whirlpools or eddies in -the water, which drag him down. How a man dragged to the bottom must -seek the reflux which will throw him up from the depths. How he -ought to move his arms. How to swim on his back. How he can and how -he cannot stay under water unless he can hold his breath [13]. How -by means of a certain machine many people may stay some time under -water. How and why I do not describe my method of remaining under -water, or how long I can stay without eating; and I do not publish -nor divulge these by reason of the evil nature of men who would use -them as means of destruction at the bottom of the sea, by sending -ships to the bottom, and sinking them together with the men in them. -And although I will impart others, there is no danger in them; -because the mouth of the tube, by which you breathe, is above the -water supported on bags or corks [19]. - -[Footnote: L. 13-19 will also be found in Vol. I No. 1.] - -On naval warfare (1115. 1116). - -1115. - -Supposing in a battle between ships and galleys that the ships are -victorious by reason of the high of heir tops, you must haul the -yard up almost to the top of the mast, and at the extremity of the -yard, that is the end which is turned towards the enemy, have a -small cage fastened, wrapped up below and all round in a great -mattress full of cotton so that it may not be injured by the bombs; -then, with the capstan, haul down the opposite end of this yard and -the top on the opposite side will go up so high, that it will be far -above the round-top of the ship, and you will easily drive out the -men that are in it. But it is necessary that the men who are in the -galley should go to the opposite side of it so as to afford a -counterpoise to the weight of the men placed inside the cage on the -yard. - -1116. - -If you want to build an armada for the sea employ these ships to ram -in the enemy's ships. That is, make ships 100 feet long and 8 feet -wide, but arranged so that the left hand rowers may have their oars -to the right side of the ship, and the right hand ones to the left -side, as is shown at M, so that the leverage of the oars may be -longer. And the said ship may be one foot and a half thick, that is -made with cross beams within and without, with planks in contrary -directions. And this ship must have attached to it, a foot below the -water, an iron-shod spike of about the weight and size of an anvil; -and this, by force of oars may, after it has given the first blow, -be drawn back, and driven forward again with fury give a second -blow, and then a third, and so many as to destroy the other ship. - -The use of swimming belts. - -1117. - -A METHOD OF ESCAPING IN A TEMPEST AND SHIPWRECK AT SEA. - -Have a coat made of leather, which must be double across the breast, -that is having a hem on each side of about a finger breadth. Thus it -will be double from the waist to the knee; and the leather must be -quite air-tight. When you want to leap into the sea, blow out the -skirt of your coat through the double hems of the breast; and jump -into the sea, and allow yourself to be carried by the waves; when -you see no shore near, give your attention to the sea you are in, -and always keep in your mouth the air-tube which leads down into the -coat; and if now and again you require to take a breath of fresh -air, and the foam prevents you, you may draw a breath of the air -within the coat. - -[Footnote: AMORETTI, _Memorie Storiche_, Tav. II. B. Fig. 5, gives -the same figure, somewhat altered. 6. _La canna dell' aria_. Compare -Vol. I. No. I. Note] - -On the gravity of water. - -1118. - -If the weight of the sea bears on its bottom, a man, lying on that -bottom and having l000 braccia of water on his back, would have -enough to crush him. - -Diving apparatus and Skating (1119-1121). - -1119. - -Of walking under water. Method of walking on water. - -[Footnote: The two sketches belonging to this passage are given by -AMORETTI, _Memorie Storiche_. Tav. II, Fig. 3 and 4.] - -1120. - -Just as on a frozen river a man may run without moving his feet, so -a car might be made that would slide by itself. - -[Footnote: The drawings of carts by the side of this text have no -direct connection with the problem as stated in words.--Compare No. -1448, l. 17.] - -1121. - -A definition as to why a man who slides on ice does not fall. -[Footnote: An indistinct sketch accompanies the passage, in the -original.] - -On Flying machines (1122-1126). - -1122. - -Man when flying must stand free from the waist upwards so as to be -able to balance himself as he does in a boat so that the centre of -gravity in himself and in the machine may counterbalance each other, -and be shifted as necessity demands for the changes of its centre of -resistance. - -1123. - -Remember that your flying machine must imitate no other than the -bat, because the web is what by its union gives the armour, or -strength to the wings. - -If you imitate the wings of feathered birds, you will find a much -stronger structure, because they are pervious; that is, their -feathers are separate and the air passes through them. But the bat -is aided by the web that connects the whole and is not pervious. - -1124. - -TO ESCAPE THE PERIL OF DESTRUCTION. - -Destruction to such a machine may occur in two ways; of which the -first is the breaking of the machine. The second would be when the -machine should turn on its edge or nearly on its edge, because it -ought always to descend in a highly oblique direction, and almost -exactly balanced on its centre. As regards the first--the breaking -of the machine--, that may be prevented by making it as strong as -possible; and in whichever direction it may tend to turn over, one -centre must be very far from the other; that is, in a machine 30 -braccia long the centres must be 4 braccia one from the other. - -[Footnote: Compare No. 1428.] - -1125. - -Bags by which a man falling from a height of 6 braccia may avoid -hurting himself, by a fall whether into water or on the ground; and -these bags, strung together like a rosary, are to be fixed on one's -back. - -1126. - -An object offers as much resistance to the air as the air does to -the object. You may see that the beating of its wings against the -air supports a heavy eagle in the highest and rarest atmosphere, -close to the sphere of elemental fire. Again you may see the air in -motion over the sea, fill the swelling sails and drive heavily laden -ships. From these instances, and the reasons given, a man with wings -large enough and duly connected might learn to overcome the -resistance of the air, and by conquering it, succeed in subjugating -it and rising above it. [Footnote: A parachute is here sketched, -with an explanatory remark. It is reproduced on Tav. XVI in the -Saggio, and in: _Leonardo da Vinci als Ingenieur etc., Ein Beitrag -zur Geschichte der Technik und der induktiven Wissenschaften, von -Dr. Hermann Grothe, Berlin_ 1874, p. 50.] - -Of mining. - -1127. - -If you want to know where a mine runs, place a drum over all the -places where you suspect that it is being made, and upon this drum -put a couple of dice, and when you are over the spot where they are -mining, the dice will jump a little on the drum at every blow which -is given underground in the mining. - -There are persons who, having the convenience of a river or a lake -in their lands, have made, close to the place where they suspect -that a mine is being made, a great reservoir of water, and have -countermined the enemy, and having found them, have turned the water -upon them and destroyed a great number in the mine. - -Of Greek fire. - -1128. - -GREEK FIRE. - -Take charcoal of willow, and saltpetre, and sulphuric acid, and -sulphur, and pitch, with frankincense and camphor, and Ethiopian -wool, and boil them all together. This fire is so ready to burn that -it clings to the timbers even under water. And add to this -composition liquid varnish, and bituminous oil, and turpentine and -strong vinegar, and mix all together and dry it in the sun, or in an -oven when the bread is taken out; and then stick it round hempen or -other tow, moulding it into a round form, and studding it all over -with very sharp nails. You must leave in this ball an opening to -serve as a fusee, and cover it with rosin and sulphur. - -Again, this fire, stuck at the top of a long plank which has one -braccio length of the end pointed with iron that it may not be burnt -by the said fire, is good for avoiding and keeping off the ships, so -as not to be overwhelmed by their onset. - -Again throw vessels of glass full of pitch on to the enemy's ships -when the men in them are intent on the battle; and then by throwing -similar burning balls upon them you have it in your power to burn -all their ships. - -[Footnote: Venturi has given another short text about the Greek fire -in a French translation (Essai Section XIV). He adds that the -original text is to be found in MS. B. 30 (?). Libri speaks of it in -a note as follows (_Histoire des sciences mathematiques en Italie -Vol. II_ p. 129): _La composition du feu gregeois est une des chases -qui ont ete les plus cherchees et qui sont encore les plus -douteuses. On dit qu'il fut invente au septieme siecle de l'ere -chretienne par l'architecte Callinique (Constantini Porphyrogenetae -opera, Lugd. Batav._ 1617,-- _in-_8vo; p. 172, _de admin, imper. -exp._ 48_), et il se trouve souvent mentionne par les Historiens -Byzantins. Tantot on le langait avec des machines, comme on -lancerait une banche, tantot on le soufflait avec de longs tubes, -comme on soufflerait un gaz ou un liquide enflamme (Annae Comnenae -Alexias_, p. 335, _lib. XI.--Aeliani et Leonis, imperatoris tactica, -Lugd.-Bat._ 1613, _in_-4. part. 2 a, p. 322, _Leonis tact. cap._ -l9.--_Joinville, histoire du Saint Louis collect. Petitot tom. II,_ -p. 235). _Les ecrivains contemporains disent que l'eau ne pouvait -pas eteindre ce feu, mais qu'avec du vinaigre et du sable on y -parvenait. Suivant quelques historiens le feu gregeois etait compose -de soufre et de resine. Marcus Graecus (Liber ignium, Paris,_ 1804, -_in_-40_) donne plusieurs manieres de le faire qui ne sont pas tres -intelligibles, mais parmi lesquelles on trouve la composition de la -poudre a canon. Leonard de Vinci (MSS. de Leonard de Vinci, vol. B. -f. 30,) dit qu'on le faisait avec du charbon de saule, du salpetre, -de l'eau de vie, de la resine, du soufre, de la poix et du camphre. -Mais il est probable que nous ne savons pas qu'elle etait sa -composition, surtout a cause du secret qu'en faisaient les Grecs. En -effet, l'empereur Constantin Porphyrogenete recommende a son fils de -ne jamais en donner aux Barbares, et de leur repondre, s'ils en -demandaient, qu'il avait ete apporti du ciel par un ange et que le -secret en avait ete confie aux Chretiens (Constantini -Porphyrogennetae opera,_ p. 26-27, _de admin. imper., cap. _12_)._] - -Of Music (1129. 1130). - -1129. - -A drum with cogs working by wheels with springs [2]. - -[Footnote: This chapter consists of explanations of the sketches -shown on Pl. CXXI. Lines 1 and 2 of the text are to be seen at the -top at the left hand side of the first sketch of a drum. Lines 3-5 -refer to the sketch immediately below this. Line 6 is written as the -side of the seventh sketch, and lines 7 and 8 at the side of the -eighth. Lines 9-16 are at the bottom in the middle. The remainder of -the text is at the side of the drawing at the bottom.] - -A square drum of which the parchment may be drawn tight or slackened -by the lever _a b_ [5]. - -A drum for harmony [6]. - -[7] A clapper for harmony; that is, three clappers together. - -[9] Just as one and the same drum makes a deep or acute sound -according as the parchments are more or less tightened, so these -parchments variously tightened on one and the same drum will make -various sounds [16]. - -Keys narrow and close together; (bicchi) far apart; these will be -right for the trumpet shown above. - -_a_ must enter in the place of the ordinary keys which have the ... -in the openings of a flute. - -1130. - -Tymbals to be played like the monochord, or the soft flute. - -[6] Here there is to be a cylinder of cane after the manner of -clappers with a musical round called a Canon, which is sung in four -parts; each singer singing the whole round. Therefore I here make a -wheel with 4 teeth so that each tooth takes by itself the part of a -singer. - -[Footnote: In the original there are some more sketches, to which -the text, from line 6, refers. They are studies for a contrivance -exactly like the cylinder in our musical boxes.] - -1131. - -Of decorations. - -White and sky-blue cloths, woven in checks to make a decoration. - -Cloths with the threads drawn at _a b c d e f g h i k_, to go round -the decoration. - -_XIX._ - -_Philosophical Maxims. Morals. Polemics and Speculations_. - -_Vasari indulges in severe strictures on Leonardo's religious views. -He speaks, among other things, of his_ "capricci nel filosofar delle -cose naturali" _and says on this point:_ "Per il che fece nell'animo -un concetto si eretico che e' non si accostava a qualsi voglia -religione, stimando per avventura assai piu lo esser filosofo che -cristiano" _(see the first edition of_ 'Le Vite'_). But this -accusation on the part of a writer in the days of the Inquisition is -not a very serious one--and the less so, since, throughout the -manuscripts, we find nothing to support it._ - -_Under the heading of "Philosophical Maxims" I have collected all -the passages which can give us a clear comprehension of Leonardo's -ideas of the world at large. It is scarcely necessary to observe -that there is absolutely nothing in them to lead to the inference -that he was an atheist. His views of nature and its laws are no -doubt very unlike those of his contemporaries, and have a much -closer affinity to those which find general acceptance at the -present day. On the other hand, it is obvious from Leonardo's will -(see No._ 1566_) that, in the year before his death, he had -professed to adhere to the fundamental doctrines of the Roman -Catholic faith, and this evidently from his own personal desire and -impulse._ - -_The incredible and demonstrably fictitious legend of Leonardo's -death in the arms of Francis the First, is given, with others, by -Vasari and further embellished by this odious comment:_ "Mostrava -tuttavia quanto avea offeso Dio e gli uomini del mondo, non avendo -operato nell'arte come si conveniva." _This last accusation, it may -be remarked, is above all evidence of the superficial character of -the information which Vasari was in a position to give about -Leonardo. It seems to imply that Leonardo was disdainful of diligent -labour. With regard to the second, referring to Leonardo's morality -and dealings with his fellow men, Vasari himself nullifies it by -asserting the very contrary in several passages. A further -refutation may be found in the following sentence from the letter in -which Melsi, the young Milanese nobleman, announces the Master's -death to Leonardo's brothers:_ Credo siate certificati della morte -di Maestro Lionardo fratello vostro, e mio quanto optimo padre, per -la cui morte sarebbe impossibile che io potesse esprimere il dolore -che io ho preso; e in mentre che queste mia membra si sosterranno -insieme, io possedero una perpetua infelicita, e meritamente perche -sviscerato et ardentissimo amore mi portava giornalmente. E dolto ad -ognuno la perdita di tal uomo, quale non e piu in podesta della -natura, ecc. - -_It is true that, in April_ 1476, _we find the names of Leonardo and -Verrocchio entered in the_ "Libro degli Uffiziali di notte e de' -Monasteri" _as breaking the laws; but we immediately after find the -note_ "Absoluti cum condizione ut retamburentur" (Tamburini _was the -name given to the warrant cases of the night police). The acquittal -therefore did not exclude the possibility of a repetition of the -charge. It was in fact repeated, two months later, and on this -occasion the Master and his pupil were again fully acquitted. -Verrocchio was at this time forty and Leonardo four-and-twenty. The -documents referring to this affair are in the State Archives of -Florence; they have been withheld from publication, but it seemed to -me desirable to give the reader this brief account of the leading -facts of the story, as the vague hints of it, which have recently -been made public, may have given to the incident an aspect which it -had not in reality, and which it does not deserve._ - -_The passages here classed under the head "Morals" reveal Leonardo -to us as a man whose life and conduct were unfailingly governed by -lofty principles and aims. He could scarcely have recorded his stern -reprobation and unmeasured contempt for men who do nothing useful -and strive only for riches, if his own life and ambitions had been -such as they have so often been misrepresented._ - -_At a period like that, when superstition still exercised unlimited -dominion over the minds not merely of the illiterate crowd, but of -the cultivated and learned classes, it was very natural that -Leonardo's views as to Alchemy, Ghosts, Magicians, and the like -should be met with stern reprobation whenever and wherever he may -have expressed them; this accounts for the argumentative tone of all -his utterances on such subjects which I have collected in -Subdivision III of this section. To these I have added some passages -which throw light on Leonardo's personal views on the Universe. They -are, without exception, characterised by a broad spirit of -naturalism of which the principles are more strictly applied in his -essays on Astronomy, and still more on Physical Geography._ - -_To avoid repetition, only such notes on Philosophy, Morals and -Polemics, have been included in this section as occur as independent -texts in the original MSS. Several moral reflections have already -been given in Vol. I, in section "Allegorical representations, -Mottoes and Emblems". Others will be found in the following section. -Nos._ 9 _to_ 12, _Vol. I, are also passages of an argumentative -character. It did not seem requisite to repeat here these and -similar passages, since their direct connection with the context is -far closer in places where they have appeared already, than it would -be here._ - -I. - -PHILOSOPHICAL MAXIMS. - -Prayers to God (1132. 1133). - -1132. - -I obey Thee Lord, first for the love I ought, in all reason to bear -Thee; secondly for that Thou canst shorten or prolong the lives of -men. - -1133. - -A PRAYER. - -Thou, O God, dost sell us all good things at the price of labour. - -The powers of Nature (1134-1139). - -1134. - -O admirable impartiality of Thine, Thou first Mover; Thou hast not -permitted that any force should fail of the order or quality of its -necessary results. - -1135. - -Necessity is the mistress and guide of nature. - -Necessity is the theme and the inventress, the eternal curb and law -of nature. - -1136. - -In many cases one and the same thing is attracted by two strong -forces, namely Necessity and Potency. Water falls in rain; the earth -absorbs it from the necessity for moisture; and the sun evaporates -it, not from necessity, but by its power. - -1137. - -Weight, force and casual impulse, together with resistance, are the -four external powers in which all the visible actions of mortals -have their being and their end. - -1138. - -Our body is dependant on heaven and heaven on the Spirit. - -1139. - -The motive power is the cause of all life. - -Psychology (1140-1147). - -1140. - -And you, O Man, who will discern in this work of mine the wonderful -works of Nature, if you think it would be a criminal thing to -destroy it, reflect how much more criminal it is to take the life of -a man; and if this, his external form, appears to thee marvellously -constructed, remember that it is nothing as compared with the soul -that dwells in that structure; for that indeed, be it what it may, -is a thing divine. Leave it then to dwell in His work at His good -will and pleasure, and let not your rage or malice destroy a -life--for indeed, he who does not value it, does not himself deserve -it [Footnote 19: In MS. II 15a is the note: _chi no stima la vita, -non la merita._]. - -[Footnote: This text is on the back of the drawings reproduced on -Pl. CVII. Compare No. 798, 35 note on p. 111: Compare also No. 837 -and 838.] - -1141. - -The soul can never be corrupted with the corruption of the body,, -but is in the body as it were the air which causes the sound of the -organ, where when a pipe bursts, the wind would cease to have any -good effect. [Footnote: Compare No. 845.] - -1142. - -The part always has a tendency to reunite with its whole in order to -escape from its imperfection. - -The spirit desires to remain with its body, because, without the -organic instruments of that body, it can neither act, nor feel -anything. - -1143. - -If any one wishes to see how the soul dwells in its body, let him -observe how this body uses its daily habitation; that is to say, if -this is devoid of order and confused, the body will be kept in -disorder and confusion by its soul. - -1144. - -Why does the eye see a thing more clearly in dreams than with the -imagination being awake? - -1145. - -The senses are of the earth; Reason, stands apart in contemplation. - -[Footnote: Compare No. 842.] - -1146. - -Every action needs to be prompted by a motive. - -To know and to will are two operations of the human mind. - -Discerning, judging, deliberating are acts of the human mind. - -1147. - -All our knowledge has its origin in our preceptions. - -Science, its principles and rules (1148--1161) - -1148. - -Science is the observation of things possible, whether present or -past; prescience is the knowledge of things which may come to pass, -though but slowly. - -1149. - -Experience, the interpreter between formative nature and the human -race, teaches how that nature acts among mortals; and being -constrained by necessity cannot act otherwise than as reason, which -is its helm, requires her to act. - -1150. - -Wisdom is the daughter of experience. - -1151. - -Nature is full of infinite causes that have never occured in -experience. - -1152. - -Truth was the only daughter of Time. - -1153. - -Experience never errs; it is only your judgments that err by -promising themselves effects such as are not caused by your -experiments. - -Experience does not err; only your judgments err by expecting from -her what is not in her power. Men wrongly complain of Experience; -with great abuse they accuse her of leading them astray but they set -Experience aside, turning from it with complaints as to our -ignorance causing us to be carried away by vain and foolish desires -to promise ourselves, in her name, things that are not in her power; -saying that she is fallacious. Men are unjust in complaining of -innocent Experience, constantly accusing her of error and of false -evidence. - -1154. - -Instrumental or mechanical science is of all the noblest and the -most useful, seeing that by means of this all animated bodies that -have movement perform all their actions; and these movements are -based on the centre of gravity which is placed in the middle -dividing unequal weights, and it has dearth and wealth of muscles -and also lever and counterlever. - -1155. - -OF MECHANICS. - -Mechanics are the Paradise of mathematical science, because here we -come to the fruits of mathematics. [Footnote: Compare No. 660, 11. -19--22 (Vol. I., p. 332). 1156. - -Every instrument requires to be made by experience. - -1157. - -The man who blames the supreme certainty of mathematics feeds on -confusion, and can never silence the contradictions of sophistical -sciences which lead to an eternal quackery. - -1158. - -There is no certainty in sciences where one of the mathematical -sciences cannot be applied, or which are not in relation with these -mathematics. - -1159. - -Any one who in discussion relies upon authority uses, not his -understanding, but rather his memory. Good culture is born of a good -disposition; and since the cause is more to be praised than the -effect, I will rather praise a good disposition without culture, -than good culture without the disposition. - -1160. - -Science is the captain, and practice the soldiers. - -1161. - -OF THE ERRORS OF THOSE WHO DEPEND ON PRACTICE WITHOUT SCIENCE. - -Those who fall in love with practice without science are like a -sailor who enters a ship without a helm or a compass, and who never -can be certain whither he is going. - -II. - -MORALS. - -What is life? (1162. 1163). - -1162. - -Now you see that the hope and the desire of returning home and to -one's former state is like the moth to the light, and that the man -who with constant longing awaits with joy each new spring time, each -new summer, each new month and new year--deeming that the things he -longs for are ever too late in coming--does not perceive that he is -longing for his own destruction. But this desire is the very -quintessence, the spirit of the elements, which finding itself -imprisoned with the soul is ever longing to return from the human -body to its giver. And you must know that this same longing is that -quintessence, inseparable from nature, and that man is the image of -the world. - -1163. - -O Time! consumer of all things; O envious age! thou dost destroy all -things and devour all things with the relentless teeth of years, -little by little in a slow death. Helen, when she looked in her -mirror, seeing the withered wrinkles made in her face by old age, -wept and wondered why she had twice been carried away. - -O Time! consumer of all things, and O envious age! by which all -things are all devoured. - -Death. - -1164. - -Every evil leaves behind a grief in our memory, except the supreme -evil, that is death, which destroys this memory together with life. - -How to spend life (1165-1170). - -1165. - -0 sleepers! what a thing is slumber! Sleep resembles death. Ah, why -then dost thou not work in such wise as that after death thou mayst -retain a resemblance to perfect life, when, during life, thou art in -sleep so like to the hapless dead? [Footnote: Compare No. 676, Vol. -I. p. 353.] - -1166. - -One pushes down the other. - -By these square-blocks are meant the life and the studies of men. - -1167. - -The knowledge of past times and of the places on the earth is both -an ornament and nutriment to the human mind. - -1168. - -To lie is so vile, that even if it were in speaking well of godly -things it would take off something from God's grace; and Truth is so -excellent, that if it praises but small things they become noble. - -Beyond a doubt truth bears the same relation to falsehood as light -to darkness; and this truth is in itself so excellent that, even -when it dwells on humble and lowly matters, it is still infinitely -above uncertainty and lies, disguised in high and lofty discourses; -because in our minds, even if lying should be their fifth element, -this does not prevent that the truth of things is the chief -nutriment of superior intellects, though not of wandering wits. - -But you who live in dreams are better pleased by the sophistical -reasons and frauds of wits in great and uncertain things, than by -those reasons which are certain and natural and not so far above us. - -1169. - -Avoid studies of which the result dies with the worker. - -1170. - -Men are in error when they lament the flight of time, accusing it of -being too swift, and not perceiving that it is sufficient as it -passes; but good memory, with which nature has endowed us, causes -things long past to seem present. - -1171. - -Learning acquired in youth arrests the evil of old age; and if you -understand that old age has wisdom for its food, you will so conduct -yourself in youth that your old age will not lack for nourishment. - -1172. - -The acquisition of any knowledge is always of use to the intellect, -because it may thus drive out useless things and retain the good. - -For nothing can be loved or hated unless it is first known. - -1173. - -As a day well spent procures a happy sleep, so a life well employed -procures a happy death. - -1174. - -The water you touch in a river is the last of that which has passed, -and the first of that which is coming. Thus it is with time present. - -Life if well spent, is long. - -1175. - -Just as food eaten without caring for it is turned into loathsome -nourishment, so study without a taste for it spoils memory, by -retaining nothing which it has taken in. - -1176. - -Just as eating against one's will is injurious to health, so study -without a liking for it spoils the memory, and it retains nothing it -takes in. - -1177. - -On Mount Etna the words freeze in your mouth and you may make ice of -them.[Footnote 2: There is no clue to explain this strange -sentence.] - -Just as iron rusts unless it is used, and water putrifies or, in -cold, turns to ice, so our intellect spoils unless it is kept in -use. - -You do ill if you praise, and still worse if you reprove in a matter -you do not understand. - -When Fortune comes, seize her in front with a sure hand, because -behind she is bald. - -1178. - -It seems to me that men of coarse and clumsy habits and of small -knowledge do not deserve such fine instruments nor so great a -variety of natural mechanism as men of speculation and of great -knowledge; but merely a sack in which their food may be stowed and -whence it may issue, since they cannot be judged to be any thing -else than vehicles for food; for it seems to me they have nothing -about them of the human species but the voice and the figure, and -for all the rest are much below beasts. - -1179. - -Some there are who are nothing else than a passage for food and -augmentors of excrement and fillers of privies, because through them -no other things in the world, nor any good effects are produced, -since nothing but full privies results from them. - -On foolishness and ignorance (1180--1182). - -1180. - -The greatest deception men suffer is from their own opinions. - -1181. - -Folly is the shield of shame, as unreadiness is that of poverty -glorified. - -1182. - -Blind ignorance misleads us thus and delights with the results of -lascivious joys. - -Because it does not know the true light. Because it does not know -what is the true light. - -Vain splendour takes from us the power of being .... behold! for its -vain splendour we go into the fire, thus blind ignorance does -mislead us. That is, blind ignorance so misleads us that ... - -O! wretched mortals, open your eyes. - -On riches (1183--1187). - -1183. - -That is not riches, which may be lost; virtue is our true good and -the true reward of its possessor. That cannot be lost; that never -deserts us, but when life leaves us. As to property and external -riches, hold them with trembling; they often leave their possessor -in contempt, and mocked at for having lost them. - -1184. - -Every man wishes to make money to give it to the doctors, destroyers -of life; they then ought to be rich. [Footnote 2: Compare No. 856.] - -Man has much power of discourse which for the most part is vain and -false; animals have but little, but it is useful and true, and a -small truth is better than a great lie. - -1185. - -He who possesses most must be most afraid of loss. - -1186. - -He who wishes to be rich in a day will be hanged in a year. - -1187. - -That man is of supreme folly who always wants for fear of wanting; -and his life flies away while he is still hoping to enjoy the good -things which he has with extreme labour acquired. - -Rules of Life (1188-1202). - -1188. - -If you governed your body by the rules of virtue you would not walk -on all fours in this world. - -You grow in reputation like bread in the hands of a child. -[Footnote: The first sentence is obscure. Compare Nos. 825, 826.] - -1189. - -Savage he is who saves himself. - -1190. - -We ought not to desire the impossible. [Footnote: The writing of -this note, which is exceedingly minute, is reproduced in facsimile -on Pl. XLI No. 5 above the first diagram. - -1191. - -Ask counsel of him who rules himself well. - -Justice requires power, insight, and will; and it resembles the -queen-bee. - -He who does not punish evil commands it to be done. - -He who takes the snake by the tail will presently be bitten by it. - -The grave will fall in upon him who digs it. - -1192. - -The man who does not restrain wantonness, allies himself with -beasts. - -You can have no dominion greater or less than that over yourself. - -He who thinks little, errs much. - -It is easier to contend with evil at the first than at the last. - -No counsel is more loyal than that given on ships which are in -peril: He may expect loss who acts on the advice of an inexperienced -youth. - -1193. - -Where there is most feeling, there is the greatest martyrdom;--a -great martyr. - -1194. - -The memory of benefits is a frail defence against ingratitude. - -Reprove your friend in secret and praise him openly. - -Be not false about the past. - -1195. - -A SIMILE FOR PATIENCE. - -Patience serves us against insults precisely as clothes do against -the cold. For if you multiply your garments as the cold increases, -that cold cannot hurt you; in the same way increase your patience -under great offences, and they cannot hurt your feelings. - -1196. - -To speak well of a base man is much the same as speaking ill of a -good man. - -1197. - -Envy wounds with false accusations, that is with detraction, a thing -which scares virtue. - -1198. - -We are deceived by promises and time disappoints us ... [Footnote 2: -The rest of this passage may be rendered in various ways, but none -of them give a satisfactory meaning.] - -1199. - -Fear arises sooner than any thing else. - -1200. - -Just as courage imperils life, fear protects it. - -Threats alone are the weapons of the threatened man. - -Wherever good fortune enters, envy lays siege to the place and -attacks it; and when it departs, sorrow and repentance remain -behind. - -He who walks straight rarely falls. - -It is bad if you praise, and worse if you reprove a thing, I mean, -if you do not understand the matter well. - -It is ill to praise, and worse to reprimand in matters that you do -not understand. - -1201. - -Words which do not satisfy the ear of the hearer weary him or vex -him, and the symptoms of this you will often see in such hearers in -their frequent yawns; you therefore, who speak before men whose good -will you desire, when you see such an excess of fatigue, abridge -your speech, or change your discourse; and if you do otherwise, then -instead of the favour you desire, you will get dislike and -hostility. - -And if you would see in what a man takes pleasure, without hearing -him speak, change the subject of your discourse in talking to him, -and when you presently see him intent, without yawning or wrinkling -his brow or other actions of various kinds, you may be certain that -the matter of which you are speaking is such as is agreeable to him -&c. - -1202. - -The lover is moved by the beloved object as the senses are by -sensible objects; and they unite and become one and the same thing. -The work is the first thing born of this union; if the thing loved -is base the lover becomes base. - -When the thing taken into union is perfectly adapted to that which -receives it, the result is delight and pleasure and satisfaction. - -When that which loves is united to the thing beloved it can rest -there; when the burden is laid down it finds rest there. - -Politics (1203. 1204). - -1203. - -There will be eternal fame also for the inhabitants of that town, -constructed and enlarged by him. - -All communities obey and are led by their magnates, and these -magnates ally themselves with the lords and subjugate them in two -ways: either by consanguinity, or by fortune; by consanguinity, when -their children are, as it were, hostages, and a security and pledge -of their suspected fidelity; by property, when you make each of -these build a house or two inside your city which may yield some -revenue and he shall have...; 10 towns, five thousand houses with -thirty thousand inhabitants, and you will disperse this great -congregation of people which stand like goats one behind the other, -filling every place with fetid smells and sowing seeds of pestilence -and death; - -And the city will gain beauty worthy of its name and to you it will -be useful by its revenues, and the eternal fame of its -aggrandizement. - -[Footnote: These notes were possibly written in preparation for a -letter. The meaning is obscure.] - -1204. - -To preserve Nature's chiefest boon, that is freedom, I can find -means of offence and defence, when it is assailed by ambitious -tyrants, and first I will speak of the situation of the walls, and -also I shall show how communities can maintain their good and just -Lords. - -[Footnote: Compare No. 1266.] - -III. - -POLEMICS.--SPECULATION. - -Against Speculators (1205. 1206). - -1205. - -Oh! speculators on things, boast not of knowing the things that -nature ordinarily brings about; but rejoice if you know the end of -those things which you yourself devise. - -1206. - -Oh! speculators on perpetual motion how many vain projects of the -like character you have created! Go and be the companions of the -searchers for gold. [Footnote: Another short passage in MS. I, -referring also to speculators, is given by LIBRI (_Hist, des -Sciences math._ III, 228): _Sicche voi speculatori non vi fidate -delli autori che anno sol col immaginatione voluto farsi interpreti -tra la natura e l'omo, ma sol di quelli che non coi cienni della -natura, ma cogli effetti delle sue esperienze anno esercitati i loro -ingegni._] - -Against alchemists (1207. 1208). - -1207. - -The false interpreters of nature declare that quicksilver is the -common seed of every metal, not remembering that nature varies the -seed according to the variety of the things she desires to produce -in the world. - -1208. - -And many have made a trade of delusions and false miracles, -deceiving the stupid multitude. - -Against friars. - -1209. - -Pharisees--that is to say, friars. - -[Footnote: Compare No. 837, 11. 54-57, No. 1296 (p. 363 and 364), -and No. 1305 (p. 370).] - -Against writers of epitomes. - -1210. - -Abbreviators do harm to knowledge and to love, seeing that the love -of any thing is the offspring of this knowledge, the love being the -more fervent in proportion as the knowledge is more certain. And -this certainty is born of a complete knowledge of all the parts, -which, when combined, compose the totality of the thing which ought -to be loved. Of what use then is he who abridges the details of -those matters of which he professes to give thorough information, -while he leaves behind the chief part of the things of which the -whole is composed? It is true that impatience, the mother of -stupidity, praises brevity, as if such persons had not life long -enough to serve them to acquire a complete knowledge of one single -subject, such as the human body; and then they want to comprehend -the mind of God in which the universe is included, weighing it -minutely and mincing it into infinite parts, as if they had to -dissect it! - -Oh! human stupidity, do you not perceive that, though you have been -with yourself all your life, you are not yet aware of the thing you -possess most of, that is of your folly? and then, with the crowd of -sophists, you deceive yourselves and others, despising the -mathematical sciences, in which truth dwells and the knowledge of -the things included in them. And then you occupy yourself with -miracles, and write that you possess information of those things of -which the human mind is incapable and which cannot be proved by any -instance from nature. And you fancy you have wrought miracles when -you spoil a work of some speculative mind, and do not perceive that -you are falling into the same error as that of a man who strips a -tree of the ornament of its branches covered with leaves mingled -with the scented blossoms or fruit....... [Footnote 48: _Givstino_, -Marcus Junianus Justinus, a Roman historian of the second century, -who compiled an epitome from the general history written by Trogus -Pompeius, who lived in the time of Augustus. The work of the latter -writer no longer exist.] as Justinus did, in abridging the histories -written by Trogus Pompeius, who had written in an ornate style all -the worthy deeds of his forefathers, full of the most admirable and -ornamental passages; and so composed a bald work worthy only of -those impatient spirits, who fancy they are losing as much time as -that which they employ usefully in studying the works of nature and -the deeds of men. But these may remain in company of beasts; among -their associates should be dogs and other animals full of rapine and -they may hunt with them after...., and then follow helpless beasts, -which in time of great snows come near to your houses asking alms as -from their master.... - -On spirits (1211--1213). - -1211. - -O mathematicians shed light on this error. - -The spirit has no voice, because where there is a voice there is a -body, and where there is a body space is occupied, and this prevents -the eye from seeing what is placed behind that space; hence the -surrounding air is filled by the body, that is by its image. - -1212. - -There can be no voice where there is no motion or percussion of the -air; there can be no percussion of the air where there is no -instrument, there can be no instrument without a body; and this -being so, a spirit can have neither voice, nor form, nor strength. -And if it were to assume a body it could not penetrate nor enter -where the passages are closed. And if any one should say that by -air, compressed and compacted together, a spirit may take bodies of -various forms and by this means speak and move with strength--to him -I reply that when there are neither nerves nor bones there can be no -force exercised in any kind of movement made by such imaginary -spirits. - -Beware of the teaching of these speculators, because their reasoning -is not confirmed by experience. - -1213. - -Of all human opinions that is to be reputed the most foolish which -deals with the belief in Necromancy, the sister of Alchemy, which -gives birth to simple and natural things. But it is all the more -worthy of reprehension than alchemy, because it brings forth nothing -but what is like itself, that is, lies; this does not happen in -Alchemy which deals with simple products of nature and whose -function cannot be exercised by nature itself, because it has no -organic instruments with which it can work, as men do by means of -their hands, who have produced, for instance, glass &c. but this -Necromancy the flag and flying banner, blown by the winds, is the -guide of the stupid crowd which is constantly witness to the -dazzling and endless effects of this art; and there are books full, -declaring that enchantments and spirits can work and speak without -tongues and without organic instruments-- without which it is -impossible to speak-- and can carry heaviest weights and raise -storms and rain; and that men can be turned into cats and wolves and -other beasts, although indeed it is those who affirm these things -who first became beasts. - -And surely if this Necromancy did exist, as is believed by small -wits, there is nothing on the earth that would be of so much -importance alike for the detriment and service of men, if it were -true that there were in such an art a power to disturb the calm -serenity of the air, converting it into darkness and making -coruscations or winds, with terrific thunder and lightnings rushing -through the darkness, and with violent storms overthrowing high -buildings and rooting up forests; and thus to oppose armies, -crushing and annihilating them; and, besides these frightful storms -may deprive the peasants of the reward of their labours.--Now what -kind of warfare is there to hurt the enemy so much as to deprive him -of the harvest? What naval warfare could be compared with this? I -say, the man who has power to command the winds and to make ruinous -gales by which any fleet may be submerged, --surely a man who could -command such violent forces would be lord of the nations, and no -human ingenuity could resist his crushing force. The hidden -treasures and gems reposing in the body of the earth would all be -made manifest to him. No lock nor fortress, though impregnable, -would be able to save any one against the will of the necromancer. -He would have himself carried through the air from East to West and -through all the opposite sides of the universe. But why should I -enlarge further upon this? What is there that could not be done by -such a craftsman? Almost nothing, except to escape death. Hereby I -have explained in part the mischief and the usefulness, contained in -this art, if it is real; and if it is real why has it not remained -among men who desire it so much, having nothing to do with any -deity? For I know that there are numberless people who would, to -satisfy a whim, destroy God and all the universe; and if this -necromancy, being, as it were, so necessary to men, has not been -left among them, it can never have existed, nor will it ever exist -according to the definition of the spirit, which is invisible in -substance; for within the elements there are no incorporate things, -because where there is no body, there is a vacuum; and no vacuum can -exist in the elements because it would be immediately filled up. -Turn over. - -1214. - -OF SPIRITS. - -We have said, on the other side of this page, that the definition of -a spirit is a power conjoined to a body; because it cannot move of -its own accord, nor can it have any kind of motion in space; and if -you were to say that it moves itself, this cannot be within the -elements. For, if the spirit is an incorporeal quantity, this -quantity is called a vacuum, and a vacuum does not exist in nature; -and granting that one were formed, it would be immediately filled up -by the rushing in of the element in which the vacuum had been -generated. Therefore, from the definition of weight, which is -this--Gravity is an accidental power, created by one element being -drawn to or suspended in another--it follows that an element, not -weighing anything compared with itself, has weight in the element -above it and lighter than it; as we see that the parts of water have -no gravity or levity compared with other water, but if you draw it -up into the air, then it would acquire weight, and if you were to -draw the air beneath the water then the water which remains above -this air would acquire weight, which weight could not sustain itself -by itself, whence collapse is inevitable. And this happens in water; -wherever the vacuum may be in this water it will fall in; and this -would happen with a spirit amid the elements, where it would -continuously generate a vacuum in whatever element it might find -itself, whence it would be inevitable that it should be constantly -flying towards the sky until it had quitted these elements. - -AS TO WHETHER A SPIRIT HAS A BODY AMID THE ELEMENTS. - -We have proved that a spirit cannot exist of itself amid the -elements without a body, nor can it move of itself by voluntary -motion unless it be to rise upwards. But now we will say how such a -spirit taking an aerial body would be inevitably melt into air; -because if it remained united, it would be separated and fall to -form a vacuum, as is said above; therefore it is inevitable, if it -is to be able to remain suspended in the air, that it should absorb -a certain quantity of air; and if it were mingled with the air, two -difficulties arise; that is to say: It must rarefy that portion of -the air with which it mingles; and for this cause the rarefied air -must fly up of itself and will not remain among the air that is -heavier than itself; and besides this the subtle spiritual essence -disunites itself, and its nature is modified, by which that nature -loses some of its first virtue. Added to these there is a third -difficulty, and this is that such a body formed of air assumed by -the spirits is exposed to the penetrating winds, which are -incessantly sundering and dispersing the united portions of the air, -revolving and whirling amidst the rest of the atmosphere; therefore -the spirit which is infused in this - -1215. - -air would be dismembered or rent and broken up with the rending of -the air into which it was incorporated. - -AS TO WHETHER THE SPIRIT, HAVING TAKEN THIS BODY OF AIR, CAN MOVE OF -ITSELF OR NOT. - -It is impossible that the spirit infused into a certain quantity of -air, should move this air; and this is proved by the above passage -where it is said: the spirit rarefies that portion of the air in -which it incorporates itself; therefore this air will rise high -above the other air and there will be a motion of the air caused by -its lightness and not by a voluntary movement of the spirit, and if -this air is encountered by the wind, according to the 3rd of this, -the air will be moved by the wind and not by the spirit incorporated -in it. - -AS TO WHETHER THE SPIRIT CAN SPEAK OR NOT. - -In order to prove whether the spirit can speak or not, it is -necessary in the first place to define what a voice is and how it is -generated; and we will say that the voice is, as it were, the -movement of air in friction against a dense body, or a dense body in -friction against the air,--which is the same thing. And this -friction of the dense and the rare condenses the rare and causes -resistance; again, the rare, when in swift motion, and the rare in -slow motion condense each other when they come in contact and make a -noise and very great uproar; and the sound or murmur made by the -rare moving through the rare with only moderate swiftness, like a -great flame generating noises in the air; and the tremendous uproar -made by the rare mingling with the rare, and when that air which is -both swift and rare rushes into that which is itself rare and in -motion, it is like the flame of fire which issues from a big gun and -striking against the air; and again when a flame issues from the -cloud, there is a concussion in the air as the bolt is generated. -Therefore we may say that the spirit cannot produce a voice without -movement of the air, and air in it there is none, nor can it emit -what it has not; and if desires to move that air in which it is -incorporated, it is necessary that the spirit should multiply -itself, and that cannot multiply which has no quantity. And in the -4th place it is said that no rare body can move, if it has not a -stable spot, whence it may take its motion; much more is it so when -an element has to move within its own element, which does not move -of itself, excepting by uniform evaporation at the centre of the -thing evaporated; as occurs in a sponge squeezed in the hand held -under water; the water escapes in every direction with equal -movement through the openings between the fingers of the hand in -which it is squeezed. - -As to whether the spirit has an articulate voice, and whether the -spirit can be heard, and what hearing is, and seeing; the wave of -the voice passes through the air as the images of objects pass to -the eye. - -Nonentity. - -1216. - -Every quantity is intellectually conceivable as infinitely -divisible. - -[Amid the vastness of the things among which we live, the existence -of nothingness holds the first place; its function extends over all -things that have no existence, and its essence, as regards time, -lies precisely between the past and the future, and has nothing in -the present. This nothingness has the part equal to the whole, and -the whole to the part, the divisible to the indivisible; and the -product of the sum is the same whether we divide or multiply, and in -addition as in subtraction; as is proved by arithmeticians by their -tenth figure which represents zero; and its power has not extension -among the things of Nature.] - -[What is called Nothingness is to be found only in time and in -speech. In time it stands between the past and future and has no -existence in the present; and thus in speech it is one of the things -of which we say: They are not, or they are impossible.] - -With regard to time, nothingness lies between the past and the -future, and has nothing to do with the present, and as to its nature -it is to be classed among things impossible: hence, from what has -been said, it has no existence; because where there is nothing there -would necessarily be a vacuum. - -[Footnote: Compare No. 916.] - -Reflections on Nature (1217-1219). - -1217. - -EXAMPLE OF THE LIGHTNING IN CLOUDS. - -[O mighty and once living instrument of formative nature. Incapable -of availing thyself of thy vast strength thou hast to abandon a life -of stillness and to obey the law which God and time gave to -procreative nature.] - -Ah! how many a time the shoals of terrified dolphins and the huge -tunny-fish were seen to flee before thy cruel fury, to escape; -whilst thy fulminations raised in the sea a sudden tempest with -buffeting and submersion of ships in the great waves; and filling -the uncovered shores with the terrified and desperate fishes which -fled from thee, and left by the sea, remained in spots where they -became the abundant prey of the people in the neighbourhood. - -O time, swift robber of all created things, how many kings, how many -nations hast thou undone, and how many changes of states and of -various events have happened since the wondrous forms of this fish -perished here in this cavernous and winding recess. Now destroyed by -time thou liest patiently in this confined space with bones stripped -and bare; serving as a support and prop for the superimposed -mountain. - -[Footnote: The character of the handwriting points to an early -period of Leonardo's life. It has become very indistinct, and is at -present exceedingly difficult to decipher. Some passages remain -doubtful.] - -[Footnote: Compare No. 1339, written on the same sheet.] - -1218. - -The watery element was left enclosed between the raised banks of the -rivers, and the sea was seen between the uplifted earth and the -surrounding air which has to envelope and enclose the complicated -machine of the earth, and whose mass, standing between the water and -the element of fire, remained much restricted and deprived of its -indispensable moisture; the rivers will be deprived of their waters, -the fruitful earth will put forth no more her light verdure; the -fields will no more be decked with waving corn; all the animals, -finding no fresh grass for pasture, will die and food will then be -lacking to the lions and wolves and other beasts of prey, and to men -who after many efforts will be compelled to abandon their life, and -the human race will die out. In this way the fertile and fruitful -earth will remain deserted, arid and sterile from the water being -shut up in its interior, and from the activity of nature it will -continue a little time to increase until the cold and subtle air -being gone, it will be forced to end with the element of fire; and -then its surface will be left burnt up to cinder and this will be -the end of all terrestrial nature. [Footnote: Compare No. 1339, -written on the same sheet.] - -1219. - -Why did nature not ordain that one animal should not live by the -death of another? Nature, being inconstant and taking pleasure in -creating and making constantly new lives and forms, because she -knows that her terrestrial materials become thereby augmented, is -more ready and more swift in her creating, than time in his -destruction; and so she has ordained that many animals shall be food -for others. Nay, this not satisfying her desire, to the same end she -frequently sends forth certain poisonous and pestilential vapours -upon the vast increase and congregation of animals; and most of all -upon men, who increase vastly because other animals do not feed upon -them; and, the causes being removed, the effects would not follow. -This earth therefore seeks to lose its life, desiring only continual -reproduction; and as, by the argument you bring forward and -demonstrate, like effects always follow like causes, animals are the -image of the world. - -_XX._ - -_Humorous Writings._ - -_Just as Michaelangelo's occasional poems reflect his private life -as well as the general disposition of his mind, we may find in the -writings collected in this section, the transcript of Leonardo's -fanciful nature, and we should probably not be far wrong in -assuming, that he himself had recited these fables in the company of -his friends or at the court festivals of princes and patrons._ Era -tanto piacevole nella conversazione-- _so relates Vasari_--che -tirava a se gli animi delle genti. _And Paulus Jovius says in his -short biography of the artist:_ Fuit ingenio valde comi, nitido, -liberali, vultu autem longe venustissimo, et cum elegantiae omnis -deliciarumque maxime theatralium mirificus inventor ac arbiter -esset, ad lyramque scito caneret, cunctis per omnem aetatem -principibus mire placuit. _There can be no doubt that the fables are -the original offspring of Leonardo's brain, and not borrowed from -any foreign source; indeed the schemes and plans for the composition -of fables collected in division V seem to afford an external proof -of this, if the fables themselves did not render it self-evident. -Several of them-- for instance No._ l279--_are so strikingly -characteristic of Leonardo's views of natural science that we cannot -do them justice till we are acquainted with his theories on such -subjects; and this is equally true of the 'Prophecies'_. - -_I have prefixed to these quaint writings the 'Studies on the life -and habits of animals' which are singular from their peculiar -aphoristic style, and I have transcribed them in exactly the order -in which they are written in MS. H. This is one of the very rare -instances in which one subject is treated in a consecutive series of -notes, all in one MS., and Leonardo has also departed from his -ordinary habits, by occasionally not completing the text on the page -it is begun. These brief notes of a somewhat mysterious bearing have -been placed here, simply because they may possibly have been -intended to serve as hints for fables or allegories. They can -scarcely be regarded as preparatory for a natural history, rather -they would seem to be extracts. On the one hand the names of some of -the animals seem to prove that Leonardo could not here be recording -observations of his own; on the other hand the notes on their habits -and life appear to me to dwell precisely on what must have -interested him most--so far as it is possible to form any complete -estimate of his nature and tastes._ - -_In No._ 1293 _lines_ 1-10, _we have a sketch of a scheme for -grouping the Prophecies. I have not however availed myself of it as -a clue to their arrangement here because, in the first place, the -texts are not so numerous as to render the suggested classification -useful to the reader, and, also, because in reading the long series, -as they occur in the original, we may follow the author's mind; and -here and there it is not difficult to see how one theme suggested -another. I have however regarded Leonardo's scheme for the -classification of the Prophecies as available for that of the Fables -and Jests, and have adhered to it as far as possible._ - -_Among the humourous writings I might perhaps have included the_ -'Rebusses', _of which there are several in the collection of -Leonardo's drawings at Windsor; it seems to me not likely that many -or all of them could be solved at the present day and the MSS. throw -no light on them. Nor should I be justified if I intended to include -in the literary works the well-known caricatures of human faces -attributed to Leonardo-- of which, however, it may be incidentally -observed, the greater number are in my opinion undoubtedly spurious. -Two only have necessarily been given owing to their presence in -text, which it was desired to reproduce: Vol. I page_ 326, _and Pl. -CXXII. It can scarcely be doubted that some satirical intention is -conveyed by the drawing on Pl. LXIV (text No. _688_). - -My reason for not presenting Leonardo to the reader as a poet is the -fact that the maxims and morals in verse which have been ascribed to -him, are not to be found in the manuscripts, and Prof. Uzielli has -already proved that they cannot be by him. Hence it would seem that -only a few short verses can be attributed to him with any -certainty._ - -I. - -STUDIES ON THE LIFE AND HABITS OF ANIMALS. - -1220. - -THE LOVE OF VIRTUE. - -The gold-finch is a bird of which it is related that, when it is -carried into the presence of a sick person, if the sick man is going -to die, the bird turns away its head and never looks at him; but if -the sick man is to be saved the bird never loses sight of him but is -the cause of curing him of all his sickness. - -Like unto this is the love of virtue. It never looks at any vile or -base thing, but rather clings always to pure and virtuous things and -takes up its abode in a noble heart; as the birds do in green woods -on flowery branches. And this Love shows itself more in adversity -than in prosperity; as light does, which shines most where the place -is darkest. - -1221. - -ENVY. - -We read of the kite that, when it sees its young ones growing too -big in the nest, out of envy it pecks their sides, and keeps them -without food. - -CHEERFULNESS. - -Cheerfulness is proper to the cock, which rejoices over every little -thing, and crows with varied and lively movements. - -SADNESS. - -Sadness resembles the raven, which, when it sees its young ones born -white, departs in great grief, and abandons them with doleful -lamentations, and does not feed them until it sees in them some few -black feathers. - -1222. - -PEACE. - -We read of the beaver that when it is pursued, knowing that it is -for the virtue [contained] in its medicinal testicles and not being -able to escape, it stops; and to be at peace with its pursuers, it -bites off its testicles with its sharp teeth, and leaves them to its -enemies. - -RAGE. - -It is said of the bear that when it goes to the haunts of bees to -take their honey, the bees having begun to sting him he leaves the -honey and rushes to revenge himself. And as he seeks to be revenged -on all those that sting him, he is revenged on none; in such wise -that his rage is turned to madness, and he flings himself on the -ground, vainly exasperating, by his hands and feet, the foes against -which he is defending himself. - -1223. - -GRATITUDE. - -The virtue of gratitude is said to be more [developed] in the birds -called hoopoes which, knowing the benefits of life and food, they -have received from their father and their mother, when they see them -grow old, make a nest for them and brood over them and feed them, -and with their beaks pull out their old and shabby feathers; and -then, with a certain herb restore their sight so that they return to -a prosperous state. - -AVARICE. - -The toad feeds on earth and always remains lean; because it never -eats enough:-- it is so afraid lest it should want for earth. - -1224. - -INGRATITUDE. - -Pigeons are a symbol of ingratitude; for when they are old enough no -longer to need to be fed, they begin to fight with their father, and -this struggle does not end until the young one drives the father out -and takes the hen and makes her his own. - -CRUELTY. - -The basilisk is so utterly cruel that when it cannot kill animals by -its baleful gaze, it turns upon herbs and plants, and fixing its -gaze on them withers them up. - -1225. - -GENEROSITY. - -It is said of the eagle that it is never so hungry but that it will -leave a part of its prey for the birds that are round it, which, -being unable to provide their own food, are necessarily dependent on -the eagle, since it is thus that they obtain food. - -DISCIPLINE. - -When the wolf goes cunningly round some stable of cattle, and by -accident puts his foot in a trap, so that he makes a noise, he bites -his foot off to punish himself for his folly. - -1226. - -FLATTERERS OR SYRENS. - -The syren sings so sweetly that she lulls the mariners to sleep; -then she climbs upon the ships and kills the sleeping mariners. - -PRUDENCE. - -The ant, by her natural foresight provides in the summer for the -winter, killing the seeds she harvests that they may not germinate, -and on them, in due time she feeds. - -FOLLY. - -The wild bull having a horror of a red colour, the hunters dress up -the trunk of a tree with red and the bull runs at this with great -frenzy, thus fixing his horns, and forthwith the hunters kill him -there. - -1227. - -JUSTICE. - -We may liken the virtue of Justice to the king of the bees which -orders and arranges every thing with judgment. For some bees are -ordered to go to the flowers, others are ordered to labour, others -to fight with the wasps, others to clear away all dirt, others to -accompagny and escort the king; and when he is old and has no wings -they carry him. And if one of them fails in his duty, he is punished -without reprieve. - -TRUTH. - -Although partridges steal each other's eggs, nevertheless the young -born of these eggs always return to their true mother. - -1228. - -FIDELITY, OR LOYALTY. - -The cranes are so faithful and loyal to their king, that at night, -when he is sleeping, some of them go round the field to keep watch -at a distance; others remain near, each holding a stone in his foot, -so that if sleep should overcome them, this stone would fall and -make so much noise that they would wake up again. And there are -others which sleep together round the king; and this they do every -night, changing in turn so that their king may never find them -wanting. - -FALSEHOOD. - -The fox when it sees a flock of herons or magpies or birds of that -kind, suddenly flings himself on the ground with his mouth open to -look as he were dead; and these birds want to peck at his tongue, -and he bites off their heads. - -1229. - -LIES. - -The mole has very small eyes and it always lives under ground; and -it lives as long as it is in the dark but when it comes into the -light it dies immediately, because it becomes known;--and so it is -with lies. - -VALOUR. - -The lion is never afraid, but rather fights with a bold spirit and -savage onslaught against a multitude of hunters, always seeking to -injure the first that injures him. - -FEAR OR COWARDICE. - -The hare is always frightened; and the leaves that fall from the -trees in autumn always keep him in terror and generally put him to -flight. - -1230. - -MAGNANIMITY. - -The falcon never preys but on large birds; and it will let itself -die rather than feed on little ones, or eat stinking meat. - -VAIN GLORY. - -As regards this vice, we read that the peacock is more guilty of it -than any other animal. For it is always contemplating the beauty of -its tail, which it spreads in the form of a wheel, and by its cries -attracts to itself the gaze of the creatures that surround it. - -And this is the last vice to be conquered. - -1231. - -CONSTANCY. - -Constancy may be symbolised by the phoenix which, knowing that by -nature it must be resuscitated, has the constancy to endure the -burning flames which consume it, and then it rises anew. - -INCONSTANCY. - -The swallow may serve for Inconstancy, for it is always in movement, -since it cannot endure the smallest discomfort. - -CONTINENCE. - -The camel is the most lustful animal there is, and will follow the -female for a thousand miles. But if you keep it constantly with its -mother or sister it will leave them alone, so temperate is its -nature. - -1232. - -INCONTINENCE. - -The unicorn, through its intemperance and not knowing how to control -itself, for the love it bears to fair maidens forgets its ferocity -and wildness; and laying aside all fear it will go up to a seated -damsel and go to sleep in her lap, and thus the hunters take it. - -HUMILITY. - -We see the most striking example of humility in the lamb which will -submit to any animal; and when they are given for food to imprisoned -lions they are as gentle to them as to their own mother, so that -very often it has been seen that the lions forbear to kill them. - -1233. - -PRIDE. - -The falcon, by reason of its haughtiness and pride, is fain to lord -it and rule over all the other birds of prey, and longs to be sole -and supreme; and very often the falcon has been seen to assault the -eagle, the Queen of birds. - -ABSTINENCE. - -The wild ass, when it goes to the well to drink, and finds the water -troubled, is never so thirsty but that it will abstain from -drinking, and wait till the water is clear again. - -GLUTTONY. - -The vulture is so addicted to gluttony that it will go a thousand -miles to eat a carrion [carcase]; therefore is it that it follows -armies. - -1234. - -CHASTITY. - -The turtle-dove is never false to its mate; and if one dies the -other preserves perpetual chastity, and never again sits on a green -bough, nor ever again drinks of clear water. - -UNCHASTITY. - -The bat, owing to unbridled lust, observes no universal rule in -pairing, but males with males and females with females pair -promiscuously, as it may happen. - -MODERATION. - -The ermine out of moderation never eats but once in the day; it will -rather let itself be taken by the hunters than take refuge in a -dirty lair, in order not to stain its purity. - -1235. - -THE EAGLE. - -The eagle when it is old flies so high that it scorches its -feathers, and Nature allowing that it should renew its youth, it -falls into shallow water [Footnote 5: The meaning is obscure.]. And -if its young ones cannot bear to gaze on the sun [Footnote 6: The -meaning is obscure.]--; it does not feed them with any bird, that -does not wish to die. Animals which much fear it do not approach its -nest, although it does not hurt them. It always leaves part of its -prey uneaten. - -LUMERPA,--FAME. - -This is found in Asia Major, and shines so brightly that it absorbs -its own shadow, and when it dies it does not lose this light, and -its feathers never fall out, but a feather pulled out shines no -longer. - -1236. - -THE PELICAN. - -This bird has a great love for its young; and when it finds them in -its nest dead from a serpent's bite, it pierces itself to the heart, -and with its blood it bathes them till they return to life. - -THE SALAMANDER. - -This has no digestive organs, and gets no food but from the fire, in -which it constantly renews its scaly skin. - -The salamander, which renews its scaly skin in the fire,--for -virtue. - -THE CAMELEON. - -This lives on air, and there it is the prey of all the birds; so in -order to be safer it flies above the clouds and finds an air so -rarefied that it cannot support the bird that follows it. - -At that height nothing can go unless it has a gift from Heaven, and -that is where the chameleon flies. - -1237. - -THE ALEPO, A FISH. - -The fish _alepo_ does not live out of water. - -THE OSTRICH. - -This bird converts iron into nourishment, and hatches its eggs by -its gaze;--Armies under commanders. - -THE SWAN. - -The swan is white without any spot, and it sings sweetly as it dies, -its life ending with that song. - -THE STORK. - -This bird, by drinking saltwater purges itself of distempers. If the -male finds his mate unfaithful, he abandons her; and when it grows -old its young ones brood over it, and feed it till it dies. - -1238. - -THE GRASSHOPPER. - -This silences the cuckoo with its song. It dies in oil and revives -in vinegar. It sings in the greatest heats - -THE BAT. - -The more light there is the blinder this creature becomes; as those -who gaze most at the sun become most dazzled.--For Vice, that cannot -remain where Virtue appears. - -THE PARTRIDGE. - -This bird changes from the female into the male and forgets its -former sex; and out of envy it steals the eggs from others and -hatches them, but the young ones follow the true mother. - -THE SWALLOW. - -This bird gives sight to its blind young ones by means of celandine. - -1239. - -THE OYSTER.--FOR TREACHERY. - -This creature, when the moon is full opens itself wide, and when the -crab looks in he throws in a piece of rock or seaweed and the oyster -cannot close again, whereby it serves for food to that crab. This is -what happens to him who opens his mouth to tell his secret. He -becomes the prey of the treacherous hearer. - -THE BASILISK.--CRUELTY. - -All snakes flie from this creature; but the weasel attacks it by -means of rue and kills it. - -THE ASP. - -This carries instantaneous death in its fangs; and, that it may not -hear the charmer it stops its ears with its tail. - -1240. - -THE DRAGON. - -This creature entangles itself in the legs of the elephant which -falls upon it, and so both die, and in its death it is avenged. - -THE VIPER. - -She, in pairing opens her mouth and at last clenches her teeth and -kills her husband. Then the young ones, growing within her body rend -her open and kill their mother. - -THE SCORPION. - -Saliva, spit out when fasting will kill a scorpion. This may be -likened to abstinence from greediness, which removes and heals the -ills which result from that gluttony, and opens the path of virtue. - -1241. - -THE CROCODILE. HYPOCRISY. - -This animal catches a man and straightway kills him; after he is -dead, it weeps for him with a lamentable voice and many tears. Then, -having done lamenting, it cruelly devours him. It is thus with the -hypocrite, who, for the smallest matter, has his face bathed with -tears, but shows the heart of a tiger and rejoices in his heart at -the woes of others, while wearing a pitiful face. - -THE TOAD. - -The toad flies from the light of the sun, and if it is held there by -force it puffs itself out so much as to hide its head below and -shield itself from the rays. Thus does the foe of clear and radiant -virtue, who can only be constrainedly brought to face it with puffed -up courage. - -1242. - -THE CATERPILLAR.--FOR VIRTUE IN GENERAL. - -The caterpillar, which by means of assiduous care is able to weave -round itself a new dwelling place with marvellous artifice and fine -workmanship, comes out of it afterwards with painted and lovely -wings, with which it rises towards Heaven. - -THE SPIDER. - -The spider brings forth out of herself the delicate and ingenious -web, which makes her a return by the prey it takes. - -[Footnote: Two notes are underneath this text. The first: _'nessuna -chosa e da ttemere piu che lla sozza fama'_ is a repetition of the -first line of the text given in Vol. I No. 695. - -The second: _faticha fugga cholla fama in braccio quasi ochultata c_ -is written in red chalk and is evidently an incomplete sentence.] - -1243. - -THE LION. - -This animal, with his thundering roar, rouses his young the third -day after they are born, teaching them the use of all their dormant -senses and all the wild things which are in the wood flee away. - -This may be compared to the children of Virtue who are roused by the -sound of praise and grow up in honourable studies, by which they are -more and more elevated; while all that is base flies at the sound, -shunning those who are virtuous. - -Again, the lion covers over its foot tracks, so that the way it has -gone may not be known to its enemies. Thus it beseems a captain to -conceal the secrets of his mind so that the enemy may not know his -purpose. - -1244. - -THE TARANTULA. - -The bite of the tarantula fixes a man's mind on one idea; that is on -the thing he was thinking of when he was bitten. - -THE SCREECH-OWL AND THE OWL. - -These punish those who are scoffing at them by pecking out their -eyes; for nature has so ordered it, that they may thus be fed. - -1245. - -THE ELEPHANT. - -The huge elephant has by nature what is rarely found in man; that is -Honesty, Prudence, Justice, and the Observance of Religion; inasmuch -as when the moon is new, these beasts go down to the rivers, and -there, solemnly cleansing themselves, they bathe, and so, having -saluted the planet, return to the woods. And when they are ill, -being laid down, they fling up plants towards Heaven as though they -would offer sacrifice. --They bury their tusks when they fall out -from old age.--Of these two tusks they use one to dig up roots for -food; but they save the point of the other for fighting with; when -they are taken by hunters and when worn out by fatigue, they dig up -these buried tusks and ransom themselves. - -1246. - -They are merciful, and know the dangers, and if one finds a man -alone and lost, he kindly puts him back in the road he has missed, -if he finds the footprints of the man before the man himself. It -dreads betrayal, so it stops and blows, pointing it out to the other -elephants who form in a troop and go warily. - -These beasts always go in troops, and the oldest goes in front and -the second in age remains the last, and thus they enclose the troop. -Out of shame they pair only at night and secretly, nor do they then -rejoin the herd but first bathe in the river. The females do not -fight as with other animals; and it is so merciful that it is most -unwilling by nature ever to hurt those weaker than itself. And if it -meets in the middle of its way a flock of sheep - -1247. - -it puts them aside with its trunk, so as not to trample them under -foot; and it never hurts any thing unless when provoked. When one -has fallen into a pit the others fill up the pit with branches, -earth and stones, thus raising the bottom that he may easily get -out. They greatly dread the noise of swine and fly in confusion, -doing no less harm then, with their feet, to their own kind than to -the enemy. They delight in rivers and are always wandering about -near them, though on account of their great weight they cannot swim. -They devour stones, and the trunks of trees are their favourite -food. They have a horror of rats. Flies delight in their smell and -settle on their back, and the beast scrapes its skin making its -folds even and kills them. - -1248. - -When they cross rivers they send their young ones up against the -stream of the water; thus, being set towards the fall, they break -the united current of the water so that the current does not carry -them away. The dragon flings itself under the elephant's body, and -with its tail it ties its legs; with its wings and with its arms it -also clings round its ribs and cuts its throat with its teeth, and -the elephant falls upon it and the dragon is burst. Thus, in its -death it is revenged on its foe. - -THE DRAGON. - -These go in companies together, and they twine themselves after the -manner of roots, and with their heads raised they cross lakes, and -swim to where they find better pasture; and if they did not thus -combine - -1249. - -they would be drowned, therefore they combine. - -THE SERPENT. - -The serpent is a very large animal. When it sees a bird in the air -it draws in its breath so strongly that it draws the birds into its -mouth too. Marcus Regulus, the consul of the Roman army was -attacked, with his army, by such an animal and almost defeated. And -this animal, being killed by a catapult, measured 123 feet, that is -64 1/2 braccia and its head was high above all the trees in a wood. - -THE BOA(?) - -This is a very large snake which entangles itself round the legs of -the cow so that it cannot move and then sucks it, in such wise that -it almost dries it up. In the time of Claudius the Emperor, there -was killed, on the Vatican Hill, - -1250. - -one which had inside it a boy, entire, that it had swallowed. - -THE MACLI.--CAUGHT WHEN ASLEEP. - -This beast is born in Scandinavia. It has the shape of a great -horse, excepting that the great length of its neck and of its ears -make a difference. It feeds on grass, going backwards, for it has so -long an upper lip that if it went forwards it would cover up the -grass. Its legs are all in one piece; for this reason when it wants -to sleep it leans against a tree, and the hunters, spying out the -place where it is wont to sleep, saw the tree almost through, and -then, when it leans against it to sleep, in its sleep it falls, and -thus the hunters take it. And every other mode of taking it is in -vain, because it is incredibly swift in running. - -1251. - -THE BISON WHICH DOES INJURY IN ITS FLIGHT. - -This beast is a native of Paeonia and has a neck with a mane like a -horse. In all its other parts it is like a bull, excepting that its -horns are in a way bent inwards so that it cannot butt; hence it has -no safety but in flight, in which it flings out its excrement to a -distance of 400 braccia in its course, and this burns like fire -wherever it touches. - -LIONS, PARDS, PANTHERS, TIGERS. - -These keep their claws in the sheath, and never put them out unless -they are on the back of their prey or their enemy. - -THE LIONESS. - -When the lioness defends her young from the hand of the hunter, in -order not to be frightened by the spears she keeps her eyes on the -ground, to the end that she may not by her flight leave her young -ones prisoners. - -1252. - -THE LION. - -This animal, which is so terrible, fears nothing more than the noise -of empty carts, and likewise the crowing of cocks. And it is much -terrified at the sight of one, and looks at its comb with a -frightened aspect, and is strangely alarmed when its face is -covered. - -THE PANTHER IN AFRICA. - -This has the form of the lioness but it is taller on its legs and -slimmer and long bodied; and it is all white and marked with black -spots after the manner of rosettes; and all animals delight to look -upon these rosettes, and they would always be standing round it if -it were not for the terror of its face; - -1253. - -therefore knowing this, it hides its face, and the surrounding -animals grow bold and come close, the better to enjoy the sight of -so much beauty; when suddenly it seizes the nearest and at once -devours it. - -CAMELS. - -The Bactrian have two humps; the Arabian one only. They are swift in -battle and most useful to carry burdens. This animal is extremely -observant of rule and measure, for it will not move if it has a -greater weight than it is used to, and if it is taken too far it -does the same, and suddenly stops and so the merchants are obliged -to lodge there. - -1254. - -THE TIGER. - -This beast is a native of Hyrcania, and it is something like the -panther from the various spots on its skin. It is an animal of -terrible swiftness; the hunter when he finds its young ones carries -them off hastily, placing mirrors in the place whence he takes them, -and at once escapes on a swift horse. The panther returning finds -the mirrors fixed on the ground and looking into them believes it -sees its young; then scratching with its paws it discovers the -cheat. Forthwith, by means of the scent of its young, it follows the -hunter, and when this hunter sees the tigress he drops one of the -young ones and she takes it, and having carried it to the den she -immediately returns to the hunter and does - -1255. - -the same till he gets into his boat. - -CATOBLEPAS. - -It is found in Ethiopia near to the source Nigricapo. It is not a -very large animal, is sluggish in all its parts, and its head is so -large that it carries it with difficulty, in such wise that it -always droops towards the ground; otherwise it would be a great pest -to man, for any one on whom it fixes its eyes dies immediately. -[Footnote: Leonardo undoubtedly derived these remarks as to the -Catoblepas from Pliny, Hist. Nat. VIII. 21 (al. 32): _Apud Hesperios -Aethiopas fons est Nigris_ (different readings), _ut plerique -existimavere, Nili caput.-----Juxta hunc fera appellatur catoblepas, -modica alioquin, ceterisque membris iners, caput tantum praegrave -aegre ferens; alias internecio humani generis, omnibus qui oculos -ejus videre, confestim morientibus._ Aelian, _Hist. An._ gives a far -more minute description of the creature, but he says that it poisons -beasts not by its gaze, but by its venomous breath. Athenaeus 221 B, -mentions both. If Leonardo had known of these two passages, he would -scarcely have omitted the poisonous breath. (H. MULLER-STRUBING.)] - -THE BASILISK. - -This is found in the province of Cyrenaica and is not more than 12 -fingers long. It has on its head a white spot after the fashion of a -diadem. It scares all serpents with its whistling. It resembles a -snake, but does not move by wriggling but from the centre forwards -to the right. It is said that one - -1256. - -of these, being killed with a spear by one who was on horse-back, -and its venom flowing on the spear, not only the man but the horse -also died. It spoils the wheat and not only that which it touches, -but where it breathes the grass dries and the stones are split. - -THE WEASEL. - -This beast finding the lair of the basilisk kills it with the smell -of its urine, and this smell, indeed, often kills the weasel itself. - -THE CERASTES. - -This has four movable little horns; so, when it wants to feed, it -hides under leaves all of its body except these little horns which, -as they move, seem to the birds to be some small worms at play. Then -they immediately swoop down to pick them and the Cerastes suddenly -twines round them and encircles and devours them. - -1257. - -THE AMPHISBOENA. - -This has two heads, one in its proper place the other at the tail; -as if one place were not enough from which to fling its venom. - -THE IACULUS. - -This lies on trees, and flings itself down like a dart, and pierces -through the wild beast and kills them. - -THE ASP. - -The bite of this animal cannot be cured unless by immediately -cutting out the bitten part. This pestilential animal has such a -love for its mate that they always go in company. And if, by mishap, -one of them is killed the other, with incredible swiftness, follows -him who has killed it; and it is so determined and eager for -vengeance that it overcomes every difficulty, and passing by every -troop it seeks to hurt none but its enemy. And it will travel any -distance, and it is impossible to avoid it unless by crossing water -and by very swift flight. It has its eyes turned inwards, and large -ears and it hears better than it sees. - -1258. - -THE ICHNEUMON. - -This animal is the mortal enemy of the asp. It is a native of Egypt -and when it sees an asp near its place, it runs at once to the bed -or mud of the Nile and with this makes itself muddy all over, then -it dries itself in the sun, smears itself again with mud, and thus, -drying one after the other, it makes itself three or four coatings -like a coat of mail. Then it attacks the asp, and fights well with -him, so that, taking its time it catches him in the throat and -destroys him. - -THE CROCODILE. - -This is found in the Nile, it has four feet and lives on land and in -water. No other terrestrial creature but this is found to have no -tongue, and it only bites by moving its upper jaw. It grows to a -length of forty feet and has claws and is armed with a hide that -will take any blow. By day it is on land and at night in the water. -It feeds on fishes, and going to sleep on the bank of the Nile with -its mouth open, a bird called - -1259. - -trochilus, a very small bird, runs at once to its mouth and hops -among its teeth and goes pecking out the remains of the food, and so -inciting it with voluptuous delight tempts it to open the whole of -its mouth, and so it sleeps. This being observed by the ichneumon it -flings itself into its mouth and perforates its stomach and bowels, -and finally kills it. - -THE DOLPHIN. - -Nature has given such knowledge to animals, that besides the -consciousness of their own advantages they know the disadvantages of -their foes. Thus the dolphin understands what strength lies in a cut -from the fins placed on his chine, and how tender is the belly of -the crocodile; hence in fighting with him it thrusts at him from -beneath and rips up his belly and so kills him. - -The crocodile is a terror to those that flee, and a base coward to -those that pursue him. - -1260. - -THE HIPPOPOTAMUS. - -This beast when it feels itself over-full goes about seeking thorns, -or where there may be the remains of canes that have been split, and -it rubs against them till a vein is opened; then when the blood has -flowed as much as he needs, he plasters himself with mud and heals -the wound. In form he is something like a horse with long haunches, -a twisted tail and the teeth of a wild boar, his neck has a mane; -the skin cannot be pierced, unless when he is bathing; he feeds on -plants in the fields and goes into them backwards so that it may -seem, as though he had come out. - -THE IBIS. - -This bird resembles a crane, and when it feels itself ill it fills -its craw with water, and with its beak makes an injection of it. - -THE STAG. - -These creatures when they feel themselves bitten by the spider -called father-long-legs, eat crabs and free themselves of the venom. - -1261. - -THE LIZARD. - -This, when fighting with serpents eats the sow-thistle and is free. - -THE SWALLOW. - -This [bird] gives sight to its blind young ones, with the juice of -the celandine. - -THE WEASEL. - -This, when chasing rats first eats of rue. - -THE WILD BOAR. - -This beast cures its sickness by eating of ivy. - -THE SNAKE. - -This creature when it wants to renew itself casts its old skin, -beginning with the head, and changing in one day and one night. - -THE PANTHER. - -This beast after its bowels have fallen out will still fight with -the dogs and hunters. - -1262. - -THE CHAMELEON. - -This creature always takes the colour of the thing on which it is -resting, whence it is often devoured together with the leaves on -which the elephant feeds. - -THE RAVEN. - -When it has killed the Chameleon it takes laurel as a purge. - -1263. - -Moderation checks all the vices. The ermine will die rather than -besmirch itself. - -OF FORESIGHT. - -The cock does not crow till it has thrice flapped its wings; the -parrot in moving among boughs never puts its feet excepting where it -has first put its beak. Vows are not made till Hope is dead. - -Motion tends towards the centre of gravity. - -1264. - -MAGNANIMITY. - -The falcon never seizes any but large birds and will sooner die than -eat [tainted] meat of bad savour. - -II. - -FABLES. - -Fables on animals (1265-1270). - -1265. - -A FABLE. - -An oyster being turned out together with other fish in the house of -a fisherman near the sea, he entreated a rat to take him to the sea. -The rat purposing to eat him bid him open; but as he bit him the -oyster squeezed his head and closed; and the cat came and killed -him. - -1266. - -A FABLE. - -The thrushes rejoiced greatly at seeing a man take the owl and -deprive her of liberty, tying her feet with strong bonds. But this -owl was afterwards by means of bird-lime the cause of the thrushes -losing not only their liberty, but their life. This is said for -those countries which rejoice in seeing their governors lose their -liberty, when by that means they themselves lose all succour, and -remain in bondage in the power of their enemies, losing their -liberty and often their life. - -1267. - -A FABLE. - -A dog, lying asleep on the fur of a sheep, one of his fleas, -perceiving the odour of the greasy wool, judged that this must be a -land of better living, and also more secure from the teeth and nails -of the dog than where he fed on the dog; and without farther -reflection he left the dog and went into the thick wool. There he -began with great labour to try to pass among the roots of the hairs; -but after much sweating had to give up the task as vain, because -these hairs were so close that they almost touched each other, and -there was no space where fleas could taste the skin. Hence, after -much labour and fatigue, he began to wish to return to his dog, who -however had already departed; so he was constrained after long -repentance and bitter tears, to die of hunger. - -1268. - -A FABLE. - -The vain and wandering butterfly, not content with being able to fly -at its ease through the air, overcome by the tempting flame of the -candle, decided to fly into it; but its sportive impulse was the -cause of a sudden fall, for its delicate wings were burnt in the -flame. And the hapless butterfly having dropped, all scorched, at -the foot of the candlestick, after much lamentation and repentance, -dried the tears from its swimming eyes, and raising its face -exclaimed: O false light! how many must thou have miserably deceived -in the past, like me; or if I must indeed see light so near, ought I -not to have known the sun from the false glare of dirty tallow? - -A FABLE. - -The monkey, finding a nest of small birds, went up to it greatly -delighted. But they, being already fledged, he could only succeed in -taking the smallest; greatly delighted he took it in his hand and -went to his abode; and having begun to look at the little bird he -took to kissing it, and from excess of love he kissed it so much and -turned it about and squeezed it till he killed it. This is said for -those who by not punishing their children let them come to mischief. - -1269. - -A FABLE. - -A rat was besieged in his little dwelling by a weasel, which with -unwearied vigilance awaited his surrender, while watching his -imminent peril through a little hole. Meanwhile the cat came by and -suddenly seized the weasel and forthwith devoured it. Then the rat -offered up a sacrifice to Jove of some of his store of nuts, humbly -thanking His providence, and came out of his hole to enjoy his -lately lost liberty. But he was instantly deprived of it, together -with his life, by the cruel claws and teeth of the lurking cat. - -1270. - -A FABLE. - -The ant found a grain of millet. The seed feeling itself taken -prisoner cried out to her: "If you will do me the kindness to allow -me accomplish my function of reproduction, I will give you a hundred -such as I am." And so it was. - -A Spider found a bunch of grapes which for its sweetness was much -resorted to by bees and divers kinds of flies. It seemed to her that -she had found a most convenient spot to spread her snare, and having -settled herself on it with her delicate web, and entered into her -new habitation, there, every day placing herself in the openings -made by the spaces between the grapes, she fell like a thief on the -wretched creatures which were not aware of her. But, after a few -days had passed, the vintager came, and cut away the bunch of grapes -and put it with others, with which it was trodden; and thus the -grapes were a snare and pitfall both for the treacherous spider and -the betrayed flies. - -An ass having gone to sleep on the ice over a deep lake, his heat -dissolved the ice and the ass awoke under water to his great grief, -and was forthwith drowned. - -A falcon, unable to endure with patience the disappearance of a -duck, which, flying before him had plunged under water, wished to -follow it under water, and having soaked his feathers had to remain -in the water while the duck rising to the air mocked at the falcon -as he drowned. - -The spider wishing to take flies in her treacherous net, was cruelly -killed in it by the hornet. - -An eagle wanting to mock at the owl was caught by the wings in -bird-lime and was taken and killed by a man. - -Fables on lifeless objects (1271--1274). - -1271. - -The water finding that its element was the lordly ocean, was seized -with a desire to rise above the air, and being encouraged by the -element of fire and rising as a very subtle vapour, it seemed as -though it were really as thin as air. But having risen very high, it -reached the air that was still more rare and cold, where the fire -forsook it, and the minute particles, being brought together, united -and became heavy; whence its haughtiness deserting it, it betook -itself to flight and it fell from the sky, and was drunk up by the -dry earth, where, being imprisoned for a long time, it did penance -for its sin. - -1272. - -A FABLE. - -The razor having one day come forth from the handle which serves as -its sheath and having placed himself in the sun, saw the sun -reflected in his body, which filled him with great pride. And -turning it over in his thoughts he began to say to himself: "And -shall I return again to that shop from which I have just come? -Certainly not; such splendid beauty shall not, please God, be turned -to such base uses. What folly it would be that could lead me to -shave the lathered beards of rustic peasants and perform such menial -service! Is this body destined for such work? Certainly not. I will -hide myself in some retired spot and there pass my life in tranquil -repose." And having thus remained hidden for some months, one day he -came out into the air, and issuing from his sheath, saw himself -turned to the similitude of a rusty saw while his surface no longer -reflected the resplendent sun. With useless repentance he vainly -deplored the irreparable mischief saying to himself: "Oh! how far -better was it to employ at the barbers my lost edge of such -exquisite keenness! Where is that lustrous surface? It has been -consumed by this vexatious and unsightly rust." - -The same thing happens to those minds which instead of exercise give -themselves up to sloth. They are like the razor here spoken of, and -lose the keenness of their edge, while the rust of ignorance spoils -their form. - -A FABLE. - -A stone of some size recently uncovered by the water lay on a -certain spot somewhat raised, and just where a delightful grove -ended by a stony road; here it was surrounded by plants decorated by -various flowers of divers colours. And as it saw the great quantity -of stones collected together in the roadway below, it began to wish -it could let itself fall down there, saying to itself: "What have I -to do here with these plants? I want to live in the company of -those, my sisters." And letting itself fall, its rapid course ended -among these longed for companions. When it had been there sometime -it began to find itself constantly toiling under the wheels of the -carts the iron-shoed feet of horses and of travellers. This one -rolled it over, that one trod upon it; sometimes it lifted itself a -little and then it was covered with mud or the dung of some animal, -and it was in vain that it looked at the spot whence it had come as -a place of solitude and tranquil place. - -Thus it happens to those who choose to leave a life of solitary -comtemplation, and come to live in cities among people full of -infinite evil. - -1273. - -Some flames had already lasted in the furnace of a glass-blower, -when they saw a candle approaching in a beautiful and glittering -candlestick. With ardent longing they strove to reach it; and one of -them, quitting its natural course, writhed up to an unburnt brand on -which it fed and passed at the opposite end out by a narrow chink to -the candle which was near. It flung itself upon it, and with fierce -jealousy and greediness it devoured it, having reduced it almost to -death, and, wishing to procure the prolongation of its life, it -tried to return to the furnace whence it had come. But in vain, for -it was compelled to die, the wood perishing together with the -candle, being at last converted, with lamentation and repentance, -into foul smoke, while leaving all its sisters in brilliant and -enduring life and beauty. - -1274. - -A small patch of snow finding itself clinging to the top of a rock -which was lying on the topmost height of a very high mountain and -being left to its own imaginings, it began to reflect in this way, -saying to itself: "Now, shall not I be thought vain and proud for -having placed myself--such a small patch of snow--in so lofty a -spot, and for allowing that so large a quantity of snow as I have -seen here around me, should take a place lower than mine? Certainly -my small dimensions by no means merit this elevation. How easily may -I, in proof of my insignificance, experience the same fate as that -which the sun brought about yesterday to my companions, who were -all, in a few hours, destroyed by the sun. And this happened from -their having placed themselves higher than became them. I will flee -from the wrath of the sun, and humble myself and find a place -befitting my small importance." Thus, flinging itself down, it began -to descend, hurrying from its high home on to the other snow; but -the more it sought a low place the more its bulk increased, so that -when at last its course was ended on a hill, it found itself no less -in size than the hill which supported it; and it was the last of the -snow which was destroyed that summer by the sun. This is said for -those who, humbling themselves, become exalted. - -Fables on plants (1275-1279). - -1275. - -The cedar, being desirous of producing a fine and noble fruit at its -summit, set to work to form it with all the strength of its sap. But -this fruit, when grown, was the cause of the tall and upright -tree-top being bent over. - -The peach, being envious of the vast quantity of fruit which she saw -borne on the nut-tree, her neighbour, determined to do the same, and -loaded herself with her own in such a way that the weight of the -fruit pulled her up by the roots and broke her down to the ground. - -The nut-tree stood always by a road side displaying the wealth of -its fruit to the passers by, and every one cast stones at it. - -The fig-tree, having no fruit, no one looked at it; then, wishing to -produce fruits that it might be praised by men, it was bent and -broken down by them. - -The fig-tree, standing by the side of the elm and seeing that its -boughs were bare of fruit, yet that it had the audacity to keep the -Sun from its own unripe figs with its branches, said to it: "Oh elm! -art thou not ashamed to stand in front of me. But wait till my -offspring are fully grown and you will see where you are!" But when -her offspring were mature, a troop of soldiers coming by fell upon -the fig-tree and her figs were all torn off her, and her boughs cut -away and broken. Then, when she was thus maimed in all her limbs, -the elm asked her, saying: "O fig-tree! which was best, to be -without offspring, or to be brought by them into so miserable a -plight!" - -1276. - -The plant complains of the old and dry stick which stands by its -side and of the dry stakes that surround it. - -One keeps it upright, the other keeps it from low company. - -1277. - -A FABLE. - -A nut, having been carried by a crow to the top of a tall campanile -and released by falling into a chink from the mortal grip of its -beak, it prayed the wall by the grace bestowed on it by God in -allowing it to be so high and thick, and to own such fine bells and -of so noble a tone, that it would succour it, and that, as it had -not been able to fall under the verdurous boughs of its venerable -father and lie in the fat earth covered up by his fallen leaves it -would not abandon it; because, finding itself in the beak of the -cruel crow, it had there made a vow that if it escaped from her it -would end its life in a little hole. At these words the wall, moved -to compassion, was content to shelter it in the spot where it had -fallen; and after a short time the nut began to split open and put -forth roots between the rifts of the stones and push them apart, and -to throw out shoots from its hollow shell; and, to be brief, these -rose above the building and the twisted roots, growing thicker, -began to thrust the walls apart, and tear out the ancient stones -from their old places. Then the wall too late and in vain bewailed -the cause of its destruction and in a short time, it wrought the -ruin of a great part of it. - -1278. - -A FABLE. - -The privet feeling its tender boughs loaded with young fruit, -pricked by the sharp claws and beak of the insolent blackbird, -complained to the blackbird with pitious remonstrance entreating her -that since she stole its delicious fruits she should not deprive it -of the leaves with which it preserved them from the burning rays of -the sun, and that she should not divest it of its tender bark by -scratching it with her sharp claws. To which the blackbird replied -with angry upbraiding: "O, be silent, uncultured shrub! Do you not -know that Nature made you produce these fruits for my nourishment; -do you not see that you are in the world [only] to serve me as food; -do you not know, base creature, that next winter you will be food -and prey for the Fire?" To which words the tree listened patiently, -and not without tears. After a short time the blackbird was taken in -a net and boughs were cut to make a cage, in which to imprison her. -Branches were cut, among others from the pliant privet, to serve for -the small rods of the cage; and seeing herself to be the cause of -the Blackbird's loss of liberty it rejoiced and spoke as follows: "O -Blackbird, I am here, and not yet burnt by fire as you said. I shall -see you in prison before you see me burnt." - -A FABLE. - -The laurel and the myrtle seeing the pear tree cut down cried out -with a loud voice: "O pear-tree! whither are you going? Where is the -pride you had when you were covered with ripe fruits? Now you will -no longer shade us with your mass of leaves." Then the pear-tree -replied: "I am going with the husbandman who has cut me down and who -will take me to the workshop of a good sculptor who by his art will -make me take the form of Jove the god; and I shall be dedicated in a -temple and adored by men in the place of Jove, while you are bound -always to remain maimed and stripped of your boughs, which will be -placed round me to do me honour. - -A FABLE. - -The chesnut, seeing a man upon the fig-tree, bending its boughs down -and pulling off the ripe fruits, which he put into his open mouth -destroying and crushing them with his hard teeth, it tossed its long -boughs and with a noisy rustle exclaimed: "O fig! how much less are -you protected by nature than I. See how in me my sweet offspring are -set in close array; first clothed in soft wrappers over which is the -hard but softly lined husk; and not content with taking this care of -me, and having given them so strong a shelter, on this she has -placed sharp and close-set spines so that the hand of man cannot -hurt me." Then the fig-tree and her offspring began to laugh and -having laughed she said: "I know man to be of such ingenuity that -with rods and stones and stakes flung up among your branches he will -bereave you of your fruits; and when they are fallen, he will -trample them with his feet or with stones, so that your offspring -will come out of their armour, crushed and maimed; while I am -touched carefully by their hands, and not like you with sticks and -stones." - -1279. - -The hapless willow, finding that she could not enjoy the pleasure of -seeing her slender branches grow or attain to the height she wished, -or point to the sky, by reason of the vine and whatever other trees -that grew near, but was always maimed and lopped and spoiled, -brought all her spirits together and gave and devoted itself -entirely to imagination, standing plunged in long meditation and -seeking, in all the world of plants, with which of them she might -ally herself and which could not need the help of her withes. Having -stood for some time in this prolific imagination, with a sudden -flash the gourd presented itself to her thoughts and tossing all her -branches with extreme delight, it seemed to her that she had found -the companion suited to her purpose, because the gourd is more apt -to bind others than to need binding; having come to this conclusion -she awaited eagerly some friendly bird who should be the mediator of -her wishes. Presently seeing near her the magpie she said to him: "O -gentle bird! by the memory of the refuge which you found this -morning among my branches, when the hungry cruel, and rapacious -falcon wanted to devour you, and by that repose which you have -always found in me when your wings craved rest, and by the pleasure -you have enjoyed among my boughs, when playing with your companions -or making love--I entreat you find the gourd and obtain from her -some of her seeds, and tell her that those that are born of them I -will treat exactly as though they were my own flesh and blood; and -in this way use all the words you can think of, which are of the -same persuasive purport; though, indeed, since you are a master of -language, I need not teach you. And if you will do me this service I -shall be happy to have your nest in the fork of my boughs, and all -your family without payment of any rent." Then the magpie, having -made and confirmed certain new stipulations with the willow,--and -principally that she should never admit upon her any snake or -polecat, cocked his tail, and put down his head, and flung himself -from the bough, throwing his weight upon his wings; and these, -beating the fleeting air, now here, now there, bearing about -inquisitively, while his tail served as a rudder to steer him, he -came to a gourd; then with a handsome bow and a few polite words, he -obtained the required seeds, and carried them to the willow, who -received him with a cheerful face. And when he had scraped away with -his foot a small quantity of the earth near the willow, describing a -circle, with his beak he planted the grains, which in a short time -began to grow, and by their growth and the branches to take up all -the boughs of the willow, while their broad leaves deprived it of -the beauty of the sun and sky. And not content with so much evil, -the gourds next began, by their rude hold, to drag the ends of the -tender shoots down towards the earth, with strange twisting and -distortion. - -Then, being much annoyed, it shook itself in vain to throw off the -gourd. After raving for some days in such plans vainly, because the -firm union forbade it, seeing the wind come by it commended itself -to him. The wind flew hard and opened the old and hollow stem of the -willow in two down to the roots, so that it fell into two parts. In -vain did it bewail itself recognising that it was born to no good -end. - -III. - -JESTS AND TALES. - -1280. - -A JEST. - -A priest, making the rounds of his parish on Easter Eve, and -sprinkling holy water in the houses as is customary, came to a -painter's room, where he sprinkled the water on some of his -pictures. The painter turned round, somewhat angered, and asked him -why this sprinkling had been bestowed on his pictures; then said the -priest, that it was the custom and his duty to do so, and that he -was doing good; and that he who did good might look for good in -return, and, indeed, for better, since God had promised that every -good deed that was done on earth should be rewarded a hundred-fold -from above. Then the painter, waiting till he went out, went to an -upper window and flung a large pail of water on the priest's back, -saying: "Here is the reward a hundred-fold from above, which you -said would come from the good you had done me with your holy water, -by which you have damaged my pictures." - -1281. - -When wine is drunk by a drunkard, that wine is revenged on the -drinker. - -1282. - -Wine, the divine juice of the grape, finding itself in a golden and -richly wrought cup, on the table of Mahomet, was puffed up with -pride at so much honour; when suddenly it was struck by a contrary -reflection, saying to itself: "What am I about, that I should -rejoice, and not perceive that I am now near to my death and shall -leave my golden abode in this cup to enter into the foul and fetid -caverns of the human body, and to be transmuted from a fragrant and -delicious liquor into a foul and base one. Nay, and as though so -much evil as this were not enough, I must for a long time lie in -hideous receptacles, together with other fetid and corrupt matter, -cast out from human intestines." And it cried to Heaven, imploring -vengeance for so much insult, and that an end might henceforth be -put to such contempt; and that, since that country produced the -finest and best grapes in the whole world, at least they should not -be turned into wine. Then Jove made that wine drunk by Mahomet to -rise in spirit to his brain; and that in so deleterious a manner -that it made him mad, and gave birth to so many follies that when he -had recovered himself, he made a law that no Asiatic should drink -wine, and henceforth the vine and its fruit were left free. - -As soon as wine has entered the stomach it begins to ferment and -swell; then the spirit of that man begins to abandon his body, -rising as it were skywards, and the brain finds itself parting from -the body. Then it begins to degrade him, and make him rave like a -madman, and then he does irreparable evil, killing his friends. - -1283. - -An artizan often going to visit a great gentleman without any -definite purpose, the gentleman asked him what he did this for. The -other said that he came there to have a pleasure which his lordship -could not have; since to him it was a satisfaction to see men -greater than himself, as is the way with the populace; while the -gentleman could only see men of less consequence than himself; and -so lords and great men were deprived of that pleasure. - -1284. - -Franciscan begging Friars are wont, at certain times, to keep fasts, -when they do not eat meat in their convents. But on journeys, as -they live on charity, they have license to eat whatever is set -before them. Now a couple of these friars on their travels, stopped -at an inn, in company with a certain merchant, and sat down with him -at the same table, where, from the poverty of the inn, nothing was -served to them but a small roast chicken. The merchant, seeing this -to be but little even for himself, turned to the friars and said: -"If my memory serves me, you do not eat any kind of flesh in your -convents at this season." At these words the friars were compelled -by their rule to admit, without cavil, that this was the truth; so -the merchant had his wish, and eat the chicken and the friars did -the best they could. After dinner the messmates departed, all three -together, and after travelling some distance they came to a river of -some width and depth. All three being on foot--the friars by reason -of their poverty, and the other from avarice--it was necessary by -the custom of company that one of the friars, being barefoot, should -carry the merchant on his shoulders: so having given his wooden -shoes into his keeping, he took up his man. But it so happened that -when the friar had got to the middle of the river, he again -remembered a rule of his order, and stopping short, he looked up, -like Saint Christopher, to the burden on his back and said: "Tell -me, have you any money about you?"--"You know I have", answered the -other, "How do you suppose that a Merchant like me should go about -otherwise?" "Alack!" cried the friar, "our rules forbid as to carry -any money on our persons," and forthwith he dropped him into the -water, which the merchant perceived was a facetious way of being -revenged on the indignity he had done them; so, with a smiling face, -and blushing somewhat with shame, he peaceably endured the revenge. - -1285. - -A JEST. - -A man wishing to prove, by the authority of Pythagoras, that he had -formerly been in the world, while another would not let him finish -his argument, the first speaker said to the second: "It is by this -token that I was formerly here, I remember that you were a miller." -The other one, feeling himself stung by these words, agreed that it -was true, and that by the same token he remembered that the speaker -had been the ass that carried the flour. - -A JEST. - -It was asked of a painter why, since he made such beautiful figures, -which were but dead things, his children were so ugly; to which the -painter replied that he made his pictures by day, and his children -by night. - -1286. - -A man saw a large sword which another one wore at his side. Said he -"Poor fellow, for a long time I have seen you tied to that weapon; -why do you not release yourself as your hands are untied, and set -yourself free?" To which the other replied: "This is none of yours, -on the contrary it is an old story." The former speaker, feeling -stung, replied: "I know that you are acquainted with so few things -in this world, that I thought anything I could tell you would be new -to you." - -1287. - -A man gave up his intimacy with one of his friends because he often -spoke ill of his other friends. The neglected friend one day -lamenting to this former friend, after much complaining, entreated -him to say what might be the cause that had made him forget so much -friendship. To which he answered: "I will no longer be intimate with -you because I love you, and I do not choose that you, by speaking -ill of me, your friend, to others, should produce in others, as in -me, a bad impression of yourself, by speaking evil to them of me, -your friend. Therefore, being no longer intimate together, it will -seem as though we had become enemies; and in speaking evil of me, as -is your wont, you will not be blamed so much as if we continued -intimate. - -1288. - -A man was arguing and boasting that he knew many and various tricks. -Another among the bystanders said: "I know how to play a trick which -will make whomsoever I like pull off his breeches." The first man-- -the boaster--said: "You won't make me pull off mine, and I bet you a -pair of hose on it." He who proposed the game, having accepted the -offer, produced breeches and drew them across the face of him who -bet the pair of hose and won the bet [4]. - -A man said to an acquaintance: "Your eyes are changed to a strange -colour." The other replied: "It often happens, but you have not -noticed it." "When does it happen?" said the former. "Every time -that my eyes see your ugly face, from the shock of so unpleasing a -sight they suddenly turn pale and change to a strange colour." - -A man said to another: "Your eyes are changed to a strange colour." -The other replied: "It is because my eyes behold your strange ugly -face." - -A man said that in his country were the strangest things in the -world. Another answered: "You, who were born there, confirm this as -true, by the strangeness of your ugly face." - -[Footnote: The joke turns, it appears, on two meanings of trarre and -is not easily translated.] - -1289. - -An old man was publicly casting contempt on a young one, and boldly -showing that he did not fear him; on which the young man replied -that his advanced age served him better as a shield than either his -tongue or his strength. - -1290. - -A JEST. - -A sick man finding himself in _articulo mortis_ heard a knock at the -door, and asking one of his servants who was knocking, the servant -went out, and answered that it was a woman calling herself Madonna -Bona. Then the sick man lifting his arms to Heaven thanked God with -a loud voice, and told the servants that they were to let her come -in at once, so that he might see one good woman before he died, -since in all his life he had never yet seen one. - -1291. - -A JEST. - -A man was desired to rise from bed, because the sun was already -risen. To which he replied: "If I had as far to go, and as much to -do as he has, I should be risen by now; but having but a little way -to go, I shall not rise yet." - -1292. - -A man, seeing a woman ready to hold up the target for a jousting -match, exclaimed, looking at the shield, and considering his spear: -"Alack! this is too small a workman for so great a business." - -IV. - -PROPHECIES. - -1293. - -THE DIVISION OF THE PROPHECIES. - -First, of things relating to animals; secondly, of irrational -creatures; thirdly of plants; fourthly, of ceremonies; fifthly, of -manners; sixthly, of cases or edicts or quarrels; seventhly, of -cases that are impossible in nature [paradoxes], as, for instance, -of those things which, the more is taken from them, the more they -grow. And reserve the great matters till the end, and the small -matters give at the beginning. And first show the evils and then the -punishment of philosophical things. - -(Of Ants.) - -These creatures will form many communities, which will hide -themselves and their young ones and victuals in dark caverns, and -they will feed themselves and their families in dark places for many -months without any light, artificial or natural. - -[Footnote: Lines 1--5l are in the original written in one column, -beginning with the text of line 11. At the end of the column is the -programme for the arrangement of the prophecies, placed here at the -head: Lines 56--79 form a second column, lines 80--97 a third one -(see the reproduction of the text on the facsimile PI. CXVIII). - -Another suggestion for the arrangement of the prophecies is to be -found among the notes 55--57 on page 357.] - -(Of Bees.) - -And many others will be deprived of their store and their food, and -will be cruelly submerged and drowned by folks devoid of reason. Oh -Justice of God! Why dost thou not wake and behold thy creatures thus -ill used? - -(Of Sheep, Cows, Goats and the like.) - -Endless multitudes of these will have their little children taken -from them ripped open and flayed and most barbarously quartered. - -(Of Nuts, and Olives, and Acorns, and Chesnuts, and such like.) - -Many offspring shall be snatched by cruel thrashing from the very -arms of their mothers, and flung on the ground, and crushed. - -(Of Children bound in Bundles.) - -O cities of the Sea! In you I see your citizens--both females and -males--tightly bound, arms and legs, with strong withes by folks who -will not understand your language. And you will only be able to -assuage your sorrows and lost liberty by means of tearful complaints -and sighing and lamentation among yourselves; for those who will -bind you will not understand you, nor will you understand them. - -(Of Cats that eat Rats.) - -In you, O cities of Africa your children will be seen quartered in -their own houses by most cruel and rapacious beasts of your own -country. - -(Of Asses that are beaten.) - -[Footnote 48: Compare No. 845.] O Nature! Wherefore art thou so -partial; being to some of thy children a tender and benign mother, -and to others a most cruel and pitiless stepmother? I see children -of thine given up to slavery to others, without any sort of -advantage, and instead of remuneration for the good they do, they -are paid with the severest suffering, and spend their whole life in -benefitting those who ill treat them. - -(Of Men who sleep on boards of Trees.) - -Men shall sleep, and eat, and dwell among trees, in the forests and -open country. - -(Of Dreaming.) - -Men will seem to see new destructions in the sky. The flames that -fall from it will seem to rise in it and to fly from it with terror. -They will hear every kind of animals speak in human language. They -will instantaneously run in person in various parts of the world, -without motion. They will see the greatest splendour in the midst of -darkness. O! marvel of the human race! What madness has led you -thus! You will speak with animals of every species and they with you -in human speech. You will see yourself fall from great heights -without any harm and torrents will accompany you, and will mingle -with their rapid course. - -(Of Christians.) - -Many who hold the faith of the Son only build temples in the name of -the Mother. - -(Of Food which has been alive.) - -[84] A great portion of bodies that have been alive will pass into -the bodies of other animals; which is as much as to say, that the -deserted tenements will pass piecemeal into the inhabited ones, -furnishing them with good things, and carrying with them their -evils. That is to say the life of man is formed from things eaten, -and these carry with them that part of man which dies . . . - -1294. - -(Of Funeral Rites, and Processions, and Lights, and Bells, and -Followers.) - -The greatest honours will be paid to men, and much pomp, without -their knowledge. - -[Footnote: A facsimile of this text is on PI. CXVI below on the -right, but the writing is larger than the other notes on the same -sheet and of a somewhat different style. The ink is also of a -different hue, as may be seen on the original sheet at Milan.] - -1295. - -(Of the Avaricious.) - -There will be many who will eagerly and with great care and -solicitude follow up a thing, which, if they only knew its -malignity, would always terrify them. - -(Of those men, who, the older they grow, the more avaricious they -become, whereas, having but little time to stay, they should become -more liberal.) - -We see those who are regarded as being most experienced and -judicious, when they least need a thing, seek and cherish it with -most avidity. - -(Of the Ditch.) - -Many will be busied in taking away from a thing, which will grow in -proportion as it is diminished. - -(Of a Weight placed on a Feather-pillow.) - -And it will be seen in many bodies that by raising the head they -swell visibly; and by laying the raised head down again, their size -will immediately be diminished. - -(Of catching Lice.) - -And many will be hunters of animals, which, the fewer there are the -more will be taken; and conversely, the more there are, the fewer -will be taken. - -(Of Drawing Water in two Buckets with a single Rope.) - -And many will be busily occupied, though the more of the thing they -draw up, the more will escape at the other end. - -(Of the Tongues of Pigs and Calves in Sausage-skins.) - -Oh! how foul a thing, that we should see the tongue of one animal in -the guts of another. - -(Of Sieves made of the Hair of Animals.) - -We shall see the food of animals pass through their skin everyway -excepting through their mouths, and penetrate from the outside -downwards to the ground. - -(Of Lanterns.) - -[Footnote 35: Lanterns were in Italy formerly made of horn.] The -cruel horns of powerful bulls will screen the lights of night -against the wild fury of the winds. - -(Of Feather-beds.) - -Flying creatures will give their very feathers to support men. - -(Of Animals which walk on Trees--wearing wooden Shoes.) - -The mire will be so great that men will walk on the trees of their -country. - -(Of the Soles of Shoes, which are made from the Ox.) - -And in many parts of the country men will be seen walking on the -skins of large beasts. - -(Of Sailing in Ships.) - -There will be great winds by reason of which things of the East will -become things of the West; and those of the South, being involved in -the course of the winds, will follow them to distant lands. - -(Of Worshipping the Pictures of Saints.) - -Men will speak to men who hear not; having their eyes open, they -will not see; they will speak to these, and they will not be -answered. They will implore favours of those who have ears and hear -not; they will make light for the blind. - -(Of Sawyers.) - -There will be many men who will move one against another, holding in -their hands a cutting tool. But these will not do each other any -injury beyond tiring each other; for, when one pushes forward the -other will draw back. But woe to him who comes between them! For he -will end by being cut in pieces. - -(Of Silk-spinning.) - -Dismal cries will be heard loud, shrieking with anguish, and the -hoarse and smothered tones of those who will be despoiled, and at -last left naked and motionless; and this by reason of the mover, -which makes every thing turn round. - -(Of putting Bread into the Mouth of the Oven and taking it out -again.) - -In every city, land, castle and house, men shall be seen, who for -want of food will take it out of the mouths of others, who will not -be able to resist in any way. - -(Of tilled Land.) - -The Earth will be seen turned up side down and facing the opposite -hemispheres, uncovering the lurking holes of the fiercest animals. - -(Of Sowing Seed.) - -Then many of the men who will remain alive, will throw the victuals -they have preserved out of their houses, a free prey to the birds -and beasts of the earth, without taking any care of them at all. - -(Of the Rains, which, by making the Rivers muddy, wash away the -Land.) - -[Footnote 81: Compare No. 945.] Something will fall from the sky -which will transport a large part of Africa which lies under that -sky towards Europe, and that of Europe towards Africa, and that of -the Scythian countries will meet with tremendous revolutions -[Footnote 84: Compare No. 945.]. - -(Of Wood that burns.) - -The trees and shrubs in the great forests will be converted into -cinder. - -(Of Kilns for Bricks and Lime.) - -Finally the earth will turn red from a conflagration of many days -and the stones will be turned to cinders. - -(Of boiled Fish.) - -The natives of the waters will die in the boiling flood. - -(Of the Olives which fall from the Olive trees, shedding oil which -makes light.) - -And things will fall with great force from above, which will give us -nourishment and light. - -(Of Owls and screech owls and what will happen to certain birds.) - -Many will perish of dashing their heads in pieces, and the eyes of -many will jump out of their heads by reason of fearful creatures -come out of the darkness. - -(Of flax which works the cure of men.) - -That which was at first bound, cast out and rent by many and various -beaters will be respected and honoured, and its precepts will be -listened to with reverence and love. - -(Of Books which teach Precepts.) - -Bodies without souls will, by their contents give us precepts by -which to die well. - -(Of Flagellants.) - -Men will hide themselves under the bark of trees, and, screaming, -they will make themselves martyrs, by striking their own limbs. - -(Of the Handles of Knives made of the Horns of Sheep.) - -We shall see the horns of certain beasts fitted to iron tools, which -will take the lives of many of their kind. - -(Of Night when no Colour can be discerned.) - -There will come a time when no difference can be discerned between -colours, on the contrary, everything will be black alike. - -(Of Swords and Spears which by themselves never hurt any one.) - -One who by himself is mild enough and void of all offence will -become terrible and fierce by being in bad company, and will most -cruelly take the life of many men, and would kill many more if they -were not hindered by bodies having no soul, that have come out of -caverns--that is, breastplates of iron. - -(Of Snares and Traps.) - -Many dead things will move furiously, and will take and bind the -living, and will ensnare them for the enemies who seek their death -and destruction. - -(Of Metals.) - -That shall be brought forth out of dark and obscure caves, which -will put the whole human race in great anxiety, peril and death. To -many that seek them, after many sorrows they will give delight, and -to those who are not in their company, death with want and -misfortune. This will lead to the commission of endless crimes; this -will increase and persuade bad men to assassinations, robberies and -treachery, and by reason of it each will be suspicious of his -partner. This will deprive free cities of their happy condition; -this will take away the lives of many; this will make men torment -each other with many artifices deceptions and treasons. O monstrous -creature! How much better would it be for men that every thing -should return to Hell! For this the vast forests will be devastated -of their trees; for this endless animals will lose their lives. - -(Of Fire.) - -One shall be born from small beginnings which will rapidly become -vast. This will respect no created thing, rather will it, by its -power, transform almost every thing from its own nature into -another. - -(Of Ships which sink.) - -Huge bodies will be seen, devoid of life, carrying, in fierce haste, -a multitude of men to the destruction of their lives. - -(Of Oxen, which are eaten.) - -The masters of estates will eat their own labourers. - -(Of beating Beds to renew them.) - -Men will be seen so deeply ungrateful that they will turn upon that -which has harboured them, for nothing at all; they will so load it -with blows that a great part of its inside will come out of its -place, and will be turned over and over in its body. - -(Of Things which are eaten and which first are killed.) - -Those who nourish them will be killed by them and afflicted by -merciless deaths. - -(Of the Reflection of Walls of Cities in the Water of their -Ditches.) - -The high walls of great cities will be seen up side down in their -ditches. - -(Of Water, which flows turbid and mixed with Soil and Dust; and of -Mist, which is mixed with the Air; and of Fire which is mixed with -its own, and each with each.) - -All the elements will be seen mixed together in a great whirling -mass, now borne towards the centre of the world, now towards the -sky; and now furiously rushing from the South towards the frozen -North, and sometimes from the East towards the West, and then again -from this hemisphere to the other. - -(The World may be divided into two Hemispheres at any Point.) - -All men will suddenly be transferred into opposite hemispheres. - -(The division of the East from the West may be made at any point.) - -All living creatures will be moved from the East to the West; and in -the same way from North to South, and vice versa. - -(Of the Motion of Water which carries wood, which is dead.) - -Bodies devoid of life will move by themselves and carry with them -endless generations of the dead, taking the wealth from the -bystanders. - -(Of Eggs which being eaten cannot form Chickens.) - -Oh! how many will they be that never come to the birth! - -(Of Fishes which are eaten unborn.) - -Endless generations will be lost by the death of the pregnant. - -(Of the Lamentation on Good Friday.) - -Throughout Europe there will be a lamentation of great nations over -the death of one man who died in the East. - -(Of Dreaming.) - -Men will walk and not stir, they will talk to those who are not -present, and hear those who do not speak. - -(Of a Man's Shadow which moves with him.) - -Shapes and figures of men and animals will be seen following these -animals and men wherever they flee. And exactly as the one moves the -other moves; but what seems so wonderful is the variety of height -they assume. - -(Of our Shadow cast by the Sun, and our Reflection in the Water at -one and the same time.) - -Many a time will one man be seen as three and all three move -together, and often the most real one quits him. - -(Of wooden Chests which contain great Treasures.) - -Within walnuts and trees and other plants vast treasures will be -found, which lie hidden there and well guarded. - -(Of putting out the Light when going to Bed.) - -Many persons puffing out a breath with too much haste, will thereby -lose their sight, and soon after all consciousness. - -(Of the Bells of Mules, which are close to their Ears.) - -In many parts of Europe instruments of various sizes will be heard -making divers harmonies, with great labour to those who hear them -most closely. - -(Of Asses.) - -The severest labour will be repaid with hunger and thirst, and -discomfort, and blows, and goadings, and curses, and great abuse. - -(Of Soldiers on horseback.) - -Many men will be seen carried by large animals, swift of pace, to -the loss of their lives and immediate death. - -In the air and on earth animals will be seen of divers colours -furiously carrying men to the destruction of their lives. - -(Of the Stars of Spurs.) - -By the aid of the stars men will be seen who will be as swift as any -swift animal. - -(Of a Stick, which is dead.) - -The motions of a dead thing will make many living ones flee with -pain and lamentation and cries. - -(Of Tinder.) - -With a stone and with iron things will be made visible which before -were not seen. - -1296. - -(Of going in Ships.) - -We shall see the trees of the great forests of Taurus and of Sinai -and of the Appenines and others, rush by means of the air, from East -to West and from North to South; and carry, by means of the air, -great multitudes of men. Oh! how many vows! Oh! how many deaths! Oh! -how many partings of friends and relations! Oh! how many will those -be who will never again see their own country nor their native land, -and who will die unburied, with their bones strewn in various parts -of the world! - -(Of moving on All Saints' Day.) - -Many will forsake their own dwellings and carry with them all their -belongings and will go to live in other parts. - -(Of All Souls' Day.) - -How many will they be who will bewail their deceased forefathers, -carrying lights to them. - -(Of Friars, who spending nothing but words, receive great gifts and -bestow Paradise.) - -Invisible money will procure the triumph of many who will spend it. - -(Of Bows made of the Horns of Oxen.) - -Many will there be who will die a painful death by means of the -horns of cattle. - -(Of writing Letters from one Country to another.) - -Men will speak with each other from the most remote countries, and -reply. - -(Of Hemispheres, which are infinite; and which are divided by an -infinite number of Lines, so that every Man always has one of these -Lines between his Feet.) - -Men standing in opposite hemispheres will converse and deride each -other and embrace each other, and understand each other's language. - -(Of Priests who say Mass.) - -There will be many men who, when they go to their labour will put on -the richest clothes, and these will be made after the fashion of -aprons [petticoats]. - -(Of Friars who are Confessors.) - -And unhappy women will, of their own free will, reveal to men all -their sins and shameful and most secret deeds. - -(Of Churches and the Habitations of Friars.) - -Many will there be who will give up work and labour and poverty of -life and goods, and will go to live among wealth in splendid -buildings, declaring that this is the way to make themselves -acceptable to God. - -(Of Selling Paradise.) - -An infinite number of men will sell publicly and unhindered things -of the very highest price, without leave from the Master of it; -while it never was theirs nor in their power; and human justice will -not prevent it. - -(Of the Dead which are carried to be buried.) - -The simple folks will carry vast quantities of lights to light up -the road for those who have entirely lost the power of sight. - -(Of Dowries for Maidens.) - -And whereas, at first, maidens could not be protected against the -violence of Men, neither by the watchfulness of parents nor by -strong walls, the time will come when the fathers and parents of -those girls will pay a large price to a man who wants to marry them, -even if they are rich, noble and most handsome. Certainly this seems -as though nature wished to eradicate the human race as being useless -to the world, and as spoiling all created things. - -(Of the Cruelty of Man.) - -Animals will be seen on the earth who will always be fighting -against each other with the greatest loss and frequent deaths on -each side. And there will be no end to their malignity; by their -strong limbs we shall see a great portion of the trees of the vast -forests laid low throughout the universe; and, when they are filled -with food the satisfaction of their desires will be to deal death -and grief and labour and wars and fury to every living thing; and -from their immoderate pride they will desire to rise towards heaven, -but the too great weight of their limbs will keep them down. Nothing -will remain on earth, or under the earth or in the waters which will -not be persecuted, disturbed and spoiled, and those of one country -removed into another. And their bodies will become the sepulture and -means of transit of all they have killed. - -O Earth! why dost thou not open and engulf them in the fissures of -thy vast abyss and caverns, and no longer display in the sight of -heaven such a cruel and horrible monster. - -1297. - -PROPHECIES. - -There will be many which will increase in their destruction. - -(The Ball of Snow rolling over Snow.) - -There will be many who, forgetting their existence and their name, -will lie as dead on the spoils of other dead creatures. - -(Sleeping on the Feathers of Birds.) - -The East will be seen to rush to the West and the South to the North -in confusion round and about the universe, with great noise and -trembling or fury. - -(In the East wind which rushes to the West.) - -The solar rays will kindle fire on the earth, by which a thing that -is under the sky will be set on fire, and, being reflected by some -obstacle, it will bend downwards. - -(The Concave Mirror kindles a Fire, with which we heat the oven, and -this has its foundation beneath its roof.) - -A great part of the sea will fly towards heaven and for a long time -will not return. (That is, in Clouds.) - -There remains the motion which divides the mover from the thing -moved. - -Those who give light for divine service will be destroyed.(The Bees -which make the Wax for Candles) - -Dead things will come from underground and by their fierce movements -will send numberless human beings out of the world. (Iron, which -comes from under ground is dead but the Weapons are made of it which -kill so many Men.) - -The greatest mountains, even those which are remote from the sea -shore, will drive the sea from its place. - -(This is by Rivers which carry the Earth they wash away from the -Mountains and bear it to the Sea-shore; and where the Earth comes -the sea must retire.) - -The water dropped from the clouds still in motion on the flanks of -mountains will lie still for a long period of time without any -motion whatever; and this will happen in many and divers lands. - -(Snow, which falls in flakes and is Water.) - -The great rocks of the mountains will throw out fire; so that they -will burn the timber of many vast forests, and many beasts both wild -and tame. - -(The Flint in the Tinder-box which makes a Fire that consumes all -the loads of Wood of which the Forests are despoiled and with this -the flesh of Beasts is cooked.) - -Oh! how many great buildings will be ruined by reason of Fire. - -(The Fire of great Guns.) - -Oxen will be to a great extent the cause of the destruction of -cities, and in the same way horses and buffaloes. - -(By drawing Guns.) - -1298. - -The Lion tribe will be seen tearing open the earth with their clawed -paws and in the caves thus made, burying themselves together with -the other animals that are beneath them. - -Animals will come forth from the earth in gloomy vesture, which will -attack the human species with astonishing assaults, and which by -their ferocious bites will make confusion of blood among those they -devour. - -Again the air will be filled with a mischievous winged race which -will assail men and beasts and feed upon them with much noise-- -filling themselves with scarlet blood. - -1299. - -Blood will be seen issuing from the torn flesh of men, and trickling -down the surface. - -Men will have such cruel maladies that they will tear their flesh -with their own nails. (The Itch.) - -Plants will be seen left without leaves, and the rivers standing -still in their channels. - -The waters of the sea will rise above the high peaks of the -mountains towards heaven and fall again on to the dwellings of men. -(That is, in Clouds.) - -The largest trees of the forest will be seen carried by the fury of -the winds from East to West. (That is across the Sea.) - -Men will cast away their own victuals. (That is, in Sowing.) - -1300. - -Human beings will be seen who will not understand each other's -speech; that is, a German with a Turk. - -Fathers will be seen giving their daughters into the power of man -and giving up all their former care in guarding them. (When Girls -are married.) - -Men will come out their graves turned into flying creatures; and -they will attack other men, taking their food from their very hand -or table. (As Flies.) - -Many will there be who, flaying their mother, will tear the skin -from her back. (Husbandmen tilling the Earth.) - -Happy will they be who lend ear to the words of the Dead. (Who read -good works and obey them.) - -1031. - -Feathers will raise men, as they do birds, towards heaven (that is, -by the letters which are written with quills.) - -The works of men's hands will occasion their death. (Swords and -Spears.) - -Men out of fear will cling to the thing they most fear. (That is -they will be miserable lest they should fall into misery.) - -Things that are separate shall be united and acquire such virtue -that they will restore to man his lost memory; that is papyrus -[sheets] which are made of separate strips and have preserved the -memory of the things and acts of men. - -The bones of the Dead will be seen to govern the fortunes of him who -moves them. (By Dice.) - -Cattle with their horns protect the Flame from its death. (In a -Lantern [Footnote 13: See note page 357.].) - -The Forests will bring forth young which will be the cause of their -death. (The handle of the hatchet.) - -1302. - -Men will deal bitter blows to that which is the cause of their life. -(In thrashing Grain.) - -The skins of animals will rouse men from their silence with great -outcries and curses. (Balls for playing Games.) - -Very often a thing that is itself broken is the occasion of much -union. (That is the Comb made of split Cane which unites the threads -of Silk.) - -The wind passing through the skins of animals will make men dance. -(That is the Bag-pipe, which makes people dance.) - -1303. - -(Of Walnut trees, that are beaten.) - -Those which have done best will be most beaten, and their offspring -taken and flayed or peeled, and their bones broken or crushed. - -(Of Sculpture.) - -Alas! what do I see? The Saviour cru- cified anew. - -(Of the Mouth of Man, which is a Sepulchre.) - -Great noise will issue from the sepulchres of those who died evil -and violent deaths. - -(Of the Skins of Animals which have the sense of feeling what is in -the things written.) - -The more you converse with skins covered with sentiments, the more -wisdom will you acquire. - -(Of Priests who bear the Host in their body.) - -Then almost all the tabernacles in which dwells the Corpus Domini, -will be plainly seen walking about of themselves on the various -roads of the world. - -1304. - -And those who feed on grass will turn night into day (Tallow.) - -And many creatures of land and water will go up among the stars -(that is Planets.) - -The dead will be seen carrying the living (in Carts and Ships in -various places.) - -Food shall be taken out of the mouth of many ( the oven's mouth.) - -And those which will have their food in their mouth will be deprived -of it by the hands of others (the oven.) - -1305. - -(Of Crucifixes which are sold.) - -I see Christ sold and crucified afresh, and his Saints suffering -Martyrdom. - -(Of Physicians, who live by sickness.) - -Men will come into so wretched a plight that they will be glad that -others will derive profit from their sufferings or from the loss of -their real wealth, that is health. - -(Of the Religion of Friars, who live by the Saints who have been -dead a great while.) - -Those who are dead will, after a thou- sand years be those who will -give a livelihood to many who are living. - -(Of Stones converted into Lime, with which prison walls are made.) - -Many things that have been before that time destroyed by fire will -deprive many men of liberty. - -1306. - -(Of Children who are suckled.) - -Many Franciscans, Dominicans and Benedictines will eat that which at -other times was eaten by others, who for some months to come will -not be able to speak. - -(Of Cockles and Sea Snails which are thrown up by the sea and which -rot inside their shells.) - -How many will there be who, after they are dead, will putrefy inside -their own houses, filling all the surrounding air with a fetid -smell. - -1307. - -(Of Mules which have on them rich burdens of silver and gold.) - -Much treasure and great riches will be laid upon four-footed beasts, -which will convey them to divers places. - -1308. - -(Of the Shadow cast by a man at night with a light.) - -Huge figures will appear in human shape, and the nearer you get to -them, the more will their immense size diminish. - -[Footnote page 1307: It seems to me probable that this note, which -occurs in the note book used in 1502, when Leonardo, in the service -of Cesare Borgia, visited Urbino, was suggested by the famous -pillage of the riches of the palace of Guidobaldo, whose treasures -Cesare Borgia at once had carried to Cesena (see GREGOROVIUS, -_Geschichte der Stadt Rom im Mittelalter_. XIII, 5, 4). ] - -1309. - -(Of Snakes, carried by Storks.) - -Serpents of great length will be seen at a great height in the air, -fighting with birds. - -(Of great guns, which come out of a pit and a mould.) - -Creatures will come from underground which with their terrific noise -will stun all who are near; and with their breath will kill men and -destroy cities and castles. - -1310. - -(Of Grain and other Seeds.) - -Men will fling out of their houses those victuals which were -intended to sustain their life. - -(Of Trees, which nourish grafted shoots.) - -Fathers and mothers will be seen to take much more delight in their -step-children then in their own children. - -(Of the Censer.) - -Some will go about in white garments with arrogant gestures -threatening others with metal and fire which will do no harm at all -to them. - -1311. - -(Of drying Fodder.) - -Innumerable lives will be destroyed and innumerable vacant spaces -will be made on the earth. - -(Of the Life of Men, who every year change their bodily substance.) - -Men, when dead, will pass through their own bowels. - -1312. - -(Shoemakers.) - -Men will take pleasure in seeing their own work destroyed and -injured. - -1313. - -(Of Kids.) - -The time of Herod will come again, for the little innocent children -will be taken from their nurses, and will die of terrible wounds -inflicted by cruel men. - -V. - -DRAUGHTS AND SCHEMES FOR THE HUMOROUS WRITINGS. - -Schemes for fables, etc. (1314-1323). - -1314. - -A FABLE. - -The crab standing under the rock to catch the fish which crept under -it, it came to pass that the rock fell with a ruinous downfall of -stones, and by their fall the crab was crushed. - -THE SAME. - -The spider, being among the grapes, caught the flies which were -feeding on those grapes. Then came the vintage, and the spider was -cut down with the grapes. - -The vine that has grown old on an old tree falls with the ruin of -that tree, and through that bad companionship must perish with it. - -The torrent carried so much earth and stones into its bed, that it -was then constrained to change its course. - -The net that was wont to take the fish was seized and carried away -by the rush of fish. - -The ball of snow when, as it rolls, it descends from the snowy -mountains, increases in size as it falls. - -The willow, which by its long shoots hopes as it grows, to outstrip -every other plant, from having associated itself with the vine which -is pruned every year was always crippled. - -1315. - -Fable of the tongue bitten by the teeth. - -The cedar puffed up with pride of its beauty, separated itself from -the trees around it and in so doing it turned away towards the wind, -which not being broken in its fury, flung it uprooted on the earth. - -The traveller's joy, not content in its hedge, began to fling its -branches out over the high road, and cling to the opposite hedge, -and for this it was broken away by the passers by. - -1316. - -The goldfinch gives victuals to its caged young. Death rather than -loss of liberty. [Footnote: Above this text is another note, also -referring to liberty; see No. 694.] - -1317. - -(Of Bags.) - -Goats will convey the wine to the city. - -1318. - -All those things which in winter are hidden under the snow, will be -uncovered and laid bare in summer. (for Falsehood, which cannot -remain hidden). - -1319. - -A FABLE. - -The lily set itself down by the shores of the Ticino, and the -current carried away bank and the lily with it. - -1320. - -A JEST. - -Why Hungarian ducats have a double cross on them. - -1321. - -A SIMILE. - -A vase of unbaked clay, when broken, may be remoulded, but not a -baked one. - -1322. - -Seeing the paper all stained with the deep blackness of ink, it he -deeply regrets it; and this proves to the paper that the words, -composed upon it were the cause of its being preserved. - -1323. - -The pen must necessarily have the penknife for a companion, and it -is a useful companionship, for one is not good for much without the -other. - -Schemes for prophecies (1324-1329). - -1324. - -The knife, which is an artificial weapon, deprives man of his nails, -his natural weapons. - -The mirror conducts itself haughtily holding mirrored in itself the -Queen. When she departs the mirror remains there ... - -1325. - -Flax is dedicated to death, and to the corruption of mortals. To -death, by being used for snares and nets for birds, animals and -fish; to corruption, by the flaxen sheets in which the dead are -wrapped when they are buried, and who become corrupt in these -winding sheets.-- And again, this flax does not separate its fibre -till it has begun to steep and putrefy, and this is the flower with -which garlands and decorations for funerals should be made. - -1326. - -(Of Peasants who work in shirts) - -Shadows will come from the East which will blacken with great colour -darkness the sky that covers Italy. - -(Of the Barbers.) - -All men will take refuge in Africa. - -1327. - -The cloth which is held in the hand in the current of a running -stream, in the waters of which the cloth leaves all its foulness and -dirt, is meant to signify this &c. - -By the thorn with inoculated good fruit is signified those natures -which of themselves were not disposed towards virtue, but by the aid -of their preceptors they have the repudation of it. - -1328. - -A COMMON THING. - -A wretched person will be flattered, and these flatterers are always -the deceivers, robbers and murderers of the wretched person. - -The image of the sun where it falls appears as a thing which covers -the person who attempts to cover it. - -(Money and Gold.) - -Out of cavernous pits a thing shall come forth which will make all -the nations of the world toil and sweat with the greatest torments, -anxiety and labour, that they may gain its aid. - -(Of the Dread of Poverty.) - -The malicious and terrible [monster] will cause so much terror of -itself in men that they will rush together, with a rapid motion, -like madmen, thinking they are escaping her boundless force. - -(Of Advice.) - -The man who may be most necessary to him who needs him, will be -repaid with ingratitude, that is greatly contemned. - -1329. - -(Of Bees.) - -They live together in communities, they are destroyed that we may -take the honey from them. Many and very great nations will be -destroyed in their own dwellings. - -1330. - -WHY DOGS TAKE PLEASURE IN SMELLING AT EACH OTHER. - -This animal has a horror of the poor, because they eat poor food, -and it loves the rich, because they have good living and especially -meat. And the excrement of animals always retains some virtue of its -origin as is shown by the faeces ... - -Now dogs have so keen a smell, that they can discern by their nose -the virtue remaining in these faeces, and if they find them in the -streets, smell them and if they smell in them the virtue of meat or -of other things, they take them, and if not, they leave them: And to -return to the question, I say that if by means of this smell they -know that dog to be well fed, they respect him, because they judge -that he has a powerful and rich master; and if they discover no such -smell with the virtue of meet, they judge that dog to be of small -account and to have a poor and humble master, and therefore they -bite that dog as they would his master. - -1331. - -The circular plans of carrying earth are very useful, inasmuch as -men never stop in their work; and it is done in many ways. By one of -these ways men carry the earth on their shoulders, by another in -chests and others on wheelbarrows. The man who carries it on his -shoulders first fills the tub on the ground, and he loses time in -hoisting it on to his shoulders. He with the chests loses no time. -[Footnote: The subject of this text has apparently no connection -with the other texts of this section.] - -Irony (1332). - -1332. - -If Petrarch was so fond of bay, it was because it is of a good taste -in sausages and with tunny; I cannot put any value on their foolery. -[Footnote: Conte Porro has published these lines in the _Archivio -Stor. Lombarda_ VIII, IV; he reads the concluding line thus: _I no -posso di loro gia (sic) co' far tesauro._--This is known to be by a -contemporary poet, as Senatore Morelli informs me.] - -Tricks (1333-1335). - -1333. - -We are two brothers, each of us has a brother. Here the way of -saying it makes it appear that the two brothers have become four. - -1334. - -TRICKS OF DIVIDING. - -Take in each hand an equal number; put 4 from the right hand into -the left; cast away the remainder; cast away an equal number from -the left hand; add 5, and now you will find 13 in this [left] hand; -that is-I made you put 4 from the right hand into the left, and cast -away the remainder; now your right hand has 4 more; then I make you -throw away as many from the right as you threw away from the left; -so, throwing from each hand a quantity of which the remainder may be -equal, you now have 4 and 4, which make 8, and that the trick may -not be detec- ted I made you put 5 more, which made 13. - -TRICKS OF DIVIDING. - -Take any number less than 12 that you please; then take of mine -enough to make up the number 12, and that which remains to me is the -number which you at first had; because when I said, take any number -less than 12 as you please, I took 12 into my hand, and of that 12 -you took such a number as made up your number of 12; and what you -added to your number, you took from mine; that is, if you had 8 to -go as far as to 12, you took of my 12, 4; hence this 4 transferred -from me to you reduced my 12 to a remainder of 8, and your 8 became -12; so that my 8 is equal to your 8, before it was made 12. - -[Footnote 1334: G. Govi _says in the_ 'Saggio' p. 22: _Si dilett -Leonarda, di giuochi di prestigi e molti (?) ne descrisse, che si -leggono poi riportati dal Paciolo nel suo libro:_ de Viribus -Quantitatis, _e che, se non tutti, sono certo in gran parte -invenzioni del Vinci._] - -1335. - -If you want to teach someone a subject you do not know yourself, let -him measure the length of an object unknown to you, and he will -learn the measure you did not know before;--Master Giovanni da Lodi. - -_XXI._ - -_Letters. Personal Records. Dated Notes._ - -_When we consider how superficial and imperfect are the accounts of -Leonardo's life written some time after his death by Vasari and -others, any notes or letters which can throw more light on his -personal circumstances cannot fail to be in the highest degree -interesting. The texts here given as Nos._ 1351--1353, _set his -residence in Rome in quite a new aspect; nay, the picture which -irresistibly dwells in our minds after reading these details of his -life in the Vatican, forms a striking contrast to the contemporary -life of Raphael at Rome._ - -_I have placed foremost of these documents the very remarkable -letters to the Defterdar of Syria. In these Leonardo speaks of -himself as having staid among the mountains of Armenia, and as the -biographies of the master tell nothing of any such distant journeys, -it would seem most obvious to treat this passage as fiction, and so -spare ourselves the onus of proof and discussion. But on close -examination no one can doubt that these documents, with the -accompanying sketches, are the work of Leonardo's own hand. Not -merely is the character of the handwriting his, but the spelling and -the language are his also. In one respect only does the writing -betray any marked deviation from the rest of the notes, especially -those treating on scientific questions; namely, in these -observations he seems to have taken particular pains to give the -most distinct and best form of expression to all he had to say; we -find erasures and emendations in almost every line. He proceeded, as -we shall see, in the same way in the sketches for letters to -Giuliano de' Medici, and what can be more natural, I may ask, than -to find the draft of a letter thus altered and improved when it is -to contain an account of a definite subject, and when personal -interests are in the scale? The finished copies as sent off are not -known to exist; if we had these instead of the rough drafts, we -might unhesitatingly have declared that some unknown Italian -engineer must have been, at that time, engaged in Armenia in the -service of the Egyptian Sultan, and that Leonardo had copied his -documents. Under this hypothesis however we should have to state -that this unknown writer must have been so far one in mind with -Leonardo as to use the same style of language and even the same -lines of thought. This explanation might--as I say--have been -possible, if only we had the finished letters. But why should these -rough drafts of letters be regarded as anything else than what they -actually and obviously are? If Leonardo had been a man of our own -time, we might perhaps have attempted to account for the facts by -saying that Leonardo, without having been in the East himself, might -have undertaken to write a Romance of which the scene was laid in -Armenia, and at the desire of his publisher had made sketches of -landscape to illustrate the text. - -I feel bound to mention this singular hypothesis as it has actually -been put forward (see No. 1336 note 5); and it would certainly seem -as though there were no other possible way of evading the conclusion -to which these letters point, and their bearing on the life of the -master,--absurd as the alternative is. But, if, on a question of -such importance, we are justified in suggesting theories that have -no foundation in probability, I could suggest another which, as -compared with that of a Fiction by Leonardo, would be neither more -nor less plausible; it is, moreover the only other hypothesis, -perhaps, which can be devised to account for these passages, if it -were possible to prove that the interpretation that the documents -themselves suggest, must be rejected a priori; viz may not Leonardo -have written them with the intention of mystifying those who, after -his death, should try to decipher these manuscripts with a view to -publishing them? But if, in fact, no objection that will stand the -test of criticism can be brought against the simple and direct -interpretation of the words as they stand, we are bound to regard -Leonardo's travels in the East as an established fact. There is, I -believe nothing in what we know of his biography to negative such a -fact, especially as the details of his life for some few years are -wholly unknown; nor need we be at a loss for evidence which may -serve to explain--at any rate to some extent--the strangeness of his -undertaking such a journey. We have no information as to Leonardo's -history between 1482 and 1486; it cannot be proved that he was -either in Milan or in Florence. On the other hand the tenor of this -letter does not require us to assume a longer absence than a year or -two. For, even if his appointment_ (offitio) _as Engineer in Syria -had been a permanent one, it might have become untenable--by the -death perhaps of the Defterdar, his patron, or by his removal from -office--, and Leonardo on his return home may have kept silence on -the subject of an episode which probably had ended in failure and -disappointment. - -From the text of No. 1379 we can hardly doubt that Leonardo intended -to make an excursion secretly from Rome to Naples, although so far -as has hitherto been known, his biographers never allude to it. In -another place (No. 1077) he says that he had worked as an Engineer -in Friuli. Are we to doubt this statement too, merely because no -biographer has hitherto given us any information on the matter? In -the geographical notes Leonardo frequently speaks of the East, and -though such passages afford no direct proof of his having been -there, they show beyond a doubt that, next to the Nile, the -Euphrates, the Tigris and the Taurus mountains had a special -interest in his eyes. As a still further proof of the futility of -the argument that there is nothing in his drawings to show that he -had travelled in the East, we find on Pl. CXX a study of oriental -heads of Armenian type,--though of course this may have been made in -Italy. - -If the style of these letters were less sober, and the expressions -less strictly to the point throughout, it miglit be possible to -regard them as a romantic fiction instead of a narrative of fact. -Nay, we have only to compare them with such obviously fanciful -passages as No. 1354, Nos. 670-673, and the Fables and Prophecies. -It is unnecessary to discuss the subject any further here; such -explanations as the letter needs are given in the foot notes. - -The drafts of letters to Lodovico il Moro are very remarkable. -Leonardo and this prince were certainly far less closely connected, -than has hitherto been supposed. It is impossible that Leonardo can -have remained so long in the service of this prince, because the -salary was good, as is commonly stated. On the contrary, it would -seem, that what kept him there, in spite of his sore need of the -money owed him by the prince, was the hope of some day being able to -carry out the project of casting the_ 'gran cavallo'. - -Drafts of Letters and Reports referring to Armenia (1336. 1337). - -1336. - -To THE DEVATDAR OF SYRIA, LIEUTENANT OF THE SACRED SULTAN OF -BABYLON. - -[3] The recent disaster in our Northern parts which I am certain -will terrify not you alone but the whole world, which - -[Footnote: Lines 1-52 are reproduced in facsimile on Pl. CXVI. - -1. _Diodario._ This word is not to be found in any Italian -dictionary, and for a long time I vainly sought an explanation of -it. The youthful reminiscences of my wife afforded the desired clue. -The chief town of each Turkish Villayet, or province --such as -Broussa, for instance, in Asia Minor, is the residence of a -Defterdar, who presides over the financial affairs of the province. -_Defterdar hane_ was, in former times, the name given to the -Ministry of Finance at Constantinople; the Minister of Finance to -the Porte is now known as the _Mallie-Nazri_ and the _Defterdars_ -are his subordinates. A _Defterdar_, at the present day is merely -the head of the finance department in each Provincial district. With -regard to my suggestion that Leonardo's _Diodario_ might be -identical with the Defterdar of former times, the late M. C. -DEFREMERIE, Arabic Professor, and Membre de l'Institut de France -wrote to me as follows: _Votre conjecture est parfaitement fondee; -diodario est Vequivalent de devadar ou plus exactement devatdar, -titre d'une importante dignite en Egypt'e, sous les Mamlouks._ - -The word however is not of Turkish, but of Perso-Arabie derivation. -[Defter written in arab?] literally _Defter_ (Arabic) meaning -_folio_; for _dar_ (Persian) Bookkeeper or holder is the English -equivalent; and the idea is that of a deputy in command. During the -Mamelook supremacy over Syria, which corresponded in date with -Leonardo's time, the office of Defterdar was the third in importance -in the State. - -_Soltano di Babilonia_. The name of Babylon was commonly applied to -Cairo in the middle ages. For instance BREIDENBACH, _Itinerarium -Hierosolyma_ p. 218 says: "At last we reached Babylon. But this is -not that Babylon which stood on the further shore of the river -Chober, but that which is called the Egyptian Babylon. It is close -by Cairo and the twain are but one and not two towns; one half is -called Cairo and the other Babylon, whence they are called together -Cairo-Babylon; originally the town is said to have been named -Memphis and then Babylon, but now it is called Cairo." Compare No. -1085, 6. - -Egypt was governed from 1382 till 1517 by the Borgite or -Tcherkessian dynasty of the Mamelook Sultans. One of the most famous -of these, Sultan Kait Bey, ruled from 1468-1496 during whose reign -the Gama (or Mosque) of Kait Bey and tomb of Kait Bey near the -Okella Kait Bey were erected in Cairo, which preserve his name to -this day. Under the rule of this great and wise prince many -foreigners, particularly Italians, found occupation in Egypt, as may -be seen in the 'Viaggio di Josaphat Barbaro', among other -travellers. "Next to Leonardo (so I learn from Prof. Jac. Burckhardt -of Bale) Kait Bey's most helpful engineer was a German who in about -1487, superintended the construction of the Mole at Alexandria. -Felix Fabri knew him and mentions him in his _Historia Suevorum_, -written in 1488." - -3. _Il nuovo accidente accaduto_, or as Leonardo first wrote and -then erased, _e accaduto un nuovo accidente_. From the sequel this -must refer to an earthquake, and indeed these were frequent at that -period, particularly in Asia Minor, where they caused immense -mischief. See No. 1101 note.] - -shall be related to you in due order, showing first the effect and -then the cause. [Footnote 4: The text here breaks off. The following -lines are a fresh beginning of a letter, evidently addressed to the -same person, but, as it would seem, written at a later date than the -previous text. The numerous corrections and amendments amply prove -that it is not a copy from any account of a journey by some unknown -person; but, on the contrary, that Leonardo was particularly anxious -to choose such words and phrases as might best express his own -ideas.] - -Finding myself in this part of Armenia [Footnote 5: _Parti -d'Erminia_. See No. 945, note. The extent of Armenia in Leonardo's -time is only approximately known. In the XVth century the Persians -governed the Eastern, and the Arabs the Southern portions. Arabic -authors--as, for instance Abulfeda--include Cilicia and a part of -Cappadocia in Armenia, and Greater Armenia was the tract of that -country known later as Turcomania, while Armenia Minor was the -territory between Cappadocia and the Euphrates. It was not till -1522, or even 1574 that the whole country came under the dominion of -the Ottoman Turks, in the reign of Selim I. - -The Mamelook Sultans of Egypt seem to have taken a particular -interest in this, the most Northern province of their empire, which -was even then in danger of being conquered by the Turks. In the -autumn of 1477 Sultan Kait Bey made a journey of inspection, -visiting Antioch and the valleys of the Tigris and Euphrates with a -numerous and brilliant escort. This tour is briefly alluded to by -_Moodshireddin_ p. 561; and by WEIL, _Geschichte der Abbasiden_ V, -p. 358. An anonymous member of the suite wrote a diary of the -expedition in Arabic, which has been published by R. V. LONZONE -(_'Viaggio in Palestina e Soria di Kaid Ba XVIII sultano della II -dinastia mamelucca, fatto nel 1477. Testo arabo. Torino 1878'_, -without notes or commentary). Compare the critique on this edition, -by J. GILDEMEISTER in _Zeitschrift des Deutschen Palaestina Vereins_ -(Vol. Ill p. 246--249). Lanzone's edition seems to be no more than -an abridged copy of the original. I owe to Professor Sche'fer, -Membre de l'Institut, the information that he is in possession of a -manuscript in which the text is fuller, and more correctly given. -The Mamelook dynasty was, as is well known, of Circassian origin, -and a large proportion of the Egyptian Army was recruited in -Circassia even so late as in the XVth century. That was a period of -political storms in Syria and Asia Minor and it is easy to suppose -that the Sultan's minister, to whom Leonardo addresses his report as -his superior, had a special interest in the welfare of those -frontier provinces. Only to mention a few historical events of -Sultan Kait Bey's reign, we find that in 1488 he assisted the -Circassians to resist the encroachments of Alaeddoulet, an Asiatic -prince who had allied himself with the Osmanli to threaten the -province; the consequence was a war in Cilicia by sea and land, -which broke out in the following year between the contending powers. -Only a few years earlier the same province had been the scene of the -so-called Caramenian war in which the united Venetian, Neapolitan -and Sclavonic fleets had been engaged. (See CORIALANO CIPPICO, -_Della guerra dei Veneziani nell' Asia dal_ 1469--1474. Venezia -1796, p. 54) and we learn incidentally that a certain Leonardo -Boldo, Governor of Scutari under Sultan Mahmoud,--as his name would -indicate, one of the numerous renegades of Italian birth--played an -important part in the negotiations for peace. - -_Tu mi mandasti_. The address _tu_ to a personage so high in office -is singular and suggests personal intimacy; Leonardo seems to have -been a favourite with the Diodario. Compare lines 54 and 55. - -I have endeavoured to show, and I believe that I am also in a -position to prove with regard to these texts, that they are draughts -of letters actually written by Leonardo; at the same time I must not -omit to mention that shortly after I had discovered - -these texts in the Codex Atlanticus and published a paper on the -subject in the _Zeitschrift fur bildende Kunst (Vol. XVI)_, Prof. -Govi put forward this hypothesis to account for their origin: - -_"Quanto alle notizie sul monte Tauro, sull'Armenia e sull' Asia -minore che si contengono negli altri frammenti, esse vennero prese -da qualche geografro o viaggiatore contemporaneo. Dall'indice -imperfetto che accompagna quei frammenti, si potrebbe dedurre che -Leonardo volesse farne un libro, che poi non venne compiuto. A ogni -modo, non e possibile di trovare in questi brani nessun indizio di -un viaggio di Leonardo in oriente, ne della sua conversione alla -religione di Maometto, come qualcuno pretenderebbe. Leonardo amava -con passione gli studi geografici, e nel suoi scritti s'incontran -spesso itinerart, indicazioni, o descrizioni di luoghi, schizzi di -carte e abbozzi topografici di varie regioni, non e quindi strano -che egli, abile narratore com'era, si fosse proposto di scrivere una -specie di Romanzo in forma epistolare svolgendone Pintreccio -nell'Asia Minore, intorno alla quale i libri d'allora, e forse -qualche viaggiatore amico suo, gli avevano somministrato alcuni -elementi piu o meno_ fantastici. (See Transunti della Reale -Accademia dei Lincei Voi. V Ser. 3). - -It is hardly necessary to point out that Prof. Govi omits to name -the sources from which Leonardo could be supposed to have drawn his -information, and I may leave it to the reader to pronounce judgment -on the anomaly which is involved in the hypothesis that we have here -a fragment of a Romance, cast in the form of a correspondence. At -the same time, I cannot but admit that the solution of the -difficulties proposed by Prof. Govi is, under the circumstances, -certainly the easiest way of dealing with the question. But we -should then be equally justified in supposing some more of -Leonardo's letters to be fragments of such romances; particularly -those of which the addresses can no longer be named. Still, as -regards these drafts of letters to the Diodario, if we accept the -Romance theory, as pro- posed by Prof. Govi, we are also compelled -to assume that Leonardo purposed from the first to illustrate his -tale; for it needs only a glance at the sketches on PI. CXVI to CXIX -to perceive that they are connected with the texts; and of course -the rest of Leonardo's numerous notes on matters pertaining to the -East, the greater part of which are here published for the first -time, may also be somehow connected with this strange romance. - -7. _Citta de Calindra (Chalindra)_. The position of this city is so -exactly determined, between the valley of the Euphrates and the -Taurus range that it ought to be possible to identify it. But it can -hardly be the same as the sea port of Cilicia with a somewhat -similar name Celenderis, Kelandria, Celendria, Kilindria, now the -Turkish Gulnar. In two Catalonian Portulans in the Bibliotheque -Natio- nale in Paris-one dating from the XV'h century, by Wilhelm -von Soler, the other by Olivez de Majorca, in l584-I find this place -called Calandra. But Leonardo's Calindra must certainly have lain -more to the North West, probably somewhere in Kurdistan. The fact -that the geographical position is so care- fully determined by -Leonardo seems to prove that it was a place of no great importance -and little known. It is singular that the words first written in 1. -8 were divisa dal lago (Lake Van?), altered afterwards to -dall'Eitfrates. - -Nostri confini, and in 1. 6 proposito nostro. These refer to the -frontier and to the affairs of the Mamelook Sultan, Lines 65 and 66 -throw some light on the purpose of Leonardo's mission. - -8. _I_ corni del gra mote Tauro. Compare the sketches PI. -CXVI-CXVIII. So long as it is im- possible to identify the situation -of Calindra it is most difficult to decide with any certainty which -peak of the Taurus is here meant; and I greatly regret that I had no -foreknowledge of this puzzling topographical question when, in 1876, -I was pursuing archaeological enquiries in the Provinces of Aleppo -and Cilicia, and had to travel for some time in view of the imposing -snow-peaks of Bulghar Dagh and Ala Tepessi. - -9-10. The opinion here expressed as to the height of the mountain -would be unmeaning, unless it had been written before Leonardo moved -to Milan, where Monte Rosa is so conspicuous an object in the -landscape. 4 _ore inanzi_ seems to mean, four hours before the sun's -rays penetrate to the bottom of the valleys.] - -to carry into effect with due love and care the task for which you -sent me [Footnote: ][6]; and to make a beginning in a place which -seemed to me to be most to our purpose, I entered into the city of -Calindrafy[7], near to our frontiers. This city is situated at the -base of that part of the Taurus mountains which is divided from the -Euphrates and looks towards the peaks of the great Mount Taurus [8] -to the West [9]. These peaks are of such a height that they seem to -touch the sky, and in all the world there is no part of the earth, -higher than its summit[10], and the rays of the sun always fall upon -it on its East side, four hours before day-time, and being of the -whitest stone [Footnote 11:_Pietra bianchissima_. The Taurus -Mountains consist in great part of limestone.] it shines -resplendently and fulfils the function to these Armenians which a -bright moon-light would in the midst of the darkness; and by its -great height it outreaches the utmost level of the clouds by a space -of four miles in a straight line. This peak is seen in many places -towards the West, illuminated by the sun after its setting the third -part of the night. This it is, which with you [Footnote 14: -_Appresso di voi_. Leonardo had at first written _noi_ as though his -meaning had,been: This peak appeared to us to be a comet when you -and I observed it in North Syria (at Aleppo? at Aintas?). The -description of the curious reflection in the evening, resembling the -"Alpine-glow" is certainly not an invented fiction, for in the next -lines an explanation of the phenomenon is offered, or at least -attempted.] we formerly in calm weather had supposed to be a comet, -and appears to us in the darkness of night, to change its form, -being sometimes divided in two or three parts, and sometimes long -and sometimes short. And this is caused by the clouds on the horizon -of the sky which interpose between part of this mountain and the -sun, and by cutting off some of the solar rays the light on the -mountain is intercepted by various intervals of clouds, and -therefore varies in the form of its brightness. - -THE DIVISIONS OF THE BOOK [Footnote 19: The next 33 lines are -evidently the contents of a connected Report or Book, but not of one -which he had at hand; more probably, indeed, of one he purposed -writing.]. - -The praise and confession of the faith [Footnote 20: _Persuasione di -fede_, of the Christian or the Mohammedan faith? We must suppose the -latter, at the beginning of a document addressed to so high a -Mohammedan official. _Predica_ probably stands as an abbreviation -for _predicazione_ (lat. _praedicatio_) in the sense of praise or -glorification; very probably it may mean some such initial doxology -as we find in Mohammedan works. (Comp. 1. 40.)]. - -The sudden inundation, to its end. - -[23] The destruction of the city. - -[24]The death of the people and their despair. - -The preacher's search, his release and benevolence [Footnote 28: The -phraseology of this is too general for any conjecture as to its -meaning to be worth hazarding.] - -Description of the cause of this fall of the mountain [Footnote 30: -_Ruina del monte_. Of course by an earthquake. In a catalogue of -earthquakes, entitled _kechf aussalssaleb an auasf ezzel-zeleh_, and -written by Djelal eddin]. - -The mischief it did. - -[32] Fall of snow. - -The finding of the prophet [33]. - -His prophesy. - -[35] The inundation of the lower portion of Eastern Armenia, the -draining of which was effected by the cutting through the Taurus -Mountains. - -How the new prophet showed [Footnote 40:_Nova profeta, 1. 33, -profeta_. Mohammed. Leonardo here refers to the Koran: - -In the name of the most merciful God.--When the earth shall be -shaken by an earthquake; and the earth shall cast forth her burdens; -and a man shall say, what aileth her? On that day the earth shall -declare her tidings, for that thy Lord will inspire her. On that day -men shall go forward in distinct classes, that they may behold their -works. And whoever shall have wrought good of the weight of an ant, -shall behold the same. And whoever shall have wrought evil of the -weight of an ant, shall behold the same. (The Koran, translated by -G. Sale, Chapter XCIX, p. 452).] that this destruction would happen -as he had foretold. - -Description of the Taurus Mountains [43] and the river Euphrates. - -Why the mountain shines at the top, from half to a third of the -night, and looks like a comet to the inhabitants of the West after -the sunset, and before day to those of the East. - -Why this comet appears of variable forms, so that it is now round -and now long, and now again divided into two or three parts, and now -in one piece, and when it is to be seen again. - -OF THE SHAPE OF THE TAURUS MOUNTAINS [Footnote 53-94: The facsimile -of this passage is given on Pl. CXVII.]. - -I am not to be accused, Oh Devatdar, of idleness, as your chidings -seem to hint; but your excessive love for me, which gave rise to the -benefits you have conferred on me [Footnote 55] is that which has -also compelled me to the utmost painstaking in seeking out and -diligently investigating the cause of so great and stupendous an -effect. And this could not be done without time; now, in order to -satisfy you fully as to the cause of so great an effect, it is -requisite that I should explain to you the form of the place, and -then I will proceed to the effect, by which I believe you will be -amply satisfied. - -[Footnote 36: _Tagliata di Monte Tauro_. The Euphrates flows through -the Taurus range near the influx of the Kura Shai; it rushes through -a rift in the wildest cliffs from 2000 to 3000 feet high and runs on -for 90 miles in 300 falls or rapids till it reaches Telek, near -which at a spot called Gleikash, or the Hart's leap, it measures -only 35 paces across. Compare the map on Pl. CXIX and the -explanation for it on p. 391.] - -[Footnote 54: The foregoing sketch of a letter, lines 5. 18, appears -to have remained a fragment when Leonardo received pressing orders -which caused him to write immediately and fully on the subject -mentioned in line 43.] - -[Footnote 59: This passage was evidently intended as an improvement -on that immediately preceding it. The purport of both is essentially -the same, but the first is pitched in a key of ill-disguised -annoyance which is absent from the second. I do not see how these -two versions can be reconciled with the romance-theory held by Prof. -Govi.] Do not be aggrieved, O Devatdar, by my delay in responding to -your pressing request, for those things which you require of me are -of such a nature that they cannot be well expressed without some -lapse of time; particularly because, in order to explain the cause -of so great an effect, it is necessary to describe with accuracy the -nature of the place; and by this means I can afterwards easily -satisfy your above-mentioned request. [Footnote 62: This passage was -evidently intended as an improvement on that immediately preceding -it. The purport of both is essentially the same, but the first is -pitched in a key of ill-disguised annoyance which is absent from the -second. I do not see how these two versions can be reconciled with -the romance-theory held by Prof. Govi.] - -I will pass over any description of the form of Asia Minor, or as to -what seas or lands form the limits of its outline and extent, -because I know that by your own diligence and carefulness in your -studies you have not remained in ignorance of these matters [65]; -and I will go on to describe the true form of the Taurus Mountain -which is the cause of this stupendous and harmful marvel, and which -will serve to advance us in our purpose [66]. This Taurus is that -mountain which, with many others is said to be the ridge of Mount -Caucasus; but wishing to be very clear about it, I desired to speak -to some of the inhabitants of the shores of the Caspian sea, who -give evidence that this must be the true Caucasus, and that though -their mountains bear the same name, yet these are higher; and to -confirm this in the Scythian tongue Caucasus means a very high -[Footnote 68: Caucasus; Herodot Kaoxaais; Armen. Kaukaz.] peak, and -in fact we have no information of there being, in the East or in the -West, any mountain so high. And the proof of this is that the -inhabitants of the countries to the West see the rays of the sun -illuminating a great part of its summit for as much as a quarter of -the longest night. And in the same way, in those countries which lie -to the East. - -OF THE STRUCTURE AND SIZE OF MOUNT TAURUS. - -[Footnote 73: The statements are of course founded on those of the -'inhabitants' spoken of in 1. 67.] The shadow of this ridge of the -Taurus is of such a height that when, in the middle of June, the Sun -is at its meridian, its shadow extends as far as the borders of -Sarmatia, twelve days off; and in the middle of December it extends -as far as the Hyperborean mountains, which are at a month's journey -to the North [75]. And the side which faces the wind is always free -from clouds and mists, because the wind which is parted in beating -on the rock, closes again on the further side of that rock, and in -its motion carries with it the clouds from all quarters and leaves -them where it strikes. And it is always full of thunderbolts from -the great quantity of clouds which accumulate there, whence the rock -is all riven and full of huge debris [Footnote 77: Sudden storms are -equally common on the heights of Ararat. It is hardly necessary to -observe that Ararat cannot be meant here. Its summit is formed like -the crater of Vesuvius. The peaks sketched on Pl. CXVI-CXVIII are -probably views of the same mountain, taken from different sides. -Near the solitary peak, Pl. CXVIII these three names are written -_goba, arnigasar, caruda_, names most likely of different peaks. Pl. -CXVI and CXVII are in the original on a single sheet folded down the -middle, 30 centimetres high and 43 1/2 wide. On the reverse of one -half of the sheet are notes on _peso_ and _bilancia_ (weight and -balance), on the other are the 'prophecies' printed under Nos. 1293 -and 1294. It is evident from the arrangement that these were written -subsequently, on the space which had been left blank. These pages -are facsimiled on Pl. CXVIII. In Pl. CXVI-CXVIII the size is smaller -than in the original; the map of Armenia, Pl. CXVIII, is on Pl. CXIX -slightly enlarged. On this map we find the following names, -beginning from the right hand at the top: _pariardes mo_ (for -Paryadres Mons, Arm. Parchar, now Barchal or Kolai Dagh; Trebizond -is on its slope). - -_Aquilone_ --North, _Antitaurus Antitaurus psis mo_ (probably meant -for Thospitis = Lake Van, Arm. Dgov Vanai, Tospoi, and the Mountain -range to the South); _Gordis mo_ (Mountains of Gordyaea), the birth -place of the Tigris; _Oriente_ --East; _Tigris_, and then, to the -left, _Eufrates_. Then, above to the left _Argeo mo_ (now Erdshigas, -an extinct volcano, 12000 feet high); _Celeno mo_ (no doubt Sultan -Dagh in Pisidia). Celeno is the Greek town of KeAouvat-- see Arian -I, 29, I--now the ruins of Dineir); _oriente_ --East; _africo -libezco_ (for libeccio--South West). In the middle of the Euphrates -river on this small map we see a shaded portion surrounded by -mountains, perhaps to indicate the inundation mentioned in l. 35. -The affluent to the Euphrates shown as coming with many windings -from the high land of 'Argeo' on the West, is the Tochma Su, which -joins the main river at Malatie. I have not been able to discover -any map of Armenia of the XVth or XVIth century in which the course -of the Euphrates is laid down with any thing like the correctness -displayed in this sketch. The best I have seen is the Catalonian -Portulan of Olivez de Majorca, executed in 1584, and it is far -behind Leonardo's.]. This mountain, at its base, is inhabited by a -very rich population and is full of most beautiful springs and -rivers, and is fertile and abounding in all good produce, -particularly in those parts which face to the South. But after -mounting about three miles we begin to find forests of great fir -trees, and beech and other similar trees; after this, for a space of -three more miles, there are meadows and vast pastures; and all the -rest, as far as the beginning of the Taurus, is eternal snows which -never disappear at any time, and extend to a height of about -fourteen miles in all. From this beginning of the Taurus up to the -height of a mile the clouds never pass away; thus we have fifteen -miles, that is, a height of about five miles in a straight line; and -the summit of the peaks of the Taurus are as much, or about that. -There, half way up, we begin to find a scorching air and never feel -a breath of wind; but nothing can live long there; there nothing is -brought forth save a few birds of prey which breed in the high -fissures of Taurus and descend below the clouds to seek their prey. -Above the wooded hills all is bare rock, that is, from the clouds -upwards; and the rock is the purest white. And it is impossible to -walk to the high summit on account of the rough and perilous ascent. - -1337. - -[Footnote: 1337. On comparing this commencement of a letter l. 1-2 -with that in l. 3 and 4 of No. 1336 it is quite evident that both -refer to the same event. (Compare also No. 1337 l. 10-l2 and 17 with -No. 1336 l. 23, 24 and 32.) But the text No. 1336, including the -fragment l. 3-4, was obviously written later than the draft here -reproduced. The _Diodario_ is not directly addressed--the person -addressed indeed is not known--and it seems to me highly probable -that it was written to some other patron and friend whose name and -position are not mentioned.] - -Having often made you, by my letters, acquainted with the things -which have happened, I think I ought not to be silent as to the -events of the last few days, which--[2]... - -Having several times-- - -Having many times rejoiced with you by letters over your prosperous -fortunes, I know now that, as a friend you will be sad with me over -the miserable state in which I find myself; and this is, that during -the last few days I have been in so much trouble, fear, peril and -loss, besides the miseries of the people here, that we have been -envious of the dead; and certainly I do not believe that since the -elements by their separation reduced the vast chaos to order, they -have ever combined their force and fury to do so much mischief to -man. As far as regards us here, what we have seen and gone through -is such that I could not imagine that things could ever rise to such -an amount of mischief, as we experienced in the space of ten hours. -In the first place we were assailed and attacked by the violence and -fury of the winds [10]; to this was added the falling of great -mountains of snow which filled up all this valley, thus destroying a -great part of our city [Footnote 11: _Della nostra citta_ (Leonardo -first wrote _di questa citta_). From this we may infer that he had -at some time lived in the place in question wherever it might be.]. -And not content with this the tempest sent a sudden flood of water -to submerge all the low part of this city [12]; added to which there -came a sudden rain, or rather a ruinous torrent and flood of water, -sand, mud, and stones, entangled with roots, and stems and fragments -of various trees; and every kind of thing flying through the air -fell upon us; finally a great fire broke out, not brought by the -wind, but carried as it would seem, by ten thousand devils, which -completely burnt up all this neighbourhood and it has not yet -ceased. And those few who remain unhurt are in such dejection and -such terror that they hardly have courage to speak to each other, as -if they were stunned. Having abandoned all our business, we stay -here together in the ruins of some churches, men and women mingled -together, small and great [Footnote 17: _Certe ruine di chiese_. -Either of Armenian churches or of Mosques, which it was not unusual -to speak of as churches. - -_Maschi e femmini insieme unite_, implies an infringement of the -usually strict rule of the separation of the sexes.], just like -herds of goats. The neighbours out of pity succoured us with -victuals, and they had previously been our enemies. And if - -[Footnote 18: _I vicini, nostri nimici_. The town must then have -stood quite close to the frontier of the country. Compare 1336. L. -7. _vicini ai nostri confini_. Dr. M. JORDAN has already published -lines 4-13 (see _Das Malerbuch, Leipzig_, 1873, p. 90:--his reading -differs from mine) under the title of "Description of a landscape -near Lake Como". We do in fact find, among other loose sheets in the -Codex Atlanticus, certain texts referring to valleys of the Alps -(see Nos. 1030, 1031 and note p. 237) and in the arrangement of the -loose sheets, of which the Codex Atlanticus has been formed, these -happen to be placed close to this text. The compiler stuck both on -the same folio sheet; and if this is not the reason for Dr. JORDAN'S -choosing such a title (Description &c.) I cannot imagine what it can -have been. It is, at any rate, a merely hypothetical statement. The -designation of the population of the country round a city as "the -enemy" (_nemici_) is hardly appropriate to Italy in the time of -Leonardo.] - -it had not been for certain people who succoured us with victuals, -all would have died of hunger. Now you see the state we are in. And -all these evils are as nothing compared with those which are -promised to us shortly. - -I know that as a friend you will grieve for my misfortunes, as I, in -former letters have shown my joy at your prosperity ... - -Notes about events observed abroad (1338-1339). - -1338. - -BOOK 43. OF THE MOVEMENT OF AIR ENCLOSED IN WATER. - -I have seen motions of the air so furious that they have carried, -mixed up in their course, the largest trees of the forest and whole -roofs of great palaces, and I have seen the same fury bore a hole -with a whirling movement digging out a gravel pit, and carrying -gravel, sand and water more than half a mile through the air. - -[Footnote: The first sixteen lines of this passage which treat of -the subject as indicated on the title line have no place in this -connexion and have been omitted.] - -[Footnote 2: _Ho veduto movimenti_ &c. Nothing of the kind happened -in Italy during Leonardo's lifetime, and it is therefore extremely -probable that this refers to the natural phenomena which are so -fully described in the foregoing passage. (Compare too, No. 1021.) -There can be no doubt that the descriptions of the Deluge in the -Libro di Pittura (Vol. I, No. 607-611), and that of the fall of a -mountain No. 610, l. 17-30 were written from the vivid impressions -derived from personal experience. Compare also Pl. XXXIV-XL.] - -1339. - -[Footnote: It may be inferred from the character of the writing, -which is in the style of the note in facsimile Vol. I, p. 297, that -this passage was written between 1470 and 1480. As the figure 6 at -the end of the text indicates, it was continued on another page, but -I have searched in vain for it. The reverse of this leaf is coloured -red for drawing in silver point, but has not been used for that -purpose but for writing on, and at about the same date. The passages -are given as Nos. 1217, 1218, 1219, 1162 and No. 994 (see note page -218). The text given above is obviously not a fragment of a letter, -but a record of some personal experience. No. 1379 also seems to -refer to Leonardo's journeys in Southern Italy.] - -Like a whirling wind which rushes down a sandy and hollow valley, -and which, in its hasty course, drives to its centre every thing -that opposes its furious course ... - -No otherwise does the Northern blast whirl round in its tempestuous -progress ... - -Nor does the tempestuous sea bellow so loud, when the Northern blast -dashes it, with its foaming waves between Scylla and Charybdis; nor -Stromboli, nor Mount Etna, when their sulphurous flames, having been -forcibly confined, rend, and burst open the mountain, fulminating -stones and earth through the air together with the flames they -vomit. - -Nor when the inflamed caverns of Mount Etna [Footnote 13: Mongibello -is a name commonly given in Sicily to Mount Etna (from Djebel, -Arab.=mountain). Fr. FERRARA, _Descrizione dell' Etna con la storia -delle eruzioni_ (Palermo, 1818, p. 88) tells us, on the authority of -the _Cronaca del Monastero Benedettino di Licordia_ of an eruption -of the Volcano with a great flow of lava on Sept. 21, 1447. The next -records of the mountain are from the years 1533 and 1536. A. Percy -neither does mention any eruptions of Etna during the years to which -this note must probably refer _Memoire des tremblements de terre de -la peninsule italique, Vol. XXII des Memoires couronnees et Memoires -des savants etrangers. Academie Royal de Belgique_). - -A literal interpretation of the passage would not, however, indicate -an allusion to any great eruption; particularly in the connection -with Stromboli, where the periodical outbreaks in very short -intervals are very striking to any observer, especially at night -time, when passing the island on the way from Naples to Messina.], -rejecting the ill-restained element vomit it forth, back to its own -region, driving furiously before it every obstacle that comes in the -way of its impetuous rage ... - -Unable to resist my eager desire and wanting to see the great ... of -the various and strange shapes made by formative nature, and having -wandered some distance among gloomy rocks, I came to the entrance of -a great cavern, in front of which I stood some time, astonished and -unaware of such a thing. Bending my back into an arch I rested my -left hand on my knee and held my right hand over my down-cast and -contracted eye brows: often bending first one way and then the -other, to see whether I could discover anything inside, and this -being forbidden by the deep darkness within, and after having -remained there some time, two contrary emotions arose in me, fear -and desire--fear of the threatening dark cavern, desire to see -whether there were any marvellous thing within it ... - -Drafts of Letters to Lodovico il Moro (1340-1345). - -1340. - -[Footnote: The numerous corrections, the alterations in the figures -(l. 18) and the absence of any signature prove that this is merely -the rough draft of a letter to Lodovico il Moro. It is one of the -very few manuscripts which are written from left to right--see the -facsimile of the beginning as here reproduced. This is probably the -final sketch of a document the clean of which copy was written in -the usual manner. Leonardo no doubt very rarely wrote so, and this -is probably the reason of the conspicuous dissimilarity in the -handwriting, when he did. (Compare Pl. XXXVIII.) It is noteworthy -too that here the orthography and abbreviations are also -exceptional. But such superficial peculiarities are not enough to -stamp the document as altogether spurious. It is neither a forgery -nor the production of any artist but Leonardo himself. As to this -point the contents leave us no doubt as to its authenticity, -particularly l. 32 (see No. 719, where this passage is repeated). -But whether the fragment, as we here see it, was written from -Leonardo's dictation--a theory favoured by the orthography, the -erasures and corrections--or whether it may be a copy made for or by -Melzi or Mazenta is comparatively unimportant. There are in the -Codex Atlanticus a few other documents not written by Leonardo -himself, but the notes in his own hand found on the reverse pages of -these leaves amply prove that they were certainly in Leonardo's -possession. This mark of ownership is wanting to the text in -question, but the compilers of the Codex Atlanticus, at any rate, -accepted it as a genuine document. - -With regard to the probable date of this projected letter see Vol. -II, p. 3.] - -Most illustrious Lord, Having now sufficiently considered the -specimens of all those who proclaim themselves skilled contrivers of -instruments of war, and that the invention and operation of the said -instruments are nothing different to those in common use: I shall -endeavour, without prejudice to any one else, to explain myself to -your Excellency showing your Lordship my secrets, and then offering -them to your best pleasure and approbation to work with effect at -opportune moments as well as all those things which, in part, shall -be briefly noted below. - -1) I have a sort of extremely light and strong bridges, adapted to -be most easily carried, and with them you may pursue, and at any -time flee from the enemy; and others, secure and indestructible by -fire and battle, easy and convenient to lift and place. Also methods -of burning and destroying those of the enemy. - -2) I know how, when a place is besieged, to take the water out of -the trenches, and make endless variety of bridges, and covered ways -and ladders, and other machines pertaining to such expeditions. - -3) Item. If, by reason of the height of the banks, or the strength -of the place and its position, it is impossible, when besieging a -place, to avail oneself of the plan of bombardment, I have methods -for destroying every rock or other fortress, even if it were founded -on a rock, &c. - -4) Again I have kinds of mortars; most convenient and easy to carry; -and with these can fling small stones almost resembling a storm; and -with the smoke of these causing great terror to the enemy, to his -great detriment and confusion. - -9) [8] And when the fight should be at sea I have kinds of many -machines most efficient for offence and defence; and vessels which -will resist the attack of the largest guns and powder and fumes. - -5) Item. I have means by secret and tortuous mines and ways, made -without noise to reach a designated [spot], even if it were needed -to pass under a trench or a river. - -6) Item. I will make covered chariots, safe and unattackable which, -entering among the enemy with their artillery, there is no body of -men so great but they would break them. And behind these, infantry -could follow quite unhurt and without any hindrance. - -7) Item. In case of need I will make big guns, mortars and light -ordnance of fine and useful forms, out of the common type. - -8) Where the operation of bombardment should fail, I would contrive -catapults, mangonels, _trabocchi_ and other machines of marvellous -efficacy and not in common use. And in short, according to the -variety of cases, I can contrive various and endless means of -offence and defence. - -10) In time of peace I believe I can give perfect satisfaction and -to the equal of any other in architecture and the composition of -buildings public and private; and in guiding water from one place to -another. - -Item: I can carry out sculpture in marble, bronze or clay, and also -in painting whatever may be done, and as well as any other, be he -whom he may. - -[32] Again, the bronze horse may be taken in hand, which is to be to -the immortal glory and eternal honour of the prince your father of -happy memory, and of the illustrious house of Sforza. - -And if any one of the above-named things seem to any one to be -impossible or not feasible, I am most ready to make the experiment -in your park, or in whatever place may please your Excellency--to -whom I commend myself with the utmost humility &c. - -1341. - -To my illustrious Lord, Lodovico, Duke of Bari, Leonardo da Vinci of -Florence-- Leonardo. - -[Footnote: Evidently a note of the superscription of a letter to the -Duke, and written, like the foregoing from left to right. The -manuscript containing it is of the year 1493. Lodovico was not -proclaimed and styled Duke of Milan till September 1494. The Dukedom -of Bari belonged to the Sforza family till 1499.] - -1342. - -You would like to see a model which will prove useful to you and to -me, also it will be of use to those who will be the cause of our -usefulness. - -[Footnote: 1342. 1343. These two notes occur in the same not very -voluminous MS. as the former one and it is possible that they are -fragments of the same letter. By the _Modello_, the equestrian -statue is probably meant, particularly as the model of this statue -was publicly exhibited in this very year, 1493, on tne occasion of -the marriage of the Emperor Maximilian with Bianca Maria Sforza.] - -1343. - -There are here, my Lord, many gentlemen who will undertake this -expense among them, if they are allowed to enjoy the use of -admission to the waters, the mills, and the passage of vessels and -when it is sold to them the price will be repaid to them by the -canal of Martesana. - -1344. - -I am greatly vexed to be in necessity, but I still more regret that -this should be the cause of the hindrance of my wish which is always -disposed to obey your Excellency. - -Perhaps your Excellency did not give further orders to Messer -Gualtieri, believing that I had money enough. - -I am greatly annoyed that you should have found me in necessity, and -that my having to earn my living should have hindered me ... - -[12] It vexes me greatly that having to earn my living has forced me -to interrupt the work and to attend to small matters, instead of -following up the work which your Lordship entrusted to me. But I -hope in a short time to have earned so much that I may carry it out -quietly to the satisfaction of your Excellency, to whom I commend -myself; and if your Lordship thought that I had money, your Lordship -was deceived. I had to feed 6 men for 56 months, and have had 50 -ducats. - -1345. - -And if any other comission is given me - by any ... -of the reward of my service. Because I am - not [able] to be ... -things assigned because meanwhile they - have ... to them ... -... which they well may settle rather than I ... -not my art which I wish to change and ... -given some clothing if I dare a sum ... - - -My Lord, I knowing your Excellency's - mind to be occupied ... -to remind your Lordship of my small matters - and the arts put to silence -that my silence might be the cause of making - your Lordship scorn ... -my life in your service. I hold myself ever - in readiness to obey ... - -[Footnote 11: See No. 723, where this passage is repeated.] - -Of the horse I will say nothing because - I know the times [are bad] -to your Lordship how I had still to receive - two years' salary of the ... -with the two skilled workmen who are constantly -in my pay and at my cost -that at last I found myself advanced the - said sum about 15 lire ... -works of fame by which I could show to - those who shall see it that I have been -everywhere, but I do not know where I -could bestow my work [more] ... - -[Footnote 17: See No. 1344 l. 12.] -I, having been working to gain my - living ... - -I not having been informed what it is, I find - myself ... - -[Footnote 19: In April, 1498, Leonardo was engaged in -painting the Saletta Nigra of the Castello at Milan. -(See G. MONGERI, _l'Arte in Milano_, 1872, p. 417.)] - -remember the commission to paint the - rooms ... - -I conveyed to your Lordship only requesting - you ... - - -[Footnote: The paper on which this is written is torn down the -middle; about half of each line remains.] - -Draft of letter to be sent to Piacenza (1346. 1347). - -[Footnote: 1346. 1347. Piacenza belonged to Milan. The Lord spoken -of in this letter, is no doubt Lodovico il Moro. One may infer from -the concluding sentence (No. 1346, l. 33. 34 and No. 1347), that -Leonardo, who no doubt compiled this letter, did not forward it to -Piacenza himself, but gave it to some influential patron, under -whose name and signature a copy of it was sent to the Commission.] - -1346. - -Magnificent Commissioners of Buildings I, understanding that your -Magnificencies have made up your minds to make certain great works -in bronze, will remind you of certain things: first that you should -not be so hasty or so quick to give the commission, lest by this -haste it should become impossible to select a good model and a good -master; and some man of small merit may be chosen, who by his -insufficiency may cause you to be abused by your descendants, -judging that this age was but ill supplied with men of good counsel -and with good masters; seeing that other cities, and chiefly the -city of the Florentines, has been as it were in these very days, -endowed with beautiful and grand works in bronze; among which are -the doors of their Baptistery. And this town of Florence, like -Piacenza, is a place of intercourse, through which many foreigners -pass; who, seeing that the works are fine and of good quality, carry -away a good impression, and will say that that city is well filled -with worthy inhabitants, seeing the works which bear witness to -their opinion; and on the other hand, I say seeing so much metal -expended and so badly wrought, it were less shame to the city if the -doors had been of plain wood; because, the material, costing so -little, would not seem to merit any great outlay of skill... - -Now the principal parts which are sought for in cities are their -cathedrals, and of these the first things which strike the eye are -the doors, by which one passes into these churches. - -Beware, gentlemen of the Commission, lest too great speed in your -determination, and so much haste to expedite the entrusting of so -great a work as that which I hear you have ordered, be the cause -that that which was intended for the honour of God and of men should -be turned to great dishonour of your judgments, and of your city, -which, being a place of mark, is the resort and gathering-place of -innumerable foreigners. And this dishonour would result if by your -lack of diligence you were to put your trust in some vaunter, who by -his tricks or by favour shown to him here should obtain such work -from you, by which lasting and very great shame would result to him -and to you. Thus I cannot help being angry when I consider what men -those are who have conferred with you as wishing to undertake this -great work without thinking of their sufficiency for it, not to say -more. This one is a potter, that one a maker of cuirasses, this one -is a bell-founder, another a bell ringer, and one is even a -bombardier; and among them one in his Lordship's service, who -boasted that he was the gossip of Messer Ambrosio Ferrere [Footnote -26: Messer Ambrogio Ferrere was Farmer of the Customs under the -Duke. Piacenza at that time belonged to Milan.], who has some power -and who has made him some promises; and if this were not enough he -would mount on horseback, and go to his Lord and obtain such letters -that you could never refuse [to give] him the work. But consider -where masters of real talent and fit for such work are brought when -they have to compete with such men as these. Open your eyes and look -carefully lest your money should be spent in buying your own -disgrace. I can declare to you that from that place you will procure -none but average works of inferior and coarse masters. There is no -capable man,--[33] and you may believe me,--except Leonardo the -Florentine, who is making the equestrian statue in bronze of the -Duke Francesco and who has no need to bring himself into notice, -because he has work for all his life time; and I doubt, whether -being so great a work, he will ever finish it [34]. - -The miserable painstakers ... with what hope may they expect a -reward of their merit? - -1347. - -There is one whom his Lordship invited from Florence to do this work -and who is a worthy master, but with so very much business he will -never finish it; and you may imagine that a difference there is to -be seen between a beautiful object and an ugly one. Quote Pliny. - -Letter to the Cardinal Ippolito d' Este. - -1348. - -[Footnote: This letter addressed to the Cardinal Ippolito d'Este is -here given from Marchese G. CAMPORI'S publication: _Nuovi documenti -per la Vita di Leonardo da Vinci. Atti e Memorie delle R. R. -Deputazioni di Storia patria per la provincie modenesi e parmenesi, -Vol. III._ It is the only text throughout this work which I have not -myself examined and copied from the original. The learned discoverer -of this letter--the only letter from Leonardo hitherto known as -having been sent--adds these interesting remarks: _Codesto Cardinale -nato ad Ercole I. nel 1470, arcivescovo di Strigonia a sette anni, -poi d'Agra, aveva conseguito nel 1497 la pingue ed ambita cattedra -di Milano, la dove avra conosciuto il Vinci, sebbene il poco amore -ch'ei professava alle arti lasci credere che le proteste di servitu -di Leonardo piu che a gratitudine per favori ricevuti e per opere a -lui allogate, accennino a speranza per un favore che si aspetta. -Notabile e ancora in questo prezioso documento la ripetuta signatura -del grande artista 'che si scrive Vincio e Vincius, non da Vinci -come si tiene comunemente, sebbene l'una e l'altra possano valere a -significare cosi il casato come il paese; restando a sapere se il -nome del paese di Vinci fosse assunto a cognome della famiglia di -Leonardo nel qual supposto piu propriamento avrebbe a chiamarsi -Leonardo Vinci, o Vincio (latinamente Vincius) com'egli stesso amo -segnarsi in questa lettera, e come scrissero parecchi contenporanei -di lui, il Casio, il Cesariano, Geoffrey Tory, il Gaurico, il -Bandello, Raffaelle Maffei, il Paciolo. Per ultimo non lascero -d'avvertire come la lettera del Vinci e assai ben conservata, di -nitida e larga scrittura in forma pienemente corrispondente a quella -dei suoi manoscritti, vergata all'uso comune da sinistra a destra, -anziche contrariamente come fu suo costume; ma indubbiamente -autentica e fornita della menzione e del suggello che fresca ancora -conserva l'impronta di una testa di profilo da un picciolo antico -cammeo._ (Compare No. 1368, note.)] - -Most Illustrious and most Reverend Lord. - The Lord Ippolito, Cardinal of Este - at Ferrare. - -Most Illustrious and most Reverend Lord. - -I arrived from Milan but a few days since and finding that my elder -brother refuses to - -carry into effect a will, made three years ago when my father -died--as also, and no less, because I would not fail in a matter I -esteem most important--I cannot forbear to crave of your most -Reverend Highness a letter of recommendation and favour to Ser -Raphaello Hieronymo, at present one of the illustrious members of -the Signoria before whom my cause is being argued; and more -particularly it has been laid by his Excellency the Gonfaloniere -into the hands of the said Ser Raphaello, that his Worship may have -to decide and end it before the festival of All Saints. And -therefore, my Lord, I entreat you, as urgently as I know how and am -able, that your Highness will write a letter to the said Ser -Raphaello in that admirable and pressing manner which your Highness -can use, recommending to him Leonardo Vincio, your most humble -servant as I am, and shall always be; requesting him and pressing -him not only to do me justice but to do so with despatch; and I have -not the least doubt, from many things that I hear, that Ser -Raphaello, being most affectionately devoted to your Highness, the -matter will issue _ad votum_. And this I shall attribute to your -most Reverend Highness' letter, to whom I once more humbly commend -myself. _Et bene valeat_. - -Florence XVIIIa 7bris 1507. -E. V. R. D. - -your humble servant -Leonardus Vincius, pictor. - -Draft of Letter to the Governor of Milan. - -1349. - -I am afraid lest the small return I have made for the great -benefits, I have received from your Excellency, have not made you -somewhat angry with me, and that this is why to so many letters -which I have written to your Lordship I have never had an answer. I -now send Salai to explain to your Lordship that I am almost at an -end of the litigation I had with my brother; that I hope to find -myself with you this Easter, and to carry with me two pictures of -two Madonnas of different sizes. These were done for our most -Christian King, or for whomsoever your Lordship may please. I should -be very glad to know on my return thence where I may have to reside, -for I would not give any more trouble to your Lordship. Also, as I -have worked for the most Christian King, whether my salary is to -continue or not. I wrote to the President as to that water which the -king granted me, and which I was not put in possession of because at -that time there was a dearth in the canal by reason of the great -droughts and because [Footnote:Compare Nos. 1009 and 1010. Leonardo -has noted the payment of the pension from the king in 1505.] its -outlets were not regulated; but he certainly promised me that when -this was done I should be put in possession. Thus I pray your -Lordship that you will take so much trouble, now that these outlets -are regulated, as to remind the President of my matter; that is, to -give me possession of this water, because on my return I hope to -make there instruments and other things which will greatly please -our most Christian King. Nothing else occurs to me. I am always -yours to command. [Footnote:1349. Charles d'Amboise, Marechal de -Chaumont, was Governor of Milan under Louis XII. Leonardo was in -personal communication with him so early as in 1503. He was absent -from Milan in the autumn of 1506 and from October l5l0--when he -besieged Pope Julius II. in Bologna--till his death, which took -place at Correggio, February 11, 1511. Francesco Vinci, Leonardo's -uncle, died--as Amoretti tells us--in the winter of l5l0-11 (or -according to Uzielli in 1506?), and Leonardo remained in Florence -for business connected with his estate. The letter written with -reference to this affair, No. 1348, is undoubtedly earlier than the -letters Nos. 1349 and 1350. Amoretti tells us, _Memorie Storiche_, -ch. II, that the following note existed on the same leaf in MS. C. -A. I have not however succeeded in finding it. The passage runs -thus: _Jo sono quasi al fine del mio letizio che io o con mie -fratetgli ... Ancora ricordo a V. Excia la facenda che o cum Ser -Juliana mio Fratello capo delli altri fratelli ricordandoli come se -offerse di conciar le cose nostre fra noi fratelli del comune della -eredita de mio Zio, e quelli costringa alla expeditione, quale -conteneva la lettera che lui me mando._] - -Drafts of Letters to the Superintendent of Canals and to Fr. Melzi. - -1350. - -Magnificent President, I am sending thither Salai, my pupil, who is -the bearer of this, and from him you will hear by word of mouth the -cause of my... - -Magnificent President, I... - -Magnificent President:--Having ofttimes remembered the proposals -made many times to me by your Excellency, I take the liberty of -writing to remind your Lordship of the promise made to me at my last -departure, that is the possession of the twelve inches of water -granted to me by the most Christian King. Your Lordship knows that I -did not enter into possession, because at that time when it was -given to me there was a dearth of water in the canal, as well by -reason of the great drought as also because the outlets were not -regulated; but your Excellency promised me that as soon as this was -done, I should have my rights. Afterwards hearing that the canal was -complete I wrote several times to your Lordship and to Messer -Girolamo da Cusano,who has in his keeping the deed of this gift; and -so also I wrote to Corigero and never had a reply. I now send -thither Salai, my pupil, the bearer of this, to whom your Lordship -may tell by word of mouth all that happened in the matter about -which I petition your Excellency. I expect to go thither this Easter -since I am nearly at the end of my lawsuit, and I will take with me -two pictures of our Lady which I have begun, and at the present time -have brought them on to a very good end; nothing else occurs to me. - -My Lord the love which your Excellency has always shown me and the -benefits that I have constantly received from you I have hitherto... - -I am fearful lest the small return I have made for the great -benefits I have received from your Excellency may not have made you -somewhat annoyed with me. And this is why, to many letters which I -have written to your Excellency I have never had an answer. I now -send to you Salai to explain to your Excellency that I am almost at -the end of my litigation with my brothers, and that I hope to be -with you this Easter and carry with me two pictures on which are two -Madonnas of different sizes which I began for the most Christian -King, or for whomsoever you please. I should be very glad to know -where, on my return from this place, I shall have to reside, because -I do not wish to give more trouble to your Lordship; and then, -having worked for the most Christian King, whether my salary is to -be continued or not. I write to the President as to the water that -the king granted me of which I had not been put in possession by -reason of the dearth in the canal, caused by the great drought and -because its outlets were not regulated; but he promised me certainly -that as soon as the regulation was made, I should be put in -possession of it; I therefore pray you that, if you should meet the -said President, you would be good enough, now that the outlets are -regulated, to remind the said President to cause me to be put in -possession of that water, since I understand it is in great measure -in his power. Nothing else occurs to me; always yours to command. - -Good day to you Messer Francesco. Why, in God's name, of all the -letters I have written to you, have you never answered one. Now wait -till I come, by God, and I shall make you write so much that perhaps -you will become sick of it. - -Dear Messer Francesco. I am sending thither Salai to learn from His -Magnificence the President to what end the regulation of the water -has come since, at my departure this regulation of the outlets of -the canal had been ordered, because His Magnificence the President -promised me that as soon as this was done I should be satisfied. It -is now some time since I heard that the canal was in order, as also -its outlets, and I immediately wrote to the President and to you, -and then I repeated it, and never had an answer. So you will have -the goodness to answer me as to that which happened, and as I am not -to hurry the matter, would you take the trouble, for the love of me, -to urge the President a little, and also Messer Girolamo Cusano, to -whom you will commend me and offer my duty to his Magnificence. - -[Footnote: 1350. 28-36. Draft of a letter to Francesco Melzi, born -l493--a youth therefore of about 17 in 1510. Leonardo addresses his -young friend as "Messer", as being the son of a noble house. Melzi -practised art under Leonardo as a dilettante and not as a pupil, -like Cesare da Sesto and others (See LERMOLIEFF, _Die Galerien_ &c., -p. 476).] - -Drafts of a letter to Giuliano de' Medici (1351-1352). - -135l. - -[Most illustrious Lord. I greatly rejoice most Illustrious Lord at -your...] - -I was so greatly rejoiced, most illustrious Lord, by the desired -restoration of your health, that it almost had the effect that [my -own health recovered]--[I have got through my illness]--my own -illness left me-- --of your Excellency's almost restored health. But -I am extremely vexed that I have not been able completely to satisfy -the wishes of your Excellency, by reason of the wickedness of that -deceiver, for whom I left nothing undone which could be done for him -by me and by which I might be of use to him; and in the first place -his allowances were paid to him before the time, which I believe he -would willingly deny, if I had not the writing signed by myself and -the interpreter. And I, seeing that he did not work for me unless he -had no work to do for others, which he was very careful in -solliciting, invited him to dine with me, and to work afterwards -near me, because, besides the saving of expense, he - -[Footnote 1351. 1353: It is clear from the contents of this notes -that they refer to Leonardo's residence in Rome in 1513-1515. Nor -can there be any doubt that they were addressed to Leonardo's patron -at the time: Giuliano de' Medici, third son of Lorenzo the -Magnificent and brother of Pope Leo X (born 1478). In 1512 he became -the head of the Florentine Republic. The Pope invited him to Rome, -where he settled; in 1513 he was named patrician with much splendid -ceremonial. The medal struck in honour of the event bears the words -MAG. IVLIAN. MEDICES. Leonardo too uses the style "Magnifico", in -his letter. Compare also No. 1377. - -GlNO CAPPONI (_Storia della Repubblica di Firenze_, Vol. III, p. -139) thus describes the character of Giuliano de' Medici, who died -in 1516: _Era il migliore della famiglia, di vita placida, grande -spenditore, tenendo intorno a se uomini ingegnosi, ed ogni nuova -cosa voleva provare._ - -See too GREGOROVIUS, _Geschichte der Stadi Rom_, VIII (book XIV. -III, 2): _Die Luftschlosser furstlicher Grosse, wozu ihn der Papst -hatte erheben wollen zerfielen. Julian war der edelste aller -damaligen Medici, ein Mensch von innerlicher Richtung, unbefriedigt -durch das Leben, mitten im Sonnenglanz der Herrlichkeit Leo's X. -eine dunkle Gestalt die wie ein Schatten voruberzog._ Giuliano lived -in the Vatican, and it may be safely inferred from No. 1352 l. 2, -and No. 1353 l. 4, that Leonardo did the same. - -From the following unpublished notice in the Vatican archives, which -M. Eug. Muntz, librarian of the Ecole des Beaux arts, Paris, has -done me the favour to communicate to me, we get a more accurate view -of Leonardo's relation to the often named GIORGIO TEDESCO: - -_Nota delle provisione_ (sic) _a da pagare per me in nome del nostro -ill. S. Bernardo Bini e chompa di Roma, e prima della illma sua -chonsorte ogni mese d. 800. - -A Ldo da Vinci per sua provisione d. XXXIII, e piu d. VII al detto -per la provisione di Giorgio tedescho, che sono in tutto d. 40. - -From this we learn, that seven ducats formed the German's monthly -wages, but according to No. 1353 l. 7 he pretended that eight ducats -had been agreed upon.] - -would acquire the Italian language. He always promised, but would -never do so. And this I did also, because that Giovanni, the German -who makes the mirrors, was there always in the workshop, and wanted -to see and to know all that was being done there and made it known -outside ... strongly criticising it; and because he dined with those -of the Pope's guard, and then they went out with guns killing birds -among the ruins; and this went on from after dinner till the -evening; and when I sent Lorenzo to urge him to work he said that he -would not have so many masters over him, and that his work was for -your Excellency's Wardrobe; and thus two months passed and so it -went on; and one day finding Gian Niccolo of the Wardrobe and asking -whether the German had finished the work for your Magnificence, he -told me this was not true, but only that he had given him two guns -to clean. Afterwards, when I had urged him farther, be left the -workshop and began to work in his room, and lost much time in making -another pair of pincers and files and other tools with screws; and -there he worked at mills for twisting silk which he hid when any one -of my people went in, and with a thousand oaths and mutterings, so -that none of them would go there any more. - -I was so greatly rejoiced, most Illustrious Lord, by the desired -restoration of your health, that my own illness almost left me. But -I am greatly vexed at not having been able to completely satisfy -your Excellency's wishes by reason of the wickedness of that German -deceiver, for whom I left nothing undone by which I could have hope -to please him; and secondly I invited him to lodge and board with -me, by which means I should constantly see the work he was doing and -with greater ease correct his errors while, besides this, he would -learn the Italian tongue, by means of which be could with more ease -talk without an interpreter; his moneys were always given him in -advance of the time when due. Afterwards he wanted to have the -models finished in wood, just as they were to be in iron, and wished -to carry them away to his own country. But this I refused him, -telling him that I would give him, in drawing, the breadth, length, -height and form of what he had to do; and so we remained in -ill-will. - -The next thing was that he made himself another workshop and pincers -and tools in his room where he slept, and there he worked for -others; afterwards he went to dine with the Swiss of the guard, -where there are idle fellows, in which he beat them all; and most -times they went two or three together with guns, to shoot birds -among the ruins, and this went on till evening. - -At last I found how this master Giovanni the mirror-maker was he who -had done it all, for two reasons; the first because he had said that -my coming here had deprived him of the countenance and favour of -your Lordship which always... The other is that he said that his -iron-workers' rooms suited him for working at his mirrors, and of -this he gave proof; for besides making him my enemy, he made him -sell all he had and leave his workshop to him, where he works with a -number of workmen making numerous mirrors to send to the fairs. - -1352. - -I was so greatly rejoiced, most Illustrious Lord, by the wished for -recovery of your health, that my own ills have almost left me; and I -say God be praised for it. But it vexes me greatly that I have not -been able completely to satisfy your Excellency's wishes by reason -of the wickedness of that German deceiver, for whom I left nothing -undone by which I could hope to please him; and secondly I invited -him to lodge and board with me, by which means I should see -constantly the work he was doing, for which purpose I would have a -table fixed at the foot of one of these windows, where he could work -with the file and finish the things made below; and so I should -constantly see the work he might do, and it could be corrected with -greater ease. - -Draft of letter written at Rome. - -1353. - -This other hindered me in anatomy, blaming it before the Pope; and -likewise at the hospital; and he has filled [4] this whole Belvedere -with workshops for mirrors; and he did the same thing in Maestro -Giorgio's room. He said that he had been promised [7] eight ducats -every month, beginning with the first day, when he set out, or at -latest when he spoke with you; and that you agreed. - -Seeing that he seldom stayed in the workshop, and that he ate a -great deal, I sent him word that, if he liked I could deal with him -separately for each thing that he might make, and would give him -what we might agree to be a fair valuation. He took counsel with his -neighbour and gave up his room, selling every thing, and went to -find... - -Miscellaneous Records (1354. 1355). - -1354. - -[Footnote: A puzzling passage, meant, as it would seem, for a jest. -Compare the description of Giants in Dante, _Inf_. XXI and XXII. -Perhaps Leonardo had the Giant Antaeus in his mind. Of him the myth -relates that he was a son of Ge, that he fed on lions; that he -hunted in Libya and killed the inhabitants. He enjoyed the -peculiarity of renewing his strength whenever he fell and came in -contact with his mother earth; but that Hercules lifted him up and -so conquered and strangled him. Lucan gives a full account of the -struggle. Pharsalia IV, 617. The reading of this passage, which is -very indistinctly written, is in many places doubtful.] - -Dear Benedetto de' Pertarti. When the proud giant fell because of -the bloody and miry state of the ground it was as though a mountain -had fallen so that the country shook as with an earthquake, and -terror fell on Pluto in hell. From the violence of the shock he lay -as stunned on the level ground. Suddenly the people, seeing him as -one killed by a thunderbolt, turned back; like ants running wildly -over the body of the fallen oak, so these rushing over his ample -limbs.......... them with frequent wounds; by which, the giant being -roused and feeling himself almost covered by the multitude, he -suddenly perceives the smarting of the stabs, and sent forth a roar -which sounded like a terrific clap of thunder; and placing his hands -on the ground he raised his terrible face: and having lifted one -hand to his head he found it full of men and rabble sticking to it -like the minute creatures which not unfrequently are found there; -wherefore with a shake of his head he sends the men flying through -the air just as hail does when driven by the fury of the winds. Many -of these men were found to be dead; stamping with his feet. - -And clinging to his hair, and striving to hide in it, they behaved -like sailors in a storm, who run up the ropes to lessen the force of -the wind [by taking in sail]. - -News of things from the East. - -Be it known to you that in the month of June there appeared a Giant, -who came from the Lybian desert... mad with rage like ants.... -struck down by the rude. - -This great Giant was born in Mount Atlas and was a hero ... and had -to fight against the Egyptians and Arabs, Medes and Persians. He -lived in the sea on whales, grampuses and ships. - -Mars fearing for his life took refuge under the... of Jove. - -And at the great fall it seemed as though the whole province quaked. - -1355. - -This spirit returns to the brain whence it had departed, with a loud -voice and with these words, it moved... - -And if any man though he may have wisdom or goodness ......... - -[Footnote: This passage, very difficult to decipher, is on the -reverse of a drawing at Windsor, Pl. CXXII, which possibly has some -connection with it. The drawing is slightly reduced in this -reproduction; the original being 25 cm. high by 19 cm. wide.] - -O blessed and happy spirit whence comest thou? Well have I known -this man, much against my will. This one is a receptacle of -villainy; he is a perfect heap of the utmost ingratitude combined -with every vice. But of what use is it to fatigue myself with vain -words? Nothing is to be found in them but every form of sin ... And -if there should be found among them any that possesses any good, -they will not be treated differently to myself by other men; and in -fine, I come to the conclusion that it is bad if they are hostile, -and worse if they are friendly. - -Miscellaneous drafts of letters and personal records (1356--1368). - -1356. - -All the ills that are or ever were, if they could be set to work by -him, would not satisfy the desires of his iniquitous soul; and I -could not in any length of time describe his nature to you, but I -conclude... - -1357. - -I know one who, having promised me much, less than my due, being -disappointed of his presumptuous desires, has tried to deprive me of -all my friends; and as he has found them wise and not pliable to his -will, he has menaced me that, having found means of denouncing me, -he would deprive me of my benefactors. Hence I have informed your -Lordship of this, to the end [that this man who wishes to sow the -usual scandals, may find no soil fit for sowing the thoughts and -deeds of his evil nature] so that he, trying to make your Lordship, -the instrument of his iniquitous and maliceous nature may be -disappointed of his desire. - -1358. - -[Footnote: Below this text we read gusstino--Giustino and in another -passage on the same page Justin is quoted (No. 1210, 1. 48). The two -have however no real connection.] - -And in this case I know that I shall make few enemies seeing that no -one will believe what I can say of him; for they are but few whom -his vices have disgusted, and he only dislikes those men whose -natures are contrary to those vices. And many hate their fathers, -and break off friendship with those who reprove their vices; and he -will not permit any examples against them, nor any advice. - -If you meet with any one who is virtuous do not drive him from you; -do him honour, so that he may not have to flee from you and be -reduced to hiding in hermitages, or caves or other solitary places -to escape from your treachery; if there is such an one among you do -him honour, for these are our Saints upon earth; these are they who -deserve statues from us, and images; but remember that their images -are not to be eaten by you, as is still done in some parts of India -[Footnote 15: In explanation of this passage I have received the -following communication from Dr. G. W. LEITNER of Lahore: "So far as -Indian customs are known to us, this practice spoken of by Leonardo -as 'still existing in some parts of India' is perfectly unknown; and -it is equally opposed to the spirit of Hinduism, Mohammedanism and -Sikhism. In central Thibet the ashes of the dead, when burnt, are -mixed with dough, and small figures--usually of Buddha--are stamped -out of them and some are laid in the grave while others are -distributed among the relations. The custom spoken of by Leonardo -may have prevailed there but I never heard of it." Possibly Leonardo -refers here to customs of nations of America.] where, when the -images have according to them, performed some miracle, the priests -cut them in pieces, being of wood, and give them to all the people -of the country, not without payment; and each one grates his portion -very fine, and puts it upon the first food he eats; and thus -believes that by faith he has eaten his saint who then preserves him -from all perils. What do you think here, Man, of your own species? -Are you so wise as you believe yourselves to be? Are these things to -be done by men? - -1359. - -As I told you in past days, you know that I am without any.... -Francesco d'Antonio. Bernardo di Maestro Jacopo. - -1360. - -Tell me how the things happened. - -1361. - -j lorezo\\\ 2 inbiadali\\\ 3 inferri de\\\ 4in lorezo\\\ 5[inno -abuil]\\ 6 in acocatu\\\ 7 per la sella\\\ 8colte di lor\\\ 9v -cavallott\\\ I0el uiagg\\\ IIal\\\ I2a lurez\\\ 13in biada\\\ -14inferri\\\ 15abuss\\\ 16in viagg\\\ 17alorz\\\ [Footnote: This -seems to be the beginning of a letter, but only the first words of -the lines have been preserved, the leaf being torn down the middle. -No translation is possible.] - -1362. - -And so may it please our great Author that I may demonstrate the -nature of man and his customs, in the way I describe his figure. - -[Footnote: A preparatory note for the passage given as No. 798, 11. -41--42.] - -1363. - -This writing distinctly about the kite seems to be my destiny, -because among the first recollections of my infancy, it seemed to me -that, as I was in my cradle, a kite came to me and opened my mouth -with its tail, and struck me several times with its tail inside my -lips. - -[Footnote: This note probably refers to the text No. 1221.] - -1364. - -[When I did well, as a boy you used to put me in prison. Now if I do -it being grown up, you will do worse to me.] - -1365. - -Tell me if anything was ever done. - -1366. - -Tell me if ever I did a thing which me .... - -1367. - -Do not reveal, if liberty is precious to you; my face is the prison -of love. - -[Footnote: This note seems to be a quotation.] - -1368. - -Maestro Leonardo of Florence. - -[Footnote: So Leonardo writes his name on a sheet with sundry short -notes, evidently to try a pen. Compare the signature with those in -Nos. 1341, 1348 and 1374 (see also No. 1346, l. 33). The form -"Lionardo" does not occur in the autographs. The Portrait of the -Master in the Royal Library at Turin, which is reproduced--slightly -diminished--on Pl. I, has in the original two lines of writing -underneath; one in red chalk of two or three words is partly -effaced: _lionardo it... lm_ (or _lai_?); the second written in -pencil is as follows: _fatto da lui stesso assai vecchio_. In both -of these the writing is very like the Master's, but is certainly -only an imitation.] - -Notes bearing Dates (1369--1378). - -1369. - -The day of Santa Maria _della Neve_ [of the Snows] August the 2nd -1473. [Footnote: W. An. I. 1368. 1369. This date is on a drawing of -a rocky landscape. See _Chronique des Arts_ 1881 no. 23: _Leonard de -Vinci a-t-il ete au Righi le 5 aout 1473_? letter by H. de -Geymuller. The next following date in the MSS. is 1478 (see No. -663). - -1370. - -On the 2nd of April 1489, book entitled 'Of the human figure'. -[Footnote: While the letters in the MS. notes of 1473 and 1478 are -very ornate, this note and the texts on anatomy on the same sheet -(for instance No. 805) are in the same simple hand as we see on Pl. -CXVI and CXIX. No 1370 is the only dated note of the years between -1480 and 1489, and the characters are in all essential points -identical with those that we see in the latest manuscripts written -in France (compare the facsimiles on Pl. CXV and p. 254), so that it -is hardly possible to determine exactly the date of a manuscript -from the style of the handwriting, if it does not betray the -peculiarities of style as displayed in the few notes dated previous -to l480.--Compare the facsimile of the manuscripts 1479 on Pl.LXII, -No. 2; No. 664, note, Vol. I p. 346. This shows already a marked -simplicity as compared with the calligraphy of I478. - -The text No. 720 belongs to the year 1490; No. 1510 to the year -1492; No. 1459, No. 1384 and No. 1460 to the year 1493; No. 1463, -No. 1517, No. 1024, 1025 and 1461 to the year 1494; Nos. 1523 and -1524 to the year 1497. - -1371. - -On the 1st of August 1499, I wrote here of motion and of weight. - -[Footnote:1371. _Scrissi qui_. Leonardo does not say where; still we -may assume that it was not in Milan. Amoretti writes, _Memorie -Storiche_, chap. XIX: _Sembra pertanto che non nel 1499 ma nel 1500, -dopo il ritorno e la prigionia del duca, sia da qui partito Lionardo -per andare a Firenze; ed e quindi probabile, che i mesi di governo -nuovo e incerto abbia passati coll' amico suo Francesco Melzi a -Vaprio, ove meglio che altrove studiar potea la natura, e -soprattutta le acque, e l'Adda specialmente, che gia era stato -l'ogetto delle sue idrostatiche ricerche_. At that time Melzi was -only six years of age. The next date is 1502; to this year belong -No. 1034, 1040, 1042, 1048 and 1053. The note No. 1525 belongs to -the year 1503.] - -1372. - -On the 9th of July 1504, Wednesday, at seven o'clock, died Ser Piero -da Vinci, notary at the Palazzo del Podesta, my father, --at seven -o'clock, being eighty years old, leaving behind ten sons and two -daughters. - -[Footnote: This statement of Ser Piero's age contradicts that of the -_Riassunto della portata di Antonio da Vinci_ (Leonardo's -grandfather), who speaks of Ser Piero as being thirty years old in -1457; and that of the _Riassunto della portata di Ser Piero e -Francesco_, sons of Antonia da Vinci, where Ser Piero is mentioned -as being forty in 1469. These documents were published by G. -UZIELLI, _Ricerche intorno a L. da Vinci, Firenze_, 1872, pp. 144 -and 146. Leonardo was, as is well known, a natural son. His mother -'La Catarina' was married in 1457 to Acchattabriga di Piero del -Vaccha da Vinci. She died in 1519. Leonardo never mentions her in -the Manuscripts. In the year of Leonardo's birth Ser Piero married -Albiera di Giovanni Amadoci, and after her death at the age of -thirty eight he again married, Francesca, daughter of Ser Giovanni -Lanfredi, then only fifteen. Their children were Leonardo's -halfbrothers, Antonio (b. 1476), Ser Giuliano (b. 1479), Lorenzo (b. -1484), a girl, Violante (b. 1485), and another boy Domenico (b. -1486); Domenico's descendants still exist as a family. Ser Piero -married for the third time Lucrezia di Guglielmo Cortigiani by whom -he had six children: Margherita (b. 1491), Benedetto (b. 1492), -Pandolfo (b. 1494), Guglielmo (b. 1496), Bartolommeo (b. 1497), and -Giovanni) date of birth unknown). Pierino da Vinci the sculptor -(about 1520-1554) was the son of Bartolommeo, the fifth of these -children. The dates of their deaths are not known, but we may infer -from the above passage that they were all still living in 1505.] - -1373. - -On Wednesday at seven o'clock died Ser Piero da Vinci on the 9th of -July 1504. - -[Footnote: This and the previous text it may be remarked are the -only mention made by Leonardo of his father; Nos. 1526, 1527 and No. -1463 are of the year 1504.] - -1374. - -Begun by me, Leonardo da Vinci, on the l2th of July 1505. - -[Footnote: Thus he writes on the first page of the MS. The title is -on the foregoing coversheet as follows: _Libro titolato -disstrafformatione coe_ (cioe) _d'un corpo nvn_ (in un) _altro sanza -diminuitione e acresscemento di materia._] - -1375. - -Begun at Milan on the l2th of September 1508. - -[Footnote: No. 1528 and No. 1529 belong to the same year. The text -Vol. I, No. 4 belongs to the following year 1509 (1508 old style); -so also does No. 1009.-- Nos. 1022, 1057 and 1464 belong to 1511.] - -1376. - -On the 9th of January 1513. - -[Footnote: No. 1465 belongs to the same year. No. 1065 has the next -date 1514.] - -1377. - -The Magnifico Giuliano de' Medici left Rome on the 9th of January -1515, just at daybreak, to take a wife in Savoy; and on the same day -fell the death of the king of France. - -[Footnote: Giuliano de Medici, brother to Pope Leo X.; see note to -Nos. 1351-1353. In February, 1515, he was married to Filiberta, -daughter of Filippo, Duke of Savoy, and aunt to Francis I, Louis -XII's successor on the throne of France. Louis XII died on Jan. 1st, -and not on Jan. 9th as is here stated.-- This addition is written in -paler ink and evidently at a later date.] - -1378. - -On the 24th of June, St John's day, 1518 at Amboise, in the palace -of... - -[Footnote: _Castello del clli_. The meaning of this word is obscure; -it is perhaps not written at full length.] - -_XXII._ - -_Miscellaneous Notes._ - -_The incidental memoranda scattered here and there throughout the -MSS. can have been for the most part intelligible to the writer -only; in many cases their meaning and connection are all the more -obscure because we are in ignorance about the persons with whom -Leonardo used to converse nor can we say what part he may have -played in the various events of his time. Vasari and other early -biographers give us a very superficial and far from accurate picture -of Leonardo's private life. Though his own memoranda, referring for -the most part to incidents of no permanent interest, do not go far -towards supplying this deficiency, they are nevertheless of some -importance and interest as helping us to solve the numerous -mysteries in which the history of Leonardo's long life remains -involved. We may at any rate assume, from Leonardo's having -committed to paper notes on more or less trivial matters on his -pupils, on his house-keeping, on various known and unknown -personages, and a hundred other trifies--that at the time they must -have been in some way important to him._ - -_I have endeavoured to make these 'Miscellaneous Notes' as complete -as possible, for in many cases an incidental memorandum will help to -explain the meaning of some other note of a similar kind. The first -portion of these notes (Nos. l379--l457), as well as those referring -to his pupils and to other artists and artificers who lived in his -house (1458--1468,) are arranged in chronological order. A -considerable proportion of these notes belong to the period between -1490 and 1500, when Leonardo was living at Milan under the patronage -of Lodovico il Moro, a time concerning which we have otherwise only -very scanty information. If Leonardo did really--as has always been -supposed,--spend also the greater part of the preceding decade in -Milan, it seems hardly likely that we should not find a single note -indicative of the fact, or referring to any event of that period, on -the numerous loose leaves in his writing that exist. Leonardo's life -in Milan between 1489 and 1500 must have been comparatively -uneventful. The MSS. and memoranda of those years seem to prove that -it was a tranquil period of intellectual and artistic labour rather -than of bustling court life. Whatever may have been the fate of the -MSS. and note books of the foregoing years--whether they were -destroyed by Leonardo himself or have been lost--it is certainly -strange that nothing whatever exists to inform us as to his life and -doings in Milan earlier than the consecutive series of manuscripts -which begin in the year 1489._ - -_There is nothing surprising in the fact that the notes regarding -his pupils are few and meagre. Excepting for the record of money -transactions only very exceptional circumstances would have prompted -him to make any written observations on the persons with whom he was -in daily intercourse, among whom, of course, were his pupils. Of -them all none is so frequently mentioned as Salai, but the character -of the notes does not--as it seems to me--justify us in supposing -that he was any thing more than a sort of factotum of Leonardo's -(see 1519, note)._ - -_Leonardo's quotations from books and his lists of titles supply -nothing more than a hint as to his occasional literary studies or -recreations. It was evidently no part of his ambition to be deeply -read (see Nrs. 10, 11, 1159) and he more than once expressly states -(in various passages which will be found in the foregoing sections) -that he did not recognise the authority of the Ancients, on -scientific questions, which in his day was held paramount. -Archimedes is the sole exception, and Leonardo frankly owns his -admiration for the illustrious Greek to whose genius his own was so -much akin (see No. 1476). All his notes on various authors, -excepting those which have already been inserted in the previous -section, have been arranged alphabetically for the sake of -convenience (1469--1508)._ - -_The passages next in order contain accounts and inventories -principally of household property. The publication of these--often -very trivial entries--is only justifiable as proving that the -wealth, the splendid mode of life and lavish expenditure which have -been attributed to Leonardo are altogether mythical; unless we put -forward the very improbable hypothesis that these notes as to money -in hand, outlay and receipts, refer throughout to an exceptional -state of his affairs, viz. when he was short of money._ - -_The memoranda collected at the end (No. 1505--1565) are, in the -original, in the usual writing, from left to right. Besides, the -style of the handwriting is at variance with what we should expect -it to be, if really Leonardo himself had written these notes. Most -of them are to be found in juxtaposition with undoubtedly authentic -writing of his. But this may be easily explained, if we take into -account the fact, that Leonardo frequently wrote on loose sheets. He -may therefore have occasionally used paper on which others had made -short memoranda, for the most part as it would seem, for his use. At -the end of all I have given Leonardo's will from the copy of it -preserved in the Melzi Library. It has already been printed by -Amoretti and by Uzielli. It is not known what has become of the -original document._ - -Memoranda before 1500 (1379-l413). - -1379. - -Find Longhi and tell him that you wait for him at Rome and will go -with him to Naples; make you pay the donation [Footnote 2: _Libro di -Vitolone_ see No. 1506 note.] and take the book by Vitolone, and the -measurements of the public buildings. [3] Have two covered boxes -made to be carried on mules, but bed-covers will be best; this makes -three, of which you will leave one at Vinci. [4] Obtain -the.............. from Giovanni Lombardo the linen draper of Verona. -Buy handkerchiefs and towels,.... and shoes, 4 pairs of hose, a -jerkin of... and skins, to make new ones; the lake of Alessandro. -[Footnote: 7 and fol. It would seem from the text that Leonardo -intended to have instructions in painting on paper. It is hardly -necessary to point out that the Art of illuminating was quite -separate from that of painting.] - -Sell what you cannot take with you. Get from Jean de Paris the -method of painting in tempera and the way of making white [Footnote: -The mysterious looking words, quite distinctly written, in line 1: -_ingol, amor a, ilopan a_ and on line 2: _enoiganod al_ are -obviously in cipher and the solution is a simple one; by reading -them backwards we find for _ingol_: logni-probably _longi_, -evidently the name of a person; for _amor a_: _a Roma_, for _ilopan -a_: _a Napoli_. Leonardo has done the same in two passages treating -on some secrets of his art Nos. 641 and 729, the only other places -in which we find this cipher employed; we may therefore conclude -that it was for the sake of secrecy that he used it. - -There can be no doubt, from the tenor of this passage, that Leonardo -projected a secret excursion to Naples. Nothing has hitherto been -known of this journey, but the significance of the passage will be -easily understood by a reference to the following notes, from which -we may infer that Leonardo really had at the time plans for -travelling further than Naples. From lines 3, 4 and 7 it is evident -that he purposed, after selling every thing that was not easily -portable, to leave a chest in the care of his relations at Vinci. -His luggage was to be packed into two trunks especially adapted for -transport by mules. The exact meaning of many sentences in the -following notes must necessarily remain obscure. These brief remarks -on small and irrelevant affairs and so forth are however of no -historical value. The notes referring to the preparations for his -journey are more intelligible.] - -salt, and how to make tinted paper; sheets of paper folded up; and -his box of colours; learn to work flesh colours in tempera, learn to -dissolve gum lac, linseed ... white, of the garlic of Piacenza; take -'de Ponderibus'; take the works of Leonardo of Cremona. Remove the -small furnace ... seed of lilies and of... Sell the boards of the -support. Make him who stole it, give you the ... learn levelling and -how much soil a man can dig out in a day. - -1380. - -This was done by Leone in the piazza of the castle with a chain and -an arrow. [Footnote: This note must have been made in Milan; as we -know from the date of the MS.] - -1381. - -NAMES OF ENGINEERS. - -Callias of Rhodes, Epimachus the Athenian, Diogenes, a philosopher, -of Rhodes, Calcedonius of Thrace, Febar of Tyre, Callimachus the -architect, a master of fires. [Footnote: Callias, Architect of -Aradus, mentioned by Vitruvius (X, 16, 5).--Epimachus, of Athens, -invented a battering-enginee for Demetrius Poliorketes (Vitruvius X, -16, 4).--Callimachus, the inventor of the Corinthian capital (Vitr. -IV, I, 9), and of the method of boring marble (Paus. I, 26, 7), was -also famous for his casts in bronze (Plin. XXXIV, 8, 19). He -invented a lamp for the temple of Athene Polias, on the Acropolis of -Athens (Paus. I, 26, 7)--The other names, here mentioned, cannot be -identified.] - -1382. - -Ask maestro Lodovico for 'the conduits of water'. [Footnote: -Condotti d'acqua. Possibly a book, a MS. or a map.] - -1383. - -... at Pistoja, Fioravante di Domenico at Florence is my most -beloved friend, as though he were my [brother]. [Footnote: On the -same sheet is the text No. 663.] - -1384. - -On the 16th day of July. - -Caterina came on 16th day of July, 1493. - -Messer Mariolo's Morel the Florentin, has a big horse with a fine -neck and a beautiful head. - -The white stallion belonging to the falconer has fine hind quarters; -it is behind the Comasina Gate. - -The big horse of Cermonino, of Signor Giulio. [Footnote: Compare -Nos. 1522 and 1517. Caterina seems to have been his housekeeper.] - -1385. - -OF THE INSTRUMENT. - -Any one who spends one ducat may take the instrument; and he will -not pay more than half a ducat as a premium to the inventor of the -instrument and one grosso to the workman every year. I do not want -sub-officials. [Footnote: Refers perhaps to the regulation of the -water in the canals.] - -1386. - -Maestro Giuliano da Marliano has a fine herbal. He lives opposite to -Strami the Carpenters. [Footnote: Compare No. 616, note. 4. -legnamiere (milanese dialect) = legnajuolo.] - -1387. - -Christofano da Castiglione who lives at the Pieta has a fine head. - -1388. - -Work of ... of the stable of Galeazzo; by the road of Brera -[Footnote 4: Brera, see No. 1448, II, 13]; benefice of Stanghe -[Footnote 5:Stanghe, see No. 1509.]; benefice of Porta Nuova; -benefice of Monza; Indaco's mistake; give first the benefices; then -the works; then ingratitude, indignity and lamentations. - -1389. - -Chiliarch--captain of 1000. - -Prefects--captains. - -A legion, six thousand and sixty three men. - -1390. - -A nun lives at La Colomba at Cremona; she works good straw plait, -and a friar of Saint Francis. [Footnote: _La Colomba_ is to this day -the name of a small house at Cremona, decorated with frescoes.] - -1391. - -Needle,--Niccolao,--thread,--Ferrando, -lacopo -Andrea,--canvas,--stone,--colours, --brushes,--pallet,--sponge,--the -panel of the Duke. - -1392. - -Messer Gian Domenico Mezzabarba and Messer Giovanni Franceso -Mezzabarba. By the side of Messer Piero d'Anghiera. - -1393. - -Conte Francesco Torello. - -1394. - -Giuliano Trombetta,--Antonio di Ferrara, --Oil of .... [Footnote: -Near this text is the sketch of a head drawn in red chalk.] - -1395. - -Paul was snatched up to heaven. [Footnote: See the facsimile of this -note on Pl. XXIII No. 2.] - -1396. - -Giuliano da Maria, physician, has a steward without hands. - -1397. - -Have some ears of corn of large size sent from Florence. - -1398. - -See the bedstead at Santa Maria. Secret. - -1399. - -Arrigo is to have 11 gold Ducats. Arrigo is to have 4 gold ducats in -the middle of August. - -1400. - -Give your master the instance of a captain who does not himself win -the victory, but the soldiers do by his counsels; and so he still -deserves the reward. - -1401. - -Messer Pier Antonio. - -1402. - -Oil,--yellow,--Ambrosio,--the mouth, --the farmhouse. - -1403. - -My dear Alessandro from Parma, by the hand of ... - -1404. - -Giovannina, has a fantastic face,--is at Santa Caterina, at the -Hospital. [Footnote: Compare the text on the same page: No. 667.] - -1405. - -24 tavole make 1 perch. 4 trabochi make 1 tavola. 4 braccia and a -half make a trabocco. A perch contains 1936 square braccia, or 1944. - -1406. - -The road of Messer Mariolo is 13 1/4 braccia wide; the House of -Evangelista is 75. - -It enters 7 1/2 braccia in the house of Mariolo. [Footnote: On this -page and that which faces it, MS.I2 7la, are two diagrams with -numerous reference numbers, evidently relating to the measurements -of a street.] - -1407. - -I ask at what part of its curved motion the moving cause will leave -the thing moved and moveable. - -Speak to Pietro Monti of these methods of throwing spears. - -1408. - -Antonio de' Risi is at the council of Justice. - -1409. - -Paolo said that no machine that moves another .... [Footnote: The -passage, of which the beginning is here given, deals with questions -in mechanics. The instances in which Leonardo quotes the opinions of -his contemporaries on scientific matters are so rare as to be worth -noticing. Compare No. 901. ] - -1410. - -Caravaggio. [Footnote: _Caravaggio_, a village not far from the Adda -between Milan and Brescia, where Polidoro and Michelangelo da -Caravaggio were born. This note is given in facsimile on Pl. XIII, -No. I (above, to the left). On Pl. XIII, No. 2 above to the right we -read _cerovazo_.] - -1411. - -Pulleys,--nails,--rope,--mercury,--cloth, Monday. - -1412. - -MEMORANDUM. - -Maghino, Speculus of Master Giovanni the Frenchman; Galenus on -utility. - -1413. - -Near to Cordusio is Pier Antonio da Tossano and his brother -Serafino. [Footnote: This note is written between lines 23 and 24 of -the text No. 710. Corduso, Cordusio (_curia ducis_) = Cordus in the -Milanese dialect, is the name of a Piazza between the Via del -Broletto and the Piazza de' Mercanti at Milan.. In the time of il -Moro it was the centre of the town. The persons here named were -members of the noble Milanese family de'Fossani; Ambrogio da -Possano, the contemporary painter, had no connection with them.] - -1414. - -Memoranda after 1500 (1414--1434) - -1414. - -Paul of Vannochio at Siena ... The upper chamber for the apostles. - -[4] Buildings by Bramante. - -The governor of the castle made a prisoner. - -[6] Visconti carried away and his son killed. [Footnote 6: Visconti. -_Chi fosse quel Visconte non sapremmo indovinare fra tanti di questo -nome. Arluno narra che allora atterrate furono le case de' Viconti, -de' Castiglioni, de' Sanseverini, e de' Botta e non e improbabile -che ne fossero insultati e morti i padroni. Molti Visconti annovera -lo stesso Cronista che per essersi rallegrati del ritorno del duca -in Milano furono da' Francesi arrestati, e strascinati in Francia -come prigionieri di stato; e fra questi Messer Francesco Visconti, e -suo figliuolo Battista_. (AMORETTI, Mem. Stor. XIX.).] - -Giovanni della Rosa deprived of his money. - -Borgonzio began ....; and moreover his fortunes fled. [Footnote 8: -Borgonzio o Brugonzio Botta fu regolatore delle ducali entrate sotto -il Moro, alla cui fuga la casa sua fu pur messa a sacco da' -partitanti francesi. (AMORETTI, l. c.)] - -The Duke has lost the state, property and liberty and none of his -entreprises was carried out by him. - -[Footnote: l. 4--10 This passage evidently refers to events in Milan -at the time of the overthrow of Ludovico il Moro. Amoretti published -it in the '_Memorie Storiche_' and added copious notes.] - -1415. - -Ambrosio Petri, St. Mark, 4 boards for the window, 2 ..., 3 the -saints of chapels, 5 the Genoese at home. - -1416. - -Piece of tapestry,--pair of compasses,-- Tommaso's book,--the book -of Giovanni Benci,--the box in the custom-house,--to cut the -cloth,--the sword-belt,--to sole the boots, --a light hat,--the cane -from the ruined houses,--the debt for the table linen, ---swimming-belt,--a book of white paper for drawing,--charcoal.--How -much is a florin ...., a leather bodice. - -1417. - -Borges shall get for you the Archimedes from the bishop of Padua, -and Vitellozzo the one from Borgo a San Sepolcro [Footnote 3: Borgo -a San Sepolcro, where Luca Paciolo, Leonardo's friend, was born.] - -[Footnote: Borges. A Spanish name.] - -1418. - -Marzocco's tablet. - -1419. - -Marcello lives in the house of Giacomo da Mengardino. - -1420. - -Where is Valentino?--boots,--boxes in the -custom-house,...,--[Footnote 5: Carmine. A church and monastery at -Florence.] the monk at the Carmine,--squares,--[Footnotes 7 and 8: -Martelli, Borgherini; names of Florentine families. See No. 4.] -Piero Martelli,--[8] Salvi Borgherini,--send back the bags,--a -support for the spectacles,--[Footnote 11: San Gallo; possibly -Giuliano da San Gallo, the Florentine architect.] the nude study of -San Gallo,--the cloak. Porphyry,--groups,--square,--[Footnote 16: -Pandolfini, see No. 1544 note.] Pandolfino. [Footnote: Valentino. -Cesare Borgia is probably meant. After being made Archbishop of -Valence by Alexander VI he was commonly called Valentinus or -Valentino. With reference to Leonardo's engagements by him see pp. -224 and 243, note.] - -1421. - -Concave mirrors; philosophy of Aristotle;[Footnote 2: _Avicenna_ -(Leonardo here writes it Avinega) the Arab philosopher, 980-1037, -for centuries the unimpeachable authority on all medical questions. -Leonardo possibly points here to a printed edition: _Avicennae -canonum libri V, latine_ 1476 _Patavis._ Other editions are, Padua -1479, and Venice 1490.] the books of Avicenna Italian and Latin -vocabulary; Messer Ottaviano Palavicino or his Vitruvius [Footnote -3: _Vitruvius._ See Vol. I, No. 343 note.]. bohemian knives; -Vitruvius[Footnote 6: _Vitruvius._ See Vol. I, No. 343 note.]; go -every Saturday to the hot bath where you will see naked men; - -'Meteora' [Footnote 7: _Meteora._ See No. 1448, 25.], - -Archimedes, on the centre of gravity; [Footnote 9: The works of -Archimedes were not printed during Leonardo's life-time.] anatomy -[Footnote 10: Compare No. 1494.] Alessandro Benedetto; The Dante of -Niccolo della Croce; Inflate the lungs of a pig and observe whether -they increase in width and in length, or in width diminishing in -length. - -[Footnote 14: _Johannes Marliani sua etate philosophorum et -medicorum principis et ducalis phisic. primi de proportione motuum -velocitate questio subtilissima incipit ex ejusdem Marliani -originali feliciter extracta, M(ilano)_ 1482. - -Another work by him has the title: _Marlianus mediolanensis. Questio -de caliditate corporum humanorum tempore hiemis ed estatis et de -antiparistasi ad celebrem philosophorum et medicorum universitatem -ticinensem._ 1474.] Marliano, on Calculation, to Bertuccio. -Albertus, on heaven and earth [Footnote 15: See No. 1469, 1. 7.], -[from the monk Bernardino]. Horace has written on the movements of -the heavens. - -[Footnote: _Filosofia d'Aristotele_ see No. 1481 note.] - -1422. - -Of the three regular bodies as opposed to some commentators who -disparage the Ancients, who were the originators of grammar and the -sciences and ... - -1423. - -The room in the tower of Vaneri. - -[Footnote: This note is written inside the sketch of a plan of a -house. On the same page is the date 1513 (see No. 1376).] - -1424. - -The figures you will have to reserve for the last book on shadows -that they may appear in the study of Gerardo the illuminator at San -Marco at Florence. - -[Go to see Melzo, and the Ambassador, and Maestro Bernardo]. - -[Footnote: L. 1-3 are in the original written between lines 3 and 4 -of No. 292. But the sense is not clear in this connection. It is -scarcely possible to devine the meaning of the following sentence. - -2. 3. _Gherardo_ Miniatore, a famous illuminator, 1445-1497, to whom -Vasari dedicated a section of his Lives (Vol. II pp. 237-243, ed. -Sansoni 1879). - -5. _Bernardo_, possibly the painter Bernardo Zenale.] - -1425. - -Hermes the philosopher. - -1426. - -Suisset, viz. calculator,--Tisber, --Angelo Fossobron,--Alberto. - -1427. - -The structure of the drawbridge shown me by Donnino, and why _c_ and -_d_ thrust downwards. - -[Footnote: The sketch on the same page as this text represents two -poles one across the other. At the ends of the longest are the -letter _c_ and _d_. The sense of the passage is not rendered any -clearer.] - -1428. - -The great bird will take its first flight;-- on the back of his -great swan,--filling the universe with wonders; filling all writings -with his fame and bringing eternal glory to his birthplace. - -[Footnote: This seems to be a speculation about the flying machine -(compare p. 271).] - -1429. - -This stratagem was used by the Gauls against the Romans, and so -great a mortality ensued that all Rome was dressed in mourning. - -[Footnote: Leonardo perhaps alludes to the Gauls under Brennus, who -laid his sword in the scale when the tribute was weighed.] - -1430. - -Alberto da Imola;--Algebra, that is, the demonstration of the -equality of one thing to another. - -1431. - -Johannes Rubicissa e Robbia. - -1432. - -Ask the wife of Biagio Crivelli how the capon nurtures and hatches -the eggs of the hen,--he being drunk. - -1433. - -The book on Water to Messer Marco Antonio. - -[Footnote: Possibly Marc-Antonio della Torre, see p. 97.] - -1434. - -Have Avicenna's work on useful inventions translated; spectacles -with the case, steel and fork and...., charcoal, boards, and paper, -and chalk and white, and wax;.... .... for glass, a saw for bones -with fine teeth, a chisel, inkstand ........ three herbs, and Agnolo -Benedetto. Get a skull, nut,--mustard. - -Boots,--gloves, socks, combs, papers, towels, shirts,.... -shoe-tapes,--..... shoes, penknife, pens. A skin for the chest. - -[Footnote: 4. Lapis. Compare Condivi, _Vita di Michelagnolo -Buonarotti_, Chap. XVIII.: _Ma egli_ (Michelangelo) _non avendo che -mostrare, prese una penna (percioche in quel tempo il lapis non era -in uso) e con tal leggiadria gli dipinse una mano ecc._ The incident -is of the year l496.--Lapis means pencil, and chalk (_matita_). -Between lines 7 and 8 are the texts given as Nos. 819 and No. 7.] - -Undated memoranda (1435-1457). - -1435. - -The book of Piero Crescenze,--studies from the nude by Giovanni -Ambrosio,--compasses, --the book of Giovanni Giacomo. - -1436. - -MEMORARDUM. - -To make some provisions for my garden, --Giordano, _De -Ponderibus_[Footnote 3: _Giordano_. Jordanus Nemorarius, a -mathematician of the beginning of the XIIIth century. No particulars -of his life are known. The title of his principal work is: -_Arithmetica decem libris demonstrata_, first published at Paris -1496. In 1523 appeared at Nuremberg: _Liber Jordani Nemorarii de -ponderibus, propositiones XIII et earundem demonstrationes, -multarumque rerum rationes sane pulcherrimas complectens, nunc in -lucem editus._],--the peacemaker, the flow and ebb of the sea,--have -two baggage trunks made, look to Beltraffio's [Footnote 6: -_Beltraffio_, see No. 465, note 2. - -There are sketches by the side of lines 8 and 10.] lathe and have -taken the stone,--out leave the books belonging to Messer Andrea the -German,-- make scales of a long reed and weigh the substance when -hot and again when cold. The mirror of Master Luigi; _A b_ the flow -and ebb of the water is shown at the mill of Vaprio,--a cap. - -1437. - -Giovanni Fabre,--Lazaro del Volpe,-- the common,--Ser Piero. - -[Footnote: These names are inserted on a plan of plots of land -adjoining the Arno.] - -1438. - -[Lactantius], [the book of Benozzo], groups,--to bind the book,--a -lantern,--Ser Pecantino,--Pandolfino.--[Rosso]--a square, --small -knives,--carriages,--curry combs-- cup. - -1439. - -Quadrant of Carlo Marmocchi,--Messer Francesco Araldo,--Ser -Benedetto d'Accie perello,--Benedetto on arithmetic,--Maestro Paulo, -physician,--Domenico di Michelino,-- ...... of the Alberti,--Messer -Giovanni Argimboldi. - -1440. - -Colours, formula,--Archimedes,--Marcantonio. - -Tinned iron,--pierced iron. - -1441. - -See the shop that was formerly Bartolommeo's, the stationer. - -[Footnote: 6. _Marc Antonio_, see No. 1433.] - -1442. - -The first book is by Michele di Francesco Nabini; it treats on -science. - -1443. - -Messer Francesco, physician of Lucca, with the Cardinal Farnese. - -[Footnote: _Alessandro Farnese_, afterwards Pope Paul III was -created in 1493 Cardinal di San Cosimo e San Damiano, by Alexander -VI.] - -1444. - -Pandolfino's book [Footnote 1: _Pandolfino, Agnolo_, of Florence. It -is to this day doubtful whether he or L. B. Alberti was the author -of the famous work '_Del Governo della Famiglia_'. It is the more -probable that Leonardo should have meant this work by the words _il -libro_, because no other book is known to have been written by -Pandolfino. This being the case this allusion of Leonardo's is an -important evidence in favour of Pandolfino's authorship (compare No. -1454, line 3).],--knives,--a pen for ruling,--to have the vest -dyed,--The library at St.-Mark's,--The library at Santo -Spirito,--Lactantius of the Daldi [Footnote 7: The works of -Lactantius were published very often in Italy during Leonardo's -lifetime. The first edition published in 1465 "_in monastero -sublacensi_" was also the first book printed in Italy.],--Antonio -Covoni,--A book by Maestro Paolo Infermieri, --Boots, shoes and -hose,--(Shell)lac, --An apprentice to do the models for me. Grammar, -by Lorenzo de Medici,--Giovanni del Sodo,--Sansovino, [Footnote 15: -_Sansovino_, Andrea--the _sculptor_; 1460-1529.]--a ruler,--a very -sharp knife,--Spectacles,--fractions...., ---repair.........,--Tomaso's book,-- Michelagnolo's little chain; -Learn the multiplication of roots from Maestro Luca;--my map of the -world which Giovanni Benci has [Footnote 25: Leonardo here probably -alludes to the map, not executed by him (See p. 224), which is with -the collection of his MSS. at Windsor, and was published in the -_Archaeologia_ Vol. XI (see p. 224).];-Socks,--clothes from the -customhouse-officier,--Red Cordova leather,--The map of the world, -of Giovanni Benci,--a print, the districts about Milan--Market book. - -Get the Friar di Brera to show you [the book] '_de Ponderibus_' -[Footnote 11: _Brera_, now _Palazzo delle Scienze ed Arti. Until -1571 it was the monastery of the order of the Umiliati and -afterwards of the Jesuits. - -_De ponderibus_, compare No. 1436, 3.],-- - -Of the measurement of San Lorenzo,-- - -I lent certain groups to Fra Filippo de Brera, [Footnote 13: -_Brera_, now _Palazzo delle Scienze ed Arti. Until 1571 it was the -monastery of the order of the Umiliati and afterwards of the -Jesuits. - -_De ponderibus_, compare No. 1436, 3.]-- - -Memorandum: to ask Maestro Giovannino as to the mode in which the -tower of Ferrara is walled without loopholes,-- - -Ask Maestro Antonio how mortars are placed on bastions by day or by -night,-- - -Ask Benedetto Portinari how the people go on the ice in Flanders,-- - -On proportions by Alchino, with notes by Marliano, from Messer -Fazio,-- - -The measurement of the sun, promised me by Maestro Giovanni, the -Frenchman,-- - -The cross bow of Maestro Gianetto,-- - -The book by Giovanni Taverna that Messer Fazio,-- - -You will draw Milan [21],-- - -The measurement of the canal, locks and supports, and large boats; -and the expense,-- - -Plan of Milan [Footnote 23: _Fondamento_ is commonly used by -Leonardo to mean ground-plan. See for instance p. 53.],-- - -Groups by Bramante [Footnote 24: _Gruppi_. See Vol. I p. 355, No. -600, note 9.],-- - -The book on celestial phenomena by Aristoteles, in Italian [Footnote -25: _Meteora_. By this Leonardo means no doubt the four books. He -must refer here to a MS. translation, as no Italian translation is -known to have been published (see No. 1477 note).],-- - -Try to get Vitolone, which is in the library at Pavia [Footnote 26: -_Vitolone_ see No. 1506, note. - -_Libreria di Pavia_. One of the most famous of Italian libraries. -After the victory of Novara in April 1500, Louis XII had it conveyed -to France, '_come trofeo di vittoria_'!] and which treats of -Mathematics,--He had a master [learned] in waterworks and get him to -explain the repairs and the costs, and a lock and a canal and a mill -in the Lombard fashion. - -A grandson of Gian Angelo's, the painter has a book on water which -was his fathers. - -Paolino Scarpellino, called Assiolo has great knowledge of water -works. - -[Footnote 12: _Sco Lorenzo_. A church at Milan, see pp. 39, 40 and -50.] - -[Footnote 13. 24: _Gruppi_. See Vol. I p. 355, No. 600, note 9.] - -[Footnote 16: The _Portinari_ were one of the great merchant- -families of Florence.] - -1449. - -Francesco d'Antonio at Florence. - -1450. - -Giuliano Condi[1],--Tomaso Ridolfi,-- Tomaso Paganelli,--Nicolo del -Nero,--Simone Zasti,--Nasi,--the heir of Lionardo Manelli, ---Guglielmo di Ser Martino,--Bartolomeo del Tovaglia,--Andrea -Arrigucci,-- Nicolo Capponi,--Giovanni Portinari. - -[Footnote: I. _Guiliano Gondi_. Ser Piero da Vinci, Leonardo's -father, lived till 1480, in a house belonging to Giuliano Gondi. In -1498 this was pulled down to make room for the fine Palazzo built on -the Piazza San Firenze by Giuliano di San Gallo, which still exists. -In the _Riassunto del Catasto di Ser Piero da Vinci_, 1480, Leonardo -is not mentioned; it is evident therefore that he was living -elsewhere. It may be noticed incidentally that in the _Catasto di -Giuliano Gondi_ of the same year the following mention is made of -his four eldest sons: - -_Lionardo mio figliuolo d'eta d'anni 29, non fa nulla, Giovambatista -d'eta d'anni 28 in Ghostantinopoli, Billichozo d'eta d'anni 24 a -Napoli, Simone d'eta d'anni 23 in Ungheria._ - -He himself was a merchant of gold filigree (_facciamo lavorare una -bottegha d'arte di seta ... facciamo un pocho di trafico a Napoli_}. -As he was 59 years old in 1480, he certainly would not have been -alive at the time of Leonardo's death. But Leonardo must have been -on intimate terms with the family till the end of his life, for in a -letter dated June 1. 1519, in which Fr. Melzi, writing from Amboise, -announces Leonardo's death to Giuliano da Vinci at Florence (see p. -284), he says at the end "_Datemene risposta per i Gondi_" (see -UZIELLI, _Ricerche_, passim). - -Most of the other names on the list are those of well-known -Florentine families.] - -1451. - -Pandolfino. - -1452. - -Vespuccio will give me a book of Geometry. - -[Footnote: See No. 844, note, p. 130.] - -1453. - -Marcantonio Colonna at Santi Apostoli. - -[Footnote: In July 1506 Pope Julius II gave Donna Lucrezia della -Rovere, the daughter of his sister Lucchina, in marriage to the -youthful Marcantonio Colonna, who, like his brothers Prospero and -Fabrizio, became one of the most famous Captains of his family. He -gave to him Frascati and made him a present of the palazzo he had -built, when Cardinal, near the church of Santi Apostoli which is now -known as the Palazzo Colonna (see GREGOROVIUS, _Gesch. der Stadt -Rom._ Vol. VIII, book XIV I, 3. And COPPI, _Mem. Colonnesi_ p. -251).] - -1454. - -A box, a cage,-- A square, to make the bird [Footnote 2: Vasari -states that Leonardo invented mechanical birds which moved through -the air. Compare No. 703.],-- Pandolfino's book, mortar [?],-- Small -knives, Venieri for the - -[Footnote: Much of No. 1444 is repeated in this memorandum.] - -Pen for ruling, stone,--star,-- - -To have the vest dyed, Alfieri's tazza,-- - -The Libraries, the book on celestial - phenomena,-- - -Lactantius of the go to the house of -Daldi,-- the Pazzi, - -Book from Maestro small box,-- -Paolo Infermieri,-- - -Boots, shoes and small gimlet,-- -hose, - -Lac, .......,-- - -An apprentice for .....,-- -models, - -Grammar of Lo- the amount of the -renzo de' Medici, ... - -Giovanni del Sodo ..... -for...,--the broken - -Sansovino, the.... - -Piero di Cosino the wings,-- - -[Footnote 16: _Pier di Cosimo_ the well known Florentine painter -1462-1521. See VASARI, _Vite_ (Vol. IV, p. 134 ed. Sansoni 1880) -about Leonardo's influence on Piero di Cosimo's style of painting.] - -Filippo and Lorenzo [Footnote 17: _Filippo e Lorenzo_; probably the -painters Filippino Lippi and Lorenzo di Credi. L. di Credi's -pictures and Vasari's history of that painter bear ample evidence to -his intimate relations with Leonardo.],--A ruler-,-- Spectacles,--to -do the..... again,--Tomaso's book,--Michelagnolo's chain,--The -multiplication of roots,--Of the bow and strinch,--The map of the -world from Benci,-- Socks,--The clothes from the custom-house -officier,--Cordova leather,--Market books, --waters of -Cronaca,--waters of Tanaglino..., --the caps,--Rosso's mirror; to -see him make it,--1/3 of which I have 5/6,--on the celestial -phenomena, by Aristotle [Footnote 36: _Meteora_. See No. 1448, -25.],--boxes of Lorenzo di Pier Francesco [Footnote 37: _Lorenzo di -Pier Francesco_ and his brother _Giovanni_ were a lateral branch of -the _Medici_ family and changed their name for that of -Popolani.],--Maestro Piero of the Borgo,--To have my book -bound,--Show the book to Serigatto,-- and get the rule of the clock -[Footnote 41: Possibly this refers to the clock on the tower of the -Palazzo Vecchio at Florence. In February 1512 it had been repaired, -and so arranged as to indicate the hours after the French manner -(twelve hours a. m. and as many p. m.).],-- -ring,--nutmeg,--gum,--the square,--Giovan' Batista at the piazza, -de' Mozzi,--Giovanni Benci has my book and jaspers,--brass for the -spectacles. - -1455. - -Search in Florence for...... - -1456. - -Bernardo da Ponte ... Val di Lugano ... many veins for anatomical -demonstration. - -[Footnote: This fragmentary note is written on the margin of a -drawing of two legs.] - -1457. - -Paolo of Tavechia, to see the marks in the German stones. - -[Footnote: This note occurs on a pen and ink drawing made by -Leonardo as a sketch for the celebrated large cartoon in the -possession of the Royal Academy of Arts, in London. This cartoon is -commonly supposed to be identical with that described and lauded by -Vasari, which was exhibited in Florence at the time and which now -seems to be lost. Mr. Alfred Marks, of Long Ditton, in his valuable -paper (read before the Royal Soc. of Literature, June 28, 1882) "On -the St. Anne of Leonardo da Vinci", has adduced proof that the -cartoon now in the Royal Academy was executed earlier at Milan. The -note here given, which is written on the sheet containing the study -for the said cartoon, has evidently no reference to the drawing on -which it is written but is obviously of the same date. Though I have -not any opening here for discussing this question of the cartoon, it -seemed to me important to point out that the character of the -writing in this note does not confirm the opinion hitherto held that -the Royal Academy cartoon was the one described by Vasari, but, on -the contrary, supports the hypothesis put forward by Mr. Marks.] - -Notes on pupils (1458-1468.) - -1458. - -Giacomo came to live with me on St.-Mary Magdalen's[Footnote: _Il di -della Maddalena._ July 22.] day, 1490, aged 10 years. The second day -I had two shirts cut out for him, a pair of hose, and a jerkin, and -when I put aside some money to pay for these things he stole 4 -_lire_ the money out of the purse; and I could never make him -confess, though I was quite certain of the fact.--Thief, liar, -obstinate, glutton. - -The day after, I went to sup with Giacomo Andrea, and the said -Giacomo supped for two and did mischief for four; for he brake 3 -cruets, spilled the wine, and after this came to sup where I .... - -Item: on the 7th day of September he stole a silver point of the -value of 22 soldi from Marco[Footnote 6: _Marco_, probably -Leonardo's pupil Marco d'Oggionno; 1470 is supposed to be the date -of his birth and 1540 of his death. - -_Che stava con meco._ We may infer from this that he left the master -shortly after this, his term of study having perhaps expired.] who -was living with me, 4 _lire_ this being of silver; and he took it -from his studio, and when the said Marco had searched for it a long -while he found it hidden in the said Giacomo's box 4 _lire_. - -Item: on the 26th January following, I, being in the house of Messer -Galeazzo da San Severino [Footnote 9: Galeazzo. See No. 718 note.], -was arranging the festival for his jousting, and certain footmen -having undressed to try on some costumes of wild men for the said -festival, Giacomo went to the purse of one of them which lay on the -bed with other clothes, 2 lire 4 S, and took out such money as was -in it. - -Item: when I was in the same house, Maestro Agostino da Pavia gave -to me a Turkish hide to have (2 lire.) a pair of short boots made of -it; this Giacomo stole it of me within a month and sold it to a -cobbler for 20 soldi, with which money, by his own confession, he -bought anise comfits. - -Item: again, on the 2nd April, Giovan Antonio [Footnote 16: Giovan -Antonio, probably Beltraffio, 1467 to 1516.] having left a silver -point on a drawing of his, Giacomo stole it, and this was of the -value of 24 soldi (1 lira 4 S.) - -The first year- - -A cloak, 2 lire, -6 shirts, 4 lire, -3 jerkins, 6 lire, -4 pairs of hose, 7 lire 8 soldi, -1 lined doublet, 5 lire, -24 pairs of shoes, 6 lire 5 soldi, -A cap, 1 lira, -laces, 1 lira. - -[Footnote: Leonardo here gives a detailed account not only of the -loss he and others incurred through Giacomo but of the wild tricks -of the youth, and we may therefore assume that the note was not made -merely as a record for his own use, but as a report to be forwarded -to the lad's father or other responsible guardian.] - -1459. - -On the last day but one of September; - -Thursday the 27th day of September Maestro Tommaso came back and -worked for himself until the last day but one of February. On the -18th day of March, 1493, Giulio, a German, came to live with -me,--Lucia, Piero, Leonardo. - -On the 6th day of October. - -1460. - -1493. On the 1st day of November we settled accounts. Giulio had to -pay 4 months; and Maestro Tommaso 9 months; Maestro Tommaso -afterwards made 6 candlesticks, 10 days' work; Giulio some -fire-tongs 15 days work. Then he worked for himself till the 27th -May, and worked for me at a lever till the 18th July; then for -himself till the 7th of August, and for one day, on the fifteenth, -for a lady. Then again for me at 2 locks until the 20th of August. - -1461. - -On the 23rd day of August, 12 lire from Pulisona. On the 14th of -March 1494, Galeazzo came to live with me, agreeing to pay 5 lire a -month for his cost paying on the l4th day of each month. - -His father gave me 2 Rhenish florins. - -On the l4th of July, I had from Galeazzo 2 Rhenish florins. - -1462. - -On the 15th day of September Giulio began the lock of my studio -1494. - -1463. - -Saturday morning the 3rd of August 1504 Jacopo the German came to -live with me in the house, and agreed with me that I should charge -him a carlino a day. - -1464. - -1511. On the 26th of September Antonio broke his leg; he must rest -40 days. - -[Footnote: This note refers possibly to Beltraffio.] - -1465. - -I left Milan for Rome on the 24th day of September, 1513, with -Giovanni [Footnote 2: _Giovan;_ it is not likely that Leonardo -should have called Giovan' Antonio Beltraffio at one time Giovanni, -as in this note and another time Antonio, as in No. 1464 while in -No. 1458 l. 16 we find _Giovan'Antonio_, and in No. 1436, l.6 -_Beltraffio_. Possibly the Giovanni here spoken of is Leonardo's -less known pupil Giovan Pietrino (see No. 1467, 5).], Francesco di -Melzi [Footnote 2,3: _Francesco de' Melzi_ is often mentioned, see -Nos. 1350.], Salai [Footnote 3: _Salai_. See No. 1519 note.], -Lorenzo and il Fanfoia. - -[Footnote 4: _Lorenzo_. See No. 1351, l. 10 (p. 408). Amoretti gives -the following note in _Mem. Stor. XXIII:_ 1505. _Martedi--sera a di -14 d'aprile. Venne Lorenzo a stare con mecho: disse essere d'eta -d'anni 17 .. a di 15 del detto aprile ebbi scudi 25 d'oro dal -chamerlingo di Santa Maria nuova._ This, he asserts is derived from -a MS. marked S, in quarto. This MS. seems to have vanished and left -no trace behind; Amoretti himself had not seen it, but copied from a -selection of extracts made by Oltrocchi before the Leonardo MSS. -were conveyed to Paris on the responsibility of the first French -Republic. Lorenzo, by this, must have been born in 1487. The -sculptor Lorenzetto was born in 1490. Amoretti has been led by the -above passage to make the following absurd observations: - -_Cotesto Lorenzo, che poi gli fu sempre compagno, almeno sin che -stette in Italia, sarebb' egli Lorenzo Lotto bergamasco? Sappiamo -essere stato questo valente dipintore uno de'bravi scolari del -Vinci_ (?). - -_Il Fafoia_, perhaps a nickname. Cesare da Sesto, Leonardo's pupil, -seems to have been in Rome in these years, as we learn from a -drawing by him in the Louvre. - -1466. - -On the 3rd day of January. - -Benedetto came on the 17th of October; he stayed with me two months -and 13 days of last year, in which time he earned 38 lire, 18 soldi -and 8 dinari; he had of this 26 lire and 8 soldi, and there remains -to be paid for the past year 12 lire 10 soldi. - -Giodatti (?) came on the 8th day of September, at 4 soldi a month, -and stayed with me 3 months and 24 days, and earned 59 lire 14 soldi -and 8 dinari; he has had 43 lire, 4 soldi, there remains to pay 16 -lire, 10 soldi and 8 dinari. - -Benedetto, 24 grossoni. - -[Footnote: This seems to be an account for two assistants. The name -of the second is scarcely legible. The year is not given. The note -is nevertheless of chronological value. The first line tells us the -date when the note was registered, January 3d, and the observations -that follow refer to events of the previous month 'of last year' -_(dell'anno passato)_. Leonardo cannot therefore have written thus -in Florence where the year was, at that period, calculated as -beginning in the month of March (see Vol. I, No. 4, note 2). He must -then have been in Milan. What is more important is that we thus -learn how to date the beginning of the year in all the notes written -at Milan. This clears up Uzielli's doubts: _A Milano facevasi -cominciar l'anno ab incarnatione, cioe il 25 Marzo e a nativitate, -cioe il 25 Decembre. Ci sembra probabile che Leonardo dovesse -prescegliere lo stile che era in uso a Firenze._ (_Ricerche_, p. 84, -note.)] - -1467. - -Gian Maria 4, -Benedetto 4, -Gian Pietro [5] 3, -Salai 3, -Bartolomeo 3, -Gherardo 4. - -1468. - -Salai, 20 lire, -Bonifacio, 2 lire, -Bartolomeo, 4 lire, -Arrigo [Harry], 15 lire. - -Quotations and notes on books and authors (1469-1508). - -1469. - -Book on Arithmetic [Footnote 1: _"La nobel opera de arithmethica ne -la qual se tracta tute cosse amercantia pertinente facta & compilata -per Piero borgi da Veniesia", in-40. In fine: "Nela inclita cita di -Venetia a corni. 2 augusto. 1484. fu imposto fine ala presente -opera." Segn. a--p. quaderni. V'ha pero un' altra opera simile di -Filippo Calandro, 1491. E da consultarsi su quest' ultimo, Federici: -Memorie Trevigiane, Fiore di virtu: pag. 73. "Libricciuolo composto -di bello stile verso il 1320 e piu volte impresso nel secolo XV -(ristampato poi anche piu tardi). Gli accademici della Crusca lo -ammettono nella serie dei testi di lingua. Vedasi Gamba, Razzolini, -Panzer, Brunet, Lechi, ecc._ (G. D'A.)], 'Flowers of Virtue', - -Pliny [Footnote 2: _"Historia naturale di C. Plinio Secondo, -tradocta di lingua latina in fiorentina per Christophoro Laudino & -Opus Nicolai Jansonis gallici imp. anno salutis M.CCCC.LXXVI. -Venetiis" in-fol.--Diogene Laertio. Incomincia: "El libro de la vita -de philosophi etc.: Impressum Venetiis" per Bernardinum Celerium de -Luere, 1480", in-40_ (G. D'A.).], 'Lives of the Philosophers', - -The Bible [Footnote 3: _"La Bibia volgare historiata (per Nicolo di -Mallermi) Venecia ... M.CCCC.LXXI in kalende di Augusto (per -Vindelino de Spira)" 2 vol. in-fol. a 2 col. di 50 lin,; od altra -ediz. della stessa versione del Mallermi, Venetia 1471, e sempre: -"Venecia per Gabriel de Piero 1477," in-fol.; 2 vol.; Ottavio Scotto -da Modoetia 1481," "Venetia 1487 per Joan Rosso Vercellese," "1490 -Giovanni Ragazo di Monteferato a instantia di Luchanthonio di -Giunta, ecc."--Lapidario Teofrasto? Mandebille: "Le grand -lapidaire," versione italiana ms.?... Giorgio Agricola non puo -essere, perche nato nel 1494, forse Alberto Magno: de mineralibus. -Potrebbe essere una traduzione del poema latino (Liber lapidum seu -de gemmis) di Marbordio Veterio di Rennes (morto nel 1123 da lui -stesso tradotto in francese dal greco di Evao re d'Arabia celebre -medico che l'aveva composto per l'imperatore Tiberio. Marbodio -scrisse il suo prima per Filippo Augusto re di Francia. Vi sono -anche traduzioni in prosa. "Il lapidario o la forza e la virtu delle -pietre preziose, delle Erbe e degli Animali."_ (G. D'A.)], -'Lapidary', - -'On warfare' [Footnote 4: _Il Vegezio? ... Il Frontino? ... Il -Cornazzano?... Noi crediamo piuttosto il Valturio. Questo libro -doveva essere uno de'favoriti di Leonardo poiche libro di scienza e -d'arte nel tempo stesso._], 'Epistles of Filelfo', - -[Footnote: The late Marchese Girolamo d'Adda published a highly -valuable and interesting disquisition on this passage under the -title: _Leonardo da Vinci e la sua Libreria, note di un bibliofilo -(Milano 1873. Ed. di soli 75 esemplari_; privately printed). In the -autumn of 1880 the Marchese d'Adda showed me a considerable mass of -additional notes prepared for a second edition. This, as he then -intended, was to come out after the publication of this work of -mine. After the much regretted death of the elder Marchese, his son, -the Marchese Gioachino d'Adda was so liberal as to place these MS. -materials at my disposal for the present work, through the kind -intervention of Signor Gustavo Frizzoni. The following passages, -with the initials G. d'A. are prints from the valuable notes in that -publication, the MS. additions I have marked. I did not however -think myself justified in reproducing here the acute and interesting -observations on the contents of most of the rare books here -enumerated.] - -[Footnote: 1467. 5. See No. 1465, 2.] - -The first decade, [5] 'On the preservation of health', The third -decade, [6] Ciecho d'Ascoli, The fourth decade, [7] Albertus Magnus, -Guido, [8] New treatise on rhetorics, Piero Crescentio, [9] -Cibaldone, 'Quadriregio', [10] Aesop, - -Donato, [Footnote 11: "_Donatus latine & italice: Impressum Venetiis -impensis Johannis Baptistae de Sessa anno_ 1499, _in_-4deg.".-- "_El -Psalterio de David in lingua volgare (da Malermi Venetia nel -M.CCCC.LXXVI,_" in-fol. s. n._ (G. D'A.)] Psalms, - -Justinus, [Footnote 12: Compare No. 1210, 48.--_La versione di -Girolamo Squarzafico:_ "_Il libro di Justino posto diligentemente in -materna lingua. Venetia ale spesse (sic) di Johane de Colonia & -Johane Gheretze_ ... l477," _in-fol._--"_Marsilii Ficini, Theologia -platonica, sive de animarum immortalitate, Florentine, per Ant. -Misconimum_ 1482," _in-fol., ovvero qualche versione italiana di -questo stesso libro, ms._ (G. D'A.)] 'On the immortality of the -soul, - -Guido [Footnote 13: _Forse_ "_la Historia Trojana Guidonis_" _od il -_"_manipulus_" _di_ "_Guido da Monterocherii_"_ ma piu probabilmente -_"_Guido d'Arezzo_"_ il di cui libro: _"_Micrologus, seu disciplina -artis musicae_"_ poteva da Leonardo aversi ms.; di questi ne -esistono in molto biblioteche, e fu poi impresso nel 1784 dal -Gerbert._ - -_Molte sono le edizione dei sonetti di Burchiello Fiorentino, -impresse nel secolo XV. La prima e piu rara e recercata:_ -"_Incominciano li sonetti, ecc. (per Christoforo Arnaldo)_"_, in_-4deg. -_senza numeri, richiami o segnature, del_ 1475, _e fors' anche del_ -1472, _secondo Morelli e Dibdin, ecc._ (G. D'A.)] Burchiello, - -'Doctrinale' [Footnote 14: _Versione italiana det "Doctrinal de -Sapience" di Guy de Roy, e foris'anche l'originale in lingua -francese.--_ - -_Di Pulci Luigi, benche nell' edizione:_ "_Florentiae_ 1479" _in_-4deg. -si dica: _"_Il Driadeo composto in rima octava per Lucio Pulcro_"_ -Altre ediz, del secolo XV, _"_Florentie Miscomini_ 1481, _in_-40, -_Firenze, apud S. Jacob, de Ripoli,_ 1483,_" _in_-4deg. _e "Antoni de -Francesco,_ 1487," _in_-4deg. _e Francesco di Jacopo_ 1489,_in_-4deg. _ed -altre ancora di Venezia e senza alcuna nota ecc._ (G. D'A.)] -Driadeo, - -Morgante [Footnote 15: _Una delle edizioni del Morgante impresse nel -secolo XV, ecc.--_ - -_Quale delle opere di Francesco Petrarca, sarebbe malagevole -l'indovinare, ma probabilmente il Canzoniere._ (G. D'A.)] Petrarch. - -John de Mandeville [Footnote 16: _Sono i viaggi del cavaliere_ -"_Mandeville_" _gentiluomo inglese. Scrisse il suo libro in lingua -francese. Fu stampato replicatamente nel secolo XV in francese, in -inglese ed in italiano ed in tedesco; del secolo XV ne annoverano -forse piu di 27 edizioni, di cui ne conosciamo_ 8 _in francese, -quattro in latino, sei in tedesco e molte altre in volgare._ (G. -D'A.)] - -'On honest recreation' [Footnote 17: _Il Platina (Bartolomeo Sacchi) -la versione italiana_ "_de la honesta voluptate, & valetudine (& de -li obsonnii) Venetia (senza nome di tipografo)_ 1487," _piccolo -in_-4deg. _gotico._ (G. D'A.)--Compare No. 844, 21.] - -Manganello, [Footnote 18: _Il Manganello: Satira eccessivamente -vivace contro le donne ad imitazione della Sesta di Giovenale. -Manganello non e soltanto il titolo del libricino, sua ben anche il -nome dell'autore ch'era un_ "_milanese_". _Di questo libercolo -rarissimo, che sembra impresso a Venezia dallo Zoppino (Nicolo -d'Aristotile detto il), senza data, ma dei primissimi anni del -secolo XVI, e forse piu antico, come vedremo in appresso, non se ne -conoscono fra biblioteche pubbliche e private che due soli esemplari -in Europa._ (G. D'A.)] - -The Chronicle of Isidoro, [Footnote 19: "_Cronica desidero_", -_sembra si deggia leggere piuttosto_ "_cronico disidoro_"_; ed in -questo caso s'intenderebbe la_ "_cronica d'Isidoro_" _tanto in voga -a quel tempo_ "_Comenza la Cronica di Sancto Isidoro menore con -alchune additione cavate del testo & istorie de la Bibia & del libro -di Paulo Oroso .... Impresso in Ascoli in casa del reverendo misser -Pascale ..... per mano di Guglielmo de Linis de Alamania -M.CCCC.LXXVII_" _in_-4deg. _di_ 157 _ff. E il primo libro impresso ad -Ascoli e l'edizione principe di questa cronica in oggi assai rara. -Non lo e meno l'edizione di Cividal del Friuli_, 1480, _e quella ben -anche di Aquila_, 1482, _sempre in-_4deg.. _Vedasi Panzer, Hain, Brunet -e P. Dechamps._ (G. D'A.)] - -The Epistles of Ovid, [Footnote 20: "_Le pistole di Ovidio tradotte -in prosa. Napoli Sixt. Riessinger_", _in_-4deg., _oppure:_ "_Epistole -volgarizzate_ 1489," _in_-4deg. _a due col._ "_impresse ne la cita -(sic) di Bressa per pre: Baptista de Farfengo,_" _(in ottave) o:_ -"_El libro dele Epistole di Ovidio in rima volgare per messere -Dominico de Monticelli toschano. Brescia Farfengo_," _in_-4deg. _got. -(in rima volgare)_, 1491, _ed anche la versione di Luca Pulci. -Firenze, Mischomini_, 1481, _in_-4deg.. (G. D'A.) ] - -Epistles of Filelfo, [Footnote 21: See l. 4.] - -Sphere, [Footnote 22: "_Jo: de Sacrobusto_," _o_ "_Goro Dati_," _o_ -"_Tolosano da Colle_" _di cui molteplici edizioni del secolo XV._ -(G. D'A.)] - -The Jests of Poggio, [Footnote 23: _Tre edizioni delle facezie del -Poggio abbiamo in lingua italiana della fine del secolo XV, tutte -senza data. "Facetie de Poggio fiorentino traducte de latino in -vulgare ornatissimo," in-40, segn. a--e in caratteri romani; -l'altra: "Facetie traducte de latino in vulgare," in-40, caratteri -gotici, ecc._ (G. D'A.)] Chiromancy, [Footnote 24: "_Die Kunst -Cyromantia etc, in tedesco. 26 ff. di testo e figure il tutte -eseguito su tavole di legno verso la fine del secolo XV da Giorgio -Schapff". Dibdin, Heinecken, Sotheby e Chatto ne diedero una lunga -descrizione; i primi tre accompagnati da fac-simili. La data 1448 -che si legge alla fine del titolo si riferisce al periodo della -composizione del testo, non a quello della stampa del volume benche -tabellario. Altri molti libri di Chiromanzia si conoscono di quel -tempo e sarebbe opera vana il citarli tutti._ (G. D'A.)] - -Formulary of letters, [Footnote 25: _Miniatore Bartolomeo. -"Formulario de epistole vulgare missive e responsive, & altri fiori -de ornali parlamenti al principe Hercule d'Esti ecc. composto ecc. -Bologna per Ugo di Rugerii," in-40, del secolo XV. Altra edizione di -"Venetia Bernardino di Novara, 1487" e "Milano per Joanne Angelo -Scinzenzeler 1500," in-40._ (G. D'A.) - -Five books out of this list are noted by Leonardo in another MS. -(Tr. 3): _donato, -- lapidario, -- plinio, -- abacho, -- morgante._] - -1470. - -Nonius Marcellus, Festus Pompeius, Marcus Varro. - -[Footnote: Nonius Marcellus and Sextus Pompeius Festus were Roman -grammarians of about the fourth century A. D. Early publications of -the works of Marcellus are: _De proprietate sermonis, Romae_ (about -1470), and 1471 (place of publication unknown). _Compendiosa -doctrina, ad filium, de proprietate sermonum._ Venice, 1476. BRUNET, -_Manuel du libraire_ (IV, p. 97) notes: _Le texte de cet ancien -grammairien a ete reimprime plusieurs fois a la fin du XVe siecle, -avec ceux de Pomponius Festus et de Terentius Varro. La plus -ancienne edition qui reunisse ces trois auteurs est celle de Parme, -1480 ... Celles de Venise, 1483, 1490, 1498, et de Milan, 1500, -toutes in-fol., ont peu de valeur._] - -1471. - -Map of Elephanta in India which Antonello Merciaio has from maestro -Maffeo;--there for seven years the earth rises and for seven years -it sinks;--Enquire at the stationers about Vitruvius. - -1472. - -See 'On Ships' Messer Battista, and Frontinus 'On Acqueducts' -[Footnote 2: 2. _Vitruvius de Arch., et Frontinus de Aquedoctibus._ -Florence, 1513.--This is the earliest edition of Frontinus.--The -note referring to this author thus suggests a solution of the -problem of the date of the Leicester Manuscript.]. - -[Footnote: Compare No. 1113, 25.] - -1473. - -Anaxagoras: Every thing proceeds from every thing, and every thing -becomes every thing, and every thing can be turned into every thing -else, because that which exists in the elements is composed of those -elements. - -1474. - -The Archimedes belonging to the Bishop of Padua. - -[Footnote: See No. 1421, 1. 3, 6 and Vol. I, No. 343.] - -1475. - -Archimedes gave the quadrature of a polygonal figure, but not of the -circle. Hence Archimedes never squared any figure with curved sides. -He squared the circle minus the smallest portion that the intellect -can conceive, that is the smallest point visible. - -[Footnote: Compare No. 1504.] - -1476. - -If any man could have discovered the utmost powers of the cannon, in -all its various forms and have given such a secret to the Romans, -with what rapidity would they have conquered every country and have -vanquished every army, and what reward could have been great enough -for such a service! Archimedes indeed, although he had greatly -damaged the Romans in the siege of Syracuse, nevertheless did not -fail of being offered great rewards from these very Romans; and when -Syracuse was taken, diligent search was made for Archimedes; and he -being found dead greater lamentation was made for him by the Senate -and people of Rome than if they had lost all their army; and they -did not fail to honour him with burial and with a statue. At their -head was Marcus Marcellus. And after the second destruction of -Syracuse, the sepulchre of Archimedes was found again by Cato[25], -in the ruins of a temple. So Cato had the temple restored and the -sepulchre he so highly honoured.... Whence it is written that Cato -said that he was not so proud of any thing he had done as of having -paid such honour to Archimedes. - -[Footnote: Where Leonardo found the statement that Cato had found -and restored the tomb of Archimedes, I do not know. It is a merit -that Cicero claims as his own (Tusc. V, 23) and certainly with a -full right to it. None of Archimedes' biographers --not even the -diligent Mazzucchelli, mentions any version in which Cato is named. -It is evidently a slip of the memory on Leonardo's part. Besides, -according to the passage in Cicero, the grave was not found _'nelle -ruine d'un tempio'_--which is highly improbable as relating to a -Greek--but in an open spot (H. MULLER-STRUBING).--See too, as to -Archimedes, No. 1417. - -Leonardo says somewhere in MS. C.A.: _Architronito e una macchina di -fino rame, invenzlon d' Archimede_ (see _'Saggio'_, p. 20).] - -1477. - -Aristotle, Book 3 of the Physics, and Albertus Magnus, and Thomas -Aquinas and the others on the rebound of bodies, in the 7th on -Physics, on heaven and earth. - -1478. - -Aristotle says that if a force can move a body a given distance in a -given time, the same force will move half the same body twice as far -in the same time. - -1479. - -Aristotle in Book 3 of the Ethics: Man merits praise or blame solely -in such matters as lie within his option to do or not to do. - -1480. - -Aristotle says that every body tends to maintain its nature. - -1481. - -On the increase of the Nile, a small book by Aristotle. [Footnote: -_De inundatione Nili_, is quoted here and by others as a work of -Aristotle. The Greek original is lost, but a Latin version of the -beginning exists (Arist. Opp. IV p. 213 ed. Did. Par.). - -In his quotations from Aristotle Leonardo possibly refers to one of -the following editions: _Aristotelis libri IV de coelo et mundo; de -anima libri III; libri VIII physi- corum; libri de generatione et -corruptione; de sensu et sensato... omnia latine, interprete -Averroe, Venetiis 1483_ (first Latin edition). There is also a -separate edition of _Liber de coelo et mundo_, dated 1473.] - -1482. - -Avicenna will have it that soul gives birth to soul as body to body, -and each member to itself. - -[Footnote: Avicenna, see too No. 1421, 1. 2.] - -1483. - -Avicenna on liquids. - -1484. - -Roger Bacon, done in print. [Footnote: The earliest printed edition -known to Brunet of the works of Roger Bacon, is a French -translation, which appeared about fourty years after Leonardo's -death.] - -1485. - -Cleomedes the philosopher. - -[Footnote: Cleomede. A Greek mathematician of the IVth century B. C. -We have a Cyclic theory of Meteorica by him. His works were not -published before Leonardo's death.] - -1486. - -CORNELIUS CELSUS. - -The highest good is wisdom, the chief evil is suffering in the body. -Because, as we are composed of two things, that is soul and body, of -which the first is the better, the body is the inferior; wisdom -belongs to the better part, and the chief evil belongs to the worse -part and is the worst of all. As the best thing of all in the soul -is wisdom, so the worst in the body is suffering. Therefore just as -bodily pain is the chief evil, wisdom is the chief good of the soul, -that is with the wise man; and nothing else can be compared with it. - -[Footnote: _Aulus Cornelius Celsus_, a Roman physician, known as the -Roman Hippocrates, probably contemporary with Augustus. Only his -eight Books 'De Medicina', are preserved. The earliest editions are: -_Cornelius Celsus, de medicina libr. VIII._, Milan 1481 Venice 1493 -and 1497.] - -1487. - -Demetrius was wont to say that there was no difference between the -speech and words of the foolish and ignorant, and the noises and -rumblings of the wind in an inflated stomach. Nor did he say so -without reason, for he saw no difference between the parts whence -the noise issued; whether their lower parts or their mouth, since -one and the other were of equal use and importance. - -[Footnote: Compare Vol. I, No. 10.] - -1488. - -Maestro Stefano Caponi, a physician, lives at the piscina, and has -Euclid _De Ponderibus_. - -1489. - -5th Book of Euclid. First definition: a part is a quantity of less -magnitude than the greater magnitude when the less is contained a -certain number of times in the greater. - -A part properly speaking is that which may be multiplied, that is -when, being multiplied by a certain number, it forms exactly the -whole. A common aggregate part ... - -Second definition. A greater magnitude is said to be a multiple of a -less, when the greater is measured by the less. - -By the first we define the lesser [magnitude] and by the second the -greater is defined. A part is spoken - -1490. - -of in relation to the whole; and all their relations lie between -these two extremes, and are called multiples. - -1491. - -Hippocrates says that the origin of men's sperm derives from the -brain, and from the lungs and testicles of our parents, where the -final decocture is made, and all the other limbs transmit their -substance to this sperm by means of expiration, because there are no -channels through which they might come to the sperm. - -[Footnote: The works of Hippocrates were printed first after -Leonardo's death.] - -1492. - -Lucretius in his third [book] 'De Rerum Natura'. The hands, nails -and teeth were (165) the weapons of ancient man. - -They also use for a standard a bunch of grass tied to a pole (167). - -[Footnote: _Lucretius, de rerum natura libri VI_ were printed first -about 1473, at Verona in 1486, at Brescia in 1495, at Venice in 1500 -and in 1515, and at Florence in 1515. The numbers 165 and 167 noted -by Leonardo at the end of the two passages seem to indicate pages, -but if so, none of the editions just mentioned can here be meant, -nor do these numbers refer to the verses in the poems of Lucretius.] - -1493. - -Ammianus Marcellinus asserts that seven hundred thousand volumes of -books were burnt in the siege of Alexandria in the time of Julius -Cesar. - -[Footnote: _Ammiani Marcellini historiarum libri qui extant XIII_, -published at Rome in 1474.] - -1494. - -Mondino says that the muscles which raise the toes are in the -outward side of the thigh, and he adds that there are no muscles in -the back [upper side] of the feet, because nature desired to make -them light, so as to move with ease; and if they had been fleshy -they would be heavier; and here experience shows ... - -[Footnote: _"Mundini anatomia. Mundinus, Anothomia (sic). Mundini -praestantissimorum doctorum almi studii ticiensis (sic) cura -diligentissime emendata. Impressa Papiae per magistrum Antonium de -Carfano 1478," in-fol.; ristampata: "Bononiae Johan. de Noerdlingen, -1482," in-fol.; "Padova per Mattheum Cerdonis de Vuindischgretz, -1484," in-40; "Lipsia, 1493," in-40; "Venezia, 1494," in-40 e ivi -"1498," con fig. Queste figure per altro non sono, come si e -preteso, le prime che fossero introdotte in un trattato di Notamia. -Nel 'fasciculus Medicinae' di Giovanni Ketham, che riproduce -l''Anatomia' del Mundinus, impresso pure a Venezia da J. e G. de -Gregoriis, 1491, in-fol., contengonsi intagli in legno (si vogliono -disegnati non gia incisi da Andrea Mantegna) di grande dimensione, e -che furono piu volte riprodotti negli anni successivi. Quest' -edizione del "fasciculus" del 1491, sta fra nostri libri e potrebbe -benissimo essere il volume d'Anatomia notato da Leonardo._ (G. -D'A.)] - -1495. - -Of the error of those who practice without knowledge;--[3] See first -the 'Ars poetica' of Horace [5]. - -[Footnote: A 3-5 are written on the margin at the side of the title -line of the text given, entire as No. 19] - -1496. - -The heirs of Maestro Giovanni Ghiringallo have the works of -Pelacano. - -1497. - -The catapult, as we are told by Nonius and Pliny, is a machine -devised by those &c. - -[Footnote: _Plinius_, see No. 946.] - -1498. - -I have found in a history of the Spaniards that in their wars with -the English Archimedes of Syracuse who at that time was living at -the court of Ecliderides, King of the Cirodastri. And in maritime -warfare he ordered that the ships should have tall masts, and that -on their tops there should be a spar fixed [Footnote 6: Compare No. -1115.] of 40 feet long and one third of a foot thick. At one end of -this was a small grappling iron and at the other a counterpoise; and -there was also attached 12 feet of chain; and, at the end of this -chain, as much rope as would reach from the chain to the base of the -top, where it was fixed with a small rope; from this base it ran -down to the bottom of the mast where a very strong spar was attached -and to this was fastened the end of the rope. But to go on to the -use of his machine; I say that below this grappling iron was a fire -[Footnote 14: Compare No. 1128.] which, with tremendous noise, threw -down its rays and a shower of burning pitch; which, pouring down on -the [enemy's] top, compelled the men who were in it to abandon the -top to which the grappling-iron had clung. This was hooked on to the -edges of the top and then suddenly the cord attached at the base of -the top to support the cord which went from the grappling iron, was -cut, giving way and drawing in the enemy's ship; and if the -anchor--was cast ... - -[Footnote: Archimedes never visited Spain, and the names here -mentioned cannot be explained. Leonardo seems to quote here from a -book, perhaps by some questionable mediaeval writer. Prof. C. Justi -writes to me from Madrid, that Spanish savants have no knowledge of -the sources from which this story may have been derived.] - -1499. - -Theophrastus on the ebb and flow of the tide, and of eddies, and on -water. [Footnote: The Greek philosophers had no opportunity to study -the phenomenon of the ebb and flow of the tide and none of them -wrote about it. The movement of the waters in the Euripus however -was to a few of them a puzzling problem.] - -1500. - -Tryphon of Alexandria, who spent his life at Apollonia, a city of -Albania (163). [Footnote: Tryphon of Alexandria, a Greek Grammarian -of the time of Augustus. His treatise TtaOY Aeijecu appeared first -at Milan in 1476, in Constantin Laskaris's Greek Grammar.] - -1501. - -Messer Vincenzio Aliprando, who lives near the Inn of the Bear, has -Giacomo Andrea's Vitruvius. - -1502. - -Vitruvius says that small models are of no avail for ascertaining -the effects of large ones; and I here propose to prove that this -conclusion is a false one. And chiefly by bringing forward the very -same argument which led him to this conclusion; that is, by an -experiment with an auger. For he proves that if a man, by a certain -exertion of strength, makes a hole of a given diameter, and -afterwards another hole of double the diameter, this cannot be made -with only double the exertion of the man's strength, but needs much -more. To this it may very well be answered that an auger - -1503. - -of double the diameter cannot be moved by double the exertion, be- -cause the superficies of a body of the same form but twice as large -has four times the extent of the superficies of the smaller, as is -shown in the two figures a and n. - -1504. - -OF SQUARING THE CIRCLE, AND WHO IT WAS THAT FIRST DISCOVERED IT BY -ACCIDENT. - -Vitruvius, measuring miles by means of the repeated revolutions of -the wheels which move vehicles, extended over many Stadia the lines -of the circumferences of the circles of these wheels. He became -aware of them by the animals that moved the vehicles. But he did not -discern that this was a means of finding a square equal to a circle. -This was first done by Archimedes of Syracuse, who by multiplying -the second diameter of a circle by half its circumference produced a -rectangular quadrilateral equal figure to the circle [Footnote 10: -Compare No. 1475.]. - -[Footnote: _Vitruvius_, see also Nos. 1113 and 343.] - -1505. - -Virgil says that a blank shield is devoid of merit because among the -people of Athens the true recognition confirmed by testimonies ... - -[Footnote: The end of the text cannot be deciphered.] - -1506. - -In Vitolone there are 805 conclusions [problems] in perspective. - -[Footnote: _(Witelo, Vitellion, Vitellon) Vitellione. E da vedersi -su questo ottico prospettico del secolo XIII Luca Pacioli, Paolo -Lomazzo, Leonardo da Vinci, ecc. e fra i moderni il Graesse, il -Libri, il Brunet, e le Memorie pubblicate dal principe Boncompagni, -e 'Sur l' orthographe du nom et sur la patrie de Witelo (Vitellion) -note de Maximilien Curtze, professeur a Thorn', ove sono descritti i -molti codici esistenti nelle biblioteche d' Europa. Bernardino Baldi -nelle sue 'Vite de'matematici', manoscritto presso il principe -Boncompagni, ha una biografia del Vitellione. Questo scritto del -Baldi reca la data 25 agosto 1588. Discorsero poi di lui Federigo -Risnerio e Giovanni di Monteregio nella prefazione dell' Alfagrano, -Giovanni Boteone, Girolamo Cardano, 'De subtilitate', che nota gli -errori di Vitellione. Visse, secondo il Baldi, intorno all' anno -1269, ma secondo il Reinoldo fioriva nel 1299, avendo dedicata la -sua opera ad un frate Guglielmo di Monteca, che visse di que' tempi. - -Intorno ad un manoscritto dell' ottica di Vitellione, citato da Luca -Pacioli v'ha un secondo esemplare del Kurlz, con aggiunte del -principe Boncompagni, e le illustrazioni del cav. Enrico Narducci. -Nel 'Catalogo di manoscritti' posseduti da D. Baldassare de' -principi Boncompagni, compilato da esso Narducci, Roma, 1862, sotto -al n. 358, troviamo citato: Vitellio, 'Perspectiva', manoscritto del -secolo XIV. La 'Prospettiva di Vitelleone' (sic) Thuringo-poloni e -citata due volte da Paolo Lomazzo nel Trattato dell' arte della -pittura. Vitellio o Vitello o Witelo. Il suo libro fu impresso in -foglio a Norimberga nel 1535; la secondo edizione e del 1551, sempre -di Norimberga, ed una terza di Basilea, 1572._ (See _Indagini -Storiche ... sulla Libreria-Visconteo-Sforzesca del Castello di -Pavia ... per cura di_ G. D'A., _Milano 1879. P. I. Appendice p. -113. 114)._] - -1507. - -Vitolone, at Saint Mark's. - -[Footnote: _Altro codice di cotesta 'Prospettiva' del Vitolone -troviamo notato nel 'Canone bibliographico di Nicolo V', conservato -alla, Magliabecchiana, in copia dell' originale verosimilmente -inviato dal Parentucelli a Cosimo de' Medici (Magliab. cod. segn. 1 -VII, 30 carte da 193 a 198). Proviene dal Convento di San Marco e lo -aveva trascritto frate Leonardo Scruberti fiorentino, dell' ordine -dei predicatori che fu anche bibliotecario della Medicea pubblica in -San Marco_ (See _Indagini Storiche ... per cura di_ G. D'A. _Parte -I, p. 97)._] - -1508. - -How this proposition of Xenophon is false. - -If you take away unequal quantities from unequal quantities, but in -the same proportion, &c. [Footnote: Xenophon's works were published -several times during Leonardo's lifetime.] - -Inventories and accounts (1509--1545). - -1509. - -On the 28th day of April I received from the Marchesino 103 lire and -12 dinari. [Footnote: Instead of the indication of the year there is -a blank space after _d'aprile_.--Marchesino Stange was one of -Lodovico il Moro's officials.--Compare No. 1388.] - -1510. - -On the 10th day of July 1492 in 135 -Rhenish florins 1. 445 -in dinari of 6 soldi 1. 112 S 16 -in dinari of 5 1/2 soldi 1. 29 S 13 -9 in gold and 3 scudi 1. 53 - ----------------------------- - 1. 811 in all - -1511. - -On the first day of February, lire 1200. - -1512. - -The hall towards the court is 126 paces long and 27 braccia wide. - -1513. - -The narrow cornice above the hall lire 30. - -The cornice beneath that, being one for each picture, lire 7, and -for the cost of blue, gold, white, plaster, indigo and glue 3 lire; -time 3 days. - -The pictures below these mouldings with their pilasters, 12 lire -each. - -I calculate the cost for smalt, blue and gold and other colours at 1 -1/2 lire. - -The days I calculate at 3, for the invention of the composition, -pilasters and other things. - -1514. - -Item for each vault 7 lire - -outlay for blue and gold 3 1/2 - -time, 4 days - -for the windows 1 1/2 - -The cornice below the windows 16 soldi per braccio - -item for 24 pictures of Roman history 14 lire each - -The philosophers 10 lire - -the pilasters, one ounce of blue 10 soldi - -for gold 15 soldi - -Total 2 and 1/2 lire. - -1515. - -The cornice above lire 30 - -The cornice below lire 7 - -The compositions, one with another lire 13 - -1516. - -Salai, 6 lire ... 4 soldi ... 10 soldi for a chain;-- - -On the l4th of March I had 13 lire S. 4; 16 lire remain. - -1517. - -How many braccia high is the level of the walls?-- - -123 braccia - -How large is the hall? - -How large is the garland? - -30 ducats. - -On the 29th day of January, 1494 - -cloth for hose lire 4 S 3 - -lining S 16 - -making S 8 - -to Salai S 3 - -a jasper ring S 13 - -a sparkling stone S 11 - -to Caterina S 10 - -to Caterina S 10 - -1518. - -The wheel lire 7 - -the tire lire 10 - -the shield lire 4 - -the cushion lire 8 - -the ends of the axle-tree lire 2 - -bed and frame lire 30 - -conduit lire 10 - -S.K.M.II.2 4a] - -1519. - -Parsley 10 parts - -mint 1 part - -thyme 1 part - -Vinegar ... and a little salt two pieces of canvas for Salai. - -[Footnote: This note, of about the year 1494, is the earliest -mention of Salai, and the last is of the year 1513 (see No. 1465, -3). From the various notes in the MSS. he seems to have been -Leonardo's assistant and keeper only, and scarcely himself a -painter. At any rate no signed or otherwise authenticated picture by -him is known to exist. Vasari speaks somewhat doubtfully on this -point.] - -1520. - -On Tuesday I bought wine for morning [drinking]; on Friday the 4th -day of September the same. - -[Footnote: This note enables us to fix the date of the Manuscript, -in which it is to be found. In 1495 the 4th of September fell on a -Friday; the contents of the Manuscript do not permit us to assign it -to a much earlier or later date (Compare No. 1522, and Note).] - -1521. - -The cistern ... at the Hospital, --2 ducats, --beans, --white maize, ---red maize, --millet, --buckwheat, --kidney beans, --beans, --peas. - -1522. - -EXPENSES OF THE INTERMENT OF CATERINA. - -For the 3 lbs of tapers 27 S -For the bier 8 S -A pall over the bier 12 S -For bearing and placing the cross 4 S -For bearing the body 8 S -For 4 priests and 4 clerks 20 S -Bell, book and sponge 2 S -For the gravediggers 16 S -To the senior 8 S -For a license from the authorities 1 S -106 S - -The doctor 2 S -Sugar and candles 12 S -120 S - -[Footnote: See Nos. 1384 and 1517.] - -1523. - -Salai's cloak, the 4th of April 1497. -4 braccia of silver cloth l. 15 S 4 -green velvet to trim it l. 9 S -- -binding l.-- S 9 -loops l.-- S 12 -the making l. 1 S 5 -binding for the front l.-- S 5 -stitching _________ -here are 13 grossoni of his l. 26 S 5 -Salai stole the soldi. - -1524. - -On Monday I bought 4 braccia of cloth lire 13 S 14 1/2 on the 17th -of, October 1497. - -1525. - -Memorandum. That on the 8th day of April 1503, I, Leonardo da Vinci, -lent to Vante, miniature painter 4 gold ducats, in gold. Salai -carried them to him and gave them into his own hand, and he said he -would repay within the space of 40 days. - -Memorandum. That on the same day I paid to Salai 3 gold ducats which -he said he wanted for a pair of rose-coloured hose with their -trimming; and there remain 9 ducats due to him--excepting that he -owes me 20 ducats, that is 17 I lent him at Milan, and 3 at Venice. - -Memorandum. That I gave Salai 21 braccia of cloth to make a shirt, -at 10 soldi the braccio, which I gave him on the 20th day of April -1503. - -[Footnote: With regard to Vante or Attavante, the miniature painter -(not Nanni as I formerly deciphered this name, which is difficult to -read; see _Zeitschrift fur Bild. Kunst_, 1879, p. 155), and Vasari, -Lives of Frate Giovanni da Fiesole, of Bartolommeo della Gatta, and -of Gherardo, _miniatore._ He, like Leonardo, was one of the -committee of artists who, in 1503, considered the erection and -placing of Michel Angelo's David. The date of his death is not -known; he was of the same age as Leonardo. Further details will be -found in '_Notizie di Attavante miniatore, e di alcuni suoi lavori_' -(Milanese's ed. of Vasari, III, 231-235).] - -1526. - -On the morning of San Peter's day, June 29th, 1504, I took io -ducats, of which I gave one to Tommaso my servant to spend. - -On Monday morning 1 florin to Salai to spend on the house. - -On Thursday I took 1 florin for my own spending. - -Wednesday evening 1 florin to Tommaso, before supper. - -Saturday morning 1 florin to Tommaso. - -Monday morning 1 florin less 10 soldi. - -Thursday to Salai 1 florin less 10 soldi. - -For a jerkin, 1 florin. - -For a jerkin And a cap 2 florins. - -To the hosier, 1 florin. - -To Salai, 1 florin. - -Friday morning, the 19th of July, 1 florin, less 6 soldi. I have 7 -fl. left, and 22 in the box. - -Tuesday, the 23th day of July, 1 florin to Tommaso. - -Monday morning, to Tommaso 1 florin. - -[Wednesday morning 1 fl. to Tommaso.] - -Thursday morning the 1st day of August 1 fl. to Tommaso. - -Sunday, the 4th of August, 1 florin. - -Friday, the 9th day of August 1504, I took 10 ducats out of the box. - -1527. - -1504. On the 9th day of August, 1504, I took 10 florins in gold[2] -... [3] on Friday the 9th day of August fifteen grossoni that is fl. -5 S 5 ... given to me 1 florin in gold on the 12th day of August [4] -... on the 14th of August, 32 grossoni to Tommaso. On the 18th of -the same 5 grossoni to Salai. On the 8th of September 6 grossoni to -the workman to spend; that is on the day of our Lady's birth. On the -16th day of September I gave 4 grossoni to Tommaso: on a Sunday. - -[Footnote: In the original, the passage given as No. 1463 is written -between lines 2 and 3 of this text, and it is possible that the -entries in lines 3 and 4 refer to the payments of Jacopo Tedesco, -who is there mentioned. The first words of these lines are very -illegible.] - -[Footnote 7: _Al fattore._ Il Fattore, was, as is well known, the -nick-name of Giovanni Franceso Penni, born in Florence in 1486, and -subsequently a pupil of Raphael's. According to Vasari he was known -by it even as a boy. Whether he is spoken of in this passage, or -whether the word Fattore should be translated literally, I will not -undertake to decide. The latter seems to me more probably right.] - -1528. - -On the day of October, 1508, I had 30 scudi; 13 I lent to Salai to -make up his sister's dowry, and 17 I have left. - -1529. - -Memorandum of the money I have had from the King as my salary from -July 1508 till April next 1509. First 100 scudi, then 70, then 50, -then 20 and then 200 florins at 48 soldi the florin. [Footnote: -Compare No. 1350 and 1561.] - -1530. - -Saturday the 2nd day of March I had from Santa Maria Novella 5 gold -ducats, leaving 450. Of these I gave 2 the same day to Salai, who -had lent them to me. [Footnote: See '_Conto corrente di Leonardo da -Vinci con lo Spedale di S. Maria Nuova_' [1500 a 1507, 1513-1520] -published by G. UZIELLI, _Ricerche intorno a Leonardo da Vinci, -Firenze,_ 1872, pp. 164, 165, 218 and 219. The date here given by -Leonardo does not occur in either of the accounts.] - -1531. - -Thursday, the eighth day of June, I took 17 grossoni, 18 soldi; on -the same Thursday in the morning I gave to Salai 22 soldi for the -expenses. - -1532. - -To Salai 4 grossoni, and for one braccio of velvet, 5 lire, and 1/2; -viz. 10 soldi for loops of silver; Salai 14 soldi for binding, the -making of the cloak 25 soldi. [Footnote: Compare No. 1523.] - -1533. - -I gave to Salai 93 lire 6 soldi, of which I have had 67 lire and -there remain 26 lire 6 soldi. - -1534. - -To Salai S 42 - -2 dozen of laces S 8 - -for papers S 3 d 8 - -a pair of shoes S 14 - -for velvet S 14 - -a sword and knife S 21 - -to the barber S 11 - -to Paolo for a ... S 20 - -For having his fortune told S 6 - -1535. - -On Friday morning, -one florin to Salai to -spend; 3 soldi received - -bread S.. d - -wine S.. d - -grapes S.. d - -mushrooms S.. d - -fruit S.. d - -[Footnote 6: Compare Nos. 1545, l. 4 and 5, -with similar entries for horse's fodder.] -bran S.. d - -at the barber's S.. d - -for shoes S.. d - -1536. - -On Thursday morning one florin. - -1537. - -On Saint Ambrose's day from the morning to Thursday 36 soldi. - -1538. - -The moneys I have had from Ser Matteo; -first 20 grassoni, then on 13 occasions 3 f. -and then 61 grassoni, then 3, and then 33; -46 soldi 12 grossoni. - -1539. - -For paper S 18 - -for canvas S 30 - -for paper S 10 d 19 - -Total S 73 - -1540. - -20 pounds of German -blue, at one ducat the pound lire 80 S d - -60 pounds of white, S.. -the pound lire 15 S d - -1 1/2 pound at 4 S the pound lire 6 S d - -2 pounds of cinnabar at -S 18 the pound lire 1 S 16 d - -6 pounds of green at S 12 -the pound lire 3 S 12 d - -4 pounds of yellow at S 12 -the pound lire 2 S 8 d - -1 pound of minium at S 8 -the pound lire 0 S 8 d - -4 pounds of ... at S 2 -the pound lire 0 S 8 d - -6 pounds of ochre at S 1 -the pound lire 0 S 6 d - -black ... at S 2 the pound -for 20 lire 2 S 0 d - -wax to make the stars -29 pounds at S--the pound lire 0 S 0 d - -40 pounds of oil for painting -at 5 soldi the pound lire 10 S 0 d - -Altogether lire 120 d 18 -without the gold. 18 - -tin for putting on the gold 120 18 - -58 - -1541. - -Two large hatchets and one very small one, 8 brass spoons, 4 -tablecloths, 2 towels, 15 small napkins, 2 coarse napkins, 2 coarse -cloths, 2 wrappers, 3 pairs of sheets, 2 pairs new and 1 old. - -1542. - -Bed 7 0 S - -ring 7 0 - -crockery 2 5 - -gardener 1 2 - -..... 2 8 - -porters 2 1 - -glasses 1 - -fuel 3 6 - -a lock 1 - -Section title: Miscellaneous Notes. - -1543. - -New tin-ware 3 pairs of sheets -6 small bowls, each of 4 breadths, -6 bowls, 2 small sheets, -2 large dishes, 2 tablecloths and 1/2, -2 dishes medium size, 16 coarse cloths, -2 small ones 8 shirts, - Old tin-ware 9 napkins, -3 small bowls, 2 hand-towels. -4 bowls, -3 square stones, -2 small bowls, -1 large bowl, -1 platter, -4 candlesticks, -1 small candlestick. - -1544. - -Hose S 40 -straw S 60 -wheat S 42 -wine S 54 -bread S 18 -meat S 54 -eggs S 5 -salad S 3 -the Barber S 2 d 6 -horses S 1 - -1545. - - Sunday - -meat S 10 d -wine S 12 d -bran S 5 d 4 -herbs S 10 d -buttermilk S 4 d 4 -melon S 3 d -bread S 3 d 1 -____________________ - Monday S 9 8 -____________________ -..... S 6 d -wine S 12 d -bran S 9 d 4 -buttermilk S 4 d 4 -herbs S 8 d -____________________ - Tuesday S d -_____________________ -meat S 0 d 8 -wine S 12 d -bread S 3 d -meal S 5 d 4 -herbs S 8 d -_____________________ - Wednesday -_____________________ -wine S 5 d -melon S 2 d -meal S 5 d 4 -vegetables S 8 - -Notes by unknown persons among the MSS. (1546-1565). - -1546. - -Miseracione divina sacro sancte Romane ecclesie tituli n cardinalis -2wulgariter nuncupatus venerabili religioso fratri Johanni Mair -d'Nustorf 3ordinis praedicatorum provintie teutonie (?) conventus -Wiennensis capellano 4 nostro commensali salutem in dno sempiternam -Religione zelus rite ac in [ferite?] 5honestas aliarumque -laudabilium probitatis et virtutum merita quibus apud nos fide -6digno commendationis testimonio Magistri videlicet ordinis felicis -recordacionis Leonardi de 7Mansuetis de Perusio sigillo suo ... us -dans tibi ad ... opera virtutum comen(salem)? 8 locum et tempus -success(ores) cujus similiter officium ministratus qui -praedecessoris sui donum (?) 9confirmavit et de novo dedit -aliorumque plurima [laudatis] qui opera tua laudant 10nos inducunt -ut tibi (?) reddamus ad gratiam liberalem hinc est quod nos -cupientes. [Footnote: The meaning of this document, which is very -difficult to decipher, and is written in unintelligible Latin, is, -that Leonardo di Mansuetis recommends the Rev. Mair of Nusdorf, -chaplain at Vienna, to some third person; and says also that -something, which had to be proved, has been proved. The rest of the -passages on the same leaf are undoubtedly in Leonardo's hand. (Nos. -483, 661, 519, 578, 392, 582, 887 and 894.)] - -1547. - -Johannes Antonius di Johannes Ambrosius de Bolate. He who lets time -pass and does not grow in virtue, the more I think of it the more I -grieve. No man has it in him to be virtuous who will give up honour -for gain. Good fortune is valueless to him who knows not toil. The -man becomes happy who follows Christ. There is no perfect gift -without great suffering. Our glories and our triumphs pass away. -Foul lust, and dreams, and luxury, and sloth have banished every -virtue from the world; so that our Nature, wandering and perplexed, -has almost lost the old and better track. Henceforth it were well to -rouse thyself from sleep. The master said that lying in down will -not bring thee to Fame; nor staying beneath the quilts. He who, -without Fame, burns his life to waste, leaves no more vestige of -himself on earth than wind-blown smoke, or the foam upon the sea. -[Footnote: From the last sentence we may infer that this text is by -the hand of a pupil of Leonardo's.-- On the same sheet are the notes -Nos.1175 and 715 in Leonardo's own handwriting.] - -1548. - -On the morning of Santo Zanobio the -29th of May 1504, I had from Lionardo Vinci -15 gold ducats and began to spend them. -to Mona Margarita S 62 d 4 -to remake the ring S 19 d 8 -clothes S 13 -good beef S 4 -eggs S 6 -debt at the bank S 7 -velvet S 12 -wine S 6 d 4 -meat S 4 -mulberries S 2 d 4 -mushrooms S 3 d 4 -salad S 1 -fruit S 1 d 4 -candles S 3 -... S 1 -flour S 2 - - Sunday 198 8 - -bread S 6 -wine S 9 d 4 -meat S 7 -soup S 2 -fruit S 3 d 4 -candles S 3 d - -Monday 31 - -bread S 6 d 4 -meat S 10 d 8 -wine S 9 d 4 -fruit S 4 -soup S 1 d 8 - - 32 - -1549. - -Tuesday - -bread S 6 -meat S 11 -wine S 7 -fruit S 9 -soup S 2 -salad S 1 - -[Footnote 1548 and 1549: On the same sheet is the text No. 1015 in Leonardo's own handwriting.] - -1550. - -To Monna Margarita S 5 -to Tomaso S 14 -to Monna Margarita d 5 S 2 -on the day of San Zanobi -left ... after -payment d 13 S 2 d 4 -of Monna Margarita - - altogether d 14 S 5 d 4 - -1551. - -On Monday, the l3th of February, I lent lire S 7 to Lionardo to -spend, Friday d 7. - -[Footnote: This note is followed by an account very like the one -given as No. 1549.] - -1552. - -Stephano Chigi, Canonico ..., servant of the honorable Count Grimani -at S. Apostoli. - -[Footnote: Compare No. 674, 21-23.] - -1553. - -Having become anxious ... Bernardo di Simone, Silvestro di Stefano, -Bernardo di Jacopo, Francesco di Matteo Bonciani, Antonio di -Giovanni Ruberti, Antonio da Pistoia.... Antonio; He who has time -and waits for time, will lose his friends and his money. - -1554. - -Reverend Maestro, Domino Giovanni, I spoke to Maestro Zacaria as a -brother about this business, and I made him satisfied with the -arrangement that I had wished; that is, as regards the commission -that I had from the parties and I say that between us there is no -need to pay money down, as regard the pictures of the ... - -1555. - -Of things seen through a mist that which is nearest its farthest -limit will be least visible, and all the more so as they are more -remote. - -1556. - -Theodoricus Rex Semper Augustus. - -1557. - -Either you say Hesperia alone, and it will mean Italy, or you add -ultima, and it will mean Spain. Umbria, part of Tuscany. - -[Footnote: The notes in Greek, Nos. 1557, 1558 and 1562 stand in -close connection with each other, but the meaning of some words is -very doubtful, and a translation is thus rendered impossible.] - -1558. - -[Footnote: Greek Characters] - -1559. - -Canonica of ... on the 5th of July 1507; my dearly beloved mother, -sisters and cousin I herewith inform you that thanks to God I am ... -about the sword which I ... bring it to Maso at the piazza ... and I -will settle the business of Piero so that ... - -[Footnote: AMORETTI, _Mem. Stor. XXIV_, quotes the first three lines -of this letter as by Leonardo. The character of the writing however -does not favour this hypothesis, and still less the contents. I -should regard it rather a rough draft of a letter by young Melzi. I -have not succeeded in deciphering completely the 13 lines of this -text. Amoretti reads at the beginning _Canonica di Vaprio_, but -_Vaprio_ seems to me a very doubtful reading.] - -1560. - - Ut bene respondet Naturae ars docta! dedisset - Vincius, ut tribuit cetera - sic animam - - Noluit ut similis magis haec foret: altera sic est: - Possidet illius Maurus amans animam. - -[Footnote: These three epigrams on the portrait of Lucrezia -Crivelli, a picture by Leonardo which must have been lost at a very -early date, seem to have been dedicated to Leonardo by the poet. -Leonardo used the reverse of the sheet for notes on geometry.] - -Hujus quam cernis nomen Lucretia, Divi Omnia cui larga contribuere -manu. Rara huic forma data est; pinxit Leonardos, amavit Maurus, -pictorum primus hic, ille ducum. - -Naturam, ac superas hac laesit imagine Divas Pictor: tantum hominis -posse manum haec doluit, Illae longa dari tam magnae tempera formae, -Quae spatio fuerat deperitura brevi. - -1561. - -Egidius Romanus on the formation of the human body in the mother's -womb [Footnote 1: _Liber magistri Egidii de pulsibus matrice -conipositus (cum commentario Gentilis de Fulgineo)_ published in -1484 at Padova, in 1494 and in 1514 at Venice, and in 1505 at -Lyons.]. - -[Footnote 2:2. This text appears to be in a handwriting different -from that in the note, l. 1. Here the reading is not so simple as -AMORETTI gave it, _Mem. Star. XXV: A Monsieur Lyonard Peintre du Roy -pour Amboyse_. He says too that this address is of the year 1509, -and Mr. Ravaisson remarks: "_De cette suscription il semble qu'on -peut inferer que Leonard etait alors en France, a la cour de Louis -XII ... Pour conclure je crois qu'il n'est pas prouve que Leonard de -Vinci n'ait pas fait un voyage de quelques mois en France sous Louis -XII, entre le printemps de 1509 et l'automne de_ 1510."--I must -confess that I myself have not succeeded in deciphering completely -this French writing of which two words remain to me doubtful. But so -much seems to be quite evident that this is not an address of a -letter at all, but a certificate or note. _Amboise_[l. 6] I believe -to be the signature of Charles d'Amboise the Governor of Milan. If -this explanation is the right one, it can be easily explained by the -contents of Nos. 1350 and 1529. The note, line 1, was perhaps added -later by another hand; and Leonardo himself wrote afterwards on the -same sheet some geometrical explanations. I must also point out that -the statement that this sheet belongs to the year 1509 has -absolutely no foundation in fact. There is no clue whatever for -giving a precise date to this note.] To Monsieur le Vinci,--the -horses of the king's equerry.... Continue the payment to Ms. -Lyonard, Painter to the King. - -[6] Amboise. - -1562. - -[Footnote: Greek Characters] - -1563. - -Memorandum to Maestro Lionardo to have ... the state of Florence. - -1564. - -To remind your Excellency that Ridolfo Manini brought to Florence a -quantity of crystal besides other stones such as are ... - -1565. - -XVI C. 6 de Ciuitate Dei, se Antipodes. - -[Footnote: A facsimile of this note, which refers to a well known -book by St. Augustin, is given on page 254.] - -1566. - -Leonardo's Will. - -Be it known to all persons, present and to come that at the court of -our Lord the King at Amboise before ourselves in person, Messer -Leonardo da Vinci painter to the King, at present staying at the -place known as Cloux near Amboise, duly considering the certainty of -death and the uncertainty of its time, has acknowledged and declared -in the said court and before us that he has made, according to the -tenor of these presents, his testament and the declaration of his -last will, as follows. And first he commends his soul to our Lord, -Almighty God, and to the Glorious Virgin Mary, and to our lord Saint -Michael, to all the blessed Angels and Saints male and female in -Paradise. - -Item. The said Testator desires to be buried within the church of -Saint Florentin at Amboise, and that his body shall be borne thither -by the chaplains of the church. - -Item. That his body may be followed from the said place to the said -church of Saint Florentin by the _collegium_ of the said church, -that is to say by the rector and the prior, or by their vicars and -chaplains of the church of Saint Denis of Amboise, also the lesser -friars of the place, and before his body shall be carried to the -said church this Testator desires, that in the said church of Saint -Florentin three grand masses shall be celebrated by the deacon and -sub-deacon and that on the day when these three high masses are -celebrated, thirty low masses shall also be performed at Saint -Gregoire. - -Item. That in the said church of Saint Denis similar services shall -be performed, as above. - -Item. That the same shall be done in the church of the said friars -and lesser brethren. - -Item. The aforesaid Testator gives and bequeaths to Messer Francesco -da Melzo, nobleman, of Milan, in remuneration for services and -favours done to him in the past, each - -[Footnote: See page 420.] - -and all of the books the Testator is at present possessed of, and -the instruments and portraits appertaining to his art and calling as -a painter. - -Item. The same Testator gives and bequeaths henceforth for ever to -Battista de Vilanis his servant one half, that is the moity, of his -garden which is outside the walls of Milan, and the other half of -the same garden to Salai his servant; in which garden aforesaid -Salai has built and constructed a house which shall be and remain -henceforth in all perpetuity the property of the said Salai, his -heirs and successors; and this is in remuneration for the good and -kind services which the said de Vilanis and Salai, his servants have -done him in past times until now. - -Item. The said Testator gives to Maturina his waiting woman a cloak -of good black cloth lined with fur, a ... of cloth and two ducats -paid once only; and this likewise is in remuneration for good -service rendered to him in past times by the said Maturina. - -Item. He desires that at his funeral sixty tapers shall be carried -which shall be borne by sixty poor men, to whom shall be given money -for carrying them; at the discretion of the said Melzo, and these -tapers shall be distributed among the four above mentioned churches. - -Item. The said Testator gives to each of the said churches ten lbs. -of wax in thick tapers, which shall be placed in the said churches -to be used on the day when those said services are celebrated. - -Item. That alms shall be given to the poor of the Hotel-Dieu, to the -poor of Saint Lazare d'Amboise and, to that end, there shall be -given and paid to the treasurers of that same fraternity the sum and -amount of seventy soldi of Tours. - -Item. The said Testator gives and bequeaths to the said Messer -Francesco Melzo, being present and agreeing, the remainder of his -pension and the sums of money which are owing to him from the past -time till the day of his death by the receiver or treasurer-general -M. Johan Sapin, and each and every sum of money that he has already -received from the aforesaid Sapin of his said pension, and in case -he should die before the said Melzo and not otherwise; which moneys -are at present in the possession of the said Testator in the said -place called Cloux, as he says. And he likewise gives and bequeaths -to the said Melzo all and each of his clothes which he at present -possesses at the said place of Cloux, and all in remuneration for -the good and kind services done by him in past times till now, as -well as in payment for the trouble and annoyance he may incur with -regard to the execution of this present testament, which however, -shall all be at the expense of the said Testator. - -And he orders and desires that the sum of four hundred scudi del -Sole, which he has deposited in the hands of the treasurer of Santa -Maria Nuova in the city of Florence, may be given to his brothers -now living in Florence with all the interest and usufruct that may -have accrued up to the present time, and be due from the aforesaid -treasurer to the aforesaid Testator on account of the said four -hundred crowns, since they were given and consigned by the Testator -to the said treasurers. - -Item. He desires and orders that the said Messer Francesco de Melzo -shall be and remain the sole and only executor of the said will of -the said Testator; and that the said testament shall be executed in -its full and complete meaning and according to that which is here -narrated and said, to have, hold, keep and observe, the said Messer -Leonardo da Vinci, constituted Testator, has obliged and obliges by -these presents the said his heirs and successors with all his goods -moveable and immoveable present and to come, and has renounced and -expressly renounces by these presents all and each of the things -which to that are contrary. Given at the said place of Cloux in the -presence of Magister Spirito Fieri vicar, of the church of Saint -Denis at Amboise, of M. Guglielmo Croysant priest and chaplain, of -Magister Cipriane Fulchin, Brother Francesco de Corion, and of -Francesco da Milano, a brother of the Convent of the Minorites at -Amboise, witnesses summoned and required to that end by the -indictment of the said court in the presence of the aforesaid M. -Francesco de Melze who accepting and agreeing to the same has -promised by his faith and his oath which he has administered to us -personally and has sworn to us never to do nor say nor act in any -way to the contrary. And it is sealed by his request with the royal -seal apposed to legal contracts at Amboise, and in token of good -faith. - -Given on the XXIIIrd day of April MDXVIII, before Easter. - -And on the XXIIIrd day of this month of April MDXVIII, in the -presence of M. Guglielmo Borian, Royal notary in the court of the -bailiwick of Amboise, the aforesaid M. Leonardo de Vinci gave and -bequeathed, by his last will and testament, as aforesaid, to the -said M. Baptista de Vilanis, being present and agreeing, the right -of water which the King Louis XII, of pious memory lately deceased -gave to this same de Vinci, the stream of the canal of Santo -Cristoforo in the duchy of Milan, to belong to the said Vilanis for -ever in such wise and manner that the said gentleman made him this -gift in the presence of M. Francesco da Melzo, gentleman, of Milan -and in mine. - -And on the aforesaid day in the said month of April in the said year -MDXVIII the same M. Leonardo de Vinci by his last will and testament -gave to the aforesaid M. Baptista de Vilanis, being present and -agreeing, each and all of the articles of furniture and utensils of -his house at present at the said place of Cloux, in the event of the -said de Vilanis surviving the aforesaid M. Leonardo de Vinci, in the -presence of the said M. Francesco Melzo and of me Notary &c. 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Do not change or edit the -header without written permission. - -Please read the "legal small print," and other information about the -eBook and Project Gutenberg at the bottom of this file. Included is -important information about your specific rights and restrictions in -how the file may be used. You can also find out about how to make a -donation to Project Gutenberg, and how to get involved. - - -**Welcome To The World of Free Plain Vanilla Electronic Texts** - -**eBooks Readable By Both Humans and By Computers, Since 1971** - -*****These eBooks Were Prepared By Thousands of Volunteers!***** - - -Title: The Notebooks of Leonardo Da Vinci, Complete - -Author: Leonardo Da Vinci - -Release Date: Jan, 2004 [EBook #5000] -[Yes, we are more than one year ahead of schedule] -[Most recently updated June 26, 2002] - -Edition: 10 - -Language: English - -Character set encoding: ASCII - -*** START OF THE PROJECT GUTENBERG EBOOK, THE NOTEBOOKS OF LEONARDO DA - VINCI, COMPLETE *** - - - - -This eBook was produced by Charles Aldarondo and the Distributed -Proofreaders team. - - - -The Notebooks of Leonardo Da Vinci - -Volume 1 - -Translated by Jean Paul Richter - -1888 - - - - - - -PREFACE. - - - - - -A singular fatality has ruled the destiny of nearly all the most -famous of Leonardo da Vinci's works. Two of the three most important -were never completed, obstacles having arisen during his life-time, -which obliged him to leave them unfinished; namely the Sforza -Monument and the Wall-painting of the Battle of Anghiari, while the -third--the picture of the Last Supper at Milan--has suffered -irremediable injury from decay and the repeated restorations to -which it was recklessly subjected during the XVIIth and XVIIIth -centuries. Nevertheless, no other picture of the Renaissance has -become so wellknown and popular through copies of every description. - -Vasari says, and rightly, in his Life of Leonardo, "that he laboured -much more by his word than in fact or by deed", and the biographer -evidently had in his mind the numerous works in Manuscript which -have been preserved to this day. To us, now, it seems almost -inexplicable that these valuable and interesting original texts -should have remained so long unpublished, and indeed forgotten. It -is certain that during the XVIth and XVIIth centuries their -exceptional value was highly appreciated. This is proved not merely -by the prices which they commanded, but also by the exceptional -interest which has been attached to the change of ownership of -merely a few pages of Manuscript. - -That, notwithstanding this eagerness to possess the Manuscripts, -their contents remained a mystery, can only be accounted for by the -many and great difficulties attending the task of deciphering them. -The handwriting is so peculiar that it requires considerable -practice to read even a few detached phrases, much more to solve -with any certainty the numerous difficulties of alternative -readings, and to master the sense as a connected whole. Vasari -observes with reference to Leonardos writing: "he wrote backwards, -in rude characters, and with the left hand, so that any one who is -not practised in reading them, cannot understand them". The aid of a -mirror in reading reversed handwriting appears to me available only -for a first experimental reading. Speaking from my own experience, -the persistent use of it is too fatiguing and inconvenient to be -practically advisable, considering the enormous mass of Manuscripts -to be deciphered. And as, after all, Leonardo's handwriting runs -backwards just as all Oriental character runs backwards--that is -to say from right to left--the difficulty of reading direct from the -writing is not insuperable. This obvious peculiarity in the writing -is not, however, by any means the only obstacle in the way of -mastering the text. Leonardo made use of an orthography peculiar to -himself; he had a fashion of amalgamating several short words into -one long one, or, again, he would quite arbitrarily divide a long -word into two separate halves; added to this there is no punctuation -whatever to regulate the division and construction of the sentences, -nor are there any accents--and the reader may imagine that such -difficulties were almost sufficient to make the task seem a -desperate one to a beginner. It is therefore not surprising that the -good intentions of some of Leonardo s most reverent admirers should -have failed. - -Leonardos literary labours in various departments both of Art and of -Science were those essentially of an enquirer, hence the analytical -method is that which he employs in arguing out his investigations -and dissertations. The vast structure of his scientific theories is -consequently built up of numerous separate researches, and it is -much to be lamented that he should never have collated and arranged -them. His love for detailed research--as it seems to me--was the -reason that in almost all the Manuscripts, the different paragraphs -appear to us to be in utter confusion; on one and the same page, -observations on the most dissimilar subjects follow each other -without any connection. A page, for instance, will begin with some -principles of astronomy, or the motion of the earth; then come the -laws of sound, and finally some precepts as to colour. Another page -will begin with his investigations on the structure of the -intestines, and end with philosophical remarks as to the relations -of poetry to painting; and so forth. - -Leonardo himself lamented this confusion, and for that reason I do -not think that the publication of the texts in the order in which -they occur in the originals would at all fulfil his intentions. No -reader could find his way through such a labyrinth; Leonardo himself -could not have done it. - -Added to this, more than half of the five thousand manuscript pages -which now remain to us, are written on loose leaves, and at present -arranged in a manner which has no justification beyond the fancy of -the collector who first brought them together to make volumes of -more or less extent. Nay, even in the volumes, the pages of which -were numbered by Leonardo himself, their order, so far as the -connection of the texts was concerned, was obviously a matter of -indifference to him. The only point he seems to have kept in view, -when first writing down his notes, was that each observation should -be complete to the end on the page on which it was begun. The -exceptions to this rule are extremely few, and it is certainly -noteworthy that we find in such cases, in bound volumes with his -numbered pages, the written observations: "turn over", "This is the -continuation of the previous page", and the like. Is not this -sufficient to prove that it was only in quite exceptional cases that -the writer intended the consecutive pages to remain connected, when -he should, at last, carry out the often planned arrangement of his -writings? - -What this final arrangement was to be, Leonardo has in most cases -indicated with considerable completeness. In other cases this -authoritative clue is wanting, but the difficulties arising from -this are not insuperable; for, as the subject of the separate -paragraphs is always distinct and well defined in itself, it is -quite possible to construct a well-planned whole, out of the -scattered materials of his scientific system, and I may venture to -state that I have devoted especial care and thought to the due -execution of this responsible task. - -The beginning of Leonardo's literary labours dates from about his -thirty-seventh year, and he seems to have carried them on without -any serious interruption till his death. Thus the Manuscripts that -remain represent a period of about thirty years. Within this space -of time his handwriting altered so little that it is impossible to -judge from it of the date of any particular text. The exact dates, -indeed, can only be assigned to certain note-books in which the year -is incidentally indicated, and in which the order of the leaves has -not been altered since Leonardo used them. The assistance these -afford for a chronological arrangement of the Manuscripts is -generally self evident. By this clue I have assigned to the original -Manuscripts now scattered through England, Italy and France, the -order of their production, as in many matters of detail it is highly -important to be able to verify the time and place at which certain -observations were made and registered. For this purpose the -Bibliography of the Manuscripts given at the end of Vol. II, may be -regarded as an Index, not far short of complete, of all Leonardo s -literary works now extant. The consecutive numbers (from 1 to 1566) -at the head of each passage in this work, indicate their logical -sequence with reference to the subjects; while the letters and -figures to the left of each paragraph refer to the original -Manuscript and number of the page, on which that particular passage -is to be found. Thus the reader, by referring to the List of -Manuscripts at the beginning of Volume I, and to the Bibliography at -the end of Volume II, can, in every instance, easily ascertain, not -merely the period to which the passage belongs, but also exactly -where it stood in the original document. Thus, too, by following the -sequence of the numbers in the Bibliographical index, the reader may -reconstruct the original order of the Manuscripts and recompose the -various texts to be found on the original sheets--so much of it, -that is to say, as by its subject-matter came within the scope of -this work. It may, however, be here observed that Leonardo s -Manuscripts contain, besides the passages here printed, a great -number of notes and dissertations on Mechanics, Physics, and some -other subjects, many of which could only be satisfactorily dealt -with by specialists. I have given as complete a review of these -writings as seemed necessary in the Bibliographical notes. - -In 1651, Raphael Trichet Dufresne, of Paris, published a selection -from Leonardo's writings on painting, and this treatise became so -popular that it has since been reprinted about two-and-twenty times, -and in six different languages. But none of these editions were -derived from the original texts, which were supposed to have been -lost, but from early copies, in which Leonardo's text had been more -or less mutilated, and which were all fragmentary. The oldest and on -the whole the best copy of Leonardo's essays and precepts on -Painting is in the Vatican Library; this has been twice printed, -first by Manzi, in 1817, and secondly by Ludwig, in 1882. Still, -this ancient copy, and the published editions of it, contain much -for which it would be rash to hold Leonardo responsible, and some -portions--such as the very important rules for the proportions of -the human figure--are wholly wanting; on the other hand they contain -passages which, if they are genuine, cannot now be verified from any -original Manuscript extant. These copies, at any rate neither give -us the original order of the texts, as written by Leonardo, nor do -they afford any substitute, by connecting them on a rational scheme; -indeed, in their chaotic confusion they are anything rather than -satisfactory reading. The fault, no doubt, rests with the compiler -of the Vatican copy, which would seem to be the source whence all -the published and extensively known texts were derived; for, instead -of arranging the passages himself, he was satisfied with recording a -suggestion for a final arrangement of them into eight distinct -parts, without attempting to carry out his scheme. Under the -mistaken idea that this plan of distribution might be that, not of -the compiler, but of Leonardo himself, the various editors, down to -the present day, have very injudiciously continued to adopt this -order--or rather disorder. - -I, like other enquirers, had given up the original Manuscript of the -Trattato della Pittura for lost, till, in the beginning of 1880, I -was enabled, by the liberality of Lord Ashburnham, to inspect his -Manuscripts, and was so happy as to discover among them the original -text of the best-known portion of the Trattato in his magnificent -library at Ashburnham Place. Though this discovery was of a fragment -only--but a considerable fragment--inciting me to further search, -it gave the key to the mystery which had so long enveloped the first -origin of all the known copies of the Trattato. The extensive -researches I was subsequently enabled to prosecute, and the results -of which are combined in this work, were only rendered possible by -the unrestricted permission granted me to investigate all the -Manuscripts by Leonardo dispersed throughout Europe, and to -reproduce the highly important original sketches they contain, by -the process of "photogravure". Her Majesty the Queen graciously -accorded me special permission to copy for publication the -Manuscripts at the Royal Library at Windsor. The Commission Centrale -Administrative de l'Institut de France, Paris, gave me, in the most -liberal manner, in answer to an application from Sir Frederic -Leighton, P. R. A., Corresponding member of the Institut, free -permission to work for several months in their private collection at -deciphering the Manuscripts preserved there. The same favour which -Lord Ashburnham had already granted me was extended to me by the -Earl of Leicester, the Marchese Trivulsi, and the Curators of the -Ambrosian Library at Milan, by the Conte Manzoni at Rome and by -other private owners of Manuscripts of Leonardo's; as also by the -Directors of the Louvre at Paris; the Accademia at Venice; the -Uffizi at Florence; the Royal Library at Turin; and the British -Museum, and the South Kensington Museum. I am also greatly indebted -to the Librarians of these various collections for much assistance -in my labours; and more particularly to Monsieur Louis Lalanne, of -the Institut de France, the Abbate Ceriani, of the Ambrosian -Library, Mr. Maude Thompson, Keeper of Manuscripts at the British -Museum, Mr. Holmes, the Queens Librarian at Windsor, the Revd Vere -Bayne, Librarian of Christ Church College at Oxford, and the Revd A. -Napier, Librarian to the Earl of Leicester at Holkham Hall. - -In correcting the Italian text for the press, I have had the -advantage of valuable advice from the Commendatore Giov. Morelli, -Senatore del Regno, and from Signor Gustavo Frizzoni, of Milan. The -translation, under many difficulties, of the Italian text into -English, is mainly due to Mrs. R. C. Bell; while the rendering of -several of the most puzzling and important passages, particularly in -the second half of Vol. I, I owe to the indefatigable interest taken -in this work by Mr. E. J. Poynter R. A. Finally I must express my -thanks to Mr. Alfred Marks, of Long Ditton, who has most kindly -assisted me throughout in the revision of the proof sheets. - -The notes and dissertations on the texts on Architecture in Vol. II -I owe to my friend Baron Henri de Geymuller, of Paris. - -I may further mention with regard to the illustrations, that the -negatives for the production of the "photo-gravures" by Monsieur -Dujardin of Paris were all taken direct from the originals. - -It is scarcely necessary to add that most of the drawings here -reproduced in facsimile have never been published before. As I am -now, on the termination of a work of several years' duration, in a -position to review the general tenour of Leonardos writings, I may -perhaps be permitted to add a word as to my own estimate of the -value of their contents. I have already shown that it is due to -nothing but a fortuitous succession of unfortunate circumstances, -that we should not, long since, have known Leonardo, not merely as a -Painter, but as an Author, a Philosopher, and a Naturalist. There -can be no doubt that in more than one department his principles and -discoveries were infinitely more in accord with the teachings of -modern science, than with the views of his contemporaries. For this -reason his extraordinary gifts and merits are far more likely to be -appreciated in our own time than they could have been during the -preceding centuries. He has been unjustly accused of having -squandered his powers, by beginning a variety of studies and then, -having hardly begun, throwing them aside. The truth is that the -labours of three centuries have hardly sufficed for the elucidation -of some of the problems which occupied his mighty mind. - -Alexander von Humboldt has borne witness that "he was the first to -start on the road towards the point where all the impressions of our -senses converge in the idea of the Unity of Nature" Nay, yet more -may be said. The very words which are inscribed on the monument of -Alexander von Humboldt himself, at Berlin, are perhaps the most -appropriate in which we can sum up our estimate of Leonardo's -genius: - -"Majestati naturae par ingenium." - -LONDON, April 1883. - -F. P. R. - - - - - - - -CONTENTS OF VOLUME I. - - - - - -PROLEGOMENA AND GENERAL INTRODUCTION TO THE BOOK ON PAINTING - -Clavis Sigillorum and Index of Manuscripts.--The author's intention -to publish his MSS. (1).--The preparation of the MSS. for -publication (2).--Admonition to readers (3).--The disorder in the -MSS. (4).--Suggestions for the arrangement of MSS. treating of -particular subjects (5--8).--General introductions to the book on -painting (9--13).--The plan of the book on painting (14--17).--The -use of the book on painting (18).--Necessity of theoretical -knowledge (19, 20).--The function of the eye (21--23).--Variability -of the eye (24).--Focus of sight (25).--Differences of perception by -one eye and by both eyes (26--29).--The comparative size of the -image depends on the amount of light (30--39). - -II. - -LINEAR PERSPECTIVE - -General remarks on perspective (40--41).--The elements of -perspective:--of the point (42--46).--Of the line (47--48).--The -nature of the outline (49).--Definition of perspective (50).--The -perception of the object depends on the direction of the eye -(51).--Experimental proof of the existence of the pyramid of sight -(52--55).--The relations of the distance point to the vanishing -point (55--56).--How to measure the pyramid of vision (57).--The -production of the pyramid of vision (58--64).--Proof by experiment -(65--66).--General conclusions (67).--That the contrary is -impossible (68).--A parallel case (69).--The function of the eye, as -explained by the camera obscura (70--71).--The practice of -perspective (72--73).--Refraction of the rays falling upon the eye -(74--75).--The inversion of the images (76).--The intersection of -the rays (77--82).--Demonstration of perspective by means of a -vertical glass plane (83--85.)--The angle of sight varies with the -distance (86--88).--Opposite pyramids in juxtaposition (89).--On -simple and complex perspective (90).--The proper distance of objects -from the eye (91--92).--The relative size of objects with regard to -their distance from the eye (93--98).--The apparent size of objects -denned by calculation (99--106).--On natural perspective (107--109). - -III. - -SIX BOOKS ON LIGHT AND SHADE - -GENERAL INTRODUCTION.--Prolegomena (110).--Scheme of the books on -light and shade (111).--Different principles and plans of treatment -(112--116).--Different sorts of light (117--118).--Definition of -the nature of shadows (119--122).--Of the various kinds of shadows -(123--125).--Of the various kinds of light (126--127).--General -remarks (128--129).--FIRST BOOK ON LIGHT AND SHADE.--On the nature -of light (130--131).--The difference between light and lustre -(132--135).--The relations of luminous to illuminated bodies (136). ---Experiments on the relation of light and shadow within a room -(137--140).--Light and shadow with regard to the position of the -eye (141--145).--The law of the incidence of light -(146--147).--SECOND BOOK ON LIGHT AND SHADE.--Gradations of strength -in the shadows (148--149).--On the intensity of shadows as dependent -on the distance from the light (150--152).--On the proportion of -light and shadow (153--157).--THIRD BOOK ON LIGHT AND -SHADE.--Definition of derived shadow (158--159).--Different sorts of -derived shadows (160--162).--On the relation of derived and primary -shadow (163--165).--On the shape of derived shadows (166--174).--On -the relative intensity of derived shadows (175--179).--Shadow as -produced by two lights of different size (180--181).--The effect of -light at different distances (182).--Further complications in the -derived shadows (183--187).--FOURTH BOOK ON LIGHT AND SHADE.--On the -shape of cast shadows (188--191).--On the outlines of cast shadows -(192--195).--On the relative size of cast shadows (196. -197).--Effects on cast shadows by the tone of the back ground -(198).--A disputed proposition (199).--On the relative depth of -cast shadows (200--202).--FIFTH BOOK ON LIGHT AND -SHADE.--Principles of reflection (203. 204).--On reverberation -(205).--Reflection on water (206. 207).--Experiments with the mirror -(208--210).--Appendix:--On shadows in movement (211--212).--SIXTH -BOOK ON LIGHT AND SHADE.--The effect of rays passing through holes -(213. 214).--On gradation of shadows (215. 216).--On relative -proportion of light and shadows (216--221). - -IV. - -PERSPECTIVE OF DISAPPEARANCE - -Definition (222. 223).--An illustration by experiment (224).--A -guiding rule (225).---An experiment (226).--On indistinctness at -short distances (227--231).--On indistinctness at great distances -(232--234).--The importance of light and shade in the Prospettiva -de' perdimenti (235--239).--The effect of light or dark backgrounds -on the apparent size of objects (240--250).--Propositions on -Prospettiva de' perdimenti from MS. C. (250--262). - -V. - -THEORY OF COLOURS - -The reciprocal effects of colours on objects placed opposite each -other (263--271).--Combination of different colours in cast shadows -(272).--The effect of colours in the camera obscura (273. 274).--On -the colours of derived shadows (275. 276).--On the nature of colours -(277. 278).--On gradations in the depth of colours (279. 280).--On -the reflection of colours (281--283).--On the use of dark and light -colours in painting (284--286).--On the colours of the rainbow -(287--288). - -VI. - -PERSPECTIVE OF COLOUR AND AERIAL PERSPECTIVE - -General rules (289--291).--An exceptional case (292).--An experiment -(293).--The practice of the Prospettiva de' colori (294).--The rules -of aerial perspective (295--297).--On the relative density of the -atmosphere (298--299).--On the colour of the atmosphere (300--307). - -VII. - -ON THE PROPORTIONS AND ON THE MOVEMENTS OF THE HUMAN FIGURE - -Preliminary observations (308. 309).--Proportions of the head and -face (310--318).--Proportions of the head seen in front -(319--321).--Proportions of the foot (322--323).--Relative -proportions of the hand and foot (324).--Relative proportions of -the foot and of the face (325--327).--Proportions of the leg -(328--331).--On the central point of the whole body (332).--The -relative proportions of the torso and of the whole figure -(333).--The relative proportions of the head and of the torso -(334).--The relative proportions of the torso and of the leg (335. -336).--The relative proportions of the torso and of the foot -(337).--The proportions of the whole figure (338--341).--The torso -from the front and back (342).--Vitruvius' scheme of proportions -(343).--The arm and head (344).--Proportions of the arm -(345--349).--The movement of the arm (350--354).--The movement of -the torso (355--361).--The proportions vary at different ages -(362--367).--The movement of the human figure (368--375).--Of -walking up and down (375--379).--On the human body in action -(380--388).--On hair falling down in curls (389).--On draperies - -(390--392). - -VIII. - -BOTANY FOR PAINTERS, AND ELEMENTS OF LANDSCAPE PAINTING - -Classification of trees (393).--The relative thickness of the -branches to the trunk (394--396).--The law of proportion in the -growth of the branches (397--402).--The direction of growth -(403--407).--The forms of trees (408--411).--The insertion of the -leaves (412--419).--Light on branches and leaves (420--422).--The -proportions of light and shade in a leaf (423--426).--Of the -transparency of leaves (427--429).--The gradations of shade and -colour in leaves (430--434).--A classification of trees according to -their colours (435).--The proportions of light and shade in trees -(436--440).--The distribution of light and shade with reference to -the position of the spectator (441--443).--The effects of morning -light (444--448).--The effects of midday light (449).--The -appearance of trees in the distance (450--451).--The cast shadow of -trees (452. 453).--Light and shade on groups of trees -(454--457).--On the treatment of light for landscapes -(458--464).--On the treatment of light for views of towns -(465--469).--The effect of wind on trees (470--473).--Light and -shade on clouds (474--477).--On images reflected in water (478).--Of -rainbows and rain (479. 480).--Of flower seeds (481). - -IX. - -THE PRACTICE OF PAINTING - -I. MORAL PRECEPTS FOR THE STUDENT OF PAINTING.--How to ascertain the -dispositions for an artistic career (482).--The course of -instruction for an artist (483--485).--The study of the antique -(486. 487).--The necessity of anatomical knowledge (488. 489).--How -to acquire practice (490).--Industry and thoroughness the first -conditions (491--493.)--The artist's private life and choice of -company (493. 494).--The distribution of time for studying (495-- -497).--On the productive power of minor artists (498--501).--A -caution against one-sided study (502).--How to acquire universality -(503--506).--Useful games and exercises (507. 508).--II. THE -ARTIST'S STUDIO.--INSTRUMENTS AND HELPS FOR THE APPLICATION OF -PERSPECTIVE.--ON JUDGING OF A PICTURE.--On the size of the studio -(509).--On the construction of windows (510--512).--On the best -light for painting (513--520).--On various helps in preparing a -picture (521--530).--On the management of works (531. 532).--On the -limitations of painting (533--535).--On the choice of a position -(536. 537).--The apparent size of figures in a picture (538. -539).--The right position of the artist, when painting and of the -spectator (540--547).--III. THE PRACTICAL METHODS OF LIGHT AND SHADE -AND AERIAL PERSPECTIVE.--Gradations of light and shade (548).--On -the choice of light for a picture (549--554).--The distribution of -light and shade (555--559).--The juxtaposition of light and shade -(560. 561).--On the lighting of the background (562--565).--On the -lighting of white objects (566).--The methods of aerial perspective -(567--570).--IV. OF PORTRAIT AND FIGURE PAINTING.--Of sketching -figures and portraits (571. 572).--The position of the head -(573).--Of the light on the face (574--576).--General suggestions -for historical pictures (577--581).--How to represent the -differences of age and sex (582. 583).--Of representing the emotions -(584).--Of representing imaginary animals (585).--The selection of -forms (586--591).--How to pose figures (592).--Of appropriate -gestures (593--600).--V. SUGGESTIONS FOR COMPOSITIONS.--Of painting -battle-pieces (601--603).--Of depicting night-scenes (604).--Of -depicting a tempest (605. 606).--Of representing the deluge -(607--609).--Of depicting natural phenomena (610. 611).--VI. THE -ARTIST'S MATERIALS.--Of chalk and paper (612--617).--On the -preparation and use of colours (618--627).--Of preparing the panel -(628).--The preparation of oils (629--634).--On varnishes (635-- -637).--On chemical _materials (638--650).--VII. PHILOSOPHY AND -HISTORY OF THE ART OF PAINTING.--The relation of art and nature -(651. 652).--Painting is superior to poetry (653. 654).--Painting is -superior to sculpture (655. 656).--Aphorisms (657--659).--On the -history of painting (660. 661).--The painter's scope (662). - -X. - -STUDIES AND SKETCHES FOR PICTURES AND DECORATIONS - -On pictures of the Madonna (663).--Bernardo di Bandino's portrait -(664).--Notes on the Last Supper (665--668).--On the battle of -Anghiari (669).--Allegorical representations referring to the duke -of Milan (670--673).--Allegorical representations -(674--678).--Arrangement of a picture (679).--List of drawings -(680).--Mottoes and Emblems (681--702). - - - - - - -The author's intention to publish his MSS. - -1. - -How by a certain machine many may stay some time under water. And -how and wherefore I do not describe my method of remaining under -water and how long I can remain without eating. And I do not publish -nor divulge these, by reason of the evil nature of men, who would -use them for assassinations at the bottom of the sea by destroying -ships, and sinking them, together with the men in them. Nevertheless -I will impart others, which are not dangerous because the mouth of -the tube through which you breathe is above the water, supported on -air sacks or cork. - -[Footnote: The leaf on which this passage is written, is headed with -the words _Casi_ 39, and most of these cases begin with the word -'_Come_', like the two here given, which are the 26th and 27th. 7. -_Sughero_. In the Codex Antlanticus 377a; 1170a there is a sketch, -drawn with the pen, representing a man with a tube in his mouth, and -at the farther end of the tube a disk. By the tube the word -'_Channa_' is written, and by the disk the word '_sughero_'.] - -The preparation of the MSS. for publication. - -2. - -When you put together the science of the motions of water, remember -to include under each proposition its application and use, in order -that this science may not be useless.-- - -[Footnote: A comparatively small portion of Leonardo's notes on -water-power was published at Bologna in 1828, under the title: "_Del -moto e misura dell'Acqua, di L. da Vinci_".] - -Admonition to readers. - -3. - -Let no man who is not a Mathematician read the elements of my work. - -The disorder in the MSS. - -4. - -Begun at Florence, in the house of Piero di Braccio Martelli, on the -22nd day of March 1508. And this is to be a collection without -order, taken from many papers which I have copied here, hoping to -arrange them later each in its place, according to the subjects of -which they may treat. But I believe that before I am at the end of -this [task] I shall have to repeat the same things several times; -for which, O reader! do not blame me, for the subjects are many and -memory cannot retain them [all] and say: 'I will not write this -because I wrote it before.' And if I wished to avoid falling into -this fault, it would be necessary in every case when I wanted to -copy [a passage] that, not to repeat myself, I should read over all -that had gone before; and all the more since the intervals are long -between one time of writing and the next. - -[Footnote: 1. In the history of Florence in the early part of the -XVIth century _Piero di Braccio Martelli_ is frequently mentioned as -_Commissario della Signoria_. He was famous for his learning and at -his death left four books on Mathematics ready for the press; comp. -LITTA, _Famiglie celebri Italiane_, _Famiglia Martelli di -Firenze_.--In the Official Catalogue of MSS. in the Brit. Mus., New -Series Vol. I., where this passage is printed, _Barto_ has been -wrongly given for Braccio. - -2. _addi 22 di marzo 1508_. The Christian era was computed in -Florence at that time from the Incarnation (Lady day, March 25th). -Hence this should be 1509 by our reckoning. - -3. _racolto tratto di molte carte le quali io ho qui copiate_. We -must suppose that Leonardo means that he has copied out his own MSS. -and not those of others. The first thirteen leaves of the MS. in the -Brit. Mus. are a fair copy of some notes on physics.] - -Suggestions for the arrangement of MSS treating of particular -subjects.(5-8). - -5. - -Of digging a canal. Put this in the Book of useful inventions and in -proving them bring forward the propositions already proved. And this -is the proper order; since if you wished to show the usefulness of -any plan you would be obliged again to devise new machines to prove -its utility and thus would confuse the order of the forty Books and -also the order of the diagrams; that is to say you would have to mix -up practice with theory, which would produce a confused and -incoherent work. - -6. - -I am not to blame for putting forward, in the course of my work on -science, any general rule derived from a previous conclusion. - -7. - -The Book of the science of Mechanics must precede the Book of useful -inventions.--Have your books on anatomy bound! [Footnote: 4. The -numerous notes on anatomy written on loose leaves and now in the -Royal collection at Windsor can best be classified in four Books, -corresponding to the different character and size of the paper. When -Leonardo speaks of '_li tua libri di notomia_', he probably means -the MSS. which still exist; if this hypothesis is correct the -present condition of these leaves might seem to prove that he only -carried out his purpose with one of the Books on anatomy. A borrowed -book on Anatomy is mentioned in F.O.] - -8. - -The order of your book must proceed on this plan: first simple -beams, then (those) supported from below, then suspended in part, -then wholly [suspended]. Then beams as supporting other weights -[Footnote: 4. Leonardo's notes on Mechanics are extraordinarily -numerous; but, for the reasons assigned in my introduction, they -have not been included in the present work.]. - -General introductions to the book on Painting (9-13). - -9. - -INTRODUCTION. - -Seeing that I can find no subject specially useful or -pleasing--since the men who have come before me have taken for their -own every useful or necessary theme--I must do like one who, being -poor, comes last to the fair, and can find no other way of providing -himself than by taking all the things already seen by other buyers, -and not taken but refused by reason of their lesser value. I, then, -will load my humble pack with this despised and rejected -merchandise, the refuse of so many buyers; and will go about to -distribute it, not indeed in great cities, but in the poorer towns, -taking such a price as the wares I offer may be worth. [Footnote: It -need hardly be pointed out that there is in this 'Proemio' a covert -irony. In the second and third prefaces, Leonardo characterises his -rivals and opponents more closely. His protest is directed against -Neo-latinism as professed by most of the humanists of his time; its -futility is now no longer questioned.] - -10. - -INTRODUCTION. - -I know that many will call this useless work [Footnote: 3. questa -essere opera inutile. By opera we must here understand libro di -pittura and particularly the treatise on Perspective.]; and they -will be those of whom Demetrius [Footnote: 4. Demetrio. "With regard -to the passage attributed to Demetrius", Dr. H. MULLER STRUBING -writes, "I know not what to make of it. It is certainly not -Demetrius Phalereus that is meant and it can hardly be Demetrius -Poliorcetes. Who then can it be--for the name is a very common one? -It may be a clerical error for Demades and the maxim is quite in the -spirit of his writings I have not however been able to find any -corresponding passage either in the 'Fragments' (C. MULLER, _Orat. -Att._, II. 441) nor in the Supplements collected by DIETZ (_Rhein. -Mus._, vol. 29, p. 108)." - -The same passage occurs as a simple Memorandum in the MS. Tr. 57, -apparently as a note for this '_Proemio_' thus affording some data -as to the time where these introductions were written.] declared -that he took no more account of the wind that came out their mouth -in words, than of that they expelled from their lower parts: men who -desire nothing but material riches and are absolutely devoid of that -of wisdom, which is the food and the only true riches of the mind. -For so much more worthy as the soul is than the body, so much more -noble are the possessions of the soul than those of the body. And -often, when I see one of these men take this work in his hand, I -wonder that he does not put it to his nose, like a monkey, or ask me -if it is something good to eat. - -[Footnote: In the original, the Proemio di prospettiva cioe -dell'uffitio dell'occhio (see No. 21) stands between this and the -preceding one, No. 9.] - -INTRODUCTION. - -I am fully concious that, not being a literary man, certain -presumptuous persons will think that they may reasonably blame me; -alleging that I am not a man of letters. Foolish folks! do they not -know that I might retort as Marius did to the Roman Patricians -[Footnote 21: _Come Mario disse ai patriti Romani_. "I am unable to -find the words here attributed by Leonardo to Marius, either in -Plutarch's Life of Marius or in the Apophthegmata (_Moralia_, -p.202). Nor do they occur in the writings of Valerius Maximus (who -frequently mentions Marius) nor in Velleius Paterculus (II, 11 to -43), Dio Cassius, Aulus Gellius, or Macrobius. Professor E. -MENDELSON of Dorpat, the editor of Herodian, assures me that no such -passage is the found in that author" (communication from Dr. MULLER -STRUBING). Leonardo evidently meant to allude to some well known -incident in Roman history and the mention of Marius is the result -probably of some confusion. We may perhaps read, for Marius, -Menenius Agrippa, though in that case it is true we must alter -Patriti to Plebei. The change is a serious one. but it would render -the passage perfectly clear.] by saying: That they, who deck -themselves out in the labours of others will not allow me my own. -They will say that I, having no literary skill, cannot properly -express that which I desire to treat of [Footnote 26: _le mie cose -.... che d'altra parola_. This can hardly be reconciled with Mons. -RAVAISSON'S estimate of L. da Vinci's learning. "_Leonard de Vinci -etait un admirateur et un disciple des anciens, aussi bien dans -l'art que dans la science et il tenait a passer pour tel meme aux -yeux de la posterite._" _Gaz. des Beaux arts. Oct. 1877.]; but they -do not know that my subjects are to be dealt with by experience -rather than by words [Footnote 28: See Footnote 26]; and -[experience] has been the mistress of those who wrote well. And so, -as mistress, I will cite her in all cases. - -11. - -Though I may not, like them, be able to quote other authors, I shall -rely on that which is much greater and more worthy:--on experience, -the mistress of their Masters. They go about puffed up and pompous, -dressed and decorated with [the fruits], not of their own labours, -but of those of others. And they will not allow me my own. They will -scorn me as an inventor; but how much more might they--who are not -inventors but vaunters and declaimers of the works of others--be -blamed. - -INTRODUCTION. - -And those men who are inventors and interpreters between Nature and -Man, as compared with boasters and declaimers of the works of -others, must be regarded and not otherwise esteemed than as the -object in front of a mirror, when compared with its image seen in -the mirror. For the first is something in itself, and the other -nothingness.--Folks little indebted to Nature, since it is only by -chance that they wear the human form and without it I might class -them with the herds of beasts. - -12. - -Many will think they may reasonably blame me by alleging that my -proofs are opposed to the authority of certain men held in the -highest reverence by their inexperienced judgments; not considering -that my works are the issue of pure and simple experience, who is -the one true mistress. These rules are sufficient to enable you to -know the true from the false--and this aids men to look only for -things that are possible and with due moderation--and not to wrap -yourself in ignorance, a thing which can have no good result, so -that in despair you would give yourself up to melancholy. - -13. - -Among all the studies of natural causes and reasons Light chiefly -delights the beholder; and among the great features of Mathematics -the certainty of its demonstrations is what preeminently (tends to) -elevate the mind of the investigator. Perspective, therefore, must -be preferred to all the discourses and systems of human learning. In -this branch [of science] the beam of light is explained on those -methods of demonstration which form the glory not so much of -Mathematics as of Physics and are graced with the flowers of both -[Footnote: 5. Such of Leonardo's notes on Optics or on Perspective -as bear exclusively on Mathematics or Physics could not be included -in the arrangement of the _libro di pittura_ which is here presented -to the reader. They are however but few.]. But its axioms being laid -down at great length, I shall abridge them to a conclusive brevity, -arranging them on the method both of their natural order and of -mathematical demonstration; sometimes by deduction of the effects -from the causes, and sometimes arguing the causes from the effects; -adding also to my own conclusions some which, though not included in -them, may nevertheless be inferred from them. Thus, if the Lord--who -is the light of all things--vouchsafe to enlighten me, I will treat -of Light; wherefore I will divide the present work into 3 Parts -[Footnote: 10. In the middle ages--for instance, by ROGER BACON, by -VITELLONE, with whose works Leonardo was certainly familiar, and by -all the writers of the Renaissance Perspective and Optics were not -regarded as distinct sciences. Perspective, indeed, is in its widest -application the science of seeing. Although to Leonardo the two -sciences were clearly separate, it is not so as to their names; thus -we find axioms in Optics under the heading Perspective. According to -this arrangement of the materials for the theoretical portion of the -_libro di pittura_ propositions in Perspective and in Optics stand -side by side or occur alternately. Although this particular chapter -deals only with Optics, it is not improbable that the words _partiro -la presente opera in 3 parti_ may refer to the same division into -three sections which is spoken of in chapters 14 to 17.]. - -The plan of the book on Painting (14--17). - -14. - -ON THE THREE BRANCHES OF PERSPECTIVE. - -There are three branches of perspective; the first deals with the -reasons of the (apparent) diminution of objects as they recede from -the eye, and is known as Diminishing Perspective.--The second -contains the way in which colours vary as they recede from the eye. -The third and last is concerned with the explanation of how the -objects [in a picture] ought to be less finished in proportion as -they are remote (and the names are as follows): - -Linear Perspective. The Perspective of Colour. The Perspective of -Disappearance. - -[Footnote: 13. From the character of the handwriting I infer that -this passage was written before the year 1490.]. - -15. - -ON PAINTING AND PERSPECTIVE. - -The divisions of Perspective are 3, as used in drawing; of these, -the first includes the diminution in size of opaque objects; the -second treats of the diminution and loss of outline in such opaque -objects; the third, of the diminution and loss of colour at long -distances. - -[Footnote: The division is here the same as in the previous chapter -No. 14, and this is worthy of note when we connect it with the fact -that a space of about 20 years must have intervened between the -writing of the two passages.] - -16. - -THE DISCOURSE ON PAINTING. - -Perspective, as bearing on drawing, is divided into three principal -sections; of which the first treats of the diminution in the size of -bodies at different distances. The second part is that which treats -of the diminution in colour in these objects. The third [deals with] -the diminished distinctness of the forms and outlines displayed by -the objects at various distances. - -17. - -ON THE SECTIONS OF [THE BOOK ON] PAINTING. - -The first thing in painting is that the objects it represents should -appear in relief, and that the grounds surrounding them at different -distances shall appear within the vertical plane of the foreground -of the picture by means of the 3 branches of Perspective, which are: -the diminution in the distinctness of the forms of the objects, the -diminution in their magnitude; and the diminution in their colour. -And of these 3 classes of Perspective the first results from [the -structure of] the eye, while the other two are caused by the -atmosphere which intervenes between the eye and the objects seen by -it. The second essential in painting is appropriate action and a due -variety in the figures, so that the men may not all look like -brothers, &c. - -[Footnote: This and the two foregoing chapters must have been -written in 1513 to 1516. They undoubtedly indicate the scheme which -Leonardo wished to carry out in arranging his researches on -Perspective as applied to Painting. This is important because it is -an evidence against the supposition of H. LUDWIG and others, that -Leonardo had collected his principles of Perspective in one book so -early as before 1500; a Book which, according to the hypothesis, -must have been lost at a very early period, or destroyed possibly, -by the French (!) in 1500 (see H. LUDWIG. L. da Vinci: _Das Buch van -der Malerei_. Vienna 1882 III, 7 and 8).] - -The use of the book on Painting. - -18. - -These rules are of use only in correcting the figures; since every -man makes some mistakes in his first compositions and he who knows -them not, cannot amend them. But you, knowing your errors, will -correct your works and where you find mistakes amend them, and -remember never to fall into them again. But if you try to apply -these rules in composition you will never make an end, and will -produce confusion in your works. - -These rules will enable you to have a free and sound judgment; since -good judgment is born of clear understanding, and a clear -understanding comes of reasons derived from sound rules, and sound -rules are the issue of sound experience--the common mother of all -the sciences and arts. Hence, bearing in mind the precepts of my -rules, you will be able, merely by your amended judgment, to -criticise and recognise every thing that is out of proportion in a -work, whether in the perspective or in the figures or any thing -else. - -Necessity of theoretical knowledge (19. 20). - -19. - -OF THE MISTAKES MADE BY THOSE WHO PRACTISE WITHOUT KNOWLEDGE. - -Those who are in love with practice without knowledge are like the -sailor who gets into a ship without rudder or compass and who never -can be certain whether he is going. Practice must always be founded -on sound theory, and to this Perspective is the guide and the -gateway; and without this nothing can be done well in the matter of -drawing. - -20. - -The painter who draws merely by practice and by eye, without any -reason, is like a mirror which copies every thing placed in front of -it without being conscious of their existence. - -The function of the eye (21-23). - -21. - -INTRODUCTION TO PERSPECTIVE:--THAT IS OF THE FUNCTION OF THE EYE. - -Behold here O reader! a thing concerning which we cannot trust our -forefathers, the ancients, who tried to define what the Soul and -Life are--which are beyond proof, whereas those things, which can at -any time be clearly known and proved by experience, remained for -many ages unknown or falsely understood. The eye, whose function we -so certainly know by experience, has, down to my own time, been -defined by an infinite number of authors as one thing; but I find, -by experience, that it is quite another. [Footnote 13: Compare the -note to No. 70.] - -[Footnote: In section 13 we already find it indicated that the study -of Perspective and of Optics is to be based on that of the functions -of the eye. Leonardo also refers to the science of the eye, in his -astronomical researches, for instance in MS. F 25b '_Ordine del -provare la terra essere una stella: Imprima difinisce l'occhio'_, -&c. Compare also MS. E 15b and F 60b. The principles of astronomical -perspective.] - -22. - -Here [in the eye] forms, here colours, here the character of every -part of the universe are concentrated to a point; and that point is -so marvellous a thing ... Oh! marvellous, O stupendous Necessity--by -thy laws thou dost compel every effect to be the direct result of -its cause, by the shortest path. These [indeed] are miracles;... - -In so small a space it can be reproduced and rearranged in its whole -expanse. Describe in your anatomy what proportion there is between -the diameters of all the images in the eye and the distance from -them of the crystalline lens. - -23. - -OF THE 10 ATTRIBUTES OF THE EYE, ALL CONCERNED IN PAINTING. - -Painting is concerned with all the 10 attributes of sight; which -are:--Darkness, Light, Solidity and Colour, Form and Position, -Distance and Propinquity, Motion and Rest. This little work of mine -will be a tissue [of the studies] of these attributes, reminding the -painter of the rules and methods by which he should use his art to -imitate all the works of Nature which adorn the world. - -24. - -ON PAINTING. - -Variability of the eye. - -1st. The pupil of the eye contracts, in proportion to the increase -of light which is reflected in it. 2nd. The pupil of the eye expands -in proportion to the diminution in the day light, or any other -light, that is reflected in it. 3rd. [Footnote: 8. The subject of -this third proposition we find fully discussed in MS. G. 44a.]. The -eye perceives and recognises the objects of its vision with greater -intensity in proportion as the pupil is more widely dilated; and -this can be proved by the case of nocturnal animals, such as cats, -and certain birds--as the owl and others--in which the pupil varies -in a high degree from large to small, &c., when in the dark or in -the light. 4th. The eye [out of doors] in an illuminated atmosphere -sees darkness behind the windows of houses which [nevertheless] are -light. 5th. All colours when placed in the shade appear of an equal -degree of darkness, among themselves. 6th. But all colours when -placed in a full light, never vary from their true and essential -hue. - -25. - -OF THE EYE. - -Focus of sight. - -If the eye is required to look at an object placed too near to it, -it cannot judge of it well--as happens to a man who tries to see the -tip of his nose. Hence, as a general rule, Nature teaches us that an -object can never be seen perfectly unless the space between it and -the eye is equal, at least, to the length of the face. - -Differences of perception by one eye and by both eyes (26-29). - -26. - -OF THE EYE. - -When both eyes direct the pyramid of sight to an object, that object -becomes clearly seen and comprehended by the eyes. - -27. - -Objects seen by one and the same eye appear sometimes large, and -sometimes small. - -28. - -The motion of a spectator who sees an object at rest often makes it -seem as though the object at rest had acquired the motion of the -moving body, while the moving person appears to be at rest. - -ON PAINTING. - -Objects in relief, when seen from a short distance with one eye, -look like a perfect picture. If you look with the eye _a_, _b_ at -the spot _c_, this point _c_ will appear to be at _d_, _f_, and if -you look at it with the eye _g_, _h_ will appear to be at _m_. A -picture can never contain in itself both aspects. - -29. - -Let the object in relief _t_ be seen by both eyes; if you will look -at the object with the right eye _m_, keeping the left eye _n_ shut, -the object will appear, or fill up the space, at _a_; and if you -shut the right eye and open the left, the object (will occupy the) -space _b_; and if you open both eyes, the object will no longer -appear at _a_ or _b_, but at _e_, _r_, _f_. Why will not a picture -seen by both eyes produce the effect of relief, as [real] relief -does when seen by both eyes; and why should a picture seen with one -eye give the same effect of relief as real relief would under the -same conditions of light and shade? - -[Footnote: In the sketch, _m_ is the left eye and _n_ the right, -while the text reverses this lettering. We must therefore suppose -that the face in which the eyes _m_ and _n_ are placed is opposite -to the spectator.] - -30. - -The comparative size of the image depends on the amount of light -(30-39). - -The eye will hold and retain in itself the image of a luminous body -better than that of a shaded object. The reason is that the eye is -in itself perfectly dark and since two things that are alike cannot -be distinguished, therefore the night, and other dark objects cannot -be seen or recognised by the eye. Light is totally contrary and -gives more distinctness, and counteracts and differs from the usual -darkness of the eye, hence it leaves the impression of its image. - -31. - -Every object we see will appear larger at midnight than at midday, -and larger in the morning than at midday. - -This happens because the pupil of the eye is much smaller at midday -than at any other time. - -32. - -The pupil which is largest will see objects the largest. This is -evident when we look at luminous bodies, and particularly at those -in the sky. When the eye comes out of darkness and suddenly looks up -at these bodies, they at first appear larger and then diminish; and -if you were to look at those bodies through a small opening, you -would see them smaller still, because a smaller part of the pupil -would exercise its function. - -[Footnote: 9. _buso_ in the Lomb. dialect is the same as _buco_.] - -33. - -When the eye, coming out of darkness suddenly sees a luminous body, -it will appear much larger at first sight than after long looking at -it. The illuminated object will look larger and more brilliant, when -seen with two eyes than with only one. A luminous object will appear -smaller in size, when the eye sees it through a smaller opening. A -luminous body of an oval form will appear rounder in proportion as -it is farther from the eye. - -34. - -Why when the eye has just seen the light, does the half light look -dark to it, and in the same way if it turns from the darkness the -half light look very bright? - -35. - -ON PAINTING. - -If the eye, when [out of doors] in the luminous atmosphere, sees a -place in shadow, this will look very much darker than it really is. -This happens only because the eye when out in the air contracts the -pupil in proportion as the atmosphere reflected in it is more -luminous. And the more the pupil contracts, the less luminous do the -objects appear that it sees. But as soon as the eye enters into a -shady place the darkness of the shadow suddenly seems to diminish. -This occurs because the greater the darkness into which the pupil -goes the more its size increases, and this increase makes the -darkness seem less. - -[Footnote 14: _La luce entrera_. _Luce_ occurs here in the sense of -pupil of the eye as in no 51: C. A. 84b; 245a; I--5; and in many -other places.] - -36. - -ON PERSPECTIVE. - -The eye which turns from a white object in the light of the sun and -goes into a less fully lighted place will see everything as dark. -And this happens either because the pupils of the eyes which have -rested on this brilliantly lighted white object have contracted so -much that, given at first a certain extent of surface, they will -have lost more than 3/4 of their size; and, lacking in size, they -are also deficient in [seeing] power. Though you might say to me: A -little bird (then) coming down would see comparatively little, and -from the smallness of his pupils the white might seem black! To this -I should reply that here we must have regard to the proportion of -the mass of that portion of the brain which is given up to the sense -of sight and to nothing else. Or--to return--this pupil in Man -dilates and contracts according to the brightness or darkness of -(surrounding) objects; and since it takes some time to dilate and -contract, it cannot see immediately on going out of the light and -into the shade, nor, in the same way, out of the shade into the -light, and this very thing has already deceived me in painting an -eye, and from that I learnt it. - -37. - -Experiment [showing] the dilatation and contraction of the pupil, -from the motion of the sun and other luminaries. In proportion as -the sky is darker the stars appear of larger size, and if you were -to light up the medium these stars would look smaller; and this -difference arises solely from the pupil which dilates and contracts -with the amount of light in the medium which is interposed between -the eye and the luminous body. Let the experiment be made, by -placing a candle above your head at the same time that you look at a -star; then gradually lower the candle till it is on a level with the -ray that comes from the star to the eye, and then you will see the -star diminish so much that you will almost lose sight of it. - -[Footnote: No reference is made in the text to the letters on the -accompanying diagram.] - -38. - -The pupil of the eye, in the open air, changes in size with every -degree of motion from the sun; and at every degree of its changes -one and the same object seen by it will appear of a different size; -although most frequently the relative scale of surrounding objects -does not allow us to detect these variations in any single object we -may look at. - -39. - -The eye--which sees all objects reversed--retains the images for -some time. This conclusion is proved by the results; because, the -eye having gazed at light retains some impression of it. After -looking (at it) there remain in the eye images of intense -brightness, that make any less brilliant spot seem dark until the -eye has lost the last trace of the impression of the stronger light. - -_II. - -Linear Perspective. - -We see clearly from the concluding sentence of section 49, where the -author directly addresses the painter, that he must certainly have -intended to include the elements of mathematics in his Book on the -art of Painting. They are therefore here placed at the beginning. In -section 50 the theory of the "Pyramid of Sight" is distinctly and -expressly put forward as the fundamental principle of linear -perspective, and sections 52 to 57 treat of it fully. This theory of -sight can scarcely be traced to any author of antiquity. Such -passages as occur in Euclid for instance, may, it is true, have -proved suggestive to the painters of the Renaissance, but it would -be rash to say any thing decisive on this point. - -Leon Battista Alberti treats of the "Pyramid of Sight" at some -length in his first Book of Painting; but his explanation differs -widely from Leonardo's in the details. Leonardo, like Alberti, may -have borrowed the broad lines of his theory from some views commonly -accepted among painters at the time; but he certainly worked out its -application in a perfectly original manner. - -The axioms as to the perception of the pyramid of rays are followed -by explanations of its origin, and proofs of its universal -application (58--69). The author recurs to the subject with endless -variations; it is evidently of fundamental importance in his -artistic theory and practice. It is unnecessary to discuss how far -this theory has any scientific value at the present day; so much as -this, at any rate, seems certain: that from the artist's point of -view it may still claim to be of immense practical utility. - -According to Leonardo, on one hand, the laws of perspective are an -inalienable condition of the existence of objects in space; on the -other hand, by a natural law, the eye, whatever it sees and wherever -it turns, is subjected to the perception of the pyramid of rays in -the form of a minute target. Thus it sees objects in perspective -independently of the will of the spectator, since the eye receives -the images by means of the pyramid of rays "just as a magnet -attracts iron". - -In connection with this we have the function of the eye explained by -the Camera obscura, and this is all the more interesting and -important because no writer previous to Leonardo had treated of this -subject_ (70--73). _Subsequent passages, of no less special interest, -betray his knowledge of refraction and of the inversion of the image -in the camera and in the eye_ (74--82). - -_From the principle of the transmission of the image to the eye and -to the camera obscura he deduces the means of producing an -artificial construction of the pyramid of rays or--which is the same -thing--of the image. The fundamental axioms as to the angle of sight -and the vanishing point are thus presented in a manner which is as -complete as it is simple and intelligible_ (86--89). - -_Leonardo distinguishes between simple and complex perspective_ (90, -91). _The last sections treat of the apparent size of objects at -various distances and of the way to estimate it_ (92--109). - -General remarks on perspective (40-41). - -40. - -ON PAINTING. - -Perspective is the best guide to the art of Painting. - -[Footnote: 40. Compare 53, 2.] - -41. - -The art of perspective is of such a nature as to make what is flat -appear in relief and what is in relief flat. - -The elements of perspective--Of the Point (42-46). - -42. - -All the problems of perspective are made clear by the five terms of -mathematicians, which are:--the point, the line, the angle, the -superficies and the solid. The point is unique of its kind. And the -point has neither height, breadth, length, nor depth, whence it is -to be regarded as indivisible and as having no dimensions in space. -The line is of three kinds, straight, curved and sinuous and it has -neither breadth, height, nor depth. Hence it is indivisible, -excepting in its length, and its ends are two points. The angle is -the junction of two lines in a point. - -43. - -A point is not part of a line. - -44. - -OF THE NATURAL POINT. - -The smallest natural point is larger than all mathematical points, -and this is proved because the natural point has continuity, and any -thing that is continuous is infinitely divisible; but the -mathematical point is indivisible because it has no size. - -[Footnote: This definition was inserted by Leonardo on a MS. copy on -parchment of the well-known _"Trattato d'Architettura civile e -militare"_ &c. by FRANCESCO DI GIORGIO; opposite a passage where the -author says: _'In prima he da sapere che punto e quella parie della -quale he nulla--Linia he luncheza senza apieza; &c.] - -45. - -1, The superficies is a limitation of the body. 2, and the -limitation of a body is no part of that body. 4, and the limitation -of one body is that which begins another. 3, that which is not part -of any body is nothing. Nothing is that which fills no space. - -If one single point placed in a circle may be the starting point of -an infinite number of lines, and the termination of an infinite -number of lines, there must be an infinite number of points -separable from this point, and these when reunited become one again; -whence it follows that the part may be equal to the whole. - -46. - -The point, being indivisible, occupies no space. That which occupies -no space is nothing. The limiting surface of one thing is the -beginning of another. 2. That which is no part of any body is called -nothing. 1. That which has no limitations, has no form. The -limitations of two conterminous bodies are interchangeably the -surface of each. All the surfaces of a body are not parts of that -body. - -Of the line (47-48). - -47. - -DEFINITION OF THE NATURE OF THE LINE. - -The line has in itself neither matter nor substance and may rather -be called an imaginary idea than a real object; and this being its -nature it occupies no space. Therefore an infinite number of lines -may be conceived of as intersecting each other at a point, which has -no dimensions and is only of the thickness (if thickness it may be -called) of one single line. - -HOW WE MAY CONCLUDE THAT A SUPERFICIES TERMINATES IN A POINT? - -An angular surface is reduced to a point where it terminates in an -angle. Or, if the sides of that angle are produced in a straight -line, then--beyond that angle--another surface is generated, -smaller, or equal to, or larger than the first. - -48. - -OF DRAWING OUTLINE. - -Consider with the greatest care the form of the outlines of every -object, and the character of their undulations. And these -undulations must be separately studied, as to whether the curves are -composed of arched convexities or angular concavities. - -49. - -The nature of the outline. - -The boundaries of bodies are the least of all things. The -proposition is proved to be true, because the boundary of a thing is -a surface, which is not part of the body contained within that -surface; nor is it part of the air surrounding that body, but is the -medium interposted between the air and the body, as is proved in its -place. But the lateral boundaries of these bodies is the line -forming the boundary of the surface, which line is of invisible -thickness. Wherefore O painter! do not surround your bodies with -lines, and above all when representing objects smaller than nature; -for not only will their external outlines become indistinct, but -their parts will be invisible from distance. - -50. - -Definition of Perspective. - -[Drawing is based upon perspective, which is nothing else than a -thorough knowledge of the function of the eye. And this function -simply consists in receiving in a pyramid the forms and colours of -all the objects placed before it. I say in a pyramid, because there -is no object so small that it will not be larger than the spot where -these pyramids are received into the eye. Therefore, if you extend -the lines from the edges of each body as they converge you will -bring them to a single point, and necessarily the said lines must -form a pyramid.] - -[Perspective is nothing more than a rational demonstration applied -to the consideration of how objects in front of the eye transmit -their image to it, by means of a pyramid of lines. The _Pyramid_ is -the name I apply to the lines which, starting from the surface and -edges of each object, converge from a distance and meet in a single -point.] - -[Perspective is a rational demonstration, by which we may -practically and clearly understand how objects transmit their own -image, by lines forming a Pyramid (centred) in the eye.] - -Perspective is a rational demonstration by which experience confirms -that every object sends its image to the eye by a pyramid of lines; -and bodies of equal size will result in a pyramid of larger or -smaller size, according to the difference in their distance, one -from the other. By a pyramid of lines I mean those which start from -the surface and edges of bodies, and, converging from a distance -meet in a single point. A point is said to be that which [having no -dimensions] cannot be divided, and this point placed in the eye -receives all the points of the cone. - -[Footnote: 50. 1-5. Compare with this the Proem. No. 21. The -paragraphs placed in brackets: lines 1-9, 10-14, and 17--20, are -evidently mere sketches and, as such, were cancelled by the writer; -but they serve as a commentary on the final paragraph, lines 22-29.] - -51. - -IN WHAT WAY THE EYE SEES OBJECTS PLACED IN FRONT OF IT. - -The perception of the object depends on the direction of the eye. - -Supposing that the ball figured above is the ball of the eye and let -the small portion of the ball which is cut off by the line _s t_ be -the pupil and all the objects mirrored on the centre of the face of -the eye, by means of the pupil, pass on at once and enter the pupil, -passing through the crystalline humour, which does not interfere in -the pupil with the things seen by means of the light. And the pupil -having received the objects, by means of the light, immediately -refers them and transmits them to the intellect by the line _a b_. -And you must know that the pupil transmits nothing perfectly to the -intellect or common sense excepting when the objects presented to it -by means of light, reach it by the line _a b;_ as, for instance, by -the line _b c_. For although the lines _m n_ and _f g_ may be seen -by the pupil they are not perfectly taken in, because they do not -coincide with the line _a b_. And the proof is this: If the eye, -shown above, wants to count the letters placed in front, the eye -will be obliged to turn from letter to letter, because it cannot -discern them unless they lie in the line _a b;_ as, for instance, in -the line _a c_. All visible objects reach the eye by the lines of a -pyramid, and the point of the pyramid is the apex and centre of it, -in the centre of the pupil, as figured above. - -[Footnote: 51. In this problem the eye is conceived of as fixed and -immovable; this is plain from line 11.] - -Experimental proof of the existence of the pyramid of sight (52-55). - -52. - -Perspective is a rational demonstration, confirmed by experience, -that all objects transmit their image to the eye by a pyramid of -lines. - -By a pyramid of lines I understand those lines which start from the -edges of the surface of bodies, and converging from a distance, meet -in a single point; and this point, in the present instance, I will -show to be situated in the eye which is the universal judge of all -objects. By a point I mean that which cannot be divided into parts; -therefore this point, which is situated in the eye, being -indivisible, no body is seen by the eye, that is not larger than -this point. This being the case it is inevitable that the lines -which come from the object to the point must form a pyramid. And if -any man seeks to prove that the sense of sight does not reside in -this point, but rather in the black spot which is visible in the -middle of the pupil, I might reply to him that a small object could -never diminish at any distance, as it might be a grain of millet or -of oats or of some similar thing, and that object, if it were larger -than the said [black] spot would never be seen as a whole; as may be -seen in the diagram below. Let _a_. be the seat of sight, _b e_ the -lines which reach the eye. Let _e d_ be the grains of millet within -these lines. You plainly see that these will never diminish by -distance, and that the body _m n_ could not be entirely covered by -it. Therefore you must confess that the eye contains within itself -one single indivisible point _a_, to which all the points converge -of the pyramid of lines starting from an object, as is shown below. -Let _a_. _b_. be the eye; in the centre of it is the point above -mentioned. If the line _e f_ is to enter as an image into so small -an opening in the eye, you must confess that the smaller object -cannot enter into what is smaller than itself unless it is -diminished, and by diminishing it must take the form of a pyramid. - -53. - -PERSPECTIVE. - -Perspective comes in where judgment fails [as to the distance] in -objects which diminish. The eye can never be a true judge for -determining with exactitude how near one object is to another which -is equal to it [in size], if the top of that other is on the level -of the eye which sees them on that side, excepting by means of the -vertical plane which is the standard and guide of perspective. Let -_n_ be the eye, _e f_ the vertical plane above mentioned. Let _a b c -d_ be the three divisions, one below the other; if the lines _a n_ -and _c n_ are of a given length and the eye _n_ is in the centre, -then _a b_ will look as large as _b c. c d_ is lower and farther off -from _n_, therefore it will look smaller. And the same effect will -appear in the three divisions of a face when the eye of the painter -who is drawing it is on a level with the eye of the person he is -painting. - -54. - -TO PROVE HOW OBJECTS REACH THE EYE. - -If you look at the sun or some other luminous body and then shut -your eyes you will see it again inside your eye for a long time. -This is evidence that images enter into the eye. - -The relations of the distance points to the vanishing point (55-56). - -55. - -ELEMENTS OF PERSPECTIVE. - -All objects transmit their image to the eye in pyramids, and the -nearer to the eye these pyramids are intersected the smaller will -the image appear of the objects which cause them. Therefore, you may -intersect the pyramid with a vertical plane [Footnote 4: _Pariete_. -Compare the definitions in 85, 2-5, 6-27. These lines refer -exclusively to the third diagram. For the better understanding of -this it should be observed that _c s_ must be regarded as -representing the section or profile of a square plane, placed -horizontally (comp. lines 11, 14, 17) for which the word _pianura_ -is subsequently employed (20, 22). Lines 6-13 contain certain -preliminary observations to guide the reader in understanding the -diagram; the last three seem to have been added as a supplement. -Leonardo's mistake in writing _t denota_ (line 6) for _f denota_ has -been rectified.] which reaches the base of the pyramid as is shown -in the plane _a n_. - -The eye _f_ and the eye _t_ are one and the same thing; but the eye -_f_ marks the distance, that is to say how far you are standing from -the object; and the eye _t_ shows you the direction of it; that is -whether you are opposite, or on one side, or at an angle to the -object you are looking at. And remember that the eye _f_ and the eye -_t_ must always be kept on the same level. For example if you raise -or lower the eye from the distance point _f_ you must do the same -with the direction point _t_. And if the point _f_ shows how far the -eye is distant from the square plane but does not show on which side -it is placed--and, if in the same way, the point _t_ show _s_ the -direction and not the distance, in order to ascertain both you must -use both points and they will be one and the same thing. If the eye -_f_ could see a perfect square of which all the sides were equal to -the distance between _s_ and _c_, and if at the nearest end of the -side towards the eye a pole were placed, or some other straight -object, set up by a perpendicular line as shown at _r s_--then, I -say, that if you were to look at the side of the square that is -nearest to you it will appear at the bottom of the vertical plane _r -s_, and then look at the farther side and it would appear to you at -the height of the point _n_ on the vertical plane. Thus, by this -example, you can understand that if the eye is above a number of -objects all placed on the same level, one beyond another, the more -remote they are the higher they will seem, up to the level of the -eye, but no higher; because objects placed upon the level on which -your feet stand, so long as it is flat--even if it be extended into -infinity--would never be seen above the eye; since the eye has in -itself the point towards which all the cones tend and converge which -convey the images of the objects to the eye. And this point always -coincides with the point of diminution which is the extreme of all -we can see. And from the base line of the first pyramid as far as -the diminishing point - -[Footnote: The two diagrams above the chapter are explained by the -first five lines. They have, however, more letters than are referred -to in the text, a circumstance we frequently find occasion to -remark.] - -56. - -there are only bases without pyramids which constantly diminish up -to this point. And from the first base where the vertical plane is -placed towards the point in the eye there will be only pyramids -without bases; as shown in the example given above. Now, let _a b_ -be the said vertical plane and _r_ the point of the pyramid -terminating in the eye, and _n_ the point of diminution which is -always in a straight line opposite the eye and always moves as the -eye moves--just as when a rod is moved its shadow moves, and moves -with it, precisely as the shadow moves with a body. And each point -is the apex of a pyramid, all having a common base with the -intervening vertical plane. But although their bases are equal their -angles are not equal, because the diminishing point is the -termination of a smaller angle than that of the eye. If you ask me: -"By what practical experience can you show me these points?" I -reply--so far as concerns the diminishing point which moves with you ---when you walk by a ploughed field look at the straight furrows -which come down with their ends to the path where you are walking, -and you will see that each pair of furrows will look as though they -tried to get nearer and meet at the [farther] end. - -[Footnote: For the easier understanding of the diagram and of its -connection with the preceding I may here remark that the square -plane shown above in profile by the line _c s_ is here indicated by -_e d o p_. According to lines 1, 3 _a b_ must be imagined as a plane -of glass placed perpendicularly at _o p_.] - -57. - -How to measure the pyramid of vision. - -As regards the point in the eye; it is made more intelligible by -this: If you look into the eye of another person you will see your -own image. Now imagine 2 lines starting from your ears and going to -the ears of that image which you see in the other man's eye; you -will understand that these lines converge in such a way that they -would meet in a point a little way beyond your own image mirrored in -the eye. And if you want to measure the diminution of the pyramid in -the air which occupies the space between the object seen and the -eye, you must do it according to the diagram figured below. Let _m -n_ be a tower, and _e f_ a, rod, which you must move backwards and -forwards till its ends correspond with those of the tower [Footnote -9: _I sua stremi .. della storre_ (its ends ... of the tower) this -is the case at _e f_.]; then bring it nearer to the eye, at _c d_ -and you will see that the image of the tower seems smaller, as at _r -o_. Then [again] bring it closer to the eye and you will see the rod -project far beyond the image of the tower from _a_ to _b_ and from -_t_ to _b_, and so you will discern that, a little farther within, -the lines must converge in a point. - -The Production of pyramid of Vision (58-60). - -58. - -PERSPECTIVE. - -The instant the atmosphere is illuminated it will be filled with an -infinite number of images which are produced by the various bodies -and colours assembled in it. And the eye is the target, a loadstone, -of these images. - -59. - -The whole surface of opaque bodies displays its whole image in all -the illuminated atmosphere which surrounds them on all sides. - -60. - -That the atmosphere attracts to itself, like a loadstone, all the -images of the objects that exist in it, and not their forms merely -but their nature may be clearly seen by the sun, which is a hot and -luminous body. All the atmosphere, which is the all-pervading -matter, absorbs light and heat, and reflects in itself the image of -the source of that heat and splendour and, in each minutest portion, -does the same. The Northpole does the same as the loadstone shows; -and the moon and the other planets, without suffering any -diminution, do the same. Among terrestrial things musk does the same -and other perfumes. - -61. - -All bodies together, and each by itself, give off to the surrounding -air an infinite number of images which are all-pervading and each -complete, each conveying the nature, colour and form of the body -which produces it. - -It can clearly be shown that all bodies are, by their images, -all-pervading in the surrounding atmosphere, and each complete in -itself as to substance form and colour; this is seen by the images -of the various bodies which are reproduced in one single perforation -through which they transmit the objects by lines which intersect and -cause reversed pyramids, from the objects, so that they are upside -down on the dark plane where they are first reflected. The reason of -this is-- - -[Footnote: The diagram intended to illustrate the statement (Pl. II -No. i) occurs in the original between lines 3 and 4. The three -circles must be understood to represent three luminous bodies which -transmit their images through perforations in a wall into a dark -chamber, according to a law which is more fully explained in 75?81. -So far as concerns the present passage the diagram is only intended -to explain that the images of the three bodies may be made to -coalesce at any given spot. In the circles are written, -giallo--yellow, biacho--white, rosso--red. - -The text breaks off at line 8. The paragraph No.40 follows here in -the original MS.] - -62. - -Every point is the termination of an infinite number of lines, which -diverge to form a base, and immediately, from the base the same -lines converge to a pyramid [imaging] both the colour and form. No -sooner is a form created or compounded than suddenly infinite lines -and angles are produced from it; and these lines, distributing -themselves and intersecting each other in the air, give rise to an -infinite number of angles opposite to each other. Given a base, each -opposite angle, will form a triangle having a form and proportion -equal to the larger angle; and if the base goes twice into each of -the 2 lines of the pyramid the smaller triangle will do the same. - -63. - -Every body in light and shade fills the surrounding air with -infinite images of itself; and these, by infinite pyramids diffused -in the air, represent this body throughout space and on every side. -Each pyramid that is composed of a long assemblage of rays includes -within itself an infinite number of pyramids and each has the same -power as all, and all as each. A circle of equidistant pyramids of -vision will give to their object angles of equal size; and an eye at -each point will see the object of the same size. The body of the -atmosphere is full of infinite pyramids composed of radiating -straight lines, which are produced from the surface of the bodies in -light and shade, existing in the air; and the farther they are from -the object which produces them the more acute they become and -although in their distribution they intersect and cross they never -mingle together, but pass through all the surrounding air, -independently converging, spreading, and diffused. And they are all -of equal power [and value]; all equal to each, and each equal to -all. By these the images of objects are transmitted through all -space and in every direction, and each pyramid, in itself, includes, -in each minutest part, the whole form of the body causing it. - -64. - -The body of the atmosphere is full of infinite radiating pyramids -produced by the objects existing in it. These intersect and cross -each other with independent convergence without interfering with -each other and pass through all the surrounding atmosphere; and are -of equal force and value--all being equal to each, each to all. And -by means of these, images of the body are transmitted everywhere and -on all sides, and each receives in itself every minutest portion of -the object that produces it. - -Proof by experiment (65-66). - -65. - -PERSPECTIVE. - -The air is filled with endless images of the objects distributed in -it; and all are represented in all, and all in one, and all in each, -whence it happens that if two mirrors are placed in such a manner as -to face each other exactly, the first will be reflected in the -second and the second in the first. The first being reflected in the -second takes to it the image of itself with all the images -represented in it, among which is the image of the second mirror, -and so, image within image, they go on to infinity in such a manner -as that each mirror has within it a mirror, each smaller than the -last and one inside the other. Thus, by this example, it is clearly -proved that every object sends its image to every spot whence the -object itself can be seen; and the converse: That the same object -may receive in itself all the images of the objects that are in -front of it. Hence the eye transmits through the atmosphere its own -image to all the objects that are in front of it and receives them -into itself, that is to say on its surface, whence they are taken in -by the common sense, which considers them and if they are pleasing -commits them to the memory. Whence I am of opinion: That the -invisible images in the eyes are produced towards the object, as the -image of the object to the eye. That the images of the objects must -be disseminated through the air. An instance may be seen in several -mirrors placed in a circle, which will reflect each other endlessly. -When one has reached the other it is returned to the object that -produced it, and thence--being diminished--it is returned again to -the object and then comes back once more, and this happens -endlessly. If you put a light between two flat mirrors with a -distance of 1 braccio between them you will see in each of them an -infinite number of lights, one smaller than another, to the last. If -at night you put a light between the walls of a room, all the parts -of that wall will be tinted with the image of that light. And they -will receive the light and the light will fall on them, mutually, -that is to say, when there is no obstacle to interrupt the -transmission of the images. This same example is seen in a greater -degree in the distribution of the solar rays which all together, and -each by itself, convey to the object the image of the body which -causes it. That each body by itself alone fills with its images the -atmosphere around it, and that the same air is able, at the same -time, to receive the images of the endless other objects which are -in it, this is clearly proved by these examples. And every object is -everywhere visible in the whole of the atmosphere, and the whole in -every smallest part of it; and all the objects in the whole, and all -in each smallest part; each in all and all in every part. - -66. - -The images of objects are all diffused through the atmosphere which -receives them; and all on every side in it. To prove this, let _a c -e_ be objects of which the images are admitted to a dark chamber by -the small holes _n p_ and thrown upon the plane _f i_ opposite to -these holes. As many images will be produced in the chamber on the -plane as the number of the said holes. - -67. - -General conclusions. - -All objects project their whole image and likeness, diffused and -mingled in the whole of the atmosphere, opposite to themselves. The -image of every point of the bodily surface, exists in every part of -the atmosphere. All the images of the objects are in every part of -the atmosphere. The whole, and each part of the image of the -atmosphere is [reflected] in each point of the surface of the bodies -presented to it. Therefore both the part and the whole of the images -of the objects exist, both in the whole and in the parts of the -surface of these visible bodies. Whence we may evidently say that -the image of each object exists, as a whole and in every part, in -each part and in the whole interchangeably in every existing body. -As is seen in two mirrors placed opposite to each other. - -68. - -That the contrary is impossible. - -It is impossible that the eye should project from itself, by visual -rays, the visual virtue, since, as soon as it opens, that front -portion [of the eye] which would give rise to this emanation would -have to go forth to the object and this it could not do without -time. And this being so, it could not travel so high as the sun in a -month's time when the eye wanted to see it. And if it could reach -the sun it would necessarily follow that it should perpetually -remain in a continuous line from the eye to the sun and should -always diverge in such a way as to form between the sun and the eye -the base and the apex of a pyramid. This being the case, if the eye -consisted of a million worlds, it would not prevent its being -consumed in the projection of its virtue; and if this virtue would -have to travel through the air as perfumes do, the winds would bent -it and carry it into another place. But we do [in fact] see the mass -of the sun with the same rapidity as [an object] at the distance of -a braccio, and the power of sight is not disturbed by the blowing of -the winds nor by any other accident. - -[Footnote: The view here refuted by Leonardo was maintained among -others by Bramantino, Leonardo's Milanese contemporary. LOMAZZO -writes as follows in his Trattato dell' Arte della pittura &c. -(Milano 1584. Libr. V cp. XXI): Sovviemmi di aver gia letto in certi -scritti alcune cose di Bramantino milanese, celebratissimo pittore, -attenente alla prospettiva, le quali ho voluto riferire, e quasi -intessere in questo luogo, affinche sappiamo qual fosse l'opinione -di cosi chiaro e famoso pittore intorno alla prospettiva . . Scrive -Bramantino che la prospettiva e una cosa che contrafa il naturale, e -che cio si fa in tre modi - -Circa il primo modo che si fa con ragione, per essere la cosa in -poche parole conclusa da Bramantino in maniera che giudico non -potersi dir meglio, contenendovi si tutta Parte del principio al -fine, io riferiro per appunto le proprie parole sue (cp. XXII, Prima -prospettiva di Bramantino). La prima prospettiva fa le cose di -punto, e l'altra non mai, e la terza piu appresso. Adunque la prima -si dimanda prospettiva, cioe ragione, la quale fa l'effetto dell' -occhio, facendo crescere e calare secondo gli effetti degli occhi. -Questo crescere e calare non procede della cosa propria, che in se -per esser lontana, ovvero vicina, per quello effetto non puo -crescere e sminuire, ma procede dagli effetti degli occhi, i quali -sono piccioli, e percio volendo vedere tanto gran cosa_, bisogna che -mandino fuora la virtu visiva, _la quale si dilata in tanta -larghezza, che piglia tutto quello che vuoi vedere, ed_ arrivando a -quella cosa la vede dove e: _e da lei agli occhi per quello circuito -fino all' occhio, e tutto quello termine e pieno di quella cosa_. - -It is worthy of note that Leonardo had made his memorandum refuting -this view, at Milan in 1492] - -69. - -A parallel case. - -Just as a stone flung into the water becomes the centre and cause of -many circles, and as sound diffuses itself in circles in the air: so -any object, placed in the luminous atmosphere, diffuses itself in -circles, and fills the surrounding air with infinite images of -itself. And is repeated, the whole every-where, and the whole in -every smallest part. This can be proved by experiment, since if you -shut a window that faces west and make a hole [Footnote: 6. Here the -text breaks off.] . . - -[Footnote: Compare LIBRI, _Histoire des sciences mathematiques en -Italie_. Tome III, p. 43.] - -The function of the eye as explained by the camera obscura (70. 71). - -70. - -If the object in front of the eye sends its image to the eye, the -eye, on the other hand, sends its image to the object, and no -portion whatever of the object is lost in the images it throws off, -for any reason either in the eye or the object. Therefore we may -rather believe it to be the nature and potency of our luminous -atmosphere which absorbs the images of the objects existing in it, -than the nature of the objects, to send their images through the -air. If the object opposite to the eye were to send its image to the -eye, the eye would have to do the same to the object, whence it -might seem that these images were an emanation. But, if so, it would -be necessary [to admit] that every object became rapidly smaller; -because each object appears by its images in the surrounding -atmosphere. That is: the whole object in the whole atmosphere, and -in each part; and all the objects in the whole atmosphere and all of -them in each part; speaking of that atmosphere which is able to -contain in itself the straight and radiating lines of the images -projected by the objects. From this it seems necessary to admit that -it is in the nature of the atmosphere, which subsists between the -objects, and which attracts the images of things to itself like a -loadstone, being placed between them. - -PROVE HOW ALL OBJECTS, PLACED IN ONE POSITION, ARE ALL EVERYWHERE -AND ALL IN EACH PART. - -I say that if the front of a building--or any open piazza or -field--which is illuminated by the sun has a dwelling opposite to -it, and if, in the front which does not face the sun, you make a -small round hole, all the illuminated objects will project their -images through that hole and be visible inside the dwelling on the -opposite wall which may be made white; and there, in fact, they will -be upside down, and if you make similar openings in several places -in the same wall you will have the same result from each. Hence the -images of the illuminated objects are all everywhere on this wall -and all in each minutest part of it. The reason, as we clearly know, -is that this hole must admit some light to the said dwelling, and -the light admitted by it is derived from one or many luminous -bodies. If these bodies are of various colours and shapes the rays -forming the images are of various colours and shapes, and so will -the representations be on the wall. - -[Footnote: 70. 15--23. This section has already been published in the -"_Saggio delle Opere di Leonardo da Vinci_" Milan 1872, pp. 13, 14. -G. Govi observes upon it, that Leonardo is not to be regarded as the -inventor of the Camera obscura, but that he was the first to explain -by it the structure of the eye. An account of the Camera obscura -first occurs in CESARE CESARINI's Italian version of Vitruvius, pub. -1523, four years after Leonardo's death. Cesarini expressly names -Benedettino Don Papnutio as the inventor of the Camera obscura. In -his explanation of the function of the eye by a comparison with the -Camera obscura Leonardo was the precursor of G. CARDANO, Professor -of Medicine at Bologna (died 1576) and it appears highly probable -that this is, in fact, the very discovery which Leonardo ascribes to -himself in section 21 without giving any further details.] - -71. - -HOW THE IMAGES OF OBJECTS RECEIVED BY THE EYE INTERSECT WITHIN THE -CRYSTALLINE HUMOUR OF THE EYE. - -An experiment, showing how objects transmit their images or -pictures, intersecting within the eye in the crystalline humour, is -seen when by some small round hole penetrate the images of -illuminated objects into a very dark chamber. Then, receive these -images on a white paper placed within this dark room and rather near -to the hole and you will see all the objects on the paper in their -proper forms and colours, but much smaller; and they will be upside -down by reason of that very intersection. These images being -transmitted from a place illuminated by the sun will seem actually -painted on this paper which must be extremely thin and looked at -from behind. And let the little perforation be made in a very thin -plate of iron. Let _a b e d e_ be the object illuminated by the sun -and _o r_ the front of the dark chamber in which is the said hole at -_n m_. Let _s t_ be the sheet of paper intercepting the rays of the -images of these objects upside down, because the rays being -straight, _a_ on the right hand becomes _k_ on the left, and _e_ on -the left becomes _f_ on the right; and the same takes place inside -the pupil. - -[Footnote: This chapter is already known through a translation into -French by VENTURI. Compare his '_Essai sur les ouvrages -physico-mathematiques de L. da Vinci avec des fragments tires de ses -Manuscrits, apportes de l'Italie. Lu a la premiere classe de -l'Institut national des Sciences et Arts.' Paris, An V_ (1797).] - -The practice of perspective (72. 73). - -72. - -In the practice of perspective the same rules apply to light and to -the eye. - -73. - -The object which is opposite to the pupil of the eye is seen by that -pupil and that which is opposite to the eye is seen by the pupil. - -Refraction of the rays falling upon the eye (74. 75) - -74. - -The lines sent forth by the image of an object to the eye do not -reach the point within the eye in straight lines. - -75. - -If the judgment of the eye is situated within it, the straight lines -of the images are refracted on its surface because they pass through -the rarer to the denser medium. If, when you are under water, you -look at objects in the air you will see them out of their true -place; and the same with objects under water seen from the air. - -The intersection of the rays (76-82). - -76. - -The inversion of the images. - -All the images of objects which pass through a window [glass pane] -from the free outer air to the air confined within walls, are seen -on the opposite side; and an object which moves in the outer air -from east to west will seem in its shadow, on the wall which is -lighted by this confined air, to have an opposite motion. - -77. - -THE PRINCIPLE ON WHICH THE IMAGES OF BODIES PASS IN BETWEEN THE -MARGINS OF THE OPENINGS BY WHICH THEY ENTER. - -What difference is there in the way in which images pass through -narrow openings and through large openings, or in those which pass -by the sides of shaded bodies? By moving the edges of the opening -through which the images are admitted, the images of immovable -objects are made to move. And this happens, as is shown in the 9th -which demonstrates: [Footnote 11: _per la 9a che dicie_. When -Leonardo refers thus to a number it serves to indicate marginal -diagrams; this can in some instances be distinctly proved. The ninth -sketch on the page W. L. 145 b corresponds to the middle sketch of -the three reproduced.] the images of any object are all everywhere, -and all in each part of the surrounding air. It follows that if one -of the edges of the hole by which the images are admitted to a dark -chamber is moved it cuts off those rays of the image that were in -contact with it and gets nearer to other rays which previously were -remote from it &c. - -OF THE MOVEMENT OF THE EDGE AT THE RIGHT OR LEFT, OR THE UPPER, OR -LOWER EDGE. - -If you move the right side of the opening the image on the left will -move [being that] of the object which entered on the right side of -the opening; and the same result will happen with all the other -sides of the opening. This can be proved by the 2nd of this which -shows: all the rays which convey the images of objects through the -air are straight lines. Hence, if the images of very large bodies -have to pass through very small holes, and beyond these holes -recover their large size, the lines must necessarily intersect. - -[Footnote: 77. 2. In the first of the three diagrams Leonardo had -drawn only one of the two margins, et _m_.] - -78. - -Necessity has provided that all the images of objects in front of -the eye shall intersect in two places. One of these intersections is -in the pupil, the other in the crystalline lens; and if this were -not the case the eye could not see so great a number of objects as -it does. This can be proved, since all the lines which intersect do -so in a point. Because nothing is seen of objects excepting their -surface; and their edges are lines, in contradistinction to the -definition of a surface. And each minute part of a line is equal to -a point; for _smallest_ is said of that than which nothing can be -smaller, and this definition is equivalent to the definition of the -point. Hence it is possible for the whole circumference of a circle -to transmit its image to the point of intersection, as is shown in -the 4th of this which shows: all the smallest parts of the images -cross each other without interfering with each other. These -demonstrations are to illustrate the eye. No image, even of the -smallest object, enters the eye without being turned upside down; -but as it penetrates into the crystalline lens it is once more -reversed and thus the image is restored to the same position within -the eye as that of the object outside the eye. - -79. - -OF THE CENTRAL LINE OF THE EYE. - -Only one line of the image, of all those that reach the visual -virtue, has no intersection; and this has no sensible dimensions -because it is a mathematical line which originates from a -mathematical point, which has no dimensions. - -According to my adversary, necessity requires that the central line -of every image that enters by small and narrow openings into a dark -chamber shall be turned upside down, together with the images of the -bodies that surround it. - -80. - -AS TO WHETHER THE CENTRAL LINE OF THE IMAGE CAN BE INTERSECTED, OR -NOT, WITHIN THE OPENING. - -It is impossible that the line should intersect itself; that is, -that its right should cross over to its left side, and so, its left -side become its right side. Because such an intersection demands two -lines, one from each side; for there can be no motion from right to -left or from left to right in itself without such extension and -thickness as admit of such motion. And if there is extension it is -no longer a line but a surface, and we are investigating the -properties of a line, and not of a surface. And as the line, having -no centre of thickness cannot be divided, we must conclude that the -line can have no sides to intersect each other. This is proved by -the movement of the line _a f_ to _a b_ and of the line _e b_ to _e -f_, which are the sides of the surface _a f e b_. But if you move -the line _a b_ and the line _e f_, with the frontends _a e_, to the -spot _c_, you will have moved the opposite ends _f b_ towards each -other at the point _d_. And from the two lines you will have drawn -the straight line _c d_ which cuts the middle of the intersection of -these two lines at the point _n_ without any intersection. For, you -imagine these two lines as having breadth, it is evident that by -this motion the first will entirely cover the other--being equal -with it--without any intersection, in the position _c d_. And this -is sufficient to prove our proposition. - -81. - -HOW THE INNUMERABLE RAYS FROM INNUMERABLE IMAGES CAN CONVERGE TO A -POINT. - -Just as all lines can meet at a point without interfering with each -other--being without breadth or thickness--in the same way all the -images of surfaces can meet there; and as each given point faces the -object opposite to it and each object faces an opposite point, the -converging rays of the image can pass through the point and diverge -again beyond it to reproduce and re-magnify the real size of that -image. But their impressions will appear reversed--as is shown in -the first, above; where it is said that every image intersects as it -enters the narrow openings made in a very thin substance. - -Read the marginal text on the other side. - -In proportion as the opening is smaller than the shaded body, so -much less will the images transmitted through this opening intersect -each other. The sides of images which pass through openings into a -dark room intersect at a point which is nearer to the opening in -proportion as the opening is narrower. To prove this let _a b_ be an -object in light and shade which sends not its shadow but the image -of its darkened form through the opening _d e_ which is as wide as -this shaded body; and its sides _a b_, being straight lines (as has -been proved) must intersect between the shaded object and the -opening; but nearer to the opening in proportion as it is smaller -than the object in shade. As is shown, on your right hand and your -left hand, in the two diagrams _a_ _b_ _c_ _n_ _m_ _o_ where, the -right opening _d_ _e_, being equal in width to the shaded object _a_ -_b_, the intersection of the sides of the said shaded object occurs -half way between the opening and the shaded object at the point _c_. -But this cannot happen in the left hand figure, the opening _o_ -being much smaller than the shaded object _n_ _m_. - -It is impossible that the images of objects should be seen between -the objects and the openings through which the images of these -bodies are admitted; and this is plain, because where the atmosphere -is illuminated these images are not formed visibly. - -When the images are made double by mutually crossing each other they -are invariably doubly as dark in tone. To prove this let _d_ _e_ _h_ -be such a doubling which although it is only seen within the space -between the bodies in _b_ and _i_ this will not hinder its being -seen from _f_ _g_ or from _f_ _m_; being composed of the images _a_ -_b_ _i_ _k_ which run together in _d_ _e_ _h_. - -[Footnote: 81. On the original diagram at the beginning of this -chapter Leonardo has written "_azurro_" (blue) where in the -facsimile I have marked _A_, and "_giallo_" (yellow) where _B_ -stands.] - -[Footnote: 15--23. These lines stand between the diagrams I and III.] - -[Footnote: 24--53. These lines stand between the diagrams I and II.] - -[Footnote: 54--97 are written along the left side of diagram I.] - -82. - -An experiment showing that though the pupil may not be moved from -its position the objects seen by it may appear to move from their -places. - -If you look at an object at some distance from you and which is -below the eye, and fix both your eyes upon it and with one hand -firmly hold the upper lid open while with the other you push up the -under lid--still keeping your eyes fixed on the object gazed at--you -will see that object double; one [image] remaining steady, and the -other moving in a contrary direction to the pressure of your finger -on the lower eyelid. How false the opinion is of those who say that -this happens because the pupil of the eye is displaced from its -position. - -How the above mentioned facts prove that the pupil acts upside down -in seeing. - -[Footnote: 82. 14--17. The subject indicated by these two headings is -fully discussed in the two chapters that follow them in the -original; but it did not seem to me appropriate to include them -here.] - -Demostration of perspective by means of a vertical glass plane -(83-85). - -83. - -OF THE PLANE OF GLASS. - -Perspective is nothing else than seeing place [or objects] behind a -plane of glass, quite transparent, on the surface of which the -objects behind that glass are to be drawn. These can be traced in -pyramids to the point in the eye, and these pyramids are intersected -on the glass plane. - -84. - -Pictorial perspective can never make an object at the same distance, -look of the same size as it appears to the eye. You see that the -apex of the pyramid _f c d_ is as far from the object _c_ _d_ as the -same point _f_ is from the object _a_ _b_; and yet _c_ _d_, which is -the base made by the painter's point, is smaller than _a_ _b_ which -is the base of the lines from the objects converging in the eye and -refracted at _s_ _t_, the surface of the eye. This may be proved by -experiment, by the lines of vision and then by the lines of the -painter's plumbline by cutting the real lines of vision on one and -the same plane and measuring on it one and the same object. - -85. - -PERSPECTIVE. - -The vertical plane is a perpendicular line, imagined as in front of -the central point where the apex of the pyramids converge. And this -plane bears the same relation to this point as a plane of glass -would, through which you might see the various objects and draw them -on it. And the objects thus drawn would be smaller than the -originals, in proportion as the distance between the glass and the -eye was smaller than that between the glass and the objects. - -PERSPECTIVE. - -The different converging pyramids produced by the objects, will -show, on the plane, the various sizes and remoteness of the objects -causing them. - -PERSPECTIVE. - -All those horizontal planes of which the extremes are met by -perpendicular lines forming right angles, if they are of equal width -the more they rise to the level of eye the less this is seen, and -the more the eye is above them the more will their real width be -seen. - -PERSPECTIVE. - -The farther a spherical body is from the eye the more you will see -of it. - -The angle of sight varies with the distance (86-88) - -86. - -A simple and natural method; showing how objects appear to the eye -without any other medium. - -The object that is nearest to the eye always seems larger than -another of the same size at greater distance. The eye _m_, seeing -the spaces _o v x_, hardly detects the difference between them, and -the. reason of this is that it is close to them [Footnote 6: It is -quite inconceivable to me why M. RAVAISSON, in a note to his French -translation of this simple passage should have remarked: _Il est -clair que c'est par erreur que Leonard a ecrit_ per esser visino _au -lieu de_ per non esser visino. (See his printed ed. of MS. A. p. -38.)]; but if these spaces are marked on the vertical plane _n o_ -the space _o v_ will be seen at _o r_, and in the same way the space -_v x_ will appear at _r q_. And if you carry this out in any place -where you can walk round, it will look out of proportion by reason -of the great difference in the spaces _o r_ and _r q_. And this -proceeds from the eye being so much below [near] the plane that the -plane is foreshortened. Hence, if you wanted to carry it out, you -would have [to arrange] to see the perspective through a single hole -which must be at the point _m_, or else you must go to a distance of -at least 3 times the height of the object you see. The plane _o p_ -being always equally remote from the eye will reproduce the objects -in a satisfactory way, so that they may be seen from place to place. - -87. - -How every large mass sends forth its images, which may diminish -through infinity. - -The images of any large mass being infinitely divisible may be -infinitely diminished. - -88. - -Objects of equal size, situated in various places, will be seen by -different pyramids which will each be smaller in proportion as the -object is farther off. - -89. - -Perspective, in dealing with distances, makes use of two opposite -pyramids, one of which has its apex in the eye and the base as -distant as the horizon. The other has the base towards the eye and -the apex on the horizon. Now, the first includes the [visible] -universe, embracing all the mass of the objects that lie in front of -the eye; as it might be a vast landscape seen through a very small -opening; for the more remote the objects are from the eye, the -greater number can be seen through the opening, and thus the pyramid -is constructed with the base on the horizon and the apex in the eye, -as has been said. The second pyramid is extended to a spot which is -smaller in proportion as it is farther from the eye; and this second -perspective [= pyramid] results from the first. - -90. - -SIMPLE PERSPECTIVE. - -Simple perspective is that which is constructed by art on a vertical -plane which is equally distant from the eye in every part. Complex -perspective is that which is constructed on a ground-plan in which -none of the parts are equally distant from the eye. - -91. - -PERSPECTIVE. - -No surface can be seen exactly as it is, if the eye that sees it is -not equally remote from all its edges. - -92. - -WHY WHEN AN OBJECT IS PLACED CLOSE TO THE EYE ITS EDGES ARE -INDISTINCT. - -When an object opposite the eye is brought too close to it, its -edges must become too confused to be distinguished; as it happens -with objects close to a light, which cast a large and indistinct -shadow, so is it with an eye which estimates objects opposite to it; -in all cases of linear perspective, the eye acts in the same way as -the light. And the reason is that the eye has one leading line (of -vision) which dilates with distance and embraces with true -discernment large objects at a distance as well as small ones that -are close. But since the eye sends out a multitude of lines which -surround this chief central one and since these which are farthest -from the centre in this cone of lines are less able to discern with -accuracy, it follows that an object brought close to the eye is not -at a due distance, but is too near for the central line to be able -to discern the outlines of the object. So the edges fall within the -lines of weaker discerning power, and these are to the function of -the eye like dogs in the chase which can put up the game but cannot -take it. Thus these cannot take in the objects, but induce the -central line of sight to turn upon them, when they have put them up. -Hence the objects which are seen with these lines of sight have -confused outlines. - -The relative size of objects with regard to their distance from the -eye (93-98). - -93. - -PERSPECTIVE. - -Small objects close at hand and large ones at a distance, being seen -within equal angles, will appear of the same size. - -94. - -PERSPECTIVE. - -There is no object so large but that at a great distance from the -eye it does not appear smaller than a smaller object near. - -95. - -Among objects of equal size that which is most remote from the eye -will look the smallest. [Footnote: This axiom, sufficiently clear in -itself, is in the original illustrated by a very large diagram, -constructed like that here reproduced under No. 108. - -The same idea is repeated in C. A. I a; I a, stated as follows: -_Infra le cose d'equal grandeza quella si dimostra di minor figura -che sara piu distante dall' ochio_.--] - -96. - -Why an object is less distinct when brought near to the eye, and why -with spectacles, or without the naked eye sees badly either close or -far off [as the case may be]. - -97. - -PERSPECTIVE. - -Among objects of equal size, that which is most remote from the eye -will look the smallest. - -98. - -PERSPECTIVE. - -No second object can be so much lower than the first as that the eye -will not see it higher than the first, if the eye is above the -second. - -PERSPECTIVE. - -And this second object will never be so much higher than the first -as that the eye, being below them, will not see the second as lower -than the first. - -PERSPECTIVE. - -If the eye sees a second square through the centre of a smaller one, -that is nearer, the second, larger square will appear to be -surrounded by the smaller one. - -PERSPECTIVE--PROPOSITION. - -Objects that are farther off can never be so large but that those in -front, though smaller, will conceal or surround them. - -DEFINITION. - -This proposition can be proved by experiment. For if you look -through a small hole there is nothing so large that it cannot be -seen through it and the object so seen appears surrounded and -enclosed by the outline of the sides of the hole. And if you stop it -up, this small stopping will conceal the view of the largest object. - -The apparent size of objects defined by calculation (99-105) - -99. - -OF LINEAR PERSPECTIVE. - -Linear Perspective deals with the action of the lines of sight, in -proving by measurement how much smaller is a second object than the -first, and how much the third is smaller than the second; and so on -by degrees to the end of things visible. I find by experience that -if a second object is as far beyond the first as the first is from -the eye, although they are of the same size, the second will seem -half the size of the first and if the third object is of the same -size as the 2nd, and the 3rd is as far beyond the second as the 2nd -from the first, it will appear of half the size of the second; and -so on by degrees, at equal distances, the next farthest will be half -the size of the former object. So long as the space does not exceed -the length of 20 braccia. But, beyond 20 braccia figures of equal -size will lose 2/4 and at 40 braccia they will lose 9/10, and 19/20 -at 60 braccia, and so on diminishing by degrees. This is if the -picture plane is distant from you twice your own height. If it is -only as far off as your own height, there will be a great difference -between the first braccia and the second. - -[Footnote: This chapter is included in DUFRESNE'S and MANZI'S -editions of the Treatise on Painting. H. LUDWIG, in his commentary, -calls this chapter "_eines der wichtigsten im ganzen Tractat_", but -at the same time he asserts that its substance has been so -completely disfigured in the best MS. copies that we ought not to -regard Leonardo as responsible for it. However, in the case of this -chapter, the old MS. copies agree with the original as it is -reproduced above. From the chapters given later in this edition, -which were written at a subsequent date, it would appear that -Leonardo corrected himself on these points.] - -100. - -OF THE DIMINUTION OF OBJECTS AT VARIOUS DISTANCES. - -A second object as far distant from the first as the first is from -the eye will appear half the size of the first, though they be of -the same size really. - -OF THE DEGREES OF DIMINUTION. - -If you place the vertical plane at one braccio from the eye, the -first object, being at a distance of 4 braccia from your eye will -diminish to 3/4 of its height at that plane; and if it is 8 braccia -from the eye, to 7/8; and if it is 16 braccia off, it will diminish -to 15/16 of its height and so on by degrees, as the space doubles -the diminution will double. - -101. - -Begin from the line _m f_ with the eye below; then go up and do the -same with the line _n f_, then with the eye above and close to the 2 -gauges on the ground look at _m n_; then as _c m_ is to _m n_ so -will _n m_ be to _n s_. - -If _a n_ goes 3 times into _f b, m p_ will do the same into _p g_. -Then go backwards so far as that _c d_ goes twice into _a n_ and _p -g_ will be equal to _g h_. And _m p_ will go into _h p_ as often as -_d c_ into _o p_. - -[Footnote: The first three lines are unfortunately very obscure.] - -102. - -I GIVE THE DEGREES OF THE OBJECTS SEEN BY THE EYE AS THE MUSICIAN -DOES THE NOTES HEARD BY THE EAR. - -Although the objects seen by the eye do, in fact, touch each other -as they recede, I will nevertheless found my rule on spaces of 20 -braccia each; as a musician does with notes, which, though they can -be carried on one into the next, he divides into degrees from note -to note calling them 1st, 2nd, 3rd, 4th, 5th; and has affixed a name -to each degree in raising or lowering the voice. - -103. - -PERSPECTIVE. - -Let _f_ be the level and distance of the eye; and _a_ the vertical -plane, as high as a man; let _e_ be a man, then I say that on the -plane this will be the distance from the plane to the 2nd man. - -104. - -The differences in the diminution of objects of equal size in -consequence of their various remoteness from the eye will bear among -themselves the same proportions as those of the spaces between the -eye and the different objects. - -Find out how much a man diminishes at a certain distance and what -its length is; and then at twice that distance and at 3 times, and -so make your general rule. - -105. - -The eye cannot judge where an object high up ought to descend. - -106. - -PERSPECTIVE. - -If two similar and equal objects are placed one beyond the other at -a given distance the difference in their size will appear greater in -proportion as they are nearer to the eye that sees them. And -conversely there will seem to be less difference in their size in -proportion as they are remote from the eve. - -This is proved by the proportions of their distances among -themselves; for, if the first of these two objects were as far from -the eye, as the 2nd from the first this would be called the second -proportion: since, if the first is at 1 braccia from the eye and the -2nd at two braccia, two being twice as much as one, the first object -will look twice as large as the second. But if you place the first -at a hundred braccia from you and the second at a hundred and one, -you will find that the first is only so much larger than the second -as 100 is less than 101; and the converse is equally true. And -again, the same thing is proved by the 4th of this book which shows -that among objects that are equal, there is the same proportion in -the diminution of the size as in the increase in the distance from -the eye of the spectator. - -On natural perspective (107--109). - -107. - -OF EQUAL OBJECTS THE MOST REMOTE LOOK THE SMALLEST. - -The practice of perspective may be divided into ... parts [Footnote -4: _in_ ... _parte_. The space for the number is left blank in the -original.], of which the first treats of objects seen by the eye at -any distance; and it shows all these objects just as the eye sees -them diminished, without obliging a man to stand in one place rather -than another so long as the plane does not produce a second -foreshortening. - -But the second practice is a combination of perspective derived -partly from art and partly from nature and the work done by its -rules is in every portion of it, influenced by natural perspective -and artificial perspective. By natural perspective I mean that the -plane on which this perspective is represented is a flat surface, -and this plane, although it is parallel both in length and height, -is forced to diminish in its remoter parts more than in its nearer -ones. And this is proved by the first of what has been said above, -and its diminution is natural. But artificial perspective, that is -that which is devised by art, does the contrary; for objects equal -in size increase on the plane where it is foreshortened in -proportion as the eye is more natural and nearer to the plane, and -as the part of the plane on which it is figured is farther from the -eye. - -And let this plane be _d e_ on which are seen 3 equal circles which -are beyond this plane _d e_, that is the circles _a b c_. Now you -see that the eye _h_ sees on the vertical plane the sections of the -images, largest of those that are farthest and smallest of the -nearest. - -108. - -Here follows what is wanting in the margin at the foot on the other -side of this page. - -Natural perspective acts in a contrary way; for, at greater -distances the object seen appears smaller, and at a smaller distance -the object appears larger. But this said invention requires the -spectator to stand with his eye at a small hole and then, at that -small hole, it will be very plain. But since many (men's) eyes -endeavour at the same time to see one and the same picture produced -by this artifice only one can see clearly the effect of this -perspective and all the others will see confusion. It is well -therefore to avoid such complex perspective and hold to simple -perspective which does not regard planes as foreshortened, but as -much as possible in their proper form. This simple perspective, in -which the plane intersects the pyramids by which the images are -conveyed to the eye at an equal distance from the eye is our -constant experience, from the curved form of the pupil of the eye on -which the pyramids are intersected at an equal distance from the -visual virtue. - -[Footnote 24: _la prima di sopra_ i. e. the first of the three -diagrams which, in the original MS., are placed in the margin at the -beginning of this chapter.] - -109. - -OF A MIXTURE OF NATURAL AND ARTIFICIAL PERSPECTIVE. - -This diagram distinguishes natural from artificial perspective. But -before proceeding any farther I will define what is natural and what -is artificial perspective. Natural perspective says that the more -remote of a series of objects of equal size will look the smaller, -and conversely, the nearer will look the larger and the apparent -size will diminish in proportion to the distance. But in artificial -perspective when objects of unequal size are placed at various -distances, the smallest is nearer to the eye than the largest and -the greatest distance looks as though it were the least of all; and -the cause of this is the plane on which the objects are represented; -and which is at unequal distances from the eye throughout its -length. And this diminution of the plane is natural, but the -perspective shown upon it is artificial since it nowhere agrees with -the true diminution of the said plane. Whence it follows, that when -the eye is somewhat removed from the [station point of the] -perspective that it has been gazing at, all the objects represented -look monstrous, and this does not occur in natural perspective, -which has been defined above. Let us say then, that the square _a b -c d_ figured above is foreshortened being seen by the eye situated -in the centre of the side which is in front. But a mixture of -artificial and natural perspective will be seen in this tetragon -called _el main_ [Footnote 20: _el main_ is quite legibly written in -the original; the meaning and derivation of the word are equally -doubtful.], that is to say _e f g h_ which must appear to the eye of -the spectator to be equal to _a b c d_ so long as the eye remains in -its first position between _c_ and _d_. And this will be seen to -have a good effect, because the natural perspective of the plane -will conceal the defects which would [otherwise] seem monstrous. - -_III._ - -_Six books on Light and Shade._ - -_Linear Perspective cannot be immediately followed by either the_ -"prospettiva de' perdimenti" _or the_ "prospettiva de' colori" _or -the aerial perspective; since these branches of the subject -presuppose a knowledge of the principles of Light and Shade. No -apology, therefore, is here needed for placing these immediately -after Linear Perspective._ - -_We have various plans suggested by Leonardo for the arrangement of -the mass of materials treating of this subject. Among these I have -given the preference to a scheme propounded in No._ III, _because, -in all probability, we have here a final and definite purpose -expressed. Several authors have expressed it as their opinion that -the Paris Manuscript_ C _is a complete and finished treatise on -Light and Shade. Certainly, the Principles of Light and Shade form -by far the larger portion of this MS. which consists of two separate -parts; still, the materials are far from being finally arranged. It -is also evident that he here investigates the subject from the point -of view of the Physicist rather than from that of the Painter._ - -_The plan of a scheme of arrangement suggested in No._ III _and -adopted by me has been strictly adhered to for the first four Books. -For the three last, however, few materials have come down to us; and -it must be admitted that these three Books would find a far more -appropriate place in a work on Physics than in a treatise on -Painting. For this reason I have collected in Book V all the -chapters on Reflections, and in Book VI I have put together and -arranged all the sections of MS._ C _that belong to the book on -Painting, so far as they relate to Light and Shade, while the -sections of the same MS. which treat of the_ "Prospettiva de' -perdimenti" _have, of course, been excluded from the series on Light -and Shade._ - -[Footnote III: This text has already been published with some slight -variations in Dozio's pamphlet _Degli scritti e disegni di Leonardo -da Vinci_, Milan 1871, pp. 30--31. Dozio did not transcribe it from -the original MS. which seems to have remained unknown to him, but -from an old copy (MS. H. 227 in the Ambrosian Library).] - -GENERAL INTRODUCTION. - -Prolegomena. - -110. - -You must first explain the theory and then the practice. First you -must describe the shadows and lights on opaque objects, and then on -transparent bodies. - -Scheme of the books on Light and shade. - -111. - -INTRODUCTION. - -[Having already treated of the nature of shadows and the way in -which they are cast [Footnote 2: _Avendo io tractato._--We may -suppose that he here refers to some particular MS., possibly Paris -C.], I will now consider the places on which they fall; and their -curvature, obliquity, flatness or, in short, any character I may be -able to detect in them.] - -Shadow is the obstruction of light. Shadows appear to me to be of -supreme importance in perspective, because, without them opaque and -solid bodies will be ill defined; that which is contained within -their outlines and their boundaries themselves will be -ill-understood unless they are shown against a background of a -different tone from themselves. And therefore in my first -proposition concerning shadow I state that every opaque body is -surrounded and its whole surface enveloped in shadow and light. And -on this proposition I build up the first Book. Besides this, shadows -have in themselves various degrees of darkness, because they are -caused by the absence of a variable amount of the luminous rays; and -these I call Primary shadows because they are the first, and -inseparable from the object to which they belong. And on this I will -found my second Book. From these primary shadows there result -certain shaded rays which are diffused through the atmosphere and -these vary in character according to that of the primary shadows -whence they are derived. I shall therefore call these shadows -Derived shadows because they are produced by other shadows; and the -third Book will treat of these. Again these derived shadows, where -they are intercepted by various objects, produce effects as various -as the places where they are cast and of this I will treat in the -fourth Book. And since all round the derived shadows, where the -derived shadows are intercepted, there is always a space where the -light falls and by reflected dispersion is thrown back towards its -cause, it meets the original shadow and mingles with it and modifies -it somewhat in its nature; and on this I will compose my fifth Book. -Besides this, in the sixth Book I will investigate the many and -various diversities of reflections resulting from these rays which -will modify the original [shadow] by [imparting] some of the various -colours from the different objects whence these reflected rays are -derived. Again, the seventh Book will treat of the various distances -that may exist between the spot where the reflected rays fall and -that where they originate, and the various shades of colour which -they will acquire in falling on opaque bodies. - -Different principles and plans of treatment (112--116). - -112. - -First I will treat of light falling through windows which I will -call Restricted [Light] and then I will treat of light in the open -country, to which I will give the name of diffused Light. Then I -will treat of the light of luminous bodies. - -113. - -OF PAINTING. - -The conditions of shadow and light [as seen] by the eye are 3. Of -these the first is when the eye and the light are on the same side -of the object seen; the 2nd is when the eye is in front of the -object and the light is behind it. The 3rd is when the eye is in -front of the object and the light is on one side, in such a way as -that a line drawn from the object to the eye and one from the object -to the light should form a right angle where they meet. - -114. - -OF PAINTING. - -This is another section: that is, of the nature of a reflection -(from) an object placed between the eye and the light under various -aspects. - -115. - -OF PAINTING. - -As regards all visible objects 3 things must be considered. These -are the position of the eye which sees: that of the object seen -[with regard] to the light, and the position of the light which -illuminates the object, _b_ is the eye, _a_ the object seen, _c_ the -light, _a_ is the eye, _b_ the illuminating body, _c_ is the -illuminated object. - -116. - -Let _a_ be the light, _b_ the eye, _c_ the object seen by the eye -and in the light. These show, first, the eye between the light and -the body; the 2nd, the light between the eye and the body; the 3rd -the body between the eye and the light, _a_ is the eye, _b_ the -illuminated object, _c_ the light. - -117. - -OF PAINTING. - -OF THE THREE KINDS OF LIGHT THAT ILLUMINATE OPAQUE BODIES. - -The first kind of Light which may illuminate opaque bodies is called -Direct light--as that of the sun or any other light from a window or -flame. The second is Diffused [universal] light, such as we see in -cloudy weather or in mist and the like. The 3rd is Subdued light, -that is when the sun is entirely below the horizon, either in the -evening or morning. - -118. - -OF LIGHT. - -The lights which may illuminate opaque bodies are of 4 kinds. These -are: diffused light as that of the atmosphere, within our horizon. -And Direct, as that of the sun, or of a window or door or other -opening. The third is Reflected light; and there is a 4th which is -that which passes through [semi] transparent bodies, as linen or -paper or the like, but not transparent like glass, or crystal, or -other diaphanous bodies, which produce the same effect as though -nothing intervened between the shaded object and the light that -falls upon it; and this we will discuss fully in our discourse. - -Definition of the nature of shadows (119--122). - -119. - -WHAT LIGHT AND SHADOW ARE. - -Shadow is the absence of light, merely the obstruction of the -luminous rays by an opaque body. Shadow is of the nature of -darkness. Light [on an object] is of the nature of a luminous body; -one conceals and the other reveals. They are always associated and -inseparable from all objects. But shadow is a more powerful agent -than light, for it can impede and entirely deprive bodies of their -light, while light can never entirely expel shadow from a body, that -is from an opaque body. - -120. - -Shadow is the diminution of light by the intervention of an opaque -body. Shadow is the counterpart of the luminous rays which are cut -off by an opaque body. - -This is proved because the shadow cast is the same in shape and size -as the luminous rays were which are transformed into a shadow. - -121. - -Shadow is the diminution alike of light and of darkness, and stands -between darkness and light. - -A shadow may be infinitely dark, and also of infinite degrees of -absence of darkness. - -The beginnings and ends of shadow lie between the light and darkness -and may be infinitely diminished and infinitely increased. Shadow is -the means by which bodies display their form. - -The forms of bodies could not be understood in detail but for -shadow. - -122. - -OF THE NATURE OF SHADOW. - -Shadow partakes of the nature of universal matter. All such matters -are more powerful in their beginning and grow weaker towards the -end, I say at the beginning, whatever their form or condition may be -and whether visible or invisible. And it is not from small -beginnings that they grow to a great size in time; as it might be a -great oak which has a feeble beginning from a small acorn. Yet I may -say that the oak is most powerful at its beginning, that is where it -springs from the earth, which is where it is largest (To return:) -Darkness, then, is the strongest degree of shadow and light is its -least. Therefore, O Painter, make your shadow darkest close to the -object that casts it, and make the end of it fading into light, -seeming to have no end. - -Of the various kinds of shadows. (123-125). - -123. - -Darkness is absence of light. Shadow is diminution of light. -Primitive shadow is that which is inseparable from a body not in the -light. Derived shadow is that which is disengaged from a body in -shadow and pervades the air. A cast transparent shadow is that which -is surrounded by an illuminated surface. A simple shadow is one -which receives no light from the luminous body which causes it. A -simple shadow begins within the line which starts from the edge of -the luminous body _a b_. - -124. - -A simple shadow is one where no light at all interferes with it. - -A compound shadow is one which is somewhat illuminated by one or -more lights. - -125. - -WHAT IS THE DIFFERENCE BETWEEN A SHADOW THAT IS INSEPARABLE FROM A -BODY AND A CAST SHADOW? - -An inseparable shadow is that which is never absent from the -illuminated body. As, for instance a ball, which so long as it is in -the light always has one side in shadow which never leaves it for -any movement or change of position in the ball. A separate shadow -may be and may not be produced by the body itself. Suppose the ball -to be one braccia distant from a wall with a light on the opposite -side of it; this light will throw upon the wall exactly as broad a -shadow as is to be seen on the side of the ball that is turned -towards the wall. That portion of the cast shadow will not be -visible when the light is below the ball and the shadow is thrown up -towards the sky and finding no obstruction on its way is lost. - -126. - -HOW THERE ARE 2 KINDS OF LIGHT, ONE SEPARABLE FROM, AND THE OTHER -INSEPARABLE FROM BODIES. - -Of the various kinds of light (126, 127). - -Separate light is that which falls upon the body. Inseparable light -is the side of the body that is illuminated by that light. One is -called primary, the other derived. And, in the same way there are -two kinds of shadow:--One primary and the other derived. The primary -is that which is inseparable from the body, the derived is that -which proceeds from the body conveying to the surface of the wall -the form of the body causing it. - -127. - -How there are 2 different kinds of light; one being called diffused, -the other restricted. The diffused is that which freely illuminates -objects. The restricted is that which being admitted through an -opening or window illuminates them on that side only. - -[Footnote: At the spot marked _A_ in the first diagram Leonardo -wrote _lume costretto_ (restricted light). At the spot _B_ on the -second diagram he wrote _lume libero_ (diffused light).] - -General remarks (128. 129). - -128. - -Light is the chaser away of darkness. Shade is the obstruction of -light. Primary light is that which falls on objects and causes light -and shade. And derived lights are those portions of a body which are -illuminated by the primary light. A primary shadow is that side of a -body on which the light cannot fall. - -The general distribution of shadow and light is that sum total of -the rays thrown off by a shaded or illuminated body passing through -the air without any interference and the spot which intercepts and -cuts off the distribution of the dark and light rays. - -And the eye can best distinguish the forms of objects when it is -placed between the shaded and the illuminated parts. - -129. - -MEMORANDUM OF THINGS I REQUIRE TO HAVE GRANTED [AS AXIOMS] IN MY -EXPLANATION OF PERSPECTIVE. - -I ask to have this much granted me--to assert that every ray -passing through air of equal density throughout, travels in a -straight line from its cause to the object or place it falls upon. - -FIRST BOOK ON LIGHT AND SHADE. - -On the nature of light (130. 131). - -130. - -The reason by which we know that a light radiates from a single -centre is this: We plainly see that a large light is often much -broader than some small object which nevertheless--and although the -rays [of the large light] are much more than twice the extent [of -the small body]--always has its shadow cast on the nearest surface -very visibly. Let _c f_ be a broad light and _n_ be the object in -front of it, casting a shadow on the plane, and let _a b_ be the -plane. It is clear that it is not the broad light that will cast the -shadow _n_ on the plane, but that the light has within it a centre -is shown by this experiment. The shadow falls on the plane as is -shown at _m o t r_. - -[Footnote 13: In the original MS. no explanatory text is placed -after this title-line; but a space is left for it and the text -beginning at line 15 comes next.] Why, to two [eyes] or in front of -two eyes do 3 objects appear as two? - -Why, when you estimate the direction of an object with two sights -the nearer appears confused. I say that the eye projects an infinite -number of lines which mingle or join those reaching it which come to -it from the object looked at. And it is only the central and -sensible line that can discern and discriminate colours and objects; -all the others are false and illusory. And if you place 2 objects at -half an arm's length apart if the nearer of the two is close to the -eye its form will remain far more confused than that of the second; -the reason is that the first is overcome by a greater number of -false lines than the second and so is rendered vague. - -Light acts in the same manner, for in the effects of its lines -(=rays), and particularly in perspective, it much resembles the eye; -and its central rays are what cast the true shadow. When the object -in front of it is too quickly overcome with dim rays it will cast a -broad and disproportionate shadow, ill defined; but when the object -which is to cast the shadow and cuts off the rays near to the place -where the shadow falls, then the shadow is distinct; and the more so -in proportion as the light is far off, because at a long distance -the central ray is less overcome by false rays; because the lines -from the eye and the solar and other luminous rays passing through -the atmosphere are obliged to travel in straight lines. Unless they -are deflected by a denser or rarer air, when they will be bent at -some point, but so long as the air is free from grossness or -moisture they will preserve their direct course, always carrying the -image of the object that intercepts them back to their point of -origin. And if this is the eye, the intercepting object will be seen -by its colour, as well as by form and size. But if the intercepting -plane has in it some small perforation opening into a darker -chamber--not darker in colour, but by absence of light--you will see -the rays enter through this hole and transmitting to the plane -beyond all the details of the object they proceed from both as to -colour and form; only every thing will be upside down. But the size -[of the image] where the lines are reconstructed will be in -proportion to the relative distance of the aperture from the plane -on which the lines fall [on one hand] and from their origin [on the -other]. There they intersect and form 2 pyramids with their point -meeting [a common apex] and their bases opposite. Let _a b_ be the -point of origin of the lines, _d e_ the first plane, and _c_ the -aperture with the intersection of the lines; _f g_ is the inner -plane. You will find that _a_ falls upon the inner plane below at -_g_, and _b_ which is below will go up to the spot _f_; it will be -quite evident to experimenters that every luminous body has in -itself a core or centre, from which and to which all the lines -radiate which are sent forth by the surface of the luminous body and -reflected back to it; or which, having been thrown out and not -intercepted, are dispersed in the air. - -131. - -THE RAYS WHETHER SHADED OR LUMINOUS HAVE GREATER STRENGTH AND EFFECT -AT THEIR POINTS THAN AT THEIR SIDES. - -Although the points of luminous pyramids may extend into shaded -places and those of pyramids of shadow into illuminated places, and -though among the luminous pyramids one may start from a broader base -than another; nevertheless, if by reason of their various length -these luminous pyramids acquire angles of equal size their light -will be equal; and the case will be the same with the pyramids of -shadow; as may be seen in the intersected pyramids _a b c_ and _d e -f_, which though their bases differ in size are equal as to breadth -and light. - -[Footnote: 51--55: This supplementary paragraph is indicated as being -a continuation of line 45, by two small crosses.] - -The difference between light and lustre (132--135). - -132. - -Of the difference between light and lustre; and that lustre is not -included among colours, but is saturation of whiteness, and derived -from the surface of wet bodies; light partakes of the colour of the -object which reflects it (to the eye) as gold or silver or the like. - -133. - -OF THE HIGHEST LIGHTS WHICH TURN AND MOVE AS THE EYE MOVES WHICH -SEES THE OBJECT. - -Suppose the body to be the round object figured here and let the -light be at the point _a_, and let the illuminated side of the -object be _b c_ and the eye at the point _d_: I say that, as lustre -is every where and complete in each part, if you stand at the point -_d_ the lustre will appear at _c_, and in proportion as the eye -moves from _d_ to _a_, the lustre will move from _c_ to _n_. - -134. - -OF PAINTING. - -Heigh light or lustre on any object is not situated [necessarily] in -the middle of an illuminated object, but moves as and where the eye -moves in looking at it. - -135. - -OF LIGHT AND LUSTRE. - -What is the difference between light and the lustre which is seen on -the polished surface of opaque bodies? - -The lights which are produced from the polished surface of opaque -bodies will be stationary on stationary objects even if the eye on -which they strike moves. But reflected lights will, on those same -objects, appear in as many different places on the surface as -different positions are taken by the eye. - -WHAT BODIES HAVE LIGHT UPON THEM WITHOUT LUSTRE? - -Opaque bodies which have a hard and rough surface never display any -lustre in any portion of the side on which the light falls. - -WHAT BODIES WILL DISPLAY LUSTRE BUT NOT LOOK ILLUMINATED? - -Those bodies which are opaque and hard with a hard surface reflect -light [lustre] from every spot on the illuminated side which is in a -position to receive light at the same angle of incidence as they -occupy with regard to the eye; but, as the surface mirrors all the -surrounding objects, the illuminated [body] is not recognisable in -these portions of the illuminated body. - -136. - -The relations of luminous to illuminated bodies. - -The middle of the light and shade on an object in light and shade is -opposite to the middle of the primary light. All light and shadow -expresses itself in pyramidal lines. The middle of the shadow on any -object must necessarily be opposite the middle of its light, with a -direct line passing through the centre of the body. The middle of -the light will be at _a_, that of the shadow at _b_. [Again, in -bodies shown in light and shade the middle of each must coincide -with the centre of the body, and a straight line will pass through -both and through that centre.] - -[Footnote: In the original MS., at the spot marked _a_ of the first -diagram Leonardo wrote _primitiuo_, and at the spot marked -_c_--_primitiva_ (primary); at the spot marked _b_ he wrote -_dirivatiuo_ and at _d deriuatiua_ (derived).] - -Experiments on the relation of light and shadow within a room -(137--140). - -137. - -SHOWS HOW LIGHT FROM ANY SIDE CONVERGES TO ONE POINT. - -Although the balls _a b c_ are lighted from one window, -nevertheless, if you follow the lines of their shadows you will see -they intersect at a point forming the angle _n_. - -[Footnote: The diagram belonging to this passage is slightly -sketched on Pl. XXXII; a square with three balls below it. The first -three lines of the text belonging to it are written above the sketch -and the six others below it.] - -138. - -Every shadow cast by a body has a central line directed to a single -point produced by the intersection of luminous lines in the middle -of the opening and thickness of the window. The proposition stated -above, is plainly seen by experiment. Thus if you draw a place with -a window looking northwards, and let this be _s f_, you will see a -line starting from the horizon to the east, which, touching the 2 -angles of the window _o f_, reaches _d_; and from the horizon on the -west another line, touching the other 2 angles _r s_, and ending at -_c_; and their intersection falls exactly in the middle of the -opening and thickness of the window. Again, you can still better -confirm this proof by placing two sticks, as shown at _g h_; and you -will see the line drawn from the centre of the shadow directed to -the centre _m_ and prolonged to the horizon _n f_. - -[Footnote: _B_ here stands for _cerchio del' orizonte tramontano_ on -the original diagram (the circle of the horizon towards the North); -_A_ for _levante_ (East) and _C_ for _ponete_ (West).] - -139. - -Every shadow with all its variations, which becomes larger as its -distance from the object is greater, has its external lines -intersecting in the middle, between the light and the object. This -proposition is very evident and is confirmed by experience. For, if -_a b_ is a window without any object interposed, the luminous -atmosphere to the right hand at _a_ is seen to the left at _d_. And -the atmosphere at the left illuminates on the right at _c_, and the -lines intersect at the point _m_. - -[Footnote: _A_ here stands for _levante_ (East), _B_ for _ponente_ -(West).] - -140. - -Every body in light and shade is situated between 2 pyramids one -dark and the other luminous, one is visible the other is not. But -this only happens when the light enters by a window. Supposing _a b_ -to be the window and _r_ the body in light and shade, the light to -the right hand _z_ will pass the object to the left and go on to -_p_; the light to the left at _k_ will pass to the right of the -object at _i_ and go on to _m_ and the two lines will intersect at -_c_ and form a pyramid. Then again _a_ _b_ falls on the shaded body -at _i_ _g_ and forms a pyramid _f_ _i_ _g_. _f_ will be dark because -the light _a_ _b_ can never fall there; _i_ _g_ _c_ will be -illuminated because the light falls upon it. - -Light and shadow with regard to the position of the eye (141--145). - -141. - -Every shaded body that is larger than the pupil and that interposes -between the luminous body and the eye will be seen dark. - -When the eye is placed between the luminous body and the objects -illuminated by it, these objects will be seen without any shadow. - -[Footnote: The diagram which in the original stands above line 1 is -given on Plate II, No 2. Then, after a blank space of about eight -lines, the diagram Plate II No 3 is placed in the original. There is -no explanation of it beyond the one line written under it.] - -142. - -Why the 2 lights one on each side of a body having two pyramidal -sides of an obtuse apex leave it devoid of shadow. - -[Footnote: The sketch illustrating this is on Plate XLI No 1.] - -143. - -A body in shadow situated between the light and the eye can never -display its illuminated portion unless the eye can see the whole of -the primary light. - -[Footnote: _A_ stands for _corpo_ (body), _B_ for _lume_ (light).] - -144. - -The eye which looks (at a spot) half way between the shadow and the -light which surrounds the body in shadow will see that the deepest -shadows on that body will meet the eye at equal angles, that is at -the same angle as that of sight. - -[Footnote: In both these diagrams _A_ stands for _lume_ (light) _B_ -for _ombra_ (shadow).] - -145. - -OF THE DIFFERENT LIGHT AND SHADE IN VARIOUS ASPECTS AND OF OBJECTS -PLACED IN THEM. - -If the sun is in the East and you look towards the West you will see -every thing in full light and totally without shadow because you see -them from the same side as the sun: and if you look towards the -South or North you will see all objects in light and shade, because -you see both the side towards the sun and the side away from it; and -if you look towards the coming of the sun all objects will show you -their shaded side, because on that side the sun cannot fall upon -them. - -The law of the incidence of light. - -146. - -The edges of a window which are illuminated by 2 lights of equal -degrees of brightness will not reflect light of equal brightness -into the chamber within. - -If _b_ is a candle and _a c_ our hemisphere both will illuminate the -edges of the window _m_ _n_, but light _b_ will only illuminate _f -g_ and the hemisphere _a_ will light all of _d e_. - -147. - -OF PAINTING. - -That part of a body which receives the luminous rays at equal angles -will be in a higher light than any other part of it. - -And the part which the luminous rays strike between less equal -angles will be less strongly illuminated. - -SECOND BOOK ON LIGHT AND SHADE. - -Gradations of strength in the shadows (148. 149). - -148. - -THAT PORTION OF A BODY IN LIGHT AND SHADE WILL BE LEAST LUMINOUS -WHICH IS SEEN UNDER THE LEAST AMOUNT OF LIGHT. - -That part of the object which is marked _m_ is in the highest light -because it faces the window _a d_ by the line _a f_; _n_ is in the -second grade because the light _b d_ strikes it by the line _b e_; -_o_ is in the third grade, as the light falls on it from _c d_ by -the line _c h_; _p_ is the lowest light but one as _c d_ falls on it -by the line _d v_; _q_ is the deepest shadow for no light falls on -it from any part of the window. - -In proportion as _c d_ goes into _a d_ so will _n r s_ be darker -than _m_, and all the rest is space without shadow. - -[Footnote: The diagram belonging to this chapter is No. 1 on Plate -III. The letters _a b e d_ and _r_ are not reproduced in facsimile -of the original, but have been replaced by ordinary type in the -margin. 5-12. The original text of these lines is reproduced within -the diagram.--Compare No 275.] - -149. - -The light which falls on a shaded body at the acutest angle receives -the highest light, and the darkest portion is that which receives it -at an obtuse angle and both the light and the shadow form pyramids. -The angle _c_ receives the highest grade of light because it is -directly in front of the window _a b_ and the whole horizon of the -sky _m x_. The angle _a_ differs but little from _c_ because the -angles which divide it are not so unequal as those below, and only -that portion of the horizon is intercepted which lies between _y_ -and _x_. Although it gains as much on the other side its line is -nevertheless not very strong because one angle is smaller than its -fellow. The angles _e i_ will have less light because they do not -see much of the light _m s_ and the light _v x_ and their angles are -very unequal. Yhe angle _k_ and the angle _f_ are each placed -between very unequal angles and therefore have but little light, -because at _k_ it has only the light _p t_, and at _f_ only _t q_; -_o g_ is the lowest grade of light because this part has no light at -all from the sky; and thence come the lines which will reconstruct a -pyramid that is the counterpart of the pyramid _c_; and this pyramid -_l_ is in the first grade of shadow; for this too is placed between -equal angles directly opposite to each other on either side of a -straight line which passes through the centre of the body and goes -to the centre of the light. The several luminous images cast within -the frame of the window at the points _a_ and _b_ make a light which -surrounds the derived shadow cast by the solid body at the points 4 -and 6. The shaded images increase from _o g_ and end at 7 and 8. - -[Footnote: The diagram belonging to this chapter is No. 2 on Plate -III. In the original it is placed between lines 3 and 4, and in the -reproduction these are shown in part. The semi circle above is -marked _orizonte_ (horizon). The number 6 at the left hand side, -outside the facsimile, is in the place of a figure which has become -indistinct in the original.] - -On the intensity of shadows as dependent on the distance from the -light (150-152). - -150. - -The smaller the light that falls upon an object the more shadow it -will display. And the light will illuminate a smaller portion of the -object in proportion as it is nearer to it; and conversely, a larger -extent of it in proportion as it is farther off. - -A light which is smaller than the object on which it falls will -light up a smaller extent of it in proportion as it is nearer to it, -and the converse, as it is farther from it. But when the light is -larger than the object illuminated it will light a larger extent of -the object in proportion as it is nearer and the converse when they -are farther apart. - -151. - -That portion of an illuminated object which is nearest to the source -of light will be the most strongly illuminated. - -152. - -That portion of the primary shadow will be least dark which is -farthest from the edges. - -The derived shadow will be darker than the primary shadow where it -is contiguous with it. - -On the proportion of light and shade (153-157). - -153. - -That portion of an opaque body will be more in shade or more in -light, which is nearer to the dark body, by which it is shaded, or -to the light that illuminates it. - -Objects seen in light and shade show in greater relief than those -which are wholly in light or in shadow. - -154. - -OF PERSPECTIVE. - -The shaded and illuminated sides of opaque objects will display the -same proportion of light and darkness as their objects [Footnote 6: -The meaning of _obbietti_ (objects) is explained in no 153, lines -1-4.--Between the title-line and the next there is, in the -original, a small diagram representing a circle described round a -square.]. - -155. - -OF PAINTING. - -The outlines and form of any part of a body in light and shade are -indistinct in the shadows and in the high lights; but in the -portions between the light and the shadows they are highly -conspicuous. - -156. - -OF PAINTING. - -Among objects in various degrees of shade, when the light proceeds -from a single source, there will be the same proportion in their -shadows as in the natural diminution of the light and the same must -be understood of the degrees of light. - -157. - -A single and distinct luminous body causes stronger relief in the -object than a diffused light; as may be seen by comparing one side -of a landscape illuminated by the sun, and one overshadowed by -clouds, and so illuminated only by the diffused light of the -atmosphere. - -THIRD BOOK ON LIGHT AND SHADE. - -Definition of derived shadow (158. 159). - -158. - -Derived shadow cannot exist without primary shadow. This is proved -by the first of this which says: Darkness is the total absence of -light, and shadow is an alleviation of darkness and of light, and it -is more or less dark or light in proportion as the darkness is -modified by the light. - -159. - -Shadow is diminution of light. - -Darkness is absence of light. - -Shadow is divided into two kinds, of which the first is called -primary shadow, the second is derived shadow. The primary shadow is -always the basis of the derived shadow. - -The edges of the derived shadow are straight lines. - -[Footnote: The theory of the _ombra_ dirivativa_--a technical -expression for which there is no precise English equivalent is -elaborately treated by Leonardo. But both text and diagrams (as Pl. -IV, 1-3 and Pl. V) must at once convince the student that the -distinction he makes between _ombra primitiva_ and _ombra -dirivativa_ is not merely justifiable but scientific. _Ombra -dirivativa_ is by no means a mere abstract idea. This is easily -proved by repeating the experiment made by Leonardo, and by filling -with smoke the room in which the existence of the _ombra dirivativa_ -is investigated, when the shadow becomes visible. Nor is it -difficult to perceive how much of Leonardo's teaching depended on -this theory. The recognised, but extremely complicated science of -cast shadows--_percussione dell' ombre dirivative_ as Leonardo -calls them--is thus rendered more intelligible if not actually -simpler, and we must assume this theory as our chief guide through -the investigations which follow.] - -The darkness of the derived shadow diminishes in proportion as it is -remote from the primary shadow. - -Different sorts of derived shadows (160-162). - -160. - -SHADOW AND LIGHT. - -The forms of shadows are three: inasmuch as if the solid body which -casts the shadow is equal (in size) to the light, the shadow -resembles a column without any termination (in length). If the body -is larger than the light the shadow resembles a truncated and -inverted pyramid, and its length has also no defined termination. -But if the body is smaller than the light, the shadow will resemble -a pyramid and come to an end, as is seen in eclipses of the moon. - -161. - -OF SIMPLE DERIVED SHADOWS. - -The simple derived shadow is of two kinds: one kind which has its -length defined, and two kinds which are undefined; and the defined -shadow is pyramidal. Of the two undefined, one is a column and the -other spreads out; and all three have rectilinear outlines. But the -converging, that is the pyramidal, shadow proceeds from a body that -is smaller than the light, and the columnar from a body equal in -size to the light, and the spreading shadow from a body larger than -the light; &c. - -OF COMPOUND DERIVED SHADOWS. - -Compound derived shadows are of two kinds; that is columnar and -spreading. - -162. - -OF SHADOW. - -Derived shadows are of three kinds of which one is spreading, the -second columnar, the third converging to the point where the two -sides meet and intersect, and beyond this intersection the sides are -infinitely prolonged or straight lines. And if you say, this shadow -must terminate at the angle where the sides meet and extend no -farther, I deny this, because above in the first on shadow I have -proved: that a thing is completely terminated when no portion of it -goes beyond its terminating lines. Now here, in this shadow, we see -the converse of this, in as much as where this derived shadow -originates we obviously have the figures of two pyramids of shadow -which meet at their angles. Hence, if, as [my] opponent says, the -first pyramid of shadow terminates the derivative shadow at the -angle whence it starts, then the second pyramid of shadow--so says -the adversary--must be caused by the angle and not from the body in -shadow; and this is disproved with the help of the 2nd of this which -says: Shadow is a condition produced by a body casting a shadow, and -interposed between this shadow and the luminous body. By this it is -made clear that the shadow is not produced by the angle of the -derived shadow but only by the body casting the shadow; &c. If a -spherical solid body is illuminated by a light of elongated form the -shadow produced by the longest portion of this light will have less -defined outlines than that which is produced by the breadth of the -same light. And this is proved by what was said before, which is: -That a shadow will have less defined outlines in proportion as the -light which causes it is larger, and conversely, the outlines are -clearer in proportion as it is smaller. - -[Footnote: The two diagrams to this chapter are on Plate IV, No. 1.] - -On the relation of derived and primary shadow (163-165). - -163. - -The derived shadow can never resemble the body from which it -proceeds unless the light is of the same form and size as the body -causing the shadow. - -The derived shadow cannot be of the same form as the primary shadow -unless it is intercepted by a plane parallel to it. - -164. - -HOW A CAST SHADOW CAN NEVER BE OF THE SAME SIZE AS THE BODY THAT -CASTS IT. - -If the rays of light proceed, as experience shows, from a single -point and are diffused in a sphere round this point, radiating and -dispersed through the air, the farther they spread the wider they -must spread; and an object placed between the light and a wall is -always imaged larger in its shadow, because the rays that strike it -[Footnote: 7. The following lines are wanting to complete the -logical connection.] would, by the time they have reached the wall, -have become larger. - -165. - -Any shadow cast by a body in light and shade is of the same nature -and character as that which is inseparable from the body. The centre -of the length of a shadow always corresponds to that of the luminous -body [Footnote 6: This second statement of the same idea as in the -former sentence, but in different words, does not, in the original, -come next to the foregoing; sections 172 and 127 are placed between -them.]. It is inevitable that every shadow must have its centre in a -line with the centre of the light. - -On the shape of derived shadows (166-174). - -166. - -OF THE PYRAMIDAL SHADOW. - -The pyramidal shadow produced by a columnar body will be narrower -than the body itself in proportion as the simple derived shadow is -intersected farther from the body which casts it. - -[Footnote 166: Compare the first diagram to No. 161. If we here -conceive of the outlines of the pyramid of shadow on the ground as -prolonged beyond its apex this gives rise to a second pyramid; this -is what is spoken of at the beginning of No. 166.] - -167. - -The cast shadow will be longest when the light is lowest. - -The cast shadow will be shortest when the light is highest. - -168. - -Both the primary and derived shadow will be larger when caused by -the light of a candle than by diffused light. The difference between -the larger and smaller shadows will be in inverse proportion to the -larger and smaller lights causing them. - -[Footnote: In the diagrams _A_ stands for _celo_ (sky), _B_ for -_cadela_ (candle).] - -169. - -ALL BODIES, IN PROPORTION AS THEY ARE NEARER TO, OR FARTHER FROM THE -SOURCE OF LIGHT, WILL PRODUCE LONGER OR SHORTER DERIVED SHADOWS. - -Among bodies of equal size, that one which is illuminated by the -largest light will have the shortest shadow. Experiment confirms -this proposition. Thus the body _m_ _n_ is surrounded by a larger -amount of light than the body _p q_, as is shown above. Let us say -that _v c a b d x_ is the sky, the source of light, and that _s t_ -is a window by which the luminous rays enter, and so _m n_ and _p q_ -are bodies in light and shade as exposed to this light; _m n_ will -have a small derived shadow, because its original shadow will be -small; and the derivative light will be large, again, because the -original light _c d_ will be large and _p q_ will have more derived -shadow because its original shadow will be larger, and its derived -light will be smaller than that of the body _m n_ because that -portion of the hemisphere _a b_ which illuminates it is smaller than -the hemisphere _c d_ which illuminates the body _m n_. - -[Footnote: The diagram, given on Pl. IV, No. 2, stands in the -original between lines 2 and 7, while the text of lines 3 to 6 is -written on its left side. In the reproduction of this diagram the -letter _v_ at the outer right-hand end has been omitted.] - -170. - -The shadow _m_ bears the same proportion to the shadow _n_ as the -line _b c_ to the line _f c_. - -171. - -OF PAINTING. - -Of different shadows of equal strength that which is nearest the eye -will seem the least strong. - -Why is the shadow _e a b_ in the first grade of strength, _b c_ in -the second; _c d_ in the third? The reason is that as from _e a b_ -the sky is nowhere visible, it gets no light whatever from the sky, -and so has no direct [primary] light. _b c_ faces the portion of the -sky _f g_ and is illuminated by it. _c d_ faces the sky at _h k_. _c -d_, being exposed to a larger extent of sky than _b c_, it is -reasonable that it should be more lighted. And thus, up to a certain -distance, the wall _a d_ will grow lighter for the reasons here -given, until the darkness of the room overpowers the light from the -window. - -172. - -When the light of the atmosphere is restricted [by an opening] and -illuminates bodies which cast shadows, these bodies being equally -distant from the centre of the window, that which is most obliquely -placed will cast the largest shadow beyond it. - -173. - -These bodies standing apart in a room lighted by a single window -will have derivative shadows more or less short according as they -are more or less opposite to the window. Among the shadows cast by -bodies of equal mass but at unequal distances from the opening by -which they are illuminated, that shadow will be the longest of the -body which is least in the light. And in proportion as one body is -better illuminated than another its shadow will be shorter than -another. The proportion _n m_ and _e v k_ bear to _r t_ and _v x_ -corresponds with that of the shadow _x_ to 4 and _y_. - -The reason why those bodies which are placed most in front of the -middle of the window throw shorter shadows than those obliquely -situated is:--That the window appears in its proper form and to the -obliquely placed ones it appears foreshortened; to those in the -middle, the window shows its full size, to the oblique ones it -appears smaller; the one in the middle faces the whole hemisphere -that is _e f_ and those on the side have only a strip; that is _q r_ -faces _a b_; and _m n_ faces _c d_; the body in the middle having a -larger quantity of light than those at the sides is lighted from a -point much below its centre, and thus the shadow is shorter. And the -pyramid _g_ 4 goes into _l y_ exactly as often as _a b_ goes into _e -f_. The axis of every derivative shadow passes through 6 1/2 -[Footnote 31: _passa per_ 6 1/2 (passes through 6 1/2). The meaning -of these words is probably this: Each of the three axes of the -derived shadow intersects the centre (_mezzo_) of the primary shadow -(_ombra originale_) and, by prolongation upwards crosses six lines. - -This is self evident only in the middle diagram; but it is equally -true of the side figures if we conceive of the lines 4 _f_, _x n v -m_, _y l k v_, and 4 _e_, as prolonged beyond the semicircle of the -horizon.] and is in a straight line with the centre of the primary -shadow, with the centre of the body casting it and of the derivative -light and with the centre of the window and, finally, with the -centre of that portion of the source of light which is the celestial -hemisphere, _y h_ is the centre of the derived shade, _l h_ of the -primary shadow, _l_ of the body throwing it, _l k_ of the derived -light, _v_ is the centre of the window, _e_ is the final centre of -the original light afforded by that portion of the hemisphere of the -sky which illuminates the solid body. - -[Footnote: Compare the diagram on Pl. IV, No. 3. In the original -this drawing is placed between lines 3 and 22; the rest, from line 4 -to line 21, is written on the left hand margin.] - -174. - -THE FARTHER THE DERIVED SHADOW IS PROLONGED THE LIGHTER IT BECOMES. - -You will find that the proportion of the diameter of the derived -shadow to that of the primary shadow will be the same as that -between the darkness of the primary shadow and that of the derived -shadow. - -[Footnote 6: Compare No. 177.] Let _a b_ be the diameter of the -primary shadow and _c d_ that of the derived shadow, I say that _a -b_ going, as you see, three times into _d c_, the shadow _d c_ will -be three times as light as the shadow _a b_. [Footnote 8: Compare -No. 177.] - -If the size of the illuminating body is larger than that of the -illuminated body an intersection of shadow will occur, beyond which -the shadows will run off in two opposite directions as if they were -caused by two separate lights. - -On the relative intensity of derived shadows (175-179). - -175. - -ON PAINTING. - -The derived shadow is stronger in proportion as it is nearer to its -place of origin. - -176. - -HOW SHADOWS FADE AWAY AT LONG DISTANCES. - -Shadows fade and are lost at long distances because the larger -quantity of illuminated air which lies between the eye and the -object seen tints the shadow with its own colour. - -177. - -_a b_ will be darker than _c d_ in proportion as _c d_ is broader -than _a b_. - -[Footnote: In the original MS. the word _lume_ (light) is written at -the apex of the pyramid.] - -178. - -It can be proved why the shadow _o p c h_ is darker in proportion as -it is nearer to the line _p h_ and is lighter in proportion as it is -nearer to the line _o c_. Let the light _a b_, be a window, and let -the dark wall in which this window is, be _b s_, that is, one of the -sides of the wall. - -Then we may say that the line _p h_ is darker than any other part of -the space _o p c h_, because this line faces the whole surface in -shadow of [Footnote: In the original the diagram is placed between -lines 27 and 28.] the wall _b s_. The line _o c_ is lighter than the -other part of this space _o p c h_, because this line faces the -luminous space _a b_. - -Where the shadow is larger, or smaller, or equal the body which -casts it. - -[First of the character of divided lights. [Footnote 14: _lumi -divisi_. The text here breaks off abruptly.] - -OF THE COMPOUND SHADOW _F, R, C, H_ CAUSED BY A SINGLE LIGHT. - -The shadow _f r c h_ is under such conditions as that where it is -farthest from its inner side it loses depth in proportion. To prove -this: - -Let _d a_, be the light and _f n_ the solid body, and let _a e_ be -one of the side walls of the window that is _d a_. Then I -say--according to the 2nd [proposition]: that the surface of any -body is affected by the tone of the objects surrounding it,--that -the side _r c_, which faces the dark wall _a e_ must participate of -its darkness and, in the same way that the outer surface which faces -the light _d a_ participates of the light; thus we get the outlines -of the extremes on each side of the centre included between them.] - -This is divided into four parts. The first the extremes, which -include the compound shadow, secondly the compound shadow between -these extremes. - -179. - -THE ACTION OF THE LIGHT AS FROM ITS CENTRE. - -If it were the whole of the light that caused the shadows beyond the -bodies placed in front of it, it would follow that any body much -smaller than the light would cast a pyramidal shadow; but experience -not showing this, it must be the centre of the light that produces -this effect. - -[Footnote: The diagram belonging to this passage is between lines 4 -and 5 in the original. Comp. the reproduction Pl. IV, No. 4. The -text and drawing of this chapter have already been published with -tolerable accuracy. See M. JORDAN: "_Das Malerbuch des Leonardo da -Vinci_". Leipzig 1873, P. 90.] - -PROOF. - -Let _a b_ be the width of the light from a window, which falls on a -stick set up at one foot from _a c_ [Footnote 6: _bastone_ (stick). -The diagram has a sphere in place of a stick.]. And let _a d_ be the -space where all the light from the window is visible. At _c e_ that -part of the window which is between _l b_ cannot be seen. In the -same way _a m_ cannot be seen from _d f_ and therefore in these two -portions the light begins to fail. - -Shadow as produced by two lights of different size (180. 181). - -180. - -A body in light and shade placed between two equal lights side by -side will cast shadows in proportion to the [amount of] light. And -the shadows will be one darker than the other in proportion as one -light is nearer to the said body than the other on the opposite -side. - -A body placed at an equal distance between two lights will cast two -shadows, one deeper than the other in proportion, as the light which -causes it is brighter than the other. - -[Footnote: In the MS. the larger diagram is placed above the first -line; the smaller one between l. 4 & 5.] - -181. - -A light which is smaller than the body it illuminates produces -shadows of which the outlines end within [the surface of] the body, -and not much compound shadow; and falls on less than half of it. A -light which is larger than the body it illuminates, falls on more -than half of it, and produces much compound shadow. - -The effect of light at different distances. - -182. - -OF THE SHADOW CAST BY A BODY PLACED BETWEEN 2 EQUAL LIGHTS. - -A body placed between 2 equal lights will cast 2 shadows of itself -in the direction of the lines of the 2 lights; and if you move this -body placing it nearer to one of the lights the shadow cast towards -the nearer light will be less deep than that which falls towards the -more distant one. - -Further complications in the derived shadows (183-187). - -183. - -The greatest depth of shadow is in the simple derived shadow because -it is not lighted by either of the two lights _a b, c d_. - -The next less deep shadow is the derived shadow _e f n_; and in this -the shadow is less by half, because it is illuminated by a single -light, that is _c d_. - -This is uniform in natural tone because it is lighted throughout by -one only of the two luminous bodies [10]. But it varies with the -conditions of shadow, inasmuch as the farther it is away from the -light the less it is illuminated by it [13]. - -The third degree of depth is the middle shadow [Footnote 15: We -gather from what follows that _q g r_ here means _ombra media_ (the -middle shadow).]. But this is not uniform in natural tone; because -the nearer it gets to the simple derived shadow the deeper it is -[Footnote 18: Compare lines 10-13], and it is the uniformly gradual -diminution by increase of distance which is what modifies it -[Footnote 20: See Footnote 18]: that is to say the depth of a shadow -increases in proportion to the distance from the two lights. - -The fourth is the shadow _k r s_ and this is all the darker in -natural tone in proportion as it is nearer to _k s_, because it gets -less of the light _a o_, but by the accident [of distance] it is -rendered less deep, because it is nearer to the light _c d_, and -thus is always exposed to both lights. - -The fifth is less deep in shadow than either of the others because -it is always entirely exposed to one of the lights and to the whole -or part of the other; and it is less deep in proportion as it is -nearer to the two lights, and in proportion as it is turned towards -the outer side _x t_; because it is more exposed to the second light -_a b_. - -[Footnote: The diagram to this section is given on Pl. V. To the -left is the facsimile of the beginning of the text belonging to it.] - -184. - -OF SIMPLE SHADOWS. - -Why, at the intersections _a_, _b_ of the two compound shadows _e f_ -and _m e_, is a simple shadow pfoduced as at _e h_ and _m g_, while -no such simple shadow is produced at the other two intersections _c -d_ made by the very same compound shadows? - -ANSWER. - -Compound shadow are a mixture of light and shade and simple shadows -are simply darkness. Hence, of the two lights _n_ and _o_, one falls -on the compound shadow from one side, and the other on the compound -shadow from the other side, but where they intersect no light falls, -as at _a b_; therefore it is a simple shadow. Where there is a -compound shadow one light or the other falls; and here a difficulty -arises for my adversary since he says that, where the compound -shadows intersect, both the lights which produce the shadows must of -necessity fall and therefore these shadows ought to be neutralised; -inasmuch as the two lights do not fall there, we say that the shadow -is a simple one and where only one of the two lights falls, we say -the shadow is compound, and where both the lights fall the shadow is -neutralised; for where both lights fall, no shadow of any kind is -produced, but only a light background limiting the shadow. Here I -shall say that what my adversary said was true: but he only mentions -such truths as are in his favour; and if we go on to the rest he -must conclude that my proposition is true. And that is: That if both -lights fell on the point of intersection, the shadows would be -neutralised. This I confess to be true if [neither of] the two -shadows fell in the same spot; because, where a shadow and a light -fall, a compound shadow is produced, and wherever two shadows or two -equal lights fall, the shadow cannot vary in any part of it, the -shadows and the lights both being equal. And this is proved in the -eighth [proposition] on proportion where it is said that if a given -quantity has a single unit of force and resistance, a double -quantity will have double force and double resistance. - -DEFINITION. - -The intersection _n_ is produced by the shadows caused by the light -_b_, because this light _b_ produces the shadow _x b_, and the -shadow _s b_, but the intersection _m_ is produced by the light _a_ -which causes the shadow _s a_, and the shadow _x a_. - -But if you uncover both the lights _a b_, then you get the two -shadows _n m_ both at once, and besides these, two other, simple -shadows are produced at _r o_ where neither of the two lights falls -at all. The grades of depth in compound shadows are fewer in -proportion as the lights falling on, and crossing them are less -numerous. - -186. - -Why the intersections at _n_ being composed of two compound derived -shadows, forms a compound shadow and not a simple one, as happens -with other intersections of compound shadows. This occurs, according -to the 2nd [diagram] of this [prop.] which says:--The intersection -of derived shadows when produced by the intersection of columnar -shadows caused by a single light does not produce a simple shadow. -And this is the corollary of the 1st [prop.] which says:--The -intersection of simple derived shadows never results in a deeper -shadow, because the deepest shadows all added together cannot be -darker than one by itself. Since, if many deepest shadows increased -in depth by their duplication, they could not be called the -_deepest_ shadows, but only part-shadows. But if such intersections -are illuminated by a second light placed between the eye and the -intersecting bodies, then those shadows would become compound -shadows and be uniformly dark just as much at the intersection as -throughout the rest. In the 1st and 2nd above, the intersections _i -k_ will not be doubled in depth as it is doubled in quantity. But in -this 3rd, at the intersections _g n_ they will be double in depth -and in quantity. - -187. - -HOW AND WHEN THE SURROUNDINGS IN SHADOW MINGLE THEIR DERIVED SHADOW -WITH THE LIGHT DERIVED FROM THE LUMINOUS BODY. - -The derived shadow of the dark walls on each side of the bright -light of the window are what mingle their various degrees of shade -with the light derived from the window; and these various depths of -shade modify every portion of the light, except where it is -strongest, at _c_. To prove this let _d a_ be the primary shadow -which is turned towards the point _e_, and darkens it by its derived -shadow; as may be seen by the triangle _a e d_, in which the -angle _e_ faces the darkened base _d a e_; the point _v_ faces the -dark shadow _a s_ which is part of _a d_, and as the whole is -greater than a part, _e_ which faces the whole base [of the -triangle], will be in deeper shadow than _v_ which only faces part -of it. In consequence of the conclusion [shown] in the above -diagram, _t_ will be less darkened than _v_, because the base of the -_t_ is part of the base of the _v_; and in the same way it follows -that _p_ is less in shadow than _t_, because the base of the _p_ is -part of the base of the _t_. And _c_ is the terminal point of the -derived shadow and the chief beginning of the highest light. - -[Footnote: The diagram on Pl. IV, No. 5 belongs to this passage; but -it must be noted that the text explains only the figure on the -right-hand side.] - -FOURTH BOOK ON LIGHT AND SHADE. - -On the shape of the cast shadows (188-191). - -188. - -The form of the shadow cast by any body of uniform density can never -be the same as that of the body producing it. [Footnote: Comp. the -drawing on PI. XXVIII, No. 5.] - -189. - -No cast shadow can produce the true image of the body which casts it -on a vertical plane unless the centre of the light is equally -distant from all the edges of that body. - -190. - -If a window _a b_ admits the sunlight into a room, the sunlight will -magnify the size of the window and diminish the shadow of a man in -such a way as that when the man makes that dim shadow of himself, -approach to that which defines the real size of the window, he will -see the shadows where they come into contact, dim and confused from -the strength of the light, shutting off and not allowing the solar -rays to pass; the effect of the shadow of the man cast by this -contact will be exactly that figured above. - -[Footnote: It is scarcely possible to render the meaning of this -sentence with strict accuracy; mainly because the grammatical -construction is defective in the most important part--line 4. In the -very slight original sketch the shadow touches the upper arch of the -window and the correction, here given is perhaps not justified.] - -191. - -A shadow is never seen as of uniform depth on the surface which -intercepts it unless every portion of that surface is equidistant -from the luminous body. This is proved by the 7th which says:--The -shadow will appear lighter or stronger as it is surrounded by a -darker or a lighter background. And by the 8th of this:--The -background will be in parts darker or lighter, in proportion as it -is farther from or nearer to the luminous body. And:--Of various -spots equally distant from the luminous body those will always be in -the highest light on which the rays fall at the smallest angles: The -outline of the shadow as it falls on inequalities in the surface -will be seen with all the contours similar to those of the body that -casts it, if the eye is placed just where the centre of the light -was. - -The shadow will look darkest where it is farthest from the body that -casts it. The shadow _c d_, cast by the body in shadow _a b_ which -is equally distant in all parts, is not of equal depth because it is -seen on a back ground of varying brightness. [Footnote: Compare the -three diagrams on Pl. VI, no 1 which, in the original accompany this -section.] - -On the outlines of cast shadows (192-195). - -192. - -The edges of a derived shadow will be most distinct where it is cast -nearest to the primary shadow. - -193. - -As the derived shadow gets more distant from the primary shadow, the -more the cast shadow differs from the primary shadow. - -194. - -OF SHADOWS WHICH NEVER COME TO AN END. - -The greater the difference between a light and the body lighted by -it, the light being the larger, the more vague will be the outlines -of the shadow of that object. - -The derived shadow will be most confused towards the edges of its -interception by a plane, where it is remotest from the body casting -it. - -195. - -What is the cause which makes the outlines of the shadow vague and -confused? - -Whether it is possible to give clear and definite outlines to the -edges of shadows. - -On the relative size of shadows (196. 197). - -196. - -THE BODY WHICH IS NEAREST TO THE LIGHT CASTS THE LARGEST SHADOW, AND -WHY? - -If an object placed in front of a single light is very close to it -you will see that it casts a very large shadow on the opposite wall, -and the farther you remove the object from the light the smaller -will the image of the shadow become. - -WHY A SHADOW LARGER THAN THE BODY THAT PRODUCES IT BECOMES OUT OF -PROPORTION. - -The disproportion of a shadow which is larger than the body -producing it, results from the light being smaller than the body, so -that it cannot be at an equal distance from the edges of the body -[Footnote 11: H. LUDWIG in his edition of the old copies, in the -Vatican library--in which this chapter is included under Nos. 612, -613 and 614 alters this passage as follows: _quella parte ch'e piu -propinqua piu cresce che le distanti_, although the Vatican copy -agrees with the original MS. in having _distante_ in the former and -_propinque_ in the latter place. This supposed amendment seems to me -to invert the facts. Supposing for instance, that on Pl. XXXI No. 3. -_f_ is the spot where the light is that illuminates the figure there -represented, and that the line behind the figure represents a wall -on which the shadow of the figure is thrown. It is evident, that in -that case the nearest portion, in this case the under part of the -thigh, is very little magnified in the shadow, and the remoter -parts, for instance the head, are more magnified.]; and the portions -which are most remote are made larger than the nearer portions for -this reason [Footnote 12: See Footnote 11]. - -WHY A SHADOW WHICH IS LARGER THAN THE BODY CAUSING IT HAS -ILL-DEFINED OUTLINES. - -The atmosphere which surrounds a light is almost like light itself -for brightness and colour; but the farther off it is the more it -loses this resemblance. An object which casts a large shadow and is -near to the light, is illuminated both by that light by the luminous -atmosphere; hence this diffused light gives the shadow ill-defined -edges. - -197. - -A luminous body which is long and narrow in shape gives more -confused outlines to the derived shadow than a spherical light, and -this contradicts the proposition next following: A shadow will have -its outlines more clearly defined in proportion as it is nearer to -the primary shadow or, I should say, the body casting the shadow; -[Footnote 14: The lettering refers to the lower diagram, Pl. XLI, -No. 5.] the cause of this is the elongated form of the luminous body -_a c_, &c. [Footnote 16: See Footnote 14]. - -Effects on cast shadows by the tone of the back ground. - -198. - -OF MODIFIED SHADOWS. - -Modified shadows are those which are cast on light walls or other -illuminated objects. - -A shadow looks darkest against a light background. The outlines of a -derived shadow will be clearer as they are nearer to the primary -shadow. A derived shadow will be most defined in shape where it is -intercepted, where the plane intercepts it at the most equal angle. - -Those parts of a shadow will appear darkest which have darker -objects opposite to them. And they will appear less dark when they -face lighter objects. And the larger the light object opposite, the -more the shadow will be lightened. - -And the larger the surface of the dark object the more it will -darken the derived shadow where it is intercepted. - -A disputed proposition. - -199. - -OF THE OPINION OF SOME THAT A TRIANGLE CASTS NO SHADOW ON A PLANE -SURFACE. - -Certain mathematicians have maintained that a triangle, of which the -base is turned to the light, casts no shadow on a plane; and this -they prove by saying [5] that no spherical body smaller than the -light can reach the middle with the shadow. The lines of radiant -light are straight lines [6]; therefore, suppose the light to be _g -h_ and the triangle _l m n_, and let the plane be _i k_; they say -the light _g_ falls on the side of the triangle _l n_, and the -portion of the plane _i q_. Thus again _h_ like _g_ falls on the -side _l m_, and then on _m n_ and the plane _p k_; and if the whole -plane thus faces the lights _g h_, it is evident that the triangle -has no shadow; and that which has no shadow can cast none. This, in -this case appears credible. But if the triangle _n p g_ were not -illuminated by the two lights _g_ and _h_, but by _i p_ and _g_ and -_k_ neither side is lighted by more than one single light: that is -_i p_ is invisible to _h g_ and _k_ will never be lighted by _g_; -hence _p q_ will be twice as light as the two visible portions that -are in shadow. - -[Footnote: 5--6. This passage is so obscure that it would be rash to -offer an explanation. Several words seem to have been omitted.] - -On the relative depth of cast shadows (200-202). - -200. - -A spot is most in the shade when a large number of darkened rays -fall upon it. The spot which receives the rays at the widest angle -and by darkened rays will be most in the dark; a will be twice as -dark as b, because it originates from twice as large a base at an -equal distance. A spot is most illuminated when a large number of -luminous rays fall upon it. d is the beginning of the shadow _d f_, -and tinges _c_ but _a_ little; _d e_ is half of the shadow _d f_ and -gives a deeper tone where it is cast at _b_ than at _f_. And the -whole shaded space _e_ gives its tone to the spot _a_. [Footnote: -The diagram here referred to is on Pl. XLI, No. 2.] - -201. - -_A n_ will be darker than _c r_ in proportion to the number of times -that _a b_ goes into _c d_. - -202. - -The shadow cast by an object on a plane will be smaller in -proportion as that object is lighted by feebler rays. Let _d e_ be -the object and _d c_ the plane surface; the number of times that _d -e_ will go into _f g_ gives the proportion of light at _f h_ to _d -c_. The ray of light will be weaker in proportion to its distance -from the hole through which it falls. - -FIFTH BOOK ON LIGHT AND SHADE. - -Principles of reflection (203. 204). - -203. - -OF THE WAY IN WHICH THE SHADOWS CAST BY OBJECTS OUGHT TO BE DEFINED. - -If the object is the mountain here figured, and the light is at the -point _a_, I say that from _b d_ and also from _c f_ there will be -no light but from reflected rays. And this results from the fact -that rays of light can only act in straight lines; and the same is -the case with the secondary or reflected rays. - -204. - -The edges of the derived shadow are defined by the hues of the -illuminated objects surrounding the luminous body which produces the -shadow. - -On reverberation. - -205. - -OF REVERBERATION. - -Reverberation is caused by bodies of a bright nature with a flat and -semi opaque surface which, when the light strikes upon them, throw -it back again, like the rebound of a ball, to the former object. - -WHERE THERE CAN BE NO REFLECTED LIGHTS. - -All dense bodies have their surfaces occupied by various degrees of -light and shade. The lights are of two kinds, one called original, -the other borrowed. Original light is that which is inherent in the -flame of fire or the light of the sun or of the atmosphere. Borrowed -light will be reflected light; but to return to the promised -definition: I say that this luminous reverberation is not produced -by those portions of a body which are turned towards darkened -objects, such as shaded spots, fields with grass of various height, -woods whether green or bare; in which, though that side of each -branch which is turned towards the original light has a share of -that light, nevertheless the shadows cast by each branch separately -are so numerous, as well as those cast by one branch on the others, -that finally so much shadow is the result that the light counts for -nothing. Hence objects of this kind cannot throw any reflected light -on opposite objects. - -Reflection on water (206. 207). - -206. - -PERSPECTIVE. - -The shadow or object mirrored in water in motion, that is to say in -small wavelets, will always be larger than the external object -producing it. - -207. - -It is impossible that an object mirrored on water should correspond -in form to the object mirrored, since the centre of the eye is above -the surface of the water. - -This is made plain in the figure here given, which demonstrates that -the eye sees the surface _a b_, and cannot see it at _l f_, and at -_r t_; it sees the surface of the image at _r t_, and does not see -it in the real object _c d_. Hence it is impossible to see it, as -has been said above unless the eye itself is situated on the surface -of the water as is shown below [13]. - -[Footnote: _A_ stands for _ochio_ [eye], _B_ for _aria_ [air], _C_ -for _acqua_ [water], _D_ for _cateto_ [cathetus].--In the original -MS. the second diagram is placed below line 13.] - -Experiments with the mirror (208-210). - -208. - -THE MIRROR. - -If the illuminated object is of the same size as the luminous body -and as that in which the light is reflected, the amount of the -reflected light will bear the same proportion to the intermediate -light as this second light will bear to the first, if both bodies -are smooth and white. - -209. - -Describe how it is that no object has its limitation in the mirror -but in the eye which sees it in the mirror. For if you look at your -face in the mirror, the part resembles the whole in as much as the -part is everywhere in the mirror, and the whole is in every part of -the same mirror; and the same is true of the whole image of any -object placed opposite to this mirror, &c. - -210. - -No man can see the image of another man in a mirror in its proper -place with regard to the objects; because every object falls on [the -surface of] the mirror at equal angles. And if the one man, who sees -the other in the mirror, is not in a direct line with the image he -will not see it in the place where it really falls; and if he gets -into the line, he covers the other man and puts himself in the place -occupied by his image. Let _n o_ be the mirror, _b_ the eye of your -friend and _d_ your own eye. Your friend's eye will appear to you at -_a_, and to him it will seem that yours is at _c_, and the -intersection of the visual rays will occur at _m_, so that either of -you touching _m_ will touch the eye of the other man which shall be -open. And if you touch the eye of the other man in the mirror it -will seem to him that you are touching your own. - -Appendix:--On shadows in movement (211. 212). - -211. - -OF THE SHADOW AND ITS MOTION. - -When two bodies casting shadows, and one in front of the other, are -between a window and the wall with some space between them, the -shadow of the body which is nearest to the plane of the wall will -move if the body nearest to the window is put in transverse motion -across the window. To prove this let _a_ and _b_ be two bodies -placed between the window _n m_ and the plane surface _o p_ with -sufficient space between them as shown by the space _a b_. I say -that if the body _a_ is moved towards _s_ the shadow of the body _b_ -which is at _c_ will move towards _d_. - -212. - -OF THE MOTION OF SHADOWS. - -The motion of a shadow is always more rapid than that of the body -which produces it if the light is stationary. To prove this let _a_ -be the luminous body, and _b_ the body casting the shadow, and _d_ -the shadow. Then I say that in the time while the solid body moves -from _b_ to _c_, the shadow _d_ will move to _e_; and this -proportion in the rapidity of the movements made in the same space -of time, is equal to that in the length of the space moved over. -Thus, given the proportion of the space moved over by the body _b_ -to _c_, to that moved over by the shadow _d_ to _e_, the proportion -in the rapidity of their movements will be the same. - -But if the luminous body is also in movement with a velocity equal -to that of the solid body, then the shadow and the body that casts -it will move with equal speed. And if the luminous body moves more -rapidly than the solid body, the motion of the shadow will be slower -than that of the body casting it. - -But if the luminous body moves more slowly than the solid body, then -the shadow will move more rapidly than that body. - -SIXTH BOOK ON LIGHT AND SHADE. - -The effect of rays passing through holes (213. 214). - -213. - -PERSPECTIVE. - -If you transmit the rays of the sun through a hole in the shape of a -star you will see a beautiful effect of perspective in the spot -where the sun's rays fall. - -[Footnote: In this and the following chapters of MS. C the order of -the original paging has been adhered to, and is shown in -parenthesis. Leonardo himself has but rarely worked out the subject -of these propositions. The space left for the purpose has -occasionally been made use of for quite different matter. Even the -numerous diagrams, most of them very delicately sketched, lettered -and numbered, which occur on these pages, are hardly ever explained, -with the exception of those few which are here given.] - -214. - -No small hole can so modify the convergence of rays of light as to -prevent, at a long distance, the transmission of the true form of -the luminous body causing them. It is impossible that rays of light -passing through a parallel [slit], should not display the form of -the body causing them, since all the effects produced by a luminous -body are [in fact] the reflection of that body: The moon, shaped -like a boat, if transmitted through a hole is figured in the surface -[it falls on] as a boatshaped object. [Footnote 8: In the MS. a -blank space is left after this question.] Why the eye sees bodies at -a distance, larger than they measure on the vertical plane?. - -[Footnote: This chapter, taken from another MS. may, as an -exception, be placed here, as it refers to the same subject as the -preceding section.] - -On gradation of shadows (215. 216). - -215. - -Although the breadth and length of lights and shadow will be -narrower and shorter in foreshortening, the quality and quantity of -the light and shade is not increased nor diminished. - -[3]The function of shade and light when diminished by -foreshortening, will be to give shadow and to illuminate an object -opposite, according to the quality and quantity in which they fall -on the body. - -[5]In proportion as a derived shadow is nearer to its penultimate -extremities the deeper it will appear, _g z_ beyond the intersection -faces only the part of the shadow [marked] _y z_; this by -intersection takes the shadow from _m n_ but by direct line it takes -the shadow _a m_ hence it is twice as deep as _g z_. _Y x_, by -intersection takes the shadow _n o_, but by direct line the shadow -_n m a_, therefore _x y_ is three times as dark as _z g_; _x f_, by -intersection faces _o b_ and by direct line _o n m a_, therefore we -must say that the shadow between _f x_ will be four times as dark as -the shadow _z g_, because it faces four times as much shadow. - -Let _a b_ be the side where the primary shadow is, and _b c_ the -primary light, _d_ will be the spot where it is intercepted,_f g_ -the derived shadow and _f e_ the derived light. - -And this must be at the beginning of the explanation. - -[Footnote: In the original MS. the text of No. 252 precedes the one -given here. In the text of No. 215 there is a blank space of about -four lines between the lines 2 and 3. The diagram given on Pl. VI, -No. 2 is placed between lines 4 and 5. Between lines 5 and 6 there -is another space of about three lines and one line left blank -between lines 8 and 9. The reader will find the meaning of the whole -passage much clearer if he first reads the final lines 11--13. -Compare also line 4 of No. 270.] - -On relative proportion of light and shadows (216--221). - -216. - -That part of the surface of a body on which the images [reflection] -from other bodies placed opposite fall at the largest angle will -assume their hue most strongly. In the diagram below, 8 is a larger -angle than 4, since its base _a n_ is larger than _e n_ the base of -4. This diagram below should end at _a n_ 4 8. [4]That portion of -the illuminated surface on which a shadow is cast will be brightest -which lies contiguous to the cast shadow. Just as an object which is -lighted up by a greater quantity of luminous rays becomes brighter, -so one on which a greater quantity of shadow falls, will be darker. - -Let 4 be the side of an illuminated surface 4 8, surrounding the -cast shadow _g e_ 4. And this spot 4 will be lighter than 8, because -less shadow falls on it than on 8. Since 4 faces only the shadow _i -n_; and 8 faces and receives the shadow _a e_ as well as _i n_ which -makes it twice as dark. And the same thing happens when you put the -atmosphere and the sun in the place of shade and light. - -[12] The distribution of shadow, originating in, and limited by, -plane surfaces placed near to each other, equal in tone and directly -opposite, will be darker at the ends than at the beginning, which -will be determined by the incidence of the luminous rays. You will -find the same proportion in the depth of the derived shadows _a n_ -as in the nearness of the luminous bodies _m b_, which cause them; -and if the luminous bodies were of equal size you would still -farther find the same proportion in the light cast by the luminous -circles and their shadows as in the distance of the said luminous -bodies. - -[Footnote: The diagram originally placed between lines 3 and 4 is on -Pl. VI, No. 3. In the diagram given above line 14 of the original, -and here printed in the text, the words _corpo luminoso_ [luminous -body] are written in the circle _m_, _luminoso_ in the circle _b_ -and _ombroso_ [body in shadow] in the circle _o_.] - -217. - -THAT PART OF THE REFLECTION WILL BE BRIGHTEST WHERE THE REFLECTED -RAYS ARE SHORTEST. - -[2] The darkness occasioned by the casting of combined shadows will -be in conformity with its cause, which will originate and terminate -between two plane surfaces near together, alike in tone and directly -opposite each other. - -[4] In proportion as the source of light is larger, the luminous and -shadow rays will be more mixed together. This result is produced -because wherever there is a larger quantity of luminous rays, there -is most light, but where there are fewer there is least light, -consequently the shadow rays come in and mingle with them. - -[Footnote: Diagrams are inserted before lines 2 and 4.] - -218. - -In all the proportions I lay down it must be understood that the -medium between the bodies is always the same. [2] The smaller the -luminous body the more distinct will the transmission of the shadows -be. - -[3] When of two opposite shadows, produced by the same body, one is -twice as dark as the other though similar in form, one of the two -lights causing them must have twice the diameter that the other has -and be at twice the distance from the opaque body. If the object is -lowly moved across the luminous body, and the shadow is intercepted -at some distance from the object, there will be the same relative -proportion between the motion of the derived shadow and the motion -of the primary shadow, as between the distance from the object to -the light, and that from the object to the spot where the shadow is -intercepted; so that though the object is moved slowly the shadow -moves fast. - -[Footnote: There are diagrams inserted before lines 2 and 3 but they -are not reproduced here. The diagram above line 6 is written upon as -follows: at _A lume_ (light), at _B obbietto_ (body), at _C ombra -d'obbietto_ (shadow of the object).] - -219. - -A luminous body will appear less brilliant when surrounded by a -bright background. - -[2] I have found that the stars which are nearest to the horizon -look larger than the others because light falls upon them from a -larger proportion of the solar body than when they are above us; and -having more light from the sun they give more light, and the bodies -which are most luminous appear the largest. As may be seen by the -sun through a mist, and overhead; it appears larger where there is -no mist and diminished through mist. No portion of the luminous body -is ever visible from any spot within the pyramid of pure derived -shadow. - -[Footnote: Between lines 1 and 2 there is in the original a large -diagram which does not refer to this text. ] - -220. - -A body on which the solar rays fall between the thin branches of -trees far apart will cast but a single shadow. - -[2] If an opaque body and a luminous one are (both) spherical the -base of the pyramid of rays will bear the same proportion to the -luminous body as the base of the pyramid of shade to the opaque -body. - -[4] When the transmitted shadow is intercepted by a plane surface -placed opposite to it and farther away from the luminous body than -from the object [which casts it] it will appear proportionately -darker and the edges more distinct. - -[Footnote: The diagram which, in the original, is placed above line -2, is similar to the one, here given on page 73 (section 120).--The -diagram here given in the margin stands, in the original, between -lines 3 and 4.] - -221. - -A body illuminated by the solar rays passing between the thick -branches of trees will produce as many shadows as there are branches -between the sun and itself. - -Where the shadow-rays from an opaque pyramidal body are intercepted -they will cast a shadow of bifurcate outline and various depth at -the points. A light which is broader than the apex but narrower than -the base of an opaque pyramidal body placed in front of it, will -cause that pyramid to cast a shadow of bifurcate form and various -degrees of depth. - -If an opaque body, smaller than the light, casts two shadows and if -it is the same size or larger, casts but one, it follows that a -pyramidal body, of which part is smaller, part equal to, and part -larger than, the luminous body, will cast a bifurcate shadow. - -[Footnote: Between lines 2 and 3 there are in the original two large -diagrams.] - -_IV._ - -_Perspective of Disappearance._ - -_The theory of the_ "Prospettiva de' perdimenti" _would, in many -important details, be quite unintelligible if it had not been led up -by the principles of light and shade on which it is based. The word_ -"Prospettiva" _in the language of the time included the principles -of optics; what Leonardo understood by_ "Perdimenti" _will be -clearly seen in the early chapters, Nos._ 222--224. _It is in the -very nature of the case that the farther explanations given in the -subsequent chapters must be limited to general rules. The sections -given as_ 227--231 _"On indistinctness at short distances" have, it -is true, only an indirect bearing on the subject; but on the other -hand, the following chapters,_ 232--234, _"On indistinctness at -great distances," go fully into the matter, and in chapters_ -235--239, _which treat "Of the importance of light and shade in the -Perspective of Disappearance", the practical issues are distinctly -insisted on in their relation to the theory. This is naturally -followed by the statements as to "the effect of light or dark -backgrounds on the apparent size of bodies"_ (_Nos._ 240--250). _At -the end I have placed, in the order of the original, those sections -from the MS._ C _which treat of the "Perspective of Disappearance" -and serve to some extent to complete the treatment of the subject_ -(251--262). - -Definition (222. 223). - -222. - -OF THE DIMINISHED DISTINCTNESS OF THE OUTLINES OF OPAQUE BODIES. - -If the real outlines of opaque bodies are indistinguishable at even -a very short distance, they will be more so at long distances; and, -since it is by its outlines that we are able to know the real form -of any opaque body, when by its remoteness we fail to discern it as -a whole, much more must we fail to discern its parts and outlines. - -223. - -OF THE DIMINUTION IN PERSPECTIVE OF OPAQUE OBJECTS. - -Among opaque objects of equal size the apparent diminution of size -will be in proportion to their distance from the eye of the -spectator; but it is an inverse proportion, since, where the -distance is greater, the opaque body will appear smaller, and the -less the distance the larger will the object appear. And this is the -fundamental principle of linear perspective and it -follows:--[11]every object as it becomes more remote loses first -those parts which are smallest. Thus of a horse, we should lose the -legs before the head, because the legs are thinner than the head; -and the neck before the body for the same reason. Hence it follows -that the last part of the horse which would be discernible by the -eye would be the mass of the body in an oval form, or rather in a -cylindrical form and this would lose its apparent thickness before -its length--according to the 2nd rule given above, &c. [Footnote 23: -Compare line 11.]. - -If the eye remains stationary the perspective terminates in the -distance in a point. But if the eye moves in a straight [horizontal] -line the perspective terminates in a line and the reason is that -this line is generated by the motion of the point and our sight; -therefore it follows that as we move our sight [eye], the point -moves, and as we move the point, the line is generated, &c. - -An illustration by experiment. - -224. - -Every visible body, in so far as it affects the eye, includes three -attributes; that is to say: mass, form and colour; and the mass is -recognisable at a greater distance from the place of its actual -existence than either colour or form. Again, colour is discernible -at a greater distance than form, but this law does not apply to -luminous bodies. - -The above proposition is plainly shown and proved by experiment; -because: if you see a man close to you, you discern the exact -appearance of the mass and of the form and also of the colouring; if -he goes to some distance you will not recognise who he is, because -the character of the details will disappear, if he goes still -farther you will not be able to distinguish his colouring, but he -will appear as a dark object, and still farther he will appear as a -very small dark rounded object. It appears rounded because distance -so greatly diminishes the various details that nothing remains -visible but the larger mass. And the reason is this: We know very -well that all the images of objects reach the senses by a small -aperture in the eye; hence, if the whole horizon _a d_ is admitted -through such an aperture, the object _b c_ being but a very small -fraction of this horizon what space can it fill in that minute image -of so vast a hemisphere? And because luminous bodies have more power -in darkness than any others, it is evident that, as the chamber of -the eye is very dark, as is the nature of all colored cavities, the -images of distant objects are confused and lost in the great light -of the sky; and if they are visible at all, appear dark and black, -as every small body must when seen in the diffused light of the -atmosphere. - -[Footnote: The diagram belonging to this passage is placed between -lines 5 and 6; it is No. 4 on Pl. VI. ] - -A guiding rule. - -225. - -OF THE ATMOSPHERE THAT INTERPOSES BETWEEN THE EYE AND VISIBLE -OBJECTS. - -An object will appear more or less distinct at the same distance, in -proportion as the atmosphere existing between the eye and that -object is more or less clear. Hence, as I know that the greater or -less quantity of the air that lies between the eye and the object -makes the outlines of that object more or less indistinct, you must -diminish the definiteness of outline of those objects in proportion -to their increasing distance from the eye of the spectator. - -An experiment. - -226. - -When I was once in a place on the sea, at an equal distance from the -shore and the mountains, the distance from the shore looked much -greater than that from the mountains. - -On indistinctness at short distances (227-231). - -227. - -If you place an opaque object in front of your eye at a distance of -four fingers' breadth, if it is smaller than the space between the -two eyes it will not interfere with your seeing any thing that may -be beyond it. No object situated beyond another object seen by the -eye can be concealed by this [nearer] object if it is smaller than -the space from eye to eye. - -228. - -The eye cannot take in a luminous angle which is too close to it. - -229. - -That part of a surface will be better lighted on which the light -falls at the greater angle. And that part, on which the shadow falls -at the greatest angle, will receive from those rays least of the -benefit of the light. - -230. - -OF THE EYE. - -The edges of an object placed in front of the pupil of the eye will -be less distinct in proportion as they are closer to the eye. This -is shown by the edge of the object _n_ placed in front of the pupil -_d_; in looking at this edge the pupil also sees all the space _a c_ -which is beyond the edge; and the images the eye receives from that -space are mingled with the images of the edge, so that one image -confuses the other, and this confusion hinders the pupil from -distinguishing the edge. - -231. - -The outlines of objects will be least clear when they are nearest to -the eye, and therefore remoter outlines will be clearer. Among -objects which are smaller than the pupil of the eye those will be -less distinct which are nearer to the eye. - -On indistinctness at great distances (232-234). - -232. - -Objects near to the eye will appear larger than those at a distance. - -Objects seen with two eyes will appear rounder than if they are seen -with only one. - -Objects seen between light and shadow will show the most relief. - -233. - -OF PAINTING. - -Our true perception of an object diminishes in proportion as its -size is diminished by distance. - -234. - -PERSPECTIVE. - -Why objects seen at a distance appear large to the eye and in the -image on the vertical plane they appear small. - -PERSPECTIVE. - -I ask how far away the eye can discern a non-luminous body, as, for -instance, a mountain. It will be very plainly visible if the sun is -behind it; and could be seen at a greater or less distance according -to the sun's place in the sky. - -[Footnote: The clue to the solution of this problem (lines 1-3) is -given in lines 4-6, No. 232. Objects seen with both eyes appear -solid since they are seen from two distinct points of sight -separated by the distance between the eyes, but this solidity cannot -be represented in a flat drawing. Compare No. 535.] - -The importance of light and shade in the perspective of -disappearance (235-239). - -235. - -An opaque body seen in a line in which the light falls will reveal -no prominences to the eye. For instance, let _a_ be the solid body -and _c_ the light; _c m_ and _c n_ will be the lines of incidence of -the light, that is to say the lines which transmit the light to the -object _a_. The eye being at the point _b_, I say that since the -light _c_ falls on the whole part _m n_ the portions in relief on -that side will all be illuminated. Hence the eye placed at _c_ -cannot see any light and shade and, not seeing it, every portion -will appear of the same tone, therefore the relief in the prominent -or rounded parts will not be visible. - -236. - -OF PAINTING. - -When you represent in your work shadows which you can only discern -with difficulty, and of which you cannot distinguish the edges so -that you apprehend them confusedly, you must not make them sharp or -definite lest your work should have a wooden effect. - -237. - -OF PAINTING. - -You will observe in drawing that among the shadows some are of -undistinguishable gradation and form, as is shown in the 3rd -[proposition] which says: Rounded surfaces display as many degrees -of light and shade as there are varieties of brightness and darkness -reflected from the surrounding objects. - -238. - -OF LIGHT AND SHADE. - -You who draw from nature, look (carefully) at the extent, the -degree, and the form of the lights and shadows on each muscle; and -in their position lengthwise observe towards which muscle the axis -of the central line is directed. - -239. - -An object which is [so brilliantly illuminated as to be] almost as -bright as light will be visible at a greater distance, and of larger -apparent size than is natural to objects so remote. - -The effect of light or dark backgrounds on the apparent size of -objects (240-250). - -240. - -A shadow will appear dark in proportion to the brilliancy of the -light surrounding it and conversely it will be less conspicuous -where it is seen against a darker background. - -241. - -OF ORDINARY PERSPECTIVE. - -An object of equal breadth and colour throughout, seen against a -background of various colours will appear unequal in breadth. - -And if an object of equal breadth throughout, but of various -colours, is seen against a background of uniform colour, that object -will appear of various breadth. And the more the colours of the -background or of the object seen against the ground vary, the -greater will the apparent variations in the breadth be though the -objects seen against the ground be of equal breadth [throughout]. - -242. - -A dark object seen against a bright background will appear smaller -than it is. - -A light object will look larger when it is seen against a background -darker than itself. - -243. - -OF LIGHT. - -A luminous body when obscured by a dense atmosphere will appear -smaller; as may be seen by the moon or sun veiled by mists. - -OF LIGHT. - -Of several luminous bodies of equal size and brilliancy and at an -equal distance, that will look the largest which is surrounded by -the darkest background. - -OF LIGHT. - -I find that any luminous body when seen through a dense and thick -mist diminishes in proportion to its distance from the eye. Thus it -is with the sun by day, as well as the moon and the other eternal -lights by night. And when the air is clear, these luminaries appear -larger in proportion as they are farther from the eye. - -244. - -That portion of a body of uniform breadth which is against a lighter -background will look narrower [than the rest]. - -[4] _e_ is a given object, itself dark and of uniform breadth; _a b_ -and _c d_ are two backgrounds one darker than the other; _b c_ is a -bright background, as it might be a spot lighted by the sun through -an aperture in a dark room. Then I say that the object _e g_ will -appear larger at _e f_ than at _g h_; because _e f_ has a darker -background than _g h_; and again at _f g_ it will look narrower from -being seen by the eye _o_, on the light background _b c_. [Footnote -12: The diagram to which the text, lines 1-11, refers, is placed in -the original between lines 3 and 4, and is given on Pl. XLI, No. 3. -Lines 12 to 14 are explained by the lower of the two diagrams on Pl. -XLI, No. 4. In the original these are placed after line 14.] That -part of a luminous body, of equal breadth and brilliancy throughout, -will look largest which is seen against the darkest background; and -the luminous body will seem on fire. - -245. - -WHY BODIES IN LIGHT AND SHADE HAVE THEIR OUTLINES ALTERED BY THE -COLOUR AND BRIGHTNESS OF THE OBJECTS SERVING AS A BACKGROUND TO -THEM. - -If you look at a body of which the illuminated portion lies and ends -against a dark background, that part of the light which will look -brightest will be that which lies against the dark [background] at -_d_. But if this brighter part lies against a light background, the -edge of the object, which is itself light, will be less distinct -than before, and the highest light will appear to be between the -limit of the background _m f_ and the shadow. The same thing is seen -with regard to the dark [side], inasmuch as that edge of the shaded -portion of the object which lies against a light background, as at -_l_, it looks much darker than the rest. But if this shadow lies -against a dark background, the edge of the shaded part will appear -lighter than before, and the deepest shade will appear between the -edge and the light at the point _o_. - -[Footnote: In the original diagram _o_ is inside the shaded surface -at the level of _d_.] - -246. - -An opaque body will appear smaller when it is surrounded by a highly -luminous background, and a light body will appear larger when it is -seen against a darker background. This may be seen in the height of -buildings at night, when lightning flashes behind them; it suddenly -seems, when it lightens, as though the height of the building were -diminished. For the same reason such buildings look larger in a -mist, or by night than when the atmosphere is clear and light. - -247. - -ON LIGHT BETWEEN SHADOWS - -When you are drawing any object, remember, in comparing the grades -of light in the illuminated portions, that the eye is often deceived -by seeing things lighter than they are. And the reason lies in our -comparing those parts with the contiguous parts. Since if two -[separate] parts are in different grades of light and if the less -bright is conterminous with a dark portion and the brighter is -conterminous with a light background--as the sky or something -equally bright--, then that which is less light, or I should say -less radiant, will look the brighter and the brighter will seem the -darker. - -248. - -Of objects equally dark in themselves and situated at a considerable -and equal distance, that will look the darkest which is farthest -above the earth. - -249. - -TO PROVE HOW IT IS THAT LUMINOUS BODIES APPEAR LARGER, AT A -DISTANCE, THAN THEY ARE. - -If you place two lighted candles side by side half a braccio apart, -and go from them to a distance 200 braccia you will see that by the -increased size of each they will appear as a single luminous body -with the light of the two flames, one braccio wide. - -TO PROVE HOW YOU MAY SEE THE REAL SIZE OF LUMINOUS BODIES. - -If you wish to see the real size of these luminous bodies, take a -very thin board and make in it a hole no bigger than the tag of a -lace and place it as close to your eye as possible, so that when you -look through this hole, at the said light, you can see a large space -of air round it. Then by rapidly moving this board backwards and -forwards before your eye you will see the light increase [and -diminish]. - -Propositions on perspective of disappearance from MS. C. (250-262). - -250. - -Of several bodies of equal size and equally distant from the eye, -those will look the smallest which are against the lightest -background. - -Every visible object must be surrounded by light and shade. A -perfectly spherical body surrounded by light and shade will appear -to have one side larger than the other in proportion as one is more -highly lighted than the other. - -251. - -PERSPECTIVE. - -No visible object can be well understood and comprehended by the -human eye excepting from the difference of the background against -which the edges of the object terminate and by which they are -bounded, and no object will appear [to stand out] separate from that -background so far as the outlines of its borders are concerned. The -moon, though it is at a great distance from the sun, when, in an -eclipse, it comes between our eyes and the sun, appears to the eyes -of men to be close to the sun and affixed to it, because the sun is -then the background to the moon. - -252. - -A luminous body will appear more brilliant in proportion as it is -surrounded by deeper shadow. [Footnote: The diagram which, in the -original, is placed after this text, has no connection with it.] - -253. - -The straight edges of a body will appear broken when they are -conterminous with a dark space streaked with rays of light. -[Footnote: Here again the diagrams in the original have no -connection with the text.] - -254. - -Of several bodies, all equally large and equally distant, that which -is most brightly illuminated will appear to the eye nearest and -largest. [Footnote: Here again the diagrams in the original have no -connection with the text.] - -255. - -If several luminous bodies are seen from a great distance although -they are really separate they will appear united as one body. - -256. - -If several objects in shadow, standing very close together, are seen -against a bright background they will appear separated by wide -intervals. - -257. - -Of several bodies of equal size and tone, that which is farthest -will appear the lightest and smallest. - -258. - -Of several objects equal in size, brightness of background and -length that which has the flattest surface will look the largest. A -bar of iron equally thick throughout and of which half is red hot, -affords an example, for the red hot part looks thicker than the -rest. - -259. - -Of several bodies of equal size and length, and alike in form and in -depth of shade, that will appear smallest which is surrounded by the -most luminous background. - -260. - -DIFFERENT PORTIONS OF A WALL SURFACE WILL BE DARKER OR BRIGHTER IN -PROPORTION AS THE LIGHT OR SHADOW FALLS ON THEM AT A LARGER ANGLE. - -The foregoing proposition can be clearly proved in this way. Let us -say that _m q_ is the luminous body, then _f g_ will be the opaque -body; and let _a e_ be the above-mentioned plane on which the said -angles fall, showing [plainly] the nature and character of their -bases. Then: _a_ will be more luminous than _b_; the base of the -angle _a_ is larger than that of _b_ and it therefore makes a -greater angle which will be _a m q_; and the pyramid _b p m_ will be -narrower and _m o c_ will be still finer, and so on by degrees, in -proportion as they are nearer to _e_, the pyramids will become -narrower and darker. That portion of the wall will be the darkest -where the breadth of the pyramid of shadow is greater than the -breadth of the pyramid of light. - -At the point _a_ the pyramid of light is equal in strength to the -pyramid of shadow, because the base _f g_ is equal to the base _r -f_. At the point _d_ the pyramid of light is narrower than the -pyramid of shadow by so much as the base _s f_ is less than the base -_f g_. - -Divide the foregoing proposition into two diagrams, one with the -pyramids of light and shadow, the other with the pyramids of light -[only]. - -261. - -Among shadows of equal depth those which are nearest to the eye will -look least deep. - -262. - -The more brilliant the light given by a luminous body, the deeper -will the shadows be cast by the objects it illuminates. - -_V._ - -_Theory of colours._ - -_Leonardo's theory of colours is even more intimately connected with -his principles of light and shade than his Perspective of -Disappearance and is in fact merely an appendix or supplement to -those principles, as we gather from the titles to sections_ 264, -267_, and _276_, while others again_ (_Nos._ 281, 282_) are headed_ -Prospettiva. - -_A very few of these chapters are to be found in the oldest copies -and editions of the Treatise on Painting, and although the material -they afford is but meager and the connection between them but -slight, we must still attribute to them a special theoretical value -as well as practical utility--all the more so because our knowledge -of the theory and use of colours at the time of the Renaissance is -still extremely limited._ - -The reciprocal effects of colours on objects placed opposite each -other (263-272). - -263. - -OF PAINTING. - -The hue of an illuminated object is affected by that of the luminous -body. - -264. - -OF SHADOW. - -The surface of any opaque body is affected by the colour of -surrounding objects. - -265. - -A shadow is always affected by the colour of the surface on which it -is cast. - -266. - -An image produced in a mirror is affected by the colour of the -mirror. - -267. - -OF LIGHT AND SHADE. - -Every portion of the surface of a body is varied [in hue] by the -[reflected] colour of the object that may be opposite to it. - -EXAMPLE. - -If you place a spherical body between various objects that is to say -with [direct] sunlight on one side of it, and on the other a wall -illuminated by the sun, which wall may be green or of any other -colour, while the surface on which it is placed may be red, and the -two lateral sides are in shadow, you will see that the natural -colour of that body will assume something of the hue reflected from -those objects. The strongest will be [given by] the luminous body; -the second by the illuminated wall, the third by the shadows. There -will still be a portion which will take a tint from the colour of -the edges. - -268. - -The surface of every opaque body is affected by the colour of the -objects surrounding it. But this effect will be strong or weak in -proportion as those objects are more or less remote and more or less -strongly [coloured]. - -269. - -OF PAINTING. - -The surface of every opaque body assumes the hues reflected from -surrounding objects. - -The surface of an opaque body assumes the hues of surrounding -objects more strongly in proportion as the rays that form the images -of those objects strike the surface at more equal angles. - -And the surface of an opaque body assumes a stronger hue from the -surrounding objects in proportion as that surface is whiter and the -colour of the object brighter or more highly illuminated. - -270. - -OF THE RAYS WHICH CONVEY THROUGH THE AIR THE IMAGES OF OBJECTS. - -All the minutest parts of the image intersect each other without -interfering with each other. To prove this let _r_ be one of the -sides of the hole, opposite to which let _s_ be the eye which sees -the lower end _o_ of the line _n o_. The other extremity cannot -transmit its image to the eye _s_ as it has to strike the end _r_ -and it is the same with regard to _m_ at the middle of the line. The -case is the same with the upper extremity _n_ and the eye _u_. And -if the end _n_ is red the eye _u_ on that side of the holes will not -see the green colour of _o_, but only the red of _n_ according to -the 7th of this where it is said: Every form projects images from -itself by the shortest line, which necessarily is a straight line, -&c. - -[Footnote: 13. This probably refers to the diagram given under No. -66.] - -271. - -OF PAINTING. - -The surface of a body assumes in some degree the hue of those around -it. The colours of illuminated objects are reflected from the -surfaces of one to the other in various spots, according to the -various positions of those objects. Let _o_ be a blue object in full -light, facing all by itself the space _b c_ on the white sphere _a b -e d e f_, and it will give it a blue tinge, _m_ is a yellow body -reflected onto the space _a b_ at the same time as _o_ the blue -body, and they give it a green colour (by the 2nd [proposition] of -this which shows that blue and yellow make a beautiful green &c.) -And the rest will be set forth in the Book on Painting. In that Book -it will be shown, that, by transmitting the images of objects and -the colours of bodies illuminated by sunlight through a small round -perforation and into a dark chamber onto a plane surface, which -itself is quite white, &c. - -But every thing will be upside down. - -Combination of different colours in cast shadows. - -272. - -That which casts the shadow does not face it, because the shadows -are produced by the light which causes and surrounds the shadows. -The shadow caused by the light _e_, which is yellow, has a blue -tinge, because the shadow of the body _a_ is cast upon the pavement -at _b_, where the blue light falls; and the shadow produced by the -light _d_, which is blue, will be yellow at _c_, because the yellow -light falls there and the surrounding background to these shadows _b -c_ will, besides its natural colour, assume a hue compounded of -yellow and blue, because it is lighted by the yellow light and by -the blue light both at once. - -Shadows of various colours, as affected by the lights falling on -them. That light which causes the shadow does not face it. - -[Footnote: In the original diagram we find in the circle _e_ -"_giallo_" (yellow) and the cirle _d_ "_azurro"_ (blue) and also -under the circle of shadow to the left "_giallo_" is written and -under that to the right "_azurro_". - -In the second diagram where four circles are placed in a row we find -written, beginning at the left hand, "_giallo_" (yellow), "_azurro_" -(blue), "_verde_" (green), "_rosso_" (red).] - -The effect of colours in the camera obscura (273-274). - -273. - -The edges of a colour(ed object) transmitted through a small hole -are more conspicuous than the central portions. - -The edges of the images, of whatever colour, which are transmitted -through a small aperture into a dark chamber will always be stronger -than the middle portions. - -274. - -OF THE INTERSECTIONS OF THE IMAGES IN THE PUPIL OF THE EYE. - -The intersections of the images as they enter the pupil do not -mingle in confusion in the space where that intersection unites -them; as is evident, since, if the rays of the sun pass through two -panes of glass in close contact, of which one is blue and the other -yellow, the rays, in penetrating them, do not become blue or yellow -but a beautiful green. And the same thing would happen in the eye, -if the images which were yellow or green should mingle where they -[meet and] intersect as they enter the pupil. As this does not -happen such a mingling does not exist. - -OF THE NATURE OF THE RAYS COMPOSED OF THE IMAGES OF OBJECTS, AND OF -THEIR INTERSECTIONS. - -The directness of the rays which transmit the forms and colours of -the bodies whence they proceed does not tinge the air nor can they -affect each other by contact where they intersect. They affect only -the spot where they vanish and cease to exist, because that spot -faces and is faced by the original source of these rays, and no -other object, which surrounds that original source can be seen by -the eye where these rays are cut off and destroyed, leaving there -the spoil they have conveyed to it. And this is proved by the 4th -[proposition], on the colour of bodies, which says: The surface of -every opaque body is affected by the colour of surrounding objects; -hence we may conclude that the spot which, by means of the rays -which convey the image, faces--and is faced by the cause of the -image, assumes the colour of that object. - -On the colours of derived shadows (275. 276). - -275. - -ANY SHADOW CAST BY AN OPAQUE BODY SMALLER THAN THE LIGHT CAUSING THE -SHADOW WILL THROW A DERIVED SHADOW WHICH IS TINGED BY THE COLOUR OF -THE LIGHT. - -Let _n_ be the source of the shadow _e f_; it will assume its hue. -Let _o_ be the source of _h e_ which will in the same way be tinged -by its hue and so also the colour of _v h_ will be affected by _p_ -which causes it; and the shadow of the triangle _z k y_ will be -affected by the colour of _q_, because it is produced by it. [7] In -proportion as _c d_ goes into _a d_, will _n r s_ be darker than -_m_; and the rest of the space will be shadowless [11]. _f g_ is -the highest light, because here the whole light of the window _a d_ -falls; and thus on the opaque body _m e_ is in equally high light; -_z k y_ is a triangle which includes the deepest shadow, because the -light _a d_ cannot reach any part of it. _x h_ is the 2nd grade of -shadow, because it receives only 1/3 of the light from the window, -that is _c d_. The third grade of shadow is _h e_, where two thirds -of the light from the window is visible. The last grade of shadow is -_b d e f_, because the highest grade of light from the window falls -at _f_. - -[Footnote: The diagram Pl. III, No. 1 belongs to this chapter as -well as the text given in No. 148. Lines 7-11 (compare lines 8-12 of -No. 148) which are written within the diagram, evidently apply to -both sections and have therefore been inserted in both.] - -276. - -OF THE COLOURS OF SIMPLE DERIVED SHADOWS. - -The colour of derived shadows is always affected by that of the body -towards which they are cast. To prove this: let an opaque body be -placed between the plane _s c t d_ and the blue light _d e_ and the -red light _a b_, then I say that _d e_, the blue light, will fall on -the whole surface _s c t d_ excepting at _o p_ which is covered by -the shadow of the body _q r_, as is shown by the straight lines _d q -o e r p_. And the same occurs with the light _a b_ which falls on -the whole surface _s c t d_ excepting at the spot obscured by the -shadow _q r_; as is shown by the lines _d q o_, and _e r p_. Hence -we may conclude that the shadow _n m_ is exposed to the blue light -_d e_; but, as the red light _a b_ cannot fall there, _n m_ will -appear as a blue shadow on a red background tinted with blue, -because on the surface _s c t d_ both lights can fall. But in the -shadows only one single light falls; for this reason these shadows -are of medium depth, since, if no light whatever mingled with the -shadow, it would be of the first degree of darkness &c. But in the -shadow at _o p_ the blue light does not fall, because the body _q r_ -interposes and intercepts it there. Only the red light _a b_ falls -there and tinges the shadow of a red hue and so a ruddy shadow -appears on the background of mingled red and blue. - -The shadow of _q r_ at _o p_ is red, being caused by the blue light -_d e_; and the shadow of _q r_ at _o' p'_ is blue being caused by -the red light _a b_. Hence we say that the blue light in this -instance causes a red derived shadow from the opaque body _q' r'_, -while the red light causes the same body to cast a blue derived -shadow; but the primary shadow [on the dark side of the body itself] -is not of either of those hues, but a mixture of red and blue. - -The derived shadows will be equal in depth if they are produced by -lights of equal strength and at an equal distance; this is proved. -[Footnote 53: The text is unfinished in the original.] - -[Footnote: In the original diagram Leonardo has written within the -circle _q r corpo obroso_ (body in shadow); at the spot marked _A, -luminoso azzurro_ (blue luminous body); at _B, luminoso rosso_ (red -luminous body). At _E_ we read _ombra azzurra_ (blue tinted shadow) -and at _D ombra rossa_ (red tinted shadow).] - -On the nature of colours (277. 278). - -277. - -No white or black is transparent. - -278. - -OF PAINTING. - -[Footnote 2: See Footnote 3] Since white is not a colour but the -neutral recipient of every colour [Footnote 3: _il bianco non e -colore ma e inpotentia ricettiva d'ogni colore_ (white is not a -colour, but the neutral recipient of every colour). LEON BATT. -ALBERTI "_Della pittura_" libro I, asserts on the contrary: "_Il -bianco e'l nero non sono veri colori, ma sono alteratione delli -altri colori_" (ed. JANITSCHEK, p. 67; Vienna 1877).], when it is -seen in the open air and high up, all its shadows are bluish; and -this is caused, according to the 4th [prop.], which says: the -surface of every opaque body assumes the hue of the surrounding -objects. Now this white [body] being deprived of the light of the -sun by the interposition of some body between the sun and itself, -all that portion of it which is exposed to the sun and atmosphere -assumes the colour of the sun and atmosphere; the side on which the -sun does not fall remains in shadow and assumes the hue of the -atmosphere. And if this white object did not reflect the green of -the fields all the way to the horizon nor get the brightness of the -horizon itself, it would certainly appear simply of the same hue as -the atmosphere. - -On gradations in the depth of colours (279. 280). - -279. - -Since black, when painted next to white, looks no blacker than when -next to black; and white when next to black looks no whiter than -white, as is seen by the images transmitted through a small hole or -by the edges of any opaque screen ... - -280. - -OF COLOURS. - -Of several colours, all equally white, that will look whitest which -is against the darkest background. And black will look intensest -against the whitest background. - -And red will look most vivid against the yellowest background; and -the same is the case with all colours when surrounded by their -strongest contrasts. - -On the reflection of colours (281-283). - -281. - -PERSPECTIVE. - -Every object devoid of colour in itself is more or less tinged by -the colour [of the object] placed opposite. This may be seen by -experience, inasmuch as any object which mirrors another assumes the -colour of the object mirrored in it. And if the surface thus -partially coloured is white the portion which has a red reflection -will appear red, or any other colour, whether bright or dark. - -PERSPECTIVE. - -Every opaque and colourless body assumes the hue of the colour -reflected on it; as happens with a white wall. - -282. - -PERSPECTIVE. - -That side of an object in light and shade which is towards the light -transmits the images of its details more distinctly and immediately -to the eye than the side which is in shadow. - -PERSPECTIVE. - -The solar rays reflected on a square mirror will be thrown back to -distant objects in a circular form. - -PERSPECTIVE. - -Any white and opaque surface will be partially coloured by -reflections from surrounding objects. - -[Footnote 281. 282: The title line of these chapters is in the -original simply _"pro"_, which may be an abbreviation for either -_Propositione_ or _Prospettiva_--taking Prospettiva of course in its -widest sense, as we often find it used in Leonardo's writings. The -title _"pro"_ has here been understood to mean _Prospettiva_, in -accordance with the suggestion afforded by page 10b of this same -MS., where the first section is headed _Prospettiva_ in full (see -No. 94), while the four following sections are headed merely _"pro"_ -(see No. 85).] - -283. - -WHAT PORTION OF A COLOURED SURFACE OUGHT IN REASON TO BE THE MOST -INTENSE. - -If _a_ is the light, and _b_ illuminated by it in a direct line, -_c_, on which the light cannot fall, is lighted only by reflection -from _b_ which, let us say, is red. Hence the light reflected from -it, will be affected by the hue of the surface causing it and will -tinge the surface _c_ with red. And if _c_ is also red you will see -it much more intense than _b_; and if it were yellow you would see -there a colour between yellow and red. - -On the use of dark and light colours in painting (284--286). - -284. - -WHY BEAUTIFUL COLOURS MUST BE IN THE [HIGHEST] LIGHT. - -Since we see that the quality of colour is known [only] by means of -light, it is to be supposed that where there is most light the true -character of a colour in light will be best seen; and where there is -most shadow the colour will be affected by the tone of that. Hence, -O Painter! remember to show the true quality of colours in bright -lights. - -285. - -An object represented in white and black will display stronger -relief than in any other way; hence I would remind you O Painter! to -dress your figures in the lightest colours you can, since, if you -put them in dark colours, they will be in too slight relief and -inconspicuous from a distance. And the reason is that the shadows of -all objects are dark. And if you make a dress dark there is little -variety in the lights and shadows, while in light colours there are -many grades. - -286. - -OF PAINTING. - -Colours seen in shadow will display more or less of their natural -brilliancy in proportion as they are in fainter or deeper shadow. - -But if these same colours are situated in a well-lighted place, they -will appear brighter in proportion as the light is more brilliant. - -THE ADVERSARY. - -The variety of colours in shadow must be as great as that of the -colours in the objects in that shadow. - -THE ANSWER. - -Colours seen in shadow will display less variety in proportion as -the shadows in which they lie are deeper. And evidence of this is to -be had by looking from an open space into the doorways of dark and -shadowy churches, where the pictures which are painted in various -colours all look of uniform darkness. - -Hence at a considerable distance all the shadows of different -colours will appear of the same darkness. - -It is the light side of an object in light and shade which shows the -true colour. - -On the colours of the rainbow (287. 288). - -287. - -Treat of the rainbow in the last book on Painting, but first write -the book on colours produced by the mixture of other colours, so as -to be able to prove by those painters' colours how the colours of -the rainbow are produced. - -288. - -WHETHER THE COLOURS OF THE RAINBOW ARE PRODUCED BY THE SUN. - -The colours of the rainbow are not produced by the sun, for they -occur in many ways without the sunshine; as may be seen by holding a -glass of water up to the eye; when, in the glass--where there are -those minute bubbles always seen in coarse glass--each bubble, even -though the sun does not fall on it, will produce on one side all the -colours of the rainbow; as you may see by placing the glass between -the day light and your eye in such a way as that it is close to the -eye, while on one side the glass admits the [diffused] light of the -atmosphere, and on the other side the shadow of the wall on one side -of the window; either left or right, it matters not which. Then, by -turning the glass round you will see these colours all round the -bubbles in the glass &c. And the rest shall be said in its place. - -THAT THE EYE HAS NO PART IN PRODUCING THE COLOURS OF THE RAINBOW. - -In the experiment just described, the eye would seem to have some -share in the colours of the rainbow, since these bubbles in the -glass do not display the colours except through the medium of the -eye. But, if you place the glass full of water on the window sill, -in such a position as that the outer side is exposed to the sun's -rays, you will see the same colours produced in the spot of light -thrown through the glass and upon the floor, in a dark place, below -the window; and as the eye is not here concerned in it, we may -evidently, and with certainty pronounce that the eye has no share in -producing them. - -OF THE COLOURS IN THE FEATHERS OF CERTAIN BIRDS. - -There are many birds in various regions of the world on whose -feathers we see the most splendid colours produced as they move, as -we see in our own country in the feathers of peacocks or on the -necks of ducks or pigeons, &c. - -Again, on the surface of antique glass found underground and on the -roots of turnips kept for some time at the bottom of wells or other -stagnant waters [we see] that each root displays colours similar to -those of the real rainbow. They may also be seen when oil has been -placed on the top of water and in the solar rays reflected from the -surface of a diamond or beryl; again, through the angular facet of a -beryl every dark object against a background of the atmosphere or -any thing else equally pale-coloured is surrounded by these rainbow -colours between the atmosphere and the dark body; and in many other -circumstances which I will not mention, as these suffice for my -purpose. - -_VI._ - -_'Prospettiva de' colri' (Perspective of Colour)_ - -_and_ - -_'Prospettiva aerea' (Aerial Perspective)._ - -_Leonardo distinctly separates these branches of his subject, as may -be seen in the beginning of No._ 295. _Attempts have been made to -cast doubts on the results which Leonardo arrived at by experiment -on the perspective of colour, but not with justice, as may be seen -from the original text of section_ 294. - -_The question as to the composition of the atmosphere, which is -inseparable from a discussion on Aerial Perspective, forms a -separate theory which is treated at considerable length. Indeed the -author enters into it so fully that we cannot escape the conviction -that he must have dwelt with particular pleasure on this part of his -subject, and that he attached great importance to giving it a -character of general applicability._ - -General rules (289--291). - -289. - -The variety of colour in objects cannot be discerned at a great -distance, excepting in those parts which are directly lighted up by -the solar rays. - -290. - -As to the colours of objects: at long distances no difference is -perceptible in the parts in shadow. - -291. - -OF THE VISIBILITY OF COLOURS. - -Which colour strikes most? An object at a distance is most -conspicuous, when it is lightest, and the darkest is least visible. - -An exceptional case. - -292. - -Of the edges [outlines] of shadows. Some have misty and ill defined -edges, others distinct ones. - -No opaque body can be devoid of light and shade, except it is in a -mist, on ground covered with snow, or when snow is falling on the -open country which has no light on it and is surrounded with -darkness. - -And this occurs [only] in spherical bodies, because in other bodies -which have limbs and parts, those sides of limbs which face each -other reflect on each other the accidental [hue and tone] of their -surface. - -An experiment. - -293. - -ALL COLOURS ARE AT A DISTANCE UNDISTINGUISHABLE AND UNDISCERNIBLE. - -All colours at a distance are undistinguishable in shadow, because -an object which is not in the highest light is incapable of -transmitting its image to the eye through an atmosphere more -luminous than itself; since the lesser brightness must be absorbed -by the greater. For instance: We, in a house, can see that all the -colours on the surface of the walls are clearly and instantly -visible when the windows of the house are open; but if we were to go -out of the house and look in at the windows from a little distance -to see the paintings on those walls, instead of the paintings we -should see an uniform deep and colourless shadow. - -The practice of the prospettiva de colori. - -294. - -HOW A PAINTER SHOULD CARRY OUT THE PERSPECTIVE OF COLOUR IN -PRACTICE. - -In order to put into practice this perspective of the variation and -loss or diminution of the essential character of colours, observe at -every hundred braccia some objects standing in the landscape, such -as trees, houses, men and particular places. Then in front of the -first tree have a very steady plate of glass and keep your eye very -steady, and then, on this plate of glass, draw a tree, tracing it -over the form of that tree. Then move it on one side so far as that -the real tree is close by the side of the tree you have drawn; then -colour your drawing in such a way as that in colour and form the two -may be alike, and that both, if you close one eye, seem to be -painted on the glass and at the same distance. Then, by the same -method, represent a second tree, and a third, with a distance of a -hundred braccia between each. And these will serve as a standard and -guide whenever you work on your own pictures, wherever they may -apply, and will enable you to give due distance in those works. [14] -But I have found that as a rule the second is 4/5 of the first when -it is 20 braccia beyond it. - -[Footnote: This chapter is one of those copied in the Manuscript of -the Vatican library Urbinas 1270, and the original text is rendered -here with no other alterations, but in the orthography. H. LUDWIG, -in his edition of this copy translates lines 14 and 15 thus: "_Ich -finde aber als Regel, dass der zweite um vier Funftel des ersten -abnimmt, wenn er namlich zwanzig Ellen vom ersten entfernt ist -(?)"_. He adds in his commentary: "_Das Ende der Nummer ist wohl -jedenfalls verstummelt_". However the translation given above shows -that it admits of a different rendering.] - -The rules of aerial perspective (295--297). - -295. - -OF AERIAL PERSPECTIVE. - -There is another kind of perspective which I call Aerial -Perspective, because by the atmosphere we are able to distinguish -the variations in distance of different buildings, which appear -placed on a single line; as, for instance, when we see several -buildings beyond a wall, all of which, as they appear above the top -of the wall, look of the same size, while you wish to represent them -in a picture as more remote one than another and to give the effect -of a somewhat dense atmosphere. You know that in an atmosphere of -equal density the remotest objects seen through it, as mountains, in -consequence of the great quantity of atmosphere between your eye and -them--appear blue and almost of the same hue as the atmosphere -itself [Footnote 10: _quado il sole e per leuante_ (when the sun is -in the East). Apparently the author refers here to morning light in -general. H. LUDWIG however translates this passage from the Vatican -copy "_wenn namlich die Sonne (dahinter) im Osten steht_".] when the -sun is in the East [Footnote 11: See Footnote 10]. Hence you must -make the nearest building above the wall of its real colour, but the -more distant ones make less defined and bluer. Those you wish should -look farthest away you must make proportionately bluer; thus, if one -is to be five times as distant, make it five times bluer. And by -this rule the buildings which above a [given] line appear of the -same size, will plainly be distinguished as to which are the more -remote and which larger than the others. - -296. - -The medium lying between the eye and the object seen, tinges that -object with its colour, as the blueness of the atmosphere makes the -distant mountains appear blue and red glass makes objects seen -beyond it, look red. The light shed round them by the stars is -obscured by the darkness of the night which lies between the eye and -the radiant light of the stars. - -297. - -Take care that the perspective of colour does not disagree with the -size of your objects, hat is to say: that the colours diminish from -their natural [vividness] in proportion as the objects at various -distances dimmish from their natural size. - -On the relative density of the atmosphere (298--290). - -298. - -WHY THE ATMOSPHERE MUST BE REPRESENTED AS PALER TOWARDS THE LOWER -PORTION. - -Because the atmosphere is dense near the earth, and the higher it is -the rarer it becomes. When the sun is in the East if you look -towards the West and a little way to the South and North, you will -see that this dense atmosphere receives more light from the sun than -the rarer; because the rays meet with greater resistance. And if the -sky, as you see it, ends on a low plain, that lowest portion of the -sky will be seen through a denser and whiter atmosphere, which will -weaken its true colour as seen through that medium, and there the -sky will look whiter than it is above you, where the line of sight -travels through a smaller space of air charged with heavy vapour. -And if you turn to the East, the atmosphere will appear darker as -you look lower down because the luminous rays pass less freely -through the lower atmosphere. - -299. - -OF THE MODE OF TREATING REMOTE OBJECTS IN PAINTING. - -It is easy to perceive that the atmosphere which lies closest to the -level ground is denser than the rest, and that where it is higher -up, it is rarer and more transparent. The lower portions of large -and lofty objects which are at a distance are not much seen, because -you see them along a line which passes through a denser and thicker -section of the atmosphere. The summits of such heights are seen -along a line which, though it starts from your eye in a dense -atmosphere, still, as it ends at the top of those lofty objects, -ceases in a much rarer atmosphere than exists at their base; for -this reason the farther this line extends from your eye, from point -to point the atmosphere becomes more and more rare. Hence, O -Painter! when you represent mountains, see that from hill to hill -the bases are paler than the summits, and in proportion as they -recede beyond each other make the bases paler than the summits; -while, the higher they are the more you must show of their true form -and colour. - -On the colour of the atmosphere (300-307). - -300. - -OF THE COLOUR OF THE ATMOSPHERE. - -I say that the blueness we see in the atmosphere is not intrinsic -colour, but is caused by warm vapour evaporated in minute and -insensible atoms on which the solar rays fall, rendering them -luminous against the infinite darkness of the fiery sphere which -lies beyond and includes it. And this may be seen, as I saw it by -any one going up [Footnote 5: With regard to the place spoken of as -_M'oboso_ (compare No. 301 line 20) its identity will be discussed -under Leonardo's Topographical notes in Vol. II.] Monboso, a peak of -the Alps which divide France from Italy. The base of this mountain -gives birth to the four rivers which flow in four different -directions through the whole of Europe. And no mountain has its base -at so great a height as this, which lifts itself almost above the -clouds; and snow seldom falls there, but only hail in the summer, -when the clouds are highest. And this hail lies [unmelted] there, so -that if it were not for the absorption of the rising and falling -clouds, which does not happen twice in an age, an enormous mass of -ice would be piled up there by the hail, and in the middle of July I -found it very considerable. There I saw above me the dark sky, and -the sun as it fell on the mountain was far brighter here than in the -plains below, because a smaller extent of atmosphere lay between the -summit of the mountain and the sun. Again as an illustration of the -colour of the atmosphere I will mention the smoke of old and dry -wood, which, as it comes out of a chimney, appears to turn very -blue, when seen between the eye and the dark distance. But as it -rises, and comes between the eye and the bright atmosphere, it at -once shows of an ashy grey colour; and this happens because it no -longer has darkness beyond it, but this bright and luminous space. -If the smoke is from young, green wood, it will not appear blue, -because, not being transparent and being full of superabundant -moisture, it has the effect of condensed clouds which take distinct -lights and shadows like a solid body. The same occurs with the -atmosphere, which, when overcharged with moisture appears white, and -the small amount of heated moisture makes it dark, of a dark blue -colour; and this will suffice us so far as concerns the colour of -the atmosphere; though it might be added that, if this transparent -blue were the natural colour of the atmosphere, it would follow that -wherever a larger mass air intervened between the eye and the -element of fire, the azure colour would be more intense; as we see -in blue glass and in sapphires, which are darker in proportion as -they are larger. But the atmosphere in such circumstances behaves in -an opposite manner, inasmuch as where a greater quantity of it lies -between the eye and the sphere of fire, it is seen much whiter. This -occurs towards the horizon. And the less the extent of atmosphere -between the eye and the sphere of fire, the deeper is the blue -colour, as may be seen even on low plains. Hence it follows, as I -say, that the atmosphere assumes this azure hue by reason of the -particles of moisture which catch the rays of the sun. Again, we may -note the difference in particles of dust, or particles of smoke, in -the sun beams admitted through holes into a dark chamber, when the -former will look ash grey and the thin smoke will appear of a most -beautiful blue; and it may be seen again in in the dark shadows of -distant mountains when the air between the eye and those shadows -will look very blue, though the brightest parts of those mountains -will not differ much from their true colour. But if any one wishes -for a final proof let him paint a board with various colours, among -them an intense black; and over all let him lay a very thin and -transparent [coating of] white. He will then see that this -transparent white will nowhere show a more beautiful blue than over -the black--but it must be very thin and finely ground. - -[Footnote 7: _reta_ here has the sense of _malanno_.] - -301. - -Experience shows us that the air must have darkness beyond it and -yet it appears blue. If you produce a small quantity of smoke from -dry wood and the rays of the sun fall on this smoke, and if you then -place behind the smoke a piece of black velvet on which the sun does -not shine, you will see that all the smoke which is between the eye -and the black stuff will appear of a beautiful blue colour. And if -instead of the velvet you place a white cloth smoke, that is too -thick smoke, hinders, and too thin smoke does not produce, the -perfection of this blue colour. Hence a moderate amount of smoke -produces the finest blue. Water violently ejected in a fine spray -and in a dark chamber where the sun beams are admitted produces -these blue rays and the more vividly if it is distilled water, and -thin smoke looks blue. This I mention in order to show that the -blueness of the atmosphere is caused by the darkness beyond it, and -these instances are given for those who cannot confirm my experience -on Monboso. - -302. - -When the smoke from dry wood is seen between the eye of the -spectator and some dark space [or object], it will look blue. Thus -the sky looks blue by reason of the darkness beyond it. And if you -look towards the horizon of the sky, you will see the atmosphere is -not blue, and this is caused by its density. And thus at each -degree, as you raise your eyes above the horizon up to the sky over -your head, you will see the atmosphere look darker [blue] and this -is because a smaller density of air lies between your eye and the -[outer] darkness. And if you go to the top of a high mountain the -sky will look proportionately darker above you as the atmosphere -becomes rarer between you and the [outer] darkness; and this will be -more visible at each degree of increasing height till at last we -should find darkness. - -That smoke will look bluest which rises from the driest wood and -which is nearest to the fire and is seen against the darkest -background, and with the sunlight upon it. - -303. - -A dark object will appear bluest in proportion as it has a greater -mass of luminous atmosphere between it and the eye. As may be seen -in the colour of the sky. - -304. - -The atmosphere is blue by reason of the darkness above it because -black and white make blue. - -305. - -In the morning the mist is denser above than below, because the sun -draws it upwards; hence tall buildings, even if the summit is at the -same distance as the base have the summit invisible. Therefore, -also, the sky looks darkest [in colour] overhead, and towards the -horizon it is not blue but rather between smoke and dust colour. - -The atmosphere, when full of mist, is quite devoid of blueness, and -only appears of the colour of clouds, which shine white when the -weather is fine. And the more you turn to the west the darker it -will be, and the brighter as you look to the east. And the verdure -of the fields is bluish in a thin mist, but grows grey in a dense -one. - -The buildings in the west will only show their illuminated side, -where the sun shines, and the mist hides the rest. When the sun -rises and chases away the haze, the hills on the side where it lifts -begin to grow clearer, and look blue, and seem to smoke with the -vanishing mists; and the buildings reveal their lights and shadows; -through the thinner vapour they show only their lights and through -the thicker air nothing at all. This is when the movement of the -mist makes it part horizontally, and then the edges of the mist will -be indistinct against the blue of the sky, and towards the earth it -will look almost like dust blown up. In proportion as the atmosphere -is dense the buildings of a city and the trees in a landscape will -look fewer, because only the tallest and largest will be seen. - -Darkness affects every thing with its hue, and the more an object -differs from darkness, the more we see its real and natural colour. -The mountains will look few, because only those will be seen which -are farthest apart; since, at such a distance, the density increases -to such a degree that it causes a brightness by which the darkness -of the hills becomes divided and vanishes indeed towards the top. -There is less [mist] between lower and nearer hills and yet little -is to be distinguished, and least towards the bottom. - -306. - -The surface of an object partakes of the colour of the light which -illuminates it; and of the colour of the atmosphere which lies -between the eye and that object, that is of the colour of the -transparent medium lying between the object and the eye; and among -colours of a similar character the second will be of the same tone -as the first, and this is caused by the increased thickness of the -colour of the medium lying between the object and the eye. - -307. OF PAINTING. - -Of various colours which are none of them blue that which at a great -distance will look bluest is the nearest to black; and so, -conversely, the colour which is least like black will at a great -distance best preserve its own colour. - -Hence the green of fields will assume a bluer hue than yellow or -white will, and conversely yellow or white will change less than -green, and red still less. - -_VII._ - -_On the Proportions and on the Movements of the Human Figure._ - -_Leonardo's researches on the proportions and movements of the human -figure must have been for the most part completed and written before -the year_ 1498; _for LUCA PACIOLO writes, in the dedication to -Ludovico il Moro, of his book_ Divina Proportione, _which was -published in that year:_ "Leonardo da venci ... hauedo gia co tutta -diligetia al degno libro de pictura e movimenti humani posto fine". - -_The selection of Leonardo's axioms contained in the Vatican copy -attributes these words to the author:_ "e il resto si dira nella -universale misura del huomo". (_MANZI, p. 147; LUDWIG, No. 264_). -_LOMAZZO, again, in his_ Idea del Tempio della Pittura Milano 1590, -cap. IV, _says:_ "Lionardo Vinci ... dimostro anco in figura tutte -le proporzioni dei membri del corpo umano". - -_The Vatican copy includes but very few sections of the_ "Universale -misura del huomo" _and until now nothing has been made known of the -original MSS. on the subject which have supplied the very extensive -materials for this portion of the work. The collection at Windsor, -belonging to her Majesty the Queen, includes by far the most -important part of Leonardo's investigations on this subject, -constituting about half of the whole of the materials here -published; and the large number of original drawings adds greatly to -the interest which the subject itself must command. Luca Paciolo -would seem to have had these MSS. (which I have distinguished by the -initials W. P.) in his mind when he wrote the passage quoted above. -Still, certain notes of a later date--such as Nos. 360, 362 and 363, -from MS. E, written in 1513--14, sufficiently prove that Leonardo did -not consider his earlier studies on the Proportions and Movements of -the Human Figure final and complete, as we might suppose from Luca -Paciolo's statement. Or else he took the subject up again at a -subsequent period, since his former researches had been carried on -at Milan between 1490 and 1500. Indeed it is highly probable that -the anatomical studies which he was pursuing zvith so much zeal -between 1510--16 should have led him to reconsider the subject of -Proportion. - -Preliminary observations (308. 309). - -308. - -Every man, at three years old is half the full height he will grow -to at last. - -309. - -If a man 2 braccia high is too small, one of four is too tall, the -medium being what is admirable. Between 2 and 4 comes 3; therefore -take a man of 3 braccia in height and measure him by the rule I will -give you. If you tell me that I may be mistaken, and judge a man to -be well proportioned who does not conform to this division, I answer -that you must look at many men of 3 braccia, and out of the larger -number who are alike in their limbs choose one of those who are most -graceful and take your measurements. The length of the hand is 1/3 -of a braccio [8 inches] and this is found 9 times in man. And the -face [Footnote 7: The account here given of the _braccio_ is of -importance in understanding some of the succeeding chapters. _Testa_ -must here be understood to mean the face. The statements in this -section are illustrated in part on Pl. XI.] is the same, and from -the pit of the throat to the shoulder, and from the shoulder to the -nipple, and from one nipple to the other, and from each nipple to -the pit of the throat. - -Proportions of the head and face (310-318). - -310. - -The space between the parting of the lips [the mouth] and the base -of the nose is one-seventh of the face. - -The space from the mouth to the bottom of the chin _c d_ is the -fourth part of the face and equal to the width of the mouth. - -The space from the chin to the base of the nose _e f_ is the third -part of the face and equal to the length of the nose and to the -forehead. - -The distance from the middle of the nose to the bottom of the chin -_g h_, is half the length of the face. - -The distance from the top of the nose, where the eyebrows begin, to -the bottom of the chin, _i k_, is two thirds of the face. - -The space from the parting of the lips to the top of the chin _l m_, -that is where the chin ends and passes into the lower lip of the -mouth, is the third of the distance from the parting of the lips to -the bottom of the chin and is the twelfth part of the face. From the -top to the bottom of the chin _m n_ is the sixth part of the face -and is the fifty fourth part of a man's height. - -From the farthest projection of the chin to the throat _o p_ is -equal to the space between the mouth and the bottom of the chin, and -a fourth of the face. - -The distance from the top of the throat to the pit of the throat -below _q r_ is half the length of the face and the eighteenth part -of a man's height. - -From the chin to the back of the neck _s t_, is the same distance as -between the mouth and the roots of the hair, that is three quarters -of the head. - -From the chin to the jaw bone _v x_ is half the head and equal to -the thickness of the neck in profile. - -The thickness of the head from the brow to the nape is once and 3/4 -that of the neck. - -[Footnote: The drawings to this text, lines 1-10 are on Pl. VII, No. -I. The two upper sketches of heads, Pl. VII, No. 2, belong to lines -11-14, and in the original are placed immediately below the sketches -reproduced on Pl. VII, No. 1.] - -311. - -The distance from the attachment of one ear to the other is equal to -that from the meeting of the eyebrows to the chin, and in a fine -face the width of the mouth is equal to the length from the parting -of the lips to the bottom of the chin. - -312. - -The cut or depression below the lower lip of the mouth is half way -between the bottom of the nose and the bottom of the chin. - -The face forms a square in itself; that is its width is from the -outer corner of one eye to the other, and its height is from the -very top of the nose to the bottom of the lower lip of the mouth; -then what remains above and below this square amounts to the height -of such another square, _a_ _b_ is equal to the space between _c_ -_d_; _d_ _n_ in the same way to _n_ _c_, and likewise _s_ _r_, _q_ -_p_, _h_ _k_ are equal to each other. - -It is as far between _m_ and _s_ as from the bottom of the nose to -the chin. The ear is exactly as long as the nose. It is as far from -_x_ to _j_ as from the nose to the chin. The parting of the mouth -seen in profile slopes to the angle of the jaw. The ear should be as -high as from the bottom of the nose to the top of the eye-lid. The -space between the eyes is equal to the width of an eye. The ear is -over the middle of the neck, when seen in profile. The distance from -4 to 5 is equal to that from s_ to _r_. - -[Footnote: See Pl. VIII, No. I, where the text of lines 3-13 is also -given in facsimile.] - -313. - -(_a_ _b_) is equal to (_c_ _d_). - -[Footnote: See Pl. VII, No. 3. Reference may also be made here to -two pen and ink drawings of heads in profile with figured -measurements, of which there is no description in the MS. These are -given on Pl. XVII, No. 2.--A head, to the left, with part of the -torso [W. P. 5a], No. 1 on the same plate is from MS. A 2b and in -the original occurs on a page with wholly irrelevant text on matters -of natural history. M. RAVAISSON in his edition of the Paris MS. A -has reproduced this head and discussed it fully [note on page 12]; -he has however somewhat altered the original measurements. The -complicated calculations which M. RAVAISSON has given appear to me -in no way justified. The sketch, as we see it, can hardly have been -intended for any thing more than an experimental attempt to -ascertain relative proportions. We do not find that Leonardo made -use of circular lines in any other study of the proportions of the -human head. At the same time we see that the proportions of this -sketch are not in accordance with the rules which he usually -observed (see for instance No. 310).] - -The head _a_ _f_ 1/6 larger than _n_ _f_. - -315. - -From the eyebrow to the junction of the lip with the chin, and the -angle of the jaw and the upper angle where the ear joins the temple -will be a perfect square. And each side by itself is half the head. - -The hollow of the cheek bone occurs half way between the tip of the -nose and the top of the jaw bone, which is the lower angle of the -setting on of the ear, in the frame here represented. - -From the angle of the eye-socket to the ear is as far as the length -of the ear, or the third of the face. - -[Footnote: See Pl. IX. The text, in the original is written behind -the head. The handwriting would seem to indicate a date earlier than -1480. On the same leaf there is a drawing in red chalk of two -horsemen of which only a portion of the upper figure is here -visible. The whole leaf measures 22 1/2 centimetres wide by 29 long, -and is numbered 127 in the top right-hand corner.] - -316. - -From _a_ to _b_--that is to say from the roots of the hair in front -to the top of the head--ought to be equal to _c_ _d_;--that is from -the bottom of the nose to the meeting of the lips in the middle of -the mouth. From the inner corner of the eye _m_ to the top of the -head _a_ is as far as from _m_ down to the chin _s_. _s_ _c_ _f_ _b_ -are all at equal distances from each other. - -[Footnote: The drawing in silver-point on bluish tinted paper--Pl. -X--which belongs to this chapter has been partly drawn over in ink -by Leonardo himself.] - -317. - -From the top of the head to the bottom of the chin is 1/9, and from -the roots of the hair to the chin is 1/9 of the distance from the -roots of the hair to the ground. The greatest width of the face is -equal to the space between the mouth and the roots of the hair and -is 1/12 of the whole height. From the top of the ear to the top of -the head is equal to the distance from the bottom of the chin to the -lachrymatory duct of the eye; and also equal to the distance from -the angle of the chin to that of the jaw; that is the 1/16 of the -whole. The small cartilage which projects over the opening of the -ear towards the nose is half-way between the nape and the eyebrow; -the thickness of the neck in profile is equal to the space between -the chin and the eyes, and to the space between the chin and the -jaw, and it is 1/18 of the height of the man. - -318. - -_a b_, _c d_, _e f_, _g h_, _i k_ are equal to each other in size -excepting that _d f_ is accidental. - -[Footnote: See Pl. XI.] - -Proportions of the head seen in front (319-321). - -319. - -_a n o f_ are equal to the mouth. - -_a c_ and _a f_ are equal to the space between one eye and the -other. - -_n m o f q r_ are equal to half the width of the eye lids, that is -from the inner [lachrymatory] corner of the eye to its outer corner; -and in like manner the division between the chin and the mouth; and -in the same way the narrowest part of the nose between the eyes. And -these spaces, each in itself, is the 19th part of the head, _n o_ is -equal to the length of the eye or of the space between the eyes. - -_m c_ is 1/3 of _n m_ measuring from the outer corner of the eyelids -to the letter _c_. _b s_ will be equal to the width of the nostril. - -[Footnote: See Pl. XII.] - -320. - -The distance between the centres of the pupils of the eyes is 1/3 of -the face. The space between the outer corners of the eyes, that is -where the eye ends in the eye socket which contains it, thus the -outer corners, is half the face. - -The greatest width of the face at the line of the eyes is equal to -the distance from the roots of the hair in front to the parting of -the lips. - -[Footnote: There are, with this section, two sketches of eyes, not -reproduced here.] - -321. - -The nose will make a double square; that is the width of the nose at -the nostrils goes twice into the length from the tip of the nose to -the eyebrows. And, in the same way, in profile the distance from the -extreme side of the nostril where it joins the cheek to the tip of -the nose is equal to the width of the nose in front from one nostril -to the other. If you divide the whole length of the nose--that is -from the tip to the insertion of the eyebrows, into 4 equal parts, -you will find that one of these parts extends from the tip of the -nostrils to the base of the nose, and the upper division lies -between the inner corner of the eye and the insertion of the -eyebrows; and the two middle parts [together] are equal to the -length of the eye from the inner to the outer corner. - -[Footnote: The two bottom sketches on Pl. VII, No. 4 face the six -lines of this section,--With regard to the proportions of the head -in profile see No. 312.] - -322. - -The great toe is the sixth part of the foot, taking the measure in -profile, on the inside of the foot, from where this toe springs from -the ball of the sole of the foot to its tip _a b_; and it is equal -to the distance from the mouth to the bottom of the chin. If you -draw the foot in profile from the outside, make the little toe begin -at three quarters of the length of the foot, and you will find the -same distance from the insertion of this toe as to the farthest -prominence of the great toe. - -323. - -For each man respectively the distance between _a b_ is equal to _c -d_. - -324. - -Relative proportion of the hand and foot. - -The foot is as much longer than the hand as the thickness of the arm -at the wrist where it is thinnest seen facing. - -Again, you will find that the foot is as much longer than the hand -as the space between the inner angle of the little toe to the last -projection of the big toe, if you measure along the length of the -foot. - -The palm of the hand without the fingers goes twice into the length -of the foot without the toes. - -If you hold your hand with the fingers straight out and close -together you will find it to be of the same width as the widest part -of the foot, that is where it is joined onto the toes. - -And if you measure from the prominence of the inner ancle to the end -of the great toe you will find this measure to be as long as the -whole hand. - -From the top angle of the foot to the insertion of the toes is equal -to the hand from wrist joint to the tip of the thumb. - -The smallest width of the hand is equal to the smallest width of the -foot between its joint into the leg and the insertion of the toes. - -The width of the heel at the lower part is equal to that of the arm -where it joins the hand; and also to the leg where it is thinnest -when viewed in front. - -The length of the longest toe, from its first division from the -great toe to its tip is the fourth of the foot from the centre of -the ancle bone to the tip, and it is equal to the width of the -mouth. The distance between the mouth and the chin is equal to that -of the knuckles and of the three middle fingers and to the length of -their first joints if the hand is spread, and equal to the distance -from the joint of the thumb to the outset of the nails, that is the -fourth part of the hand and of the face. - -The space between the extreme poles inside and outside the foot -called the ancle or ancle bone _a b_ is equal to the space between -the mouth and the inner corner of the eye. - -325. - -The foot, from where it is attached to the leg, to the tip of the -great toe is as long as the space between the upper part of the chin -and the roots of the hair _a b_; and equal to five sixths of the -face. - -326. - -_a d_ is a head's length, _c b_ is a head's length. The four smaller -toes are all equally thick from the nail at the top to the bottom, -and are 1/13 of the foot. - -[Footnote: See Pl. XIV, No. 1, a drawing of a foot with the text in -three lines below it.] - -327. - -The whole length of the foot will lie between the elbow and the -wrist and between the elbow and the inner angle of the arm towards -the breast when the arm is folded. The foot is as long as the whole -head of a man, that is from under the chin to the topmost part of -the head[Footnote 2: _nel modo che qui i figurato_. See Pl. VII, No. -4, the upper figure. The text breaks off at the end of line 2 and -the text given under No. 321 follows below. It may be here remarked -that the second sketch on W. P. 311 has in the original no -explanatory text.] in the way here figured. - -Proportions of the leg (328-331). - -328. - -The greatest thickness of the calf of the leg is at a third of its -height _a b_, and is a twentieth part thicker than the greatest -thickness of the foot. - -_a c_ is half of the head, and equal to _d b_ and to the insertion -of the five toes _e f_. _d k_ diminishes one sixth in the leg _g h_. -_g h_ is 1/3 of the head; _m n_ increases one sixth from _a e_ and -is 7/12 of the head, _o p_ is 1/10 less than _d k_ and is 6/17 of -the head. _a_ is at half the distance between _b q_, and is 1/4 of -the man. _r_ is half way between _s_ and _b_[Footnote 11: _b_ is -here and later on measured on the right side of the foot as seen by -the spectator.]. The concavity of the knee outside _r_ is higher -than that inside _a_. The half of the whole height of the leg from -the foot _r_, is half way between the prominence _s_ and the ground -_b_. _v_ is half way between _t_ and _b_. The thickness of the thigh -seen in front is equal to the greatest width of the face, that is -2/3 of the length from the chin to the top of the head; _z r_ is 5/6 -of 7 to _v_; _m n_ is equal to 7 _v_ and is 1/4 of _r b_, _x y_ goes -3 times into _r b_, and into _r s_. - -[Footnote 22-35: The sketch illustrating these lines is on Pl. XIII, -No. 2.] - -[Footnote 22: a b _entra in_ c f 6 _e_ 6 _in_ c n. Accurate -measurement however obliges us to read 7 for 6.] _a b_ goes six -times into _c f_ and six times into _c n_ and is equal to _g h_; _i -k l m_ goes 4 times into _d f_, and 4 times into _d n_ and is 3/7 of -the foot; _p q r s_ goes 3 times into _d f, and 3 times into _b n_; -[Footnote: 25. _y_ is not to be found on the diagram and _x_ occurs -twice; this makes the passage very obscure.] _x y_ is 1/8 of _x f_ -and is equal to _n q_. 3 7 is 1/9 of _n f_; 4 5 is 1/10 of _n f_ -[Footnote: 22-27. Compare with this lines 18-24 of No. 331, and the -sketch of a leg in profile Pl. XV.]. - -I want to know how much a man increases in height by standing on -tip-toe and how much _p g_ diminishes by stooping; and how much it -increases at _n q_ likewise in bending the foot. - -[Footnote 34: _e f_ 4 _dal cazo_. By reading _i_ for _e_ the sense -of this passage is made clear.] _e f_ is four times in the distance -between the genitals and the sole of the foot; [Footnote 35: 2 is -not to be found in the sketch which renders the passage obscure. The -two last lines are plainly legible in the facsimile.] 3 7 is six -times from 3 to 2 and is equal to _g h_ and _i k_. - -[Footnote: The drawing of a leg seen in front Pl. XIII, No. 1 -belongs to the text from lines 3-21. The measurements in this -section should be compared with the text No. 331, lines 1-13, and -the sketch of a leg seen in front on Pl. XV.] - -329. - -The length of the foot from the end of the toes to the heel goes -twice into that from the heel to the knee, that is where the leg -bone [fibula] joins the thigh bone [femur]. - -330. - -_a n b_ are equal; _c n d_ are equal; _n c_ makes two feet; _n d_ -makes 2 feet. - -[Footnote: See the lower sketch, Pl. XIV, No. 1.] - -331. - -_m n o_ are equal. The narrowest width of the leg seen in front goes -8 times from the sole of the foot to the joint of the knee, and is -the same width as the arm, seen in front at the wrist, and as the -longest measure of the ear, and as the three chief divisions into -which we divide the face; and this measurement goes 4 times from the -wrist joint of the hand to the point of the elbow. [14] The foot is -as long as the space from the knee between _a_ and _b_; and the -patella of the knee is as long as the leg between _r_ and _s_. - -[18] The least thickness of the leg in profile goes 6 times from the -sole of the foot to the knee joint and is the same width as the -space between the outer corner of the eye and the opening of the -ear, and as the thickest part of the arm seen in profile and between -the inner corner of the eye and the insertion of the hair. - -_a b c_ [_d_] are all relatively of equal length, _c d_ goes twice -from the sole of the foot to the centre of the knee and the same -from the knee to the hip. - -[28]_a b c_ are equal; _a_ to _b_ is 2 feet--that is to say -measuring from the heel to the tip of the great toe. - -[Footnote: See Pl. XV. The text of lines 2-17 is to the left of the -front view of the leg, to which it refers. Lines 18-27 are in the -middle column and refer to the leg seen in profile and turned to the -left, on the right hand side of the writing. Lines 20-30 are above, -to the left and apply to the sketch below them. - -Some farther remarks on the proportion of the leg will be found in -No. 336, lines 6, 7.] - -On the central point of the whole body. - -332. - -In kneeling down a man will lose the fourth part of his height. - -When a man kneels down with his hands folded on his breast the navel -will mark half his height and likewise the points of the elbows. - -Half the height of a man who sits--that is from the seat to the top -of the head--will be where the arms fold below the breast, and -below the shoulders. The seated portion--that is from the seat to -the top of the head--will be more than half the man's [whole height] -by the length of the scrotum. - -[Footnote: See Pl. VIII, No. 2.] - -The relative proportions of the torso and of the whole figure. - -333. - -The cubit is one fourth of the height of a man and is equal to the -greatest width of the shoulders. From the joint of one shoulder to -the other is two faces and is equal to the distance from the top of -the breast to the navel. [Footnote 9: _dalla detta somita_. It would -seem more accurate to read here _dal detto ombilico_.] From this -point to the genitals is a face's length. - -[Footnote: Compare with this the sketches on the other page of the -same leaf. Pl. VIII, No. 2.] - -The relative proportions of the head and of the torso. - -334. - -From the roots of the hair to the top of the breast _a b_ is the -sixth part of the height of a man and this measure is equal. - -From the outside part of one shoulder to the other is the same -distance as from the top of the breast to the navel and this measure -goes four times from the sole of the foot to the lower end of the -nose. - -The [thickness of] the arm where it springs from the shoulder in -front goes 6 times into the space between the two outside edges of -the shoulders and 3 times into the face, and four times into the -length of the foot and three into the hand, inside or outside. - -[Footnote: The three sketches Pl. XIV, No. 2 belong to this text.] - -The relative proportions of the torso and of the leg (335. 336). - -335. - -_a b c_ are equal to each other and to the space from the armpit of -the shoulder to the genitals and to the distance from the tip of the -fingers of the hand to the joint of the arm, and to the half of the -breast; and you must know that _c b_ is the third part of the height -of a man from the shoulders to the ground; _d e f_ are equal to each -other and equal to the greatest width of the shoulders. - -[Footnote: See Pl. XVI, No. 1.] - -336. - ---Top of the chin--hip--the insertion of the middle finger. The end -of the calf of the leg on the inside of the thigh.--The end of the -swelling of the shin bone of the leg. [6] The smallest thickness of -the leg goes 3 times into the thigh seen in front. - -[Footnote: See Pl. XVII, No. 2, middle sketch.] - -The relative proportions of the torso and of the foot. - -337. - -The torso _a b_ in its thinnest part measures a foot; and from _a_ -to _b_ is 2 feet, which makes two squares to the seat--its thinnest -part goes 3 times into the length, thus making 3 squares. - -[Footnote: See Pl, VII, No. 2, the lower sketch.] - -The proportions of the whole figure (338-341). - -338. - -A man when he lies down is reduced to 1/9 of his height. - -339. - -The opening of the ear, the joint of the shoulder, that of the hip -and the ancle are in perpendicular lines; _a n_ is equal to _m o_. - -[Footnote: See Pl. XVI, No. 2, the upper sketch.] - -340. - -From the chin to the roots of the hair is 1/10 of the whole figure. -From the joint of the palm of the hand to the tip of the longest -finger is 1/10. From the chin to the top of the head 1/8; and from -the pit of the stomach to the top of the breast is 1/6, and from the -pit below the breast bone to the top of the head 1/4. From the chin -to the nostrils 1/3 Part of the face, the same from the nostrils to -the brow and from the brow to the roots of the hair, and the foot is -1/6, the elbow 1/4, the width of the shoulders 1/4. - -341. - -The width of the shoulders is 1/4 of the whole. From the joint of -the shoulder to the hand is 1/3, from the parting of the lips to -below the shoulder-blade is one foot. - -The greatest thickness of a man from the breast to the spine is one -8th of his height and is equal to the space between the bottom of -the chin and the top of the head. - -The greatest width is at the shoulders and goes 4. - -The torso from the front and back. - -342. - -The width of a man under the arms is the same as at the hips. - -A man's width across the hips is equal to the distance from the top -of the hip to the bottom of the buttock, when a man stands equally -balanced on both feet; and there is the same distance from the top -of the hip to the armpit. The waist, or narrower part above the hips -will be half way between the arm pits and the bottom of the buttock. - -[Footnote: The lower sketch Pl. XVI, No. 2, is drawn by the side of -line 1.] - -Vitruvius' scheme of proportions. - -343. - -Vitruvius, the architect, says in his work on architecture that the -measurements of the human body are distributed by Nature as follows: -that is that 4 fingers make 1 palm, and 4 palms make 1 foot, 6 palms -make 1 cubit; 4 cubits make a man's height. And 4 cubits make one -pace and 24 palms make a man; and these measures he used in his -buildings. If you open your legs so much as to decrease your height -1/14 and spread and raise your arms till your middle fingers touch -the level of the top of your head you must know that the centre of -the outspread limbs will be in the navel and the space between the -legs will be an equilateral triangle. - -The length of a man's outspread arms is equal to his height. - -From the roots of the hair to the bottom of the chin is the tenth of -a man's height; from the bottom of the chin to the top of his head -is one eighth of his height; from the top of the breast to the top -of his head will be one sixth of a man. From the top of the breast -to the roots of the hair will be the seventh part of the whole man. -From the nipples to the top of the head will be the fourth part of a -man. The greatest width of the shoulders contains in itself the -fourth part of the man. From the elbow to the tip of the hand will -be the fifth part of a man; and from the elbow to the angle of the -armpit will be the eighth part of the man. The whole hand will be -the tenth part of the man; the beginning of the genitals marks the -middle of the man. The foot is the seventh part of the man. From the -sole of the foot to below the knee will be the fourth part of the -man. From below the knee to the beginning of the genitals will be -the fourth part of the man. The distance from the bottom of the chin -to the nose and from the roots of the hair to the eyebrows is, in -each case the same, and like the ear, a third of the face. - -[Footnote: See Pl. XVIII. The original leaf is 21 centimetres wide -and 33 1/2 long. At the ends of the scale below the figure are -written the words _diti_ (fingers) and _palmi_ (palms). The passage -quoted from Vitruvius is Book III, Cap. 1, and Leonardo's drawing is -given in the editions of Vitruvius by FRA GIOCONDO (Venezia 1511, -fol., Firenze 1513, 8vo.) and by CESARIANO (Como 1521).] - -The arm and head. - -344. - -From _b_ to _a_ is one head, as well as from _c_ to _a_ and this -happens when the elbow forms a right angle. - -[Footnote: See Pl. XLI, No. 1.] - -Proportions of the arm (345-349). - -345. - -From the tip of the longest finger of the hand to the shoulder joint -is four hands or, if you will, four faces. - -_a b c_ are equal and each interval is 2 heads. - -[Footnote: Lines 1-3 are given on Pl. XV below the front view of the -leg; lines 4 and 5 are below again, on the left side. The lettering -refers to the bent arm near the text.] - -346. - -The hand from the longest finger to the wrist joint goes 4 times -from the tip of the longest finger to the shoulder joint. - -347. - -_a b c_ are equal to each other and to the foot and to the space -between the nipple and the navel _d e_ will be the third part of the -whole man. - -_f g_ is the fourth part of a man and is equal to _g h_ and measures -a cubit. - -[Footnote: See Pl. XIX, No. 1. 1. _mamolino_ (=_bambino_, little -child) may mean here the navel.] - -348. - -_a b_ goes 4 times into _a c_ and 9 into _a m_. The greatest -thickness of the arm between the elbow and the hand goes 6 times -into _a m_ and is equal to _r f_. The greatest thickness of the arm -between the shoulder and the elbow goes 4 times into _c m_, and is -equal to _h n g_. The smallest thickness of the arm above the elbow -_x y_ is not the base of a square, but is equal to half the space -_h_ 3 which is found between the inner joint of the arm and the -wrist joint. - -[11]The width of the wrist goes 12 times into the whole arm; that is -from the tip of the fingers to the shoulder joint; that is 3 times -into the hand and 9 into the arm. - -The arm when bent is 4 heads. - -The arm from the shoulder to the elbow in bending increases in -length, that is in the length from the shoulder to the elbow, and -this increase is equal to the thickness of the arm at the wrist when -seen in profile. And the space between the bottom of the chin and -the parting of the lips, is equal to the thickness of the 2 middle -fingers, and to the width of the mouth and to the space between the -roots of the hair on the forehead and the top of the head [Footnote: -_Queste cose_. This passage seems to have been written on purpose to -rectify the foregoing lines. The error is explained by the -accompanying sketch of the bones of the arm.]. All these distances -are equal to each other, but they are not equal to the -above-mentioned increase in the arm. - -The arm between the elbow and wrist never increases by being bent or -extended. - -The arm, from the shoulder to the inner joint when extended. - -When the arm is extended, _p n_ is equal to _n a_. And when it is -bent _n a_ diminishes 1/6 of its length and _p n_ does the same. The -outer elbow joint increases 1/7 when bent; and thus by being bent it -increases to the length of 2 heads. And on the inner side, by -bending, it is found that whereas the arm from where it joins the -side to the wrist, was 2 heads and a half, in bending it loses the -half head and measures only two: one from the [shoulder] joint to -the end [by the elbow], and the other to the hand. - -The arm when folded will measure 2 faces up to the shoulder from the -elbow and 2 from the elbow to the insertion of the four fingers on -the palm of the hand. The length from the base of the fingers to the -elbow never alters in any position of the arm. - -If the arm is extended it decreases by 1/3 of the length between _b_ -and _h_; and if--being extended--it is bent, it will increase the -half of _o e_. [Footnote 59-61: The figure sketched in the margin is -however drawn to different proportions.] The length from the -shoulder to the elbow is the same as from the base of the thumb, -inside, to the elbow _a b c_. - -[Footnote 62-64: The arm sketch on the margin of the MS. is -identically the same as that given below on Pl. XX which may -therefore be referred to in this place. In line 62 we read therefore -_z c_ for _m n_.] The smallest thickness of the arm in profile _z c_ -goes 6 times between the knuckles of the hand and the dimple of the -elbow when extended and 14 times in the whole arm and 42 in the -whole man [64]. The greatest thickness of the arm in profile is -equal to the greatest thickness of the arm in front; but the first -is placed at a third of the arm from the shoulder joint to the elbow -and the other at a third from the elbow towards the hand. - -[Footnote: Compare Pl. XVII. Lines 1-10 and 11-15 are written in two -columns below the extended arm, and at the tips of the fingers we -find the words: _fine d'unghie_ (ends of the nails). Part of the -text--lines 22 to 25--is visible by the side of the sketches on Pl. -XXXV, No. 1.] - -349. - -From the top of the shoulder to the point of the elbow is as far as -from that point to the joints of the four fingers with the palm of -the hand, and each is 2 faces. - -[5]_a e_ is equal to the palm of the hand, _r f_ and _o g_ are equal -to half a head and each goes 4 times into _a b_ and _b c_. From _c_ -to _m_ is 1/2 a head; _m n_ is 1/3 of a head and goes 6 times into -_c b_ and into _b a_; _a b_ loses 1/7 of its length when the arm is -extended; _c b_ never alters; _o_ will always be the middle point -between _a_ and _s_. - -_y l_ is the fleshy part of the arm and measures one head; and when -the arm is bent this shrinks 2/5 of its length; _o a_ in bending -loses 1/6 and so does _o r_. - -_a b_ is 1/7 of _r c_. _f s_ will be 1/8 of _r c_, and each of those -2 measurements is the largest of the arm; _k h_ is the thinnest part -between the shoulder and the elbow and it is 1/8 of the whole arm _r -c_; _o p_ is 1/5 of _r l_; _c z_ goes 13 times into _r c_. - -[Footnote: See Pl. XX where the text is also seen from lines 5-23.] - -The movement of the arm (350-354). - -350. - -In the innermost bend of the joints of every limb the reliefs are -converted into a hollow, and likewise every hollow of the innermost -bends becomes a convexity when the limb is straightened to the -utmost. And in this very great mistakes are often made by those who -have insufficient knowledge and trust to their own invention and do -not have recourse to the imitation of nature; and these variations -occur more in the middle of the sides than in front, and more at the -back than at the sides. - -351. - -When the arm is bent at an angle at the elbow, it will produce some -angle; the more acute the angle is, the more will the muscles within -the bend be shortened; while the muscles outside will become of -greater length than before. As is shown in the example; _d c e_ will -shrink considerably; and _b n_ will be much extended. - -[Footnote: See Pl. XIX, No. 2.] - -352. - -OF PAINTING. - -The arm, as it turns, thrusts back its shoulder towards the middle -of the back. - -353. - -The principal movements of the hand are 10; that is forwards, -backwards, to right and to left, in a circular motion, up or down, -to close and to open, and to spread the fingers or to press them -together. - -354. - -OF THE MOTIONS OF THE FINGERS. - -The movements of the fingers principally consist in extending and -bending them. This extension and bending vary in manner; that is, -sometimes they bend altogether at the first joint; sometimes they -bend, or extend, half way, at the 2nd joint; and sometimes they bend -in their whole length and in all the three joints at once. If the 2 -first joints are hindered from bending, then the 3rd joint can be -bent with greater ease than before; it can never bend of itself, if -the other joints are free, unless all three joints are bent. Besides -all these movements there are 4 other principal motions of which 2 -are up and down, the two others from side to side; and each of these -is effected by a single tendon. From these there follow an infinite -number of other movements always effected by two tendons; one tendon -ceasing to act, the other takes up the movement. The tendons are -made thick inside the fingers and thin outside; and the tendons -inside are attached to every joint but outside they are not. - -[Footnote 26: This head line has, in the original, no text to -follow.] Of the strength [and effect] of the 3 tendons inside the -fingers at the 3 joints. - -The movement of the torso (355-361). - -355. - -Observe the altered position of the shoulder in all the movements of -the arm, going up and down, inwards and outwards, to the back and to -the front, and also in circular movements and any others. - -And do the same with reference to the neck, hands and feet and the -breast above the lips &c. - -356. - -Three are the principal muscles of the shoulder, that is _b c d_, -and two are the lateral muscles which move it forward and backward, -that is _a o_; _a_ moves it forward, and _o_ pulls it back; and bed -raises it; _a b c_ moves it upwards and forwards, and _c d o_ -upwards and backwards. Its own weight almost suffices to move it -downwards. - -The muscle _d_ acts with the muscle _c_ when the arm moves forward; -and in moving backward the muscle _b_ acts with the muscle _c_. - -[Footnote: See Pl. XXI. In the original the lettering has been -written in ink upon the red chalk drawing and the outlines of the -figures have in most places been inked over.] - -357. - -OF THE LOINS, WHEN BENT. - -The loins or backbone being bent. The breasts are are always lower -than the shoulderblades of the back. - -If the breast bone is arched the breasts are higher than the -shoulderblades. - -If the loins are upright the breast will always be found at the same -level as the shoulderblades. - -[Footnote: See Pl. XXII, No. 1.] - -358. - -_a b_ the tendon and ankle in raising the heel approach each other -by a finger's breadth; in lowering it they separate by a finger's -breadth. - -[Footnote: See Pl. XXII, No. 2. Compare this facsimile and text with -Pl. III, No. 2, and p. 152 of MANZI'S edition. Also with No. 274 of -LUDWIG'S edition of the Vatican Copy.] - -359. - -Just so much as the part _d a_ of the nude figure decreases in this -position so much does the opposite part increase; that is: in -proportion as the length of the part _d a_ diminishes the normal -size so does the opposite upper part increase beyond its [normal] -size. The navel does not change its position to the male organ; and -this shrinking arises because when a figure stands on one foot, that -foot becomes the centre [of gravity] of the superimposed weight. -This being so, the middle between the shoulders is thrust above it -out of it perpendicular line, and this line, which forms the central -line of the external parts of the body, becomes bent at its upper -extremity [so as to be] above the foot which supports the body; and -the transverse lines are forced into such angles that their ends are -lower on the side which is supported. As is shown at _a b c_. - -[Footnote: See Pl. XXII, No. 3.] - -360. - -OF PAINTING. - -Note in the motions and attitudes of figures how the limbs vary, and -their feeling, for the shoulderblades in the motions of the arms and -shoulders vary the [line of the] back bone very much. And you will -find all the causes of this in my book of Anatomy. - -361. - -OF [CHANGE OF] ATTITUDE. - -The pit of the throat is over the feet, and by throwing one arm -forward the pit of the throat is thrown off that foot. And if the -leg is thrown forward the pit of the throat is thrown forward; and. -so it varies in every attitude. - -362. - -OF PAINTING. - -Indicate which are the muscles, and which the tendons, which become -prominent or retreat in the different movements of each limb; or -which do neither [but are passive]. And remember that these -indications of action are of the first importance and necessity in -any painter or sculptor who professes to be a master &c. - -And indicate the same in a child, and from birth to decrepitude at -every stage of its life; as infancy, childhood, boyhood, youth &c. - -And in each express the alterations in the limbs and joints, which -swell and which grow thinner. - -363. - -O Anatomical Painter! beware lest the too strong indication of the -bones, sinews and muscles, be the cause of your becoming wooden in -your painting by your wish to make your nude figures display all -their feeling. Therefore, in endeavouring to remedy this, look in -what manner the muscles clothe or cover their bones in old or lean -persons; and besides this, observe the rule as to how these same -muscles fill up the spaces of the surface that extend between them, -which are the muscles which never lose their prominence in any -amount of fatness; and which too are the muscles of which the -attachments are lost to sight in the very least plumpness. And in -many cases several muscles look like one single muscle in the -increase of fat; and in many cases, in growing lean or old, one -single muscle divides into several muscles. And in this treatise, -each in its place, all their peculiarities will be explained--and -particularly as to the spaces between the joints of each limb &c. -Again, do not fail [to observe] the variations in the forms of the -above mentioned muscles, round and about the joints of the limbs of -any animal, as caused by the diversity of the motions of each limb; -for on some side of those joints the prominence of these muscles is -wholly lost in the increase or diminution of the flesh of which -these muscles are composed, &c. - -[Footnote: DE ROSSI remarks on this chapter, in the Roman edition of -the Trattato, p. 504: "_Non in questo luogo solo, ma in altri ancora -osservera il lettore, che Lionardo va fungendo quelli che fanno -abuso della loro dottrina anatomica, e sicuramente con cio ha in -mira il suo rivale Bonarroti, che di anatomia facea tanta pompa_." -Note, that Leonardo wrote this passage in Rome, probably under the -immediate impression of MICHAELANGELO'S paintings in the Sistine -Chapel and of RAPHAEL'S Isaiah in Sant' Agostino.] - -364. - -OF THE DIFFERENT MEASUREMENTS OF BOYS AND MEN. - -There is a great difference in the length between the joints in men -and boys for, in man, from the top of the shoulder [by the neck] to -the elbow, and from the elbow to the tip of the thumb and from one -shoulder to the other, is in each instance two heads, while in a boy -it is but one because Nature constructs in us the mass which is the -home of the intellect, before forming that which contains the vital -elements. - -365. - -OF PAINTING. - -Which are the muscles which subdivide in old age or in youth, when -becoming lean? Which are the parts of the limbs of the human frame -where no amount of fat makes the flesh thicker, nor any degree of -leanness ever diminishes it? - -The thing sought for in this question will be found in all the -external joints of the bones, as the shoulder, elbow, wrists, -finger-joints, hips, knees, ankle-bone and toes and the like; all of -which shall be told in its place. The greatest thickness acquired by -any limb is at the part of the muscles which is farthest from its -attachments. - -Flesh never increases on those portions of the limb where the bones -are near to the surface. - -At _b r d a c e f_ the increase or diminution of the flesh never -makes any considerable difference. Nature has placed in front of man -all those parts which feel most pain under a blow; and these are the -shin of the leg, the forehead, and the nose. And this was done for -the preservation of man, since, if such pain were not felt in these -parts, the number of blows to which they would be exposed must be -the cause of their destruction. - -Describe why the bones of the arm and leg are double near the hand -and foot [respectively]. - -And where the flesh is thicker or thinner in the bending of the -limbs. - -366. - -OF PAINTING. - -Every part of the whole must be in proportion to the whole. Thus, if -a man is of a stout short figure he will be the same in all his -parts: that is with short and thick arms, wide thick hands, with -short fingers with their joints of the same character, and so on -with the rest. I would have the same thing understood as applying to -all animals and plants; in diminishing, [the various parts] do so in -due proportion to the size, as also in enlarging. - -367. - -OF THE AGREEMENT OF THE PROPORTION OF THE LIMBS. - -And again, remember to be very careful in giving your figures limbs, -that they must appear to agree with the size of the body and -likewise to the age. Thus a youth has limbs that are not very -muscular not strongly veined, and the surface is delicate and round, -and tender in colour. In man the limbs are sinewy and muscular, -while in old men the surface is wrinkled, rugged and knotty, and the -sinews very prominent. - -HOW YOUNG BOYS HAVE THEIR JOINTS JUST THE REVERSE OF THOSE OF MEN, -AS TO SIZE. - -Little children have all the joints slender and the portions between -them are thick; and this happens because nothing but the skin covers -the joints without any other flesh and has the character of sinew, -connecting the bones like a ligature. And the fat fleshiness is laid -on between one joint and the next, and between the skin and the -bones. But, since the bones are thicker at the joints than between -them, as a mass grows up the flesh ceases to have that superfluity -which it had, between the skin and the bones; whence the skin clings -more closely to the bone and the limbs grow more slender. But since -there is nothing over the joints but the cartilaginous and sinewy -skin this cannot dry up, and, not drying up, cannot shrink. Thus, -and for this reason, children are slender at the joints and fat -between the joints; as may be seen in the joints of the fingers, -arms, and shoulders, which are slender and dimpled, while in man on -the contrary all the joints of the fingers, arms, and legs are -thick; and wherever children have hollows men have prominences. - -The movement of the human figure (368-375). - -368. - -Of the manner of representing the 18 actions of man. Repose, -movement, running, standing, supported, sitting, leaning, kneeling, -lying down, suspended. Carrying or being carried, thrusting, -pulling, striking, being struck, pressing down and lifting up. - -[As to how a figure should stand with a weight in its hand [Footnote -8: The original text ends here.] Remember]. - -369. - -A sitting man cannot raise himself if that part of his body which is -front of his axis [centre of gravity] does not weigh more than that -which is behind that axis [or centre] without using his arms. - -A man who is mounting any slope finds that he must involuntarily -throw the most weight forward, on the higher foot, rather than -behind--that is in front of the axis and not behind it. Hence a man -will always, involuntarily, throw the greater weight towards the -point whither he desires to move than in any other direction. - -The faster a man runs, the more he leans forward towards the point -he runs to and throws more weight in front of his axis than behind. -A man who runs down hill throws the axis onto his heels, and one who -runs up hill throws it into the points of his feet; and a man -running on level ground throws it first on his heels and then on the -points of his feet. - -This man cannot carry his own weight unless, by drawing his body -back he balances the weight in front, in such a way as that the foot -on which he stands is the centre of gravity. - -[Footnote: See Pl. XXII, No. 4.] - -370. - -How a man proceeds to raise himself to his feet, when he is sitting -on level ground. - -371. - -A man when walking has his head in advance of his feet. - -A man when walking across a long level plain first leans [rather] -backwards and then as much forwards. - -[Footnote 3-6: He strides forward with the air of a man going down -hill; when weary, on the contrary he walks like a man going up -hill.] - -372. - -A man when running throws less weight on his legs than when standing -still. And in the same way a horse which is running feels less the -weight of the man he carries. Hence many persons think it wonderful -that, in running, the horse can rest on one single foot. From this -it may be stated that when a weight is in progressive motion the -more rapid it is the less is the perpendicular weight towards the -centre. - -373. - -If a man, in taking a jump from firm ground, can leap 3 braccia, and -when he was taking his leap it were to recede 1/3 of a braccio, that -would be taken off his former leap; and so if it were thrust forward -1/3 of a braccio, by how much would his leap be increased? - -374. - -OF DRAWING. - -When a man who is running wants to neutralise the impetus that -carries him on he prepares a contrary impetus which is generated by -his hanging backwards. This can be proved, since, if the impetus -carries a moving body with a momentum equal to 4 and the moving body -wants to turn and fall back with a momentum of 4, then one momentum -neutralises the other contrary one, and the impetus is neutralised. - -Of walking up and down (375-379) - -375. - -When a man wants to stop running and check the impetus he is forced -to hang back and take short quick steps. [Footnote: Lines 5-31 refer -to the two upper figures, and the lower figure to the right is -explained by the last part of the chapter.] The centre of gravity of -a man who lifts one of his feet from the ground always rests on the -centre of the sole of the foot [he stands on]. - -A man, in going up stairs involuntarily throws so much weight -forward and on the side of the upper foot as to be a counterpoise to -the lower leg, so that the labour of this lower leg is limited to -moving itself. - -The first thing a man does in mounting steps is to relieve the leg -he is about to lift of the weight of the body which was resting on -that leg; and besides this, he gives to the opposite leg all the -rest of the bulk of the whole man, including [the weight of] the -other leg; he then raises the other leg and sets the foot upon the -step to which he wishes to raise himself. Having done this he -restores to the upper foot all the weight of the body and of the leg -itself, and places his hand on his thigh and throws his head forward -and repeats the movement towards the point of the upper foot, -quickly lifting the heel of the lower one; and with this impetus he -lifts himself up and at the same time extends the arm which rested -on his knee; and this extension of the arm carries up the body and -the head, and so straightens the spine which was curved. - -[32] The higher the step is which a man has to mount, the farther -forward will he place his head in advance of his upper foot, so as -to weigh more on _a_ than on _b_; this man will not be on the step -_m_. As is shown by the line _g f_. - -[Footnote: See Pl. XXIII, No. 1. The lower sketch to the left -belongs to the four first lines.] - -376. - -I ask the weight [pressure] of this man at every degree of motion on -these steps, what weight he gives to _b_ and to _c_. - -[Footnote 8: These lines are, in the original, written in ink] -Observe the perpendicular line below the centre of gravity of the -man. - -[Footnote: See Pl. XXIII, No. 2.] - -377. - -In going up stairs if you place your hands on your knees all the -labour taken by the arms is removed from the sinews at the back of -the knees. - -[Footnote: See Pl. XXIII, No. 3.] - -378. - -The sinew which guides the leg, and which is connected with the -patella of the knee, feels it a greater labour to carry the man -upwards, in proportion as the leg is more bent; and the muscle which -acts upon the angle made by the thigh where it joins the body has -less difficulty and has a less weight to lift, because it has not -the [additional] weight of the thigh itself. And besides this it has -stronger muscles, being those which form the buttock. - -379. - -A man coming down hill takes little steps, because the weight rests -upon the hinder foot, while a man mounting takes wide steps, because -his weight rests on the foremost foot. - -[Footnote: See Pl. XXIII, No. 4.] - -On the human body in action (380-388). - -380. - -OF THE HUMAN BODY IN ACTION. - -When you want to represent a man as moving some weight consider what -the movements are that are to be represented by different lines; -that is to say either from below upwards, with a simple movement, as -a man does who stoops forward to take up a weight which he will lift -as he straightens himself. Or as a man does who wants to squash -something backwards, or to force it forwards or to pull it downwards -with ropes passed through pullies [Footnote 10: Compare the sketch -on page 198 and on 201 (S. K. M. II.1 86b).]. And here remember that -the weight of a man pulls in proportion as his centre of gravity is -distant from his fulcrum, and to this is added the force given by -his legs and bent back as he raises himself. - -381. - -Again, a man has even a greater store of strength in his legs than -he needs for his own weight; and to see if this is true, make a man -stand on the shore-sand and then put another man on his back, and -you will see how much he will sink in. Then take the man from off -his back and make him jump straight up as high as he can, and you -will find that the print of his feet will be made deeper by the jump -than from having the man on his back. Hence, here, by 2 methods it -is proved that a man has double the strength he requires to support -his own body. - -382. - -OF PAINTING. - -If you have to draw a man who is in motion, or lifting or pulling, -or carrying a weight equal to his own, in what way must you set on -his legs below his body? - -[Footnote: In the MS. this question remains unanswered.] - -383. - -OF THE STRENGTH OF MAN. - -A man pulling a [dead] weight balanced against himself cannot pull -more than his own weight. And if he has to raise it he will [be able -to] raise as much more than his weight as his strength may be more -than that of other men. [Footnote 7: The stroke at the end of this -line finishes in the original in a sort of loop or flourish, and a -similar flourish occurs at the end of the previous passage written -on the same page. M. RAVAISSON regards these as numbers (compare the -photograph of page 30b in his edition of MS. A). He remarks: "_Ce -chiffre_ 8 _et, a la fin de l'alinea precedent, le chiffre_ 7 _sont, -dans le manuscrit, des renvois_."] The greatest force a man can -apply, with equal velocity and impetus, will be when he sets his -feet on one end of the balance [or lever] and then presses his -shoulders against some stable body. This will raise a weight at the -other end of the balance [lever], equal to his own weight and [added -to that] as much weight as he can carry on his shoulders. - -384. - -No animal can simply move [by its dead weight] a greater weight than -the sum of its own weight outside the centre of his fulcrum. - -385. - -A man who wants to send an arrow very far from the bow must be -standing entirely on one foot and raising the other so far from the -foot he stands on as to afford the requisite counterpoise to his -body which is thrown on the front foot. And he must not hold his arm -fully extended, and in order that he may be more able to bear the -strain he must hold a piece of wood which there is in all crossbows, -extending from the hand to the breast, and when he wishes to shoot -he suddenly leaps forward at the same instant and extends his arm -with the bow and releases the string. And if he dexterously does -every thing at once it will go a very long way. - -386. - -When two men are at the opposite ends of a plank that is balanced, -and if they are of equal weight, and if one of them wants to make a -leap into the air, then his leap will be made down from his end of -the plank and the man will never go up again but must remain in his -place till the man at the other end dashes up the board. - -[Footnote: See Pl. XXIV, No. 3.] - -387. - -Of delivering a blow to the right or left. - -[Footnote: Four sketches on Pl. XXIV, No. 1 belong to this passage. -The rest of the sketches and notes on that page are of a -miscellaneous nature.] - -388. - -Why an impetus is not spent at once [but diminishes] gradually in -some one direction? [Footnote 1: The paper has been damaged at the -end of line 1.] The impetus acquired in the line _a b c d_ is spent -in the line _d e_ but not so completely but that some of its force -remains in it and to this force is added the momentum in the line _d -e_ with the force of the motive power, and it must follow than the -impetus multiplied by the blow is greater that the simple impetus -produced by the momentum _d e_. - -[Footnote 8: The sketch No. 2 on Pl. XXIV stands, in the original, -between lines 7 and 8. Compare also the sketches on Pl. LIV.] A man -who has to deal a great blow with his weapon prepares himself with -all his force on the opposite side to that where the spot is which -he is to hit; and this is because a body as it gains in velocity -gains in force against the object which impedes its motion. - -On hair falling down in curls. - -389. - -Observe the motion of the surface of the water which resembles that -of hair, and has two motions, of which one goes on with the flow of -the surface, the other forms the lines of the eddies; thus the water -forms eddying whirlpools one part of which are due to the impetus of -the principal current and the other to the incidental motion and -return flow. - -[Footnote: See Pl. XXV. Where also the text of this passage is given -in facsimile.] - -On draperies (390--392). - -390. - -OF THE NATURE OF THE FOLDS IN DRAPERY. - -That part of a fold which is farthest from the ends where it is -confined will fall most nearly in its natural form. - -Every thing by nature tends to remain at rest. Drapery, being of -equal density and thickness on its wrong side and on its right, has -a tendency to lie flat; therefore when you give it a fold or plait -forcing it out of its flatness note well the result of the -constraint in the part where it is most confined; and the part which -is farthest from this constraint you will see relapses most into the -natural state; that is to say lies free and flowing. - -EXAMPLE. - -[Footnote 13: _a c sia_. In the original text _b_ is written instead -of _c_--an evident slip of the pen.] Let _a b c_ be the fold of the -drapery spoken of above, _a c_ will be the places where this folded -drapery is held fast. I maintain that the part of the drapery which -is farthest from the plaited ends will revert most to its natural -form. - -Therefore, _b_ being farthest from _a_ and _c_ in the fold _a b c_ -it will be wider there than anywhere else. - -[Footnote: See Pl. XXVIII, No. 6, and compare the drawing from -Windsor Pl. XXX for farther illustration of what is here stated.] - -391. - -OF SMALL FOLDS IN DRAPERIES. - -How figures dressed in a cloak should not show the shape so much as -that the cloak looks as if it were next the flesh; since you surely -cannot wish the cloak to be next the flesh, for you must suppose -that between the flesh and the cloak there are other garments which -prevent the forms of the limbs appearing distinctly through the -cloak. And those limbs which you allow to be seen you must make -thicker so that the other garments may appear to be under the cloak. -But only give something of the true thickness of the limbs to a -nymph [Footnote 9: _Una nifa_. Compare the beautiful drawing of a -Nymph, in black chalk from the Windsor collection, Pl. XXVI.] or an -angel, which are represented in thin draperies, pressed and clinging -to the limbs of the figures by the action of the wind. - -392. - -You ought not to give to drapery a great confusion of many folds, -but rather only introduce them where they are held by the hands or -the arms; the rest you may let fall simply where it is its nature to -flow; and do not let the nude forms be broken by too many details -and interrupted folds. How draperies should be drawn from nature: -that is to say if youwant to represent woollen cloth draw the folds -from that; and if it is to be silk, or fine cloth or coarse, or of -linen or of crape, vary the folds in each and do not represent -dresses, as many do, from models covered with paper or thin leather -which will deceive you greatly. - -[Footnote: The little pen and ink drawing from Windsor (W. 102), -given on Pl. XXVIII, No. 7, clearly illustrates the statement made -at the beginning of this passage; the writing of the cipher 19 on -the same page is in Leonardo's hand; the cipher 21 is certainly -not.] - -_VIII._ - -_Botany for Painters and Elements of Landscape Painting._ - -_The chapters composing this portion of the work consist of -observations on Form, Light and Shade in Plants, and particularly in -Trees summed up in certain general rules by which the author intends -to guide the artist in the pictorial representation of landscape._ - -_With these the first principles of a_ Theory of Landscape painting -_are laid down--a theory as profoundly thought out in its main -lines as it is lucidly worked out in its details. In reading these -chapters the conviction is irresistible that such a_ Botany for -painters _is or ought to be of similar importance in the practice of -painting as the principles of the Proportions and Movements of the -human figure_ i. e. Anatomy for painters. - -_There can be no doubt that Leonardo, in laying down these rules, -did not intend to write on Botany in the proper scientific -sense--his own researches on that subject have no place here; it -need only be observed that they are easily distinguished by their -character and contents from those which are here collected and -arranged under the title 'Botany for painters'. In some cases where -this division might appear doubtful,--as for instance in No._ -402--_the Painter is directly addressed and enjoined to take the -rule to heart as of special importance in his art._ - -_The original materials are principally derived from MS._ G, _in -which we often find this subject treated on several pages in -succession without any of that intermixture of other matters, which -is so frequent in Leonardo's writings. This MS., too, is one of the -latest; when it was written, the great painter was already more than -sixty years of age, so we can scarcely doubt that he regarded all he -wrote as his final views on the subject. And the same remark applies -to the chapters from MSS._ E _and_ M _which were also written -between_ 1513--15. - -_For the sake of clearness, however, it has been desirable to -sacrifice--with few exceptions--the original order of the passages -as written, though it was with much reluctance and only after long -hesitation that I resigned myself to this necessity. Nor do I mean -to impugn the logical connection of the author's ideas in his MS.; -but it will be easily understood that the sequence of disconnected -notes, as they occurred to Leonardo and were written down from time -to time, might be hardly satisfactory as a systematic arrangement of -his principles. The reader will find in the Appendix an exact -account of the order of the chapters in the original MS. and from -the data there given can restore them at will. As the materials are -here arranged, the structure of the tree as regards the growth of -the branches comes first_ (394-411) _and then the insertion of the -leaves on the stems_ (412-419). _Then follow the laws of Light and -Shade as applied, first, to the leaves (420-434), and, secondly, to -the whole tree and to groups of trees_ (435-457). _After the remarks -on the Light and Shade in landscapes generally_ (458-464), _we find -special observations on that of views of towns and buildings_ -(465-469). _To the theory of Landscape Painting belong also the -passages on the effect of Wind on Trees_ (470-473) _and on the Light -and Shade of Clouds_ (474-477), _since we find in these certain -comparisons with the effect of Light and Shade on Trees_ (e. g.: _in -No._ 476, 4. 5; _and No._ 477, 9. 12). _The chapters given in the -Appendix Nos._ 478 _and_ 481 _have hardly any connection with the -subjects previously treated._ - -Classification of trees. - -393. - -TREES. - -Small, lofty, straggling, thick, that is as to foliage, dark, light, -russet, branched at the top; some directed towards the eye, some -downwards; with white stems; this transparent in the air, that not; -some standing close together, some scattered. - -The relative thickness of the branches to the trunk (393--396). - -394. - -All the branches of a tree at every stage of its height when put -together are equal in thickness to the trunk [below them]. - -All the branches of a water [course] at every stage of its course, -if they are of equal rapidity, are equal to the body of the main -stream. - -395. - -Every year when the boughs of a plant [or tree] have made an end of -maturing their growth, they will have made, when put together, a -thickness equal to that of the main stem; and at every stage of its -ramification you will find the thickness of the said main stem; as: -_i k_, _g h_, _e f_, _c d_, _a b_, will always be equal to each -other; unless the tree is pollard--if so the rule does not hold -good. - -All the branches have a direction which tends to the centre of the -tree _m_. - -[Footnote: The two sketches of leafless trees one above another on -the left hand side of Pl. XXVII, No. 1, belong to this passage.] - -396. - -If the plant n grows to the thickness shown at m, its branches will -correspond [in thickness] to the junction a b in consequence of the -growth inside as well as outside. - -The branches of trees or plants have a twist wherever a minor branch -is given off; and this giving off the branch forms a fork; this said -fork occurs between two angles of which the largest will be that -which is on the side of the larger branch, and in proportion, unless -accident has spoilt it. - -[Footnote: The sketches illustrating this are on the right hand side -of PI. XXVII, No. I, and the text is also given there in facsimile.] - -397. - -There is no boss on branches which has not been produced by some -branch which has failed. - -The lower shoots on the branches of trees grow more than the upper -ones and this occurs only because the sap that nourishes them, being -heavy, tends downwards more than upwards; and again, because those -[branches] which grow downwards turn away from the shade which -exists towards the centre of the plant. The older the branches are, -the greater is the difference between their upper and their lower -shoots and in those dating from the same year or epoch. - -[Footnote: The sketch accompanying this in the MS. is so effaced -that an exact reproduction was impossible.] - -398. - -OF THE SCARS ON TREES. - -The scars on trees grow to a greater thickness than is required by -the sap of the limb which nourishes them. - -399. - -The plant which gives out the smallest ramifications will preserve -the straightest line in the course of its growth. - -[Footnote: This passage is illustrated by two partly effaced -sketches. One of these closely resembles the lower one given under -No. 408, the other also represents short closely set boughs on an -upright trunk.] - -400. - -OF THE RAMIFICATION. - -The beginning of the ramification [the shoot] always has the central -line [axis] of its thickness directed to the central line [axis] of -the plant itself. - -401. - -In starting from the main stem the branches always form a base with -a prominence as is shown at _a b c d_. - -402. - -WHY, VERY FREQUENTLY, TIMBER HAS VEINS THAT ARE NOT STRAIGHT. - -When the branches which grow the second year above the branch of the -preceding year, are not of equal thickness above the antecedent -branches, but are on one side, then the vigour of the lower branch -is diverted to nourish the one above it, although it may be somewhat -on one side. - -But if the ramifications are equal in their growth, the veins of the -main stem will be straight [parallel] and equidistant at every -degree of the height of the plant. - -Wherefore, O Painter! you, who do not know these laws! in order to -escape the blame of those who understand them, it will be well that -you should represent every thing from nature, and not despise such -study as those do who work [only] for money. - -The direction of growth (403-407). - -403. - -OF THE RAMIFICATIONS OF PLANTS. - -The plants which spread very much have the angles of the spaces -which divide their branches more obtuse in proportion as their point -of origin is lower down; that is nearer to the thickest and oldest -portion of the tree. Therefore in the youngest portions of the tree -the angles of ramification are more acute. [Footnote: Compare the -sketches on the lower portion of Pl. XXVII, No. 2.] - -404. - -The tips of the boughs of plants [and trees], unless they are borne -down by the weight of their fruits, turn towards the sky as much as -possible. - -The upper side of their leaves is turned towards the sky that it may -receive the nourishment of the dew which falls at night. - -The sun gives spirit and life to plants and the earth nourishes them -with moisture. [9] With regard to this I made the experiment of -leaving only one small root on a gourd and this I kept nourished -with water, and the gourd brought to perfection all the fruits it -could produce, which were about 60 gourds of the long kind, andi set -my mind diligently [to consider] this vitality and perceived that -the dews of night were what supplied it abundantly with moisture -through the insertion of its large leaves and gave nourishment to -the plant and its offspring--or the seeds which its offspring had -to produce--[21]. - -The rule of the leaves produced on the last shoot of the year will -be that they will grow in a contrary direction on the twin branches; -that is, that the insertion of the leaves turns round each branch in -such a way, as that the sixth leaf above is produced over the sixth -leaf below, and the way they turn is that if one turns towards its -companion to the right, the other turns to the left, the leaf -serving as the nourishing breast for the shoot or fruit which grows -the following year. - -[Footnote: A French translation of lines 9-12 was given by M. -RAVAISSON in the _Gazette des Beaux Arts_, Oct. 1877; his paper also -contains some valuable information as to botanical science in the -ancient classical writers and at the time of the Renaissance.] - -405. - -The lowest branches of those trees which have large leaves and heavy -fruits, such as nut-trees, fig-trees and the like, always droop -towards the ground. - -The branches always originate above [in the axis of] the leaves. - -406. - -The upper shoots of the lateral branches of plants lie closer to the -parent branch than the lower ones. - -407. - -The lowest branches, after they have formed the angle of their -separation from the parent stem, always bend downwards so as not to -crowd against the other branches which follow them on the same stem -and to be better able to take the air which nourishes them. As is -shown by the angle _b a c_; the branch _a c_ after it has made the -corner of the angle _a c_ bends downwards to _c d_ and the lesser -shoot _c_ dries up, being too thin. - -The main branch always goes below, as is shown by the branch _f n -m_, which does not go to _f n o_. - -The forms of trees (408--411). - -408. - -The elm always gives a greater length to the last branches of the -year's growth than to the lower ones; and Nature does this because -the highest branches are those which have to add to the size of the -tree; and those at the bottom must get dry because they grow in the -shade and their growth would be an impediment to the entrance of the -solar rays and the air among the main branches of the tree. - -The main branches of the lower part bend down more than those above, -so as to be more oblique than those upper ones, and also because -they are larger and older. - -409. - -In general almost all the upright portions of trees curve somewhat -turning the convexity towards the South; and their branches are -longer and thicker and more abundant towards the South than towards -the North. And this occurs because the sun draws the sap towards -that surface of the tree which is nearest to it. - -And this may be observed if the sun is not screened off by other -plants. - -410. - -The cherry-tree is of the character of the fir tree as regards its -ramification placed in stages round its main stem; and its branches -spring, 4 or five or 6 [together] opposite each other; and the tips -of the topmost shoots form a pyramid from the middle upwards; and -the walnut and oak form a hemisphere from the middle upwards. - -411. - -The bough of the walnut which is only hit and beaten when it has -brought to perfection... - -[Footnote: The end of the text and the sketch in red chalk belonging -to it, are entirely effaced.] - -The insertion of the leaves (412--419). - -412. - -OF THE INSERTION OF THE BRANCHES ON PLANTS. - -Such as the growth of the ramification of plants is on their -principal branches, so is that of the leaves on the shoots of the -same plant. These leaves have [Footnote 6: _Quattro modi_ (four -modes). Only three are described in the text, the fourth is only -suggested by a sketch. - -This passage occurs in MANZI'S edition of the Trattato, p. 399, but -without the sketches and the text is mutilated in an important part. -The whole passage has been commented on, from MANZI'S version, in -Part I of the _Nuovo Giornale Botanico Italiano_, by Prof. G. -UZIELLI (Florence 1869, Vol. I). He remarks as to the 'four modes': -"_Leonardo, come si vede nelle linie sententi da solo tre esempli. -Questa ed altre inessattezze fanno desiderare, sia esaminato di -nuovo il manoscritto Vaticano_". This has since been done by D. -KNAPP of Tubingen, and his accurate copy has been published by H. -LUDWIG, the painter. The passage in question occurs in his edition -as No. 833; and there also the drawings are wanting. The space for -them has been left vacant, but in the Vatican copy '_niente_' has -been written on the margin; and in it, as well as in LUDWIG'S and -MANZI'S edition, the text is mutilated.] four modes of growing one -above another. The first, which is the most general, is that the -sixth always originates over the sixth below [Footnote 8: _la sesta -di sotto. "Disposizione 2/5 o 1/5. Leonardo osservo probabilmente -soltanto la prima"_ (UZIELLl).]; the second is that two third ones -above are over the two third ones below [Footnote 10: _terze di -sotto: "Intende qui senza dubbio parlare di foglie decussate, in cui -il terzo verticello e nel piano del primo"_ (UZIELLI).]; and the -third way is that the third above is over the third below [Footnote -11: 3a _di sotto: "Disposizione 1/2"_ (UZIELLI).]. - -[Footnote: See the four sketches on the upper portion of the page -reproduced as fig. 2 on P1. XXVII.] - -413. - -A DESCRIPTION OF THE ELM. - -The ramification of the elm has the largest branch at the top. The -first and the last but one are smaller, when the main trunk is -straight. - -The space between the insertion of one leaf to the rest is half the -extreme length of the leaf or somewhat less, for the leaves are at -an interval which is about the 3rd of the width of the leaf. - -The elm has more leaves near the top of the boughs than at the base; -and the broad [surface] of the leaves varies little as to [angle -and] aspect. - -[Footnote: See Pl. XXVII, No. 3. Above the sketch and close under -the number of the page is the word '_olmo_' (elm).] - -414. - -In the walnut tree the leaves which are distributed on the shoots of -this year are further apart from each other and more numerous in -proportion as the branch from which this shoot springs is a young -one. And they are inserted more closely and less in number when the -shoot that bears them springs from an old branch. Its fruits are -borne at the ends of the shoots. And its largest boughs are the -lowest on the boughs they spring from. And this arises from the -weight of its sap which is more apt to descend than to rise, and -consequently the branches which spring from them and rise towards -the sky are small and slender [20]; and when the shoot turns towards -the sky its leaves spread out from it [at an angle] with an equal -distribution of their tips; and if the shoot turns to the horizon -the leaves lie flat; and this arises from the fact that leaves -without exception, turn their underside to the earth [29]. - -The shoots are smaller in proportion as they spring nearer to the -base of the bough they spring from. - -[Footnote: See the two sketches on Pl XXVII, No. 4. The second -refers to the passage lines 20-30.] - -415. - -OF THE INSERTION OF THE LEAVES ON THE BRANCHES. - -The thickness of a branch never diminishes within the space between -one leaf and the next excepting by so much as the thickness of the -bud which is above the leaf and this thickness is taken off from the -branch above [the node] as far as the next leaf. - -Nature has so placed the leaves of the latest shoots of many plants -that the sixth leaf is always above the first, and so on in -succession, if the rule is not [accidentally] interfered with; and -this occurs for two useful ends in the plant: First that as the -shoot and the fruit of the following year spring from the bud or eye -which lies above and in close contact with the insertion of the leaf -[in the axil], the water which falls upon the shoot can run down to -nourish the bud, by the drop being caught in the hollow [axil] at -the insertion of the leaf. And the second advantage is, that as -these shoots develop in the following year one will not cover the -next below, since the 5 come forth on five different sides; and the -sixth which is above the first is at some distance. - -416. - -OF THE RAMIFICATIONS OF TREES AND THEIR FOLIAGE. - -The ramifications of any tree, such as the elm, are wide and slender -after the manner of a hand with spread fingers, foreshortened. And -these are seen in the distribution [thus]: the lower portions are -seen from above; and those that are above are seen from below; and -those in the middle, some from below and some from above. The upper -part is the extreme [top] of this ramification and the middle -portion is more foreshortened than any other of those which are -turned with their tips towards you. And of those parts of the middle -of the height of the tree, the longest will be towards the top of -the tree and will produce a ramification like the foliage of the -common willow, which grows on the banks of rivers. - -Other ramifications are spherical, as those of such trees as put -forth their shoots and leaves in the order of the sixth being placed -above the first. Others are thin and light like the willow and -others. - -417. - -You will see in the lower branches of the elder, which puts forth -leaves two and two placed crosswise [at right angles] one above -another, that if the stem rises straight up towards the sky this -order never fails; and its largest leaves are on the thickest part -of the stem and the smallest on the slenderest part, that is towards -the top. But, to return to the lower branches, I say that the leaves -on these are placed on them crosswise like [those on] the upper -branches; and as, by the law of all leaves, they are compelled to -turn their upper surface towards the sky to catch the dew at night, -it is necessary that those so placed should twist round and no -longer form a cross. - -[Footnote: See Pl. XXVII, No. 5.] - -418. - -A leaf always turns its upper side towards the sky so that it may -the better receive, on all its surface, the dew which drops gently -from the atmosphere. And these leaves are so distributed on the -plant as that one shall cover the other as little as possible, but -shall lie alternately one above another as may be seen in the ivy -which covers the walls. And this alternation serves two ends; that -is, to leave intervals by which the air and sun may penetrate -between them. The 2nd reason is that the drops which fall from the -first leaf may fall onto the fourth or--in other trees--onto the -sixth. - -419. - -Every shoot and every fruit is produced above the insertion [in the -axil] of its leaf which serves it as a mother, giving it water from -the rain and moisture from the dew which falls at night from above, -and often it protects them against the too great heat of the rays of -the sun. - -LIGHT ON BRANCHES AND LEAVES (420--422). - -420. - -That part of the body will be most illuminated which is hit by the -luminous ray coming between right angles. - -[Footnote: See Pl. XXVIII, No. 1.] - -421. - -Young plants have more transparent leaves and a more lustrous bark -than old ones; and particularly the walnut is lighter coloured in -May than in September. - -422. - -OF THE ACCIDENTS OF COLOURING IN TREES. - -The accidents of colour in the foliage of trees are 4. That is: -shadow, light, lustre [reflected light] and transparency. - -OF THE VISIBILITY OF THESE ACCIDENTS. - -These accidents of colour in the foliage of trees become confused at -a great distance and that which has most breadth [whether light or -shade, &c.] will be most conspicuous. - -The proportions of light and shade in a leaf (423-426). - -423. - -OF THE SHADOWS OF A LEAF. - -Sometimes a leaf has three accidents [of light] that is: shade, -lustre [reflected light] and transparency [transmitted light]. Thus, -if the light were at _n_ as regards the leaf _s_, and the eye at -_m_, it would see _a_ in full light, _b_ in shadow and _c_ -transparent. - -424. - -A leaf with a concave surface seen from the under side and -up-side-down will sometimes show itself as half in shade, and half -transparent. Thus, if _o p_ is the leaf and the light _m_ and the -eye _n_, this will see _o_ in shadow because the light does not fall -upon it between equal angles, neither on the upper nor the under -side, and _p_ is lighted on the upper side and the light is -transmitted to its under side. [Footnote: See Pl. XXVIII, No. 2, the -upper sketch on the page. In the original they are drawn in red -chalk.] - -425. - -Although those leaves which have a polished surface are to a great -extent of the same colour on the right side and on the reverse, it -may happen that the side which is turned towards the atmosphere will -have something of the colour of the atmosphere; and it will seem to -have more of this colour of the atmosphere in proportion as the eye -is nearer to it and sees it more foreshortened. And, without -exception the shadows show as darker on the upper side than on the -lower, from the contrast offered by the high lights which limit the -shadows. - -The under side of the leaf, although its colour may be in itself the -same as that of the upper side, shows a still finer colour--a colour -that is green verging on yellow--and this happens when the leaf is -placed between - -426. - -the eye and the light which falls upon it from the opposite side. - -And its shadows are in the same positions as those were of the -opposite side. Therefore, O Painter! when you do trees close at -hand, remember that if the eye is almost under the tree you will see -its leaves [some] on the upper and [some] on the under side, and the -upper side will be bluer in proportion as they are seen more -foreshortened, and the same leaf sometimes shows part of the right -side and part of the under side, whence you must make it of two -colours. - -Of the transparency of leaves (427-429). - -427. - -The shadows in transparent leaves seen from the under side are the -same shadows as there are on the right side of this leaf, they will -show through to the underside together with lights, but the lustre -[reflected light] can never show through. - -428. - -When one green has another [green] behind it, the lustre on the -leaves and their transparent [lights] show more strongly than in -those which are [seen] against the brightness of the atmosphere. - -And if the sun illuminates the leaves without their coming between -it and the eye and without the eye facing the sun, then the -reflected lights and the transparent lights are very strong. - -It is very effective to show some branches which are low down and -dark and so set off the illuminated greens which are at some -distance from the dark greens seen below. That part is darkest which -is nearest to the eye or which is farthest from the luminous -atmosphere. - -429. - -Never paint leaves transparent to the sun, because they are -confused; and this is because on the transparency of one leaf will -be seen the shadow of another leaf which is above it. This shadow -has a distinct outline and a certain depth of shade and sometimes is -[as much as] half or a third of the leaf which is shaded; and -consequently such an arrangement is very confused and the imitation -of it should be avoided. - -The light shines least through a leaf when it falls upon it at an -acute angle. - -The gradations of shade and colour in leaves (430-434). - -430. - -The shadows of plants are never black, for where the atmosphere -penetrates there can never be utter darkness. - -431. - -If the light comes from _m_ and the eye is at _n_ the eye will see -the colour of the leaves _a b_ all affected by the colour of _m_ ---that is of the atmosphere; and _b c_ will be seen from the under -side as transparent, with a beautiful green colour verging on -yellow. - -If _m_ is the luminous body lighting up the leaf _s_ all the eyes -that see the under side of this leaf will see it of a beautiful -light green, being transparent. - -In very many cases the positions of the leaves will be without -shadow [or in full light], and their under side will be transparent -and the right side lustrous [reflecting light]. - -432. - -The willow and other similar trees, which have their boughs lopped -every 3 or 4 years, put forth very straight branches, and their -shadow is about the middle where these boughs spring; and towards -the extreme ends they cast but little shade from having small leaves -and few and slender branches. Hence the boughs which rise towards -the sky will have but little shade and little relief; and the -branches which are at an angle from the horizon, downwards, spring -from the dark part of the shadow and grow thinner by degrees up to -their ends, and these will be in strong relief, being in gradations -of light against a background of shadow. - -That tree will have the least shadow which has the fewest branches -and few leaves. - -433. - -OF DARK LEAVES IN FRONT OF TRANSPARENT ONES. - -When the leaves are interposed between the light and the eye, then -that which is nearest to the eye will be the darkest, and the most -distant will be the lightest, not being seen against the atmosphere; -and this is seen in the leaves which are away from the centre of the -tree, that is towards the light. - -[Footnote: See Pl. XXVIII, No. 2, the lower sketch.] - -434. - -OF THE LIGHTS ON DARK LEAVES. - -The lights on such leaves which are darkest, will be most near to -the colour of the atmosphere that is reflected in them. And the -cause of this is that the light on the illuminated portion mingles -with the dark hue to compose a blue colour; and this light is -produced by the blueness of the atmosphere which is reflected in the -smooth surface of these leaves and adds to the blue hue which this -light usually produces when it falls on dark objects. - -OF THE LIGHTS ON LEAVES OF A YELLOWISH GREEN. - -But leaves of a green verging on yellow when they reflect the -atmosphere do not produce a reflection verging on blue, inasmuch as -every thing which appears in a mirror takes some colour from that -mirror, hence the blue of the atmosphere being reflected in the -yellow of the leaf appears green, because blue and yellow mixed -together make a very fine green colour, therefore the lustre of -light leaves verging on yellow will be greenish yellow. - -A classification of trees according to their colours. - -435. - -The trees in a landscape are of various kinds of green, inasmuch as -some verge towards blackness, as firs, pines, cypresses, laurels, -box and the like. Some tend to yellow such as walnuts, and pears, -vines and verdure. Some are both yellowish and dark as chesnuts, -holm-oak. Some turn red in autumn as the service-tree, pomegranate, -vine, and cherry; and some are whitish as the willow, olive, reeds -and the like. Trees are of various forms ... - -The proportions of light and shade in trees (436-440). - -436. - -OF A GENERALLY DISTRIBUTED LIGHT AS LIGHTING UP TREES. - -That part of the trees will be seen to lie in the least dark shadow -which is farthest from the earth. - -To prove it let _a p_ be the tree, _n b c_ the illuminated -hemisphere [the sky], the under portion of the tree faces the earth -_p c_, that is on the side _o_, and it faces a small part of the -hemisphere at _c d_. But the highest part of the convexity a faces -the greatest part of the hemisphere, that is _b c_. For this -reason--and because it does not face the darkness of the earth--it -is in fuller light. But if the tree has dense foliage, as the -laurel, arbutus, box or holm oak, it will be different; because, -although _a_ does not face the earth, it faces the dark [green] of -the leaves cut up by many shadows, and this darkness is reflected -onto the under sides of the leaves immediately above. Thus these -trees have their darkest shadows nearest to the middle of the tree. - -437. - -OF THE SHADOWS OF VERDURE. diff --git a/docs/examples/kernel/davinci1.txt b/docs/examples/kernel/davinci1.txt deleted file mode 100644 index a71df3b..0000000 --- a/docs/examples/kernel/davinci1.txt +++ /dev/null @@ -1,8050 +0,0 @@ - -The shadows of verdure are always somewhat blue, and so is every -shadow of every object; and they assume this hue more in proportion -as they are remote from the eye, and less in proportion as they are -nearer. The leaves which reflect the blue of the atmosphere always -present themselves to the eye edgewise. - -OF THE ILLUMINATED PART OF VERDURE AND OF MOUNTAINS. - -The illuminated portion, at a great distance, will appear most -nearly of its natural colour where the strongest light falls upon -it. - -438. - -OF TREES THAT ARE LIGHTED BY THE SUN AND BY THE ATMOSPHERE. - -In trees that are illuminated [both] by the sun and the atmosphere -and that have leaves of a dark colour, one side will be illuminated -by the atmosphere [only] and in consequence of this light will tend -to blueness, while on the other side they will be illuminated by the -atmosphere and the sun; and the side which the eye sees illuminated -by the sun will reflect light. - -439. - -OF DEPICTING A FOREST SCENE. - -The trees and plants which are most thickly branched with slender -branches ought to have less dark shadow than those trees and plants -which, having broader leaves, will cast more shadow. - -440. - -ON PAINTING. - -In the position of the eye which sees that portion of a tree -illuminated which turns towards the light, one tree will never be -seen to be illuminated equally with the other. To prove this, let -the eye be _c_ which sees the two trees _b d_ which are illuminated -by the sun _a_; I say that this eye _c_ will not see the light in -the same proportion to the shade, in one tree as in the other. -Because, the tree which is nearest to the sun will display so much -the stronger shadow than the more distant one, in proportion as one -tree is nearer to the rays of the sun that converge to the eye than -the other; &c. - -You see that the eye _c_ sees nothing of the tree _d_ but shadow, -while the same eye _c_ sees the tree _b_ half in light and half in -shade. - -When a tree is seen from below, the eye sees the top of it as placed -within the circle made by its boughs[23]. - -Remember, O Painter! that the variety of depth of shade in any one -particular species of tree is in proportion to the rarity or density -of their branches. - -[Footnote: The two lower sketches on the left of Pl XXVIII, No. 3, -refer to lines 21-23. The upper sketch has apparently been effaced -by Leonardo himself.] - -The distribution of light and shade with reference to the position -of the spectator (441-443). - -441. - -The shadows of trees placed in a landscape do not display themselves -in the same position in the trees on the right hand and those on the -left; still more so if the sun is to the right or left. As is proved -by the 4th which says: Opaque bodies placed between the light and -the eye display themselves entirely in shadow; and by the 5th: The -eye when placed between the opaque body and the light sees the -opaque body entirely illuminated. And by the 6th: When the eye and -the opaque body are placed between darkness and light, it will be -seen half in shadow and half in light. - -[Footnote: See the figure on the right hand side of Pl. XXVIII, No. -3. The first five lines of the text are written below the diagram -and above it are the last eight lines of the text, given as No. -461.] - -442. - -OF THE HERBS OF THE FIELD. - -Of the plants which take a shadow from the plants which spring among -them, those which are on this side [in front] of the shadow have the -stems lighted up on a background of shadow, and the plants on which -the shadows fall have their stems dark on a light background; that -is on the background beyond the shadow. - -OF TREES WHICH ARE BETWEEN THE EYE AND THE LIGHT. - -Of the trees which are between the eye and the light the part in -front will be light; but this light will be broken by the -ramifications of transparent leaves--being seen from the under -side--and lustrous leaves--being seen from the upper side; and the -background below and behind will be dark green, being in shadow from -the front portion of the said tree. This occurs in trees placed -above the eye. - -443. - -FROM WHENCE TO DEPICT A LANDSCAPE - -Landscapes should be represented so that the trees may be half in -light and half in shadow; but it is better to do them when the sun -is covered with clouds, for then the trees are lighted by the -general light of the sky, and the general darkness of the earth. And -then they are darkest in certain parts in proportion as those parts -are nearest to the middle of the tree and to the earth. - -The effects of morning light (444-448). - -444. - -OF TREES TO THE SOUTH. - -When the sun is in the east the trees to the South and to the North -have almost as much light as shadow. But a greater share of light in -proportion as they lie to the West and a greater share of shadow in -proportion as they lie to the East. - -OF MEADOWS. - -If the sun is in the East the verdure of the meadows and of other -small plants is of a most beautiful green from being transparent to -the sun; this does not occur in the meadows to the West, and in -those to the South and North the grass is of a moderately brilliant -green. - -445. - -OF THE 4 POINTS OF THE COMPASS [IN LANDSCAPES]. - -When the sun is in the East all the portions of plants lighted by it -are of a most lively verdure, and this happens because the leaves -lighted by the sun within the half of the horizon that is the -Eastern half, are transparent; and within the Western semicircle the -verdure is of a dull hue and the moist air is turbid and of the -colour of grey ashes, not being transparent like that in the East, -which is quite clear and all the more so in proportion as it is -moister. - -The shadows of the trees to the East cover a large portion of them -and are darker in proportion as the foliage of the trees is thicker. - -446. - -OF TREES IN THE EAST. - -When the sun is in the East the trees seen towards the East will -have the light which surrounds them all round their shadows, -excepting on the side towards the earth; unless the tree has been -pruned [below] in the past year. And the trees to the South and -North will be half in shade and half in light, and more or less in -shade or in light in proportion as they are more or less to the East -or to the West. - -The [position of] the eye above or below varies the shadows and -lights in trees, inasmuch as the eye placed above sees the tree with -the little shadow, and the eye placed below with a great deal of -shadow. - -The colour of the green in plants varies as much as their species. - -447. - -OF THE SHADOWS IN TREES. - -The sun being in the East [to the right], the trees to the West [or -left] of the eye will show in small relief and almost imperceptible -gradations, because the atmosphere which lies between the eye and -those trees is very dense [Footnote 7: _per la 7a di questo_. This -possibly referred to something written on the seventh page of this -note book marked _G_. Unfortunately it has been cut out and lost.], -see the 7th of this--and they have no shade; for though a shadow -exists in every detail of the ramification, it results that the -images of the shade and light that reach the eye are confused and -mingled together and cannot be perceived on account of their -minuteness. And the principal lights are in the middle of the trees, -and the shadows to wards the edges; and their separation is shown by -the shadows of the intervals between the trees; but when the forests -are thick with trees the thin edges are but little seen. - -448. - -OF TREES TO THE EAST. - -When the sun is in the East the trees are darker towards the middle -while their edges are light. - -The effects of midday light. - -449. - -OBJECTS IN HIGH LIGHT SHOW BUT LITTLE, BUT BETWEEN LIGHT AND SHADOW -THEY STAND OUT WELL. - -To represent a landscape choose that the sun shall be at noon and -look towards the West or East and then draw. And if you turn towards -the North, every object placed on that side will have no shadow, -particularly those which are nearest to the [direction of the] -shadow of your head. And if you turn towards the South every object -on that side will be wholly in shadow. All the trees which are -towards the sun and have the atmosphere for their background are -dark, and the other trees which lie against that darkness will be -black [very dark] in the middle and lighter towards the edges. - -The appearance of trees in the distance (450. 451). - -450. - -OF THE SPACES [SHOWING THE SKY] IN TREES THEMSELVES. - -The spaces between the parts in the mass of trees, and the spaces -between the trees in the air, are, at great distances, invisible to -the eye; for, where it is an effort [even] to see the whole it is -most difficult to discern the parts.--But a confused mixture is the -result, partaking chiefly of the [hue] which predominates. The -spaces between the leaves consist of particles of illuminated air -which are very much smaller than the tree and are lost sight of -sooner than the tree; but it does not therefore follow that they are -not there. Hence, necessarily, a compounded [effect] is produced of -the sky and of the shadows of the tree in shade, which both together -strike the eye which sees them. - -OF TREES WHICH CONCEAL THESE SPACES IN ONE ANOTHER. - -That part of a tree will show the fewest spaces, behind which a -large number of trees are standing between the tree and the air -[sky]; thus in the tree _a_ the spaces are not concealed nor in _b_, -as there is no tree behind. But in _c_ only half shows the spaces -filled up by the tree _d_, and part of the tree _d_ is filled up by -the tree _e_ and a little farther on all the spaces in the mass of -the trees are lost, and only that at the side remains. - -451. - -OF TREES. - -What outlines are seen in trees at a distance against the sky which -serves as their background? - -The outlines of the ramification of trees, where they lie against -the illuminated sky, display a form which more nearly approaches the -spherical on proportion as they are remote, and the nearer they are -the less they appear in this spherical form; as in the first tree -_a_ which, being near to the eye, displays the true form of its -ramification; but this shows less in _b_ and is altogether lost in -_c_, where not merely the branches of the tree cannot be seen but -the whole tree is distinguished with difficulty. Every object in -shadow, of whatever form it may be, at a great distance appears to -be spherical. And this occurs because, if it is a square body, at a -very short distance it loses its angles, and a little farther off it -loses still more of its smaller sides which remain. And thus before -the whole is lost [to sight] the parts are lost, being smaller than -the whole; as a man, who in such a distant position loses his legs, -arms and head before [the mass of] his body, then the outlines of -length are lost before those of breadth, and where they have become -equal it would be a square if the angles remained; but as they are -lost it is round. - -[Footnote: The sketch No. 4, Pl. XXVIII, belongs to this passage.] - -The cast shadow of trees (452. 453). - -452. - -The image of the shadow of any object of uniform breadth can never -be [exactly] the same as that of the body which casts it. - -[Footnote: See Pl. XXVIII, No. 5.] - -Light and shade on groups of trees (453-457). - -453. - -All trees seen against the sun are dark towards the middle and this -shadow will be of the shape of the tree when apart from others. - -The shadows cast by trees on which the sun shines are as dark as -those of the middle of the tree. - -The shadow cast by a tree is never less than the mass of the tree -but becomes taller in proportion as the spot on which it falls, -slopes towards the centre of the world. - -The shadow will be densest in the middle of the tree when the tree -has the fewest branches. - -[Footnote: The three diagrams which accompany this text are placed, -in the original, before lines 7-11. At the spots marked _B_ Leonardo -wrote _Albero_ (tree). At _A_ is the word _Sole_ (sun), at _C Monte_ -(mountain) at _D piano_ (plain) and at _E cima_ (summit).] - -Every branch participates of the central shadow of every other -branch and consequently [of that] of the whole tree. - -The form of any shadow from a branch or tree is circumscribed by the -light which falls from the side whence the light comes; and this -illumination gives the shape of the shadow, and this may be of the -distance of a mile from the side where the sun is. - -If it happens that a cloud should anywhere overshadow some part of a -hill the [shadow of the] trees there will change less than in the -plains; for these trees on the hills have their branches thicker, -because they grow less high each year than in the plains. Therefore -as these branches are dark by nature and being so full of shade, the -shadow of the clouds cannot darken them any more; but the open -spaces between the trees, which have no strong shadow change very -much in tone and particularly those which vary from green; that is -ploughed lands or fallen mountains or barren lands or rocks. Where -the trees are against the atmosphere they appear all the same -colour--if indeed they are not very close together or very thickly -covered with leaves like the fir and similar trees. When you see the -trees from the side from which the sun lights them, you will see -them almost all of the same tone, and the shadows in them will be -hidden by the leaves in the light, which come between your eye and -those shadows. - -TREES AT A SHORT DISTANCE. - -[Footnote 29: The heading _alberi vicini_ (trees at a short -distance) is in the original manuscript written in the margin.] When -the trees are situated between the sun and the eye, beyond the -shadow which spreads from their centre, the green of their leaves -will be seen transparent; but this transparency will be broken in -many places by the leaves and boughs in shadow which will come -between you and them, or, in their upper portions, they will be -accompanied by many lights reflected from the leaves. - -454. - -The trees of the landscape stand out but little from each other; -because their illuminated portions come against the illuminated -portions of those beyond and differ little from them in light and -shade. - -455. - -Of trees seen from below and against the light, one beyond the other -and near together. The topmost part of the first will be in great -part transparent and light, and will stand out against the dark -portion of the second tree. And thus it will be with all in -succession that are placed under the same conditions. - -Let _s_ be the light, and _r_ the eye, _c d n_ the first tree, _a b -c_ the second. Then I say that _r_, the eye, will see the portion _c -f_ in great part transparent and lighted by the light _s_ which -falls upon it from the opposite side, and it will see it, on a dark -ground _b c_ because that is the dark part and shadow of the tree _a -b c_. - -But if the eye is placed at _t_ it will see _o p_ dark on the light -background _n g_. - -Of the transparent and shadowy parts of trees, that which is nearest -to you is the darkest. - -456. - -That part of a tree which has shadow for background, is all of one -tone, and wherever the trees or branches are thickest they will be -darkest, because there are no little intervals of air. But where the -boughs lie against a background of other boughs, the brighter parts -are seen lightest and the leaves lustrous from the sunlight falling -on them. - -457. - -In the composition of leafy trees be careful not to repeat too often -the same colour of one tree against the same colour of another -[behind it]; but vary it with a lighter, or a darker, or a stronger -green. - -On the treatment of light for landscapes (458-464). - -458. - -The landscape has a finer azure [tone] when, in fine weather the sun -is at noon than at any other time of the day, because the air is -purified of moisture; and looking at it under that aspect you will -see the trees of a beautiful green at the outside and the shadows -dark towards the middle; and in the remoter distance the atmosphere -which comes between you and them looks more beautiful when there is -something dark beyond. And still the azure is most beautiful. The -objects seen from the side on which the sun shines will not show you -their shadows. But, if you are lower than the sun, you can see what -is not seen by the sun and that will be all in shade. The leaves of -the trees, which come between you and the sun are of two principal -colours which are a splendid lustre of green, and the reflection of -the atmosphere which lights up the objects which cannot be seen by -the sun, and the shaded portions which only face the earth, and the -darkest which are surrounded by something that is not dark. The -trees in the landscape which are between you and the sun are far -more beautiful than those you see when you are between the sun and -them; and this is so because those which face the sun show their -leaves as transparent towards the ends of their branches, and those -that are not transparent--that is at the ends--reflect the light; -and the shadows are dark because they are not concealed by any -thing. - -The trees, when you place yourself between them and the sun, will -only display to you their light and natural colour, which, in -itself, is not very strong, and besides this some reflected lights -which, being against a background which does not differ very much -from themselves in tone, are not conspicuous; and if you are lower -down than they are situated, they may also show those portions on -which the light of the sun does not fall and these will be dark. - -In the Wind. - -But, if you are on the side whence the wind blows, you will see the -trees look very much lighter than on the other sides, and this -happens because the wind turns up the under side of the leaves, -which, in all trees, is much whiter than the upper sides; and, more -especially, will they be very light indeed if the wind blows from -the quarter where the sun is, and if you have your back turned to -it. - -[Footnote: At _S_, in the original is the word _Sole_ (sun) and at -_N parte di nuvolo_ (the side of the clouds).] - -459. - -When the sun is covered by clouds, objects are less conspicuous, -because there is little difference between the light and shade of -the trees and of the buildings being illuminated by the brightness -of the atmosphere which surrounds the objects in such a way that the -shadows are few, and these few fade away so that their outline is -lost in haze. - -460. - -OF TREES AND LIGHTS ON THEM. - -The best method of practice in representing country scenes, or I -should say landscapes with their trees, is to choose them so that -the sun is covered with clouds so that the landscape receives an -universal light and not the direct light of the sun, which makes the -shadows sharp and too strongly different from the lights. - -461. - -OF PAINTING. - -In landscapes which represent [a scene in] winter. The mountains -should not be shown blue, as we see in the mountains in the summer. -And this is proved [Footnote 5. 6.: _Per la_ 4_a di questo_. It is -impossible to ascertain what this quotation refers to. _Questo_ -certainly does not mean the MS. in hand, nor any other now known to -us. The same remark applies to the phrase in line 15: _per la_ 2_a -di questo_.] in the 4th of this which says: Among mountains seen -from a great distance those will look of the bluest colour which are -in themselves the darkest; hence, when the trees are stripped of -their leaves, they will show a bluer tinge which will be in itself -darker; therefore, when the trees have lost their leaves they will -look of a gray colour, while, with their leaves, they are green, and -in proportion as the green is darker than the grey hue the green -will be of a bluer tinge than the gray. Also by the 2nd of this: The -shadows of trees covered with leaves are darker than the shadows of -those trees which have lost their leaves in proportion as the trees -covered with leaves are denser than those without leaves--and thus -my meaning is proved. - -The definition of the blue colour of the atmosphere explains why the -landscape is bluer in the summer than in the winter. - -462. - -OF PAINTING IN A LANDSCAPE. - -If the slope of a hill comes between the eye and the horizon, -sloping towards the eye, while the eye is opposite the middle of the -height of this slope, then that hill will increase in darkness -throughout its length. This is proved by the 7th of this which says -that a tree looks darkest when it is seen from below; the -proposition is verified, since this hill will, on its upper half -show all its trees as much from the side which is lighted by the -light of the sky, as from that which is in shade from the darkness -of the earth; whence it must result that these trees are of a medium -darkness. And from this [middle] spot towards the base of the hill, -these trees will be lighter by degrees by the converse of the 7th -and by the said 7th: For trees so placed, the nearer they are to the -summit of the hill the darker they necessarily become. But this -darkness is not in proportion to the distance, by the 8th of this -which says: That object shows darkest which is [seen] in the -clearest atmosphere; and by the 10th: That shows darkest which -stands out against a lighter background. - -[Footnote: The quotation in this passage again cannot be verified.] - -463. - -OF LANDSCAPES. - -The colours of the shadows in mountains at a great distance take a -most lovely blue, much purer than their illuminated portions. And -from this it follows that when the rock of a mountain is reddish the -illuminated portions are violet (?) and the more they are lighted -the more they display their proper colour. - -464. - -A place is most luminous when it is most remote from mountains. - -On the treatment of light for views of towns (465-469). - -465. - -OF LIGHT AND SHADOW IN A TOWN. - -When the sun is in the East and the eye is above the centre of a -town, the eye will see the Southern part of the town with its roofs -half in shade and half in light, and the same towards the North; the -Eastern side will be all in shadow and the Western will be all in -light. - -466. - -Of the houses of a town, in which the divisions between the houses -may be distinguished by the light which fall on the mist at the -bottom. If the eye is above the houses the light seen in the space -that is between one house and the next sinks by degrees into thicker -mist; and yet, being less transparent, it appears whiter; and if the -houses are some higher than the others, since the true [colour] is -always more discernible through the thinner atmosphere, the houses -will look darker in proportion as they are higher up. Let _n o p q_ -represent the various density of the atmosphere thick with moisture, -_a_ being the eye, the house _b c_ will look lightest at the bottom, -because it is in a thicker atmosphere; the lines _c d f_ will appear -equally light, for although _f_ is more distant than _c_, it is -raised into a thinner atmosphere, if the houses _b e_ are of the -same height, because they cross a brightness which is varied by -mist, but this is only because the line of the eye which starts from -above ends by piercing a lower and denser atmosphere at _d_ than at -_b_. Thus the line a _f_ is lower at _f_ than at _c_; and the house -_f_ will be seen darker at _e_ from the line _e k_ as far as _m_, -than the tops of the houses standing in front of it. - -467. - -OF TOWNS OR OTHER BUILDINGS SEEN IN THE EVENING OR THE MORNING -THROUGH THE MIST. - -Of buildings seen at a great distance in the evening or the morning, -as in mist or dense atmosphere, only those portions are seen in -brightness which are lighted up by the sun which is near the -horizon; and those portions which are not lighted up by the sun -remain almost of the same colour and medium tone as the mist. - -WHY OBJECTS WHICH ARE HIGH UP AND AT A DISTANCE ARE DARKER THAN THE -LOWER ONES, EVEN IF THE MIST IS UNIFORMLY DENSE. - -Of objects standing in a mist or other dense atmosphere, whether -from vapour or smoke or distance, those will be most visible which -are the highest. And among objects of equal height that will be the -darkest [strongest] which has for background the deepest mist. Thus -the eye _h_ looking at _a b c_, towers of equal height, one with -another, sees _c_ the top of the first tower at _r_, at two degrees -of depth in the mist; and sees the height of the middle tower _b_ -through one single degree of mist. Therefore the top of the tower -_c_ appears stronger than the top of the tower _b_, &c. - -468. - -OF THE SMOKE OF A TOWN. - -Smoke is seen better and more distinctly on the Eastern side than on -the Western when the sun is in the East; and this arises from two -causes; the first is that the sun, with its rays, shines through the -particles of the smoke and lights them up and makes them visible. -The second is that the roofs of the houses seen in the East at this -time are in shadow, because their obliquity does not allow of their -being illuminated by the sun. And the same thing occurs with dust; -and both one and the other look the lighter in proportion as they -are denser, and they are densest towards the middle. - -469. - -OF SMOKE AND DUST. - -If the sun is in the East the smoke of cities will not be visible in -the West, because on that side it is not seen penetrated by the -solar rays, nor on a dark background; since the roofs of the houses -turn the same side to the eye as they turn towards the sun, and on -this light background the smoke is not very visible. - -But dust, under the same aspect, will look darker than smoke being -of denser material than smoke which is moist. - -The effect of wind on trees (470-473). - -470. - -OF REPRESENTING WIND. - -In representing wind, besides the bending of the boughs and the -reversing of their leaves towards the quarter whence the wind comes, -you should also represent them amid clouds of fine dust mingled with -the troubled air. - -471. - -Describe landscapes with the wind, and the water, and the setting -and rising of the sun. - -THE WIND. - -All the leaves which hung towards the earth by the bending of the -shoots with their branches, are turned up side down by the gusts of -wind, and here their perspective is reversed; for, if the tree is -between you and the quarter of the wind, the leaves which are -towards you remain in their natural aspect, while those on the -opposite side which ought to have their points in a contrary -direction have, by being turned over, their points turned towards -you. - -472. - -Trees struck by the force of the wind bend to the side towards which -the wind is blowing; and the wind being past they bend in the -contrary direction, that is in reverse motion. - -473. - -That portion of a tree which is farthest from the force which -strikes it is the most injured by the blow because it bears most -strain; thus nature has foreseen this case by thickening them in -that part where they can be most hurt; and most in such trees as -grow to great heights, as pines and the like. [Footnote: Compare the -sketch drawn with a pen and washed with Indian ink on Pl. XL, No. 1. -In the Vatican copy we find, under a section entitled '_del fumo_', -the following remark: _Era sotto di questo capitulo un rompimento di -montagna, per dentro delle quali roture scherzaua fiame di fuoco, -disegnate di penna et ombrate d'acquarella, da uedere cosa mirabile -et uiua (Ed. MANZI, p. 235. Ed. LUDWIG, Vol. I, 460). This appears -to refer to the left hand portion of the drawing here given from the -Windsor collection, and from this it must be inferred, that the leaf -as it now exists in the library of the Queen of England, was already -separated from the original MS. at the time when the Vatican copy -was made.] - -Light and shade on clouds (474-477). - -474. - -Describe how the clouds are formed and how they dissolve, and what -cause raises vapour. - -475. - -The shadows in clouds are lighter in proportion as they are nearer -to the horizon. - -[Footnote: The drawing belonging to this was in black chalk and is -totally effaced.] - -476. - -When clouds come between the sun and the eye all the upper edges of -their round forms are light, and towards the middle they are dark, -and this happens because towards the top these edges have the sun -above them while you are below them; and the same thing happens with -the position of the branches of trees; and again the clouds, like -the trees, being somewhat transparent, are lighted up in part, and -at the edges they show thinner. - -But, when the eye is between the cloud and the sun, the cloud has -the contrary effect to the former, for the edges of its mass are -dark and it is light towards the middle; and this happens because -you see the same side as faces the sun, and because the edges have -some transparency and reveal to the eye that portion which is hidden -beyond them, and which, as it does not catch the sunlight like that -portion turned towards it, is necessarily somewhat darker. Again, it -may be that you see the details of these rounded masses from the -lower side, while the sun shines on the upper side and as they are -not so situated as to reflect the light of the sun, as in the first -instance they remain dark. - -The black clouds which are often seen higher up than those which are -illuminated by the sun are shaded by other clouds, lying between -them and the sun. - -Again, the rounded forms of the clouds that face the sun, show their -edges dark because they lie against the light background; and to see -that this is true, you may look at the top of any cloud that is -wholly light because it lies against the blue of the atmosphere, -which is darker than the cloud. - -[Footnote: A drawing in red chalk from the Windsor collection (see -Pl. XXIX), representing a landscape with storm-clouds, may serve to -illustrate this section as well as the following one.] - -477. - -OF CLOUDS, SMOKE AND DUST AND THE FLAMES OF A FURNACE OR OF A -BURNING KILN. - -The clouds do not show their rounded forms excepting on the sides -which face the sun; on the others the roundness is imperceptible -because they are in the shade. [Footnote: The text of this chapter -is given in facsimile on Pls. XXXVI and XXXVII. The two halves of -the leaf form but one in the original. On the margin close to lines -4 and 5 is the note: _rossore d'aria inverso l'orizonte_--(of the -redness of the atmosphere near the horizon). The sketches on the -lower portion of the page will be spoken of in No. 668.] - -If the sun is in the East and the clouds in the West, the eye placed -between the sun and the clouds sees the edges of the rounded forms -composing these clouds as dark, and the portions which are -surrounded by this dark [edge] are light. And this occurs because -the edges of the rounded forms of these clouds are turned towards -the upper or lateral sky, which is reflected in them. - -Both the cloud and the tree display no roundness at all on their -shaded side. - -On images reflected in water. - -478. - -Painters often deceive themselves, by representing water in which -they make the water reflect the objects seen by the man. But the -water reflects the object from one side and the man sees it from the -other; and it often happens that the painter sees an object from -below, and thus one and the same object is seen from hind part -before and upside down, because the water shows the image of the -object in one way, and the eye sees it in another. - -Of rainbows and rain (479. 480). - -479. - -The colours in the middle of the rainbow mingle together. - -The bow in itself is not in the rain nor in the eye that sees it; -though it is generated by the rain, the sun, and the eye. The -rainbow is always seen by the eye that is between the rain and the -body of the sun; hence if the sun is in the East and the rain is in -the West it will appear on the rain in the West. - -480. - -When the air is condensed into rain it would produce a vacuum if the -rest of the air did not prevent this by filling its place, as it -does with a violent rush; and this is the wind which rises in the -summer time, accompanied by heavy rain. - -Of flower seeds. - -481. - -All the flowers which turn towards the sun perfect their seeds; but -not the others; that is to say those which get only the reflection -of the sun. - -IX. - -_The Practice of Painting._ - -_It is hardly necessary to offer any excuses for the division -carried out in the arrangement of the text into practical -suggestions and theoretical enquiries. It was evidently intended by -Leonardo himself as we conclude from incidental remarks in the MSS. -(for instance No_ 110_). The fact that this arrangement was never -carried out either in the old MS. copies or in any edition since, is -easily accounted for by the general disorder which results from the -provisional distribution of the various chapters in the old copies. -We have every reason to believe that the earliest copyists, in -distributing the materials collected by them, did not in the least -consider the order in which the original MS.lay before them._ - -_It is evident that almost all the chapters which refer to the -calling and life of the painter--and which are here brought together -in the first section (Nos._ 482-508_)--may be referred to two -distinct periods in Leonardo's life; most of them can be dated as -belonging to the year_ 1492 _or to_ 1515. _At about this later time -Leonardo may have formed the project of completing his Libro della -Pittura, after an interval of some years, as it would seem, during -which his interest in the subject had fallen somewhat into the -background._ - -_In the second section, which treats first of the artist's studio, -the construction of a suitable window forms the object of careful -investigations; the special importance attached to this by Leonardo -is sufficiently obvious. His theory of the incidence of light which -was fully discussed in a former part of this work, was to him by no -means of mere abstract value, but, being deduced, as he says, from -experience (or experiment) was required to prove its utility in -practice. Connected with this we find suggestions for the choice of -a light with practical hints as to sketching a picture and some -other precepts of a practical character which must come under -consideration in the course of completing the painting. In all this -I have followed the same principle of arrangement in the text as was -carried out in the Theory of Painting, thus the suggestions for the -Perspective of a picture, (Nos._ 536-569_), are followed by the -theory of light and shade for the practical method of optics (Nos._ -548--566_) and this by the practical precepts or the treatment of -aerial perspective (_567--570_)._ - -_In the passage on Portrait and Figure Painting the principles of -painting as applied to a bust and head are separated and placed -first, since the advice to figure painters must have some connection -with the principles of the treatment of composition by which they -are followed._ - -_But this arrangement of the text made it seem advisable not to pick -out the practical precepts as to the representation of trees and -landscape from the close connection in which they were originally -placed--unlike the rest of the practical precepts--with the theory -of this branch of the subject. They must therefore be sought under -the section entitled Botany for Painters._ - -_As a supplement to the_ Libro di Pittura _I have here added those -texts which treat of the Painter's materials,--as chalk, drawing -paper, colours and their preparation, of the management of oils and -varnishes; in the appendix are some notes on chemical substances. -Possibly some of these, if not all, may have stood in connection -with the preparation of colours. It is in the very nature of things -that Leonardo's incidental indications as to colours and the like -should be now-a-days extremely obscure and could only be explained -by professional experts--by them even in but few instances. It might -therefore have seemed advisable to reproduce exactly the original -text without offering any translation. The rendering here given is -merely an attempt to suggest what Leonardo's meaning may have been._ - -_LOMAZZO tells us in his_ Trattato dell'arte della Pittura, Scultura -ed Architettura (Milano 1584, libro II, Cap. XIV): "Va discorrendo -ed argomentando Leonardo Vinci in un suo libro letto da me (?) -questi anni passati, ch'egli scrisse di mano stanca ai prieghi di -LUDOVICO SFORZA duca di Milano, in determinazione di questa -questione, se e piu nobile la pittura o la scultura; dicendo che -quanto piu un'arte porta seco fatica di corpo, e sudore, tanto piu e -vile, e men pregiata". _But the existence of any book specially -written for Lodovico il Moro on the superiority of Painting over -sculpture is perhaps mythical. The various passages in praise of -Painting as compared not merely with Sculpture but with Poetry, are -scattered among MSS. of very different dates._ - -_Besides, the way, in which the subject is discussed appears not to -support the supposition, that these texts were prepared at a special -request of the Duke._ - -I. - -MORAL PRECEPTS FOR THE STUDENT OF PAINTING. - -How to ascertain the dispositions for an artistic career. - -482. - -A WARNING CONCERNING YOUTHS WISHING TO BE PAINTERS. - -Many are they who have a taste and love for drawing, but no talent; -and this will be discernible in boys who are not diligent and never -finish their drawings with shading. - -The course of instruction for an artist (483-485). - -483. - -The youth should first learn perspective, then the proportions of -objects. Then he may copy from some good master, to accustom himself -to fine forms. Then from nature, to confirm by practice the rules he -has learnt. Then see for a time the works of various masters. Then -get the habit of putting his art into practice and work. - -[Footnote: The Vatican copy and numerous abridgements all place this -chapter at the beginning of the _Trattato_, and in consequence -DUFRESNE and all subsequent editors have done the same. In the -Vatican copy however all the general considerations on the relation -of painting to the other arts are placed first, as introductory.] - -484. - -OF THE ORDER OF LEARNING TO DRAW. - -First draw from drawings by good masters done from works of art and -from nature, and not from memory; then from plastic work, with the -guidance of the drawing done from it; and then from good natural -models and this you must put into practice. - -485. - -PRECEPTS FOR DRAWING. - -The artist ought first to exercise his hand by copying drawings from -the hand of a good master. And having acquired that practice, under -the criticism of his master, he should next practise drawing objects -in relief of a good style, following the rules which will presently -be given. - -The study of the antique (486. 487). - -486. - -OF DRAWING. - -Which is best, to draw from nature or from the antique? and which is -more difficult to do outlines or light and shade? - -487. - -It is better to imitate [copy] the antique than modern work. - -[Footnote 486, 487: These are the only two passages in which -Leonardo alludes to the importance of antique art in the training of -an artist. The question asked in No. 486 remains unanswered by him -and it seems to me very doubtful whether the opinion stated in No. -487 is to be regarded as a reply to it. This opinion stands in the -MS. in a connection--as will be explained later on--which seems to -require us to limit its application to a single special case. At any -rate we may suspect that when Leonardo put the question, he felt -some hesitation as to the answer. Among his very numerous drawings I -have not been able to find a single study from the antique, though a -drawing in black chalk, at Windsor, of a man on horseback (PI. -LXXIII) may perhaps be a reminiscence of the statue of Marcus -Aurelius at Rome. It seems to me that the drapery in a pen and ink -drawing of a bust, also at Windsor, has been borrowed from an -antique model (Pl. XXX). G. G. Rossi has, I believe, correctly -interpreted Leonardo's feeling towards the antique in the following -note on this passage in manzi's edition, p. 501: "Sappiamo dalla -storia, che i valorosi artisti Toscani dell'eta dell'oro dell'arte -studiarono sugli antichi marmi raccolti dal Magnifico LORENZO DE' -MEDICI. Pare che il Vinci a tali monumenti non si accostasse. Quest' -uomo sempre riconosce per maestra la natura, e questo principio lo -stringeva alla sola imitazione di essa"--Compare No. 10, 26--28 -footnote.] - -The necessity of anatomical knowledge (488. 489). - -488. - -OF PAINTING. - -It is indispensable to a Painter who would be thoroughly familiar -with the limbs in all the positions and actions of which they are -capable, in the nude, to know the anatomy of the sinews, bones, -muscles and tendons so that, in their various movements and -exertions, he may know which nerve or muscle is the cause of each -movement and show those only as prominent and thickened, and not the -others all over [the limb], as many do who, to seem great -draughtsmen, draw their nude figures looking like wood, devoid of -grace; so that you would think you were looking at a sack of walnuts -rather than the human form, or a bundle of radishes rather than the -muscles of figures. - -489. - -HOW IT IS NECESSARY TO A PAINTER THAT HE SHOULD KNOW THE INTRINSIC -FORMS [STRUCTURE] OF MAN. - -The painter who is familiar with the nature of the sinews, muscles, -and tendons, will know very well, in giving movement to a limb, how -many and which sinews cause it; and which muscle, by swelling, -causes the contraction of that sinew; and which sinews, expanded -into the thinnest cartilage, surround and support the said muscle. -Thus he will variously and constantly demonstrate the different -muscles by means of the various attitudes of his figures, and will -not do, as many who, in a variety of movements, still display the -very same things [modelling] in the arms, back, breast and legs. And -these things are not to be regarded as minor faults. - -How to acquire practice. - -490. - -OF STUDY AND THE ORDER OF STUDY. - -I say that first you ought to learn the limbs and their mechanism, -and having this knowledge, their actions should come next, according -to the circumstances in which they occur in man. And thirdly to -compose subjects, the studies for which should be taken from natural -actions and made from time to time, as circumstances allow; and pay -attention to them in the streets and _piazze_ and fields, and note -them down with a brief indication of the forms; [Footnote 5: Lines -5-7 explained by the lower portion of the sketch No. 1 on Pl. XXXI.] -thus for a head make an o, and for an arm a straight or a bent line, -and the same for the legs and the body, [Footnote 7: Lines 5-7 -explained by the lower portion of the sketch No. 1 on Pl. XXXI.] and -when you return home work out these notes in a complete form. The -Adversary says that to acquire practice and do a great deal of work -it is better that the first period of study should be employed in -drawing various compositions done on paper or on walls by divers -masters, and that in this way practice is rapidly gained, and good -methods; to which I reply that the method will be good, if it is -based on works of good composition and by skilled masters. But since -such masters are so rare that there are but few of them to be found, -it is a surer way to go to natural objects, than to those which are -imitated from nature with great deterioration, and so form bad -methods; for he who can go to the fountain does not go to the -water-jar. - -[Footnote: This passage has been published by Dr. M. JORDAN, _Das -Malerbuck des L. da Vinci_, p. 89; his reading however varies -slightly from mine.] - -Industry and thoroughness the first conditions (491-493.) - -491. - -WHAT RULES SHOULD BE GIVEN TO BOYS LEARNING TO PAINT. - -We know for certain that sight is one of the most rapid actions we -can perform. In an instant we see an infinite number of forms, still -we only take in thoroughly one object at a time. Supposing that you, -Reader, were to glance rapidly at the whole of this written page, -you would instantly perceive that it was covered with various -letters; but you could not, in the time, recognise what the letters -were, nor what they were meant to tell. Hence you would need to see -them word by word, line by line to be able to understand the -letters. Again, if you wish to go to the top of a building you must -go up step by step; otherwise it will be impossible that you should -reach the top. Thus I say to you, whom nature prompts to pursue this -art, if you wish to have a sound knowledge of the forms of objects -begin with the details of them, and do not go on to the second -[step] till you have the first well fixed in memory and in practice. -And if you do otherwise you will throw away your time, or certainly -greatly prolong your studies. And remember to acquire diligence -rather than rapidity. - -492. - -HOW THAT DILIGENCE [ACCURACY] SHOULD FIRST BE LEARNT RATHER THAN -RAPID EXECUTION. - -If you, who draw, desire to study well and to good purpose, always -go slowly to work in your drawing; and discriminate in. the lights, -which have the highest degree of brightness, and to what extent and -likewise in the shadows, which are those that are darker than the -others and in what way they intermingle; then their masses and the -relative proportions of one to the other. And note in their -outlines, which way they tend; and which part of the lines is curved -to one side or the other, and where they are more or less -conspicuous and consequently broad or fine; and finally, that your -light and shade blend without strokes and borders [but] looking like -smoke. And when you have thus schooled your hand and your judgment -by such diligence, you will acquire rapidity before you are aware. - -The artist's private life and choice of company (493-494). - -493. - -OF THE LIFE OF THE PAINTER IN THE COUNTRY. - -A painter needs such mathematics as belong to painting. And the -absence of all companions who are alienated from his studies; his -brain must be easily impressed by the variety of objects, which -successively come before him, and also free from other cares -[Footnote 6: Leonardo here seems to be speaking of his own method of -work as displayed in his MSS. and this passage explains, at least in -part, the peculiarities in their arrangement.]. And if, when -considering and defining one subject, a second subject -intervenes--as happens when an object occupies the mind, then he -must decide which of these cases is the more difficult to work out, -and follow that up until it becomes quite clear, and then work out -the explanation of the other [Footnote 11: Leonardo here seems to be -speaking of his own method of work as displayed in his MSS. and this -passage explains, at least in part, the peculiarities in their -arrangement.]. And above all he must keep his mind as clear as the -surface of a mirror, which assumes colours as various as those of -the different objects. And his companions should be like him as to -their studies, and if such cannot be found he should keep his -speculations to himself alone, so that at last he will find no more -useful company [than his own]. - -[Footnote: In the title line Leonardo had originally written _del -pictore filosofo_ (the philosophical painter), but he himself struck -out_filosofo_. Compare in No. 363 _pictora notomista_ (anatomical -painter). The original text is partly reproduced on Pl. CI.] - -494. - -OF THE LIFE OF THE PAINTER IN HIS STUDIO. - -To the end that well-being of the body may not injure that of the -mind, the painter or draughtsman must remain solitary, and -particularly when intent on those studies and reflections which will -constantly rise up before his eye, giving materials to be well -stored in the memory. While you are alone you are entirely your own -[master] and if you have one companion you are but half your own, -and the less so in proportion to the indiscretion of his behaviour. -And if you have many companions you will fall deeper into the same -trouble. If you should say: "I will go my own way and withdraw -apart, the better to study the forms of natural objects", I tell -you, you will not be able to help often listening to their chatter. -And so, since one cannot serve two masters, you will badly fill the -part of a companion, and carry out your studies of art even worse. -And if you say: "I will withdraw so far that their words cannot -reach me and they cannot disturb me", I can tell you that you will -be thought mad. But, you see, you will at any rate be alone. And if -you must have companions ship find it in your studio. This may -assist you to have the advantages which arise from various -speculations. All other company may be highly mischievous. - -The distribution of time for studying (495-497). - -495. - -OF WHETHER IT IS BETTER TO DRAW WITH COMPANIONS OR NOT. - -I say and insist that drawing in company is much better than alone, -for many reasons. The first is that you would be ashamed to be seen -behindhand among the students, and such shame will lead you to -careful study. Secondly, a wholesome emulation will stimulate you to -be among those who are more praised than yourself, and this praise -of others will spur you on. Another is that you can learn from the -drawings of others who do better than yourself; and if you are -better than they, you can profit by your contempt for their defects, -while the praise of others will incite you to farther merits. - -[Footnote: The contradiction by this passage of the foregoing -chapter is only apparent. It is quite clear, from the nature of the -reasoning which is here used to prove that it is more improving to -work with others than to work alone, that the studies of pupils only -are under consideration here.] - -496. - -OF STUDYING, IN THE DARK, WHEN YOU WAKE, OR IN BED BEFORE YOU GO TO -SLEEP. - -I myself have proved it to be of no small use, when in bed in the -dark, to recall in fancy the external details of forms previously -studied, or other noteworthy things conceived by subtle speculation; -and this is certainly an admirable exercise, and useful for -impressing things on the memory. - -497. - -OF THE TIME FOR STUDYING SELECTION OF SUBJECTS. - -Winter evenings ought to be employed by young students in looking -over the things prepared during the summer; that is, all the -drawings from the nude done in the summer should be brought together -and a choice made of the best [studies of] limbs and bodies among -them, to apply in practice and commit to memory. - -OF POSITIONS. - -After this in the following summer you should select some one who is -well grown and who has not been brought up in doublets, and so may -not be of stiff carriage, and make him go through a number of agile -and graceful actions; and if his muscles do not show plainly within -the outlines of his limbs that does not matter at all. It is enough -that you can see good attitudes and you can correct [the drawing of] -the limbs by those you studied in the winter. - -[Footnote: An injunction to study in the evening occurs also in No. -524.] - -On the productive power of minor artists (498-501). - -498. - -He is a poor disciple who does not excel his master. - -499. - -Nor is the painter praiseworthy who does but one thing well, as the -nude figure, heads, draperies, animals, landscapes or other such -details, irrespective of other work; for there can be no mind so -inept, that after devoting itself to one single thing and doing it -constantly, it should fail to do it well. - -[Footnote: In MANZI'S edition (p. 502) the painter G. G. Bossi -indignantly remarks on this passage. "_Parla il Vince in questo -luogo come se tutti gli artisti avessero quella sublimita d'ingegno -capace di abbracciare tutte le cose, di cui era egli dotato"_ And he -then mentions the case of CLAUDE LORRAIN. But he overlooks the fact -that in Leonardo's time landscape painting made no pretensions to -independence but was reckoned among the details (_particulari_, -lines 3, 4).] - -500. - -THAT A PAINTER IS NOT ADMIRABLE UNLESS HE IS UNIVERSAL. - -Some may distinctly assert that those persons are under a delusion -who call that painter a good master who can do nothing well but a -head or a figure. Certainly this is no great achievement; after -studying one single thing for a life-time who would not have -attained some perfection in it? But, since we know that painting -embraces and includes in itself every object produced by nature or -resulting from the fortuitous actions of men, in short, all that the -eye can see, he seems to me but a poor master who can only do a -figure well. For do you not perceive how many and various actions -are performed by men only; how many different animals there are, as -well as trees, plants, flowers, with many mountainous regions and -plains, springs and rivers, cities with public and private -buildings, machines, too, fit for the purposes of men, divers -costumes, decorations and arts? And all these things ought to be -regarded as of equal importance and value, by the man who can be -termed a good painter. - -501. - -OF THE MISERABLE PRETENCES MADE BY THOSE WHO FALSELY AND UNWORTHILY -ACQUIRE THE NAME OF PAINTERS. - -Now there is a certain race of painters who, having studied but -little, must need take as their standard of beauty mere gold and -azure, and these, with supreme conceit, declare that they will not -give good work for miserable payment, and that they could do as well -as any other if they were well paid. But, ye foolish folks! cannot -such artists keep some good work, and then say: this is a costly -work and this more moderate and this is average work and show that -they can work at all prices? - -A caution against one-sided study. - -502. - -HOW, IN IMPORTANT WORKS, A MAN SHOULD NOT TRUST ENTIRELY TO HIS -MEMORY WITHOUT CONDESCENDING TO DRAW FROM NATURE. - -Any master who should venture to boast that he could remember all -the forms and effects of nature would certainly appear to me to be -graced with extreme ignorance, inasmuch as these effects are -infinite and our memory is not extensive enough to retain them. -Hence, O! painter, beware lest the lust of gain should supplant in -you the dignity of art; for the acquisition of glory is a much -greater thing than the glory of riches. Hence, for these and other -reasons which might be given, first strive in drawing to represent -your intention to the eye by expressive forms, and the idea -originally formed in your imagination; then go on taking out or -putting in, until you have satisfied yourself. Then have living men, -draped or nude, as you may have purposed in your work, and take care -that in dimensions and size, as determined by perspective, nothing -is left in the work which is not in harmony with reason and the -effects in nature. And this will be the way to win honour in your -art. - -How to acquire universality (503-506). - -503. - -OF VARIETY IN THE FIGURES. - -The painter should aim at universality, because there is a great -want of self-respect in doing one thing well and another badly, as -many do who study only the [rules of] measure and proportion in the -nude figure and do not seek after variety; for a man may be well -proportioned, or he may be fat and short, or tall and thin, or -medium. And a painter who takes no account of these varieties always -makes his figures on one pattern so that they might all be taken for -brothers; and this is a defect that demands stern reprehension. - -504. - -HOW SOMETHING MAY BE LEARNT EVERYWHERE. - -Nature has beneficently provided that throughout the world you may -find something to imitate. - -505. - -OF THE MEANS OF ACQUIRING UNIVERSALITY. - -It is an easy matter to men to acquire universality, for all -terrestrial animals resemble each other as to their limbs, that is -in their muscles, sinews and bones; and they do not vary excepting -in length or in thickness, as will be shown under Anatomy. But then -there are aquatic animals which are of great variety; I will not try -to convince the painter that there is any rule for them for they are -of infinite variety, and so is the insect tribe. - -506. - -PAINTING. - -The mind of the painter must resemble a mirror, which always takes -the colour of the object it reflects and is completely occupied by -the images of as many objects as are in front of it. Therefore you -must know, Oh Painter! that you cannot be a good one if you are not -the universal master of representing by your art every kind of form -produced by nature. And this you will not know how to do if you do -not see them, and retain them in your mind. Hence as you go through -the fields, turn your attention to various objects, and, in turn -look now at this thing and now at that, collecting a store of divers -facts selected and chosen from those of less value. But do not do -like some painters who, when they are wearied with exercising their -fancy dismiss their work from their thoughts and take exercise in -walking for relaxation, but still keep fatigue in their mind which, -though they see various objects [around them], does not apprehend -them; but, even when they meet friends or relations and are saluted -by them, although they see and hear them, take no more cognisance of -them than if they had met so much empty air. - -Useful games and exercises (507. 508). - -507. - -OF GAMES TO BE PLAYED BY THOSE WHO DRAW. - -When, Oh draughtsmen, you desire to find relaxation in games you -should always practise such things as may be of use in your -profession, by giving your eye good practice in judging accurately -of the breadth and length of objects. Thus, to accustom your mind to -such things, let one of you draw a straight line at random on a -wall, and each of you, taking a blade of grass or of straw in his -hand, try to cut it to the length that the line drawn appears to him -to be, standing at a distance of 10 braccia; then each one may go up -to the line to measure the length he has judged it to be. And he who -has come nearest with his measure to the length of the pattern is -the best man, and the winner, and shall receive the prize you have -settled beforehand. Again you should take forshortened measures: -that is take a spear, or any other cane or reed, and fix on a point -at a certain distance; and let each one estimate how many times he -judges that its length will go into that distance. Again, who will -draw best a line one braccio long, which shall be tested by a -thread. And such games give occasion to good practice for the eye, -which is of the first importance in painting. - -508. - -A WAY OF DEVELOPING AND AROUSING THE MIND TO VARIOUS INVENTIONS. - -I cannot forbear to mention among these precepts a new device for -study which, although it may seem but trivial and almost ludicrous, -is nevertheless extremely useful in arousing the mind to various -inventions. And this is, when you look at a wall spotted with -stains, or with a mixture of stones, if you have to devise some -scene, you may discover a resemblance to various landscapes, -beautified with mountains, rivers, rocks, trees, plains, wide -valleys and hills in varied arrangement; or again you may see -battles and figures in action; or strange faces and costumes, and an -endless variety of objects, which you could reduce to complete and -well drawn forms. And these appear on such walls confusedly, like -the sound of bells in whose jangle you may find any name or word you -choose to imagine. - -II. - -THE ARTIST'S STUDIO.--INSTRUMENTS AND HELPS FOR THE APPLICATION OF -PERSPECTIVE.--ON JUDGING OF A PICTURE. - -On the size of the studio. - -509. - -Small rooms or dwellings discipline the mind, large ones weaken it. - -On the construction of windows (510-512). - -510. - -The larger the wall the less the light will be. - -511. - -The different kinds of light afforded in cellars by various forms of -windows. The least useful and the coldest is the window at _a_. The -most useful, the lightest and warmest and most open to the sky is -the window at _b_. The window at _c_ is of medium utility. - -[Footnote: From a reference to the notes on the right light for -painting it becomes evident that the observations made on -cellar-windows have a direct bearing on the construction of the -studio-window. In the diagram _b_ as well as in that under No. 510 -the window-opening is reduced to a minimum, but only, it would seem, -in order to emphasize the advantage of walls constructed on the plan -there shown.] - -512. - -OF THE PAINTER'S WINDOW AND ITS ADVANTAGE. - -The painter who works from nature should have a window, which he can -raise and lower. The reason is that sometimes you will want to -finish a thing you are drawing, close to the light. - -Let _a b c d_ be the chest on which the work may be raised or -lowered, so that the work moves up and down and not the painter. And -every evening you can let down the work and shut it up above so that -in the evening it may be in the fashion of a chest which, when shut -up, may serve the purpose of a bench. - -[Footnote: See Pl. XXXI, No. 2. In this plate the lines have -unfortunately lost their sharpness, for the accidental loss of the -negative has necessitated a reproduction from a positive. But having -formerly published this sketch by another process, in VON LUTZOW'S -_Zeitschrift fur bildende Kunst_ (Vol. XVII, pg. 13) I have -reproduced it here in the text. The sharpness of the outline in the -original sketch is here preserved but it gives it from the reversed -side.] - -On the best light for painting (513-520). - -513. - -Which light is best for drawing from nature; whether high or low, or -large or small, or strong and broad, or strong and small, or broad -and weak or small and weak? - -[Footnote: The question here put is unanswered in the original MS.] - -514. - -OF THE QUALITY OF THE LIGHT. - -A broad light high up and not too strong will render the details of -objects very agreeable. - -515. - -THAT THE LIGHT FOR DRAWING FROM NATURE SHOULD BE HIGH UP. - -The light for drawing from nature should come from the North in -order that it may not vary. And if you have it from the South, keep -the window screened with cloth, so that with the sun shining the -whole day the light may not vary. The height of the light should be -so arranged as that every object shall cast a shadow on the ground -of the same length as itself. - -516. - -THE KIND OF LIGHT REQUISITE FOR PAINTING LIGHT AND SHADE. - -An object will display the greatest difference of light and shade -when it is seen in the strongest light, as by sunlight, or, at -night, by the light of a fire. But this should not be much used in -painting because the works remain crude and ungraceful. - -An object seen in a moderate light displays little difference in the -light and shade; and this is the case towards evening or when the -day is cloudy, and works then painted are tender and every kind of -face becomes graceful. Thus, in every thing extremes are to be -avoided: Too much light gives crudeness; too little prevents our -seeing. The medium is best. - -OF SMALL LIGHTS. - -Again, lights cast from a small window give strong differences of -light and shade, all the more if the room lighted by it be large, -and this is not good for painting. - -517. - -PAINTING. - -The luminous air which enters by passing through orifices in walls -into dark rooms will render the place less dark in proportion as the -opening cuts into the walls which surround and cover in the -pavement. - -518. - -OF THE QUALITY OF LIGHT. - -In proportion to the number of times that _a b_ goes into _c d_ will -it be more luminous than _c d_. And similarly, in proportion as the -point _e_ goes into _c d_ will it be more luminous than _c d;_ and -this light is useful for carvers of delicate work. [Footnote 5: For -the same reason a window thus constructed would be convenient for an -illuminator or a miniature painter.] - -[Footnote: M. RAVAISSON in his edition of the Paris MS. A remarks on -this passage: _"La figure porte les lettres_ f _et_ g, _auxquelles -rien ne renvoie dans l'explication; par consequent, cette -explication est incomplete. La figure semblerait, d'ailleurs, se -rapporter a l'effet de la reflexion par un miroir concave."_ So far -as I can see the text is not imperfect, nor is the sense obscure. It -is hardly necessary to observe that _c d_ here indicate the wall of -the room opposite to the window _e_ and the semicircle described by -_f g_ stands for the arch of the sky; this occurs in various -diagrams, for example under 511. A similar semicircle, Pl III, No. 2 -(and compare No. 149) is expressly called '_orizonte_' in writing.] - -519. - -That the light should fall upon a picture from one window only. This -may be seen in the case of objects in this form. If you want to -represent a round ball at a certain height you must make it oval in -this shape, and stand so far off as that by foreshortening it -appears round. - -520. - -OF SELECTING THE LIGHT WHICH GIVES MOST GRACE TO FACES. - -If you should have a court yard that you can at pleasure cover with -a linen awning that light will be good. Or when you want to take a -portrait do it in dull weather, or as evening falls, making the -sitter stand with his back to one of the walls of the court yard. -Note in the streets, as evening falls, the faces of the men and -women, and when the weather is dull, what softness and delicacy you -may perceive in them. Hence, Oh Painter! have a court arranged with -the walls tinted black and a narrow roof projecting within the -walls. It should be 10 braccia wide and 20 braccia long and 10 -braccia high and covered with a linen awning; or else paint a work -towards evening or when it is cloudy or misty, and this is a perfect -light. - -On various helps in preparing a picture (521-530). - -521. - -To draw a nude figure from nature, or any thing else, hold in your -hand a plumb-line to enable you to judge of the relative position -of objects. - -522. - -OF DRAWING AN OBJECT. - -When you draw take care to set up a principal line which you must -observe all throughout the object you are drawing; every thing -should bear relation to the direction of this principal line. - -523. - -OF A MODE OF DRAWING A PLACE ACCURATELY. - -Have a piece of glass as large as a half sheet of royal folio paper -and set thus firmly in front of your eyes that is, between your eye -and the thing you want to draw; then place yourself at a distance of -2/3 of a braccia from the glass fixing your head with a machine in -such a way that you cannot move it at all. Then shut or entirely -cover one eye and with a brush or red chalk draw upon the glass that -which you see beyond it; then trace it on paper from the glass, -afterwards transfer it onto good paper, and paint it if you like, -carefully attending to the arial perspective. - -HOW TO LEARN TO PLACE YOUR FIGURES CORRECTLY. - -If you want to acquire a practice of good and correct attitudes for -your figures, make a square frame or net, and square it out with -thread; place this between your eye and the nude model you are -drawing, and draw these same squares on the paper on which you mean -to draw the figure, but very delicately. Then place a pellet of wax -on a spot of the net which will serve as a fixed point, which, -whenever you look at your model, must cover the pit of the throat; -or, if his back is turned, it may cover one of the vertebrae of the -neck. Thus these threads will guide you as to each part of the body -which, in any given attitude will be found below the pit of the -throat, or the angles of the shoulders, or the nipples, or hips and -other parts of the body; and the transverse lines of the net will -show you how much the figure is higher over the leg on which it is -posed than over the other, and the same with the hips, and the knees -and the feet. But always fix the net perpendicularly so that all the -divisions that you see the model divided into by the net work -correspond with your drawing of the model on the net work you have -sketched. The squares you draw may be as much smaller than those of -the net as you wish that your figure should be smaller than nature. -Afterwards remember when drawing figures, to use the rule of the -corresponding proportions of the limbs as you have learnt it from -the frame and net. This should be 3 braccia and a half high and 3 -braccia wide; 7 braccia distant from you and 1 braccio from the -model. - -[Footnote: Leonardo is commonly credited with the invention of the -arrangement of a plate of glass commonly known as the "vertical -plane." Professor E. VON BRUCKE in his _"Bruchstucke aus der Theorie -der bildenden Kunste,"_ Leipzig 1877, pg. 3, writes on this -contrivance. _"Unsere Glastafel ist die sogenannte Glastafel des -Leonardo da Vinci, die in Gestalt einer Glastafel vorgestellte -Bildflache."_] - -524. - -A METHOD OF DRAWING AN OBJECT IN RELIEF AT NIGHT. - -Place a sheet of not too transparent paper between the relievo and -the light and you can draw thus very well. - -[Footnote: Bodies thus illuminated will show on the surface of the -paper how the copyist has to distribute light and shade.] - -525. - -If you want to represent a figure on a wall, the wall being -foreshortened, while the figure is to appear in its proper form, and -as standing free from the wall, you must proceed thus: have a thin -plate of iron and make a small hole in the centre; this hole must be -round. Set a light close to it in such a position as that it shines -through the central hole, then place any object or figure you please -so close to the wall that it touches it and draw the outline of the -shadow on the wall; then fill in the shade and add the lights; place -the person who is to see it so that he looks through that same hole -where at first the light was; and you will never be able to persuade -yourself that the image is not detached from the wall. - -[Footnote: _uno piccolo spiracelo nel mezzo_. M. RAVAISSON, in his -edition of MS. A (Paris), p. 52, reads _nel muro_--evidently a -mistake for _nel mezzo_ which is quite plainly written; and he -translates it _"fait lui une petite ouverture dans le mur,"_ adding -in a note: _"les mots 'dans le mur' paraissent etre de trop. -Leonardo a du les ecrire par distraction"_ But _'nel mezzo'_ is -clearly legible even on the photograph facsimile given by Ravaisson -himself, and the objection he raises disappears at once. It is not -always wise or safe to try to prove our author's absence of mind or -inadvertence by apparent difficulties in the sense or connection of -the text.] - -526. - -TO DRAW A FIGURE ON A WALL 12 BRACCIA HIGH WHICH SHALL LOOK 24 -BRACCIA HIGH. - -If you wish to draw a figure or any other object to look 24 braccia -high you must do it in this way. First, on the surface _m r_ draw -half the man you wish to represent; then the other half; then put on -the vault _m n_ [the rest of] the figure spoken of above; first set -out the vertical plane on the floor of a room of the same shape as -the wall with the coved part on which you are to paint your figure. -Then, behind it, draw a figure set out in profile of whatever size -you please, and draw lines from it to the point _f_ and, as these -lines cut _m n_ on the vertical plane, so will the figure come on -the wall, of which the vertical plane gives a likeness, and you will -have all the [relative] heights and prominences of the figure. And -the breadth or thickness which are on the upright wall _m n_ are to -be drawn in their proper form, since, as the wall recedes the figure -will be foreshortened by itself; but [that part of] the figure which -goes into the cove you must foreshorten, as if it were standing -upright; this diminution you must set out on a flat floor and there -must stand the figure which is to be transferred from the vertical -plane _r n_[Footnote 17: _che leverai dalla pariete r n_. The -letters refer to the larger sketch, No. 3 on Pl. XXXI.] in its real -size and reduce it once more on a vertical plane; and this will be a -good method [Footnote 18: Leonardo here says nothing as to how the -image foreshortened by perspective and thus produced on the vertical -plane is to be transferred to the wall; but from what is said in -Nos. 525 and 523 we may conclude that he was familiar with the -process of casting the enlarged shadow of a squaring net on the -surface of a wall to guide him in drawing the figure. - -_Pariete di rilieuo; "sur une parai en relief"_ (RAVAISSON). _"Auf -einer Schnittlinie zum Aufrichten"_ (LUDWIG). The explanation of -this puzzling expression must be sought in No. 545, lines 15-17.]. - -[Footnote: See Pl. XXXI. 3. The second sketch, which in the plate is -incomplete, is here reproduced and completed from the original to -illustrate the text. In the original the larger diagram is placed -between lines 5 and 6. - -1. 2. C. A. 157a; 463a has the similar heading: '_del cressciere -della figura_', and the text begins: "_Se voli fare 1a figura -grande_ b c" but here it breaks off. The translation here given -renders the meaning of the passage as I think it must be understood. -The MS. is perfectly legible and the construction of the sentence is -simple and clear; difficulties can only arise from the very fullness -of the meaning, particularly towards the end of the passage.] - -527. - -If you would to draw a cube in an angle of a wall, first draw the -object in its own proper shape and raise it onto a vertical plane -until it resembles the angle in which the said object is to be -represented. - -528. - -Why are paintings seen more correctly in a mirror than out of it? - -529. - -HOW THE MIRROR IS THE MASTER [AND GUIDE] OF PAINTERS. - -When you want to see if your picture corresponds throughout with the -objects you have drawn from nature, take a mirror and look in that -at the reflection of the real things, and compare the reflected -image with your picture, and consider whether the subject of the two -images duly corresponds in both, particularly studying the mirror. -You should take the mirror for your guide--that is to say a flat -mirror--because on its surface the objects appear in many respects -as in a painting. Thus you see, in a painting done on a flat -surface, objects which appear in relief, and in the mirror--also a -flat surface--they look the same. The picture has one plane surface -and the same with the mirror. The picture is intangible, in so far -as that which appears round and prominent cannot be grasped in the -hands; and it is the same with the mirror. And since you can see -that the mirror, by means of outlines, shadows and lights, makes -objects appear in relief, you, who have in your colours far stronger -lights and shades than those in the mirror, can certainly, if you -compose your picture well, make that also look like a natural scene -reflected in a large mirror. - -[Footnote: I understand the concluding lines of this passage as -follows: If you draw the upper half a figure on a large sheet of -paper laid out on the floor of a room (_sala be piana_) to the same -scale (_con le sue vere grosseze_) as the lower half, already drawn -upon the wall (lines 10, 11)you must then reduce them on a '_pariete -di rilievo_,' a curved vertical plane which serves as a model to -reproduce the form of the vault.] - -530. - -OF JUDGING YOUR OWN PICTURES. - -We know very well that errors are better recognised in the works of -others than in our own; and that often, while reproving little -faults in others, you may ignore great ones in yourself. To avoid -such ignorance, in the first place make yourself a master of -perspective, then acquire perfect knowledge of the proportions of -men and other animals, and also, study good architecture, that is so -far as concerns the forms of buildings and other objects which are -on the face of the earth; these forms are infinite, and the better -you know them the more admirable will your work be. And in cases -where you lack experience do not shrink from drawing them from -nature. But, to carry out my promise above [in the title]--I say -that when you paint you should have a flat mirror and often look at -your work as reflected in it, when you will see it reversed, and it -will appear to you like some other painter's work, so you will be -better able to judge of its faults than in any other way. Again, it -is well that you should often leave off work and take a little -relaxation, because, when you come back to it you are a better -judge; for sitting too close at work may greatly deceive you. Again, -it is good to retire to a distance because the work looks smaller -and your eye takes in more of it at a glance and sees more easily -the discords or disproportion in the limbs and colours of the -objects. - -On the management of works (531. 532). - -531. - -OF A METHOD OF LEARNING WELL BY HEART. - -When you want to know a thing you have studied in your memory -proceed in this way: When you have drawn the same thing so many -times that you think you know it by heart, test it by drawing it -without the model; but have the model traced on flat thin glass and -lay this on the drawing you have made without the model, and note -carefully where the tracing does not coincide with your drawing, and -where you find you have gone wrong; and bear in mind not to repeat -the same mistakes. Then return to the model, and draw the part in -which you were wrong again and again till you have it well in your -mind. If you have no flat glass for tracing on, take some very thin -kidts-kin parchment, well oiled and dried. And when you have used it -for one drawing you can wash it clean with a sponge and make a -second. - -532. - -THAT A PAINTER OUGHT TO BE CURIOUS TO HEAR THE OPINIONS OF EVERY ONE -ON HIS WORK. - -Certainly while a man is painting he ought not to shrink from -hearing every opinion. For we know very well that a man, though he -may not be a painter, is familiar with the forms of other men and -very capable of judging whether they are hump backed, or have one -shoulder higher or lower than the other, or too big a mouth or nose, -and other defects; and, as we know that men are competent to judge -of the works of nature, how much more ought we to admit that they -can judge of our errors; since you know how much a man may be -deceived in his own work. And if you are not conscious of this in -yourself study it in others and profit by their faults. Therefore be -curious to hear with patience the opinions of others, consider and -weigh well whether those who find fault have ground or not for -blame, and, if so amend; but, if not make as though you had not -heard, or if he should be a man you esteem show him by argument the -cause of his mistake. - -On the limitations of painting (533-535) - -533. - -HOW IN SMALL OBJECTS ERRORS ARE LESS EVIDENT THAN IN LARGE ONES. - -In objects of minute size the extent of error is not so perceptible -as in large ones; and the reason is that if this small object is a -representation of a man or of some other animal, from the immense -diminution the details cannot be worked out by the artist with the -finish that is requisite. Hence it is not actually complete; and, -not being complete, its faults cannot be determined. For instance: -Look at a man at a distance of 300 braccia and judge attentively -whether he be handsome or ugly, or very remarkable or of ordinary -appearance. You will find that with the utmost effort you cannot -persuade yourself to decide. And the reason is that at such a -distance the man is so much diminished that the character of the -details cannot be determined. And if you wish to see how much this -man is diminished [by distance] hold one of your fingers at a span's -distance from your eye, and raise or lower it till the top joint -touches the feet of the figure you are looking at, and you will see -an incredible reduction. For this reason we often doubt as to the -person of a friend at a distance. - -534. - -WHY A PAINTING CAN NEVER APPEAR DETACHED AS NATURAL OBJECTS DO. - -Painters often fall into despair of imitating nature when they see -their pictures fail in that relief and vividness which objects have -that are seen in a mirror; while they allege that they have colours -which for brightness or depth far exceed the strength of light and -shade in the reflections in the mirror, thus displaying their own -ignorance rather than the real cause, because they do not know it. -It is impossible that painted objects should appear in such relief -as to resemble those reflected in the mirror, although both are seen -on a flat surface, unless they are seen with only one eye; and the -reason is that two eyes see one object behind another as _a_ and _b_ -see _m_ and _n_. _m_ cannot exactly occupy [the space of] _n_ -because the base of the visual lines is so broad that the second -body is seen beyond the first. But if you close one eye, as at _s_ -the body _f_ will conceal _r_, because the line of sight proceeds -from a single point and makes its base in the first body, whence the -second, of the same size, can never be seen. - -[Footnote: This passage contains the solution of the problem -proposed in No. 29, lines 10-14. Leonardo was evidently familiar -with the law of optics on which the construction of the stereoscope -depends. Compare E. VON BRUCKE, _Bruchstucke aus der Theorie der -bildenden Kunste_, pg. 69: "_Schon Leonardo da Vinci wusste, dass -ein noch so gut gemaltes Bild nie den vollen Eindruck der -Korperlichkeit geben kann, wie ihn die Natur selbst giebt. Er -erklart dies auch in Kap. LIII und Kap. CCCXLI_ (ed. DU FRESNE) -_des_ 'Trattato' _in sachgemasser Weise aus dem Sehen mit beiden -Augen_." - -Chap. 53 of DU FRESNE'S edition corresponds to No. 534 of this -work.] - -535. - -WHY OF TWO OBJECTS OF EQUAL SIZE A PAINTED ONE WILL LOOK LARGER THAN -A SOLID ONE. - -The reason of this is not so easy to demonstrate as many others. -Still I will endeavour to accomplish it, if not wholly, at any rate -in part. The perspective of diminution demonstrates by reason, that -objects diminish in proportion as they are farther from the eye, and -this reasoning is confirmed by experience. Hence, the lines of sight -that extend between the object and the eye, when they are directed -to the surface of a painting are all intersected at uniform limits, -while those lines which are directed towards a piece of sculpture -are intersected at various limits and are of various lengths. The -lines which are longest extend to a more remote limb than the others -and therefore that limb looks smaller. As there are numerous lines -each longer than the others--since there are numerous parts, each -more remote than the others and these, being farther off, -necessarily appear smaller, and by appearing smaller it follows that -their diminution makes the whole mass of the object look smaller. -But this does not occur in painting; since the lines of sight all -end at the same distance there can be no diminution, hence the parts -not being diminished the whole object is undiminished, and for this -reason painting does not diminish, as a piece of sculpture does. - -On the choice of a position (536-537) - -536. - -HOW HIGH THE POINT OF SIGHT SHOULD BE PLACED. - -The point of sight must be at the level of the eye of an ordinary -man, and the farthest limit of the plain where it touches the sky -must be placed at the level of that line where the earth and sky -meet; excepting mountains, which are independent of it. - -537. - -OF THE WAY TO DRAW FIGURES FOR HISTORICAL PICTURES. - -The painter must always study on the wall on which he is to picture -a story the height of the position where he wishes to arrange his -figures; and when drawing his studies for them from nature he must -place himself with his eye as much below the object he is drawing -as, in the picture, it will have to be above the eye of the -spectator. Otherwise the work will look wrong. - -The apparent size of figures in a picture (538-539) - -538. - -OF PLACING A FIGURE IN THE FOREGROUND OF A HISTORICAL PICTURE. - -You must make the foremost figure in the picture less than the size -of nature in proportion to the number of braccia at which you place -it from the front line, and make the others in proportion by the -above rule. - -539. - -PERSPECTIVE. - -You are asked, O Painter, why the figures you draw on a small scale -according to the laws of perspective do not appear--notwithstanding -the demonstration of distance--as large as real ones--their height -being the same as in those painted on the wall. - -And why [painted] objects seen at a small distance appear larger -than the real ones? - -The right position of the artist, when painting, and of the -spectator (540-547) - -540. - -OF PAINTING. - -When you draw from nature stand at a distance of 3 times the height -of the object you wish to draw. - -541. - -OF DRAWING FROM RELIEF. - -In drawing from the round the draughtsman should so place himself -that the eye of the figure he is drawing is on a level with his own. -This should be done with any head he may have to represent from -nature because, without exception, the figures or persons you meet -in the streets have their eyes on the same level as your own; and if -you place them higher or lower you will see that your drawing will -not be true. - -542. - -WHY GROUPS OF FIGURES ONE ABOVE ANOTHER ARE TO BE AVOIDED. - -The universal practice which painters adopt on the walls of chapels -is greatly and reasonably to be condemned. Inasmuch as they -represent one historical subject on one level with a landscape and -buildings, and then go up a step and paint another, varying the -point [of sight], and then a third and a fourth, in such a way as -that on one wall there are 4 points of sight, which is supreme folly -in such painters. We know that the point of sight is opposite the -eye of the spectator of the scene; and if you would [have me] tell -you how to represent the life of a saint divided into several -pictures on one and the same wall, I answer that you must set out -the foreground with its point of sight on a level with the eye of -the spectator of the scene, and upon this plane represent the more -important part of the story large and then, diminishing by degrees -the figures, and the buildings on various hills and open spaces, you -can represent all the events of the history. And on the remainder of -the wall up to the top put trees, large as compared with the -figures, or angels if they are appropriate to the story, or birds or -clouds or similar objects; otherwise do not trouble yourself with it -for your whole work will be wrong. - -543. - -A PICTURE OF OBJECTS IN PERSPECTIVE WILL LOOK MORE LIFELIKE WHEN -SEEN FROM THE POINT FROM WHICH THE OBJECTS WERE DRAWN. - -If you want to represent an object near to you which is to have the -effect of nature, it is impossible that your perspective should not -look wrong, with every false relation and disagreement of proportion -that can be imagined in a wretched work, unless the spectator, when -he looks at it, has his eye at the very distance and height and -direction where the eye or the point of sight was placed in doing -this perspective. Hence it would be necessary to make a window, or -rather a hole, of the size of your face through which you can look -at the work; and if you do this, beyond all doubt your work, if it -is correct as to light and shade, will have the effect of nature; -nay you will hardly persuade yourself that those objects are -painted; otherwise do not trouble yourself about it, unless indeed -you make your view at least 20 times as far off as the greatest -width or height of the objects represented, and this will satisfy -any spectator placed anywhere opposite to the picture. - -If you want the proof briefly shown, take a piece of wood in the -form of a little column, eight times as high as it is thick, like a -column without any plinth or capital; then mark off on a flat wall -40 equal spaces, equal to its width so that between them they make -40 columns resembling your little column; you then must fix, -opposite the centre space, and at 4 braccia from the wall, a thin -strip of iron with a small round hole in the middle about as large -as a big pearl. Close to this hole place a light touching it. Then -place your column against each mark on the wall and draw the outline -of its shadow; afterwards shade it and look through the hole in the -iron plate. - -[Footnote: In the original there is a wide space between lines 3 and -4 in which we find two sketches not belonging to the text. It is -unnecessary to give prominence to the points in which my reading -differs from that of M. RAVAISSON or to justify myself, since they -are all of secondary importance and can also be immediately verified -from the photograph facsimile in his edition.] - -544. - -A diminished object should be seen from the same distance, height -and direction as the point of sight of your eye, or else your -knowledge will produce no good effect. - -And if you will not, or cannot, act on this principle--because as -the plane on which you paint is to be seen by several persons you -would need several points of sight which would make it look -discordant and wrong--place yourself at a distance of at least 10 -times the size of the objects. - -The lesser fault you can fall into then, will be that of -representing all the objects in the foreground of their proper size, -and on whichever side you are standing the objects thus seen will -diminish themselves while the spaces between them will have no -definite ratio. For, if you place yourself in the middle of a -straight row [of objects], and look at several columns arranged in a -line you will see, beyond a few columns separated by intervals, that -the columns touch; and beyond where they touch they cover each -other, till the last column projects but very little beyond the last -but one. Thus the spaces between the columns are by degrees entirely -lost. So, if your method of perspective is good, it will produce the -same effect; this effect results from standing near the line in -which the columns are placed. This method is not satisfactory unless -the objects seen are viewed from a small hole, in the middle of -which is your point of sight; but if you proceed thus your work will -be perfect and will deceive the beholder, who will see the columns -as they are here figured. - -Here the eye is in the middle, at the point _a_ and near to the -columns. - -[Footnote: The diagram which stands above this chapter in the -original with the note belonging to it: "a b _e la ripruova_" (_a b_ -is the proof) has obviously no connection with the text. The second -sketch alone is reproduced and stands in the original between lines -22 and 23.] - -545. - -If you cannot arrange that those who look at your work should stand -at one particular point, when constructing your work, stand back -until your eye is at least 20 times as far off as the greatest -height and width of your work. This will make so little difference -when the eye of the spectator moves, that it will be hardly -appreciable, and it will look very good. - -If the point of sight is at _t_ you would make the figures on the -circle _d b e_ all of one size, as each of them bears the same -relation to the point _t_. But consider the diagram given below and -you will see that this is wrong, and why I shall make _b_ smaller -than _d e_ [Footnote 8: The second diagram of this chapter stands in -the original between lines 8 and 9.]. - -It is easy to understand that if 2 objects equal to each other are -placed side by side the one at 3 braccia distance looks smaller than -that placed at 2 braccia. This however is rather theoretical than -for practice, because you stand close by [Footnote 11: Instead of -'_se preso_' (=_sie presso_) M. RAVAISSON reads '_sempre se_' which -gives rise to the unmeaning rendering: '_parceque toujours_ ...']. - -All the objects in the foreground, whether large or small, are to be -drawn of their proper size, and if you see them from a distance they -will appear just as they ought, and if you see them close they will -diminish of themselves. - -[Footnote 15: Compare No. 526 line 18.] Take care that the vertical -plan on which you work out the perspective of the objects seen is of -the same form as the wall on which the work is to be executed. - -546. - -OF PAINTING. - -The size of the figures represented ought to show you the distance -they are seen from. If you see a figure as large as nature you know -it appears to be close to the eye. - -547. - -WHERE A SPECTATOR SHOULD STAND TO LOOK AT A PICTURE. - -Supposing _a b_ to be the picture and _d_ to be the light, I say -that if you place yourself between _c_ and _e_ you will not -understand the picture well and particularly if it is done in oils, -or still more if it is varnished, because it will be lustrous and -somewhat of the nature of a mirror. And for this reason the nearer -you go towards the point _c_, the less you will see, because the -rays of light falling from the window on the picture are reflected -to that point. But if you place yourself between _e_ and _d_ you -will get a good view of it, and the more so as you approach the -point _d_, because that spot is least exposed to these reflected -rays of light. - -III. - -THE PRACTICAL METHODS OF LIGHT AND SHADE AND AERIAL PERSPECTIVE. - -Gradations of light and shade. - -548. - -OF PAINTING: OF THE DARKNESS OF THE SHADOWS, OR I MAY SAY, THE -BRIGHTNESS OF THE LIGHTS. - -Although practical painters attribute to all shaded objects--trees, -fields, hair, beards and skin--four degrees of darkness in each -colour they use: that is to say first a dark foundation, secondly a -spot of colour somewhat resembling the form of the details, thirdly -a somewhat brighter and more defined portion, fourthly the lights -which are more conspicuous than other parts of the figure; still to -me it appears that these gradations are infinite upon a continuous -surface which is in itself infinitely divisible, and I prove it -thus:--[Footnote 7: See Pl. XXXI, No. 1; the two upper sketches.] -Let _a g_ be a continuous surface and let _d_ be the light which -illuminates it; I say--by the 4th [proposition] which says that that -side of an illuminated body is most highly lighted which is nearest -to the source of light--that therefore _g_ must be darker than _c_ -in proportion as the line _d g_ is longer than the line _d c_, and -consequently that these gradations of light--or rather of shadow, -are not 4 only, but may be conceived of as infinite, because _c d_ -is a continuous surface and every continuous surface is infinitely -divisible; hence the varieties in the length of lines extending -between the light and the illuminated object are infinite, and the -proportion of the light will be the same as that of the length of -the lines between them; extending from the centre of the luminous -body to the surface of the illuminated object. - -On the choice of light for a picture (549-554). - -549. - -HOW THE PAINTER MUST PLACE HIMSELF WITH REFERENCE TO THE LIGHT, TO -GIVE THE EFFECT OF RELIEF. - -Let _a b_ be the window, _m_ the point of light. I say that on -whichever side the painter places himself he will be well placed if -only his eye is between the shaded and the illuminated portions of -the object he is drawing; and this place you will find by putting -yourself between the point _m_ and the division between the shadow -and the light on the object to be drawn. - -550. - -THAT SHADOWS CAST BY A PARTICULAR LIGHT SHOULD BE AVOIDED, BECAUSE -THEY ARE EQUALLY STRONG AT THE ENDS AND AT THE BEGINNING. - -The shadows cast by the sun or any other particular light have not a -pleasing effect on the body to which they belong, because the parts -remain confuse, being divided by distinct outlines of light and -shade. And the shadows are of equal strength at the end and at the -beginning. - -551. - -HOW LIGHT SHOULD BE THROWN UPON FIGURES. - -The light must be arranged in accordance with the natural conditions -under which you wish to represent your figures: that is, if you -represent them in the sunshine make the shadows dark with large -spaces of light, and mark their shadows and those of all the -surrounding objects strongly on the ground. And if you represent -them as in dull weather give little difference of light and shade, -without any shadows at their feet. If you represent them as within -doors, make a strong difference between the lights and shadows, with -shadows on the ground. If the window is screened and the walls -white, there will be little difference of light. If it is lighted by -firelight make the high lights ruddy and strong, and the shadows -dark, and those cast on the walls and on the floor will be clearly -defined and the farther they are from the body the broader and -longer will they be. If the light is partly from the fire and partly -from the outer day, that of day will be the stronger and that of the -fire almost as red as fire itself. Above all see that the figures -you paint are broadly lighted and from above, that is to say all -living persons that you paint; for you will see that all the people -you meet out in the street are lighted from above, and you must know -that if you saw your most intimate friend with a light [on his face] -from below you would find it difficult to recognise him. - -552. - -OF HELPING THE APPARENT RELIEF OF A PICTURE BY GIVING IT ARTIFICIAL -LIGHT AND SHADE. - -To increase relief of a picture you may place, between your figure -and the solid object on which its shadow falls, a line of bright -light, dividing the figure from the object in shadow. And on the -same object you shall represent two light parts which will surround -the shadow cast upon the wall by the figure placed opposite [6]; and -do this frequently with the limbs which you wish should stand out -somewhat from the body they belong to; particularly when the arms -cross the front of the breast show, between the shadow cast by the -arms on the breast and the shadow on the arms themselves, a little -light seeming to fall through a space between the breast and the -arms; and the more you wish the arm to look detached from the breast -the broader you must make the light; always contrive also to arrange -the figures against the background in such a way as that the parts -in shadow are against a light background and the illuminated -portions against a dark background. - -[Footnote 6: Compare the two diagrams under No. 565.] - -553. - -OF SITUATION. - -Remember [to note] the situation of your figures; for the light and -shade will be one thing if the object is in a dark place with a -particular light, and another thing if it is in a light place with -direct sunlight; one thing in a dark place with a diffused evening -light or a cloudy sky, and another in the diffused light of the -atmosphere lighted by the sun. - -554. - -OF THE JUDGMENT TO BE MADE OF A PAINTER'S WORK. - -First you must consider whether the figures have the relief required -by their situation and the light which illuminates them; for the -shadows should not be the same at the extreme ends of the -composition as in the middle, because it is one thing when figures -are surrounded by shadows and another when they have shadows only on -one side. Those which are in the middle of the picture are -surrounded by shadows, because they are shaded by the figures which -stand between them and the light. And those are lighted on one side -only which stand between the principal group and the light, because -where they do not look towards the light they face the group and the -darkness of the group is thrown on them: and where they do not face -the group they face the brilliant light and it is their own darkness -shadowing them, which appears there. - -In the second place observe the distribution or arrangement of -figures, and whether they are distributed appropriately to the -circumstances of the story. Thirdly, whether the figures are -actively intent on their particular business. - -555. - -OF THE TREATMENT OF THE LIGHTS. - -First give a general shadow to the whole of that extended part which -is away from the light. Then put in the half shadows and the strong -shadows, comparing them with each other and, in the same way give -the extended light in half tint, afterwards adding the half lights -and the high lights, likewise comparing them together. - -The distribution of light and shade (556-559) - -556. - -OF SHADOWS ON BODIES. - -When you represent the dark shadows in bodies in light and shade, -always show the cause of the shadow, and the same with reflections; -because the dark shadows are produced by dark objects and the -reflections by objects only moderately lighted, that is with -diminished light. And there is the same proportion between the -highly lighted part of a body and the part lighted by a reflection -as between the origin of the lights on the body and the origin of -the reflections. - -557. - -OF LIGHTS AND SHADOWS. - -I must remind you to take care that every portion of a body, and -every smallest detail which is ever so little in relief, must be -given its proper importance as to light and shade. - -558. - -OF THE WAY TO MAKE THE SHADOW ON FIGURES CORRESPOND TO THE LIGHT AND -TO [THE COLOUR] OF THE BODY. - -When you draw a figure and you wish to see whether the shadow is the -proper complement to the light, and neither redder nor yellower than -is the nature of the colour you wish to represent in shade, proceed -thus. Cast a shadow with your finger on the illuminated portion, and -if the accidental shadow that you have made is like the natural -shadow cast by your finger on your work, well and good; and by -putting your finger nearer or farther off, you can make darker or -lighter shadows, which you must compare with your own. - -559. - -OF SURROUNDING BODIES BY VARIOUS FORMS OF SHADOW. - -Take care that the shadows cast upon the surface of the bodies by -different objects must undulate according to the various curves of -the limbs which cast the shadows, and of the objects on which they -are cast. - -The juxtaposition of light and shade (560, 561). - -560. - -ON PAINTING. - -The comparison of the various qualities of shadows and lights not -infrequently seems ambiguous and confused to the painter who desires -to imitate and copy the objects he sees. The reason is this: If you -see a white drapery side by side with a black one, that part of the -white drapery which lies against the black one will certainly look -much whiter than the part which lies against something whiter than -itself. [Footnote: It is evident from this that so early as in 1492 -Leonardo's writing in perspective was so far advanced that he could -quote his own statements.--As bearing on this subject compare what -is said in No. 280.] And the reason of this is shown in my [book on] -perspective. - -561. - -OF SHADOWS. - -Where a shadow ends in the light, note carefully where it is paler -or deeper and where it is more or less indistinct towards the light; -and, above all, in [painting] youthful figures I remind you not to -make the shadow end like a stone, because flesh has a certain -transparency, as may be seen by looking at a hand held between the -eye and the sun, which shines through it ruddy and bright. Place the -most highly coloured part between the light and shadow. And to see -what shadow tint is needed on the flesh, cast a shadow on it with -your finger, and according as you wish to see it lighter or darker -hold your finger nearer to or farther from your picture, and copy -that [shadow]. - -On the lighting of the background (562-565). - -562. - -OF THE BACKGROUNDS FOR PAINTED FIGURES. - -The ground which surrounds the forms of any object you paint should -be darker than the high lights of those figures, and lighter than -their shadowed part: &c. - -563. - -OF THE BACKGROUND THAT THE PAINTER SHOULD ADOPT IN HIS WORKS. - -Since experience shows us that all bodies are surrounded by light -and shade it is necessary that you, O Painter, should so arrange -that the side which is in light shall terminate against a dark body -and likewise that the shadow side shall terminate against a light -body. And by [following] this rule you will add greatly to the -relief of your figures. - -564. - -A most important part of painting consists in the backgrounds of the -objects represented; against these backgrounds the outlines of -those natural objects which are convex are always visible, and also -the forms of these bodies against the background, even though the -colours of the bodies should be the same as that of the background. -This is caused by the convex edges of the objects not being -illuminated in the same way as, by the same light, the background is -illuminated, since these edges will often be lighter or darker than -the background. But if the edge is of the same colour as the -background, beyond a doubt it will in that part of the picture -interfere with your perception of the outline, and such a choice in -a picture ought to be rejected by the judgment of good painters, -inasmuch as the purpose of the painter is to make his figures appear -detached from the background; while in the case here described the -contrary occurs, not only in the picture, but in the objects -themselves. - -565. - -That you ought, when representing objects above the eye and on one -side--if you wish them to look detached from the wall--to show, -between the shadow on the object and the shadow it casts a middle -light, so that the body will appear to stand away from the wall. - -On the lighting of white objects. - -566. - -HOW WHITE BODIES SHOULD BE REPRESENTED. - -If you are representing a white body let it be surrounded by ample -space, because as white has no colour of its own, it is tinged and -altered in some degree by the colour of the objects surrounding it. -If you see a woman dressed in white in the midst of a landscape, -that side which is towards the sun is bright in colour, so much so -that in some portions it will dazzle the eyes like the sun itself; -and the side which is towards the atmosphere,--luminous through -being interwoven with the sun's rays and penetrated by them--since -the atmosphere itself is blue, that side of the woman's figure will -appear steeped in blue. If the surface of the ground about her be -meadows and if she be standing between a field lighted up by the sun -and the sun itself, you will see every portion of those folds which -are towards the meadow tinged by the reflected rays with the colour -of that meadow. Thus the white is transmuted into the colours of the -luminous and of the non-luminous objects near it. - -The methods of aerial (567--570). - -567. - -WHY FACES [SEEN] AT A DISTANCE LOOK DARK. - -We see quite plainly that all the images of visible objects that lie -before us, whether large or small, reach our sense by the minute -aperture of the eye; and if, through so small a passage the image -can pass of the vast extent of sky and earth, the face of a -man--being by comparison with such large images almost nothing by -reason of the distance which diminishes it,--fills up so little of -the eye that it is indistinguishable. Having, also, to be -transmitted from the surface to the sense through a dark medium, -that is to say the crystalline lens which looks dark, this image, -not being strong in colour becomes affected by this darkness on its -passage, and on reaching the sense it appears dark; no other reason -can in any way be assigned. If the point in the eye is black, it is -because it is full of a transparent humour as clear as air and acts -like a perforation in a board; on looking into it it appears dark -and the objects seen through the bright air and a dark one become -confused in this darkness. - -WHY A MAN SEEN AT A CERTAIN DISTANCE IS NOT RECOGNISABLE. - -The perspective of diminution shows us that the farther away an -object is the smaller it looks. If you look at a man at a distance -from you of an arrow's flight, and hold the eye of a small needle -close to your own eye, you can see through it several men whose -images are transmitted to the eye and will all be comprised within -the size of the needle's eye; hence, if the man who is at the -distance of an arrow's flight can send his whole image to your eye, -occupying only a small space in the needle's eye how can you -[expect] in so small a figure to distinguish or see the nose or -mouth or any detail of his person? and, not seeing these you cannot -recognise the man, since these features, which he does not show, are -what give men different aspects. - -568. - -THE REASON WHY SMALL FIGURES SHOULD NOT BE MADE FINISHED. - -I say that the reason that objects appear diminished in size is -because they are remote from the eye; this being the case it is -evident that there must be a great extent of atmosphere between the -eye and the objects, and this air interferes with the distinctness -of the forms of the object. Hence the minute details of these -objects will be indistinguishable and unrecognisable. Therefore, O -Painter, make your smaller figures merely indicated and not highly -finished, otherwise you will produce effects the opposite to nature, -your supreme guide. The object is small by reason of the great -distance between it and the eye, this great distance is filled with -air, that mass of air forms a dense body which intervenes and -prevents the eye seeing the minute details of objects. - -569. - -Whenever a figure is placed at a considerable distance you lose -first the distinctness of the smallest parts; while the larger parts -are left to the last, losing all distinctness of detail and outline; -and what remains is an oval or spherical figure with confused edges. - -570. - -OF PAINTING. - -The density of a body of smoke looks white below the horizon while -above the horizon it is dark, even if the smoke is in itself of a -uniform colour, this uniformity will vary according to the variety -in the ground on which it is seen. - -IV. - -OF PORTRAIT AND FIGURE PAINTING. - -Of sketching figures and portraits (571-572). - -571. - -OF THE WAY TO LEARN TO COMPOSE FIGURES [IN GROUPS] IN HISTORICAL -PICTURES. - -When you have well learnt perspective and have by heart the parts -and forms of objects, you must go about, and constantly, as you go, -observe, note and consider the circumstances and behaviour of men in -talking, quarrelling or laughing or fighting together: the action of -the men themselves and the actions of the bystanders, who separate -them or who look on. And take a note of them with slight strokes -thus, in a little book which you should always carry with you. And -it should be of tinted paper, that it may not be rubbed out, but -change the old [when full] for a new one; since these things should -not be rubbed out but preserved with great care; for the forms, and -positions of objects are so infinite that the memory is incapable of -retaining them, wherefore keep these [sketches] as your guides and -masters. - -[Footnote: Among Leonardo's numerous note books of pocket size not -one has coloured paper, so no sketches answering to this description -can be pointed out. The fact that most of the notes are written in -ink, militates against the supposition that they were made in the -open air.] - -572. - -OF A METHOD OF KEEPING IN MIND THE FORM OF A FACE. - -If you want to acquire facility for bearing in mind the expression -of a face, first make yourself familiar with a variety of [forms of] -several heads, eyes, noses, mouths, chins and cheeks and necks and -shoulders: And to put a case: Noses are of 10 types: straight, -bulbous, hollow, prominent above or below the middle, aquiline, -regular, flat, round or pointed. These hold good as to profile. In -full face they are of 11 types; these are equal thick in the middle, -thin in the middle, with the tip thick and the root narrow, or -narrow at the tip and wide at the root; with the nostrils wide or -narrow, high or low, and the openings wide or hidden by the point; -and you will find an equal variety in the other details; which -things you must draw from nature and fix them in your mind. Or else, -when you have to draw a face by heart, carry with you a little book -in which you have noted such features; and when you have cast a -glance at the face of the person you wish to draw, you can look, in -private, which nose or mouth is most like, or there make a little -mark to recognise it again at home. Of grotesque faces I need say -nothing, because they are kept in mind without difficulty. - -The position of the head. - -573. - -HOW YOU SHOULD SET TO WORK TO DRAW A HEAD OF WHICH ALL THE PARTS -SHALL AGREE WITH THE POSITION GIVEN TO IT. - -To draw a head in which the features shall agree with the turn and -bend of the head, pursue this method. You know that the eyes, -eyebrows, nostrils, corners of the mouth, and sides of the chin, the -jaws, cheeks, ears and all the parts of a face are squarely and -straightly set upon the face. - -[Footnote: Compare the drawings and the text belonging to them on -Pl. IX. (No. 315), Pl. X (No. 316), Pl. XL (No. 318) and Pl. XII. -(No. 319).] - -Therefore when you have sketched the face draw lines passing from -one corner of the eye to the other; and so for the placing of each -feature; and after having drawn the ends of the lines beyond the two -sides of the face, look if the spaces inside the same parallel lines -on the right and on the left are equal [12]. But be sure to remember -to make these lines tend to the point of sight. - -[Footnote: See Pl. XXXI, No. 4, the slight sketch on the left hand -side. The text of this passage is written by the side of it. In this -sketch the lines seem intentionally incorrect and converging to the -right (compare I. 12) instead of parallel. Compare too with this -text the drawing in red chalk from Windsor Castle which is -reproduced on Pl. XL, No. 2.] - -Of the light on the face (574-576). - -574. - -HOW TO KNOW WHICH SIDE OF AN OBJECT IS TO BE MORE OR LESS LUMINOUS -THAN THE OTHER. - -Let _f_ be the light, the head will be the object illuminated by it -and that side of the head on which the rays fall most directly will -be the most highly lighted, and those parts on which the rays fall -most aslant will be less lighted. The light falls as a blow might, -since a blow which falls perpendicularly falls with the greatest -force, and when it falls obliquely it is less forcible than the -former in proportion to the width of the angle. _Exempli gratia_ if -you throw a ball at a wall of which the extremities are equally far -from you the blow will fall straight, and if you throw the ball at -the wall when standing at one end of it the ball will hit it -obliquely and the blow will not tell. - -[Footnote: See Pl. XXXI. No. 4; the sketch on the right hand side.] - -575. - -THE PROOF AND REASON WHY AMONG THE ILLUMINATED PARTS CERTAIN -PORTIONS ARE IN HIGHER LIGHT THAN OTHERS. - -Since it is proved that every definite light is, or seems to be, -derived from one single point the side illuminated by it will have -its highest light on the portion where the line of radiance falls -perpendicularly; as is shown above in the lines _a g_, and also in -_a h_ and in _l a_; and that portion of the illuminated side will be -least luminous, where the line of incidence strikes it between two -more dissimilar angles, as is seen at _b c d_. And by this means you -may also know which parts are deprived of light as is seen at _m k_. - -Where the angles made by the lines of incidence are most equal there -will be the highest light, and where they are most unequal it will -be darkest. - -I will make further mention of the reason of reflections. - -[Footnote: See Pl. XXXII. The text, here given complete, is on the -right hand side. The small circles above the beginning of lines 5 -and 11 as well as the circle above the text on Pl. XXXI, are in a -paler ink and evidently added by a later hand in order to -distinguish the text as belonging to the _Libro di Pittura_ (see -Prolegomena. No. 12, p. 3). The text on the left hand side of this -page is given as Nos. 577 and 137.] - -576. - -Where the shadow should be on the face. - -General suggestions for historical pictures (577-581). - -577. - -When you compose a historical picture take two points, one the point -of sight, and the other the source of light; and make this as -distant as possible. - -578. - -Historical pictures ought not to be crowded and confused with too -many figures. - -579. - -PRECEPTS IN PAINTING. - -Let you sketches of historical pictures be swift and the working out -of the limbs not be carried too far, but limited to the position of -the limbs, which you can afterwards finish as you please and at your -leisure. - -[Footnote: See Pl. XXXVIII, No. 2. The pen and ink drawing given -there as No. 3 may also be compared with this passage. It is in the -Windsor collection where it is numbered 101.] - -580. - -The sorest misfortune is when your views are in advance of your -work. - -581. - -Of composing historical pictures. Of not considering the limbs in -the figures in historical pictures; as many do who, in the wish to -represent the whole of a figure, spoil their compositions. And when -you place one figure behind another take care to draw the whole of -it so that the limbs which come in front of the nearer figures may -stand out in their natural size and place. - -How to represent the differences of age and sex (582-583). - -582. - -How the ages of man should be depicted: that is, Infancy, Childhood, -Youth, Manhood, Old age, Decrepitude. - -[Footnote: No answer is here given to this question, in the original -MS.] - -583. - -Old men ought to be represented with slow and heavy movements, their -legs bent at the knees, when they stand still, and their feet placed -parallel and apart; bending low with the head leaning forward, and -their arms but little extended. - -Women must be represented in modest attitudes, their legs close -together, their arms closely folded, their heads inclined and -somewhat on one side. - -Old women should be represented with eager, swift and furious -gestures, like infernal furies; but the action should be more -violent in their arms and head than in their legs. - -Little children, with lively and contorted movements when sitting, -and, when standing still, in shy and timid attitudes. - -[Footnote: _bracci raccolte_. Compare Pl. XXXIII. This drawing, in -silver point on yellowish tinted paper, the lights heightened with -white, represents two female hands laid together in a lap. Above is -a third finished study of a right hand, apparently holding a veil -from the head across the bosom. This drawing evidently dates from -before 1500 and was very probably done at Florence, perhaps as a -preparatory study for some picture. The type of hand with its -slender thin forms is more like the style of the _Vierge aux -Rochers_ in the Louvre than any later works--as the Mona Lisa for -instance.] - -Of representing the emotions. - -584. - -THAT A FIGURE IS NOT ADMIRABLE UNLESS IT EXPRESSES BY ITS ACTION THE -PASSION OF ITS SENTIMENT. - -That figure is most admirable which by its actions best expresses -the passion that animates it. - -HOW AN ANGRY MAN IS TO BE FIGURED. - -You must make an angry person holding someone by the hair, wrenching -his head against the ground, and with one knee on his ribs; his -right arm and fist raised on high. His hair must be thrown up, his -brow downcast and knit, his teeth clenched and the two corners of -his mouth grimly set; his neck swelled and bent forward as he leans -over his foe, and full of furrows. - -HOW TO REPRESENT A MAN IN DESPAIR. - -You must show a man in despair with a knife, having already torn -open his garments, and with one hand tearing open the wound. And -make him standing on his feet and his legs somewhat bent and his -whole person leaning towards the earth; his hair flying in disorder. - -Of representing imaginary animals. - -585. - -HOW YOU SHOULD MAKE AN IMAGINARY ANIMAL LOOK NATURAL. - -You know that you cannot invent animals without limbs, each of -which, in itself, must resemble those of some other animal. Hence if -you wish to make an animal, imagined by you, appear natural--let us -say a Dragon, take for its head that of a mastiff or hound, with the -eyes of a cat, the ears of a porcupine, the nose of a greyhound, the -brow of a lion, the temples of an old cock, the neck of a water -tortoise. - -[Footnote: The sketch here inserted of two men on horseback fighting -a dragon is the facsimile of a pen and ink drawing belonging to -BARON EDMOND DE ROTHSCHILD of Paris.] - -The selection of forms. - -586. - -OF THE DELUSIONS WHICH ARISE IN JUDGING OF THE LIMBS. - -A painter who has clumsy hands will paint similar hands in his -works, and the same will occur with any limb, unless long study has -taught him to avoid it. Therefore, O Painter, look carefully what -part is most ill-favoured in your own person and take particular -pains to correct it in your studies. For if you are coarse, your -figures will seem the same and devoid of charm; and it is the same -with any part that may be good or poor in yourself; it will be shown -in some degree in your figures. - -587. - -OF THE SELECTION OF BEAUTIFUL FACES. - -It seems to me to be no small charm in a painter when he gives his -figures a pleasing air, and this grace, if he have it not by nature, -he may acquire by incidental study in this way: Look about you and -take the best parts of many beautiful faces, of which the beauty is -confirmed rather by public fame than by your own judgment; for you -might be mistaken and choose faces which have some resemblance to -your own. For it would seem that such resemblances often please us; -and if you should be ugly, you would select faces that were not -beautiful and you would then make ugly faces, as many painters do. -For often a master's work resembles himself. So select beauties as I -tell you, and fix them in your mind. - -588. - -Of the limbs, which ought to be carefully selected, and of all the -other parts with regard to painting. - -589. - -When selecting figures you should choose slender ones rather than -lean and wooden ones. - -590. - -OF THE MUSCLES OF ANIMALS. - -The hollow spaces interposed between the muscles must not be of such -a character as that the skin should seem to cover two sticks laid -side by side like _c_, nor should they seem like two sticks somewhat -remote from such contact so that the skin hangs in an empty loose -curve as at _f_; but it should be like _i_, laid over the spongy fat -that lies in the angles as the angle _n m o_; which angle is formed -by the contact of the ends of the muscles and as the skin cannot -fold down into such an angle, nature has filled up such angles with -a small quantity of spongy and, as I may say, vesicular fat, with -minute bladders [in it] full of air, which is condensed or rarefied -in them according to the increase or the diminution of the substance -of the muscles; in which latter case the concavity _i_ always has a -larger curve than the muscle. - -591. - -OF UNDULATING MOVEMENTS AND EQUIPOISE IN FIGURES AND OTHER ANIMALS. - -When representing a human figure or some graceful animal, be careful -to avoid a wooden stiffness; that is to say make them move with -equipoise and balance so as not to look like a piece of wood; but -those you want to represent as strong you must not make so, -excepting in the turn of the head. - -How to pose figures. - -592. - -OF GRACE IN THE LIMBS. - -The limbs should be adapted to the body with grace and with -reference to the effect that you wish the figure to produce. And if -you wish to produce a figure that shall of itself look light and -graceful you must make the limbs elegant and extended, and without -too much display of the muscles; and those few that are needed for -your purpose you must indicate softly, that is, not very prominent -and without strong shadows; the limbs, and particularly the arms -easy; that is, none of the limbs should be in a straight line with -the adjoining parts. And if the hips, which are the pole of a man, -are by reason of his position, placed so, that the right is higher -than the left, make the point of the higher shoulder in a -perpendicular line above the highest prominence of the hip, and let -this right shoulder be lower than the left. Let the pit of the -throat always be over the centre of the joint of the foot on which -the man is leaning. The leg which is free should have the knee lower -than the other, and near the other leg. The positions of the head -and arms are endless and I shall therefore not enlarge on any rules -for them. Still, let them be easy and pleasing, with various turns -and twists, and the joints gracefully bent, that they may not look -like pieces of wood. - -Of appropriate gestures (593-600). - -593. - -A picture or representation of human figures, ought to be done in -such a way as that the spectator may easily recognise, by means of -their attitudes, the purpose in their minds. Thus, if you have to -represent a man of noble character in the act of speaking, let his -gestures be such as naturally accompany good words; and, in the same -way, if you wish to depict a man of a brutal nature, give him fierce -movements; as with his arms flung out towards the listener, and his -head and breast thrust forward beyond his feet, as if following the -speaker's hands. Thus it is with a deaf and dumb person who, when he -sees two men in conversation--although he is deprived of -hearing--can nevertheless understand, from the attitudes and -gestures of the speakers, the nature of their discussion. I once saw -in Florence a man who had become deaf who, when you spoke very loud -did not understand you, but if you spoke gently and without making -any sound, understood merely from the movement of the lips. Now -perhaps you will say that the lips of a man who speaks loudly do not -move like those of one speaking softly, and that if they were to -move them alike they would be alike understood. As to this argument, -I leave the decision to experiment; make a man speak to you gently -and note [the motion of] his lips. - -[Footnote: The first ten lines of this text have already been -published, but with a slightly different reading by Dr. M. JORDAN: -_Das Malerbuch Leonardo da Vinci's_ p. 86.] - -594. - -OF REPRESENTING A MAN SPEAKING TO A MULTITUDE. - -When you wish to represent a man speaking to a number of people, -consider the matter of which he has to treat and adapt his action to -the subject. Thus, if he speaks persuasively, let his action be -appropriate to it. If the matter in hand be to set forth an -argument, let the speaker, with the fingers of the right hand hold -one finger of the left hand, having the two smaller ones closed; and -his face alert, and turned towards the people with mouth a little -open, to look as though he spoke; and if he is sitting let him -appear as though about to rise, with his head forward. If you -represent him standing make him leaning slightly forward with body -and head towards the people. These you must represent as silent and -attentive, all looking at the orator's face with gestures of -admiration; and make some old men in astonishment at the things they -hear, with the corners of their mouths pulled down and drawn in, -their cheeks full of furrows, and their eyebrows raised, and -wrinkling the forehead where they meet. Again, some sitting with -their fingers clasped holding their weary knees. Again, some bent -old man, with one knee crossed over the other; on which let him hold -his hand with his other elbow resting in it and the hand supporting -his bearded chin. - -[Footnote: The sketches introduced here are a facsimile of a pen and -ink drawing in the Louvre which Herr CARL BRUN considers as studies -for the Last Supper in the church of _Santa Maria delle Grazie_ (see -Leonardo da Vinci, LXI, pp. 21, 27 and 28 in DOHME'S _Kunst und -Kunstler_, Leipzig, Seemann). I shall not here enter into any -discussion of this suggestion; but as a justification for -introducing the drawing in this place, I may point out that some of -the figures illustrate this passage as perfectly as though they had -been drawn for that express purpose. I have discussed the -probability of a connection between this sketch and the picture of -the Last Supper on p. 335. The original drawing is 27 3/4 -centimetres wide by 21 high.--The drawing in silver point on reddish -paper given on Pl. LII. No. 1--the original at Windsor Castle--may -also serve to illustrate the subject of appropriate gestures, -treated in Nos. 593 and 594.] - -595. - -OF THE DISPOSITION OF LIMBS. - -As regards the disposition of limbs in movement you will have to -consider that when you wish to represent a man who, by some chance, -has to turn backwards or to one side, you must not make him move his -feet and all his limbs towards the side to which he turns his head. -Rather must you make the action proceed by degrees and through the -different joints; that is, those of the foot, the knee and the hip -and the neck. And if you set him on the right leg, you must make the -left knee bend inwards, and let his foot be slightly raised on the -outside, and the left shoulder be somewhat lower than the right, -while the nape of the neck is in a line directly over the outer -ancle of the left foot. And the left shoulder will be in a -perpendicular line above the toes of the right foot. And always set -your figures so that the side to which the head turns is not the -side to which the breast faces, since nature for our convenience has -made us with a neck which bends with ease in many directions, the -eye wishing to turn to various points, the different joints. And if -at any time you make a man sitting with his arms at work on -something which is sideways to him, make the upper part of his body -turn upon the hips. - -[Footnote: Compare Pl. VII, No. 5. The original drawing at Windsor -Castle is numbered 104.] - -596. - -When you draw the nude always sketch the whole figure and then -finish those limbs which seem to you the best, but make them act -with the other limbs; otherwise you will get a habit of never -putting the limbs well together on the body. - -Never make the head turn the same way as the torso, nor the arm and -leg move together on the same side. And if the face is turned to the -right shoulder, make all the parts lower on the left side than on -the right; and when you turn the body with the breast outwards, if -the head turns to the left side make the parts on the right side -higher than those on the left. - -[Footnote: In the original MS. a much defaced sketch is to be seen -by the side of the second part of this chapter; its faded condition -has rendered reproduction impossible. In M. RAVAISSON'S facsimile -the outlines of the head have probably been touched up. This passage -however is fitly illustrated by the drawings on Pl. XXI.] - -597. - -OF PAINTING. - -Of the nature of movements in man. Do not repeat the same gestures -in the limbs of men unless you are compelled by the necessity of -their action, as is shown in _a b_. - -[Footnote: See Pl. V, where part of the text is also reproduced. The -effaced figure to the extreme left has evidently been cancelled by -Leonardo himself as unsatisfactory.] - -598. - -The motions of men must be such as suggest their dignity or their -baseness. - -599. - -OF PAINTING. - -Make your work carry out your purpose and meaning. That is when you -draw a figure consider well who it is and what you wish it to be -doing. - -OF PAINTING. - -With regard to any action which you give in a picture to an old man -or to a young one, you must make it more energetic in the young man -in proportion as he is stronger than the old one; and in the same -way with a young man and an infant. - -600. - -OF SETTING ON THE LIMBS. - -The limbs which are used for labour must be muscular and those which -are not much used you must make without muscles and softly rounded. - -OF THE ACTION OF THE FIGURES. - -Represent your figures in such action as may be fitted to express -what purpose is in the mind of each; otherwise your art will not be -admirable. - -V. - -SUGGESTIONS FOR COMPOSITIONS. - -Of painting battle pieces (601-603). - -601. - -OF THE WAY OF REPRESENTING A BATTLE. - -First you must represent the smoke of artillery mingling in the air -with the dust and tossed up by the movement of horses and the -combatants. And this mixture you must express thus: The dust, being -a thing of earth, has weight; and although from its fineness it is -easily tossed up and mingles with the air, it nevertheless readily -falls again. It is the finest part that rises highest; hence that -part will be least seen and will look almost of the same colour as -the air. The higher the smoke mixed with the dust-laden air rises -towards a certain level, the more it will look like a dark cloud; -and it will be seen that at the top, where the smoke is more -separate from the dust, the smoke will assume a bluish tinge and the -dust will tend to its colour. This mixture of air, smoke and dust -will look much lighter on the side whence the light comes than on -the opposite side. The more the combatants are in this turmoil the -less will they be seen, and the less contrast will there be in their -lights and shadows. Their faces and figures and their appearance, -and the musketeers as well as those near them you must make of a -glowing red. And this glow will diminish in proportion as it is -remote from its cause. - -The figures which are between you and the light, if they be at a -distance, will appear dark on a light background, and the lower part -of their legs near the ground will be least visible, because there -the dust is coarsest and densest [19]. And if you introduce horses -galloping outside the crowd, make the little clouds of dust distant -from each other in proportion to the strides made by the horses; and -the clouds which are furthest removed from the horses, should be -least visible; make them high and spreading and thin, and the nearer -ones will be more conspicuous and smaller and denser [23]. The air -must be full of arrows in every direction, some shooting upwards, -some falling, some flying level. The balls from the guns must have a -train of smoke following their flight. The figures in the foreground -you must make with dust on the hair and eyebrows and on other flat -places likely to retain it. The conquerors you will make rushing -onwards with their hair and other light things flying on the wind, -with their brows bent down, - -[Footnote: 19--23. Compare 608. 57--75.] - -602. - -and with the opposite limbs thrust forward; that is where a man puts -forward the right foot the left arm must be advanced. And if you -make any one fallen, you must show the place where he has slipped -and been dragged along the dust into blood stained mire; and in the -half-liquid earth arround show the print of the tramping of men and -horses who have passed that way. Make also a horse dragging the dead -body of his master, and leaving behind him, in the dust and mud, the -track where the body was dragged along. You must make the conquered -and beaten pale, their brows raised and knit, and the skin above -their brows furrowed with pain, the sides of the nose with wrinkles -going in an arch from the nostrils to the eyes, and make the -nostrils drawn up--which is the cause of the lines of which I -speak--, and the lips arched upwards and discovering the upper -teeth; and the teeth apart as with crying out and lamentation. And -make some one shielding his terrified eyes with one hand, the palm -towards the enemy, while the other rests on the ground to support -his half raised body. Others represent shouting with their mouths -open, and running away. You must scatter arms of all sorts among the -feet of the combatants, as broken shields, lances, broken swords and -other such objects. And you must make the dead partly or entirely -covered with dust, which is changed into crimson mire where it has -mingled with the flowing blood whose colour shows it issuing in a -sinuous stream from the corpse. Others must be represented in the -agonies of death grinding their teeth, rolling their eyes, with -their fists clenched against their bodies and their legs contorted. -Some might be shown disarmed and beaten down by the enemy, turning -upon the foe, with teeth and nails, to take an inhuman and bitter -revenge. You might see some riderless horse rushing among the enemy, -with his mane flying in the wind, and doing no little mischief with -his heels. Some maimed warrior may be seen fallen to the earth, -covering himself with his shield, while the enemy, bending over him, -tries to deal him a deathstroke. There again might be seen a number -of men fallen in a heap over a dead horse. You would see some of the -victors leaving the fight and issuing from the crowd, rubbing their -eyes and cheeks with both hands to clean them of the dirt made by -their watering eyes smarting from the dust and smoke. The reserves -may be seen standing, hopeful but cautious; with watchful eyes, -shading them with their hands and gazing through the dense and murky -confusion, attentive to the commands of their captain. The captain -himself, his staff raised, hurries towards these auxiliaries, -pointing to the spot where they are most needed. And there may be a -river into which horses are galloping, churning up the water all -round them into turbulent waves of foam and water, tossed into the -air and among the legs and bodies of the horses. And there must not -be a level spot that is not trampled with gore. - -603. - -OF LIGHTING THE LOWER PARTS OF BODIES CLOSE TOGETHER, AS OF MEN IN -BATTLE. - -As to men and horses represented in battle, their different parts -will be dark in proportion as they are nearer to the ground on which -they stand. And this is proved by the sides of wells which grow -darker in proportion to their depth, the reason of which is that the -deepest part of the well sees and receives a smaller amount of the -luminous atmosphere than any other part. - -And the pavement, if it be of the same colour as the legs of these -said men and horses, will always be more lighted and at a more -direct angle than the said legs &c. - -604. - -OF THE WAY TO REPRESENT A NIGHT [SCENE]. - -That which is entirely bereft of light is all darkness; given a -night under these conditions and that you want to represent a night -scene,--arrange that there shall be a great fire, then the objects -which are nearest to this fire will be most tinged with its colour; -for those objects which are nearest to a coloured light participate -most in its nature; as therefore you give the fire a red colour, you -must make all the objects illuminated by it ruddy; while those which -are farther from the fire are more tinted by the black hue of night. -The figures which are seen against the fire look dark in the glare -of the firelight because that side of the objects which you see is -tinged by the darkness of the night and not by the fire; and those -who stand at the side are half dark and half red; while those who -are visible beyond the edges of the flame will be fully lighted by -the ruddy glow against a black background. As to their gestures, -make those which are near it screen themselves with their hands and -cloaks as a defence against the intense heat, and with their faces -turned away as if about to retire. Of those farther off represent -several as raising their hands to screen their eyes, hurt by the -intolerable glare. - -Of depicting a tempest (605. 606). - -605. - -Describe a wind on land and at sea. Describe a storm of rain. - -606. - -HOW TO REPRESENT A TEMPEST. - -If you wish to represent a tempest consider and arrange well its -effects as seen, when the wind, blowing over the face of the sea and -earth, removes and carries with it such things as are not fixed to -the general mass. And to represent the storm accurately you must -first show the clouds scattered and torn, and flying with the wind, -accompanied by clouds of sand blown up from the sea shore, and -boughs and leaves swept along by the strength and fury of the blast -and scattered with other light objects through the air. Trees and -plants must be bent to the ground, almost as if they would follow -the course of the gale, with their branches twisted out of their -natural growth and their leaves tossed and turned about [Footnote -11: See Pl. XL, No. 2.]. Of the men who are there some must have -fallen to the ground and be entangled in their garments, and hardly -to be recognized for the dust, while those who remain standing may -be behind some tree, with their arms round it that the wind may not -tear them away; others with their hands over their eyes for the -dust, bending to the ground with their clothes and hair streaming in -the wind. [Footnote 15: See Pl. XXXIV, the right hand lower sketch.] -Let the sea be rough and tempestuous and full of foam whirled among -the lofty waves, while the wind flings the lighter spray through the -stormy air, till it resembles a dense and swathing mist. Of the -ships that are therein some should be shown with rent sails and the -tatters fluttering through the air, with ropes broken and masts -split and fallen. And the ship itself lying in the trough of the sea -and wrecked by the fury of the waves with the men shrieking and -clinging to the fragments of the vessel. Make the clouds driven by -the impetuosity of the wind and flung against the lofty mountain -tops, and wreathed and torn like waves beating upon rocks; the air -itself terrible from the deep darkness caused by the dust and fog -and heavy clouds. - -Of representing the deluge (607-609). - -607. - -TO REPRESENT THE DELUGE. - -The air was darkened by the heavy rain whose oblique descent driven -aslant by the rush of the winds, flew in drifts through the air not -otherwise than as we see dust, varied only by the straight lines of -the heavy drops of falling water. But it was tinged with the colour -of the fire kindled by the thunder-bolts by which the clouds were -rent and shattered; and whose flashes revealed the broad waters of -the inundated valleys, above which was seen the verdure of the -bending tree tops. Neptune will be seen in the midst of the water -with his trident, and [15] let AEolus with his winds be shown -entangling the trees floating uprooted, and whirling in the huge -waves. The horizon and the whole hemisphere were obscure, but lurid -from the flashes of the incessant lightning. Men and birds might be -seen crowded on the tall trees which remained uncovered by the -swelling waters, originators of the mountains which surround the -great abysses [Footnote 23: Compare Vol. II. No. 979.]. - -608. - -OF THE DELUGE AND HOW TO REPRESENT IT IN A PICTURE. - -Let the dark and gloomy air be seen buffeted by the rush of contrary -winds and dense from the continued rain mingled with hail and -bearing hither and thither an infinite number of branches torn from -the trees and mixed with numberless leaves. All round may be seen -venerable trees, uprooted and stripped by the fury of the winds; and -fragments of mountains, already scoured bare by the torrents, -falling into those torrents and choking their valleys till the -swollen rivers overflow and submerge the wide lowlands and their -inhabitants. Again, you might have seen on many of the hill-tops -terrified animals of different kinds, collected together and subdued -to tameness, in company with men and women who had fled there with -their children. The waters which covered the fields, with their -waves were in great part strewn with tables, bedsteads, boats and -various other contrivances made from necessity and the fear of -death, on which were men and women with their children amid sounds -of lamentation and weeping, terrified by the fury of the winds which -with their tempestuous violence rolled the waters under and over and -about the bodies of the drowned. Nor was there any object lighter -than the water which was not covered with a variety of animals -which, having come to a truce, stood together in a frightened -crowd--among them wolves, foxes, snakes and others--fleing from -death. And all the waters dashing on their shores seemed to be -battling them with the blows of drowned bodies, blows which killed -those in whom any life remained [19]. You might have seen -assemblages of men who, with weapons in their hands, defended the -small spots that remained to them against lions, wolves and beasts -of prey who sought safety there. Ah! what dreadful noises were heard -in the air rent by the fury of the thunder and the lightnings it -flashed forth, which darted from the clouds dealing ruin and -striking all that opposed its course. Ah! how many you might have -seen closing their ears with their hands to shut out the tremendous -sounds made in the darkened air by the raging of the winds mingling -with the rain, the thunders of heaven and the fury of the -thunder-bolts. Others were not content with shutting their eyes, but -laid their hands one over the other to cover them the closer that -they might not see the cruel slaughter of the human race by the -wrath of God. Ah! how many laments! and how many in their terror -flung themselves from the rocks! Huge branches of great oaks loaded -with men were seen borne through the air by the impetuous fury of -the winds. How many were the boats upset, some entire, and some -broken in pieces, on the top of people labouring to escape with -gestures and actions of grief foretelling a fearful death. Others, -with desperate act, took their own lives, hopeless of being able to -endure such suffering; and of these, some flung themselves from -lofty rocks, others strangled themselves with their own hands, other -seized their own children and violently slew them at a blow; some -wounded and killed themselves with their own weapons; others, -falling on their knees recommended themselves to God. Ah! how many -mothers wept over their drowned sons, holding them upon their knees, -with arms raised spread out towards heaven and with words and -various threatening gestures, upbraiding the wrath of the gods. -Others with clasped hands and fingers clenched gnawed them and -devoured them till they bled, crouching with their breast down on -their knees in their intense and unbearable anguish. Herds of -animals were to be seen, such as horses, oxen, goats and swine -already environed by the waters and left isolated on the high peaks -of the mountains, huddled together, those in the middle climbing to -the top and treading on the others, and fighting fiercely -themselves; and many would die for lack of food. Already had the -birds begun to settle on men and on other animals, finding no land -uncovered which was not occupied by living beings, and already had -famine, the minister of death, taken the lives of the greater number -of the animals, when the dead bodies, now fermented, where leaving -the depth of the waters and were rising to the top. Among the -buffeting waves, where they were beating one against the other, and, -like as balls full of air, rebounded from the point of concussion, -these found a resting place on the bodies of the dead. And above -these judgements, the air was seen covered with dark clouds, riven -by the forked flashes of the raging bolts of heaven, lighting up on -all sides the depth of the gloom. - -The motion of the air is seen by the motion of the dust thrown up by -the horse's running and this motion is as swift in again filling up -the vacuum left in the air which enclosed the horse, as he is rapid -in passing away from the air. - -Perhaps it will seem to you that you may reproach me with having -represented the currents made through the air by the motion of the -wind notwithstanding that the wind itself is not visible in the air. -To this I must answer that it is not the motion of the wind but only -the motion of the things carried along by it which is seen in the -air. - -THE DIVISIONS. [Footnote 76: These observations, added at the bottom -of the page containing the full description of the doluge seem to -indicate that it was Leonardo's intention to elaborate the subject -still farther in a separate treatise.] - -Darkness, wind, tempest at sea, floods of water, forests on fire, -rain, bolts from heaven, earthquakes and ruins of mountains, -overthrow of cities [Footnote 81: _Spianamenti di citta_ (overthrow -of cities). A considerable number of drawings in black chalk, at -Windsor, illustrate this catastrophe. Most of them are much rubbed; -one of the least injured is reproduced at Pl. XXXIX. Compare also -the pen and ink sketch Pl. XXXVI.]. - -Whirlwinds which carry water [spouts] branches of trees, and men -through the air. - -Boughs stripped off by the winds, mingling by the meeting of the -winds, with people upon them. - -Broken trees loaded with people. - -Ships broken to pieces, beaten on rocks. - -Flocks of sheep. Hail stones, thunderbolts, whirlwinds. - -People on trees which are unable to to support them; trees and -rocks, towers and hills covered with people, boats, tables, troughs, -and other means of floating. Hills covered with men, women and -animals; and lightning from the clouds illuminating every thing. - -[Footnote: This chapter, which, with the next one, is written on a -loose sheet, seems to be the passage to which one of the compilers -of the Vatican copy alluded when he wrote on the margin of fol. 36: -"_Qua mi ricordo della mirabile discritione del Diluuio dello -autore._" It is scarcely necessary to point out that these chapters -are among those which have never before been published. The -description in No. 607 may be regarded as a preliminary sketch for -this one. As the MS. G. (in which it is to be found) must be -attributed to the period of about 1515 we may deduce from it the -approximate date of the drawings on Pl. XXXIV, XXXV, Nos. 2 and 3, -XXXVI and XXXVII, since they obviously belong to this text. The -drawings No. 2 on Pl. XXXV are, in the original, side by side with -the text of No. 608; lines 57 to 76 are shown in the facsimile. In -the drawing in Indian ink given on Pl. XXXIV we see Wind-gods in the -sky, corresponding to the allusion to Aeolus in No. 607 1. -15.-Plates XXXVI and XXXVII form one sheet in the original. The -texts reproduced on these Plates have however no connection with the -sketches, excepting the sketches of clouds on the right hand side. -These texts are given as No. 477. The group of small figures on Pl. -XXXVII, to the left, seems to be intended for a '_congregatione -d'uomini._' See No. 608, 1. 19.] - -609. - -DESCRIPTION OF THE DELUGE. - -Let there be first represented the summit of a rugged mountain with -valleys surrounding its base, and on its sides let the surface of -the soil be seen to slide, together with the small roots of the -bushes, denuding great portions of the surrounding rocks. And -descending ruinous from these precipices in its boisterous course, -let it dash along and lay bare the twisted and gnarled roots of -large trees overthrowing their roots upwards; and let the mountains, -as they are scoured bare, discover the profound fissures made in -them by ancient earthquakes. The base of the mountains may be in -great part clothed and covered with ruins of shrubs, hurled down -from the sides of their lofty peaks, which will be mixed with mud, -roots, boughs of trees, with all sorts of leaves thrust in with the -mud and earth and stones. And into the depth of some valley may have -fallen the fragments of a mountain forming a shore to the swollen -waters of its river; which, having already burst its banks, will -rush on in monstrous waves; and the greatest will strike upon and -destroy the walls of the cities and farmhouses in the valley [14]. -Then the ruins of the high buildings in these cities will throw up a -great dust, rising up in shape like smoke or wreathed clouds against -the falling rain; But the swollen waters will sweep round the pool -which contains them striking in eddying whirlpools against the -different obstacles, and leaping into the air in muddy foam; then, -falling back, the beaten water will again be dashed into the air. -And the whirling waves which fly from the place of concussion, and -whose impetus moves them across other eddies going in a contrary -direction, after their recoil will be tossed up into the air but -without dashing off from the surface. Where the water issues from -the pool the spent waves will be seen spreading out towards the -outlet; and there falling or pouring through the air and gaining -weight and impetus they will strike on the water below piercing it -and rushing furiously to reach its depth; from which being thrown -back it returns to the surface of the lake, carrying up the air that -was submerged with it; and this remains at the outlet in foam -mingled with logs of wood and other matters lighter than water. -Round these again are formed the beginnings of waves which increase -the more in circumference as they acquire more movement; and this -movement rises less high in proportion as they acquire a broader -base and thus they are less conspicuous as they die away. But if -these waves rebound from various objects they then return in direct -opposition to the others following them, observing the same law of -increase in their curve as they have already acquired in the -movement they started with. The rain, as it falls from the clouds is -of the same colour as those clouds, that is in its shaded side; -unless indeed the sun's rays should break through them; in that case -the rain will appear less dark than the clouds. And if the heavy -masses of ruin of large mountains or of other grand buildings fall -into the vast pools of water, a great quantity will be flung into -the air and its movement will be in a contrary direction to that of -the object which struck the water; that is to say: The angle of -reflection will be equal to the angle of incidence. Of the objects -carried down by the current, those which are heaviest or rather -largest in mass will keep farthest from the two opposite shores. The -water in the eddies revolves more swiftly in proportion as it is -nearer to their centre. The crests of the waves of the sea tumble to -their bases falling with friction on the bubbles of their sides; and -this friction grinds the falling water into minute particles and -this being converted into a dense mist, mingles with the gale in the -manner of curling smoke and wreathing clouds, and at last it, rises -into the air and is converted into clouds. But the rain which falls -through the atmosphere being driven and tossed by the winds becomes -rarer or denser according to the rarity or density of the winds that -buffet it, and thus there is generated in the atmosphere a moisture -formed of the transparent particles of the rain which is near to the -eye of the spectator. The waves of the sea which break on the slope -of the mountains which bound it, will foam from the velocity with -which they fall against these hills; in rushing back they will meet -the next wave as it comes and and after a loud noise return in a -great flood to the sea whence they came. Let great numbers of -inhabitants--men and animals of all kinds--be seen driven [54] by -the rising of the deluge to the peaks of the mountains in the midst -of the waters aforesaid. - -The wave of the sea at Piombino is all foaming water. [Footnote 55. -56: These two lines are written below the bottom sketch on Pl. XXXV, -3. The MS. Leic. being written about the year 1510 or later, it does -not seem to me to follow that the sketches must have been made at -Piombino, where Leonardo was in the year 1502 and possibly returned -there subsequently (see Vol. II. Topographical notes).] - -Of the water which leaps up from the spot where great masses fall on -its surface. Of the winds of Piombino at Piombino. Eddies of wind -and rain with boughs and shrubs mixed in the air. Emptying the boats -of the rain water. - -[Footnote: The sketches on Pl. XXXV 3 stand by the side of lines 14 -to 54.] - -Of depicting natural phenomena (610. 611). - -610. - -The tremendous fury of the wind driven by the falling in of the -hills on the caves within--by the falling of the hills which served -as roofs to these caverns. - -A stone flung through the air leaves on the eye which sees it the -impression of its motion, and the same effect is produced by the -drops of water which fall from the clouds when it [16] rains. - -[17] A mountain falling on a town, will fling up dust in the form of -clouds; but the colour of this dust will differ from that of the -clouds. Where the rain is thickest let the colour of the dust be -less conspicuous and where the dust is thickest let the rain be less -conspicuous. And where the rain is mingled with the wind and with -the dust the clouds created by the rain must be more transparent -than those of dust [alone]. And when flames of fire are mingled with -clouds of smoke and water very opaque and dark clouds will be formed -[Footnote 26-28: Compare Pl. XL, 1--the drawing in Indian ink on the -left hand side, which seems to be a reminiscence of his observations -of an eruption (see his remarks on Mount Etna in Vol II).]. And the -rest of this subject will be treated in detail in the book on -painting. - -[Footnote: See the sketches and text on Pl. XXXVIII, No. 1. Lines -1-16 are there given on the left hand side, 17-30 on the right. The -four lines at the bottom on the right are given as No. 472. Above -these texts, which are written backwards, there are in the original -sixteen lines in a larger writing from left to right, but only half -of this is here visible. They treat of the physical laws of motion -of air and water. It does not seem to me that there is any reason -for concluding that this writing from left to right is spurious. -Compare with it the facsimile of the rough copy of Leonardo's letter -to Ludovico il Moro in Vol. II.] - -611. - -People were to be seen eagerly embarking victuals on various kinds -of hastily made barks. But little of the waves were visible in those -places where the dark clouds and rain were reflected. - -But where the flashes caused by the bolts of heaven were reflected, -there were seen as many bright spots, caused by the image of the -flashes, as there were waves to reflect them to the eye of the -spectator. - -The number of the images produced by the flash of lightning on the -waves of the water were multiplied in proportion to the distance of -the spectator's eye. - -So also the number of the images was diminished in proportion as -they were nearer the eye which saw them [Footnote 22. 23: _Com'e -provato_. See Vol. II, Nos. 874-878 and 892-901], as it has been -proved in the definition of the luminosity of the moon, and of our -marine horizon when the sun's rays are reflected in it and the eye -which receives the reflection is remote from the sea. - -VI. - -THE ARTIST'S MATERIALS. - -Of chalk and paper (612--617). - -612. - -To make points [crayons] for colouring dry. Temper with a little wax -and do not dry it; which wax you must dissolve with water: so that -when the white lead is thus tempered, the water being distilled, may -go off in vapour and the wax may remain; you will thus make good -crayons; but you must know that the colours must be ground with a -hot stone. - -613. - -Chalk dissolves in wine and in vinegar or in aqua fortis and can be -recombined with gum. - -614. - -PAPER FOR DRAWING UPON IN BLACK BY THE AID OF YOUR SPITTLE. - -Take powdered gall nuts and vitriol, powder them and spread them on -paper like a varnish, then write on it with a pen wetted with -spittle and it will turn as black as ink. - -615. - -If you want to make foreshortened letters stretch the paper in a -drawing frame and then draw your letters and cut them out, and make -the sunbeams pass through the holes on to another stretched paper, -and then fill up the angles that are wanting. - -616. - -This paper should be painted over with candle soot tempered with -thin glue, then smear the leaf thinly with white lead in oil as is -done to the letters in printing, and then print in the ordinary way. -Thus the leaf will appear shaded in the hollows and lighted on the -parts in relief; which however comes out here just the contrary. - -[Footnote: This text, which accompanies a facsimile impression of a -leaf of sage, has already been published in the _Saggio delle Opere -di L. da Vinci_, Milano 1872, p. 11. G. GOVI observes on this -passage: "_Forse aveva egli pensato ancora a farsi un erbario, od -almeno a riprodurre facilmente su carta le forme e i particolari -delle foglie di diverse piante; poiche (modificando un metodo che -probabilmente gli eia stato insegnato da altri, e che piu tardi si -legge ripetuto in molti ricettarii e libri di segreti), accanto a -una foglia di Salvia impressa in nero su carta bianca, lascio -scritto: Questa carta ... - -Erano i primi tentativi di quella riproduzione immediata delle parti -vegetali, che poi sotto il nome d'Impressione Naturale, fu condotta -a tanta perfezione in questi ultimi tempi dal signor de Hauer e da -altri_."] - -617. - -Very excellent will be a stiff white paper, made of the usual -mixture and filtered milk of an herb called calves foot; and when -this paper is prepared and damped and folded and wrapped up it may -be mixed with the mixture and thus left to dry; but if you break it -before it is moistened it becomes somewhat like the thin paste -called _lasagne_ and you may then damp it and wrap it up and put it -in the mixture and leave it to dry; or again this paper may be -covered with stiff transparent white and _sardonio_ and then damped -so that it may not form angles and then covered up with strong -transparent size and as soon as it is firm cut it two fingers, and -leave it to dry; again you may make stiff cardboard of _sardonio_ -and dry it and then place it between two sheets of papyrus and break -it inside with a wooden mallet with a handle and then open it with -care holding the lower sheet of paper flat and firm so that the -broken pieces be not separated; then have a sheet of paper covered -with hot glue and apply it on the top of all these pieces and let -them stick fast; then turn it upside down and apply transparent size -several times in the spaces between the pieces, each time pouring in -first some black and then some stiff white and each time leaving it -to dry; then smooth it and polish it. - -On the preparation and use of colours (618-627). - -618. - -To make a fine green take green and mix it with bitumen and you will -make the shadows darker. Then, for lighter [shades] green with -yellow ochre, and for still lighter green with yellow, and for the -high lights pure yellow; then mix green and turmeric together and -glaze every thing with it. To make a fine red take cinnabar or red -chalk or burnt ochre for the dark shadows and for the lighter ones -red chalk and vermilion and for the lights pure vermilion and then -glaze with fine lake. To make good oil for painting. One part of -oil, one of the first refining and one of the second. - -619. - -Use black in the shadow, and in the lights white, yellow, green, -vermilion and lake. Medium shadows; take the shadow as above and mix -it with the flesh tints just alluded to, adding to it a little -yellow and a little green and occasionally some lake; for the -shadows take green and lake for the middle shades. - -[Footnote 618 and 619: If we may judge from the flourishes with -which the writing is ornamented these passages must have been -written in Leonardo's youth.] - -620. - -You can make a fine ochre by the same method as you use to make -white. - -621. - -A FINE YELLOW. - -Dissolve realgar with one part of orpiment, with aqua fortis. - -WHITE. - -Put the white into an earthen pot, and lay it no thicker than a -string, and let it stand in the sun undisturbed for 2 days; and in -the morning when the sun has dried off the night dews. - -622. - -To make reddish black for flesh tints take red rock crystals from -Rocca Nova or garnets and mix them a little; again armenian bole is -good in part. - -623. - -The shadow will be burnt ,terra-verte'. - -624. - -THE PROPORTIONS OF COLOURS. - -If one ounce of black mixed with one ounce of white gives a certain -shade of darkness, what shade of darkness will be produced by 2 -ounces of black to 1 ounce of white? - -625. - -Remix black, greenish yellow and at the end blue. - -626. - -Verdigris with aloes, or gall or turmeric makes a fine green and so -it does with saffron or burnt orpiment; but I doubt whether in a -short time they will not turn black. Ultramarine blue and glass -yellow mixed together make a beautiful green for fresco, that is -wall-painting. Lac and verdigris make a good shadow for blue in oil -painting. - -627. - -Grind verdigris many times coloured with lemon juice and keep it -away from yellow (?). - -Of preparing the panel. - -628. - -TO PREPARE A PANEL FOR PAINTING ON. - -The panel should be cypress or pear or service-tree or walnut. You -must coat it over with mastic and turpentine twice distilled and -white or, if you like, lime, and put it in a frame so that it may -expand and shrink according to its moisture and dryness. Then give -it [a coat] of aqua vitae in which you have dissolved arsenic or -[corrosive] sublimate, 2 or 3 times. Then apply boiled linseed oil -in such a way as that it may penetrate every part, and before it is -cold rub it well with a cloth to dry it. Over this apply liquid -varnish and white with a stick, then wash it with urine when it is -dry, and dry it again. Then pounce and outline your drawing finely -and over it lay a priming of 30 parts of verdigris with one of -verdigris with two of yellow. - -[Footnote: M. RAVAISSON'S reading varies from mine in the following -passages: - -1._opero allor [?] bo [alloro?]_ = "_ou bien de [laurier]_." - -6. _fregalo bene con un panno_. He reads _pane_ for _panno_ and -renders it. "_Frotte le bien avec un pain de facon [jusqu'a ce] -qu'il_" etc. - -7. _colla stecca po laua_. He reads "_polacca_" = "_avec le couteau -de bois [?] polonais [?]_."] - -The preparation of oils (629--634). - -629. - -OIL. - -Make some oil of mustard seed; and if you wish to make it with -greater ease mix the ground seeds with linseed oil and put it all -under the press. - -630. - -TO REMOVE THE SMELL OF OIL. - -Take the rank oil and put ten pints into a jar and make a mark on -the jar at the height of the oil; then add to it a pint of vinegar -and make it boil till the oil has sunk to the level of the mark and -thus you will be certain that the oil is returned to its original -quantity and the vinegar will have gone off in vapour, carrying with -it the evil smell; and I believe you may do the same with nut oil or -any other oil that smells badly. - -631. - -Since walnuts are enveloped in a thin rind, which partakes of the -nature of ..., if you do not remove it when you make the oil from -them, this skin tinges the oil, and when you work with it this skin -separates from the oil and rises to the surface of the painting, and -this is what makes it change. - -632. - -TO RESTORE OIL COLOURS THAT HAVE BECOME DRY. - -If you want to restore oil colours that have become dry keep them -soaking in soft soap for a night and, with your finger, mix them up -with the soft soap; then pour them into a cup and wash them with -water, and in this way you can restore colours that have got dry. -But take care that each colour has its own vessel to itself adding -the colour by degrees as you restore it and mind that they are -thoroughly softened, and when you wish to use them for tempera wash -them five and six times with spring water, and leave them to settle; -if the soft soap should be thick with any of the colours pass it -through a filter. [Footnote: The same remark applies to these -sections as to No. 618 and 619.] - -633. - -OIL. - -Mustard seed pounded with linseed oil. - -634. - -... outside the bowl 2 fingers lower than the level of the oil, and -pass it into the neck of a bottle and let it stand and thus all the -oil will separate from this milky liquid; it will enter the bottle -and be as clear as crystal; and grind your colours with this, and -every coarse or viscid part will remain in the liquid. You must know -that all the oils that have been created in seads or fruits are -quite clear by nature, and the yellow colour you see in them only -comes of your not knowing how to draw it out. Fire or heat by its -nature has the power to make them acquire colour. See for example -the exudation or gums of trees which partake of the nature of rosin; -in a short time they harden because there is more heat in them than -in oil; and after some time they acquire a certain yellow hue -tending to black. But oil, not having so much heat does not do so; -although it hardens to some extent into sediment it becomes finer. -The change in oil which occurs in painting proceeds from a certain -fungus of the nature of a husk which exists in the skin which covers -the nut, and this being crushed along with the nuts and being of a -nature much resembling oil mixes with it; it is of so subtle a -nature that it combines with all colours and then comes to the -surface, and this it is which makes them change. And if you want the -oil to be good and not to thicken, put into it a little camphor -melted over a slow fire and mix it well with the oil and it will -never harden. - -[Footnote: The same remark applies to these sections as to No. 618 -and 619.] - -On varnishes [or powders] (635-637). - -635. - -VARNISH [OR POWDER]. - -Take cypress [oil] and distil it and have a large pitcher, and put -in the extract with so much water as may make it appear like amber, -and cover it tightly so that none may evaporate. And when it is -dissolved you may add in your pitcher as much of the said solution, -as shall make it liquid to your taste. And you must know that amber -is the gum of the cypress-tree. - -VARNISH [OR POWDER]. - -And since varnish [powder] is the resin of juniper, if you distil -juniper you can dissolve the said varnish [powder] in the essence, -as explained above. - -636. - -VARNISH [OR POWDER]. - -Notch a juniper tree and give it water at the roots, mix the liquor -which exudes with nut-oil and you will have a perfect varnish -[powder], made like amber varnish [powder], fine and of the best -quality make it in May or April. - -637. - -VARNISH [OR POWDER]. - -Mercury with Jupiter and Venus,--a paste made of these must be -corrected by the mould (?) continuously, until Mercury separates -itself entirely from Jupiter and Venus. [Footnote: Here, and in No. -641 _Mercurio_ seems to mean quicksilver, _Giove_ stands for iron, -_Venere_ for copper and _Saturno_ for lead.] - -On chemical materials (638-650). - -638. - -Note how aqua vitae absorbs into itself all the colours and smells -of flowers. If you want to make blue put iris flowers into it and -for red solanum berries (?) - -639. - -Salt may be made from human excrement burnt and calcined and made -into lees, and dried by a slow fire, and all dung in like manner -yields salt, and these salts when distilled are very pungent. - -640. - -Sea water filtered through mud or clay, leaves all its saltness in -it. Woollen stuffs placed on board ship absorb fresh water. If sea -water is distilled under a retort it becomes of the first excellence -and any one who has a little stove in his kitchen can, with the same -wood as he cooks with, distil a great quantity of water if the -retort is a large one. - -641. - -MOULD(?). - -The mould (?) may be of Venus, or of Jupiter and Saturn and placed -frequently in the fire. And it should be worked with fine emery and -the mould (?) should be of Venus and Jupiter impasted over (?) -Venus. But first you will test Venus and Mercury mixed with Jove, -and take means to cause Mercury to disperse; and then fold them well -together so that Venus or Jupiter be connected as thinly as -possible. - -[Footnote: See the note to 637.] - -642. - -Nitre, vitriol, cinnabar, alum, salt ammoniac, sublimated mercury, -rock salt, alcali salt, common salt, rock alum, alum schist (?), -arsenic, sublimate, realgar, tartar, orpiment, verdegris. - -643. - -Pitch four ounces virgin wax, four ounces incense, two ounces oil of -roses one ounce. - -644. - -Four ounces virgin wax, four ounces Greek pitch, two ounces incense, -one ounce oil of roses, first melt the wax and oil then the Greek -pitch then the other things in powder. - -645. - -Very thin glass may be cut with scissors and when placed over inlaid -work of bone, gilt, or stained of other colours you can saw it -through together with the bone and then put it together and it will -retain a lustre that will not be scratched nor worn away by rubbing -with the hand. - -646. - -TO DILUTE WHITE WINE AND MAKE IT PURPLE. - -Powder gall nuts and let this stand 8 days in the white wine; and in -the same way dissolve vitriol in water, and let the water stand and -settle very clear, and the wine likewise, each by itself, and strain -them well; and when you dilute the white wine with the water the -wine will become red. - -647. - -Put marcasite into aqua fortis and if it turns green, know that it -has copper in it. Take it out with saltpetre and soft soap. - -648. - -A white horse may have the spots removed with the Spanish haematite -or with aqua fortis or with ... Removes the black hair on a white -horse with the singeing iron. Force him to the ground. - -649. - -FIRE. - -If you want to make a fire which will set a hall in a blaze without -injury do this: first perfume the hall with a dense smoke of incense -or some other odoriferous substance: It is a good trick to play. Or -boil ten pounds of brandy to evaporate, but see that the hall is -completely closed and throw up some powdered varnish among the fumes -and this powder will be supported by the smoke; then go into the -room suddenly with a lighted torch and at once it will be in a -blaze. - -650. - -FIRE. - -Take away that yellow surface which covers oranges and distill them -in an alembic, until the distillation may be said to be perfect. - -FIRE. - -Close a room tightly and have a brasier of brass or iron with fire -in it and sprinkle on it two pints of aqua vitae, a little at a -time, so that it may be converted into smoke. Then make some one -come in with a light and suddenly you will see the room in a blaze -like a flash of lightning, and it will do no harm to any one. - -VII. - -PHILOSOPHY AND HISTORY OF THE ART OF PAINTING. - -The relation of art and nature (651. 652). - -651. - -What is fair in men, passes away, but not so in art. - -652. - -HE WHO DESPISES PAINTING LOVES NEITHER PHILOSOPHY NOR NATURE. - -If you condemn painting, which is the only imitator of all visible -works of nature, you will certainly despise a subtle invention which -brings philosophy and subtle speculation to the consideration of the -nature of all forms--seas and plains, trees, animals, plants and -flowers--which are surrounded by shade and light. And this is true -knowledge and the legitimate issue of nature; for painting is born -of nature--or, to speak more correctly, we will say it is the -grandchild of nature; for all visible things are produced by nature, -and these her children have given birth to painting. Hence we may -justly call it the grandchild of nature and related to God. - -Painting is superior to poetry (653. 654). - -653. - -THAT PAINTING SURPASSES ALL HUMAN WORKS BY THE SUBTLE CONSIDERATIONS -BELONGING TO IT. - -The eye, which is called the window of the soul, is the principal -means by which the central sense can most completely and abundantly -appreciate the infinite works of nature; and the ear is the second, -which acquires dignity by hearing of the things the eye has seen. If -you, historians, or poets, or mathematicians had not seen things -with your eyes you could not report of them in writing. And if you, -0 poet, tell a story with your pen, the painter with his brush can -tell it more easily, with simpler completeness and less tedious to -be understood. And if you call painting dumb poetry, the painter may -call poetry blind painting. Now which is the worse defect? to be -blind or dumb? Though the poet is as free as the painter in the -invention of his fictions they are not so satisfactory to men as -paintings; for, though poetry is able to describe forms, actions and -places in words, the painter deals with the actual similitude of the -forms, in order to represent them. Now tell me which is the nearer -to the actual man: the name of man or the image of the man. The name -of man differs in different countries, but his form is never changed -but by death. - -654. - -And if the poet gratifies the sense by means of the ear, the painter -does so by the eye--the worthier sense; but I will say no more of -this but that, if a good painter represents the fury of a battle, -and if a poet describes one, and they are both together put before -the public, you will see where most of the spectators will stop, to -which they will pay most attention, on which they will bestow most -praise, and which will satisfy them best. Undoubtedly painting being -by a long way the more intelligible and beautiful, will please most. -Write up the name of God [Christ] in some spot and setup His image -opposite and you will see which will be most reverenced. Painting -comprehends in itself all the forms of nature, while you have -nothing but words, which are not universal as form is, and if you -have the effects of the representation, we have the representation -of the effects. Take a poet who describes the beauty of a lady to -her lover and a painter who represents her and you will see to which -nature guides the enamoured critic. Certainly the proof should be -allowed to rest on the verdict of experience. You have ranked -painting among the mechanical arts but, in truth, if painters were -as apt at praising their own works in writing as you are, it would -not lie under the stigma of so base a name. If you call it -mechanical because it is, in the first place, manual, and that it is -the hand which produces what is to be found in the imagination, you -too writers, who set down manually with the pen what is devised in -your mind. And if you say it is mechanical because it is done for -money, who falls into this error--if error it can be called--more -than you? If you lecture in the schools do you not go to whoever -pays you most? Do you do any work without pay? Still, I do not say -this as blaming such views, for every form of labour looks for its -reward. And if a poet should say: "I will invent a fiction with a -great purpose," the painter can do the same, as Apelles painted -Calumny. If you were to say that poetry is more eternal, I say the -works of a coppersmith are more eternal still, for time preserves -them longer than your works or ours; nevertheless they have not much -imagination [29]. And a picture, if painted on copper with enamel -colours may be yet more permanent. We, by our arts may be called the -grandsons of God. If poetry deals with moral philosophy, painting -deals with natural philosophy. Poetry describes the action of the -mind, painting considers what the mind may effect by the motions [of -the body]. If poetry can terrify people by hideous fictions, -painting can do as much by depicting the same things in action. -Supposing that a poet applies himself to represent beauty, ferocity, -or a base, a foul or a monstrous thing, as against a painter, he may -in his ways bring forth a variety of forms; but will the painter not -satisfy more? are there not pictures to be seen, so like the actual -things, that they deceive men and animals? - -Painting is superior to sculpture (655. 656). - -655. - -THAT SCULPTURE IS LESS INTELLECTUAL THAN PAINTING, AND LACKS MANY -CHARACTERISTICS OF NATURE. - -I myself, having exercised myself no less in sculpture than in -painting and doing both one and the other in the same degree, it -seems to me that I can, without invidiousness, pronounce an opinion -as to which of the two is of the greatest merit and difficulty and -perfection. In the first place sculpture requires a certain light, -that is from above, a picture carries everywhere with it its own -light and shade. Thus sculpture owes its importance to light and -shade, and the sculptor is aided in this by the nature, of the -relief which is inherent in it, while the painter whose art -expresses the accidental aspects of nature, places his effects in -the spots where nature must necessarily produce them. The sculptor -cannot diversify his work by the various natural colours of objects; -painting is not defective in any particular. The sculptor when he -uses perspective cannot make it in any way appear true; that of the -painter can appear like a hundred miles beyond the picture itself. -Their works have no aerial perspective whatever, they cannot -represent transparent bodies, they cannot represent luminous bodies, -nor reflected lights, nor lustrous bodies--as mirrors and the like -polished surfaces, nor mists, nor dark skies, nor an infinite number -of things which need not be told for fear of tedium. As regards the -power of resisting time, though they have this resistance [Footnote -19: From what is here said as to painting on copper it is very -evident that Leonardo was not acquainted with the method of painting -in oil on thin copper plates, introduced by the Flemish painters of -the XVIIth century. J. LERMOLIEFF has already pointed out that in -the various collections containing pictures by the great masters of -the Italian Renaissance, those painted on copper (for instance the -famous reading Magdalen in the Dresden Gallery) are the works of a -much later date (see _Zeitschrift fur bildende Kunst_. Vol. X pg. -333, and: _Werke italienischer Master in den Galerien von Munchen, -Dresden und Berlin_. Leipzig 1880, pg. 158 and 159.)--Compare No. -654, 29.], a picture painted on thick copper covered with white -enamel on which it is painted with enamel colours and then put into -the fire again and baked, far exceeds sculpture in permanence. It -may be said that if a mistake is made it is not easy to remedy it; -it is but a poor argument to try to prove that a work be the nobler -because oversights are irremediable; I should rather say that it -will be more difficult to improve the mind of the master who makes -such mistakes than to repair the work he has spoilt. - -656. - -We know very well that a really experienced and good painter will -not make such mistakes; on the contrary, with sound rules he will -remove so little at a time that he will bring his work to a good -issue. Again the sculptor if working in clay or wax, can add or -reduce, and when his model is finished it can easily be cast in -bronze, and this is the last operation and is the most permanent -form of sculpture. Inasmuch as that which is merely of marble is -liable to ruin, but not bronze. Hence a painting done on copper -which as I said of painting may be added to or altered, resembles -sculpture in bronze, which, having first been made in wax could then -be altered or added to; and if sculpture in bronze is durable, this -work in copper and enamel is absolutely imperishable. Bronze is but -dark and rough after all, but this latter is covered with various -and lovely colours in infinite variety, as has been said above; or -if you will have me only speak of painting on panel, I am content to -pronounce between it and sculpture; saying that painting is the more -beautiful and the more imaginative and the more copious, while -sculpture is the more durable but it has nothing else. Sculpture -shows with little labour what in painting appears a miraculous thing -to do; to make what is impalpable appear palpable, flat objects -appear in relief, distant objects seem close. In fact painting is -adorned with infinite possibilities which sculpture cannot command. - -Aphorisms (657-659). - -657. - -OF PAINTING. - -Men and words are ready made, and you, O Painter, if you do not know -how to make your figures move, are like an orator who knows not how -to use his words. - -658. - -As soon as the poet ceases to represent in words what exists in -nature, he in fact ceases to resemble the painter; for if the poet, -leaving such representation, proceeds to describe the flowery and -flattering speech of the figure, which he wishes to make the -speaker, he then is an orator and no longer a poet nor a painter. -And if he speaks of the heavens he becomes an astrologer, and -philosopher; and a theologian, if he discourses of nature or God. -But, if he restricts himself to the description of objects, he would -enter the lists against the painter, if with words he could satisfy -the eye as the painter does. - -659. - -Though you may be able to tell or write the exact description of -forms, the painter can so depict them that they will appear alive, -with the shadow and light which show the expression of a face; which -you cannot accomplish with the pen though it can be achieved by the -brush. - -On the history of painting (660. 661). - -660. - -THAT PAINTING DECLINES AND DETERIORATES FROM AGE TO AGE, WHEN -PAINTERS HAVE NO OTHER STANDARD THAN PAINTING ALREADY DONE. - -Hence the painter will produce pictures of small merit if he takes -for his standard the pictures of others. But if he will study from -natural objects he will bear good fruit; as was seen in the painters -after the Romans who always imitated each other and so their art -constantly declined from age to age. After these came Giotto the -Florentine who--not content with imitating the works of Cimabue his -master--being born in the mountains and in a solitude inhabited only -by goats and such beasts, and being guided by nature to his art, -began by drawing on the rocks the movements of the goats of which he -was keeper. And thus he began to draw all the animals which were to -be found in the country, and in such wise that after much study he -excelled not only all the masters of his time but all those of many -bygone ages. Afterwards this art declined again, because everyone -imitated the pictures that were already done; thus it went on from -century to century until Tomaso, of Florence, nicknamed Masaccio, -showed by his perfect works how those who take for their standard -any one but nature--the mistress of all masters--weary themselves in -vain. And, I would say about these mathematical studies that those -who only study the authorities and not the works of nature are -descendants but not sons of nature the mistress of all good authors. -Oh! how great is the folly of those who blame those who learn from -nature [Footnote 22: _lasciando stare li autori_. In this -observation we may detect an indirect evidence that Leonardo -regarded his knowledge of natural history as derived from his own -investigations, as well as his theories of perspective and optics. -Compare what he says in praise of experience (Vol II; _XIX_).], -setting aside those authorities who themselves were the disciples of -nature. - -661. - -That the first drawing was a simple line drawn round the shadow of a -man cast by the sun on a wall. - -The painter's scope. - -662. - -The painter strives and competes with nature. - -_X. - -Studies and Sketches for Pictures and Decorations. - -An artist's manuscript notes can hardly be expected to contain any -thing more than incidental references to those masterpieces of his -work of which the fame, sounded in the writings of his -contemporaries, has left a glorious echo to posterity. We need not -therefore be surprised to find that the texts here reproduced do not -afford us such comprehensive information as we could wish. On the -other hand, the sketches and studies prepared by Leonardo for the -two grandest compositions he ever executed: The Fresco of the Last -Supper in the Refectory of Santa Maria delle Grazie at Milan, and -the Cartoon of the Battle of Anghiari, for the Palazzo della -Signoria at Florence--have been preserved; and, though far from -complete, are so much more numerous than the manuscript notes, that -we are justified in asserting that in value and interest they amply -compensate for the meagerness of the written suggestions. - -The notes for the composition of the Last Supper, which are given -under nos._ 665 _and_ 666 _occur in a MS. at South Kensington, II2, -written in the years_ 1494-1495. _This MS. sketch was noted down not -more than three or four years before the painting was executed, -which justifies the inference that at the time when it was written -the painter had not made up his mind definitely even as to the -general scheme of the work; and from this we may also conclude that -the drawings of apostles' heads at Windsor, in red chalk, must be -ascribed to a later date. They are studies for the head of St. -Matthew, the fourth figure on Christ's left hand--see Pl. XL VII, -the sketch (in black chalk) for the head of St. Philip, the third -figure on the left hand--see Pl. XL VIII, for St. Peter's right -arm--see Pl. XLIX, and for the expressive head of Judas which has -unfortunately somewhat suffered by subsequent restoration of -outlines,--see Pl. L. According to a tradition, as unfounded as it -is improbable, Leonardo made use of the head of Padre Bandelli, the -prior of the convent, as the prototype of his Judas; this however -has already been contradicted by Amoretti "Memorie storiche" cap. -XIV. The study of the head of a criminal on Pl. LI has, it seems to -me, a better claim to be regarded as one of the preparatory sketches -for the head of Judas. The Windsor collection contains two old -copies of the head of St. Simon, the figure to the extreme left of -Christ, both of about equal merit (they are marked as Nos._ 21 _and_ -36_)--the second was reproduced on Pl. VIII of the Grosvenor -Gallery Publication in_ 1878. _There is also at Windsor a drawing in -black chalk of folded hands (marked with the old No._ 212; _No. LXI -of the Grosvenor Gallery Publication) which I believe to be a copy -of the hands of St. John, by some unknown pupil. A reproduction of -the excellent drawings of heads of Apostles in the possession of H. -R. H. the Grand Duchess of Weimar would have been out of my province -in this work, and, with regard to them, I must confine myself to -pointing out that the difference in style does not allow of our -placing the Weimar drawings in the same category as those here -reproduced. The mode of grouping in the Weimar drawings is of itself -sufficient to indicate that they were not executed before the -picture was painted, but, on the contrary, afterwards, and it is, on -the face of it, incredible that so great a master should thus have -copied from his own work. - -The drawing of Christ's head, in the Brera palace at Milan was -perhaps originally the work of Leonardo's hand; it has unfortunately -been entirely retouched and re-drawn, so that no decisive opinion -can be formed as to its genuineness. - -The red chalk drawing reproduced on Pl. XLVI is in the Accademia at -Venice; it was probably made before the text, Nos._ 664 _and_ 665, -_was written. - -The two pen and ink sketches on Pl. XLV seem to belong to an even -earlier date; the more finished drawing of the two, on the right -hand, represents Christ with only St. John and Judas and a third -disciple whose action is precisely that described in No._ 666, -_Pl._ 4. _It is hardly necessary to observe that the other sketches -on this page and the lines of text below the circle (containing the -solution of a geometrical problem) have no reference to the picture -of the Last Supper. With this figure of Christ may be compared a -similar pen and ink drawing reproduced on page_ 297 _below on the -left hand; the original is in the Louvre. On this page again the -rest of the sketches have no direct bearing on the composition of -the Last Supper, not even, as it seems to me, the group of four men -at the bottom to the right hand--who are listening to a fifth, in -their midst addressing them. Moreover the writing on this page (an -explanation of a disk shaped instrument) is certainly not in the -same style as we find constantly used by Leonardo after the year_ -1489. - -_It may be incidentally remarked that no sketches are known for the -portrait of "Mona Lisa", nor do the MS. notes ever allude to it, -though according to Vasari the master had it in hand for fully four -years. - -Leonardo's cartoon for the picture of the battle of Anghiari has -shared the fate of the rival work, Michaelangelo's "Bathers summoned -to Battle". Both have been lost in some wholly inexplicable manner. -I cannot here enter into the remarkable history of this work; I can -only give an account of what has been preserved to us of Leonardo's -scheme and preparations for executing it. The extent of the material -in studies and drawings was till now quite unknown. Their -publication here may give some adequate idea of the grandeur of this -famous work. The text given as No._ 669 _contains a description of -the particulars of the battle, but for the reasons given in the note -to this text, I must abandon the idea of taking this passage as the -basis of my attempt to reconstruct the picture as the artist -conceived and executed it. - -I may here remind the reader that Leonardo prepared the cartoon in -the Sala del Papa of Santa Maria Novella at Florence and worked -there from the end of October 1503 till February 1504, and then was -busied with the painting in the Sala del Consiglio in the Palazzo -della Signoria, till the work was interrupted at the end of May -1506. (See Milanesi's note to Vasari pp. 43--45 Vol. IV ed. 1880.) -Vasari, as is well known, describes only one scene or episode of the -cartoon--the Battle for the Standard in the foreground of the -composition, as it would seem; and this only was ever finished as a -mural decoration in the Sala del Consiglio. This portion of the -composition is familiar to all from the disfigured copy engraved by -Edelinck. Mariette had already very acutely observed that Edelinck -must surely have worked from a Flemish copy of the picture. There is -in the Louvre a drawing by Rubens (No. 565) which also represents -four horsemen fighting round a standard and which agrees with -Edelinck's engraving, but the engraving reverses the drawing. An -earlier Flemish drawing, such as may have served as the model for -both Rubens and Edelinck, is in the Uffizi collection (see -Philpots's Photograph, No. 732). It seems to be a work of the second -half of the XVIth century, a time when both the picture and the -cartoon had already been destroyed. It is apparently the production -of a not very skilled hand. Raphael Trichet du Fresne, 1651, -mentions that a small picture by Leonardo himself of the Battle of -the Standard was then extant in the Tuileries; by this he probably -means the painting on panel which is now in the possession of Madame -Timbal in Paris, and which has lately been engraved by Haussoullier -as a work by Leonardo. The picture, which is very carefully painted, -seems to me however to be the work of some unknown Florentine -painter, and probably executed within the first ten years of the -XVIth century. At the same time, it would seem to be a copy not from -Leonardo's cartoon, but from his picture in the Palazzo della -Signoria; at any rate this little picture, and the small Flemish -drawing in Florence are the oldest finished copies of this episode -in the great composition of the Battle of Anghiari. - -In his Life of Raphael, Vasari tells us that Raphael copied certain -works of Leonardo's during his stay in Florence. Raphael's first -visit to Florence lasted from the middle of October 1504 till July -1505, and he revisited it in the summer of 1506. The hasty sketch, -now in the possession of the University of Oxford and reproduced on -page 337 also represents the Battle of the Standard and seems to -have been made during his first stay, and therefore not from the -fresco but from the cartoon; for, on the same sheet we also find, -besides an old man's head drawn in Leonardo's style, some studies -for the figure of St. John the Martyr which Raphael used in 1505 in -his great fresco in the Church of San Severo at Perugia. - -Of Leonardo's studies for the Battle of Anghiari I must in the first -place point to five, on three of which--Pl. LII 2, Pl. LIII, Pl. -LVI--we find studies for the episode of the Standard. The standard -bearer, who, in the above named copies is seen stooping, holding on -to the staff across his shoulder, is immediately recognisable as the -left-hand figure in Raphael's sketch, and we find it in a similar -attitude in Leonardo's pen and ink drawing in the British -Museum--Pl. LII, 2--the lower figure to the right. It is not -difficult to identify the same figure in two more complicated groups -in the pen and ink drawings, now in the Accademia at Venice--Pl. -LIII, and Pl. LIV--where we also find some studies of foot soldiers -fighting. On the sheet in the British Museum--Pl. LII, 2--we find, -among others, one group of three horses galloping forwards: one -horseman is thrown and protects himself with his buckler against the -lance thrusts of two others on horseback, who try to pierce him as -they ride past. The same action is repeated, with some variation, in -two sketches in pen and ink on a third sheet, in the Accademia at -Venice, Pl. LV; a coincidence which suggests the probability of such -an incident having actually been represented on the cartoon. We are -not, it is true, in a position to declare with any certainty which -of these three dissimilar sketches may have been the nearest to the -group finally adopted in executing the cartoon. - -With regard, however, to one of the groups of horsemen it is -possible to determine with perfect certainty not only which -arrangement was preferred, but the position it occupied in the -composition. The group of horsemen on Pl. LVII is a drawing in black -chalk at Windsor, which is there attributed to Leonardo, but which -appears to me to be the work of Cesare da Sesto, and the -Commendatore Giov. Morelli supports me in this view. It can hardly -be doubted that da Sesto, as a pupil of Leonardo's, made this -drawing from his master's cartoon, if we compare it with the copy -made by Raphael--here reproduced, for just above the fighting -horseman in Raphael's copy it is possible to detect a horse which is -seen from behind, going at a slower pace, with his tail flying out -to the right and the same horse may be seen in the very same -attitude carrying a dimly sketched rider, in the foreground of -Cesare da Sesto's drawing._ - -_If a very much rubbed drawing in black chalk at Windsor--Pl. -LVI--is, as it appears to be, the reversed impression of an original -drawing, it is not difficult to supplement from it the portions -drawn by Cesare da Sesto. Nay, it may prove possible to reconstruct -the whole of the lost cartoon from the mass of materials we now have -at hand which we may regard as the nucleus of the composition. A -large pen and ink drawing by Raphael in the Dresden collection, -representing three horsemen fighting, and another, by Cesare da -Sesto, in the Uffizi, of light horsemen fighting are a further -contribution which will help us to reconstruct it._ - -_The sketch reproduced on Pl. LV gives a suggestive example of the -way in which foot-soldiers may have been introduced into the cartoon -as fighting among the groups of horsemen; and I may here take the -opportunity of mentioning that, for reasons which it would be out of -place to enlarge upon here, I believe the two genuine drawings by -Raphael's hand in his "Venetian sketch-book" as it is called--one of -a standard bearer marching towards the left, and one of two -foot-soldiers armed with spears and fighting with a horseman--to be -undoubtedly copies from the cartoon of the Battle of Anghiari._ - -_Leonardo's two drawings, preserved in the museum at Buda-Pesth and -reproduced on pages 338 and 339 are preliminary studies for the -heads of fighting warriors. The two heads drawn in black chalk (pg. -338) and the one seen in profile, turned to the left, drawn in red -chalk (pg. 339), correspond exactly with those of two horsemen in -the scene of the fight round the standard as we see them in Madame -Timbal's picture and in the other finished copies. An old copy of -the last named drawing by a pupil of Leonardo is in MS. C. A. 187b; -561b (See Saggio, Tav. XXII). Leonardo used to make such finished -studies of heads as those, drawn on detached sheets, before -beginning his pictures from his drawings--compare the preparatory -studies for the fresco of the Last Supper, given on Pl. XLVII and -Pl. L. Other drawings of heads, all characterised by the expression -of vehement excitement that is appropriate to men fighting, are to -be seen at Windsor (No. 44) and at the Accademia at Venice (IV, 13); -at the back of one of the drawings at Buda-Pesth there is the bust -of a warrior carrying a spear on his left shoulder, holding up the -left arm (See Csatakepek a XVI--lk Szazadbol osszeallitotta Pvlszky -Karoly). These drawings may have been made for other portions of the -cartoon, of which no copies exist, and thus we are unable to -identify these preparatory drawings. Finally I may add that a sketch -of fighting horse and foot soldiers, formerly in the possession of -M. Thiers and published by Charles Blanc in his "Vies des Peintres" -can hardly be accepted as genuine. It is not to be found, as I am -informed, among the late President's property, and no one appears to -know where it now is._ - -_An attempted reconstruction of the Cartoon, which is not only -unsuccessful but perfectly unfounded, is to be seen in the -lithograph by Bergeret, published in Charles Blanc's "Vies des -peintres" and reprinted in "The great Artists. L. da Vinci", p. 80. -This misleading pasticcio may now be rejected without hesitation._ - -_There are yet a few original drawings by Leonardo which might be -mentioned here as possibly belonging to the cartoon of the Battle; -such as the pen and ink sketches on Pl. XXI and on Pl. XXXVIII, No. -3, but we should risk too wide a departure from the domain of -ascertained fact._ - -_With regard to the colours and other materials used by Leonardo the -reader may be referred to the quotations from the accounts for the -picture in question given by Milanesi in his edition of Vasari (Vol. -IV, p. 44, note) where we find entries of a similar character to -those in Leonardo's note books for the year 1505; S. K. M. 12 (see -No. 636)._ - -_That Leonardo was employed in designing decorations and other -preparations for high festivals, particularly for the court of -Milan, we learn not only from the writings of his contemporaries but -from his own incidental allusions; for instance in MS. C. l5b (1), -l. 9. In the arrangement of the texts referring to this I have -placed those first, in which historical personages are named--Nos. -670-674. Among the descriptions of Allegorical subjects two texts -lately found at Oxford have been included, Nos. 676 and 677. They -are particularly interesting because they are accompanied by large -sketches which render the meaning of the texts perfectly clear. It -is very intelligible that in other cases, where there are no -illustrative sketches, the notes must necessarily remain obscure or -admit of various interpretations. The literature of the time affords -ample evidence of the use of such allegorical representations, -particularly during the Carnival and in Leonardo's notes we find the -Carnival expressly mentioned--Nos. 685 and 704. Vasari in his Life -of Pontormo, particularly describes that artist's various -undertakings for Carnival festivities. These very graphic -descriptions appear to me to throw great light in more ways than one -on the meaning of Leonardo's various notes as to allegorical -representations and also on mottoes and emblems--Nos. 681-702. In -passing judgment on the allegorical sketches and emblems it must not -be overlooked that even as pictures they were always accompanied by -explanations in words. Several finished drawings of allegorical -compositions or figures have been preserved, but as they have no -corresponding explanation in the MSS. they had no claim to be -reproduced here. The female figure on Pl. XXVI may perhaps be -regarded as a study for such an allegorical painting, of which the -purport would have been explained by an inscription._ - -On Madonna pictures. - -663. - -[In the autumn of] 1478 I began the two Madonna [pictures]. - -[Footnote: Photographs of this page have been published by BRAUN, -No. 439, and PHILPOT, No. 718. - -1. _Incominciai_. We have no other information as to the two -pictures of the Madonna here spoken of. As Leonardo here tells us -that he had begun two Madonnas at the same time, the word -'_incominciai_' may be understood to mean that he had begun at the -same time preparatory studies for two pictures to be painted later. -If this is so, the non-existence of the pictures may be explained by -supposing that they were only planned and never executed. I may here -mention a few studies for pictures of the Madonna which probably -belong to this early time; particularly a drawing in silver-point on -bluish tinted paper at Windsor--see Pl. XL, No. 3--, a drawing of -which the details have almost disappeared in the original but have -been rendered quite distinct in the reproduction; secondly a slight -pen and ink sketch in, the Codex VALLARDI, in the Louvre, fol. 64, -No. 2316; again a silver point drawing of a Virgin and child drawn -over again with the pen in the His de la Salle collection also in -the Louvre, No. 101. (See Vicomte BOTH DE TAUZIA, _Notice des -dessins de la collection His de la Salle, exposes au Louvre_. Paris -1881, pp. 80, 81.) This drawing is, it is true, traditionally -ascribed to Raphael, but the author of the catalogue very justly -points out its great resemblance with the sketches for Madonnas in -the British Museum which are indisputably Leonardo's. Some of these -have been published by Mr. HENRY WALLIS in the Art Journal, New Ser. -No. 14, Feb. 1882. If the non-existence of the two pictures here -alluded to justifies my hypothesis that only studies for such -pictures are meant by the text, it may also be supposed that the -drawings were made for some comrade in VERROCCHIO'S atelier. (See -VASARI, Sansoni's ed. Florence 1880. Vol. IV, p. 564): "_E perche a -Lerenzo piaceva fuor di modo la maniera di Lionardo, la seppe cosi -bene imitare, che niuno fu che nella pulitezza e nel finir l'opere -con diligenza l'imitasse piu di lui_." Leonardo's notes give me no -opportunity of discussing the pictures executed by him in Florence, -before he moved to Milan. So the studies for the unfinished picture -of the Adoration of the Magi--in the Uffizi, Florence--cannot be -described here, nor would any discussion about the picture in the -Louvre "_La Vierge aux Rochers_" be appropriate in the absence of -all allusion to it in the MSS. Therefore, when I presently add a few -remarks on this painting in explanation of the Master's drawings for -it, it will be not merely with a view to facilitate critical -researches about the picture now in the National Gallery, London, -which by some critics has been pronounced to be a replica of the -Louvre picture, but also because I take this opportunity of -publishing several finished studies of the Master's which, even if -they were not made in Florence but later in Milan, must have been -prior to the painting of the Last Supper. The original picture in -Paris is at present so disfigured by dust and varnish that the -current reproductions in photography actually give evidence more of -the injuries to which the picture has been exposed than of the -original work itself. The wood-cut given on p. 344, is only intended -to give a general notion of the composition. It must be understood -that the outline and expression of the heads, which in the picture -is obscured but not destroyed, is here altogether missed. The -facsimiles which follow are from drawings which appear to me to be -studies for "_La Vierge aux Rochers_." - -1. A drawing in silver point on brown toned paper of a woman's head -looking to the left. In the Royal Library at Turin, apparently a -study from nature for the Angel's head (Pl. XLII). - -2. A study of drapery for the left leg of the same figure, done with -the brush, Indian ink on greenish paper, the lights heightened with -white. - -The original is at Windsor, No. 223. The reproduction Pl. XLIII is -defective in the shadow on the upper part of the thigh, which is not -so deep as in the original; it should also be observed that the -folds of the drapery near the hips are somewhat altered in the -finished work in the Louvre, while the London copy shows a greater -resemblance to this study in that particular. - -3. A study in red chalk for the bust of the Infant Christ--No. 3 in -the Windsor collection (Pl. XLIV). The well-known silver-point -drawing on pale green paper, in the Louvre, of a boy's head (No. 363 -in REISET, _Notice des dessins, Ecoles d'Italie_) seems to me to be -a slightly altered copy, either from the original picture or from -this red chalk study. - -4. A silver-point study on greenish paper, for the head of John the -Baptist, reproduced on p. 342. This was formerly in the Codex -Vallardi and is now exhibited among the drawings in the Louvre. The -lights are, in the original, heightened with white; the outlines, -particularly round the head and ear, are visibly restored. - -There is a study of an outstretched hand--No. 288 in the Windsor -collection--which was published in the Grosvenor Gallery -Publication, 1878, simply under the title of: "No. 72 Study of a -hand, pointing" which, on the other hand, I regard as a copy by a -pupil. The action occurs in the kneeling angel of the Paris picture -and not in the London copy. - -These four genuine studies form, I believe, a valuable substitute in -the absence of any MS. notes referring to the celebrated Paris -picture.] - -Bernardo di Bandino's Portrait. - -664. - -A tan-coloured small cap, A doublet of black serge, A black jerkin -lined A blue coat lined, with fur of foxes' breasts, and the collar -of the jerkin covered with black and white stippled velvet Bernardo -di Bandino Baroncelli; black hose. - -[Footnote: These eleven lines of text are by the side of the pen and -ink drawing of a man hanged--Pl. LXII, No. 1. This drawing was -exhibited in 1879 at the _Ecole des Beaux-Arts_ in Paris and the -compilers of the catalogue amused themselves by giving the victim's -name as follows: "_Un pendu, vetu d'une longue robe, les mains liees -sur le dos ... Bernardo di Bendino Barontigni, marchand de -pantalons_" (see _Catalogue descriptif des Dessins de Mailres -anciens exposes a l'Ecole des Beaux Arts_, Paris 1879; No. 83, pp. -9-10). Now, the criminal represented here, is none other than -Bernardino di Bandino Baroncelli the murderer of Giuliano de'Medici, -whose name as a coadjutor in the conspiracy of the Pazzi has gained -a melancholy notoriety by the tragedy of the 26th April 1478. -Bernardo was descended from an ancient family and the son of the man -who, under King Ferrante, was President of the High Court of Justice -in Naples. His ruined fortunes, it would seem, induced him to join -the Pazzi; he and Francesco Pazzi were entrusted with the task of -murdering Giuliano de'Medici on the fixed day. Their victim not -appearing in the cathedral at the hour when they expected him, the -two conspirators ran to the palace of the Medici and induced him to -accompany them. Giuliano then took his place in the chancel of the -Cathedral, and as the officiating priest raised the Host--the sign -agreed upon--Bernardo stabbed the unsuspecting Giuliano in the -breast with a short sword; Giuliano stepped backwards and fell dead. -The attempt on Lorenzo's life however, by the other conspirators at -the same moment, failed of success. Bernardo no sooner saw that -Lorenzo tried to make his escape towards the sacristy, than he -rushed upon him, and struck down Francesco Nori who endeavoured to -protect Lorenzo. How Lorenzo then took refuge behind the brazen -doors of the sacristy, and how, as soon as Giuliano's death was made -known, the further plans of the conspirators were defeated, while a -terrible vengeance overtook all the perpetrators and accomplices, -this is no place to tell. Bernardo Bandini alone seemed to be -favoured by fortune; he hid first in the tower of the Cathedral, and -then escaped undiscovered from Florence. Poliziano, who was with -Lorenzo in the Cathedral, says in his 'Conjurationis Pactianae -Commentarium': "_Bandinus fugitans in Tiphernatem incidit, a quo in -aciem receptus Senas pervenit_." And Gino Capponi in summing up the -reports of the numerous contemporary narrators of the event, says: -"_Bernardo Bandini ricoverato in Costantinopoli, fu per ordine del -Sultano preso e consegnato a un Antonio di Bernardino dei Medici, -che Lorenzo aveva mandato apposta in Turchia: cosi era grande la -potenza di quest' uomo e grande la voglia di farne mostra e che non -restasse in vita chi aveagli ucciso il fratello, fu egli applicato -appena giunto_" (_Storia della Republica di Firenze II_, 377, 378). -Details about the dates may be found in the _Chronichetta di -Belfredello Strinati Alfieri_: "_Bernardo di Bandino Bandini -sopradetto ne venne preso da Gostantinopoti a di 14. Dicembre 1479 e -disaminato, che fu al Bargello, fu impiccato alle finestre di detto -Bargello allato alla Doana a di 29. Dicembre MCCCCLXXIX che pochi di -stette_." It may however be mentioned with reference to the mode of -writing the name of the assassin that, though most of his -contemporaries wrote Bernardo Bandini, in the _Breve Chronicon -Caroli Petri de Joanninis_ he is called Bernardo di Bandini -Baroncelli; and, in the _Sententiae Domini Matthaei de Toscana_, -Bernardus Joannis Bandini de Baroncellis, as is written on -Leonardo's drawing of him when hanged. Now VASARI, in the life of -_Andrea del Castagno_ (Vol. II, 680; ed. Milanesi 1878), tells us -that in 1478 this painter was commissioned by order of the Signoria -to represent the members of the Pazzi conspiracy as traitors, on the -facade of the Palazzo del Podesta--the Bargello. This statement is -obviously founded on a mistake, for Andrea del Castagno was already -dead in 1457. He had however been commissioned to paint Rinaldo -degli Albizzi, when declared a rebel and exiled in 1434, and his -adherents, as hanging head downwards; and in consequence he had -acquired the nickname of Andrea degl' Impiccati. On the 21st July -1478 the Council of Eight came to the following resolution: "_item -servatis etc. deliberaverunt et santiaverunt Sandro Botticelli pro -ejus labore in pingendo proditores flor. quadraginta largos_" (see -G. MILANESI, _Arch. star. VI_ (1862) p. 5 note.) - -As has been told, Giuliano de' Medici was murdered on the 26th April -1478, and we see by this that only three months later Botticelli was -paid for his painting of the "_proditores_". We can however hardly -suppose that all the members of the conspiracy were depicted by him -in fresco on the facade of the palace, since no fewer than eighty -had been condemned to death. We have no means of knowing whether, -besides Botticelli, any other painters, perhaps Leonardo, was -commissioned, when the criminals had been hanged in person out of -the windows of the Palazzo del Podesta to represent them there -afterwards in effigy in memory of their disgrace. Nor do we know -whether the assassin who had escaped may at first not have been -provisionally represented as hanged in effigy. Now, when we try to -connect the historical facts with this drawing by Leonardo -reproduced on Pl. LXII, No. I, and the full description of the -conspirator's dress and its colour on the same sheet, there seems to -be no reasonable doubt that Bernardo Bandini is here represented as -he was actually hanged on December 29th, 1479, after his capture at -Constantinople. The dress is certainly not that in which he -committed the murder. A long furred coat might very well be worn at -Constantinople or at Florence in December, but hardly in April. The -doubt remains whether Leonardo described Bernardo's dress so fully -because it struck him as remarkable, or whether we may not rather -suppose that this sketch was actually made from nature with the -intention of using it as a study for a wall painting to be executed. -It cannot be denied that the drawing has all the appearance of -having been made for this purpose. Be this as it may, the sketch -under discussion proves, at any rate, that Leonardo was in Florence -in December 1479, and the note that accompanies it is valuable as -adding one more characteristic specimen to the very small number of -his MSS. that can be proved to have been written between 1470 and -1480.] - -Notes on the Last Supper (665-668). - -665. - -One who was drinking and has left the glass in its position and -turned his head towards the speaker. - -Another, twisting the fingers of his hands together turns with stern -brows to his companion [6]. Another with his hands spread open shows -the palms, and shrugs his shoulders up his ears making a mouth of -astonishment [8]. - -[9] Another speaks into his neighbour's ear and he, as he listens to -him, turns towards him to lend an ear [10], while he holds a knife -in one hand, and in the other the loaf half cut through by the -knife. [13] Another who has turned, holding a knife in his hand, -upsets with his hand a glass on the table [14]. - -[Footnote 665, 666: In the original MS. there is no sketch to -accompany these passages, and if we compare them with those drawings -made by Leonardo in preparation for the composition of the -picture--Pl. XLV, XLVI--, (compare also Pl. LII, 1 and the drawings -on p. 297) it is impossible to recognise in them a faithful -interpretation of the whole of this text; but, if we compare these -passages with the finished picture (see p. 334) we shall see that in -many places they coincide. For instance, compare No. 665, 1. 6--8, -with the fourth figure on the right hand of Christ. The various -actions described in lines 9--10, 13--14 are to be seen in the group -of Peter, John and Judas; in the finished picture however it is not -a glass but a salt cellar that Judas is upsetting.] - -666. - -Another lays his hand on the table and is looking. Another blows his -mouthful. [3] Another leans forward to see the speaker shading his -eyes with his hand. [5] Another draws back behind the one who leans -forward, and sees the speaker between the wall and the man who is -leaning [Footnote: 6. _chinato_. I have to express my regret for -having misread this word, written _cinato_ in the original, and -having altered it to _"ciclo"_ when I first published this text, in -'The Academy' for Nov. 8, 1879 immediately after I had discovered -it, and subsequently in the small biography of Leonardo da Vinci -(Great Artists) p. 29.]. - -[Footnote: In No. 666. Line I must refer to the furthest figure on -the left; 3, 5 and 6 describe actions which are given to the group -of disciples on the left hand of Christ.] - -667. - -CHRIST. - -Count Giovanni, the one with the Cardinal of Mortaro. - -[Footnote: As this note is in the same small Manuscript as the -passage here immediately preceding it, I may be justified in -assuming that Leonardo meant to use the features of the person here -named as a suitable model for the figure of Christ. The celebrated -drawing of the head of Christ, now hanging in the Brera Gallery at -Milan, has obviously been so much restored that it is now impossible -to say, whether it was ever genuine. We have only to compare it with -the undoubtedly genuine drawings of heads of the disciples in PI. -XLVII, XLVIII and L, to admit that not a single line of the Milan -drawing in its present state can be by the same hand.] - -668. - -Philip, Simon, Matthew, Thomas, James the Greater, Peter, Philip, -Andrew, Bartholomew. - -[Footnote: See PI. XLVI. The names of the disciples are given in the -order in which they are written in the original, from right to left, -above each head. The original drawing is here slightly reduced in -scale; it measures 39 centimetres in length by 26 in breadth.] - -669. - - On the battle of Anghiari. - Florentine - Neri di Gino Capponi - Bernardetto de' Medici - Micheletto, - Niccolo da Pisa - Conte Francesco - Pietro Gian Paolo - Guelfo Orsino, - Messer Rinaldo degli - Albizzi - -Begin with the address of Niccolo Piccinino to the soldiers and the -banished Florentines among whom are Messer Rinaldo degli Albizzi and -other Florentines. Then let it be shown how he first mounted on -horseback in armour; and the whole army came after him--40 squadrons -of cavalry, and 2000 foot soldiers went with him. Very early in the -morning the Patriarch went up a hill to reconnoitre the country, -that is the hills, fields and the valley watered by a river; and -from thence he beheld Niccolo Picinino coming from Borgo San -Sepolcro with his people, and with a great dust; and perceiving them -he returned to the camp of his own people and addressed them. Having -spoken he prayed to God with clasped hands, when there appeared a -cloud in which Saint Peter appeared and spoke to the Patriarch.--500 -cavalry were sent forward by the Patriarch to hinder or check the -rush of the enemy. In the foremost troop Francesco the son of -Niccolo Piccinino [24] was the first to attack the bridge which was -held by the Patriarch and the Florentines. Beyond the bridge to his -left he sent forward some infantry to engage ours, who drove them -back, among whom was their captain Micheletto [29] whose lot it was -to be that day at the head of the army. Here, at this bridge there -is a severe struggle; our men conquer and the enemy is repulsed. -Here Guido and Astorre, his brother, the Lord of Faenza with a great -number of men, re-formed and renewed the fight, and rushed upon the -Florentines with such force that they recovered the bridge and -pushed forward as far as the tents. But Simonetto advanced with 600 -horse, and fell upon the enemy and drove them back once more from -the place, and recaptured the bridge; and behind him came more men -with 2000 horse soldiers. And thus for a long time they fought with -varying fortune. But then the Patriarch, in order to divert the -enemy, sent forward Niccolo da Pisa [44] and Napoleone Orsino, a -beardless lad, followed by a great multitude of men, and then was -done another great feat of arms. At the same time Niccolo Piccinino -urged forward the remnant of his men, who once more made ours give -way; and if it had not been that the Patriarch set himself at their -head and, by his words and deeds controlled the captains, our -soldiers would have taken to flight. The Patriarch had some -artillery placed on the hill and with these he dispersed the enemy's -infantry; and the disorder was so complete that Niccolo began to -call back his son and all his men, and they took to flight towards -Borgo. And then began a great slaughter of men; none escaped but the -foremost of those who had fled or who hid themselves. The battle -continued until sunset, when the Patriarch gave his mind to -recalling his men and burying the dead, and afterwards a trophy was -erected. - -[Footnote: 669. This passage does not seem to me to be in Leonardo's -hand, though it has hitherto been generally accepted as genuine. Not -only is the writing unlike his, but the spelling also is quite -different. I would suggest that this passage is a description of the -events of the battle drawn up for the Painter by order of the -Signoria, perhaps by some historian commissioned by them, to serve -as a scheme or programme of the work. The whole tenor of the style -seems to me to argue in favour of this theory; and besides, it would -be in no way surprising that such a document should have been -preserved among Leonardo's autographs.] - -Allegorical representations referring to the duke of Milan -(670-673). - -670. - -Ermine with blood Galeazzo, between calm weather and a -representation of a tempest. - -[Footnote: 670. Only the beginning of this text is legible; the -writing is much effaced and the sense is consequently obscure. It -seems to refer like the following passage to an allegorical -picture.] - -671. - -Il Moro with spectacles, and Envy depicted with False Report and -Justice black for il Moro. - -Labour as having a branch of vine [_or_ a screw] in her hand. - -672. - -Il Moro as representing Good Fortune, with hair, and robes, and his -hands in front, and Messer Gualtieri taking him by the robes with a -respectful air from below, having come in from the front [5]. - -Again, Poverty in a hideous form running behind a youth. Il Moro -covers him with the skirt of his robe, and with his gilt sceptre he -threatens the monster. - -A plant with its roots in the air to represent one who is at his -last;--a robe and Favour. - -Of tricks [_or_ of magpies] and of burlesque poems [_or_ of -starlings]. - -Those who trust themselves to live near him, and who will be a large -crowd, these shall all die cruel deaths; and fathers and mothers -together with their families will be devoured and killed by cruel -creatures. - -[Footnote: 1--10 have already been published by _Amoretti_ in -_Memorie Storiche_ cap. XII. He adds this note with regard to -Gualtieri: "_A questo M. Gualtieri come ad uomo generoso e benefico -scrive il Bellincioni un Sonetto (pag, 174) per chiedergli un -piacere; e 'l Tantio rendendo ragione a Lodovico il Moro, perche -pubblicasse le Rime del Bellincioni; cio hammi imposto, gli dice: -l'humano fidele, prudente e sollicito executore delli tuoi -comandamenti Gualtero, che fa in tutte le cose ove tu possi far -utile, ogni studio vi metti._" A somewhat mysterious and evidently -allegorical composition--a pen and ink drawing--at Windsor, see PL -LVIII, contains a group of figures in which perhaps the idea is -worked out which is spoken of in the text, lines 1-5.] - -673. - -He was blacker than a hornet, his eyes were as red as a burning fire -and he rode on a tall horse six spans across and more than 20 long -with six giants tied up to his saddle-bow and one in his hand which -he gnawed with his teeth. And behind him came boars with tusks -sticking out of their mouths, perhaps ten spans. - -Allegorical representations (674--678). - -674. - -Above the helmet place a half globe, which is to signify our -hemisphere, in the form of a world; on which let there be a peacock, -richly decorated, and with his tail spread over the group; and every -ornament belonging to the horse should be of peacock's feathers on a -gold ground, to signify the beauty which comes of the grace bestowed -on him who is a good servant. - -On the shield a large mirror to signify that he who truly desires -favour must be mirrored in his virtues. - -On the opposite side will be represented Fortitude, in like manner -in her place with her pillar in her hand, robed in white, to signify -... And all crowned; and Prudence with 3 eyes. The housing of the -horse should be of plain cloth of gold closely sprinkled with -peacock's eyes, and this holds good for all the housings of the -horse, and the man's dress. And the man's crest and his neck-chain -are of peacock's feathers on golden ground. - -On the left side will be a wheel, the centre of which should be -attached to the centre of the horse's hinder thigh piece, and in the -centre Prudence is seen robed in red, Charity sitting in a fiery -chariot and with a branch of laurel in her hand, to signify the hope -which comes of good service. - -[21] Messer Antonio Grimani of Venice companion of Antonio Maria -[23]. - -[Footnote: _Messer Antonio Gri_. His name thus abbreviated is, there -can be no doubt, Grimani. Antonio Grimani was the famous Doge who in -1499 commanded the Venetian fleet in battle against the Turks. But -after the abortive conclusion of the expedition--Ludovico being the -ally of the Turks who took possession of Friuli--, Grimani was driven -into exile; he went to live at Rome with his son Cardinal Domenico -Grimani. On being recalled to Venice he filled the office of Doge -from 1521 to 1523. _Antonio Maria_ probably means Antonio Maria -Grimani, the Patriarch of Aquileia.] - -675. - -Fame should be depicted as covered all over with tongues instead of -feathers, and in the figure of a bird. - -676. - -Pleasure and Pain represent as twins, since there never is one -without the other; and as if they were united back to back, since -they are contrary to each other. - -[6] Clay, gold. - -[Footnote: 7. _oro. fango_: gold, clay. These words stand below the -allegorical figure.] - -If you take Pleasure know that he has behind him one who will deal -you Tribulation and Repentance. - -[9] This represents Pleasure together with Pain, and show them as -twins because one is never apart from the other. They are back to -back because they are opposed to each other; and they exist as -contraries in the same body, because they have the same basis, -inasmuch as the origin of pleasure is labour and pain, and the -various forms of evil pleasure are the origin of pain. Therefore it -is here represented with a reed in his right hand which is useless -and without strength, and the wounds it inflicts are poisoned. In -Tuscany they are put to support beds, to signify that it is here -that vain dreams come, and here a great part of life is consumed. It -is here that much precious time is wasted, that is, in the morning, -when the mind is composed and rested, and the body is made fit to -begin new labours; there again many vain pleasures are enjoyed; both -by the mind in imagining impossible things, and by the body in -taking those pleasures that are often the cause of the failing of -life. And for these reasons the reed is held as their support. - -[Footnote: 676. The pen and ink drawing on PI. LIX belongs to this -passage.] - -[Footnote: 8. _tribolatione_. In the drawing caltrops may be seen -lying in the old man's right hand, others are falling and others -again are shewn on the ground. Similar caltrops are drawn in MS. -Tri. p. 98 and underneath them, as well as on page 96 the words -_triboli di ferro_ are written. From the accompanying text it -appears that they were intended to be scattered on the ground at the -bottom of ditches to hinder the advance of the enemy. Count Giulio -Porro who published a short account of the Trivulzio MS. in the -"_Archivio Storico Lombardo_", Anno VIII part IV (Dec. 31, 1881) has -this note on the passages treating of "_triboli_": "_E qui -aggiungero che anni sono quando venne fabbricata la nuova -cavallerizza presso il castello di Milano, ne furono trovati due che -io ho veduto ed erano precisamente quali si trovano descritti e -disegnati da Leonardo in questo codice_". - -There can therefore be no doubt that this means of defence was in -general use, whether it were originally Leonardo's invention or not. -The play on the word "_tribolatione_", as it occurs in the drawing -at Oxford, must then have been quite intelligible.] - -[Footnote: 9--22. These lines, in the original, are written on the -left side of the page and refer to the figure shown on PI. LXI. Next -to it is placed the group of three figures given in PI. LX No. I. -Lines 21 and 22, which are written under it, are the only -explanation given.] - -Evil-thinking is either Envy or Ingratitude. - -677. - -Envy must be represented with a contemptuous motion of the hand -towards heaven, because if she could she would use her strength -against God; make her with her face covered by a mask of fair -seeming; show her as wounded in the eye by a palm branch and by an -olive-branch, and wounded in the ear by laurel and myrtle, to -signify that victory and truth are odious to her. Many thunderbolts -should proceed from her to signify her evil speaking. Let her be -lean and haggard because she is in perpetual torment. Make her heart -gnawed by a swelling serpent, and make her with a quiver with -tongues serving as arrows, because she often offends with it. Give -her a leopard's skin, because this creature kills the lion out of -envy and by deceit. Give her too a vase in her hand full of flowers -and scorpions and toads and other venomous creatures; make her ride -upon death, because Envy, never dying, never tires of ruling. Make -her bridle, and load her with divers kinds of arms because all her -weapons are deadly. - -Toleration. - -Intolerable. - -No sooner is Virtue born than Envy comes into the world to attack -it; and sooner will there be a body without a shadow than Virtue -without Envy. - -[Footnote: The larger of the two drawings on PI. LXI is explained by -the first 21 lines of this passage. L. 22 and 23, which are written -above the space between the two drawings, do not seem to have any -reference to either. L. 24-27 are below the allegorical twin figure -which they serve to explain.] - -678. - -When Pluto's Paradise is opened, then there may be devils placed in -twelve pots like openings into hell. Here will be Death, the Furies, -ashes, many naked children weeping; living fires made of various -colours.... - -679. - - John the Baptist - Saint Augustin - Saint Peter - Paul - Elisabeth - Saint Clara. - Bernardino - Our Lady Louis - Bonaventura - Anthony of Padua. - Saint Francis. - Francis, - Anthony, a lily and book; - Bernardino with the [monogram of] Jesus, - Louis with 3 fleur de lys on his breast and - the crown at his feet, - Bonaventura with Seraphim, - Saint Clara with the tabernacle, - Elisabeth with a Queen's crown. - -[Footnote: 679. The text of the first six lines is written within a -square space of the same size as the copy here given. The names are -written in the margin following the order in which they are here -printed. In lines 7--12 the names of those saints are repeated of -whom it seemed necessary to point out the emblems.] - -List of drawings. - -680. - - A head, full face, of a young man - with fine flowing hair, - Many flowers drawn from nature, - A head, full face, with curly hair, - Certain figures of Saint Jerome, - [6] The measurements of a figure, - Drawings of furnaces. - A head of the Duke, - [9] many designs for knots, - 4 studies for the panel of Saint Angelo - A small composition of Girolamo da Fegline, - A head of Christ done with the pen, - [13] 8 Saint Sebastians, - Several compositions of Angels, - A chalcedony, - A head in profile with fine hair, - Some pitchers seen in(?) perspective, - Some machines for ships, - Some machines for waterworks, - A head, a portrait of Atalanta raising her - face; - The head of Geronimo da Fegline, - The head of Gian Francisco Borso, - Several throats of old women, - Several heads of old men, - Several nude figures, complete, - Several arms, eyes, feet, and positions, - A Madonna, finished, - Another, nearly in profile, - Head of Our Lady ascending into Heaven, - A head of an old man with long chin, - A head of a gypsy girl, - A head with a hat on, - A representation of the Passion, a cast, - A head of a girl with her hair gathered in a knot, - A head, with the brown hair dressed. - -[Footnote: 680. This has already been published by AMORETTI _Memorie -storiche_ cap. XVI. His reading varies somewhat from that here -given, _e. g._ l. 5 and 6. _Certi Sangirolami in su d'una figura_; -and instead of I. 13. _Un San Bastiano_.] - -[Footnote: 680. 9. _Molti disegni di gruppi_. VASARI in his life of -Leonardo (IV, 21, ed. MILANESI 1880) says: "_Oltreche perse tempo -fino a disegnare_ gruppi _di corde fatti con ordine, e che da un -capo seguissi tutto il resto fino all' altro, tanto che s'empiessi -un tondo; che se ne vede in istampa uno difficilissimo e molto -bello, e nel mezzo vi sono queste parole: Leonardus Vinci -Accademia_". _Gruppi_ must here be understood as a technical -expression for those twisted ornaments which are well known through -wood cuts. AMORETTI mentions six different ones in the Ambrosian -Library. I am indebted to M. DELABORDE for kindly informing me that -the original blocks of these are preserved in his department in the -Bibliotheque Nationale in Paris. On the cover of these volumes is a -copy from one of them. The size of the original is 23 1/2 -centimetres by 26 1/4. The centre portion of another is given on p. -361. G. Govi remarks on these ornaments (_Saggio_ p. 22): "_Codesti -gruppi eran probabilmente destinati a servir di modello a ferri da -rilegatori per adornar le cartelle degli scolari (?). Fregi -somigliantissimi a questi troviamo infatti impressi in oro sui -cartoni di vari volumi contemporanei, e li vediam pur figurare nelle -lettere iniziali di alcune edizioni del tempo._" - -Durer who copied them, omitting the inscription, added to the second -impressions his own monogram. In his diary he designates them simply -as "_Die sechs Knoten_" (see THAUSING, Life of A. Durer I, 362, -363). In Leonardo's MSS. we find here and there little sketches or -suggestions for similar ornaments. Compare too G. MONGERI, _L'Arte -in Milano_, p. 315 where an ornament of the same character is given -from the old decorations of the vaulted ceiling of the Sacristy of -S. Maria delle Grazie.] - -[Footnote: 680, 17. The meaning in which the word _coppi_, literally -pitchers, is here used I am unable to determine; but a change to -_copie_ seems to me too doubtful to be risked.] - -681. - - Stubborn rigour. - Doomed rigour. - -[Footnote: See PI. LXII, No. 2, the two upper pen and ink drawings. -The originals, in the Windsor collection are slightly washed with -colour. The background is blue sky; the plough and the instrument -with the compass are reddish brown, the sun is tinted yellow]. - -682. - - Obstacles cannot crush me - Every obstacle yields to stern resolve - He who is fixed to a star does not change - his mind. - -[Footnote: This text is written to elucidate two sketches which were -obviously the first sketches for the drawings reproduced on PL LXII, -No. 2.] - -683. - -Ivy is [a type] of longevity. - -[Footnote: In the original there is, near this text, a sketch of a -coat wreathed above the waist with ivy.] - -684. - - Truth the sun. - falsehood a mask. - innocence, - malignity. - - Fire destroys falsehood, - that is sophistry, and - restores truth, driving out - darkness. - - Fire may be represented as the destroy of - all sophistry, and as the - image and demonstration of truth; - because it is light and drives - out darkness which conceals - all essences [or subtle things]. - -[Footnote: See PI. LXIII. L. 1-8 are in the middle of the page; 1. -9-14 to the right below; 1. 15-22 below in the middle column. The -rest of the text is below the sketches on the left. There are some -other passages on this page relating to geometry.] - -TRUTH. - - Fire destroys all sophistry, that is deceit; - and maintains truth alone, that is gold. - - Truth at last cannot be hidden. - Dissimulation is of no avail. Dissimulation is - to no purpose before - so great a judge. - Falsehood puts on a mask. - Nothing is hidden under the sun. - - Fire is to represent truth because it - destroys all sophistry and lies; and the - mask is for lying and falsehood - which conceal truth. - -685. - - Movement will cease before we are - weary - of being useful. - - Movement will fail sooner than usefulness. - Death sooner than I am never weary of - weariness. being useful, - In serving others I is a motto for carnval. - cannot do enough. Without fatigue. - - No labour is - sufficient to tire me. - - Hands into which - ducats and precious - stones fall like snow; they - never become tired by serving, - but this service is only for its - utility and not for our I am never weary - own benefit. of being useful. - - Naturally - nature has so disposed me. - -686. - - This shall be placed in the - hand of Ingratitude. - Wood nourishes the fire that - consumes it. - -687. - -TO REPRESENT INGRATITUDE. - - When the sun appears - which dispels darkness in - general, you put out the - light which dispelled it - for you in particular - for your need and convenience. - -688. - - On this side Adam and Eve on the other; - O misery of mankind, of how many things do - you make yourself the slave for money! - -[Footnote: See PI. LXIV. The figures of Adam and Eve in the clouds -here alluded to would seem to symbolise their superiority to all -earthly needs.] - -689. - -Thus are base unions sundered. - -[Footnote: A much blurred sketch is on the page by this text. It -seems to represent an unravelled plait or tissue.] - -690. - - Constancy does not begin, but is that - which perseveres. - -[Footnote: A drawing in red chalk, also rubbed, which stands in the -original in the middle of this text, seems to me to be intended for -a sword hilt, held in a fist.] - -691. - - Love, Fear, and Esteem,-- - Write these on three stones. Of servants. - -692. - -Prudence Strength. - -693. - - Fame alone raises herself to Heaven, - because virtuous things are in favour with God. - - Disgrace should be represented upside - down, because all her deeds are contrary to - God and tend to hell. - -694. - -Short liberty. - -695. - - Nothing is so much to be feared as Evil - Report. - This Evil Report is born of life. - -696. - -Not to disobey. - -697. - - A felled tree which is shooting - again. - - I am still hopeful. - A falcon, - Time. - -[Footnote: I. _Albero tagliato_. This emblem was displayed during -the Carnival at Florence in 1513. See VASARI VI, 251, ed. MILANESI -1881. But the coincidence is probably accidental.] - -698. - - Truth here makes Falsehood torment - lying tongues. - -699. - - Such as harm is when it hurts me not, - is good which avails me not. - -[Footnote: See PI. LX, No. 2. Compare this sketch with that on PI. -LXII, No. 2. Below the two lines of the text there are two more -lines: _li guchi (giunchi) che ritego le paglucole (pagliucole) -chelli (che li) anniegano_.] - -700. - -He who offends others, does not secure himself. - -[Footnote: See PI. LX, No. 3.] - -701. - -Ingratitude. - -[Footnote: See PI. LX, No. 4. Below the bottom sketches are the -unintelligible words "_sta stilli_." For "_Ingratitudo_" compare -also Nos. 686 and 687.] - -702. - -One's thoughts turn towards Hope. - -[Footnote: 702. By the side of this passage is a sketch of -a cage with a bird sitting in it.] - -Ornaments and Decorations for feasts (703-705). - -703. - -A bird, for a comedy. - -[Footnote: The biographies say so much, and the author's notes say -so little of the invention attributed to Leonardo of making -artificial birds fly through the air, that the text here given is of -exceptional interest from being accompanied by a sketch. It is a -very slight drawing of a bird with outspread wings, which appears to -be sliding down a stretched string. Leonardo's flying machines and -his studies of the flight of birds will be referred to later.] - -704. - -A DRESS FOR THE CARNIVAL. - -To make a beautiful dress cut it in thin cloth and give it an -odoriferous varnish, made of oil of turpentine and of varnish in -grain, with a pierced stencil, which must be wetted, that it may not -stick to the cloth; and this stencil may be made in a pattern of -knots which afterwards may be filled up with black and the ground -with white millet.[Footnote 7: The grains of black and white millet -would stick to the varnish and look like embroidery.] - -[Footnote: Ser Giuliano, da Vinci the painter's brother, had been -commissioned, with some others, to order and to execute the garments -of the Allegorical figures for the Carnival at Florence in 1515--16; -VASARI however is incorrect in saying of the Florentine Carnival of -1513: "_equelli che feciono ed ordinarono gli abiti delle figure -furono Ser Piero da Vinci, padre di Lonardo, e Bernardino di -Giordano, bellissimi ingegni_" (See MILANESI'S ed. Voi. VI, pg. -251.)] - -705. - -Snow taken from the high peaks of mountains might be carried to hot -places and let to fall at festivals in open places at summer time. - - - -*** End of Volume 1 - - -The Notebooks of Leonardo Da Vinci - -Volume 2 - -Translated by Jean Paul Richter - -1888 - - - - - - - -XI. - -The notes on Sculpture. - -Compared with the mass of manuscript treating of Painting, a very -small number of passages bearing on the practice and methods of -Sculpture are to be found scattered through the note books; these -are here given at the beginning of this section (Nos. 706-709). -There is less cause for surprise at finding that the equestrian -statue of Francesco Sforza is only incidentally spoken of; for, -although Leonardo must have worked at it for a long succession of -years, it is not in the nature of the case that it could have given -rise to much writing. We may therefore regard it as particularly -fortunate that no fewer than thirteen notes in the master's -handwriting can be brought together, which seem to throw light on -the mysterious history of this famous work. Until now writers on -Leonardo were acquainted only with the passages numbered 712, 719, -720, 722 and 723. - -In arranging these notes on sculpture I have given the precedence to -those which treat of the casting of the monument, not merely because -they are the fullest, but more especially with a view to -reconstructing the monument, an achievement which really almost lies -within our reach by combining and comparing the whole of the -materials now brought to light, alike in notes and in sketches. - -A good deal of the first two passages, Nos. 710 and 711, which refer -to this subject seems obscure and incomprehensible; still, they -supplement each other and one contributes in no small degree to the -comprehension of the other. A very interesting and instructive -commentary on these passages may be found in the fourth chapter of -Vasari's Introduzione della Scultura under the title "Come si fanno -i modelli per fare di bronzo le figure grandi e picciole, e come le -forme per buttarle; come si armino di ferri, e come si gettino di -metallo," &c. Among the drawings of models of the moulds for casting -we find only one which seems to represent the horse in the act of -galloping--No. 713. All the other designs show the horse as pacing -quietly and as these studies of the horse are accompanied by copious -notes as to the method of casting, the question as to the position -of the horse in the model finally selected, seems to be decided by -preponderating evidence. "Il cavallo dello Sforza"--C. Boito remarks -very appositely in the Saggio on page 26, "doveva sembrare fratello -al cavallo del Colleoni. E si direbbe che questo fosse figlio del -cavallo del Gattamelata, il quale pare figlio di uno dei quattro -cavalli che stavano forse sull' Arco di Nerone in Roma" (now at -Venice). The publication of the Saggio also contains the -reproduction of a drawing in red chalk, representing a horse walking -to the left and supported by a scaffolding, given here on Pl. LXXVI, -No. 1. It must remain uncertain whether this represents the model as -it stood during the preparations for casting it, or whether--as -seems to me highly improbable--this sketch shows the model as it was -exhibited in 1493 on the Piazza del Castello in Milan under a -triumphal arch, on the occasion of the marriage of the Emperor -Maximilian to Bianca Maria Sforza. The only important point here is -to prove that strong evidence seems to show that, of the numerous -studies for the equestrian statue, only those which represent the -horse pacing agree with the schemes of the final plans. - -The second group of preparatory sketches, representing the horse as -galloping, must therefore be considered separately, a distinction -which, in recapitulating the history of the origin of the monument -seems justified by the note given under No. 720. - -Galeazza Maria Sforza was assassinated in 1476 before his scheme for -erecting a monument to his father Francesco Sforza could be carried -into effect. In the following year Ludovico il Moro the young -aspirant to the throne was exiled to Pisa, and only returned to -Milan in 1479 when he was Lord (Governatore) of the State of Milan, -in 1480 after the minister Cecco Simonetta had been murdered. It may -have been soon after this that Ludovico il Moro announced a -competition for an equestrian statue, and it is tolerably certain -that Antonio del Pollajuolo took part in it, from this passage in -Vasari's Life of this artist: "E si trovo, dopo la morte sua, il -disegno e modello che a Lodovico Sforza egli aveva fatto per la -statua a cavallo di Francesco Sforza, duca di Milano; il quale -disegno e nel nostro Libro, in due modi: in uno egli ha sotto -Verona; nell'altro, egli tutto armato, e sopra un basamento pieno di -battaglie, fa saltare il cavallo addosso a un armato; ma la cagione -perche non mettesse questi disegni in opera, non ho gia potuto -sapere." One of Pollajuolo's drawings, as here described, has lately -been discovered by Senatore Giovanni Morelli in the Munich -Pinacothek. Here the profile of the horseman is a portrait of -Francesco Duke of Milan, and under the horse, who is galloping to -the left, we see a warrior thrown and lying on the ground; precisely -the same idea as we find in some of Leonardo's designs for the -monument, as on Pl. LXVI, LXVII, LXVIII, LXIX and LXXII No. 1; and, -as it is impossible to explain this remarkable coincidence by -supposing that either artist borrowed it from the other, we can only -conclude that in the terms of the competition the subject proposed -was the Duke on a horse in full gallop, with a fallen foe under its -hoofs. - -Leonardo may have been in the competition there and then, but the -means for executing the monument do not seem to have been at once -forthcoming. It was not perhaps until some years later that Leonardo -in a letter to the Duke (No. 719) reminded him of the project for -the monument. Then, after he had obeyed a summons to Milan, the plan -seems to have been so far modified, perhaps in consequence of a -remonstrance on the part of the artist, that a pacing horse was -substituted for one galloping, and it may have been at the same time -that the colossal dimensions of the statue were first decided on. -The designs given on Pl. LXX, LXXI, LXXII, 2 and 3, LXXIII and LXXIV -and on pp. 4 and 24, as well as three sketches on Pl. LXIX may be -studied with reference to the project in its new form, though it is -hardly possible to believe that in either of these we see the design -as it was actually carried out. It is probable that in Milan -Leonardo worked less on drawings, than in making small models of wax -and clay as preparatory to his larger model. Among the drawings -enumerated above, one in black chalk, Pl. LXXIII--the upper sketch -on the right hand side, reminds us strongly of the antique statue of -Marcus Aurelius. If, as it would seem, Leonardo had not until then -visited Rome, he might easily have known this statue from drawings -by his former master and friend Verrocchio, for Verrocchio had been -in Rome for a long time between 1470 and 1480. In 1473 Pope Sixtus -IV had this antique equestrian statue restored and placed on a new -pedestal in front of the church of San Giovanni in Luterano. -Leonardo, although he was painting independently as early as in 1472 -is still spoken of as working in Verrocchio's studio in 1477. Two -years later the Venetian senate decided on erecting an equestrian -statue to Colleoni; and as Verrocchio, to whom the work was -entrusted, did not at once move from Florence to Venice--where he -died in 1488 before the casting was completed--but on the contrary -remained in Florence for some years, perhaps even till 1485, -Leonardo probably had the opportunity of seeing all his designs for -the equestrian statue at Venice and the red chalk drawing on Pl. -LXXIV may be a reminiscence of it. - -The pen and ink drawing on Pl. LXXII, No. 3, reminds us of -Donatello's statue of Gattamelata at Padua. However it does not -appear that Leonardo was ever at Padua before 1499, but we may -conclude that he took a special interest in this early bronze statue -and the reports he could procure of it, form an incidental remark -which is to be found in C. A. 145a; 432a, and which will be given in -Vol. II under Ricordi or Memoranda. Among the studies--in the widest -sense of the word--made in preparation statue we may include the -Anatomy of the Horse which Lomazzo and Vas mention; the most -important parts of this work still exist in the Queen's Li Windsor. -It was beyond a doubt compiled by Leonardo when at Milan; only -interesting records to be found among these designs are reproduced -in Nos. 716a but it must be pointed out that out of 40 sheets of -studies of the movements of the belonging to that treatise, a horse -in full gallop occurs but once. - -If we may trust the account given by Paulus Jovius--about l527-- -Leonardo's horse was represented as "vehementer incitatus et -anhelatus". Jovius had probably seen the model exhibited at Milan; -but, need we, in fact, infer from this description that the horse -was galloping? Compare Vasari's description of the Gattamelata -monument at Padua: "Egli [Donatello] vi ando ben volentieri, e fece -il cavallo di bronzo, che e in sulla piazza di Sant Antonio, nel -quale si dimostra lo sbuffamento ed il fremito del cavallo, ed il -grande animo e la fierezza vivacissimamente espressa dall'arte nella -figura che lo cavalca". - -These descriptions, it seems to me, would only serve to mark the -difference between the work of the middle ages and that of the -renaissance. - -We learn from a statement of Sabba da Castiglione that, when Milan -was taken by the French in 1499, the model sustained some injury; -and this informant, who, however is not invariably trustworthy, adds -that Leonardo had devoted fully sixteen years to this work (la forma -del cavallo, intorno a cui Leonardo avea sedici anni continui -consumati). This often-quoted passage has given ground for an -assumption, which has no other evidence to support it, that Leonardo -had lived in Milan ever since 1483. But I believe it is nearer the -truth to suppose that this author's statement alludes to the fact -that about sixteen years must have past since the competition in -which Leonardo had taken part. - -I must in these remarks confine myself strictly to the task in hand -and give no more of the history of the Sforza monument than is -needed to explain the texts and drawings I have been able to -reproduce. In the first place, with regard to the drawings, I may -observe that they are all, with the following two exceptions, in the -Queen's Library at Windsor Castle; the red chalk drawing on Pl. -LXXVI No. 1 is in the MS. C. A. (see No. 7l2) and the fragmentary -pen and ink drawing on page 4 is in the Ambrosian Library. The -drawings from Windsor on Pl. LXVI have undergone a trifling -reduction from the size of the originals. - -There can no longer be the slightest doubt that the well-known -engraving of several horsemen (Passavant, Le Peintre-Graveur, Vol. -V, p. 181, No. 3) is only a copy after original drawings by -Leonardo, executed by some unknown engraver; we have only to compare -the engraving with the facsimiles of drawings on Pl. LXV, No. 2, Pl. -LXVII, LXVIII and LXIX which, it is quite evident, have served as -models for the engraver. - -On Pl. LXV No. 1, in the larger sketch to the right hand, only the -base is distinctly visible, the figure of the horseman is effaced. -Leonardo evidently found it unsatisfactory and therefore rubbed it -out. - -The base of the monument--the pedestal for the equestrian statue--is -repeatedly sketched on a magnificent plan. In the sketch just -mentioned it has the character of a shrine or aedicula to contain a -sarcophagus. Captives in chains are here represented on the -entablature with their backs turned to that portion of the monument -which more - -strictly constitutes the pedestal of the horse. The lower portion of -the aedicula is surrounded by columns. In the pen and ink drawing -Pl. LXVI--the lower drawing on the right hand side--the sarcophagus -is shown between the columns, and above the entablature is a plinth -on which the horse stands. But this arrangement perhaps seemed to -Leonardo to lack solidity, and in the little sketch on the left -hand, below, the sarcophagus is shown as lying under an arched -canopy. In this the trophies and the captive warriors are detached -from the angles. In the first of these two sketches the place for -the trophies is merely indicated by a few strokes; in the third -sketch on the left the base is altogether broader, buttresses and -pinnacles having been added so as to form three niches. The black -chalk drawing on Pl. LXVIII shows a base in which the angles are -formed by niches with pilasters. In the little sketch to the extreme -left on Pl. LXV, No. 1, the equestrian statue serves to crown a -circular temple somewhat resembling Bramante's tempietto of San -Pietro in Montario at Rome, while the sketch above to the right -displays an arrangement faintly reminding us of the tomb of the -Scaligers in Verona. The base is thus constructed of two platforms -or slabs, the upper one considerably smaller than the lower one -which is supported on flying buttresses with pinnacles. - -On looking over the numerous studies in which the horse is not -galloping but merely walking forward, we find only one drawing for -the pedestal, and this, to accord with the altered character of the -statue, is quieter and simpler in style (Pl. LXXIV). It rises almost -vertically from the ground and is exactly as long as the pacing -horse. The whole base is here arranged either as an independent -baldaquin or else as a projecting canopy over a recess in which the -figure of the deceased Duke is seen lying on his sarcophagus; in the -latter case it was probably intended as a tomb inside a church. -Here, too, it was intended to fill the angles with trophies or -captive warriors. Probably only No. 724 in the text refers to the -work for the base of the monument. - -If we compare the last mentioned sketch with the description of a -plan for an equestrian monument to Gian Giacomo Trivulzio (No. 725) -it seems by no means impossible that this drawing is a preparatory -study for the very monument concerning which the manuscript gives us -detailed information. We have no historical record regarding this -sketch nor do the archives in the Trivulzio Palace give us any -information. The simple monument to the great general in San Nazaro -Maggiore in Milan consists merely of a sarcophagus placed in recess -high on the wall of an octagonal chapel. The figure of the warrior -is lying on the sarcophagus, on which his name is inscribed; a piece -of sculpture which is certainly not Leonardo's work. Gian Giacomo -Trivulzio died at Chartres in 1518, only five months before -Leonardo, and it seems to me highly improbable that this should have -been the date of this sketch; under these circumstances it would -have been done under the auspices of Francis I, but the Italian -general was certainly not in favour with the French monarch at the -time. Gian Giacomo Trivulzio was a sworn foe to Ludovico il Moro, -whom he strove for years to overthrow. On the 6th September 1499 he -marched victorious into Milan at the head of a French army. In a -short time, however, he was forced to quit Milan again when Ludovico -il Moro bore down upon the city with a force of Swiss troops. On the -15th of April following, after defeating Lodovico at Novara, -Trivulzio once more entered Milan as a Conqueror, but his hopes of -becoming _Governatore_ of the place were soon wrecked by intrigue. -This victory and triumph, historians tell us, were signalised by -acts of vengeance against the dethroned Sforza, and it might have -been particularly flattering to him that the casting and -construction of the Sforza monument were suspended for the time. - -It must have been at this moment--as it seems to me--that he -commissioned the artist to prepare designs for his own monument, -which he probably intended should find a place in the Cathedral or -in some other church. He, the husband of Margherita di Nicolino -Colleoni, would have thought that he had a claim to the same -distinction and public homage as his less illustrious connection had -received at the hands of the Venetian republic. It was at this very -time that Trivulzio had a medal struck with a bust portrait of -himself and the following remarkable inscription on the reverse:_ -DEO FAVENTE--1499--DICTVS--10--IA--EXPVLIT--LVDOVICV--SF-- -(Sfortiam) DVC-- (ducem) MLI (Mediolani)--NOIE -(nomine)--REGIS--FRANCORVM--EODEM--ANN --(anno) RED'T (redit)--LVS -(Ludovicus)--SVPERATVS ET CAPTVS--EST--AB--EO. _In the Library of -the Palazzo Trivulzio there is a MS. of Callimachus Siculus written -at the end of the XVth or beginning of the XVIth century. At the -beginning of this MS. there is an exquisite illuminated miniature of -an equestrian statue with the name of the general on the base; it is -however very doubtful whether this has any connection with -Leonardo's design. - -Nos. 731-740, which treat of casting bronze, have probably a very -indirect bearing on the arrangements made for casting the equestrian -statue of Francesco Sforza. Some portions evidently relate to the -casting of cannon. Still, in our researches about Leonardo's work on -the monument, we may refer to them as giving us some clue to the -process of bronze casting at that period. - -Some practical hints (706-709). - -7O6. - -OF A STATUE. - -If you wish to make a figure in marble, first make one of clay, and -when you have finished it, let it dry and place it in a case which -should be large enough, after the figure is taken out of it, to -receive also the marble, from which you intend to reveal the figure -in imitation of the one in clay. After you have put the clay figure -into this said case, have little rods which will exactly slip in to -the holes in it, and thrust them so far in at each hole that each -white rod may touch the figure in different parts of it. And colour -the portion of the rod that remains outside black, and mark each rod -and each hole with a countersign so that each may fit into its -place. Then take the clay figure out of this case and put in your -piece of marble, taking off so much of the marble that all your rods -may be hidden in the holes as far as their marks; and to be the -better able to do this, make the case so that it can be lifted up; -but the bottom of it will always remain under the marble and in this -way it can be lifted with tools with great ease. - -707. - -Some have erred in teaching sculptors to measure the limbs of their -figures with threads as if they thought that these limbs were -equally round in every part where these threads were wound about -them. - -708. - -MEASUREMENT AND DIVISION OF A STATUE. - -Divide the head into 12 degrees, and each degree divide into 12 -points, and each point into 12 minutes, and the minutes into minims -and the minims into semi minims. - -Degree--point--minute--minim. - -709. - -Sculptured figures which appear in motion, will, in their standing -position, actually look as if they were falling forward. - -[Footnote: _figure di rilievo_. Leonardo applies this term -exclusively to wholly detached figures, especially to those standing -free. This note apparently refers to some particular case, though we -have no knowledge of what that may have been. If we suppose it to -refer to the first model of the equestrian statue of Francesco -Sforza (see the introduction to the notes on Sculpture) this -observation may be regarded as one of his arguments for abandoning -the first scheme of the Sforza Monument, in which the horse was to -be galloping (see page 2). It is also in favour of this theory that -the note is written in a manuscript volume already completed in -1492. Leonardo's opinions as to the shortcomings of plastic works -when compared with paintings are given under No. 655 and 656.] - -Notes on the casting of the Sforza monument (710-715). - -710. - -Three braces which bind the mould. - -[If you want to make simple casts quickly, make them in a box of -river sand wetted with vinegar.] - -[When you shall have made the mould upon the horse you must make the -thickness of the metal in clay.] - -Observe in alloying how many hours are wanted for each -hundredweight. [In casting each one keep the furnace and its fire -well stopped up.] [Let the inside of all the moulds be wetted with -linseed oil or oil of turpentine, and then take a handful of -powdered borax and Greek pitch with aqua vitae, and pitch the mould -over outside so that being under ground the damp may not [damage -it?] - -[To manage the large mould make a model of the small mould, make a -small room in proportion.] - -[Make the vents in the mould while it is on the horse.] - -Hold the hoofs in the tongs, and cast them with fish glue. Weigh the -parts of the mould and the quantity of metal it will take to fill -them, and give so much to the furnace that it may afford to each -part its amount of metal; and this you may know by weighing the clay -of each part of the mould to which the quantity in the furnace must -correspond. And this is done in order that the furnace for the legs -when filled may not have to furnish metal from the legs to help out -the head, which would be impossible. [Cast at the same casting as -the horse the little door] - -[Footnote: The importance of the notes included under this number is -not diminished by the fact that they have been lightly crossed out -with red chalk. Possibly they were the first scheme for some fuller -observations which no longer exist; or perhaps they were crossed out -when Leonardo found himself obliged to give up the idea of casting -the equestrian statue. In the original the first two sketches are -above l. 1, and the third below l. 9.] - -711. - -THE MOULD FOR THE HORSE. - -Make the horse on legs of iron, strong and well set on a good -foundation; then grease it and cover it with a coating, leaving each -coat to dry thoroughly layer by layer; and this will thicken it by -the breadth of three fingers. Now fix and bind it with iron as may -be necessary. Moreover take off the mould and then make the -thickness. Then fill the mould by degrees and make it good -throughout; encircle and bind it with its irons and bake it inside -where it has to touch the bronze. - -OF MAKING THE MOULD IN PIECES. - -Draw upon the horse, when finished, all the pieces of the mould with -which you wish to cover the horse, and in laying on the clay cut it -in every piece, so that when the mould is finished you can take it -off, and then recompose it in its former position with its joins, by -the countersigns. - -The square blocks _a b_ will be between the cover and the core, that -is in the hollow where the melted bronze is to be; and these square -blocks of bronze will support the intervals between the mould and -the cover at an equal distance, and for this reason these squares -are of great importance. - -The clay should be mixed with sand. - -Take wax, to return [what is not used] and to pay for what is used. - -Dry it in layers. - -Make the outside mould of plaster, to save time in drying and the -expense in wood; and with this plaster enclose the irons [props] -both outside and inside to a thickness of two fingers; make terra -cotta. And this mould can be made in one day; half a boat load of -plaster will serve you. - -Good. - -Dam it up again with glue and clay, or white of egg, and bricks and -rubbish. - -[Footnote: See Pl. LXXV. The figure "40," close to the sketch in the -middle of the page between lines 16 and 17 has been added by a -collector's hand. - -In the original, below line 21, a square piece of the page has been -cut out about 9 centimetres by 7 and a blank piece has been gummed -into the place. - -Lines 22-24 are written on the margin. l. 27 and 28 are close to the -second marginal sketch. l. 42 is a note written above the third -marginal sketch and on the back of this sheet is the text given as -No. 642. Compare also No. 802.] - -712. - -All the heads of the large nails. - -[Footnote: See Pl. LXXVI, No. i. This drawing has already been -published in the "_Saggio delle Opere di L. da Vinci_." Milano 1872, -Pl. XXIV, No. i. But, for various reasons I cannot regard the -editor's suggestions as satisfactory. He says: "_Veggonsi le -armature di legname colle quali forse venne sostenuto il modello, -quando per le nozze di Bianca Maria Sforza con Massimiliano -imperatore, esso fu collocato sotto un arco trionfale davanti al -Castello_." - -713. - -These bindings go inside. - -714. - -Salt may be made from human excrements, burnt and calcined, made -into lees and dried slowly at a fire, and all the excrements produce -salt in a similar way and these salts when distilled, are very -strong. - -[Footnote: VASARI repeatedly states, in the fourth chapter of his -_Introduzione della Scultura_, that in preparing to cast bronze -statues horse-dung was frequently used by sculptors. If, -notwithstanding this, it remains doubtful whether I am justified in -having introduced here this text of but little interest, no such -doubt can be attached to the sketch which accompanies it.] - -715. - -METHOD OF FOUNDING AGAIN. - -This may be done when the furnace is made [Footnote: this note is -written below the sketches.] strong and bruised. - -Models for the horse of the Sforza monument (716-718). - -7l6. - -Messer Galeazzo's big genet - -717. - -Messer Galeazzo's Sicilian horse. - -[Footnote: These notes are by the side of a drawing of a horse with -figured measurements.] - -718. - -Measurement of the Sicilian horse the leg from behind, seen in -front, lifted and extended. - -[Footnote: There is no sketch belonging to this passage. Galeazze -here probably means Galeazze di San Severino, the famous captain who -married Bianca the daughter of Ludovico il Moro.] - -Occasional references to the Sforza monument (719-724). - -719. - -Again, the bronze horse may be taken in hand, which is to be to the -immortal glory and eternal honour of the happy memory of the prince -your father, and of the illustrious house of Sforza. - -[Footnote: The letter from which this passage is here extracted will -be found complete in section XXI. (see the explanation of it, on -page 2).] - -720. - -On the 23rd of April 1490 I began this book, and recommenced the -horse. - -721. - -There is to be seen, in the mountains of Parma and Piacenza, a -multitude of shells and corals full of holes, still sticking to the -rocks, and when I was at work on the great horse for Milan, a large -sackful of them, which were found thereabout, was brought to me into -my workshop, by certain peasants. - -722. - -Believe me, Leonardo the Florentine, who has to do the equestrian -bronze statue of the Duke Francesco that he does not need to care -about it, because he has work for all his life time, and, being so -great a work, I doubt whether he can ever finish it. [Footnote: This -passage is quoted from a letter to a committee at Piacenza for whom -Leonardo seems to have undertaken to execute some work. The letter -is given entire in section XXL; in it Leonardo remonstrates as to -some unreasonable demands.] - -723. - -Of the horse I will say nothing because I know the times. [Footnote: -This passage occurs in a rough copy of a letter to Ludovico il Moro, -without date (see below among the letters).] - -724. - -During ten years the works on the marbles have been going on I will -not wait for my payment beyond the time, when my works are finished. -[Footnote: This possibly refers to the works for the pedestal of the -equestrian statue concerning which we have no farther information in -the MSS. See p. 6.] - -The project of the Trivulzio monument. - -725. - -THE MONUMENT TO MESSER GIOVANNI JACOMO DA TREVULZO. - -[2] Cost of the making and materials for the horse [5]. - -[Footnote: In the original, lines 2-5, 12-14, 33-35, are written on -the margin. This passage has been recently published by G. Govi in -Vol. V, Ser. 3a, of _Transunti, Reale Accademia dei Linea, sed. del -5 Giugno, 1881,_ with the following introductory note: _"Desidero -intanto che siano stampati questi pochi frammenti perche so che sono -stati trascritti ultimamente, e verranno messi in luce tra poco -fuori d'Italia. Li ripubblichi pure chi vuole, ma si sappia almeno -che anche tra noi si conoscevano, e s'eran raccolti da anni per -comporne, quando che fosse, una edizione ordinata degli scritti di -Leonardo."_ - -The learned editor has left out line 22 and has written 3 _pie_ for -8 _piedi_ in line 25. There are other deviations of less importance -from the original.] - -A courser, as large as life, with the rider requires for the cost of -the metal, duc. 500. - -And for cost of the iron work which is inside the model, and -charcoal, and wood, and the pit to cast it in, and for binding the -mould, and including the furnace where it is to be cast ... duc. -200. - -To make the model in clay and then in wax......... duc. 432. - -To the labourers for polishing it when it is cast. ....... duc. 450. - -in all. . duc. 1582. - -[12] Cost of the marble of the monument [14]. - -Cost of the marble according to the drawing. The piece of marble -under the horse which is 4 braccia long, 2 braccia and 2 inches wide -and 9 inches thick 58 hundredweight, at 4 Lire and 10 Soldi per -hundredweight.. duc. 58. - -And for 13 braccia and 6 inches of cornice, 7 in. wide and 4 in. -thick, 24 hundredweight....... duc. 24. - -And for the frieze and architrave, which is 4 br. and 6 in. long, 2 -br. wide and 6 in. thick, 29 hundredweight., duc. 20. - -And for the capitals made of metal, which are 8, 5 inches in. square -and 2 in. thick, at the price of 15 ducats each, will come to...... -duc. 122. - -And for 8 columns of 2 br. 7 in., 4 1/2 in. thick, 20 hundredweight -duc. 20. - -And for 8 bases which are 5 1/2 in. square and 2 in. high 5 hund'.. -duc. 5. - -And for the slab of the tombstone 4 br. io in. long, 2 br. 4 1/2 in. -wide 36 hundredweight....... duc. 36. - -And for 8 pedestal feet each 8 br. long and 6 1/2 in. wide and 6 1/2 -in. thick, 20 hundredweight come to... duc. 20. - -And for the cornice below which is 4 br. and 10 in. long, and 2 br. -and 5 in. wide, and 4 in. thick, 32 hund'.. duc. 32. - -And for the stone of which the figure of the deceased is to be made -which is 3 br. and 8 in. long, and 1 br. and 6 in. wide, and 9 in. -thick, 30 hund'.. duc. 30. - -And for the stone on which the figure lies which is 3 br. and 4 in. -long and 1 br. and 2 in., wide and 4 1/2 in. thick duc. 16. - -And for the squares of marble placed between the pedestals which are -8 and are 9 br. long and 9 in. wide, and 3 in. thick, 8 -hundredweight . . . duc. 8. in all. . duc. 389. - -[33]Cost of the work in marble[35]. - -Round the base on which the horse stands there are 8 figures at 25 -ducats each ............ duc. 200. - -And on the same base there are 8 festoons with some other ornaments, -and of these there are 4 at the price of 15 ducats each, and 4 at -the price of 8 ducats each ....... duc. 92. - -And for squaring the stones duc. 6. - -Again, for the large cornice which goes below the base on which the -horse stands, which is 13 br. and 6 in., at 2 due. per br. ...... -duc. 27. - -And for 12 br. of frieze at 5 due. per br. ........... duc. 60. - -And for 12 br. of architrave at 1 1/2 duc. per br. ....... duc. 18. - -And for 3 rosettes which will be the soffit of the monument, at 20 -ducats each .......... duc. 60. - -And for 8 fluted columns at 8 ducats each ......... duc. 64. - -And for 8 bases at 1 ducat each, duc. 8. - -And for 8 pedestals, of which 4 are at 10 duc. each, which go above -the angles; and 4 at 6 duc. each .. duc. 64. - -And for squaring and carving the moulding of the pedestals at 2 duc. -each, and there are 8 .... duc. 16. - -And for 6 square blocks with figures and trophies, at 25 duc. each -.. duc. 150. - -And for carving the moulding of the stone under the figure of the -deceased .......... duc. 40. - -For the statue of the deceased, to do it well .......... duc. 100. - -For 6 harpies with candelabra, at 25 ducats each ......... duc. 150. - -For squaring the stone on which the statue lies, and carving the -moulding ............ duc. 20. - -in all .. duc. 1075. - -The sum total of every thing added together amount to ...... duc. -3046. - -726. - -MINT AT ROME. - -It can also be made without a spring. But the screw above must -always be joined to the part of the movable sheath: [Margin note: -The mint of Rome.] [Footnote: See Pl. LXXVI. This passage is taken -from a note book which can be proved to have been used in Rome.] - -All coins which do not have the rim complete, are not to be accepted -as good; and to secure the perfection of their rim it is requisite -that, in the first place, all the coins should be a perfect circle; -and to do this a coin must before all be made perfect in weight, and -size, and thickness. Therefore have several plates of metal made of -the same size and thickness, all drawn through the same gauge so as -to come out in strips. And out of [24] these strips you will stamp -the coins, quite round, as sieves are made for sorting chestnuts -[27]; and these coins can then be stamped in the way indicated -above; &c. - -[31] The hollow of the die must be uniformly wider than the lower, -but imperceptibly [35]. - -This cuts the coins perfectly round and of the exact thickness, and -weight; and saves the man who cuts and weighs, and the man who makes -the coins round. Hence it passes only through the hands of the -gauger and of the stamper, and the coins are very superior. -[Footnote: See Pl. LXXVI No. 2. The text of lines 31-35 stands -parallel 1. 24-27. - -Farther evidence of Leonardo's occupations and engagements at Rome -under Pope Leo X. may be gathered from some rough copies of letters -which will be found in this volume. Hitherto nothing has been known -of his work in Rome beyond some doubtful, and perhaps mythical, -statements in Vasari.] - -727. - -POWDER FOR MEDALS. - -The incombustible growth of soot on wicks reduced to powder, burnt -tin and all the metals, alum, isinglass, smoke from a brass forge, -each ingredient to be moistened, with aqua vitae or malmsey or -strong malt vinegar, white wine or distilled extract of turpentine, -or oil; but there should be little moisture, and cast in moulds. -[Margin note: On the coining of medals (727. 728).] [Footnote: The -meaning of _scagliuolo_ in this passage is doubtful.] - -728. - -OF TAKING CASTS OF MEDALS. - -A paste of emery mixed with aqua vitae, or iron filings with -vinegar, or ashes of walnut leaves, or ashes of straw very finely -powdered. - -[Footnote: The meaning of _scagliuolo_ in this passage is doubtful.] - -The diameter is given in the lead enclosed; it is beaten with a -hammer and several times extended; the lead is folded and kept -wrapped up in parchment so that the powder may not be spilt; then -melt the lead, and the powder will be on the top of the melted lead, -which must then be rubbed between two plates of steel till it is -thoroughly pulverised; then wash it with aqua fortis, and the -blackness of the iron will be dissolved leaving the powder clean. - -Emery in large grains may be broken by putting it on a cloth many -times doubled, and hit it sideways with the hammer, when it will -break up; then mix it little by little and it can be founded with -ease; but if you hold it on the anvil you will never break it, when -it is large. - -Any one who grinds smalt should do it on plates of tempered steel -with a cone shaped grinder; then put it in aqua fortis, which melts -away the steel that may have been worked up and mixed with the -smalt, and which makes it black; it then remains purified and clean; -and if you grind it on porphyry the porphyry will work up and mix -with the smalt and spoil it, and aqua fortis will never remove it -because it cannot dissolve the porphyry. - -If you want a fine blue colour dissolve the smalt made with tartar, -and then remove the salt. - -Vitrified brass makes a fine red. - -729. - -STUCCO. - -Place stucco over the prominence of the..... which may be composed -of Venus and Mercury, and lay it well over that prominence of the -thickness of the side of a knife, made with the ruler and cover this -with the bell of a still, and you will have again the moisture with -which you applied the paste. The rest you may dry [Margin note: On -stucco (729. 730).] [Footnote: In this passage a few words have been -written in a sort of cipher--that is to say backwards; as in l. 3 -_erenev_ for _Venere_, l. 4 _oirucrem_ for Mercurio, l. 12 _il -orreve co ecarob_ for _il everro (?) co borace_. The meaning of the -word before _"di giesso"_ in l. 1 is unknown; and the sense, in -which _sagoma_ is used here and in other passages is obscure.-- -_Venere_ and _Mercurio_ may mean 'marble' and 'lime', of which -stucco is composed. - -12. The meaning of _orreve_ is unknown.] - -well; afterwards fire it, and beat it or burnish it with a good -burnisher, and make it thick towards the side. - -STUCCO. - -Powder ... with borax and water to a paste, and make stucco of it, -and then heat it so that it may dry, and then varnish it, with fire, -so that it shines well. - -730. - -STUCCO FOR MOULDING. - -Take of butter 6 parts, of wax 2 parts, and as much fine flour as -when put with these 2 things melted, will make them as firm as wax -or modelling clay. - -GLUE. - -Take mastic, distilled turpentine and white lead. - -On bronze casting generally (731-740). - -731. - -TO CAST. - -Tartar burnt and powdered with plaster and cast cause the plaster to -hold together when it is mixed up again; and then it will dissolve -in water. - -732. - -TO CAST BRONZE IN PLASTER. - -Take to every 2 cups of plaster 1 of ox-horns burnt, mix them -together and make your cast with it. - -733. - -When you want to take a cast in wax, burn the scum with a candle, -and the cast will come out without bubbles. - -734. - -2 ounces of plaster to a pound of metal;-- walnut, which makes it -like the curve. - -[Footnote: The second part of this is quite obscure.] - -735. - -[Dried earth 16 pounds, 100 pounds of metal wet clay 20,--of wet -100,-half,- which increases 4 Ibs. of water,--1 of wax, 1 Ib. of -metal, a little less,-the scrapings of linen with earth, measure for -measure.] [Footnote: The translation is given literally, but the -meaning is quite obscure.] - -736. - -Such as the mould is, so will the cast be. - -737. - -HOW CASTS OUGHT TO BE POLISHED. - -Make a bunch of iron wire as thick as thread, and scrub them with -[this and] water; hold a bowl underneath that it may not make a mud -below. - -HOW TO REMOVE THE ROUGH EDGES FROM BRONZE. - -Make an iron rod, after the manner of a large chisel, and with this -rub over those seams on the bronze which remain on the casts of the -guns, and which are caused by the joins in the mould; but make the -tool heavy enough, and let the strokes be long and broad. - -TO FACILITATE MELTING. - -First alloy part of the metal in the crucible, then put it in the -furnace, and this being in a molten state will assist in beginning -to melt the copper. - -TO PREVENT THE COPPER COOLING IN THE FURNACE. - -When the copper cools in the furnace, be ready, as soon as you -perceive it, to cut it with a long stick while it is still in a -paste; or if it is quite cold cut it as lead is cut with broad and -large chisels. - -IF YOU HAVE TO MAKE A LARGE CAST. - -If you have to make a cast of a hundred thousand pounds do it with -two furnaces and with 2000 pounds in each, or as much as 3000 pounds -at most. - -738. - -HOW TO PROCEED TO BREAK A LARGE MASS OF BRONZE. - -If you want to break up a large mass of bronze, first suspend it, -and then make round it a wall on the four sides, like a trough of -bricks, and make a great fire therein. When it is quite red hot give -it a blow with a heavy weight raised above it, and with great force. - -739. - -TO COMBINE LEAD WITH OTHER METAL. - -If you wish for economy in combining lead with the metal in order to -lessen the amount of tin which is necessary in the metal, first -alloy the lead with the tin and then add the molten copper. - -How TO MELT [METAL] IN A FURNACE. - -The furnace should be between four well founded pillars. - -OF THE THICKNESS OF THE COATING. - -The coating should not be more than two fingers thick, it should be -laid on in four thicknesses over fine clay and then well fixed, and -it should be fired only on the inside and then carefully covered -with ashes and cow's dung. - -OF THE THICKNESS OF THE GUN. - -The gun being made to carry 600 Ibs. of ball and more, by this rule -you will take the measure of the diameter of the ball and divide it -into 6 parts and one of these parts will be its thickness at the -muzzle; but at the breech it must always be half. And if the ball is -to be 700 lbs., 1/7th of the diameter of the ball must be its -thickness in front; and if the ball is to be 800, the eighth of its -diameter in front; and if 900, 1/8th and 1/2 [3/16], and if 1000, -1/9th. - -OF THE LENGTH OF THE BODY OF THE GUN. - -If you want it to throw a ball of stone, make the length of the gun -to be 6, or as much as 7 diameters of the ball; and if the ball is -to be of iron make it as much as 12 balls, and if the ball is to be -of lead, make it as much as 18 balls. I mean when the gun is to have -the mouth fitted to receive 600 lbs. of stone ball, and more. - -OF THE THICKNESS OF SMALL GUNS. - -The thickness at the muzzle of small guns should be from a half to -one third of the diameter of the ball, and the length from 30 to 36 -balls. - -740. - -OF LUTING THE FURNACE WITHIN. - -The furnace must be luted before you put the metal in it, with earth -from Valenza, and over that with ashes. - -[Footnote 1. 2.: _Terra di Valenza_.--Valenza is north of -Alessandria on the Po.] - -OF RESTORING THE METAL WHEN IT IS BECOMING COOL. - -When you see that the bronze is congealing take some willow-wood cut -in small chips and make up the fire with it. - -THE CAUSE OF ITS CURDLING. - -I say that the cause of this congealing often proceeds from too much -fire, or from ill-dried wood. - -TO KNOW THE CONDITION OF THE FIRE. - -You may know when the fire is good and fit for your purpose by a -clear flame, and if you see the tips of the flames dull and ending -in much smoke do not trust it, and particularly when the flux metal -is almost fluid. - -OF ALLOYING THE METAL. - -Metal for guns must invariably be made with 6 or even 8 per cent, -that is 6 of tin to one hundred of copper, for the less you put in, -the stronger will the gun be. - -WHEN THE TIN SHOULD BE ADDED TO THE COPPER. - -The tin should be put in with the copper when the copper is reduced -to a fluid. - -HOW TO HASTEN THE MELTING. - -You can hasten the melting when 2/3ds of the copper is fluid; you -can then, with a stick of chestnut-wood, repeatedly stir what of -copper remains entire amidst what is melted. - -_Introductory Observations on the Architectural Designs (XII), and -Writings on Architecture (XIII)._ - -_Until now very little has been known regarding Leonardo's labours -in the domain of Architecture. No building is known to have been -planned and executed by him, though by some contemporary writers -incidental allusion is made to his occupying himself with -architecture, and his famous letter to Lodovico il Moro,--which has -long been a well-known document,--in which he offers his service as -an architect to that prince, tends to confirm the belief that he was -something more than an amateur of the art. This hypothesis has -lately been confirmed by the publication of certain documents, -preserved at Milan, showing that Leonardo was not only employed in -preparing plans but that he took an active part, with much credit, -as member of a commission on public buildings; his name remains -linked with the history of the building of the Cathedral at Pavia -and that of the Cathedral at Milan._ - -_Leonardo's writings on Architecture are dispersed among a large -number of MSS., and it would be scarcely possible to master their -contents without the opportunity of arranging, sorting and comparing -the whole mass of materials, so as to have some comprehensive idea -of the whole. The sketches, when isolated and considered by -themselves, might appear to be of but little value; it is not till -we understand their general purport, from comparing them with each -other, that we can form any just estimate of their true worth._ - -_Leonardo seems to have had a project for writing a complete and -separate treatise on Architecture, such as his predecessors and -contemporaries had composed--Leon Battista Alberti, Filarete, -Francesco di Giorgio and perhaps also Bramante. But, on the other -hand, it cannot be denied that possibly no such scheme was connected -with the isolated notes and researches, treating on special -questions, which are given in this work; that he was merely working -at problems in which, for some reason or other he took a special -interest._ - -_A great number of important buildings were constructed in Lombardy -during the period between 1472 and 1499, and among them there are -several by unknown architects, of so high an artistic merit, that it -is certainly not improbable that either Bramante or Leonardo da -Vinci may have been, directly or indirectly, concerned in their -erection._ - -_Having been engaged, for now nearly twenty years, in a thorough -study of Bramante's life and labours, I have taken a particular -interest in detecting the distinguishing marks of his style as -compared with Leonardo's. In 1869 I made researches about the -architectural drawings of the latter in the Codex Atlanticus at -Milan, for the purpose of finding out, if possible the original -plans and sketches of the churches of Santa Maria delle Grazie at -Milan, and of the Cathedral at Pavia, which buildings have been -supposed to be the work both of Bramante and of Leonardo. Since 1876 -I have repeatedly examined Leonardo's architectural studies in the -collection of his manuscripts in the Institut de France, and some of -these I have already given to the public in my work on_ "Les Projets -Primitifs pour la Basilique de St. Pierre de Rome", _P1. 43. In 1879 -I had the opportunity of examining the manuscript in the Palazzo -Trivulzio at Milan, and in 1880 Dr Richter showed me in London the -manuscripts in the possession of Lord Ashburnham, and those in the -British Museum. I have thus had opportunities of seeing most of -Leonardo's architectural drawings in the original, but of the -manuscripts tliemselves I have deciphered only the notes which -accompany the sketches. It is to Dr Richter's exertions that we owe -the collected texts on Architecture which are now published, and -while he has undertaken to be responsible for the correct reading of -the original texts, he has also made it his task to extract the -whole of the materials from the various MSS. It has been my task to -arrange and elucidate the texts under the heads which have been -adopted in this work. MS. B. at Paris and the Codex Atlanticus at -Milan are the chief sources of our knowledge of Leonardo as an -architect, and I have recently subjected these to a thorough -re-investigation expressly with a view to this work._ - -_A complete reproduction of all Leonardo's architectural sketches -has not, indeed, been possible, but as far as the necessarily -restricted limits of the work have allowed, the utmost completeness -has been aimed at, and no efforts have been spared to include every -thing that can contribute to a knowledge of Leonardo's style. It -would have been very interesting, if it had been possible, to give -some general account at least of Leonardo's work and studies in -engineering, fortification, canal-making and the like, and it is -only on mature reflection that we have reluctantly abandoned this -idea. Leonardo's occupations in these departments have by no means -so close a relation to literary work, in the strict sense of the -word as we are fairly justified in attributing to his numerous notes -on Architecture._ - -_Leonardo's architectural studies fall naturally under two heads:_ - -_I. Those drawings and sketches, often accompanied by short remarks -and explanations, which may be regarded as designs for buildings or -monuments intended to be built. With these there are occasionally -explanatory texts._ - -_II. Theoretical investigations and treatises. A special interest -attaches to these because they discuss a variety of questions which -are of practical importance to this day. Leonardo's theory as to the -origin and progress of cracks in buildings is perhaps to be -considered as unique in its way in the literature of Architecture._ - -_HENRY DE GEYMULLER_ - -_XII._ - -_Architectural Designs._ - -_I. Plans for towns._ - -_A. Sketches for laying out a new town with a double system of high- -level and low-level road-ways._ - -_Pl. LXXVII, No. 1 (MS. B, 15b). A general view of a town, with the -roads outside it sloping up to the high-level ways within._ - -_Pl. LXXVII, No. 3 (MS. B, 16b. see No. 741; and MS. B. 15b, see No. -742) gives a partial view of the town, with its streets and houses, -with explanatory references._ - -_Pl. LXXVII, No. 2 (MS. B, 15b; see No. 743). View of a double -staircaise with two opposite flights of steps._ - -_Pl. LXXVIII, Nos. 2 and 3 (MS. B, 37a). Sketches illustrating the -connection of the two levels of roads by means of steps. The lower -galleries are lighted by openings in the upper roadway._ - -_B. Notes on removing houses (MS. Br. M., 270b, see No. 744)._ - -741. - -The roads _m_ are 6 braccia higher than the roads _p s_, and each -road must be 20 braccia wide and have 1/2 braccio slope from the -sides towards the middle; and in the middle let there be at every -braccio an opening, one braccio long and one finger wide, where the -rain water may run off into hollows made on the same level as _p s_. -And on each side at the extremity of the width of the said road let -there be an arcade, 6 braccia broad, on columns; and understand that -he who would go through the whole place by the high level streets -can use them for this purpose, and he who would go by the low level -can do the same. By the high streets no vehicles and similar objects -should circulate, but they are exclusively for the use of gentlemen. -The carts and burdens for the use and convenience of the inhabitants -have to go by the low ones. One house must turn its back to the -other, leaving the lower streets between them. Provisions, such as -wood, wine and such things are carried in by the doors _n_, and -privies, stables and other fetid matter must be emptied away -underground. From one arch to the next - -742. - -must be 300 braccia, each street receiving its light through the -openings of the upper streets, and at each arch must be a winding -stair on a circular plan because the corners of square ones are -always fouled; they must be wide, and at the first vault there must -be a door entering into public privies and the said stairs lead from -the upper to the lower streets and the high level streets begin -outside the city gates and slope up till at these gates they have -attained the height of 6 braccia. Let such a city be built near the -sea or a large river in order that the dirt of the city may be -carried off by the water. - -743. - -The construction of the stairs: The stairs _c d_ go down to _f g_, -and in the same way _f g_ goes down to _h k_. - -744. - -ON MOVING HOUSES. - -Let the houses be moved and arranged in order; and this will be done -with facility because such houses are at first made in pieces on the -open places, and can then be fitted together with their timbers in -the site where they are to be permanent. - -[9] Let the men of the country [or the village] partly inhabit the -new houses when the court is absent [12]. - -[Footnote: On the same page we find notes referring to Romolontino -and Villafranca with a sketch-map of the course of the "Sodro" and -the "(Lo)cra" (both are given in the text farther on). There can -hardly be a doubt that the last sentence of the passage given above, -refers to the court of Francis I. King of France.--L.9-13 are -written inside the larger sketch, which, in the original, is on the -right hand side of the page by the side of lines 1-8. The three -smaller sketches are below. J. P. R.] - -_II. Plans for canals and streets in a town. - -Pl. LXXIX, 1. and 2, (MS. B, 37b, see No. 745, and MS. B. 36a, see -No. 746). A Plan for streets and canals inside a town, by which the -cellars of the houses are made accessible in boats. - -The third text given under No. 747 refers to works executed by -Leonardo in France._ - -745. - -The front _a m_ will give light to the rooms; _a e_ will be 6 -braccia--_a b_ 8 braccia --_b e_ 30 braccia, in order that the rooms -under the porticoes may be lighted; _c d f_ is the place where the -boats come to the houses to be unloaded. In order to render this -arrangement practicable, and in order that the inundation of the -rivers may not penetrate into the cellars, it is necessary to chose -an appropriate situation, such as a spot near a river which can be -diverted into canals in which the level of the water will not vary -either by inundations or drought. The construction is shown below; -and make choice of a fine river, which the rains do not render -muddy, such as the Ticino, the Adda and many others. [Footnote 12: -_Tesino, Adda e molti altri, i.e._ rivers coming from the mountains -and flowing through lakes.] The construction to oblige the waters to -keep constantly at the same level will be a sort of dock, as shown -below, situated at the entrance of the town; or better still, some -way within, in order that the enemy may not destroy it [14]. - -[Footnote: L. 1-4 are on the left hand side and within the sketch -given on Pl. LXXIX, No. I. Then follows after line 14, the drawing -of a sluicegate--_conca_--of which the use is explained in the text -below it. On the page 38a, which comes next in the original MS. is -the sketch of an oval plan of a town over which is written "_modo di -canali per la citta_" and through the longer axis of it "_canale -magior_" is written with "_Tesino_" on the prolongation of the -canal. J. P. R.] - -746. - -Let the width of the streets be equal to the average height of the -houses. - -747. - -The main underground channel does not receive turbid water, but that -water runs in the ditches outside the town with four mills at the -entrance and four at the outlet; and this may be done by damming the -water above Romorantin. - -[11]There should be fountains made in each piazza[13]. - -[Footnote: In the original this text comes immediately after the -passage given as No. 744. The remainder of the writing on the same -page refers to the construction of canals and is given later, in the -"Topographical Notes". - -Lines 1-11 are written to the right of the plan lines 11-13 -underneath it. J. P. R.] - -[Footnote 10: _Romolontino_ is Romorantin, South of Orleans in -France.] - -_III. Castles and Villas. - -A. Castles. - -Pl. LXXX, No. 1 (P. V. fol. 39b; No. d'ordre 2282). The fortified -place here represented is said by Vallardi to be the_ "castello" _at -Milan, but without any satisfactory reason. The high tower behind -the_ "rivellino" _ravelin--seems to be intended as a watch-tower. - -Pl. LXXX, No. 2 (MS. B, 23b). A similarly constructed tower probably -intended for the same use. - -Pl. LXXX, No. 3 (MS. B). Sketches for corner towers with steps for a -citadel. - -Pl. LXXX, No. 4 (W. XVI). A cupola crowning a corner tower; an -interesting example of decorative fortification. In this -reproduction of the original pen and ink drawing it appears -reversed. - -B. Projects for Palaces. - -Pl. LXXXI, No. 2 (MS. C. A, 75b; 221a, see No. 748). Project for a -royal residence at Amboise in France. - -Pl. LXXXII, No. 1 (C. A 308a; 939a). A plan for a somewhat extensive -residence, and various details; but there is no text to elucidate -it; in courts are written the three names: - -Sam cosi giova - _(St. Mark)_ _(Cosmo)_ _(John)_, -arch mo nino - -C. Plans for small castles or Villas. - -The three following sketches greatly resemble each other. Pl. -LXXXII, No. 2 (MS. K3 36b; see No. 749)._ - -_Pl. LXXXII, No. 3 (MS. B 60a; See No. 750). - -Pl. LXXXIII (W. XVII). The text on this sheet refers to Cyprus (see -Topographical Notes No. 1103), but seems to have no direct -connection with the sketches inserted between. - -Pl. LXXXVIII, Nos. 6 and 7 (MS. B, 12a; see No. 751). A section of a -circular pavilion with the plan of a similar building by the side of -it. These two drawings have a special historical interest because -the text written below mentions the Duke and Duchess of Milan. - -The sketch of a villa on a terrace at the end of a garden occurs in -C. A. 150; and in C. A. 77b; 225b is another sketch of a villa -somewhat resembling the_ Belvedere _of Pope Innocent VIII, at Rome. -In C. A. 62b; 193b there is a Loggia. - -Pl. LXXXII, No. 4 (C. A. 387a; 1198a) is a tower-shaped_ Loggia -_above a fountain. The machinery is very ingeniously screened from -view._ - -748. - -The Palace of the prince must have a piazza in front of it. - -Houses intended for dancing or any kind of jumping or any other -movements with a multitude of people, must be on the ground- floor; -for I have already witnessed the destruction of some, causing death -to many persons, and above all let every wall, be it ever so thin, -rest on the ground or on arches with a good foundation. - -Let the mezzanines of the dwellings be divided by walls made of very -thin bricks, and without wood on account of fire. - -Let all the privies have ventilation [by shafts] in the thickness of -the walls, so as to exhale by the roofs. - -The mezzanines should be vaulted, and the vaults will be stronger in -proportion as they are of small size. - -The ties of oak must be enclosed in the walls in order to be -protected from fire. - -[Footnote: The remarks accompanying the plan reproduced on Pl. -LXXXI, No. 2 are as follows: Above, to the left: "_in_ a _angholo -stia la guardia de la sstalla_" (in the angle _a_ may be the keeper -of the stable). Below are the words "_strada dabosa_" (road to -Amboise), parallel with this "_fossa br 40_" (the moat 40 braccia) -fixing the width of the moat. In the large court surrounded by a -portico "_in terre No.--Largha br.80 e lugha br 120_." To the right -of the castle is a large basin for aquatic sports with the words -"_Giostre colle nave cioe li giostra li stieno sopra le na_" -(Jousting in boats that is the men are to be in boats). J. P. R.] - -The privies must be numerous and going one into the other in order -that the stench may not penetrate into the dwellings., and all their -doors must shut off themselves with counterpoises. - -The main division of the facade of this palace is into two portions; -that is to say the width of the court-yard must be half the whole -facade; the 2nd ... - -749. - -30 braccia wide on each side; the lower entrance leads into a hall -10 braccia wide and 30 braccia long with 4 recesses each with a -chimney. - -[Footnote: On each side of the castle, Pl. LXXXII. No. 2 there are -drawings of details, to the left "_Camino_" a chimney, to the right -the central lantern, sketched in red "_8 lati_" _i.e._ an octagon.] - -750. - -The firststorey [or terrace] must be entirely solid. - -751. - -The pavilion in the garden of the Duchess of Milan. - -The plan of the pavilion which is in the middle of the labyrinth of -the Duke of Milan. - -[Footnote: This passage was first published by AMORETTI in _Memorie -Storiche_ Cap. X: Una sua opera da riportarsi a quest' anno fu il -bagno fatto per la duchessa Beatrice nel parco o giardino del -Castello. Lionardo non solo ne disegno il piccolo edifizio a foggia -di padiglione, nel cod. segnato Q. 3, dandone anche separatamente la -pianta; ma sotto vi scrisse: Padiglione del giardino della duchessa; -e sotto la pianta: Fondamento del padiglione ch'e nel mezzo del -labirinto del duca di Milano; nessuna data e presso il padiglione, -disegnato nella pagina 12, ma poco sopra fra molti circoli -intrecciati vedesi = 10 Luglio 1492 = e nella pagina 2 presso ad -alcuni disegni di legumi qualcheduno ha letto Settembre 1482 in vece -di 1492, come dovea scriverevi, e probabilmente scrisse Lionardo. - -The original text however hardly bears the interpretation put upon -it by AMORETTI. He is mistaken as to the mark on the MS. as well as -in his statements as to the date, for the MS. in question has no -date; the date he gives occurs, on the contrary, in another -note-book. Finally, it appears to me quite an open question whether -Leonardo was the architect who carried out the construction of the -dome-like Pavilion here shown in section, or of the ground plan of -the Pavilion drawn by the side of it. Must we, in fact, suppose that -"_il duca di Milano_" here mentioned was, as has been generally -assumed, Ludovico il Moro? He did not hold this title from the -Emperor before 1494; till that date he was only called _Governatore_ -and Leonardo in speaking of him, mentions him generally as "_il -Moro_" even after 1494. On January 18, 1491, he married Beatrice -d'Este the daughter of Ercole I, Duke of Ferrara. She died on the -2nd January 1497, and for the reasons I have given it seems -improbable that it should be this princess who is here spoken of as -the "_Duchessa di Milano_". From the style of the handwriting it -appears to me to be beyond all doubt that the MS. B, from which this -passage is taken, is older than the dated MSS. of 1492 and 1493. In -that case the Duke of Milan here mentioned would be Gian Galeazzo -(1469-1494) and the Duchess would be his wife Isabella of Aragon, to -whom he was married on the second February 1489. J. P. R.] - -752. - -The earth that is dug out from the cellars must be raised on one -side so high as to make a terrace garden as high as the level of the -hall; but between the earth of the terrace and the wall of the -house, leave an interval in order that the damp may not spoil the -principal walls. - -_IV. Ecclesiastical Architecture. - -A. General Observations._ - -753. - -A building should always be detached on all sides so that its form -may be seen. - -[Footnote: The original text is reproduced on Pl. XCII, No. 1 to the -left hand at the bottom.] - -754. - -Here there cannot and ought not to be any _campanile_; on the -contrary it must stand apart like that of the Cathedral and of San -Giovanni at Florence, and of the Cathedral at Pisa, where the -campanile is quite detached as well as the dome. Thus each can -display its own perfection. If however you wish to join it to the -church, make the lantern serve for the campanile as in the church at -Chiaravalle. - -[Footnote: This text is written by the side of the plan given on Pl. -XCI. No. 2.] - -[Footnote 12: The Abbey of Chiaravalle, a few miles from Milan, has -a central tower on the intersection of the cross in the style of -that of the Certosa of Pavia, but the style is mediaeval (A. D. -1330). Leonardo seems here to mean, that in a building, in which the -circular form is strongly conspicuous, the campanile must either be -separated, or rise from the centre of the building and therefore -take the form of a lantern.] - -755. - -It never looks well to see the roofs of a church; they should rather -be flat and the water should run off by gutters made in the frieze. - -[Footnote: This text is to the left of the domed church reproduced -on Pl. LXXXVII, No. 2.] - -_B. The theory of Dome Architecture. - -This subject has been more extensively treated by Leonardo in -drawings than in writing. Still we may fairly assume that it was his -purpose, ultimately to embody the results of his investigation in a_ -"Trattato delle Cupole." _The amount of materials is remarkably -extensive. MS. B is particularly rich in plans and elevations of -churches with one or more domes--from the simplest form to the most -complicated that can be imagined. Considering the evident connexion -between a great number of these sketches, as well as the -impossibility of seeing in them designs or preparatory sketches for -any building intended to be erected, the conclusion is obvious that -they were not designed for any particular monument, but were -theoretical and ideal researches, made in order to obtain a clear -understanding of the laws which must govern the construction of a -great central dome, with smaller ones grouped round it; and with or -without the addition of spires, so that each of these parts by -itself and in its juxtaposition to the other parts should produce -the grandest possible effect. - -In these sketches Leonardo seems to have exhausted every imaginable -combination. [Footnote 1: In MS. B, 32b (see Pl. C III, No. 2) we -find eight geometrical patterns, each drawn in a square; and in MS. -C.A., fol. 87 to 98 form a whole series of patterns done with the -same intention.] The results of some of these problems are perhaps -not quite satisfactory; still they cannot be considered to give -evidence of a want of taste or of any other defect in Leonardo s -architectural capacity. They were no doubt intended exclusively for -his own instruction, and, before all, as it seems, to illustrate the -features or consequences resulting from a given principle._ - -_I have already, in another place,_ [Footnote 1: Les Projets -Primitifs pour la Basilique de St. Pierre de Rome, par Bramante, -Raphael etc.,Vol. I, p. 2.] _pointed out the law of construction for -buildings crowned by a large dome: namely, that such a dome, to -produce the greatest effect possible, should rise either from the -centre of a Greek cross, or from the centre of a structure of which -the plan has some symmetrical affinity to a circle, this circle -being at the same time the centre of the whole plan of the building. - -Leonardo's sketches show that he was fully aware, as was to be -expected, of this truth. Few of them exhibit the form of a Latin -cross, and when this is met with, it generally gives evidence of the -determination to assign as prominent a part as possible to the dome -in the general effect of the building. - -While it is evident, on the one hand, that the greater number of -these domes had no particular purpose, not being designed for -execution, on the other hand several reasons may be found for -Leonardo's perseverance in his studies of the subject. - -Besides the theoretical interest of the question for Leonardo and -his_ Trattato _and besides the taste for domes prevailing at that -time, it seems likely that the intended erection of some building of -the first importance like the Duomos of Pavia and Como, the church -of Sta. Maria delle Grazie at Milan, and the construction of a Dome -or central Tower_ (Tiburio) _on the cathedral of Milan, may have -stimulated Leonardo to undertake a general and thorough -investigation of the subject; whilst Leonardo's intercourse with -Bramante for ten years or more, can hardly have remained without -influence in this matter. In fact now that some of this great -Architect's studies for S. Peter's at Rome have at last become -known, he must be considered henceforth as the greatest master of -Dome-Architecture that ever existed. His influence, direct or -indirect even on a genius like Leonardo seems the more likely, since -Leonardo's sketches reveal a style most similar to that of Bramante, -whose name indeed, occurs twice in Leonardo's manuscript notes. It -must not be forgotten that Leonardo was a Florentine; the -characteristic form of the two principal domes of Florence, Sta. -Maria del Fiore and the Battisterio, constantly appear as leading -features in his sketches. - -The church of San Lorenzo at Milan, was at that time still intact. -The dome is to this day one of the most wonderful cupolas ever -constructed, and with its two smaller domes might well attract the -attention and study of a never resting genius such as Leonardo. A -whole class of these sketches betray in fact the direct influence of -the church of S. Lorenzo, and this also seems to have suggested the -plan of Bramante's dome of St. Peter's at Rome. - -In the following pages the various sketches for the construction of -domes have been classified and discussed from a general point of -view. On two sheets: Pl. LXXXIV (C.A. 354b; 118a) and Pl. LXXXV, -Nos. 1-11 (Ash. II, 6b) we see various dissimilar types, grouped -together; thus these two sheets may be regarded as a sort of -nomenclature of the different types, on which we shall now have to -treat._ - -_1. Churches formed on the plan of a Greek cross. - -Group I. - -Domes rising from a circular base. - -The simplest type of central building is a circular edifice. - -Pl. LXXXIV, No. 9. Plan of a circular building surrounded by a -colonnade. - -Pl. LXXXIV, No. 8. Elevation of the former, with a conical roof. - -Pl. XC. No. 5. A dodecagon, as most nearly approaching the circle. - -Pl. LXXXVI, No. 1, 2, 3. Four round chapels are added at the -extremities of the two principal axes;--compare this plan with fig. -1 on p. 44 and fig. 3 on p. 47 (W. P. 5b) where the outer wall is -octagonal. - -Group II. - -Domes rising from a square base. - -The plan is a square surrounded by a colonnade, and the dome seems -to be octagonal. - -Pl. LXXXIV. The square plan below the circular building No. 8, and -its elevation to the left, above the plan: here the ground-plan is -square, the upper storey octagonal. A further development of this -type is shown in two sketches C. A. 3a (not reproduced here), and in - -Pl. LXXXVI, No. 5 (which possibly belongs to No. 7 on Pl. LXXXIV). - -Pl, LXXXV, No. 4, and p. 45, Fig. 3, a Greek cross, repeated p. 45, -Fig. 3, is another development of the square central plan. - -The remainder of these studies show two different systems; in the -first the dome rises from a square plan,--in the second from an -octagonal base._ - -_Group III. - -Domes rising from a square base and four pillars. [Footnote 1: The -ancient chapel San Satiro, via del Falcone, Milan, is a specimen of -this type.]_ - -a) First type. _A Dome resting on four pillars in the centre of a -square edifice, with an apse in the middle, of each of the four -sides. We have eleven variations of this type. - -aa) Pl. LXXXVIII, No. 3. - -bb) Pl. LXXX, No. 5. - -cc) Pl. LXXXV, Nos. 2, 3, 5. - -dd) Pl. LXXXIV, No. 1 and 4 beneath. - -ee) Pl. LXXXV, Nos. 1, 7, 10, 11._ - -b) Second type. _This consists in adding aisles to the whole plan of -the first type; columns are placed between the apses and the aisles; -the plan thus obtained is very nearly identical with that of S. -Lorenzo at Milan. - -Fig. 1 on p. 56. (MS. B, 75a) shows the result of this treatment -adapted to a peculiar purpose about which we shall have to say a few -words later on. - -Pl. XCV, No. 1, shows the same plan but with the addition of a short -nave. This plan seems to have been suggested by the general -arrangement of S. Sepolcro at Milan. - -MS. B. 57b (see the sketch reproduced on p.51). By adding towers in -the four outer angles to the last named plan, we obtain a plan which -bears the general features of Bramante's plans for S. Peter's at -Rome. [Footnote 2: See_ Les projets primitifs _etc., Pl. 9-12.] (See -p. 51 Fig. 1.) - -Group IV. - -Domes rising from an octagonal base. - -This system, developed according to two different schemes, has given -rise to two classes with many varieties. - -In a) On each side of the octagon chapels of equal form are added. - -In b) The chapels are dissimilar; those which terminate the -principal axes being different in form from those which are added on -the diagonal sides of the octagon. - -a. First Class. - -The Chapel_ "degli Angeli," _at Florence, built only to a height of -about 20 feet by Brunellesco, may be considered as the prototype of -this group; and, indeed it probably suggested it. The fact that we -see in MS. B. 11b (Pl. XCIV, No. 3) by the side of Brunellesco's -plan for the Basilica of Sto. Spirito at Florence, a plan almost -identical with that of the_ Capella degli Angeli, _confirms this -supposition. Only two small differences, or we may say improvements, -have been introduced by Leonardo. Firstly the back of the chapels -contains a third niche, and each angle of the Octagon a folded -pilaster like those in Bramante's_ Sagrestia di S. M. presso San -Satiro _at Milan, instead of an interval between the two pilasters -as seen in the Battistero at Florence and in the Sacristy of Sto. -Spirito in the same town and also in the above named chapel by -Brunellesco. - -The first set of sketches which come under consideration have at -first sight the appearance of mere geometrical studies. They seem to -have been suggested by the plan given on page 44 Fig. 2 (MS. B, 55a) -in the centre of which is written_ "Santa Maria in perticha da -Pavia", _at the place marked A on the reproduction. - -a) (MS. B, 34b, page 44 Fig. 3). In the middle of each side a column -is added, and in the axes of the intercolumnar spaces a second row -of columns forms an aisle round the octagon. These are placed at the -intersection of a system of semicircles, of which the sixteen -columns on the sides of the octagon are the centres. - -b) The preceding diagram is completed and becomes more monumental in -style in the sketch next to it (MS. B, 35a, see p. 45 Fig. 1). An -outer aisle is added by circles, having for radius the distance -between the columns in the middle sides of the octagon. - -c) (MS. B. 96b, see p. 45 Fig. 2). Octagon with an aisle round it; -the angles of both are formed by columns. The outer sides are formed -by 8 niches forming chapels. The exterior is likewise octagonal, -with the angles corresponding to the centre of each of the interior -chapels. - -Pl. XCII, No. 2 (MS. B. 96b). Detail and modification of the -preceding plan--half columns against piers--an arrangement by which -the chapels of the aisle have the same width of opening as the inner -arches between the half columns. Underneath this sketch the -following note occurs:_ questo vole - avere 12 facce - co 12 -tabernaculi - come - _a_ - _b_. _(This will have twelve sides with -twelve tabernacles as_ a b._) In the remaining sketches of this -class the octagon is not formed by columns at the angles. - -The simplest type shows a niche in the middle of each side and is -repeated on several sheets, viz: MS. B 3; MS. C.A. 354b (see Pl. -LXXXIV, No. 11) and MS. Ash II 6b; (see Pl. LXXXV, No. 9 and the -elevations No. 8; Pl. XCII, No. 3; MS. B. 4b [not reproduced here] -and Pl. LXXXIV, No. 2)._ - -_Pl. XCII, 3 (MS. B, 56b) corresponds to a plan like the one in MS. -B 35a, in which the niches would be visible outside or, as in the -following sketch, with the addition of a niche in the middle of each -chapel. - -Pl. XC, No. 6. The niches themselves are surrounded by smaller -niches (see also No. 1 on the same plate). - -Octagon expanded on each side. - -A. by a square chapel: - -MS. B. 34b (not reproduced here). - -B. by a square with 3 niches: - -MS. B. 11b (see Pl. XCIV, No. 3). - -C. by octagonal chapels: - -a) MS. B, 21a; Pl. LXXXVIII, No. 4. - -b) No. 2 on the same plate. Underneath there is the remark:_ -"quest'e come le 8 cappele ano a essere facte" _(this is how the -eight chapels are to be executed). - -c) Pl. LXXXVIII, No. 5. Elevation to the plans on the same sheet, it -is accompanied by the note:_ "ciasscuno de' 9 tiburi no'uole - -passare l'alteza - di - 2 - quadri" _(neither of the 9 domes must -exceed the height of two squares). - -d) Pl. LXXXVIII, No. 1. Inside of the same octagon. MS. B, 30a, and -34b; these are three repetitions of parts of the same plan with very -slight variations. - -D. by a circular chapel: - -MS. B, 18a (see Fig. 1 on page 47) gives the plan of this -arrangement in which the exterior is square on the ground floor with -only four of the chapels projecting, as is explained in the next -sketch. - -Pl. LXXXIX, MS. B, 17b. Elevation to the preceding plan sketched on -the opposite side of the sheet, and also marked A. It is accompanied -by the following remark, indicating the theoretical character of -these studies:_ questo - edifitio - anchora - starebbe - bene -affarlo dalla linja - _a_ - _b_ - _c_ - _d_ - insu. _("This edifice -would also produce a good effect if only the part above the lines_ a -b, c d, _were executed"). - -Pl. LXXXIV, No. 11. The exterior has the form of an octagon, but the -chapels project partly beyond it. On the left side of the sketch -they appear larger than on the right side. - -Pl. XC, No. 1, (MS. B, 25b); Repetition of Pl. LXXXIV, No. 11. - -Pl. XC, No. 2. Elevation to the plan No. 1, and also to No. 6 of the -same sheet._ - -_E. By chapels formed by four niches: - -Pl. LXXXIV, No. 7 (the circular plan on the left below) shows this -arrangement in which the central dome has become circular inside and -might therefore be classed after this group. [Footnote 1: This plan -and some others of this class remind us of the plan of the Mausoleum -of Augustus as it is represented for instance by Durand. See_ Cab. -des Estampes, Bibliotheque Nationale, Paris, Topographie de Rome, V, -6, 82._] - -The sketch on the right hand side gives most likely the elevation -for the last named plan. - -F. By chapels of still richer combinations, which necessitate an -octagon of larger dimensions: - -Pl. XCI, No. 2 (MS. Ash. 11. 8b) [Footnote 2: The note accompanying -this plan is given under No. 754.]; on this plan the chapels -themselves appear to be central buildings formed like the first type -of the third group. Pl. LXXXVIII, No. 3. - -Pl. XCI, No. 2 above; the exterior of the preceding figure, -particularly interesting on account of the alternation of apses and -niches, the latter containing statues of a gigantic size, in -proportion to the dimension of the niches. - -b. Second Class. - -Composite plans of this class are generally obtained by combining -two types of the first class--the one worked out on the principal -axes, the other on the diagonal ones. - -MS. B. 22 shows an elementary combination, without any additions on -the diagonal axes, but with the dimensions of the squares on the two -principal axes exceeding those of the sides of the octagon. - -In the drawing W. P. 5b (see page 44 Fig. 1) the exterior only of -the edifice is octagonal, the interior being formed by a circular -colonnade; round chapels are placed against the four sides of the -principal axes. - -The elevation, drawn on the same sheet (see page 47 Fig. 3), shows -the whole arrangement which is closely related with the one on Pl. -LXXXVI No. 1, 2. - -MS. B. 21a shows: - -a) four sides with rectangular chapels crowned by pediments Pl. -LXXXVII No. 3 (plan and elevation); - -b) four sides with square chapels crowned by octagonal domes. Pl. -LXXXVII No. 4; the plan underneath. - -MS. B. 18a shows a variation obtained by replacing the round chapels -in the principal axes of the sketch MS. B. l8a by square ones, with -an apse. Leonardo repeated both ideas for better comparison side by -side, see page 47. Fig. 2. - -Pl. LXXXIX (MS. B. 17b). Elevation for the preceding figure. The -comparison of the drawing marked M with the plan on page 47 Fig. 2, -bearing the same mark, and of the elevation on Pl. LXXXIX below -(marked A) with the corresponding plan on page 47 is highly -instructive, as illustrating the spirit in which Leonardo pursued -these studies. - -Pl. LXXXIV No. 12 shows the design Pl. LXXXVII No. 3 combined with -apses, with the addition of round chapels on the diagonal sides. - -Pl. LXXXIV No. 13 is a variation of the preceding sketch. - -Pl. XC No. 3. MS. B. 25b. The round chapels of the preceding sketch -are replaced by octagonal chapels, above which rise campaniles. - -Pl. XC No. 4 is the elevation for the preceding plan. - -Pl. XCII No. 1. (MS. B. 39b.); the plan below. On the principal as -well as on the diagonal axes are diagonal chapels, but the latter -are separated from the dome by semicircular recesses. The -communication between these eight chapels forms a square aisle round -the central dome. - -Above this figure is the elevation, showing four campaniles on the -angles. [Footnote 1: The note accompanying this drawing is -reproduced under No. 753.] - -Pl. LXXXIV No. 3. On the principal axes are square chapels with -three niches; on the diagonals octagonal chapels with niches. Cod. -Atl. 340b gives a somewhat similar arrangement. - -MS. B. 30. The principal development is thrown on the diagonal axes -by square chapels with three niches; on the principal axes are inner -recesses communicating with outer ones. - -The plan Pl. XCIII No. 2 (MS. B. 22) differs from this only in so -far as the outer semicircles have become circular chapels, -projecting from the external square as apses; one of them serves as -the entrance by a semicircular portico. - -The elevation is drawn on the left side of the plan. - -MS. B. 19. A further development of MS. B. 18, by employing for the -four principal chapels the type Pl. LXXXVIII No. 3, as we have -already seen in Pl. XCI No. 2; the exterior presents two varieties. - -a) The outer contour follows the inner. [Footnote 2: These chapels -are here sketched in two different sizes; it is the smaller type -which is thus formed.] - -b) It is semicircular. - -Pl. LXXXVII No. 2 (MS. B. 18b) Elevation to the first variation MS. -B. 19. If we were not certain that this sketch was by Leonardo, we -might feel tempted to take it as a study by Bramante for St. Peter's -at Rome. [Footnote 3: See_ Les projets primitifs Pl. 43._]_ - -_MS. P. V. 39b. In the principal axes the chapels of MS. B. 19, and -semicircular niches on the diagonals. The exterior of the whole -edifice is also an octagon, concealing the form of the interior -chapels, but with its angles on their axes. - -Group V. - -Suggested by San Lorenzo at Milan. - -In MS. C. A. 266 IIb, 8l2b there is a plan almost identical with -that of San Lorenzo. The diagonal sides of the irregular octagon are -not indicated. - -If it could be proved that the arches which, in the actual church, -exist on these sides in the first story, were added in 1574 by -Martimo Bassi, then this plan and the following section would be -still nearer the original state of San Lorenzo than at present. A -reproduction of this slightly sketched plan has not been possible. -It may however be understood from Pl. LXXXVIII No. 3, by suppressing -the four pillars corresponding to the apses. - -Pl. LXXXVII No. 1 shows the section in elevation corresponding with -the above-named plan. The recessed chapels are decorated with large -shells in the halfdomes like the arrangement in San Lorenzo, but -with proportions like those of Bramante's Sacristy of Santa Maria -presso S. Satiro. - -MS. C. A. 266; a sheet containing three views of exteriors of Domes. -On the same sheet there is a plan similar to the one above-named but -with uninterrupted aisles and with the addition of round chapels in -the axes (compare Pl. XCVII No. 3 and page 44 Fig. 1), perhaps a -reminiscence of the two chapels annexed to San Lorenzo.--Leonardo -has here sketched the way of transforming this plan into a Latin -cross by means of a nave with side aisles. - -Pl. XCI No. 1. Plan showing a type deprived of aisles and comprised -in a square building which is surrounded by a portico. It is -accompanied by the following text:_ - -756. - -This edifice is inhabited [accessible] below and above, like San -Sepolcro, and it is the same above as below, except that the upper -story has the dome _c d_; and the [Footnote: The church of San -Sepolcro at Milan, founded in 1030 and repeatedly rebuilt after the -middle of the XVIth century, still stands over the crypt of the -original structure.] lower has the dome _a b_, and when you enter -into the crypt, you descend 10 steps, and when you mount into the -upper you ascend 20 steps, which, with 1/3 braccio for each, make 10 -braccia, and this is the height between one floor of the church and -the other. - -_Above the plan on the same sheet is a view of the exterior. By the -aid of these two figures and the description, sections of the -edifice may easily be reconstructed. But the section drawn on the -left side of the building seems not to be in keeping with the same -plan, notwithstanding the explanatory note written underneath it: -"dentro il difitio di sopra" (interior of the edifice -above)[Footnote 1: _The small inner dome corresponds to_ a b _on the -plan--it rises from the lower church into the upper-- above, and -larger, rises the dome_ c d. _The aisles above and below thus -correspond_ (e di sopra come di sotto, salvoche etc.). _The only -difference is, that in the section Leonardo has not taken the -trouble to make the form octagonal, but has merely sketched circular -lines in perspective._ J. P. R._]. - -_Before leaving this group, it is well to remark that the germ of it -seems already indicated by the diagonal lines in the plans Pl. LXXXV -No. 11 and No. 7. We shall find another application of the same type -to the Latin cross in Pl. XCVII No. 3. - -_2. Churches formed on the plan of a Latin cross. - -We find among Leonardo's studies several sketches for churches on -the plan of the Latin cross; we shall begin by describing them, and -shall add a few observations. - -A. Studies after existing Monuments. - -Pl. XCIV No. 2. (MS. B. 11b.) Plan of Santo Spirito at Florence, a -basilica built after the designs of Brunellesco.--Leonardo has added -the indication of a portico in front, either his own invention or -the reproduction of a now lost design. - -Pl. XCV No. 2. Plan accompanied by the words: "A_ e santo sepolcro -di milano di sopra"(A _is the upper church of S. Sepolcro at Milan); -although since Leonardo's time considerably spoilt, it is still the -same in plan. - -The second plan with its note: "B_ e la sua parte socto tera" (B _is -its subterranean part [the crypt]) still corresponds with the -present state of this part of the church as I have ascertained by -visiting the crypt with this plan. Excepting the addition of a few -insignificant walls, the state of this interesting part of the -church still conforms to Leonardo's sketch; but in the Vestibolo the -two columns near the entrance of the winding stairs are absent. - -B. Designs or Studies. - -PL. XCV No. 1. Plan of a church evidently suggested by that of San -Sepolcro at Milan. The central part has been added to on the -principle of the second type of Group III. Leonardo has placed the_ -"coro" _(choir) in the centre._ - -_Pl. XCVI No. 2. In the plan the dome, as regards its interior, -belongs to the First Class of Group IV, and may be grouped with the -one in MS. B. 35a. The nave seems to be a development of the type -represented in Pl. XCV No. 2, B. by adding towers and two lateral -porticos[Footnote 1: Already published in Les projets primitifs Pl. -XLIII.]. - -On the left is a view of the exterior of the preceding plan. It is -accompanied by the following note:_ - -757. - -This building is inhabited below and above; the way up is by the -campaniles, and in going up one has to use the platform, where the -drums of the four domes are, and this platform has a parapet in -front, and none of these domes communicate with the church, but they -are quite separate. - -_Pl. XCVI No. 1 (MS. C. A. 16b; 65a). Perspective view of a church -seen from behind; this recalls the Duomo at Florence, but with two -campaniles[Footnote 2: Already published in the Saggio Pl. IX.]. - -Pl. XCVII No. 3 (MS. B. 52a). The central part is a development of -S. Lorenzo at Milan, such as was executed at the Duomo of Pavia. -There is sufficient analogy between the building actually executed -and this sketch to suggest a direct connection between them. -Leonardo accompanied Francesco di Giorgio[Footnote 3: See MALASPINA, -il Duomo di Pavia. Documents.] when the latter was consulted on June -21st, 1490 as to this church; the fact that the only word -accompanying the plan is:_ "sagrestia", _seems to confirm our -supposition, for the sacristies were added only in 1492, i. e. four -years after the beginning of the Cathedral, which at that time was -most likely still sufficiently unfinished to be capable of receiving -the form of the present sketch. - -Pl. XCVII No. 2 shows the exterior of this design. Below is the -note:_ edifitio al proposito del fodameto figurato di socto -_(edifice proper for the ground plan figured below). - -Here we may also mention the plan of a Latin cross drawn in MS. C. -A. fol. 266 (see p. 50). - -Pl. XCIV No. 1 (MS. L. 15b). External side view of Brunellesco's -Florentine basilica San Lorenzo, seen from the North. - -Pl. XCIV No. 4 (V. A. V, 1). Principal front of a nave, most likely -of a church on the plan of a Latin cross. We notice here not only -the principal features which were employed afterwards in Alberti's -front of S. Maria Novella, but even details of a more advanced -style, such as we are accustomed to meet with only after the year -1520. - -In the background of Leonardo's unfinished picture of St. Jerome -(Vatican Gallery) a somewhat similar church front is indicated (see -the accompanying sketch). - -[Illustration with caption: The view of the front of a temple, -apparently a dome in the centre of four corinthian porticos bearing -pediments (published by Amoretti Tav. II. B as being by Leonardo), -is taken from a drawing, now at the Ambrosian Gallery. We cannot -consider this to be by the hand of the master.]_ - -_C. Studies for a form of a Church most proper for preaching. - -The problem as to what form of church might answer the requirements -of acoustics seems to have engaged Leonardo's very particular -attention. The designation of_ "teatro" _given to some of these -sketches, clearly shows which plan seemed to him most favourable for -hearing the preacher's voice. - -Pl. XCVII, No. 1 (MS. B, 52). Rectangular edifice divided into three -naves with an apse on either side, terminated by a semicircular -theatre with rising seats, as in antique buildings. The pulpit is in -the centre. Leonardo has written on the left side of the sketch_: -"teatro da predicare" _(Theatre for preaching). - -MS. B, 55a (see page 56, Fig. 1). A domed church after the type of -Pl. XCV, No. 1, shows four theatres occupying the apses and facing -the square_ "coro" _(choir), which is in the centre between the four -pillars of the dome.[Footnote 1: The note_ teatro de predicar, _on -the right side is, I believe, in the handwriting of Pompeo Leoni. J. -P. R.] The rising arrangement of the seats is shown in the sketch -above. At the place marked_ B _Leonardo wrote_ teatri per uldire -messa _(rows of seats to hear mass), at_ T teatri,_ and at_ C coro -_(choir). - -In MS. C.A. 260, are slight sketches of two plans for rectangular -choirs and two elevations of the altar and pulpit which seem to be -in connection with these plans. - -In MS. Ash II, 8a (see p. 56 and 57. Fig. 2 and 3)._ "Locho dove si -predica" _(Place for preaching). A most singular plan for a -building. The interior is a portion of a sphere, the centre of which -is the summit of a column destined to serve as the preacher's -pulpit. The inside is somewhat like a modern theatre, whilst the -exterior and the galleries and stairs recall the ancient -amphitheatres. - -[Illustration with caption: Page 57, Fig. 4. A plan accompanying the -two preceding drawings. If this gives the complete form Leonardo -intended for the edifice, it would have comprised only about two -thirds of the circle. Leonardo wrote in the centre_ "fondamento", _a -word he often employed for plans, and on the left side of the view -of the exterior:_ locho dove si predicha _(a place for preaching -in)._] - -_D. Design for a Mausoleum. - -Pl. XCVIII (P. V., 182._ No. d'ordre 2386). In the midst of a hilly -landscape rises an artificial mountain in the form of a gigantic -cone, crowned by an imposing temple. At two thirds of the height a -terrace is cut out with six doorways forming entrances to galleries, -each leading to three sepulchral halls, so constructed as to contain -about five hundred funeral urns, disposed in the customary antique -style. From two opposite sides steps ascend to the terrace in a -single flight and beyond it to the temple above. A large circular -opening, like that in the Pantheon, is in the dome above what may be -the altar, or perhaps the central monument on the level of the -terrace below. - -The section of a gallery given in the sketch to the right below -shows the roof to be constructed on the principle of superimposed -horizontal layers, projecting one beyond the other, and each -furnished with a sort of heel, which appears to be undercut, so as -to give the appearance of a beam from within. Granite alone would be -adequate to the dimensions here given to the key stone, as the -thickness of the layers can hardly be considered to be less than a -foot. In taking this as the basis of our calculation for the -dimensions of the whole construction, the width of the chamber would -be about 25 feet but, judging from the number of urns it -contains--and there is no reason to suppose that these urns were -larger than usual--it would seem to be no more than about 8 or 10 -feet. - -The construction of the vaults resembles those in the galleries of -some etruscan tumuli, for instance the Regulini Galeassi tomb at -Cervetri (lately discovered) and also that of the chamber and -passages of the pyramid of Cheops and of the treasury of Atreus at -Mycenae. - -The upper cone displays not only analogies with the monuments -mentioned in the note, but also with Etruscan tumuli, such as the -Cocumella tomb at Vulci, and the Regulini Galeassi tomb_[Footnote 1: -_See_ FERSGUSON, _Handbook of Architecture, I,_ 291.]. _The whole -scheme is one of the most magnificent in the history of -Architecture. - -It would be difficult to decide as to whether any monument he had -seen suggested this idea to Leonardo, but it is worth while to -enquire, if any monument, or group of monuments of an earlier date -may be supposed to have done so._[Footnote 2: _There are, in -Algiers, two Monuments, commonly called_ "Le Madracen" _and_ "Le -tombeau de la Chretienne," _which somewhat resemble Leonardo's -design. They are known to have served as the Mausolea of the Kings -of Mauritania. Pomponius Mela, the geographer of the time of the -Emperor Claudius, describes them as having been_ "Monumentum commune -regiae gentis." _See_ Le Madracen, Rapport fait par M. le Grand -Rabbin AB. CAHEN, Constantine 1873--Memoire sur les fouilles -executees au Madras'en .. par le Colonel BRUNON, Constantine -l873.--Deux Mausolees Africains, le Madracen et le tombeau de la -Chretienne par M. J. DE LAURIERE, Tours l874.--Le tombeau de la -Chretienne, Mausolee des rois Mauritaniens par M. BERBRUGGER, Alger -1867.--_I am indebted to M. LE BLANC, of the Institut, and M. LUD, -LALANNE, Bibliothecaire of the Institut for having first pointed out -to me the resemblance between these monuments; while M. ANT. HERON -DE VlLLEFOSSE of the Louvre was kind enough to place the -abovementioned rare works at my disposal. Leonardo's observations on -the coast of Africa are given later in this work. The Herodium near -Bethlehem in Palestine_ (Jebel el Fureidis, _the Frank Mountain) -was, according to the latest researches, constructed on a very -similar plan. See_ Der Frankenberg, von Baurath C. SCHICK in -Jerusalem, Zeitschrift des Deutschen Palastina-Vereins, _Leipzag_ -1880, _Vol. III, pages_ 88-99 _and Plates IV and V._ J. P. R.] - -_E. Studies for the Central Tower, or Tiburio of Milan Cathedral. - -Towards the end of the fifteenth century the Fabbricceria del Duomo -had to settle on the choice of a model for the crowning and central -part of this vast building. We learn from a notice published by G. -L. Calvi [Footnote: G. L. CALVI, Notizie sulla vita e sulle opere -dei principali architetti scultori e pittori che fiorirono in -Milano, Part III, 20. See also: H. DE GEYMULLER, Les projets -primitifs etc. I, 37 and 116-119.--The Fabbricceria of the Duomo has -lately begun the publication of the archives, which may possibly -tell us more about the part taken by Leonardo, than has hitherto -been known.] that among the artists who presented models in the year -1488 were: Bramante, Pietro da Gorgonzola, Luca Paperio (Fancelli), -and Leonardo da Vinci.-- - -Several sketches by Leonardo refer to this important project: - -Pl. XCIX, No. 2 (MS. S. K. III, No. 36a) a small plan of the whole -edifice.--The projecting chapels in the middle of the transept are -wanting here. The nave appears to be shortened and seems to be -approached by an inner "vestibolo".-- - -Pl. C, No. 2 (Tr. 21). Plan of the octagon tower, giving the -disposition of the buttresses; starting from the eight pillars -adjoining the four principal piers and intended to support the eight -angles of the Tiburio. These buttresses correspond exactly with -those described by Bramante as existing in the model presented by -Omodeo. [Footnote: Bramante's opinion was first published by G. -MONGERl, Arch. stor. Lomb. V, fasc. 3 and afterwards by me in the -publication mentioned in the preceding note.] - -Pl. C, 3 (MS. Tr. 16). Two plans showing different arrangements of -the buttresses, which seem to be formed partly by the intersection -of a system of pointed arches such as that seen in ** - -Pl. C, No. 5 (MS. B, 27a) destined to give a broader base to the -drum. The text underneath is given under No. 788. - -MS. B, 3--three slight sketches of plans in connexion with the -preceding ones._ - -_Pl. XCIX, No.1 (MS. Tr. 15) contains several small sketches of -sections and exterior views of the Dome; some of them show -buttress-walls shaped as inverted arches. Respecting these Leonardo -notes:_ - -758. - -L'arco rivescio e migliore per fare spalla che l'ordinario, perche -il rovescio trova sotto se muro resistete alla sua debolezza, e -l'ordinario no trova nel suo debole se non aria - -The inverted arch is better for giving a shoulder than the ordinary -one, because the former finds below it a wall resisting its -weakness, whilst the latter finds in its weak part nothing but air. - -[Footnote: _Three slight sketches of sections on the same -leaf--above those reproduced here--are more closely connected with -the large drawing in the centre of Pl. C, No. 4 (M.S, Tr. 41) which -shows a section of a very elevated dome, with double vaults, -connected by ribs and buttresses ingeniously disposed, so as to -bring the weight of the lantern to bear on the base of the dome. - -A sketch underneath it shows a round pillar on which is indicated -which part of its summit is to bear the weight: "il pilastro sara -charicho in . a . b." (The column will bear the weight at a b.) -Another note is above on the right side:_ Larcho regiera tanto sotto -asse chome di sopra se _(The arch supports as much below it [i. e. a -hanging weight] as above it). - -Pl. C, No. 1 (C. A. 303a). Larger sketch of half section of the -Dome, with a very complicated system of arches, and a double vault. -Each stone is shaped so as to be knit or dovetailed to its -neighbours. Thus the inside of the Dome cannot be seen from below. - -MS. C. A. 303b. A repetition of the preceding sketch with very -slight modifications._] - -[Figs. 1. and Fig. 2. two sketeches of the dome] - -MS. Tr. 9 (see Fig. 1 and 2). Section of the Dome with reverted -buttresses between the windows, above which iron anchors or chains -seem to be intended. Below is the sketch of the outside._ - -_PI. XCIX, No. 3 (C. A., 262a) four sketches of the exterior of the -Dome. - -C. A. 12. Section, showing the points of rupture of a gothic vault, -in evident connection with the sketches described above. - -It deserves to be noticed how easily and apparently without effort, -Leonardo manages to combine gothic details and structure with the -more modern shape of the Dome. - -The following notes are on the same leaf,_ oni cosa poderosa, _and_ -oni cosa poderosa desidera de(scendere); _farther below, several -multiplications most likely intended to calculate the weight of some -parts of the Dome, thus 16 x 47 = 720; 720 x 800 = 176000, next to -which is written:_ peso del pilastro di 9 teste _(weight of the -pillar 9 diameters high). - -Below:_ 176000 x 8 = 1408000; _and below:_ - -Semjlio e se ce 80 (?) il peso del tiburio _(six millions six -hundred (?) 80 the weight of the Dome). - -Bossi hazarded the theory that Leonardo might have been the -architect who built the church of Sta. Maria delle Grazie, but there -is no evidence to support this, either in documents or in the -materials supplied by Leonardos manuscripts and drawings. The sketch -given at the side shows the arrangement of the second and third -socle on the apses of the choir of that church; and it is remarkable -that those sketches, in MS. S. K. M. II2, 2a and Ib, occur with the -passage given in Volume I as No. 665 and 666 referring to the -composition of the Last Supper in the Refectory of that church._] - -_F. The Project for lifting up the Battistero of Florence and -setting it on a basement._ - -_Among the very few details Vasari gives as to the architectural -studies of Leonardo, we read: "And among these models and designs -there was one by way of which he showed several times to many -ingenious citizens who then governed Florence, his readiness to lift -up without ruining it, the church of San Giovanni in Florence (the -Battistero, opposite the Duomo) in order to place under it the -missing basement with steps; he supported his assertions with -reasons so persuasive, that while he spoke the undertaking seemed -feasable, although every one of his hearers, when he had departed, -could see by himself the impossibility of so vast an undertaking."_ - -[Footnote: _This latter statement of Vasari's must be considered to -be exaggerated. I may refer here to some data given by_ LIBRI, -Histoire des sciences mathematiques en Italie (II, 216, 217): "On a -cru dans ces derniers temps faire un miracle en mecanique en -effectuant ce transport, et cependant des l'annee 1455, Gaspard Nadi -et Aristote de Fioravantio avaient transporte, a une distance -considerable, la tour de la Magione de Bologne, avec ses fondements, -qui avait presque quatre-vingts pieds de haut. Le continuateur de la -chronique de Pugliola dit que le trajet fut de 35 pieds et que -durant le transport auquel le chroniqueur affirme avoir assiste, il -arriva un accident grave qui fit pencher de trois pieds la tour -pendant qu'elle etait suspendue, mais que cet accident fut -promptement repare (Muratori, Scriptores rer. ital. Tom. XVIII, col. -717, 718). Alidosi a rapporte une note ou Nadi rend compte de ce -transport avec une rare simplicite. D'apres cette note, on voit que -les operations de ce genre n'etaient pas nouvelles. Celle-ci ne -couta que 150 livres (monnaie d'alors) y compris le cadeau que le -Legat fit aux deux mecaniciens. Dans la meme annee, Aristote -redressa le clocher de Cento, qui penchait de plus de cinq pieds -(Alidosi, instruttione p. 188-- Muratori, Scriptores rer. ital., -tom. XXIII, col. 888.--Bossii, chronica Mediol., 1492, in-fol. ad -ann. 1455). On ne concoit pas comment les historiens des beaux-arts -ont pu negliger de tels hommes." J. P. R.] - -_In the MS. C. A. fol. 293, there are two sketches which possibly -might have a bearing on this bold enterprise. We find there a plan -of a circular or polygonal edifice surrounded by semicircular arches -in an oblique position. These may be taken for the foundation of the -steps and of the new platform. In the perspective elevation the same -edifice, forming a polygon, is shown as lifted up and resting on a -circle of inverted arches which rest on an other circle of arches in -the ordinary position, but so placed that the inverted arches above -rest on the spandrels of the lower range._ - -_What seems to confirm the supposition that the lifting up of a -building is here in question, is the indication of engines for -winding up, such as jacks, and a rack and wheel. As the lifting -apparatus represented on this sheet does not seem particularly -applicable to an undertaking of such magnitude, we may consider it -to be a first sketch or scheme for the engines to be used._ - -_G. Description of an unknown Temple._ - -759. - -Twelve flights of steps led up to the great temple, which was eight -hundred braccia in circumference and built on an octagonal plan. At -the eight corners were eight large plinths, one braccia and a half -high, and three wide, and six long at the bottom, with an angle in -the middle; on these were eight great pillars, standing on the -plinths as a foundation, and twenty four braccia high. And on the -top of these were eight capitals three braccia long and six wide, -above which were the architrave frieze and cornice, four braccia and -a half high, and this was carried on in a straight line from one -pillar to the next and so, continuing for eight hundred braccia, -surrounded the whole temple, from pillar to pillar. To support this -entablature there were ten large columns of the same height as the -pillars, three braccia thick above their bases which were one -braccia and a half high. - -The ascent to this temple was by twelve flights of steps, and the -temple was on the twelfth, of an octagonal form, and at each angle -rose a large pillar; and between the pillars were placed ten columns -of the same height as the pillars, rising at once from the pavement -to a height of twenty eight braccia and a half; and at this height -the architrave, frieze and cornice were placed which surrounded the -temple having a length of eight hundred braccia. At the same height, -and within the temple at the same level, and all round the centre of -the temple at a distance of 24 braccia farther in, are pillars -corresponding to the eight pillars in the angles, and columns -corresponding to those placed in the outer spaces. These rise to the -same height as the former ones, and over these the continuous -architrave returns towards the outer row of pillars and columns. - -[Footnote: Either this description is incomplete, or, as seems to me -highly probable, it refers to some ruin. The enormous dimensions -forbid our supposing this to be any temple in Italy or Greece. Syria -was the native land of colossal octagonal buildings, in the early -centuries A. D. The Temple of Baalbek, and others are even larger -than that here described. J. P. R.] - -_V. Palace architecture. - -But a small number of Leonardo's drawings refer to the architecture -of palaces, and our knowledge is small as to what style Leonardo -might have adopted for such buildings. - -Pl. CII No. 1 (W. XVIII). A small portion of a facade of a palace -in two stories, somewhat resembling Alberti's Palazzo -Rucellai.--Compare with this Bramante's painted front of the Casa -Silvestri, and a painting by Montorfano in San Pietro in Gessate at -Milan, third chapel on the left hand side and also with Bramante's -palaces at Rome. The pilasters with arabesques, the rustica between -them, and the figures over the window may be painted or in -sgraffito. The original is drawn in red chalk. - -Pl. LXXXI No. 1 (MS. Tr. 42). Sketch of a palace with battlements -and decorations, most likely graffiti; the details remind us of -those in the Castello at Vigevano._ [Footnote 1: _Count GIULIO -PORRO, in his valuable contribution to the_ Archivio Storico -Lombardo, Anno VIII, Fasc. IV (31 Dec. 1881): Leonardo da Vinci, -Libro di Annotazioni e Memorie, _refers to this in the following -note:_ "Alla pag. 41 vi e uno schizzo di volta ed accanto scrisse: -'il pilastro sara charicho in su 6' e potrebbe darsi che si -riferisse alla cupola della chiesa delle Grazie tanto piu che a -pag. 42 vi e un disegno che rassomiglia assai al basamento che oggi -si vede nella parte esterna del coro di quella chiesa." _This may -however be doubted. The drawing, here referred to, on page 41 of the -same manuscript, is reproduced on Pl. C No. 4 and described on page -61 as being a study for the cupola of the Duomo of Milan._ J. P. R.] - -_MS. Mz. 0", contains a design for a palace or house with a loggia -in the middle of the first story, over which rises an attic with a -Pediment reproduced on page 67. The details drawn close by on the -left seem to indicate an arrangement of coupled columns against the -wall of a first story. - -Pl. LXXXV No. 14 (MS. S. K. M. Ill 79a) contains a very slight -sketch in red chalk, which most probably is intended to represent -the facade of a palace. Inside is the short note 7 he 7 (7 and 7)._ - -_MS. J2 8a (see pages 68 Fig. 1 and 2) contains a view of an unknown -palace. Its plan is indicated at the side._ - -_In MS. Br. M. 126a(see Fig. 3 on page 68) there is a sketch of a -house, on which Leonardo notes; casa con tre terrazi (house with -three terraces)._ - -_Pl. CX, No. 4 (MS. L. 36b) represents the front of a fortified -building drawn at Cesena in 1502 (see No. 1040)._ - -_Here we may also mention the singular building in the allegorical -composition represented on Pl. LVIII in Vol. I. In front of it -appears the head of a sphinx or of a dragon which seems to be -carrying the palace away._ - -_The following texts refer to the construction of palaces and other -buildings destined for private use:_ - -760. - -In the courtyard the walls must be half the height of its width, -that is if the court be 40 braccia, the house must be 20 high as -regards the walls of the said courtyard; and this courtyard must be -half as wide as the whole front. - -[Footnote: See Pl. CI, no. 1, and compare the dimensions here given, -with No. 748 lines 26-29; and the drawing belonging to it Pl. LXXXI, -no. 2.] - -On the dispositions of a stable. - -761. - -FOR MAKING A CLEAN STABLE. - -The manner in which one must arrange a stable. You must first divide -its width in 3 parts, its depth matters not; and let these 3 -divisions be equal and 6 braccia broad for each part and 10 high, -and the middle part shall be for the use of the stablemasters; the 2 -side ones for the horses, each of which must be 6 braccia in width -and 6 in length, and be half a braccio higher at the head than -behind. Let the manger be at 2 braccia from the ground, to the -bottom of the rack, 3 braccia, and the top of it 4 braccia. Now, in -order to attain to what I promise, that is to make this place, -contrary to the general custom, clean and neat: as to the upper part -of the stable, i. e. where the hay is, that part must have at its -outer end a window 6 braccia high and 6 broad, through which by -simple means the hay is brought up to the loft, as is shown by the -machine _E_; and let this be erected in a place 6 braccia wide, and -as long as the stable, as seen at _k p_. The other two parts, which -are on either side of this, are again divided; those nearest to the -hay-loft are 4 braccia, _p s_, and only for the use and circulation -of the servants belonging to the stable; the other two which reach -to the outer walls are 2 braccia, as seen at _s k_, and these are -made for the purpose of giving hay to the mangers, by means of -funnels, narrow at the top and wide over the manger, in order that -the hay should not choke them. They must be well plastered and clean -and are represented at 4 _f s_. As to the giving the horses water, -the troughs must be of stone and above them [cisterns of] water. The -mangers may be opened as boxes are uncovered by raising the lids. -[Footnote: See Pl. LXXVIII, No.1.] - -Decorations for feasts. - -762. - -THE WAY TO CONSTRUCT A FRAME-WORK FOR DECORATING BUILDINGS. - -The way in which the poles ought to be placed for tying bunches of -juniper on to them. These poles must lie close to the framework of -the vaulting and tie the bunches on with osier withes, so as to clip -them even afterwards with shears. - -Let the distance from one circle to another be half a braccia; and -the juniper [sprigs] must lie top downwards, beginning from below. - -Round this column tie four poles to which willows about as thick as -a finger must be nailed and then begin from the bottom and work -upwards with bunches of juniper sprigs, the tops downwards, that is -upside down. [Footnote: See Pl. CII, No. 3. The words here given as -the title line, lines 1--4, are the last in the original MS.--Lines -5--16 are written under fig. 4.] - -763. - -The water should be allowed to fall from the whole circle _a b_. -[Footnote: Other drawings of fountains are given on Pl. CI (W. XX); -the original is a pen and ink drawing on blue paper; on Pl. CIII -(MS. B.) and Pl. LXXXII.] - -_VI. Studies of architectural details._ - -_Several of Leonardo's drawings of architectural details prove that, -like other great masters of that period, he had devoted his -attention to the study of the proportion of such details. As every -organic being in nature has its law of construction and growth, -these masters endeavoured, each in his way, to discover and prove a -law of proportion in architecture. The following notes in Leonardo's -manuscripts refer to this subject._ - -_MS. S. K. M. Ill, 47b (see Fig. 1). A diagram, indicating the rules -as given by Vitruvius and by Leon Battista Alberti for the -proportions of the Attic base of a column._ - -_MS. S. K. M. Ill 55a (see Fig. 2). Diagram showing the same rules._ - -764. - -B toro superiore . . . . . toro superiore -2B nestroli . . . . . . astragali quadre -3B orbiculo . . . . . . . . troclea -4B nestroli . . . . . . astragali quadre -5B toro iferiore . . . . . . toro iferiore -6B latastro . . . . . . . . plintho - -[Footnote: No explanation can be offered of the meaning of the -letter B, which precedes each name. It may be meant for _basa_ -(base). Perhaps it refers to some author on architecture or an -architect (Bramante?) who employed the designations, thus marked for -the mouldings. 3. _troclea._ Philander: _Trochlea sive trochalia aut -rechanum._ 6. _Laterculus_ or _latastrum_ is the Latin name for -_Plinthus_ (pi lambda Xiv) but Vitruvius adopted this Greek name -and "latastro" seems to have been little in use. It is to be found -besides the text given above, as far as I am aware, only two -drawings of the Uffizi Collection, where in one instance, it -indicates the _abacus_ of a Doric capital.] - -765. - -STEPS OF URRBINO. - -The plinth must be as broad as the thickness of the wall against -which the plinth is built. [Footnote: See Pl. CX No. 3. The hasty -sketch on the right hand side illustrates the unsatisfactory effect -produced when the plinth is narrower than the wall.] - -766. - -The ancient architects ...... beginning with the Egyptians (?) who, -as Diodorus Siculus writes, were the first to build and construct -large cities and castles, public and private buildings of fine form, -large and well proportioned ..... - -The column, which has its thickness at the third part .... The one -which would be thinnest in the middle, would break ...; the one -which is of equal thickness and of equal strength, is better for the -edifice. The second best as to the usefulness will be the one whose -greatest thickness is where it joins with the base. - -[Footnote: See Pl. CIII, No. 3, where the sketches belonging to -lines 10--16 are reproduced, but reversed. The sketch of columns, -here reproduced by a wood cut, stands in the original close to lines -5--8.] - -The capital must be formed in this way. Divide its thickness at the -top into 8; at the foot make it 5/7, and let it be 5/7 high and you -will have a square; afterwards divide the height into 8 parts as you -did for the column, and then take 1/8 for the echinus and another -eighth for the thickness of the abacus on the top of the capital. -The horns of the abacus of the capital have to project beyond the -greatest width of the bell 2/7, i. e. sevenths of the top of the -bell, so 1/7 falls to the projection of each horn. The truncated -part of the horns must be as broad as it is high. I leave the rest, -that is the ornaments, to the taste of the sculptors. But to return -to the columns and in order to prove the reason of their strength or -weakness according to their shape, I say that when the lines -starting from the summit of the column and ending at its base and -their direction and length ..., their distance apart or width may be -equal; I say that this column ... - -767. - -The cylinder of a body columnar in shape and its two opposite ends -are two circles enclosed between parallel lines, and through the -centre of the cylinder is a straight line, ending at the centre of -these circles, and called by the ancients the axis. - -[Footnote: Leonardo wrote these lines on the margin of a page of the -Trattato di Francesco di Giorgio, where there are several drawings -of columns, as well as a head drawn in profile inside an outline -sketch of a capital.] - -768. - -_a b_ is 1/3 of _n m_; _m o_ is 1/6 of _r o_. The ovolo projects 1/6 -of _r o_; _s_ 7 1/5 of _r o_, _a b_ is divided into 9 1/2; the -abacus is 3/9 the ovolo 4/9, the bead-moulding and the fillet 2/9 -and 1/2. - -[Footnote: See Pl. LXXXV, No. 16. In the original the drawing and -writing are both in red chalk.] - -_Pl. LXXXV No. 6 (MS. Ash. II 6b) contains a small sketch of a -capital with the following note, written in three lines:_ I chorni -del capitelo deono essere la quarta parte d'uno quadro _(The horns -of a capital must measure the fourth part of a square)._ - -_MS. S. K. M. III 72b contains two sketches of ornamentations of -windows._ - -_In MS. C. A. 308a; 938a (see Pl. LXXXII No. 1) there are several -sketches of columns. One of the two columns on the right is similar -to those employed by Bramante at the Canonica di S. Ambrogio. The -same columns appear in the sketch underneath the plan of a castle. -There they appear coupled, and in two stories one above the other. -The archivolls which seem to spring out of the columns, are shaped -like twisted cords, meant perhaps to be twisted branches. The walls -between the columns seem to be formed out of blocks of wood, the -pedestals are ornamented with a reticulated pattern. From all this -we may suppose that Leonardo here had in mind either some festive -decoration, or perhaps a pavilion for some hunting place or park. -The sketch of columns marked "35" gives an example of columns shaped -like candelabra, a form often employed at that time, particularly in -Milan, and the surrounding districts for instance in the Cortile di -Casa Castiglione now Silvestre, in the cathedral of Como, at Porta -della Rana &c._ - -769. - -CONCERNING ARCHITRAVES OF ONE OR SEVERAL PIECES. - -An architrave of several pieces is stronger than that of one single -piece, if those pieces are placed with their length in the direction -of the centre of the world. This is proved because stones have their -grain or fibre generated in the contrary direction i. e. in the -direction of the opposite horizons of the hemisphere, and this is -contrary to fibres of the plants which have ... - -[Footnote: The text is incomplete in the original.] - -_The Proportions of the stories of a building are indicated by a -sketch in MS. S. K. M. II2 11b (see Pl. LXXXV No. 15). The measures -are written on the left side, as follows: br 1 1/2--6 3/4--br -1/12--2 br--9 e 1/2--1 1/2--br 5--o 9--o 3 [br=braccia; o=oncie]. - -Pl. LXXXV No. 13 (MS. B. 62a) and Pl. XCIII No. 1. (MS. B. 15a) give -a few examples of arches supported on piers._ - -_XIII. - -Theoretical writings on Architecture. - -Leonardo's original writings on the theory of Architecture have come -down to us only in a fragmentary state; still, there seems to be no -doubt that he himself did not complete them. It would seem that -Leonardo entertained the idea of writing a large and connected book -on Architecture; and it is quite evident that the materials we -possess, which can be proved to have been written at different -periods, were noted down with a more or less definite aim and -purpose. They might all be collected under the one title: "Studies -on the Strength of Materials". Among them the investigations on the -subject of fissures in walls are particularly thorough, and very -fully reported; these passages are also especially interesting, -because Leonardo was certainly the first writer on architecture who -ever treated the subject at all. Here, as in all other cases -Leonardo carefully avoids all abstract argument. His data are not -derived from the principles of algebra, but from the laws of -mechanics, and his method throughout is strictly experimental. - -Though the conclusions drawn from his investigations may not have -that precision which we are accustomed to find in Leonardo's -scientific labours, their interest is not lessened. They prove at -any rate his deep sagacity and wonderfully clear mind. No one -perhaps, who has studied these questions since Leonardo, has -combined with a scientific mind anything like the artistic delicacy -of perception which gives interest and lucidity to his observations. - -I do not assert that the arrangement here adopted for the passages -in question is that originally intended by Leonardo; but their -distribution into five groups was suggested by the titles, or -headings, which Leonardo himself prefixed to most of these notes. -Some of the longer sections perhaps should not, to be in strict -agreement with this division, have been reproduced in their entirety -in the place where they occur. But the comparatively small amount of -the materials we possess will render them, even so, sufficiently -intelligible to the reader; it did not therefore seem necessary or -desirable to subdivide the passages merely for the sake of strict -classification._ - -_The small number of chapters given under the fifth class, treating -on the centre of gravity in roof-beams, bears no proportion to the -number of drawings and studies which refer to the same subject. Only -a small selection of these are reproduced in this work since the -majority have no explanatory text._ - -I. - -ON FISSURES IN WALLS. - -770. - -First write the treatise on the causes of the giving way of walls -and then, separately, treat of the remedies. - -Parallel fissures constantly occur in buildings which are erected on -a hill side, when the hill is composed of stratified rocks with an -oblique stratification, because water and other moisture often -penetrates these oblique seams carrying in greasy and slippery soil; -and as the strata are not continuous down to the bottom of the -valley, the rocks slide in the direction of the slope, and the -motion does not cease till they have reached the bottom of the -valley, carrying with them, as though in a boat, that portion of the -building which is separated by them from the rest. The remedy for -this is always to build thick piers under the wall which is -slipping, with arches from one to another, and with a good scarp and -let the piers have a firm foundation in the strata so that they may -not break away from them. - -In order to find the solid part of these strata, it is necessary to -make a shaft at the foot of the wall of great depth through the diff --git a/docs/examples/kernel/davinci2.txt b/docs/examples/kernel/davinci2.txt deleted file mode 100644 index 80966e1..0000000 --- a/docs/examples/kernel/davinci2.txt +++ /dev/null @@ -1,8050 +0,0 @@ -strata; and in this shaft, on the side from which the hill slopes, -smooth and flatten a space one palm wide from the top to the bottom; -and after some time this smooth portion made on the side of the -shaft, will show plainly which part of the hill is moving. - -[Footnote: See Pl. CIV.] - -771. - -The cracks in walls will never be parallel unless the part of the -wall that separates from the remainder does not slip down. - -WHAT IS THE LAW BY WHICH BUILDINGS HAVE STABILITY. - -The stability of buildings is the result of the contrary law to the -two former cases. That is to say that the walls must be all built up -equally, and by degrees, to equal heights all round the building, -and the whole thickness at once, whatever kind of walls they may be. -And although a thin wall dries more quickly than a thick one it will -not necessarily give way under the added weight day by day and thus, -[16] although a thin wall dries more quickly than a thick one, it -will not give way under the weight which the latter may acquire from -day to day. Because if double the amount of it dries in one day, one -of double the thickness will dry in two days or thereabouts; thus -the small addition of weight will be balanced by the smaller -difference of time [18]. - -The adversary says that _a_ which projects, slips down. - -And here the adversary says that _r_ slips and not _c_. - -HOW TO PROGNOSTICATE THE CAUSES OF CRACKS IN ANY SORT OF WALL. - -The part of the wall which does not slip is that in which the -obliquity projects and overhangs the portion which has parted from -it and slipped down. - -ON THE SITUATION OF FOUNDATIONS AND IN WHAT PLACES THEY ARE A CAUSE -OF RUIN. - -When the crevice in the wall is wider at the top than at the bottom, -it is a manifest sign, that the cause of the fissure in the wall is -remote from the perpendicular line through the crevice. - -[Footnote: Lines 1-5 refer to Pl. CV, No. 2. Line 9 _alle due -anteciedete_, see on the same page. - -Lines 16-18. The translation of this is doubtful, and the meaning in -any case very obscure. - -Lines 19-23 are on the right hand margin close to the two sketches -on Pl. CII, No. 3.] - -772. - -OF CRACKS IN WALLS, WHICH ARE WIDE AT THE BOTTOM AND NARROW AT THE -TOP AND OF THEIR CAUSES. - -That wall which does not dry uniformly in an equal time, always -cracks. - -A wall though of equal thickness will not dry with equal quickness -if it is not everywhere in contact with the same medium. Thus, if -one side of a wall were in contact with a damp slope and the other -were in contact with the air, then this latter side would remain of -the same size as before; that side which dries in the air will -shrink or diminish and the side which is kept damp will not dry. And -the dry portion will break away readily from the damp portion -because the damp part not shrinking in the same proportion does not -cohere and follow the movement of the part which dries continuously. - -OF ARCHED CRACKS, WIDE AT THE TOP, AND NARROW BELOW. - -Arched cracks, wide at the top and narrow below are found in -walled-up doors, which shrink more in their height than in their -breadth, and in proportion as their height is greater than their -width, and as the joints of the mortar are more numerous in the -height than in the width. - -The crack diminishes less in _r o_ than in _m n_, in proportion as -there is less material between _r_ and _o_ than between _n_ and _m_. - -Any crack made in a concave wall is wide below and narrow at the -top; and this originates, as is here shown at _b c d_, in the side -figure. - -1. That which gets wet increases in proportion to the moisture it -imbibes. - -2. And a wet object shrinks, while drying, in proportion to the -amount of moisture which evaporates from it. - -[Footnote: The text of this passage is reproduced in facsimile on -Pl. CVI to the left. L. 36-40 are written inside the sketch No. 2. -L. 41-46 are partly written over the sketch No. 3 to which they -refer.] - -773. - -OF THE CAUSES OF FISSURES IN [THE WALLS OF] PUBLIC AND PRIVATE -BUILDINGS. - -The walls give way in cracks, some of which are more or less -vertical and others are oblique. The cracks which are in a vertical -direction are caused by the joining of new walls, with old walls, -whether straight or with indentations fitting on to those of the old -wall; for, as these indentations cannot bear the too great weight of -the wall added on to them, it is inevitable that they should break, -and give way to the settling of the new wall, which will shrink one -braccia in every ten, more or less, according to the greater or -smaller quantity of mortar used between the stones of the masonry, -and whether this mortar is more or less liquid. And observe, that -the walls should always be built first and then faced with the -stones intended to face them. For, if you do not proceed thus, since -the wall settles more than the stone facing, the projections left on -the sides of the wall must inevitably give way; because the stones -used for facing the wall being larger than those over which they are -laid, they will necessarily have less mortar laid between the -joints, and consequently they settle less; and this cannot happen if -the facing is added after the wall is dry. - -_a b_ the new wall, _c_ the old wall, which has already settled; and -the part _a b_ settles afterwards, although _a_, being founded on -_c_, the old wall, cannot possibly break, having a stable foundation -on the old wall. But only the remainder _b_ of the new wall will -break away, because it is built from top to bottom of the building; -and the remainder of the new wall will overhang the gap above the -wall that has sunk. - -774. - -A new tower founded partly on old masonry. - -775. - -OF STONES WHICH DISJOIN THEMSELVES FROM THEIR MORTAR. - -Stones laid in regular courses from bottom to top and built up with -an equal quantity of mortar settle equally throughout, when the -moisture that made the mortar soft evaporates. - -By what is said above it is proved that the small extent of the new -wall between _A_ and _n_ will settle but little, in proportion to -the extent of the same wall between _c_ and _d_. The proportion will -in fact be that of the thinness of the mortar in relation to the -number of courses or to the quantity of mortar laid between the -stones above the different levels of the old wall. - -[Footnote: See Pl. CV, No. 1. The top of the tower is wanting in -this reproduction, and with it the letter _n_ which, in the -original, stands above the letter _A_ over the top of the tower, -while _c_ stands perpendicularly over _d_.] - -776. - -This wall will break under the arch _e f_, because the seven whole -square bricks are not sufficient to sustain the spring of the arch -placed on them. And these seven bricks will give way in their middle -exactly as appears in _a b_. The reason is, that the brick _a_ has -above it only the weight _a k_, whilst the last brick under the arch -has above it the weight _c d x a_. - -_c d_ seems to press on the arch towards the abutment at the point -_p_ but the weight _p o_ opposes resistence to it, whence the whole -pressure is transmitted to the root of the arch. Therefore the foot -of the arch acts like 7 6, which is more than double of _x z_. - -II. - -ON FISSURES IN NICHES. - -777. - -ON FISSURES IN NICHES. - -An arch constructed on a semicircle and bearing weights on the two -opposite thirds of its curve will give way at five points of the -curve. To prove this let the weights be at _n m_ which will break -the arch _a_, _b_, _f_. I say that, by the foregoing, as the -extremities _c_ and _a_ are equally pressed upon by the thrust _n_, -it follows, by the 5th, that the arch will give way at the point -which is furthest from the two forces acting on them and that is the -middle _e_. The same is to be understood of the opposite curve, _d g -b_; hence the weights _n m_ must sink, but they cannot sink by the -7th, without coming closer together, and they cannot come together -unless the extremities of the arch between them come closer, and if -these draw together the crown of the arch must break; and thus the -arch will give way in two places as was at first said &c. - -I ask, given a weight at _a_ what counteracts it in the direction -_n_ _f_ and by what weight must the weight at _f_ be counteracted. - -778. - -ON THE SHRINKING OF DAMP BODIES OF DIFFERENT THICKNESS AND WIDTH. - -The window _a_ is the cause of the crack at _b_; and this crack is -increased by the pressure of _n_ and _m_ which sink or penetrate -into the soil in which foundations are built more than the lighter -portion at _b_. Besides, the old foundation under _b_ has already -settled, and this the piers _n_ and _m_ have not yet done. Hence the -part _b_ does not settle down perpendicularly; on the contrary, it -is thrown outwards obliquely, and it cannot on the contrary be -thrown inwards, because a portion like this, separated from the main -wall, is larger outside than inside and the main wall, where it is -broken, is of the same shape and is also larger outside than inside; -therefore, if this separate portion were to fall inwards the larger -would have to pass through the smaller--which is impossible. Hence -it is evident that the portion of the semicircular wall when -disunited from the main wall will be thrust outwards, and not -inwards as the adversary says. - -When a dome or a half-dome is crushed from above by an excess of -weight the vault will give way, forming a crack which diminishes -towards the top and is wide below, narrow on the inner side and wide -outside; as is the case with the outer husk of a pomegranate, -divided into many parts lengthwise; for the more it is pressed in -the direction of its length, that part of the joints will open most, -which is most distant from the cause of the pressure; and for that -reason the arches of the vaults of any apse should never be more -loaded than the arches of the principal building. Because that which -weighs most, presses most on the parts below, and they sink into the -foundations; but this cannot happen to lighter structures like the -said apses. - -[Footnote: The figure on Pl. CV, No. 4 belongs to the first -paragraph of this passage, lines 1-14; fig. 5 is sketched by the -side of lines l5--and following. The sketch below of a pomegranate -refers to line 22. The drawing fig. 6 is, in the original, over line -37 and fig. 7 over line 54.] - -Which of these two cubes will shrink the more uniformly: the cube -_A_ resting on the pavement, or the cube _b_ suspended in the air, -when both cubes are equal in weight and bulk, and of clay mixed with -equal quantities of water? - -The cube placed on the pavement diminishes more in height than in -breadth, which the cube above, hanging in the air, cannot do. Thus -it is proved. The cube shown above is better shown here below. - -The final result of the two cylinders of damp clay that is _a_ and -_b_ will be the pyramidal figures below _c_ and _d_. This is proved -thus: The cylinder _a_ resting on block of stone being made of clay -mixed with a great deal of water will sink by its weight, which -presses on its base, and in proportion as it settles and spreads all -the parts will be somewhat nearer to the base because that is -charged with the whole weight. - -III. - -ON THE NATURE OF THE ARCH. - -779. - -WHAT IS AN ARCH? - -The arch is nothing else than a force originated by two weaknesses, -for the arch in buildings is composed of two segments of a circle, -each of which being very weak in itself tends to fall; but as each -opposes this tendency in the other, the two weaknesses combine to -form one strength. - -OF THE KIND OF PRESSURE IN ARCHES. - -As the arch is a composite force it remains in equilibrium because -the thrust is equal from both sides; and if one of the segments -weighs more than the other the stability is lost, because the -greater pressure will outweigh the lesser. - -OF DISTRIBUTING THE PRESSURE ABOVE AN ARCH. - -Next to giving the segments of the circle equal weight it is -necessary to load them equally, or you will fall into the same -defect as before. - -WHERE AN ARCH BREAKS. - -An arch breaks at the part which lies below half way from the -centre. - -SECOND RUPTURE OF THE ARCH. - -If the excess of weight be placed in the middle of the arch at the -point _a_, that weight tends to fall towards _b_, and the arch -breaks at 2/3 of its height at _c e_; and _g e_ is as many times -stronger than _e a_, as _m o_ goes into _m n_. - -ON ANOTHER CAUSE OF RUIN. - -The arch will likewise give way under a transversal thrust, for when -the charge is not thrown directly on the foot of the arch, the arch -lasts but a short time. - -780. - -ON THE STRENGTH OF THE ARCH. - -The way to give stability to the arch is to fill the spandrils with -good masonry up to the level of its summit. - -ON THE LOADING OF ROUND ARCHES. - -ON THE PROPER MANNER OF LOADING THE POINTED ARCH. - -ON THE EVIL EFFECTS OF LOADING THE POINTED ARCH DIRECTLY ABOVE ITS -CROWN. - -ON THE DAMAGE DONE TO THE POINTED ARCH BY THROWING THE PRESSURE ON -THE FLANKS. - -An arch of small curve is safe in itself, but if it be heavily -charged, it is necessary to strengthen the flanks well. An arch of a -very large curve is weak in itself, and stronger if it be charged, -and will do little harm to its abutments, and its places of giving -way are _o p_. - -[Footnote: Inside the large figure on the righi is the note: _Da -pesare la forza dell' archo_.] - -781. - -ON THE REMEDY FOR EARTHQUAKES. - -The arch which throws its pressure perpendicularly on the abutments -will fulfil its function whatever be its direction, upside down, -sideways or upright. - -The arch will not break if the chord of the outer arch does not -touch the inner arch. This is manifest by experience, because -whenever the chord _a o n_ of the outer arch _n r a_ approaches the -inner arch _x b y_ the arch will be weak, and it will be weaker in -proportion as the inner arch passes beyond that chord. When an arch -is loaded only on one side the thrust will press on the top of the -other side and be transmitted to the spring of the arch on that -side; and it will break at a point half way between its two -extremes, where it is farthest from the chord. - -782. - -A continuous body which has been forcibly bent into an arch, thrusts -in the direction of the straight line, which it tends to recover. - -783. - -In an arch judiciously weighted the thrust is oblique, so that the -triangle _c n b_ has no weight upon it. - -784. - -I here ask what weight will be needed to counterpoise and resist the -tendency of each of these arches to give way? - -[Footnote: The two lower sketches are taken from the MS. S. K. M. -III, 10a; they have there no explanatory text.] - -785. - -ON THE STRENGTH OF THE ARCH IN ARCHITECTURE. - -The stability of the arch built by an architect resides in the tie -and in the flanks. - -ON THE POSITION OF THE TIE IN THE ABOVE NAMED ARCH. - -The position of the tie is of the same importance at the beginning -of the arch and at the top of the perpendicular pier on which it -rests. This is proved by the 2nd "of supports" which says: that part -of a support has least resistance which is farthest from its solid -attachment; hence, as the top of the pier is farthest from the -middle of its true foundation and the same being the case at the -opposite extremities of the arch which are the points farthest from -the middle, which is really its [upper] attachment, we have -concluded that the tie _a b_ requires to be in such a position as -that its opposite ends are between the four above-mentioned -extremes. - -The adversary says that this arch must be more than half a circle, -and that then it will not need a tie, because then the ends will not -thrust outwards but inwards, as is seen in the excess at _a c_, _b -d_. To this it must be answered that this would be a very poor -device, for three reasons. The first refers to the strength of the -arch, since it is proved that the circular parallel being composed -of two semicircles will only break where these semicircles cross -each other, as is seen in the figure _n m;_ besides this it follows -that there is a wider space between the extremes of the semicircle -than between the plane of the walls; the third reason is that the -weight placed to counterbalance the strength of the arch diminishes -in proportion as the piers of the arch are wider than the space -between the piers. Fourthly in proportion as the parts at _c a b d_ -turn outwards, the piers are weaker to support the arch above them. -The 5th is that all the material and weight of the arch which are in -excess of the semicircle are useless and indeed mischievous; and -here it is to be noted that the weight placed above the arch will be -more likely to break the arch at _a b_, where the curve of the -excess begins that is added to the semicircle, than if the pier were -straight up to its junction with the semicircle [spring of the -arch]. - -AN ARCH LOADED OVER THE CROWN WILL GIVE WAY AT THE LEFT HAND AND -RIGHT HAND QUARTERS. - -This is proved by the 7th of this which says: The opposite ends of -the support are equally pressed upon by the weight suspended to -them; hence the weight shown at _f_ is felt at _b c_, that is half -at each extremity; and by the third which says: in a support of -equal strength [throughout] that portion will give way soonest which -is farthest from its attachment; whence it follows that _d_ being -equally distant from _f, e_ ..... - -If the centering of the arch does not settle as the arch settles, -the mortar, as it dries, will shrink and detach itself from the -bricks between which it was laid to keep them together; and as it -thus leaves them disjoined the vault will remain loosely built, and -the rains will soon destroy it. - -786. - -ON THE STRENGTH AND NATURE OF ARCHES, AND WHERE THEY ARE STRONG OR -WEAK; AND THE SAME AS TO COLUMNS. - -That part of the arch which is nearer to the horizontal offers least -resistance to the weight placed on it. - -When the triangle _a z n_, by settling, drives backwards the 2/3 of -each 1/2 circle that is _a s_ and in the same way _z m_, the reason -is that _a_ is perpendicularly over _b_ and so likewise _z_ is above -_f_. - -Either half of an arch, if overweighted, will break at 2/3 of its -height, the point which corresponds to the perpendicular line above -the middle of its bases, as is seen at _a b_; and this happens -because the weight tends to fall past the point _r_.--And if, -against its nature it should tend to fall towards the point _s_ the -arch _n s_ would break precisely in its middle. If the arch _n s_ -were of a single piece of timber, if the weight placed at _n_ should -tend to fall in the line _n m_, the arch would break in the middle -of the arch _e m_, otherwise it will break at one third from the top -at the point a because from _a_ to _n_ the arch is nearer to the -horizontal than from _a_ to _o_ and from _o_ to _s_, in proportion -as _p t_ is greater than _t n_, _a o_ will be stronger than _a n_ -and likewise in proportion as _s o_ is stronger than _o a_, _r p_ -will be greater than _p t_. - -The arch which is doubled to four times of its thickness will bear -four times the weight that the single arch could carry, and more in -proportion as the diameter of its thickness goes a smaller number of -times into its length. That is to say that if the thickness of the -single arch goes ten times into its length, the thickness of the -doubled arch will go five times into its length. Hence as the -thickness of the double arch goes only half as many times into its -length as that of the single arch does, it is reasonable that it -should carry half as much more weight as it would have to carry if -it were in direct proportion to the single arch. Hence as this -double arch has 4 times the thickness of the single arch, it would -seem that it ought to bear 4 times the weight; but by the above rule -it is shown that it will bear exactly 8 times as much. - -THAT PIER, WHICH is CHARGED MOST UNEQUALLY, WILL SOONEST GIVE WAY. - -The column _c b_, being charged with an equal weight, [on each side] -will be most durable, and the other two outward columns require on -the part outside of their centre as much pressure as there is inside -of their centre, that is, from the centre of the column, towards the -middle of the arch. - -Arches which depend on chains for their support will not be very -durable. - -THAT ARCH WILL BE OF LONGER DURATION WHICH HAS A GOOD ABUTMENT -OPPOSED TO ITS THRUST. - -The arch itself tends to fall. If the arch be 30 braccia and the -interval between the walls which carry it be 20, we know that 30 -cannot pass through the 20 unless 20 becomes likewise 30. Hence the -arch being crushed by the excess of weight, and the walls offering -insufficient resistance, part, and afford room between them, for the -fall of the arch. - -But if you do not wish to strengthen the arch with an iron tie you -must give it such abutments as can resist the thrust; and you can do -this thus: fill up the spandrels _m n_ with stones, and direct the -lines of the joints between them to the centre of the circle of the -arch, and the reason why this makes the arch durable is this. We -know very well that if the arch is loaded with an excess of weight -above its quarter as _a b_, the wall _f g_ will be thrust outwards -because the arch would yield in that direction; if the other quarter -_b c_ were loaded, the wall _f g_ would be thrust inwards, if it -were not for the line of stones _x y_ which resists this. - -787. - -PLAN. - -Here it is shown how the arches made in the side of the octagon -thrust the piers of the angles outwards, as is shown by the line _h -c_ and by the line _t d_ which thrust out the pier _m_; that is they -tend to force it away from the centre of such an octagon. - -788. - -An Experiment to show that a weight placed on an arch does not -discharge itself entirely on its columns; on the contrary the -greater the weight placed on the arches, the less the arch transmits -the weight to the columns. The experiment is the following. Let a -man be placed on a steel yard in the middle of the shaft of a well, -then let him spread out his hands and feet between the walls of the -well, and you will see him weigh much less on the steel yard; give -him a weight on the shoulders, you will see by experiment, that the -greater the weight you give him the greater effort he will make in -spreading his arms and legs, and in pressing against the wall and -the less weight will be thrown on the steel yard. - -IV. - -ON FOUNDATIONS, THE NATURE OF THE GROUND AND SUPPORTS. - -789. - -The first and most important thing is stability. - -As to the foundations of the component parts of temples and other -public buildings, the depths of the foundations must bear the same -proportions to each other as the weight of material which is to be -placed upon them. - -Every part of the depth of earth in a given space is composed of -layers, and each layer is composed of heavier or lighter materials, -the lowest being the heaviest. And this can be proved, because these -layers have been formed by the sediment from water carried down to -the sea, by the current of rivers which flow into it. The heaviest -part of this sediment was that which was first thrown down, and so -on by degrees; and this is the action of water when it becomes -stagnant, having first brought down the mud whence it first flowed. -And such layers of soil are seen in the banks of rivers, where their -constant flow has cut through them and divided one slope from the -other to a great depth; where in gravelly strata the waters have run -off, the materials have, in consequence, dried and been converted -into hard stone, and this happened most in what was the finest mud; -whence we conclude that every portion of the surface of the earth -was once at the centre of the earth, and _vice_versa_ &c. - -790. - -The heaviest part of the foundations of buildings settles most, and -leaves the lighter part above it separated from it. - -And the soil which is most pressed, if it be porous yields most. - -You should always make the foundations project equally beyond the -weight of the walls and piers, as shown at _m a b_. If you do as -many do, that is to say if you make a foundation of equal width from -the bottom up to the surface of the ground, and charge it above with -unequal weights, as shown at _b e_ and at _e o_, at the part of the -foundation at _b e_, the pier of the angle will weigh most and -thrust its foundation downwards, which the wall at _e o_ will not -do; since it does not cover the whole of its foundation, and -therefore thrusts less heavily and settles less. Hence, the pier _b -e_ in settling cracks and parts from the wall _e o_. This may be -seen in most buildings which are cracked round the piers. - -791. - -The window _a_ is well placed under the window _c_, and the window -_b_ is badly placed under the pier _d_, because this latter is -without support and foundation; mind therefore never to make a break -under the piers between the windows. - -792. - -OF THE SUPPORTS. - -A pillar of which the thickness is increased will gain more than its -due strength, in direct proportion to what its loses in relative -height. - -EXAMPLE. - -If a pillar should be nine times as high as it is broad--that is to -say, if it is one braccio thick, according to rule it should be nine -braccia high--then, if you place 100 such pillars together in a mass -this will be ten braccia broad and 9 high; and if the first pillar -could carry 10000 pounds the second being only about as high as it -is wide, and thus lacking 8 parts of its proper length, it, that is -to say, each pillar thus united, will bear eight times more than -when disconnected; that is to say, that if at first it would carry -ten thousand pounds, it would now carry 90 thousand. - -V. - -ON THE RESISTANCE OF BEAMS. - -793. - -That angle will offer the greatest resistance which is most acute, -and the most obtuse will be the weakest. - -[Footnote: The three smaller sketches accompany the text in the -original, but the larger one is not directly connected with it. It -is to be found on fol. 89a of the same Manuscript and there we read -in a note, written underneath, _coverchio della perdicha del -castello_ (roof of the flagstaff of the castle),--Compare also Pl. -XCIII, No. 1.] - -794. - -If the beams and the weight _o_ are 100 pounds, how much weight will -be wanted at _ae_ to resist such a weight, that it may not fall -down? - -795. - -ON THE LENGTH OF BEAMS. - -That beam which is more than 20 times as long as its greatest -thickness will be of brief duration and will break in half; and -remember, that the part built into the wall should be steeped in hot -pitch and filleted with oak boards likewise so steeped. Each beam -must pass through its walls and be secured beyond the walls with -sufficient chaining, because in consequence of earthquakes the beams -are often seen to come out of the walls and bring down the walls and -floors; whilst if they are chained they will hold the walls strongly -together and the walls will hold the floors. Again I remind you -never to put plaster over timber. Since by expansion and shrinking -of the timber produced by damp and dryness such floors often crack, -and once cracked their divisions gradually produce dust and an ugly -effect. Again remember not to lay a floor on beams supported on -arches; for, in time the floor which is made on beams settles -somewhat in the middle while that part of the floor which rests on -the arches remains in its place; hence, floors laid over two kinds -of supports look, in time, as if they were made in hills [Footnote: -19 M. RAVAISSON, in his edition of MS. A gives a very different -rendering of this passage translating it thus: _Les planchers qui -sont soutenus par deux differentes natures de supports paraissent -avec le temps faits en voute a cholli_.] - -Remarks on the style of Leonardo's architecture. - -A few remarks may here be added on the style of Leonardo's -architectural studies. However incomplete, however small in scale, -they allow us to establish a certain number of facts and -probabilities, well worthy of consideration. - -When Leonardo began his studies the great name of Brunellesco was -still the inspiration of all Florence, and we cannot doubt that -Leonardo was open to it, since we find among his sketches the plan -of the church of Santo Spirito[Footnote 1: See Pl. XCIV, No. 2. Then -only in course of erection after the designs of Brunellesco, though -he was already dead; finished in 1481.] and a lateral view of San -Lorenzo (Pl. XCIV No. 1), a plan almost identical with the chapel -Degli Angeli, only begun by him (Pl. XCIV, No. 3) while among -Leonardo's designs for domes several clearly betray the influence of -Brunellesco's Cupola and the lantern of Santa Maria del -Fiore[Footnote 2: A small sketch of the tower of the Palazzo della -Signoria (MS. C.A. 309) proves that he also studied mediaeval -monuments.] - -The beginning of the second period of modern Italian architecture -falls during the first twenty years of Leonardo's life. However the -new impetus given by Leon Battista Alberti either was not generally -understood by his contemporaries, or those who appreciated it, had -no opportunity of showing that they did so. It was only when taken -up by Bramante and developed by him to the highest rank of modern -architecture that this new influence was generally felt. Now the -peculiar feature of Leonardo's sketches is that, like the works of -Bramante, they appear to be the development and continuation of -Alberti's. - -_But a question here occurs which is difficult to answer. Did -Leonardo, till he quitted Florence, follow the direction given by -the dominant school of Brunellesco, which would then have given rise -to his "First manner", or had he, even before he left Florence, felt -Alberti's influence--either through his works (Palazzo Ruccellai, -and the front of Santa Maria Novella) or through personal -intercourse? Or was it not till he went to Milan that Alberti's work -began to impress him through Bramante, who probably had known -Alberti at Mantua about 1470 and who not only carried out Alberti's -views and ideas, but, by his designs for St. Peter's at Rome, proved -himself the greatest of modern architects. When Leonardo went to -Milan Bramante had already been living there for many years. One of -his earliest works in Milan was the church of Santa Maria presso San -Satiro, Via del Falcone[Footnote 1: Evidence of this I intend to -give later on in a Life of Bramante, which I have in preparation.]. - -Now we find among Leonardos studies of Cupolas on Plates LXXXIV and -LXXXV and in Pl. LXXX several sketches which seem to me to have been -suggested by Bramante's dome of this church. - -The MSS. B and Ash. II contain the plans of S. Sepolcro, the -pavilion in the garden of the duke of Milan, and two churches, -evidently inspired by the church of San Lorenzo at Milan. - -MS. B. contains besides two notes relating to Pavia, one of them a -design for the sacristy of the Cathedral at Pavia, which cannot be -supposed to be dated later than 1492, and it has probably some -relation to Leonardo's call to Pavia June 21, 1490[Footnote 2: The -sketch of the plan of Brunellesco's church of Santo Spirito at -Florence, which occurs in the same Manuscript, may have been done -from memory.]. These and other considerations justify us in -concluding, that Leonardo made his studies of cupolas at Milan, -probably between the years 1487 and 1492 in anticipation of the -erection of one of the grandest churches of Italy, the Cathedral of -Pavia. This may explain the decidedly Lombardo-Bramantesque tendency -in the style of these studies, among which only a few remind us of -the forms of the cupolas of S. Maria del Fiore and of the Baptistery -of Florence. Thus, although when compared with Bramante's work, -several of these sketches plainly reveal that master's influence, we -find, among the sketches of domes, some, which show already -Bramante's classic style, of which the Tempietto of San Pietro in -Montorio, his first building executed at Rome, is the foremost -example[Footnote 3: It may be mentioned here, that in 1494 Bramante -made a similar design for the lantern of the Cupola of the Church of -Santa Maria delle Grazie.]. - -On Plate LXXXIV is a sketch of the plan of a similar circular -building; and the Mausoleum on Pl. XCVIII, no less than one of the -pedestals for the statue of Francesco Sforza (Pl. LXV), is of the -same type. - -The drawings Pl. LXXXIV No. 2, Pl. LXXXVI No. 1 and 2 and the ground -flour ("flour" sic but should be "floor" ?) of the building in the -drawing Pl. XCI No. 2, with the interesting decoration by gigantic -statues in large niches, are also, I believe, more in the style -Bramante adopted at Rome, than in the Lombard style. Are we to -conclude from this that Leonardo on his part influenced Bramante in -the sense of simplifying his style and rendering it more congenial -to antique art? The answer to this important question seems at first -difficult to give, for we are here in presence of Bramante, the -greatest of modern architects, and with Leonardo, the man comparable -with no other. We have no knowledge of any buildings erected by -Leonardo, and unless we admit personal intercourse--which seems -probable, but of which there is no proof--, it would be difficult to -understand how Leonardo could have affected Bramante's style. The -converse is more easily to be admitted, since Bramante, as we have -proved elsewhere, drew and built simultaneously in different -manners, and though in Lombardy there is no building by him in his -classic style, the use of brick for building, in that part of Italy, -may easily account for it._ - -_Bramante's name is incidentally mentioned in Leonardo's manuscripts -in two passages (Nos. 1414 and 1448). On each occasion it is only a -slight passing allusion, and the nature of the context gives us no -due information as to any close connection between the two artists._ - -_It might be supposed, on the ground of Leonardo's relations with -the East given in sections XVII and XXI of this volume, that some -evidence of oriental influence might be detected in his -architectural drawings. I do not however think that any such traces -can be pointed out with certainty unless perhaps the drawing for a -Mausoleum, Pl. XC VIII._ - -_Among several studies for the construction of cupolas above a Greek -cross there are some in which the forms are decidedly monotonous. -These, it is clear, were not designed as models of taste; they must -be regarded as the results of certain investigations into the laws -of proportion, harmony and contrast._ - -_The designs for churches, on the plan of a Latin cross are -evidently intended to depart as little as possible from the form of -a Greek cross; and they also show a preference for a nave surrounded -with outer porticos._ - -_The architectural forms preferred by Leonardo are pilasters coupled -(Pl. LXXXII No. 1; or grouped (Pl. LXXX No. 5 and XCIV No. 4), often -combined with niches. We often meet with orders superposed, one in -each story, or two small orders on one story, in combination with -one great order (Pl. XCVI No. 2)._ - -The drum (tamburo) of these cupolas is generally octagonal, as in -the cathedral of Florence, and with similar round windows in its -sides. In Pl. LXXXVII No. 2 it is circular like the model actually -carried out by Michael Angelo at St. Peter's. - -The cupola itself is either hidden under a pyramidal roof, as in the -Baptistery of Florence, San Lorenzo of Milan and most of the Lombard -churches (Pl. XCI No. 1 and Pl. XCII No. 1); but it more generally -suggests the curve of Sta Maria del Fiore (Pl. LXXXVIII No. 5; Pl. -XC No. 2; Pl. LXXXIX, M; Pl XC No. 4, Pl. XCVI No. 2). In other -cases (Pl. LXXX No. 4; Pl. LXXXIX; Pl. XC No. 2) it shows the sides -of the octagon crowned by semicircular pediments, as in -Brunellesco's lantern of the Cathedral and in the model for the -Cathedral of Pavia. - -Finally, in some sketches the cupola is either semicircular, or as -in Pl. LXXXVII No. 2, shows the beautiful line, adopted sixty years -later by Michael Angelo for the existing dome of St. Peter's. - -It is worth noticing that for all these domes Leonardo is not -satisfied to decorate the exterior merely with ascending ribs or -mouldings, but employs also a system of horizontal parallels to -complete the architectural system. Not the least interesting are the -designs for the tiburio (cupola) of the Milan Cathedral. They show -some of the forms, just mentioned, adapted to the peculiar gothic -style of that monument. - -The few examples of interiors of churches recall the style employed -in Lombardy by Bramante, for instance in S. Maria di Canepanuova at -Pavia, or by Dolcebuono in the Monastero Maggiore at Milan (see Pl. -CI No. 1 [C. A. 181b; 546b]; Pl. LXXXIV No. 10). - -The few indications concerning palaces seem to prove that Leonardo -followed Alberti's example of decorating the walls with pilasters -and a flat rustica, either in stone or by graffitti (Pl. CII No. 1 -and Pl. LXXXV No. 14). - -By pointing out the analogies between Leonardo's architecture and -that of other masters we in no way pretend to depreciate his -individual and original inventive power. These are at all events -beyond dispute. The project for the Mausoleum (Pl. XCVIII) would -alone suffice to rank him among the greatest architects who ever -lived. The peculiar shape of the tower (Pl. LXXX), of the churches -for preaching (Pl. XCVII No. 1 and pages 56 and 57, Fig. 1-4), his -curious plan for a city with high and low level streets (Pl. LXXVII -and LXXVIII No. 2 and No. 3), his Loggia with fountains (Pl. LXXXII -No. 4) reveal an originality, a power and facility of invention for -almost any given problem, which are quite wonderful. - -_In addition to all these qualities he propably stood alone in his -day in one department of architectural study,--his investigations, -namely, as to the resistance of vaults, foundations, walls and -arches._ - -_As an application of these studies the plan of a semicircular vault -(Pl. CIII No. 2) may be mentioned here, disposed so as to produce no -thrust on the columns on which it rests:_ volta i botte e non -ispignie ifori le colone. _Above the geometrical patterns on the -same sheet, close to a circle inscribed in a square is the note:_ la -ragio d'una volta cioe il terzo del diamitro della sua ... del -tedesco in domo. - -_There are few data by which to judge of Leonardo's style in the -treatment of detail. On Pl. LXXXV No. 10 and Pl. CIII No. 3, we find -some details of pillars; on Pl. CI No. 3 slender pillars designed -for a fountain and on Pl. CIII No. 1 MS. B, is a pen and ink drawing -of a vase which also seems intended for a fountain. Three handles -seem to have been intended to connect the upper parts with the base. -There can be no doubt that Leonardo, like Bramante, but unlike -Michael Angelo, brought infinite delicacy of motive and execution to -bear on the details of his work._ - -_XIV._ - -_Anatomy, Zoology and Physiology._ - -_Leonardo's eminent place in the history of medicine, as a pioneer -in the sciences of Anatomy and Physiology, will never be appreciated -till it is possible to publish the mass of manuscripts in which he -largely treated of these two branches of learning. In the present -work I must necessarily limit myself to giving the reader a general -view of these labours, by publishing his introductory notes to the -various books on anatomical subjects. I have added some extracts, -and such observations as are scattered incidentally through these -treatises, as serving to throw a light on Leonardo's scientific -attitude, besides having an interest for a wider circle than that of -specialists only._ - -_VASARI expressly mentions Leonardo's anatomical studies, having had -occasion to examine the manuscript books which refer to them. -According to him Leonardo studied Anatomy in the companionship of -Marc Antonio della Torre_ "aiutato e scambievolmente -aiutando."_--This learned Anatomist taught the science in the -universities first of Padua and then of Pavia, and at Pavia he and -Leonardo may have worked and studied together. We have no clue to -any exact dates, but in the year 1506 Marc Antonio della Torre seems -to have not yet left Padua. He was scarcely thirty years old when he -died in 1512, and his writings on anatomy have not only never been -published, but no manuscript copy of them is known to exist._ - -_This is not the place to enlarge on the connection between Leonardo -and Marc Antonio della Torre. I may however observe that I have not -been able to discover in Leonardo's manuscripts on anatomy any -mention of his younger contemporary. The few quotations which occur -from writers on medicine--either of antiquity or of the middle ages -are printed in Section XXII. Here and there in the manuscripts -mention is made of an anonymous "adversary"_ (avversario) _whose -views are opposed and refuted by Leonardo, but there is no ground -for supposing that Marc Antonio della Torre should have been this -"adversary"._ - -_Only a very small selection from the mass of anatomical drawings -left by Leonardo have been published here in facsimile, but to form -any adequate idea of their scientific merit they should be compared -with the coarse and inadequate figures given in the published books -of the early part of the XVI. century. - -William Hunter, the great surgeon--a competent judge--who had an -opportunity in the time of George III. of seeing the originals in -the King's Library, has thus recorded his opinion: "I expected to -see little more than such designs in Anatomy as might be useful to a -painter in his own profession. But I saw, and indeed with -astonishment, that Leonardo had been a general and deep student. -When I consider what pains he has taken upon every part of the body, -the superiority of his universal genius, his particular excellence -in mechanics and hydraulics, and the attention with which such a man -would examine and see objects which he has to draw, I am fully -persuaded that Leonardo was the best Anatomist, at that time, in the -world ... Leonardo was certainly the first man, we know of, who -introduced the practice of making anatomical drawings" (Two -introductory letters. London 1784, pages 37 and 39). - -The illustrious German Naturalist Johan Friedrich Blumenback -esteemed them no less highly; he was one of the privileged few who, -after Hunter, had the chance of seeing these Manuscripts. He writes: -_Der Scharfblick dieses grossen Forschers und Darstellers der Natur -hat schon auf Dinge geachtet, die noch Jahrhunderte nachher -unbemerkt geblieben sind_" (see _Blumenbach's medicinische -Bibliothek_, Vol. 3, St. 4, 1795. page 728). - -These opinions were founded on the drawings alone. Up to the present -day hardly anything has been made known of the text, and, for the -reasons I have given, it is my intention to reproduce here no more -than a selection of extracts which I have made from the originals at -Windsor Castle and elsewhere. In the Bibliography of the -Manuscripts, at the end of this volume a short review is given of -the valuable contents of these Anatomical note books which are at -present almost all in the possession of her Majesty the Queen of -England. It is, I believe, possible to assign the date with -approximate accuracy to almost all the fragments, and I am thus led -to conclude that the greater part of Leonardo's anatomical -investigations were carried out after the death of della Torre. - -Merely in reading the introductory notes to his various books on -Anatomy which are here printed it is impossible to resist the -impression that the Master's anatomical studies bear to a very great -extent the stamp of originality and independent thought. - -I. - -ANATOMY. - -796. - -A general introduction - -I wish to work miracles;--it may be that I shall possess less than -other men of more peaceful lives, or than those who want to grow -rich in a day. I may live for a long time in great poverty, as -always happens, and to all eternity will happen, to alchemists, the -would-be creators of gold and silver, and to engineers who would -have dead water stir itself into life and perpetual motion, and to -those supreme fools, the necromancer and the enchanter. - -[Footnote 23: The following seems to be directed against students of -painting and young artists rather than against medical men and -anatomists.] - -And you, who say that it would be better to watch an anatomist at -work than to see these drawings, you would be right, if it were -possible to observe all the things which are demonstrated in such -drawings in a single figure, in which you, with all your cleverness, -will not see nor obtain knowledge of more than some few veins, to -obtain a true and perfect knowledge of which I have dissected more -than ten human bodies, destroying all the other members, and -removing the very minutest particles of the flesh by which these -veins are surrounded, without causing them to bleed, excepting the -insensible bleeding of the capillary veins; and as one single body -would not last so long, since it was necessary to proceed with -several bodies by degrees, until I came to an end and had a complete -knowledge; this I repeated twice, to learn the differences [59]. - -[Footnote: Lines 1-59 and 60-89 are written in two parallel columns. -When we here find Leonardo putting himself in the same category as -the Alchemists and Necromancers, whom he elsewhere mocks at so -bitterly, it is evidently meant ironically. In the same way -Leonardo, in the introduction to the Books on Perspective sets -himself with transparent satire on a level with other writers on the -subject.] - -And if you should have a love for such things you might be prevented -by loathing, and if that did not prevent you, you might be deterred -by the fear of living in the night hours in the company of those -corpses, quartered and flayed and horrible to see. And if this did -not prevent you, perhaps you might not be able to draw so well as is -necessary for such a demonstration; or, if you had the skill in -drawing, it might not be combined with knowledge of perspective; and -if it were so, you might not understand the methods of geometrical -demonstration and the method of the calculation of forces and of the -strength of the muscles; patience also may be wanting, so that you -lack perseverance. As to whether all these things were found in me -or not [Footnote 84: Leonardo frequently, and perhaps habitually, -wrote in note books of a very small size and only moderately thick; -in most of those which have been preserved undivided, each contains -less than fifty leaves. Thus a considerable number of such volumes -must have gone to make up a volume of the bulk of the '_Codex -Atlanticus_' which now contains nearly 1200 detached leaves. In the -passage under consideration, which was evidently written at a late -period of his life, Leonardo speaks of his Manuscript note-books as -numbering 12O; but we should hardly be justified in concluding from -this passage that the greater part of his Manuscripts were now -missing (see _Prolegomena_, Vol. I, pp. 5-7).], the hundred and -twenty books composed by me will give verdict Yes or No. In these I -have been hindered neither by avarice nor negligence, but simply by -want of time. Farewell [89]. - -Plans and suggestions for the arrangement of materials (797-802). - -797. - -OF THE ORDER OF THE BOOK. - -This work must begin with the conception of man, and describe the -nature of the womb and how the foetus lives in it, up to what stage -it resides there, and in what way it quickens into life and feeds. -Also its growth and what interval there is between one stage of -growth and another. What it is that forces it out from the body of -the mother, and for what reasons it sometimes comes out of the -mother's womb before the due time. - -Then I will describe which are the members, which, after the boy is -born, grow more than the others, and determine the proportions of a -boy of one year. - -Then describe the fully grown man and woman, with their proportions, -and the nature of their complexions, colour, and physiognomy. - -Then how they are composed of veins, tendons, muscles and bones. -This I shall do at the end of the book. Then, in four drawings, -represent four universal conditions of men. That is, Mirth, with -various acts of laughter, and describe the cause of laughter. -Weeping in various aspects with its causes. Contention, with various -acts of killing; flight, fear, ferocity, boldness, murder and every -thing pertaining to such cases. Then represent Labour, with pulling, -thrusting, carrying, stopping, supporting and such like things. - -Further I would describe attitudes and movements. Then perspective, -concerning the functions and effects of the eye; and of -hearing--here I will speak of music--, and treat of the other -senses. - -And then describe the nature of the senses. - -This mechanism of man we will demonstrate in ... figures; of which -the three first will show the ramification of the bones; that is: -first one to show their height and position and shape: the second -will be seen in profile and will show the depth of the whole and of -the parts, and their position. The third figure will be a -demonstration of the bones of the backparts. Then I will make three -other figures from the same point of view, with the bones sawn -across, in which will be shown their thickness and hollowness. Three -other figures of the bones complete, and of the nerves which rise -from the nape of the neck, and in what limbs they ramify. And three -others of the bones and veins, and where they ramify. Then three -figures with the muscles and three with the skin, and their proper -proportions; and three of woman, to illustrate the womb and the -menstrual veins which go to the breasts. - -[Footnote: The meaning of the word _nervo_ varies in different -passages, being sometimes used for _muscolo_ (muscle).] - -798. - -THE ORDER OF THE BOOK. - -This depicting of mine of the human body will be as clear to you as -if you had the natural man before you; and the reason is that if you -wish thoroughly to know the parts of man, anatomically, you--or your -eye--require to see it from different aspects, considering it from -below and from above and from its sides, turning it about and -seeking the origin of each member; and in this way the natural -anatomy is sufficient for your comprehension. But you must -understand that this amount of knowledge will not continue to -satisfy you; seeing the very great confusion that must result from -the combination of tissues, with veins, arteries, nerves, sinews, -muscles, bones, and blood which, of itself, tinges every part the -same colour. And the veins, which discharge this blood, are not -discerned by reason of their smallness. Moreover integrity of the -tissues, in the process of the investigating the parts within them, -is inevitably destroyed, and their transparent substance being -tinged with blood does not allow you to recognise the parts covered -by them, from the similarity of their blood-stained hue; and you -cannot know everything of the one without confusing and destroying -the other. Hence, some further anatomy drawings become necessary. Of -which you want three to give full knowledge of the veins and -arteries, everything else being destroyed with the greatest care. -And three others to display the tissues; and three for the sinews -and muscles and ligaments; and three for the bones and cartilages; -and three for the anatomy of the bones, which have to be sawn to -show which are hollow and which are not, which have marrow and which -are spongy, and which are thick from the outside inwards, and which -are thin. And some are extremely thin in some parts and thick in -others, and in some parts hollow or filled up with bone, or full of -marrow, or spongy. And all these conditions are sometimes found in -one and the same bone, and in some bones none of them. And three you -must have for the woman, in which there is much that is mysterious -by reason of the womb and the foetus. Therefore by my drawings every -part will be known to you, and all by means of demonstrations from -three different points of view of each part; for when you have seen -a limb from the front, with any muscles, sinews, or veins which take -their rise from the opposite side, the same limb will be shown to -you in a side view or from behind, exactly as if you had that same -limb in your hand and were turning it from side to side until you -had acquired a full comprehension of all you wished to know. In the -same way there will be put before you three or four demonstrations -of each limb, from various points of view, so that you will be left -with a true and complete knowledge of all you wish to learn of the -human figure[Footnote 35: Compare Pl. CVII. The original drawing at -Windsor is 28 1/2 X 19 1/2 centimetres. The upper figures are -slightly washed with Indian ink. On the back of this drawing is the -text No. 1140.]. - -Thus, in twelve entire figures, you will have set before you the -cosmography of this lesser world on the same plan as, before me, was -adopted by Ptolemy in his cosmography; and so I will afterwards -divide them into limbs as he divided the whole world into provinces; -then I will speak of the function of each part in every direction, -putting before your eyes a description of the whole form and -substance of man, as regards his movements from place to place, by -means of his different parts. And thus, if it please our great -Author, I may demonstrate the nature of men, and their customs in -the way I describe his figure. - -And remember that the anatomy of the nerves will not give the -position of their ramifications, nor show you which muscles they -branch into, by means of bodies dissected in running water or in -lime water; though indeed their origin and starting point may be -seen without such water as well as with it. But their ramifications, -when under running water, cling and unite--just like flat or hemp -carded for spinning--all into a skein, in a way which makes it -impossible to trace in which muscles or by what ramification the -nerves are distributed among those muscles. - -799. - -THE ARRANGEMENT OF ANATOMY - -First draw the bones, let us say, of the arm, and put in the motor -muscle from the shoulder to the elbow with all its lines. Then -proceed in the same way from the elbow to the wrist. Then from the -wrist to the hand and from the hand to the fingers. - -And in the arm you will put the motors of the fingers which open, -and these you will show separately in their demonstration. In the -second demonstration you will clothe these muscles with the -secondary motors of the fingers and so proceed by degrees to avoid -confusion. But first lay on the bones those muscles which lie close -to the said bones, without confusion of other muscles; and with -these you may put the nerves and veins which supply their -nourishment, after having first drawn the tree of veins and nerves -over the simple bones. - -800. - -Begin the anatomy at the head and finish at the sole of the foot. - -801. - -3 men complete, 3 with bones and nerves, 3 with the bones only. Here -we have 12 demonstrations of entire figures. - -802. - -When you have finished building up the man, you will make the statue -with all its superficial measurements. - -[Footnote: _Cresciere l'omo_. The meaning of this expression appears -to be different here and in the passage C.A. 157a, 468a (see No. -526, Note 1. 2). Here it can hardly mean anything else than -modelling, since the sculptor forms the figure by degrees, by adding -wet clay and the figure consequently increases or grows. _Tu farai -la statua_ would then mean, you must work out the figure in marble. -If this interpretation is the correct one, this passage would have -no right to find a place in the series on anatomical studies. I may -say that it was originally inserted in this connection under the -impression that _di cresciere_ should be read _descrivere_.] - -Plans for the representation of muscles by drawings (803-809). - -803. - -You must show all the motions of the bones with their joints to -follow the demonstration of the first three figures of the bones, -and this should be done in the first book. - -804. - -Remember that to be certain of the point of origin of any muscle, -you must pull the sinew from which the muscle springs in such a way -as to see that muscle move, and where it is attached to the -ligaments of the bones. - -NOTE. - -You will never get any thing but confusion in demonstrating the -muscles and their positions, origin, and termination, unless you -first make a demonstration of thin muscles after the manner of linen -threads; and thus you can represent them, one over another as nature -has placed them; and thus, too, you can name them according to the -limb they serve; for instance the motor of the point of the great -toe, of its middle bone, of its first bone, &c. And when you have -the knowledge you will draw, by the side of this, the true form and -size and position of each muscle. But remember to give the threads -which explain the situation of the muscles in the position which -corresponds to the central line of each muscle; and so these threads -will demonstrate the form of the leg and their distance in a plain -and clear manner. - -I have removed the skin from a man who was so shrunk by illness that -the muscles were worn down and remained in a state like thin -membrane, in such a way that the sinews instead of merging in -muscles ended in wide membrane; and where the bones were covered by -the skin they had very little over their natural size. - -[Footnote: The photograph No. 41 of Grosvenor Gallery Publications: -a drawing of the muscles of the foot, includes a complete facsimile -of the text of this passage.] - -805. - -Which nerve causes the motion of the eye so that the motion of one -eye moves the other? - -Of frowning the brows, of raising the brows, of lowering the -brows,--of closing the eyes, of opening the eyes,--of raising the -nostrils, of opening the lips, with the teeth shut, of pouting with -the lips, of smiling, of astonishment.-- - -Describe the beginning of man when it is caused in the womb and why -an eight months child does not live. What sneezing is. What yawning -is. Falling sickness, spasms, paralysis, shivering with cold, -sweating, fatigue, hunger, sleepiness, thirst, lust. - -Of the nerve which is the cause of movement from the shoulder to the -elbow, of the movement from the elbow to the hand, from the joint of -the hand to the springing of the fingers. From the springing of the -fingers to the middle joints, and from the middle joints to the -last. - -Of the nerve which causes the movement of the thigh, and from the -knee to the foot, and from the joint of the foot to the toes, and -then to the middle of the toes and of the rotary motion of the leg. - -806. - -ANATOMY. - -Which nerves or sinews of the hand are those which close and part -the fingers and toes latteraly? - -807. - -Remove by degrees all the parts of the front of a man in making your -dissection, till you come to the bones. Description of the parts of -the bust and of their motions. - -808. - -Give the anatomy of the leg up to the hip, in all views and in every -action and in every state; veins, arteries, nerves, sinews and -muscles, skin and bones; then the bones in sections to show the -thickness of the bones. - -[Footnote: A straightened leg in profile is sketched by the side of -this text.] - -On corpulency and leanness (809-811). - -809. - -Make the rule and give the measurement of each muscle, and give the -reasons of all their functions, and in which way they work and what -makes them work &c. - -[4] First draw the spine of the back; then clothe it by degrees, one -after the other, with each of its muscles and put in the nerves and -arteries and veins to each muscle by itself; and besides these note -the vertebrae to which they are attached; which of the intestines -come in contact with them; and which bones and other organs &c. - -The most prominent parts of lean people are most prominent in the -muscular, and equally so in fat persons. But concerning the -difference in the forms of the muscles in fat persons as compared -with muscular persons, it shall be described below. - -[Footnote: The two drawings given on Pl. CVIII no. 1 come between -lines 3 and 4. A good and very early copy of this drawing without -the written text exists in the collection of drawings belonging to -Christ's College Oxford, where it is attributed to Leonardo.] - -810. - -Describe which muscles disappear in growing fat, and which become -visible in growing lean. - -And observe that that part which on the surface of a fat person is -most concave, when he grows lean becomes more prominent. - -Where the muscles separate one from another you must give profiles -and where they coalesce ... - -811. - -OF THE HUMAN FIGURE. - -Which is the part in man, which, as he grows fatter, never gains -flesh? - -Or what part which as a man grows lean never falls away with a too -perceptible diminution? And among the parts which grow fat which is -that which grows fattest? - -Among those which grow lean which is that which grows leanest? - -In very strong men which are the muscles which are thickest and most -prominent? - -In your anatomy you must represent all the stages of the limbs from -man's creation to his death, and then till the death of the bone; -and which part of him is first decayed and which is preserved the -longest. - -And in the same way of extreme leanness and extreme fatness. - -The divisions of the head (812. 813). - -812. - -ANATOMY. - -There are eleven elementary tissues:-- Cartilage, bones, nerves, -veins, arteries, fascia, ligament and sinews, skin, muscle and fat. - -OF THE HEAD. - -The divisions of the head are 10, viz. 5 external and 5 internal, -the external are the hair, skin, muscle, fascia and the skull; the -internal are the dura mater, the pia mater, [which enclose] the -brain. The pia mater and the dura mater come again underneath and -enclose the brain; then the rete mirabile, and the occipital bone, -which supports the brain from which the nerves spring. - -813. - -_a_. hair - -_n_. skin - -_c_. muscle - -_m_. fascia - -_o_. skull _i.e._ bone - -_b_. dura mater - -_d_. pia mater - -_f_. brain - -_r_. pia mater, below - -_t_. dura mater - -_l_. rete mirablile - -_s_. the occipitul bone. - -[Footnote: See Pl. CVIII, No. 3.] - -Physiological problems (814. 815). - -814. - -Of the cause of breathing, of the cause of the motion of the heart, -of the cause of vomiting, of the cause of the descent of food from -the stomach, of the cause of emptying the intestines. - -Of the cause of the movement of the superfluous matter through the -intestines. - -Of the cause of swallowing, of the cause of coughing, of the cause -of yawning, of the cause of sneezing, of the cause of limbs getting -asleep. - -Of the cause of losing sensibility in any limb. - -Of the cause of tickling. - -Of the cause of lust and other appetites of the body, of the cause -of urine and also of all the natural excretions of the body. - -[Footnote: By the side of this text stands the pen and ink drawing -reproduced on Pl. CVIII, No. 4; a skull with indications of the -veins in the fleshy covering.] - -815. - -The tears come from the heart and not from the brain. - -Define all the parts, of which the body is composed, beginning with -the skin with its outer cuticle which is often chapped by the -influence of the sun. - -II. - -ZOOLOGY AND COMPARATIVE ANATOMY. - -The divisions of the animal kingdom (816. 817). - -816. - -_Man_. The description of man, which includes that of such creatures -as are of almost the same species, as Apes, Monkeys and the like, -which are many, - -_The Lion_ and its kindred, as Panthers. [Footnote 3: _Leonza_--wild -cat? "_Secondo alcuni, lo stesso che Leonessa; e secondo altri con -piu certezza, lo stesso che Pantera_" FANFANI, _Vocabolario_ page -858.] Wildcats (?) Tigers, Leopards, Wolfs, Lynxes, Spanish cats, -common cats and the like. - -_The Horse_ and its kindred, as Mule, Ass and the like, with incisor -teeth above and below. - -_The Bull_ and its allies with horns and without upper incisors as -the Buffalo, Stag Fallow Deer, Wild Goat, Swine, Goat, wild Goats -Muskdeers, Chamois, Giraffe. - -817. - -Describe the various forms of the intestines of the human species, -of apes and such like. Then, in what way the leonine species differ, -and then the bovine, and finally birds; and arrange this description -after the manner of a disquisition. - -Miscellaneous notes on the study of Zoology (818-821). - -818. - -Procure the placenta of a calf when it is born and observe the form -of the cotyledons, if their cotyledons are male or female. - -819. - -Describe the tongue of the woodpecker and the jaw of the crocodile. - -820. - -Of the flight of the 4th kind of butterflies that consume winged -ants. Of the three principal positions of the wings of birds in -downward flight. - -[Footnote: A passing allusion is all I can here permit myself to -Leonardo's elaborate researches into the flight of birds. Compare -the observations on this subject in the Introduction to section -XVIII and in the Bibliography of Manuscripts at the end of the -work.] - -821. - -Of the way in which the tail of a fish acts in propelling the fish; -as in the eel, snake and leech. - -[Footnote: A sketch of a fish, swimming upwards is in the original, -inserted above this text.--Compare No. 1114.] - -Comparative study of the structure of bones and of the action of -muscles (822-826). - -822. - -OF THE PALM OF THE HAND. - -Then I will discourse of the hands of each animal to show in what -they vary; as in the bear, which has the ligatures of the sinews of -the toes joined above the instep. - -823. - -A second demonstration inserted between anatomy and [the treatise -on] the living being. - -You will represent here for a comparison, the legs of a frog, which -have a great resemblance to the legs of man, both in the bones and -in the muscles. Then, in continuation, the hind legs of the hare, -which are very muscular, with strong active muscles, because they -are not encumbered with fat. - -[Footnote: This text is written by the side of a drawing in black -chalk of a nude male figure, but there is no connection between the -sketch and the text.] - -824. - -Here I make a note to demonstrate the difference there is between -man and the horse and in the same way with other animals. And first -I will begin with the bones, and then will go on to all the muscles -which spring from the bones without tendons and end in them in the -same way, and then go on to those which start with a single tendon -at one end. - -[Footnote: See Pl. CVIII, No. 2.] - -825. - -Note on the bendings of joints and in what way the flesh grows upon -them in their flexions or extensions; and of this most important -study write a separate treatise: in the description of the movements -of animals with four feet; among which is man, who likewise in his -infancy crawls on all fours. - -826. - -OF THE WAY OF WALKING IN MAN. - -The walking of man is always after the universal manner of walking -in animals with 4 legs, inasmuch as just as they move their feet -crosswise after the manner of a horse in trotting, so man moves his -4 limbs crosswise; that is, if he puts forward his right foot in -walking he puts forward, with it, his left arm and vice versa, -invariably. - -III. - -PHYSIOLOGY. - -Comparative study of the organs of sense in men and animals. - -827. - -I have found that in the composition of the human body as compared -with the bodies of animals the organs of sense are duller and -coarser. Thus it is composed of less ingenious instruments, and of -spaces less capacious for receiving the faculties of sense. I have -seen in the Lion tribe that the sense of smell is connected with -part of the substance of the brain which comes down the nostrils, -which form a spacious receptacle for the sense of smell, which -enters by a great number of cartilaginous vesicles with several -passages leading up to where the brain, as before said, comes down. - -The eyes in the Lion tribe have a large part of the head for their -sockets and the optic nerves communicate at once with the brain; but -the contrary is to be seen in man, for the sockets of the eyes are -but a small part of the head, and the optic nerves are very fine and -long and weak, and by the weakness of their action we see by day but -badly at night, while these animals can see as well at night as by -day. The proof that they can see is that they prowl for prey at -night and sleep by day, as nocturnal birds do also. - -Advantages in the structure of the eye in certain animals (828-831). - -828. - -Every object we see will appear larger at midnight than at midday, -and larger in the morning than at midday. - -This happens because the pupil of the eye is much smaller at midday -than at any other time. - -In proportion as the eye or the pupil of the owl is larger in -proportion to the animal than that of man, so much the more light -can it see at night than man can; hence at midday it can see nothing -if its pupil does not diminish; and, in the same way, at night -things look larger to it than by day. - -829. - -OF THE EYES IN ANIMALS. - -The eyes of all animals have their pupils adapted to dilate and -diminish of their own accord in proportion to the greater or less -light of the sun or other luminary. But in birds the variation is -much greater; and particularly in nocturnal birds, such as horned -owls, and in the eyes of one species of owl; in these the pupil -dilates in such away as to occupy nearly the whole eye, or -diminishes to the size of a grain of millet, and always preserves -the circular form. But in the Lion tribe, as panthers, pards, -ounces, tigers, lynxes, Spanish cats and other similar animals the -pupil diminishes from the perfect circle to the figure of a pointed -oval such as is shown in the margin. But man having a weaker sight -than any other animal is less hurt by a very strong light and his -pupil increases but little in dark places; but in the eyes of these -nocturnal animals, the horned owl--a bird which is the largest of -all nocturnal birds--the power of vision increases so much that in -the faintest nocturnal light (which we call darkness) it sees with -much more distinctness than we do in the splendour of noon day, at -which time these birds remain hidden in dark holes; or if indeed -they are compelled to come out into the open air lighted up by the -sun, they contract their pupils so much that their power of sight -diminishes together with the quantity of light admitted. - -Study the anatomy of various eyes and see which are the muscles -which open and close the said pupils of the eyes of animals. - -[Footnote: Compare No. 24, lines 8 and fol.] - -830. - -_a b n_ is the membrane which closes the eye from below, upwards, -with an opaque film, _c n b_ encloses the eye in front and behind -with a transparent membrane. - -It closes from below, upwards, because it [the eye] comes downwards. - -When the eye of a bird closes with its two lids, the first to close -is the nictitating membrane which closes from the lacrymal duct over -to the outer corner of the eye; and the outer lid closes from below -upwards, and these two intersecting motions begin first from the -lacrymatory duct, because we have already seen that in front and -below birds are protected and use only the upper portion of the eye -from fear of birds of prey which come down from above and behind; -and they uncover first the membrane from the outer corner, because -if the enemy comes from behind, they have the power of escaping to -the front; and again the muscle called the nictitating membrane is -transparent, because, if the eye had not such a screen, they could -not keep it open against the wind which strikes against the eye in -the rush of their rapid flight. And the pupil of the eye dilates and -contracts as it sees a less or greater light, that is to say intense -brilliancy. - -831. - -If at night your eye is placed between the light and the eye of a -cat, it will see the eye look like fire. - -Remarks on the organs of speech - -(832. 833). - -832. - -_a e i o u -ba be bi bo bu -ca ce ci co cu -da de di do du -fa fe fi fo fu -ga ge gi go gu -la le li lo lu -ma me mi mo mu -na ne ni no nu -pa pe pi po pu -qa qe qi qo qu -ra re ri ro ru -sa se si so su -ta te ti to tu_ - -The tongue is found to have 24 muscles which correspond to the six -muscles which compose the portion of the tongue which moves in the -mouth. - -And when _a o u_ are spoken with a clear and rapid pronunciation, it -is necessary, in order to pronounce continuously, without any pause -between, that the opening of the lips should close by degrees; that -is, they are wide apart in saying _a_, closer in saying _o_, and -much closer still to pronounce _u_. - -It may be shown how all the vowels are pronounced with the farthest -portion of the false palate which is above the epiglottis. - -833. - -If you draw in breath by the nose and send it out by the mouth you -will hear the sound made by the division that is the membrane in -[Footnote 5: The text here breaks off.]... - -On the conditions of sight (834. 835). - -834. - -OF THE NATURE OF SIGHT. - -I say that sight is exercised by all animals, by the medium of -light; and if any one adduces, as against this, the sight of -nocturnal animals, I must say that this in the same way is subject -to the very same natural laws. For it will easily be understood that -the senses which receive the images of things do not project from -themselves any visual virtue [Footnote 4: Compare No. 68.]. On the -contrary the atmospheric medium which exists between the object and -the sense incorporates in itself the figure of things, and by its -contact with the sense transmits the object to it. If the -object--whether by sound or by odour--presents its spiritual force -to the ear or the nose, then light is not required and does not act. -The forms of objects do not send their images into the air if they -are not illuminated [8]; and the eye being thus constituted cannot -receive that from the air, which the air does not possess, although -it touches its surface. If you choose to say that there are many -animals that prey at night, I answer that when the little light -which suffices the nature of their eyes is wanting, they direct -themselves by their strong sense of hearing and of smell, which are -not impeded by the darkness, and in which they are very far superior -to man. If you make a cat leap, by daylight, among a quantity of -jars and crocks you will see them remain unbroken, but if you do the -same at night, many will be broken. Night birds do not fly about -unless the moon shines full or in part; rather do they feed between -sun-down and the total darkness of the night. - -[Footnote 8: See No. 58-67.] - -No body can be apprehended without light and shade, and light and -shade are caused by light. - -835. - -WHY MEN ADVANCED IN AGE SEE BETTER AT A DISTANCE. - -Sight is better from a distance than near in those men who are -advancing in age, because the same object transmits a smaller -impression of itself to the eye when it is distant than when it is -near. - -The seat of the common sense. - -836. - -The Common Sense, is that which judges of things offered to it by -the other senses. The ancient speculators have concluded that that -part of man which constitutes his judgment is caused by a central -organ to which the other five senses refer everything by means of -impressibility; and to this centre they have given the name Common -Sense. And they say that this Sense is situated in the centre of the -head between Sensation and Memory. And this name of Common Sense is -given to it solely because it is the common judge of all the other -five senses _i.e._ Seeing, Hearing, Touch, Taste and Smell. This -Common Sense is acted upon by means of Sensation which is placed as -a medium between it and the senses. Sensation is acted upon by means -of the images of things presented to it by the external instruments, -that is to say the senses which are the medium between external -things and Sensation. In the same way the senses are acted upon by -objects. Surrounding things transmit their images to the senses and -the senses transfer them to the Sensation. Sensation sends them to -the Common Sense, and by it they are stamped upon the memory and are -there more or less retained according to the importance or force of -the impression. That sense is most rapid in its function which is -nearest to the sensitive medium and the eye, being the highest is -the chief of the others. Of this then only we will speak, and the -others we will leave in order not to make our matter too long. -Experience tells us that the eye apprehends ten different natures of -things, that is: Light and Darkness, one being the cause of the -perception of the nine others, and the other its absence:-- Colour -and substance, form and place, distance and nearness, motion and -stillness [Footnote 15: Compare No. 23.]. - -On the origin of the soul. - -837. - -Though human ingenuity may make various inventions which, by the -help of various machines answering the same end, it will never -devise any inventions more beautiful, nor more simple, nor more to -the purpose than Nature does; because in her inventions nothing is -wanting, and nothing is superfluous, and she needs no counterpoise -when she makes limbs proper for motion in the bodies of animals. But -she puts into them the soul of the body, which forms them that is -the soul of the mother which first constructs in the womb the form -of the man and in due time awakens the soul that is to inhabit it. -And this at first lies dormant and under the tutelage of the soul of -the mother, who nourishes and vivifies it by the umbilical vein, -with all its spiritual parts, and this happens because this -umbilicus is joined to the placenta and the cotyledons, by which the -child is attached to the mother. And these are the reason why a -wish, a strong craving or a fright or any other mental suffering in -the mother, has more influence on the child than on the mother; for -there are many cases when the child loses its life from them, &c. - -This discourse is not in its place here, but will be wanted for the -one on the composition of animated bodies--and the rest of the -definition of the soul I leave to the imaginations of friars, those -fathers of the people who know all secrets by inspiration. - -[Footnote 57: _lettere incoronate_. By this term Leonardo probably -understands not the Bible only, but the works of the early Fathers, -and all the books recognised as sacred by the Roman Church.] I leave -alone the sacred books; for they are supreme truth. - -On the relations of the soul to the organs of sense. - -838. - -HOW THE FIVE SENSES ARE THE MINISTERS OF THE SOUL. - -The soul seems to reside in the judgment, and the judgment would -seem to be seated in that part where all the senses meet; and this -is called the Common Sense and is not all-pervading throughout the -body, as many have thought. Rather is it entirely in one part. -Because, if it were all-pervading and the same in every part, there -would have been no need to make the instruments of the senses meet -in one centre and in one single spot; on the contrary it would have -sufficed that the eye should fulfil the function of its sensation on -its surface only, and not transmit the image of the things seen, to -the sense, by means of the optic nerves, so that the soul--for the -reason given above-- may perceive it in the surface of the eye. In -the same way as to the sense of hearing, it would have sufficed if -the voice had merely sounded in the porous cavity of the indurated -portion of the temporal bone which lies within the ear, without -making any farther transit from this bone to the common sense, where -the voice confers with and discourses to the common judgment. The -sense of smell, again, is compelled by necessity to refer itself to -that same judgment. Feeling passes through the perforated cords and -is conveyed to this common sense. These cords diverge with infinite -ramifications into the skin which encloses the members of the body -and the viscera. The perforated cords convey volition and sensation -to the subordinate limbs. These cords and the nerves direct the -motions of the muscles and sinews, between which they are placed; -these obey, and this obedience takes effect by reducing their -thickness; for in swelling, their length is reduced, and the nerves -shrink which are interwoven among the particles of the limbs; being -extended to the tips of the fingers, they transmit to the sense the -object which they touch. - -The nerves with their muscles obey the tendons as soldiers obey the -officers, and the tendons obey the Common [central] Sense as the -officers obey the general. [27] Thus the joint of the bones obeys -the nerve, and the nerve the muscle, and the muscle the tendon and -the tendon the Common Sense. And the Common Sense is the seat of the -soul [28], and memory is its ammunition, and the impressibility is -its referendary since the sense waits on the soul and not the soul -on the sense. And where the sense that ministers to the soul is not -at the service of the soul, all the functions of that sense are also -wanting in that man's life, as is seen in those born mute and blind. - -[Footnote: The peculiar use of the words _nervo_, _muscolo_, -_corda_, _senso comune_, which are here literally rendered by nerve, -muscle cord or tendon and Common Sense may be understood from lines -27 and 28.] - -On involuntary muscular action. - -839. - -HOW THE NERVES SOMETIMES ACT OF THEMSELVES WITHOUT ANY COMMANDS FROM -THE OTHER FUNCTIONS OF THE SOUL. - -This is most plainly seen; for you will see palsied and shivering -persons move, and their trembling limbs, as their head and hands, -quake without leave from their soul and their soul with all its -power cannot prevent their members from trembling. The same thing -happens in falling sickness, or in parts that have been cut off, as -in the tails of lizards. The idea or imagination is the helm and -guiding-rein of the senses, because the thing conceived of moves the -sense. Pre-imagining, is imagining the things that are to be. -Post-imagining, is imagining the things that are past. - -Miscellaneous physiological observations (840-842). - -840. - -There are four Powers: memory and intellect, desire and -covetousness. The two first are mental and the others sensual. The -three senses: sight, hearing and smell cannot well be prevented; -touch and taste not at all. Smell is connected with taste in dogs -and other gluttonous animals. - -841. - -I reveal to men the origin of the first, or perhaps second cause of -their existence. - -842. - -Lust is the cause of generation. - -Appetite is the support of life. Fear or timidity is the -prolongation of life and preservation of its instruments. - -The laws of nutrition and the support of life (843-848). - -843. - -HOW THE BODY OF ANIMALS IS CONSTANTLY DYING AND BEING RENEWED. - -The body of any thing whatever that takes nourishment constantly -dies and is constantly renewed; because nourishment can only enter -into places where the former nourishment has expired, and if it has -expired it no longer has life. And if you do not supply nourishment -equal to the nourishment which is gone, life will fail in vigour, -and if you take away this nourishment, the life is entirely -destroyed. But if you restore as much is destroyed day by day, then -as much of the life is renewed as is consumed, just as the flame of -the candle is fed by the nourishment afforded by the liquid of this -candle, which flame continually with a rapid supply restores to it -from below as much as is consumed in dying above: and from a -brilliant light is converted in dying into murky smoke; and this -death is continuous, as the smoke is continuous; and the continuance -of the smoke is equal to the continuance of the nourishment, and in -the same instant all the flame is dead and all regenerated, -simultaneously with the movement of its own nourishment. - -844. - -King of the animals--as thou hast described him--I should rather say -king of the beasts, thou being the greatest--because thou hast -spared slaying them, in order that they may give thee their children -for the benefit of the gullet, of which thou hast attempted to make -a sepulchre for all animals; and I would say still more, if it were -allowed me to speak the entire truth [5]. But we do not go outside -human matters in telling of one supreme wickedness, which does not -happen among the animals of the earth, inasmuch as among them are -found none who eat their own kind, unless through want of sense (few -indeed among them, and those being mothers, as with men, albeit they -be not many in number); and this happens only among the rapacious -animals, as with the leonine species, and leopards, panthers lynxes, -cats and the like, who sometimes eat their children; but thou, -besides thy children devourest father, mother, brothers and friends; -nor is this enough for thee, but thou goest to the chase on the -islands of others, taking other men and these half-naked, the ... -and the ... thou fattenest, and chasest them down thy own -throat[18]; now does not nature produce enough simples, for thee to -satisfy thyself? and if thou art not content with simples, canst -thou not by the mixture of them make infinite compounds, as Platina -wrote[Footnote 21: _Come scrisse il Platina_ (Bartolomeo Sacchi, a -famous humanist). The Italian edition of his treatise _De arte -coquinaria_, was published under the title _De la honestra -voluptate, e valetudine, Venezia_ 1487.], and other authors on -feeding? - -[Footnote: We are led to believe that Leonardo himself was a -vegetarian from the following interesting passage in the first of -Andrea Corsali's letters to Giuliano de'Medici: _Alcuni gentili -chiamati Guzzarati non si cibano di cosa, alcuna che tenga sangue, -ne fra essi loro consentono che si noccia ad alcuna cosa animata, -come il nostro Leonardo da Vinci_. - -5-18. Amerigo Vespucci, with whom Leonardo was personally -acquainted, writes in his second letter to Pietro Soderini, about -the inhabitants of the Canary Islands after having stayed there in -1503: "_Hanno una scelerata liberta di viuere; ... si cibano di -carne humana, di maniera che il padre magia il figliuolo, et -all'incontro il figliuolo il padre secondo che a caso e per sorte -auiene. Io viddi un certo huomo sceleratissimo che si vantaua, et si -teneua a non piccola gloria di hauer mangiato piu di trecento -huomini. Viddi anche vna certa citta, nella quale io dimorai forse -ventisette giorni, doue le carni humane, hauendole salate, eran -appicate alli traui, si come noi alli traui di cucina_ _appicchiamo -le carni di cinghali secche al sole o al fumo, et massimamente -salsiccie, et altre simil cose: anzi si marauigliauano gradem ete -che noi non magiaissimo della carne de nemici, le quali dicono -muouere appetito, et essere di marauiglioso sapore, et le lodano -come cibi soaui et delicati (Lettere due di Amerigo Vespucci -Fiorentino drizzate al magnifico Pietro Soderini, Gonfaloniere della -eccelsa Republica di Firenze_; various editions).] - -845. - -Our life is made by the death of others. - -In dead matter insensible life remains, which, reunited to the -stomachs of living beings, resumes life, both sensual and -intellectual. - -846. - -Here nature appears with many animals to have been rather a cruel -stepmother than a mother, and with others not a stepmother, but a -most tender mother. - -847. - -Man and animals are really the passage and the conduit of food, the -sepulchre of animals and resting place of the dead, one causing the -death of the other, making themselves the covering for the -corruption of other dead [bodies]. - -On the circulation of the blood (848-850). - -848. - -Death in old men, when not from fever, is caused by the veins which -go from the spleen to the valve of the liver, and which thicken so -much in the walls that they become closed up and leave no passage -for the blood that nourishes it. - -[6]The incessant current of the blood through the veins makes these -veins thicken and become callous, so that at last they close up and -prevent the passage of the blood. - -849. - -The waters return with constant motion from the lowest depths of the -sea to the utmost height of the mountains, not obeying the nature of -heavier bodies; and in this they resemble the blood of animated -beings which always moves from the sea of the heart and flows -towards the top of the head; and here it may burst a vein, as may be -seen when a vein bursts in the nose; all the blood rises from below -to the level of the burst vein. When the water rushes out from the -burst vein in the earth, it obeys the law of other bodies that are -heavier than the air since it always seeks low places. - -[Footnote: From this passage it is quite plain that Leonardo had not -merely a general suspicion of the circulation of the blood but a -very clear conception of it. Leonardo's studies on the muscles of -the heart are to be found in the MS. W. An. III. but no information -about them has hitherto been made public. The limits of my plan in -this work exclude all purely anatomical writings, therefore only a -very brief excerpt from this note book can be given here. WILLIAM -HARVEY (born 1578 and Professor of Anatomy at Cambridge from 1615) -is always considered to have been the discoverer of the circulation -of the blood. He studied medicine at Padua in 1598, and in 1628 -brought out his memorable and important work: _De motu cordis et -sanguinis_.] - -850. - -That the blood which returns when the heart opens again is not the -same as that which closes the valves of the heart. - -Some notes on medicine (851-855). - -851. - -Make them give you the definition and remedies for the case ... and -you will see that men are selected to be doctors for diseases they -do not know. - -852. - -A remedy for scratches taught me by the Herald to the King of -France. 4 ounces of virgin wax, 4 ounces of colophony, 2 ounces of -incense. Keep each thing separate; and melt the wax, and then put in -the incense and then the colophony, make a mixture of it and put it -on the sore place. - -853. - -Medicine is the restoration of discordant elements; sickness is the -discord of the elements infused into the living body. - -854. - -Those who are annoyed by sickness at sea should drink extract of -wormwood. - -855. - -To keep in health, this rule is wise: Eat only when you want and -relish food. Chew thoroughly that it may do you good. Have it well -cooked, unspiced and undisguised. He who takes medicine is ill -advised. - -[Footnote: This appears to be a sketch for a poem.] - -856. - -I teach you to preserve your health; and in this you will succed -better in proportion as you shun physicians, because their medicines -are the work of alchemists. - -[Footnote: This passage is written on the back of the drawing Pl. -CVIII. Compare also No. 1184.] - -_XV_. - -_Astronomy_. - -_Ever since the publication by Venturi in_ 1797 _and Libri in_ 1840 -_of some few passages of Leonardo's astronomical notes, scientific -astronomers have frequently expressed the opinion, that they must -have been based on very important discoveries, and that the great -painter also deserved a conspicuous place in the history of this -science. In the passages here printed, a connected view is given of -his astronomical studies as they lie scattered through the -manuscripts, which have come down to us. Unlike his other purely -scientific labours, Leonardo devotes here a good deal of attention -to the opinions of the ancients, though he does not follow the -practice universal in his day of relying on them as authorities; he -only quotes them, as we shall see, in order to refute their -arguments. His researches throughout have the stamp of independent -thought. There is nothing in these writings to lead us to suppose -that they were merely an epitome of the general learning common to -the astronomers of the period. As early as in the XIVth century -there were chairs of astronomy in the universities of Padua and -Bologna, but so late as during the entire XVIth century Astronomy -and Astrology were still closely allied._ - -_It is impossible now to decide whether Leonardo, when living in -Florence, became acquainted in his youth with the doctrines of Paolo -Toscanelli the great astronomer and mathematician (died_ 1482_), of -whose influence and teaching but little is now known, beyond the -fact that he advised and encouraged Columbus to carry out his -project of sailing round the world. His name is nowhere mentioned by -Leonardo, and from the dates of the manuscripts from which the texts -on astronomy are taken, it seems highly probable that Leonardo -devoted his attention to astronomical studies less in his youth than -in his later years. It was evidently his purpose to treat of -Astronomy in a connected form and in a separate work (see the -beginning of Nos._ 866 _and_ 892_; compare also No._ 1167_). It is -quite in accordance with his general scientific thoroughness that he -should propose to write a special treatise on Optics as an -introduction to Astronomy (see Nos._ 867 _and_ 877_). Some of the -chapters belonging to this Section bear the title "Prospettiva" -_(see Nos._ 869 _and_ 870_), this being the term universally applied -at the time to Optics as well as Perspective (see Vol. I, p._ 10, -_note to No._ 13, _l._ 10_)_. - -_At the beginning of the XVIth century the Ptolemaic theory of the -universe was still universally accepted as the true one, and -Leonardo conceives of the earth as fixed, with the moon and sun -revolving round it, as they are represented in the diagram to No._ -897. _He does not go into any theory of the motions of the planets; -with regard to these and the fixed stars he only investigates the -phenomena of their luminosity. The spherical form of the earth he -takes for granted as an axiom from the first, and he anticipates -Newton by pointing out the universality of Gravitation not merely in -the earth, but even in the moon. Although his acute research into -the nature of the moon's light and the spots on the moon did not -bring to light many results of lasting importance beyond making it -evident that they were a refutation of the errors of his -contemporaries, they contain various explanations of facts which -modern science need not modify in any essential point, and -discoveries which history has hitherto assigned to a very much later -date_. - -_The ingenious theory by which he tries to explain the nature of -what is known as earth shine, the reflection of the sun's rays by -the earth towards the moon, saying that it is a peculiar refraction, -originating in the innumerable curved surfaces of the waves of the -sea may be regarded as absurd; but it must not be forgotten that he -had no means of detecting the fundamental error on which he based -it, namely: the assumption that the moon was at a relatively short -distance from the earth. So long as the motion of the earth round -the sun remained unknown, it was of course impossible to form any -estimate of the moon's distance from the earth by a calculation of -its parallax_. - -_Before the discovery of the telescope accurate astronomical -observations were only possible to a very limited extent. It would -appear however from certain passages in the notes here printed for -the first time, that Leonardo was in a position to study the spots -in the moon more closely than he could have done with the unaided -eye. So far as can be gathered from the mysterious language in which -the description of his instrument is wrapped, he made use of -magnifying glasses; these do not however seem to have been -constructed like a telescope--telescopes were first made about_ -1600. _As LIBRI pointed out_ (Histoire des Sciences mathematiques -III, 101) _Fracastoro of Verona_ (1473-1553) _succeeded in -magnifying the moon's face by an arrangement of lenses (compare No._ -910, _note), and this gives probability to Leonardo's invention at a -not much earlier date._ - -I. - -THE EARTH AS A PLANET. - -The earth's place in the universe (857. 858). - -857. - -The equator, the line of the horizon, the ecliptic, the meridian: - -These lines are those which in all their parts are equidistant from -the centre of the globe. - -858. - -The earth is not in the centre of the Sun's orbit nor at the centre -of the universe, but in the centre of its companion elements, and -united with them. And any one standing on the moon, when it and the -sun are both beneath us, would see this our earth and the element of -water upon it just as we see the moon, and the earth would light it -as it lights us. - -The fundamental laws of the solar system (859-864). - -859. - -Force arises from dearth or abundance; it is the child of physical -motion, and the grand-child of spiritual motion, and the mother and -origin of gravity. Gravity is limited to the elements of water and -earth; but this force is unlimited, and by it infinite worlds might -be moved if instruments could be made by which the force could be -generated. - -Force, with physical motion, and gravity, with resistance are the -four external powers on which all actions of mortals depend. - -Force has its origin in spiritual motion; and this motion, flowing -through the limbs of sentient animals, enlarges their muscles. Being -enlarged by this current the muscles are shrunk in length and -contract the tendons which are connected with them, and this is the -cause of the force of the limbs in man. - -The quality and quantity of the force of a man are able to give -birth to other forces, which will be proportionally greater as the -motions produced by them last longer. - -[Footnote: Only part of this passage belongs, strictly speaking, to -this section. The principle laid down in the second paragraph is -more directly connected with the notes given in the preceding -section on Physiology.] - -860. - -Why does not the weight _o_ remain in its place? It does not remain -because it has no resistance. Where will it move to? It will move -towards the centre [of gravity]. And why by no other line? Because a -weight which has no support falls by the shortest road to the lowest -point which is the centre of the world. And why does the weight know -how to find it by so short a line? Because it is not independant and -does not move about in various directions. - -[Footnote: This text and the sketch belonging to it, are reproduced -on Pl. CXXI.] - -861. - -Let the earth turn on which side it may the surface of the waters -will never move from its spherical form, but will always remain -equidistant from the centre of the globe. - -Granting that the earth might be removed from the centre of the -globe, what would happen to the water? - -It would remain in a sphere round that centre equally thick, but the -sphere would have a smaller diameter than when it enclosed the -earth. - -[Footnote: Compare No. 896, lines 48-64; and No. 936.] - -862. - -Supposing the earth at our antipodes which supports the ocean were -to rise and stand uncovered, far out of the sea, but remaining -almost level, by what means afterwards, in the course of time, would -mountains and vallies be formed? - -And the rocks with their various strata? - -863. - -Each man is always in the middle of the surface of the earth and -under the zenith of his own hemisphere, and over the centre of the -earth. - -864. - -Mem.: That I must first show the distance of the sun from the earth; -and, by means of a ray passing through a small hole into a dark -chamber, detect its real size; and besides this, by means of the -aqueous sphere calculate the size of the globe ... - -Here it will be shown, that when the sun is in the meridian of our -hemisphere [Footnote 10: _Antipodi orientali cogli occidentali_. The -word _Antipodes_ does not here bear its literal sense, but--as we -may infer from the simultaneous reference to inhabitants of the -North and South-- is used as meaning men living at a distance of 90 -degrees from the zenith of the rational horizon of each observer.], -the antipodes to the East and to the West, alike, and at the same -time, see the sun mirrored in their waters; and the same is equally -true of the arctic and antarctic poles, if indeed they are -inhabited. - -How to prove that the earth is a planet (865-867). - -865. - -That the earth is a star. - -866. - -In your discourse you must prove that the earth is a star much like -the moon, and the glory of our universe; and then you must treat of -the size of various stars, according to the authors. - -867. - -THE METHOD OF PROVING THAT THE EARTH IS A STAR. - -First describe the eye; then show how the twinkling of a star is -really in the eye and why one star should twinkle more than another, -and how the rays from the stars originate in the eye; and add, that -if the twinkling of the stars were really in the stars --as it seems -to be--that this twinkling appears to be an extension as great as -the diameter of the body of the star; therefore, the star being -larger than the earth, this motion effected in an instant would be a -rapid doubling of the size of the star. Then prove that the surface -of the air where it lies contiguous to fire, and the surface of the -fire where it ends are those into which the solar rays penetrate, -and transmit the images of the heavenly bodies, large when they -rise, and small, when they are on the meridian. Let _a_ be the earth -and _n d m_ the surface of the air in contact with the sphere of -fire; _h f g_ is the orbit of the moon or, if you please, of the -sun; then I say that when the sun appears on the horizon _g_, its -rays are seen passing through the surface of the air at a slanting -angle, that is _o m_; this is not the case at _d k_. And so it -passes through a greater mass of air; all of _e m_ is a denser -atmosphere. - -868. - -Beyond the sun and us there is darkness and so the air appears blue. - -[Footnote: Compare Vol. I, No. 301.] - -869. - -PERSPECTIVE. - -It is possible to find means by which the eye shall not see remote -objects as much diminished as in natural perspective, which -diminishes them by reason of the convexity of the eye which -necessarily intersects, at its surface, the pyramid of every image -conveyed to the eye at a right angle on its spherical surface. But -by the method I here teach in the margin [9] these pyramids are -intersected at right angles close to the surface of the pupil. The -convex pupil of the eye can take in the whole of our hemisphere, -while this will show only a single star; but where many small stars -transmit their images to the surface of the pupil those stars are -extremely small; here only one star is seen but it will be large. -And so the moon will be seen larger and its spots of a more defined -form [Footnote 20 and fol.: Telescopes were not in use till a century -later. Compare No. 910 and page 136.]. You must place close to the -eye a glass filled with the water of which mention is made in number -4 of Book 113 "On natural substances" [Footnote 23: _libro_ 113. -This is perhaps the number of a book in some library catalogue. But -it may refer, on the other hand, to one of the 120 Books mentioned -in No. 796. l. 84.]; for this water makes objects which are enclosed -in balls of crystalline glass appear free from the glass. - -OF THE EYE. - -Among the smaller objects presented to the pupil of the eye, that -which is closest to it, will be least appreciable to the eye. And at -the same time, the experiments here made with the power of sight, -show that it is not reduced to speck if the &c. [32][Footnote 32: -Compare with this the passage in Vol. I, No. 52, written about -twenty years earlier.]. - -Read in the margin. - -[34]Those objects are seen largest which come to the eye at the -largest angles. - -But the images of the objects conveyed to the pupil of the eye are -distributed to the pupil exactly as they are distributed in the air: -and the proof of this is in what follows; that when we look at the -starry sky, without gazing more fixedly at one star than another, -the sky appears all strewn with stars; and their proportions to the -eye are the same as in the sky and likewise the spaces between them -[61]. - -[Footnote: 9. 32. _in margine:_ lines 34-61 are, in the original, -written on the margin and above them is the diagram to which -Leonardo seems to refer here.] - -870. - -PERSPECTIVE. - -Among objects moved from the eye at equal distance, that undergoes -least diminution which at first was most remote. - -When various objects are removed at equal distances farther from -their original position, that which was at first the farthest from -the eye will diminish least. And the proportion of the diminution -will be in proportion to the relative distance of the objects from -the eye before they were removed. - -That is to say in the object _t_ and the object _e_ the proportion -of their distances from the eye _a_ is quintuple. I remove each from -its place and set it farther from the eye by one of the 5 parts into -which the proposition is divided. Hence it happens that the nearest -to the eye has doubled the distance and according to the last -proposition but one of this, is diminished by the half of its whole -size; and the body _e_, by the same motion, is diminished 1/5 of its -whole size. Therefore, by that same last proposition but one, that -which is said in this last proposition is true; and this I say of -the motions of the celestial bodies which are more distant by 3500 -miles when setting than when overhead, and yet do not increase or -diminish in any sensible degree. - -871. - -_a b_ is the aperture through which the sun passes, and if you could -measure the size of the solar rays at _n m_, you could accurately -trace the real lines of the convergence of the solar rays, the -mirror being at _a b_, and then show the reflected rays at equal -angles to _n m_; but, as you want to have them at _n m_, take them -at the. inner side of the aperture at cd, where they maybe measured -at the spot where the solar rays fall. Then place your mirror at the -distance _a b_, making the rays _d b_, _c a_ fall and then be -reflected at equal angles towards _c d_; and this is the best -method, but you must use this mirror always in the same month, and -the same day, and hour and instant, and this will be better than at -no fixed time because when the sun is at a certain distance it -produces a certain pyramid of rays. - -872. - -_a_, the side of the body in light and shade _b_, faces the whole -portion of the hemisphere bed _e f_, and does not face any part of -the darkness of the earth. And the same occurs at the point _o_; -therefore the space a _o_ is throughout of one and the same -brightness, and s faces only four degrees of the hemisphere _d e f g -h_, and also the whole of the earth _s h_, which will render it -darker; and how much must be demonstrated by calculation. [Footnote: -This passage, which has perhaps a doubtful right to its place in -this connection, stands in the Manuscript between those given in -Vol. I as No. 117 and No. 427.] - -873. - -THE REASON OF THE INCREASED SIZE OF THE SUN IN THE WEST. - -Some mathematicians explain that the sun looks larger as it sets, -because the eye always sees it through a denser atmosphere, alleging -that objects seen through mist or through water appear larger. To -these I reply: No; because objects seen through a mist are similar -in colour to those at a distance; but not being similarly diminished -they appear larger. Again, nothing increases in size in smooth -water; and the proof of this may be seen by throwing a light on a -board placed half under water. But the reason why the sun looks -larger is that every luminous body appears larger in proportion as -it is more remote. [Footnote: Lines 5 and 6 are thus rendered by M. -RAVAISSON in his edition of MS. A. "_De meme, aucune chose ne croit -dans l'eau plane, et tu en feras l'experience_ en calquant un ais -sous l'eau."--Compare the diagrams in Vol. I, p. 114.] - -On the luminosity of the Earth in the universal space (874-878). - -874. - -In my book I propose to show, how the ocean and the other seas must, -by means of the sun, make our world shine with the appearance of a -moon, and to the remoter worlds it looks like a star; and this I -shall prove. - -Show, first that every light at a distance from the eye throws out -rays which appear to increase the size of the luminous body; and -from this it follows that 2 ...[Footnote 10: Here the text breaks -off; lines 11 and fol. are written in the margin.]. - -[11]The moon is cold and moist. Water is cold and moist. Thus our -seas must appear to the moon as the moon does to us. - -875. - -The waves in water magnify the image of an object reflected in it. - -Let _a_ be the sun, and _n m_ the ruffled water, _b_ the image of -the sun when the water is smooth. Let _f_ be the eye which sees the -image in all the waves included within the base of the triangle _c e -f_. Now the sun reflected in the unruffled surface occupied the -space _c d_, while in the ruffled surface it covers all the watery -space _c e_ (as is proved in the 4th of my "Perspective") [Footnote -9: _Nel quarto della mia prospettiva_. If this reference is to the -diagrams accompanying the text--as is usual with Leonardo--and not -to some particular work, the largest of the diagrams here given must -be meant. It is the lowest and actually the fifth, but he would have -called it the fourth, for the text here given is preceded on the -same page of the manuscript by a passage on whirlpools, with the -diagram belonging to it also reproduced here. The words _della mia -prospettiva_ may therefore indicate that the diagram to the -preceding chapter treating on a heterogeneal subject is to be -excluded. It is a further difficulty that this diagram belongs -properly to lines 9-10 and not to the preceding sentence. The -reflection of the sun in water is also discussed in the Theoretical -part of the Book on Painting; see Vol. I, No. 206, 207.] and it will -cover more of the water in proportion as the reflected image is -remote from the eye [10]. - -[Footnote: In the original sketch, inside the circle in the first -diagram, is written _Sole_ (sun), and to the right of it _luna_ -(moon). Thus either of these heavenly bodies may be supposed to fill -that space. Within the lower circle is written _simulacro_ (image). -In the two next diagrams at the spot here marked _L_ the word _Luna_ -is written, and in the last _sole_ is written in the top circle at -_a_.] - -The image of the sun will be more brightly shown in small waves than -in large ones--and this is because the reflections or images of the -sun are more numerous in the small waves than in large ones, and the -more numerous reflections of its radiance give a larger light than -the fewer. - -Waves which intersect like the scales of a fir cone reflect the -image of the sun with the greatest splendour; and this is the case -because the images are as many as the ridges of the waves on which -the sun shines, and the shadows between these waves are small and -not very dark; and the radiance of so many reflections together -becomes united in the image which is transmitted to the eye, so that -these shadows are imperceptible. - -That reflection of the sun will cover most space on the surface of -the water which is most remote from the eye which sees it. - -Let _a_ be the sun, _p q_ the reflection of the sun; _a b_ is the -surface of the water, in which the sun is mirrored, and _r_ the eye -which sees this reflection on the surface of the water occupying the -space _o m_. _c_ is the eye at a greater distance from the surface -of the water and also from the reflection; hence this reflection -covers a larger space of water, by the distance between _n_ and _o_. - -876. - -It is impossible that the side of a spherical mirror, illuminated by -the sun, should reflect its radiance unless this mirror were -undulating or filled with bubbles. - -You see here the sun which lights up the moon, a spherical mirror, -and all of its surface, which faces the sun is rendered radiant. - -Whence it may be concluded that what shines in the moon is water -like that of our seas, and in waves as that is; and that portion -which does not shine consists of islands and terra firma. - -This diagram, of several spherical bodies interposed between the eye -and the sun, is given to show that, just as the reflection of the -sun is seen in each of these bodies, in the same way that image may -be seen in each curve of the waves of the sea; and as in these many -spheres many reflections of the sun are seen, so in many waves there -are many images, each of which at a great distance is much magnified -to the eye. And, as this happens with each wave, the spaces -interposed between the waves are concealed; and, for this reason, it -looks as though the many suns mirrored in the many waves were but -one continuous sun; and the shadows,, mixed up with the luminous -images, render this radiance less brilliant than that of the sun -mirrored in these waves. - -[Footnote: In the original, at letter _A_ in the diagram "_Sole_" -(the sun) is written, and at _o_ "_occhio_" (the eye).] - -877. - -This will have before it the treatise on light and shade. - -The edges in the moon will be most strongly lighted and reflect most -light, because, there, nothing will be visible but the tops of the -waves of the water [Footnote 5: I have thought it unnecessary to -reproduce the detailed explanation of the theory of reflection on -waves contained in the passage which follows this.]. - -878. - -The sun will appear larger in moving water or on waves than in still -water; an example is the light reflected on the strings of a -monochord. - -II. - -THE SUN. - -The question of the true and of the apparent size of the sun -(879-884). - -879. - -IN PRAISE OF THE SUN. - -If you look at the stars, cutting off the rays (as may be done by -looking through a very small hole made with the extreme point of a -very fine needle, placed so as almost to touch the eye), you will -see those stars so minute that it would seem as though nothing could -be smaller; it is in fact their great distance which is the reason -of their diminution, for many of them are very many times larger -than the star which is the earth with water. Now reflect what this -our star must look like at such a distance, and then consider how -many stars might be added--both in longitude and latitude--between -those stars which are scattered over the darkened sky. But I cannot -forbear to condemn many of the ancients, who said that the sun was -no larger than it appears; among these was Epicurus, and I believe -that he founded his reason on the effects of a light placed in our -atmosphere equidistant from the centre of the earth. Any one looking -at it never sees it diminished in size at whatever distance; and the -rea- - -[Footnote 879-882: What Leonardo says of Epicurus-- who according to -LEWIS, _The Astronomy of the ancients_, and MADLER, _Geschichte der -Himmelskunde_, did not devote much attention to the study of -celestial phenomena--, he probably derived from Book X of Diogenes -Laertius, whose _Vitae Philosophorum_ was not printed in Greek till -1533, but the Latin translation appeared in 1475.] - -880. - -sons of its size and power I shall reserve for Book 4. But I wonder -greatly that Socrates - -[Footnote 2: _Socrates;_ I have little light to throw on this -reference. Plato's Socrates himself declares on more than one -occasion that in his youth he had turned his mind to the study of -celestial phenomena (METEWPA) but not in his later years (see G. C. -LEWIS, _The Astronomy of the ancients_, page 109; MADLER, -_Geschichte der Himmelskunde_, page 41). Here and there in Plato's -writings we find incidental notes on the sun and other heavenly -bodies. Leonardo may very well have known of these, since the Latin -version by Ficinus was printed as early as 1491; indeed an undated -edition exists which may very likely have appeared between 1480--90. - -There is but one passage in Plato, Epinomis (p. 983) where he speaks -of the physical properties of the sun and says that it is larger -than the earth. - -Aristotle who goes very fully into the subject says the same. A -complete edition of Aristotele's works was first printed in Venice -1495-98, but a Latin version of the Books _De Coelo et Mundo_ and -_De Physica_ had been printed in Venice as early as in 1483 (H. -MULLER-STRUBING).] - -should have depreciated that solar body, saying that it was of the -nature of incandescent stone, and the one who opposed him as to that -error was not far wrong. But I only wish I had words to serve me to -blame those who are fain to extol the worship of men more than that -of the sun; for in the whole universe there is nowhere to be seen a -body of greater magnitude and power than the sun. Its light gives -light to all the celestial bodies which are distributed throughout -the universe; and from it descends all vital force, for the heat -that is in living beings comes from the soul [vital spark]; and -there is no other centre of heat and light in the universe as will -be shown in Book 4; and certainly those who have chosen to worship -men as gods--as Jove, Saturn, Mars and the like--have fallen into -the gravest error, seeing that even if a man were as large as our -earth, he would look no bigger than a little star which appears but -as a speck in the universe; and seeing again that these men are -mortal, and putrid and corrupt in their sepulchres. - -Marcellus [Footnote 23: I have no means of identifying _Marcello_ -who is named in the margin. It may be Nonius Marcellus, an obscure -Roman Grammarian of uncertain date (between the IInd and Vth -centuries A. C.) the author of the treatise _De compendiosa doctrina -per litteras ad filium_ in which he treats _de rebus omnibus et -quibusdam aliis_. This was much read in the middle ages. The _editto -princeps_ is dated 1470 (H. MULLER-STRUBING).] and many others -praise the sun. - -881. - -Epicurus perhaps saw the shadows cast by columns on the walls in -front of them equal in diameter to the columns from which the -shadows were cast; and the breadth of the shadows being parallel -from beginning to end, he thought he might infer that the sun also -was directly opposite to this parallel and that consequently its -breadth was not greater than that of the column; not perceiving that -the diminution in the shadow was insensibly slight by reason of the -remoteness of the sun. If the sun were smaller than the earth, the -stars on a great portion of our hemisphere would have no light, -which is evidence against Epicurus who says the sun is only as large -as it appears. - -[Footnote: In the original the writing is across the diagram.] - -882. - -Epicurus says the sun is the size it looks. Hence as it looks about -a foot across we must consider that to be its size; it would follow -that when the moon eclipses the sun, the sun ought not to appear the -larger, as it does. Then, the moon being smaller than the sun, the -moon must be less than a foot, and consequently when our world -eclipses the moon, it must be less than a foot by a finger's -breadth; inasmuch as if the sun is a foot across, and our earth -casts a conical shadow on the moon, it is inevitable that the -luminous cause of the cone of shadow must be larger than the opaque -body which casts the cone of shadow. - -883. - -To measure how many times the diameter of the sun will go into its -course in 24 hours. - -Make a circle and place it to face the south, after the manner of a -sundial, and place a rod in the middle in such a way as that its -length points to the centre of this circle, and mark the shadow cast -in the sunshine by this rod on the circumference of the circle, and -this shadow will be--let us say-- as broad as from _a_ to _n_. Now -measure how many times this shadow will go into this circumference -of a circle, and that will give you the number of times that the -solar body will go into its orbit in 24 hours. Thus you may see -whether Epicurus was [right in] saying that the sun was only as -large as it looked; for, as the apparent diameter of the sun is -about a foot, and as that sun would go a thousand times into the -length of its course in 24 hours, it would have gone a thousand -feet, that is 300 braccia, which is the sixth of a mile. Whence it -would follow that the course of the sun during the day would be the -sixth part of a mile and that this venerable snail, the sun will -have travelled 25 braccia an hour. - -884. - -Posidonius composed books on the size of the sun. [Footnote: -Poseidonius of Apamea, commonly called the Rhodian, because he -taught in Rhodes, was a Stoic philosopher, a contemporary and friend -of Cicero's, and the author of numerous works on natural science, -among them. - -Strabo quotes no doubt from one of his works, when he says that -Poseidonius explained how it was that the sun looked larger when it -was rising or setting than during the rest of its course (III, p. -135). Kleomedes, a later Greek Naturalist also mentions this -observation of Poseidonius' without naming the title of his work; -however, as Kleomedes' Cyclia Theorica was not printed till 1535, -Leonardo must have derived his quotation from Strabo. He probably -wrote this note in 1508, and as the original Greek was first printed -in Venice in 1516, we must suppose him to quote here from the -translation by Guarinus Veronensis, which was printed as early as -1471, also at Venice (H. MULLER-STRUBING).] - -Of the nature of Sunlight. - -885. - -OF THE PROOF THAT THE SUN IS HOT BY NATURE AND NOT BY VIRTUE. - -Of the nature of Sunlight. - -That the heat of the sun resides in its nature and not in its virtue -[or mode of action] is abundantly proved by the radiance of the -solar body on which the human eye cannot dwell and besides this no -less manifestly by the rays reflected from a concave mirror, -which--when they strike the eye with such splendour that the eye -cannot bear them--have a brilliancy equal to the sun in its own -place. And that this is true I prove by the fact that if the mirror -has its concavity formed exactly as is requisite for the collecting -and reflecting of these rays, no created being could endure the -heat that strikes from the reflected rays of such a mirror. And if -you argue that the mirror itself is cold and yet send forth hot -rays, I should reply that those rays come really from the sun and -that it is the ray of the concave mirror after having passed through -the window. - -Considerations as to the size of the sun (886-891). - -886. - -The sun does not move. [Footnote: This sentence occurs incidentally -among mathematical notes, and is written in unusually large -letters.] - -887. - -PROOF THAT THE NEARER YOU ARE TO THE SOURCE OF THE SOLAR RAYS, THE -LARGER WILL THE REFLECTION OF THE SUN FROM THE SEA APPEAR TO YOU. - -[Footnote: Lines 4 and fol. Compare Vol. I, Nos. 130, 131.] If it is -from the centre that the sun employs its radiance to intensify the -power of its whole mass, it is evident that the farther its rays -extend, the more widely they will be divided; and this being so, -you, whose eye is near the water that mirrors the sun, see but a -small portion of the rays of the sun strike the surface of the -water, and reflecting the form of the sun. But if you were near to -the sun--as would be the case when the sun is on the meridian and -the sea to the westward--you would see the sun, mirrored in the sea, -of a very great size; because, as you are nearer to the sun, your -eye taking in the rays nearer to the point of radiation takes more -of them in, and a great splendour is the result. And in this way it -can be proved that the moon must have seas which reflect the sun, -and that the parts which do not shine are land. - -888. - -Take the measure of the sun at the solstice in mid-June. - -889. - -WHY THE SUN APPEARS LARGER WHEN SETTING THAN AT NOON, WHEN IT IS -NEAR TO US. - -Every object seen through a curved medium seems to be of larger size -than it is. - -[Footnote: At A is written _sole_ (the sun), at B _terra_ (the -earth).] - -890. - -Because the eye is small it can only see the image of the sun as of -a small size. If the eye were as large as the sun it would see the -image of the sun in water of the same size as the real body of the -sun, so long as the water is smooth. - -891. - -A METHOD OF SEEING THE SUN ECLIPSED WITHOUT PAIN TO THE EYE. - -Take a piece of paper and pierce holes in it with a needle, and look -at the sun through these holes. - -III. - -THE MOON. - -On the luminousity of the moon (892-901). - -892. - -OF THE MOON. - -As I propose to treat of the nature of the moon, it is necessary -that first I should describe the perspective of mirrors, whether -plane, concave or convex; and first what is meant by a luminous ray, -and how it is refracted by various kinds of media; then, when a -reflected ray is most powerful, whether when the angle of incidence -is acute, right, or obtuse, or from a convex, a plane, or a concave -surface; or from an opaque or a transparent body. Besides this, how -it is that the solar rays which fall on the waves of the sea, are -seen by the eye of the same width at the angle nearest to the eye, -as at the highest line of the waves on the horizon; but -notwithstanding this the solar rays reflected from the waves of the -sea assume the pyramidal form and consequently, at each degree of -distance increase proportionally in size, although to our sight, -they appear as parallel. - -1st. Nothing that has very little weight is opaque. - -2dly. Nothing that is excessively weighty can remain beneath that -which is heavier. - -3dly. As to whether the moon is situated in the centre of its -elements or not. - -And, if it has no proper place of its own, like the earth, in the -midst of its elements, why does it not fall to the centre of our -elements? [Footnote 26: The problem here propounded by Leonardo was -not satisfactorily answered till Newton in 1682 formulated the law -of universal attraction and gravitation. Compare No. 902, lines -5-15.] - -And, if the moon is not in the centre of its own elements and yet -does not fall, it must then be lighter than any other element. - -And, if the moon is lighter than the other elements why is it opaque -and not transparent? - -When objects of various sizes, being placed at various distances, -look of equal size, there must be the same relative proportion in -the distances as in the magnitudes of the objects. - -[Footnote: In the diagram Leonardo wrote _sole_ at the place marked -_A_.] - -893. - -OF THE MOON AND WHETHER IT IS POLISHED AND SPHERICAL. - -The image of the sun in the moon is powerfully luminous, and is only -on a small portion of its surface. And the proof may be seen by -taking a ball of burnished gold and placing it in the dark with a -light at some distance from it; and then, although it will -illuminate about half of the ball, the eye will perceive its -reflection only in a small part of its surface, and all the rest of -the surface reflects the darkness which surrounds it; so that it is -only in that spot that the image of the light is seen, and all the -rest remains invisible, the eye being at a distance from the ball. -The same thing would happen on the surface of the moon if it were -polished, lustrous and opaque, like all bodies with a reflecting -surface. - -Show how, if you were standing on the moon or on a star, our earth -would seem to reflect the sun as the moon does. - -And show that the image of the sun in the sea cannot appear one and -undivided, as it appears in a perfectly plane mirror. - -894. - -How shadows are lost at great distances, as is shown by the shadow -side of the moon which is never seen. [Footnote: Compare also Vol. -I, Nos. 175-179.] - -895. - -Either the moon has intrinsic luminosity or not. If it has, why does -it not shine without the aid of the sun? But if it has not any light -in itself it must of necessity be a spherical mirror; and if it is a -mirror, is it not proved in Perspective that the image of a luminous -object will never be equal to the extent of surface of the -reflecting body that it illuminates? And if it be thus [Footnote 13: -At A, in the diagram, Leonardo wrote "_sole_" (the sun), and at B -"_luna o noi terra_" (the moon or our earth). Compare also the text -of No. 876.], as is here shown at _r s_ in the figure, whence comes -so great an extent of radiance as that of the full moon as we see -it, at the fifteenth day of the moon? - -896. - -OF THE MOON. - -The moon has no light in itself; but so much of it as faces the sun -is illuminated, and of that illumined portion we see so much as -faces the earth. And the moon's night receives just as much light as -is lent it by our waters as they reflect the image of the sun, which -is mirrored in all those waters which are on the side towards the -sun. The outside or surface of the waters forming the seas of the -moon and of the seas of our globe is always ruffled little or much, -or more or less--and this roughness causes an extension of the -numberless images of the sun which are repeated in the ridges and -hollows, the sides and fronts of the innumerable waves; that is to -say in as many different spots on each wave as our eyes find -different positions to view them from. This could not happen, if the -aqueous sphere which covers a great part of the moon were uniformly -spherical, for then the images of the sun would be one to each -spectator, and its reflections would be separate and independent and -its radiance would always appear circular; as is plainly to be seen -in the gilt balls placed on the tops of high buildings. But if those -gilt balls were rugged or composed of several little balls, like -mulberries, which are a black fruit composed of minute round -globules, then each portion of these little balls, when seen in the -sun, would display to the eye the lustre resulting from the -reflection of the sun, and thus, in one and the same body many tiny -suns would be seen; and these often combine at a long distance and -appear as one. The lustre of the new moon is brighter and stronger, -than when the moon is full; and the reason of this is that the angle -of incidence is more obtuse in the new than in the full moon, in -which the angles [of incidence and reflection] are highly acute. The -waves of the moon therefore mirror the sun in the hollows of the -waves as well as on the ridges, and the sides remain in shadow. But -at the sides of the moon the hollows of the waves do not catch the -sunlight, but only their crests; and thus the images are fewer and -more mixed up with the shadows in the hollows; and this -intermingling of the shaded and illuminated spots comes to the eye -with a mitigated splendour, so that the edges will be darker, -because the curves of the sides of the waves are insufficient to -reflect to the eye the rays that fall upon them. Now the new moon -naturally reflects the solar rays more directly towards the eye from -the crests of the waves than from any other part, as is shown by the -form of the moon, whose rays a strike the waves _b_ and are -reflected in the line _b d_, the eye being situated at _d_. This -cannot happen at the full moon, when the solar rays, being in the -west, fall on the extreme waters of the moon to the East from _n_ to -_m_, and are not reflected to the eye in the West, but are thrown -back eastwards, with but slight deflection from the straight course -of the solar ray; and thus the angle of incidence is very wide -indeed. - -The moon is an opaque and solid body and if, on the contrary, it -were transparent, it would not receive the light of the sun. - -The yellow or yolk of an egg remains in the middle of the albumen, -without moving on either side; now it is either lighter or heavier -than this albumen, or equal to it; if it is lighter, it ought to -rise above all the albumen and stop in contact with the shell of the -egg; and if it is heavier, it ought to sink, and if it is equal, it -might just as well be at one of the ends, as in the middle or below -[54]. - -[Footnote 48-64: Compare No. 861.] - -The innumerable images of the solar rays reflected from the -innumerable waves of the sea, as they fall upon those waves, are -what cause us to see the very broad and continuous radiance on the -surface of the sea. - -897. - -That the sun could not be mirrored in the body of the moon, which is -a convex mirror, in such a way as that so much of its surface as is -illuminated by the sun, should reflect the sun unless the moon had a -surface adapted to reflect it--in waves and ridges, like the surface -of the sea when its surface is moved by the wind. - -[Footnote: In the original diagrams _sole_ is written at the place -marked _A; luna_ at _C,_ and _terra_ at the two spots marked _B_.] - -The waves in water multiply the image of the object reflected in it. - -These waves reflect light, each by its own line, as the surface of -the fir cone does [Footnote 14: See the diagram p. 145.] - -These are 2 figures one different from the other; one with -undulating water and the other with smooth water. - -It is impossible that at any distance the image of the sun cast on -the surface of a spherical body should occupy the half of the -sphere. - -Here you must prove that the earth produces all the same effects -with regard to the moon, as the moon with regard to the earth. - -The moon, with its reflected light, does not shine like the sun, -because the light of the moon is not a continuous reflection of that -of the sun on its whole surface, but only on the crests and hollows -of the waves of its waters; and thus the sun being confusedly -reflected, from the admixture of the shadows that lie between the -lustrous waves, its light is not pure and clear as the sun is. - -[Footnote 38: This refers to the small diagram placed between _B_ -and _B_.--]. The earth between the moon on the fifteenth day and the -sun. [Footnote 39: See the diagram below the one referred to in the -preceding note.] Here the sun is in the East and the moon on the -fifteenth day in the West. [Footnote 40.41: Refers to the diagram -below the others.] The moon on the fifteenth [day] between the earth -and the sun. [41]Here it is the moon which has the sun to the West -and the earth to the East. - -898. - -WHAT SORT OF THING THE MOON IS. - -The moon is not of itself luminous, but is highly fitted to -assimilate the character of light after the manner of a mirror, or -of water, or of any other reflecting body; and it grows larger in -the East and in the West, like the sun and the other planets. And -the reason is that every luminous body looks larger in proportion as -it is remote. It is easy to understand that every planet and star is -farther from us when in the West than when it is overhead, by about -3500 miles, as is proved on the margin [Footnote 7: refers to the -first diagram.--A = _sole_ (the sun), B = _terra_ (the earth), C = -_luna_ (the moon).], and if you see the sun or moon mirrored in the -water near to you, it looks to you of the same size in the water as -in the sky. But if you recede to the distance of a mile, it will -look 100 times larger; and if you see the sun reflected in the sea -at sunset, its image would look to you more than 10 miles long; -because that reflected image extends over more than 10 miles of sea. -And if you could stand where the moon is, the sun would look to you, -as if it were reflected from all the sea that it illuminates by day; -and the land amid the water would appear just like the dark spots -that are on the moon, which, when looked at from our earth, appears -to men the same as our earth would appear to any men who might dwell -in the moon. - -[Footnote: This text has already been published by LIBRI: _Histoire -des Sciences,_ III, pp. 224, 225.] - -OF THE NATURE OF THE MOON. - -When the moon is entirely lighted up to our sight, we see its full -daylight; and at that time, owing to the reflection of the solar -rays which fall on it and are thrown off towards us, its ocean casts -off less moisture towards us; and the less light it gives the more -injurious it is. - -899. - -OF THE MOON. - -I say that as the moon has no light in itself and yet is luminous, -it is inevitable but that its light is caused by some other body. - -900. - -OF THE MOON. - -All my opponent's arguments to say that there is no water in the -moon. [Footnote: The objections are very minutely noted down in the -manuscript, but they hardly seem to have a place here.] - -901. - -Answer to Maestro Andrea da Imola, who said that the solar rays -reflected from a convex mirror are mingled and lost at a short -distance; whereby it is altogether denied that the luminous side of -the moon is of the nature of a mirror, and that consequently the -light is not produced by the innumerable multitude of the waves of -that sea, which I declared to be the portion of the moon which is -illuminated by the solar rays. - -Let _o p_ be the body of the sun, _c n s_ the moon, and _b_ the eye -which, above the base _c n_ of the cathetus _c n m_, sees the body -of the sun reflected at equal angles _c n_; and the same again on -moving the eye from _b_ to _a_. [Footnote: The large diagram on the -margin of page 161 belongs to this chapter.] - -Explanation of the lumen cinereum in the moon. - -902. - -OF THE MOON. - -No solid body is less heavy than the atmosphere. - -[Footnote: 1. On the margin are the words _tola romantina, -tola--ferro stagnato_ (tinned iron); _romantina_ is some special -kind of sheet-iron no longer known by that name.] - -Having proved that the part of the moon that shines consists of -water, which mirrors the body of the sun and reflects the radiance -it receives from it; and that, if these waters were devoid of waves, -it would appear small, but of a radiance almost like the sun; --[5] -It must now be shown whether the moon is a heavy or a light body: -for, if it were a heavy body--admitting that at every grade of -distance from the earth greater levity must prevail, so that water -is lighter than the earth, and air than water, and fire than air and -so on successively--it would seem that if the moon had density as it -really has, it would have weight, and having weight, that it could -not be sustained in the space where it is, and consequently that it -would fall towards the centre of the universe and become united to -the earth; or if not the moon itself, at least its waters would fall -away and be lost from it, and descend towards the centre, leaving -the moon without any and so devoid of lustre. But as this does not -happen, as might in reason be expected, it is a manifest sign that -the moon is surrounded by its own elements: that is to say water, -air and fire; and thus is, of itself and by itself, suspended in -that part of space, as our earth with its element is in this part of -space; and that heavy bodies act in the midst of its elements just -as other heavy bodies do in ours [Footnote 15: This passage would -certainly seem to establish Leonardo's claim to be regarded as the -original discoverer of the cause of the ashy colour of the new moon -(_lumen cinereum_). His observations however, having hitherto -remained unknown to astronomers, Moestlin and Kepler have been -credited with the discoveries which they made independently a -century later. - -Some disconnected notes treat of the same subject in MS. C. A. 239b; -718b and 719b; "_Perche la luna cinta della parte alluminata dal -sole in ponente, tra maggior splendore in mezzo a tal cerchio, che -quando essa eclissava il sole. Questo accade perche nell' eclissare -il sole ella ombrava il nostro oceano, il qual caso non accade -essendo in ponente, quando il sole alluma esso oceano_." The editors -of the "_Saggio_" who first published this passage (page 12) add -another short one about the seasons in the moon which I confess not -to have seen in the original manuscript: "_La luna ha ogni mese un -verno e una state, e ha maggiori freddi e maggiori caldi, e i suoi -equinozii son piu freddi de' nostri._"] - -When the eye is in the East and sees the moon in the West near to -the setting sun, it sees it with its shaded portion surrounded by -luminous portions; and the lateral and upper portion of this light -is derived from the sun, and the lower portion from the ocean in the -West, which receives the solar rays and reflects them on the lower -waters of the moon, and indeed affords the part of the moon that is -in shadow as much radiance as the moon gives the earth at midnight. -Therefore it is not totally dark, and hence some have believed that -the moon must in parts have a light of its own besides that which is -given it by the sun; and this light is due, as has been said, to the -above- mentioned cause,--that our seas are illuminated by the sun. - -Again, it might be said that the circle of radiance shown by the -moon when it and the sun are both in the West is wholly borrowed -from the sun, when it, and the sun, and the eye are situated as is -shown above. - -[Footnote 23. 24: The larger of the two diagrams reproduced above -stands between these two lines, and the smaller one is sketched in -the margin. At the spot marked _A_ Leonardo wrote _corpo solare_ -(solar body) in the larger diagram and _Sole_ (sun) in the smaller -one. At _C luna_ (moon) is written and at _B terra_ (the earth).] - -Some might say that the air surrounding the moon as an element, -catches the light of the sun as our atmosphere does, and that it is -this which completes the luminous circle on the body of the moon. - -Some have thought that the moon has a light of its own, but this -opinion is false, because they have founded it on that dim light -seen between the hornes of the new moon, which looks dark where it -is close to the bright part, while against the darkness of the -background it looks so light that many have taken it to be a ring of -new radiance completing the circle where the tips of the horns -illuminated by the sun cease to shine [Footnote 34: See Pl. CVIII, -No. 5.]. And this difference of background arises from the fact that -the portion of that background which is conterminous with the bright -part of the moon, by comparison with that brightness looks darker -than it is; while at the upper part, where a portion of the luminous -circle is to be seen of uniform width, the result is that the moon, -being brighter there than the medium or background on which it is -seen by comparison with that darkness it looks more luminous at that -edge than it is. And that brightness at such a time itself is -derived from our ocean and other inland-seas. These are, at that -time, illuminated by the sun which is already setting in such a way -as that the sea then fulfils the same function to the dark side of -the moon as the moon at its fifteenth day does to us when the sun is -set. And the small amount of light which the dark side of the moon -receives bears the same proportion to the light of that side which -is illuminated, as that... [Footnote 42: Here the text breaks off; -lines 43-52 are written on the margin.]. - -If you want to see how much brighter the shaded portion of the moon -is than the background on which it is seen, conceal the luminous -portion of the moon with your hand or with some other more distant -object. - -On the spots in the moon (903-907). - -903. - -THE SPOTS ON THE MOON. - -Some have said that vapours rise from the moon, after the manner of -clouds and are interposed between the moon and our eyes. But, if -this were the case, these spots would never be permanent, either as -to position or form; and, seeing the moon from various aspects, even -if these spots did not move they would change in form, as objects do -which are seen from different sides. - -904. - -OF THE SPOTS ON THE MOON. - -Others say that the moon is composed of more or less transparent -parts; as though one part were something like alabaster and others -like crystal or glass. It would follow from this that the sun -casting its rays on the less transparent portions, the light would -remain on the surface, and so the denser part would be illuminated, -and the transparent portions would display the shadow of their -darker depths; and this is their account of the structure and nature -of the moon. And this opinion has found favour with many -philosophers, and particularly with Aristotle, and yet it is a false -view--for, in the various phases and frequent changes of the moon -and sun to our eyes, we should see these spots vary, at one time -looking dark and at another light: they would be dark when the sun -is in the West and the moon in the middle of the sky; for then the -transparent hollows would be in shadow as far as the tops of the -edges of those transparent hollows, because the sun could not then -fling his rays into the mouth of the hollows, which however, at full -moon, would be seen in bright light, at which time the moon is in -the East and faces the sun in the West; then the sun would -illuminate even the lowest depths of these transparent places and -thus, as there would be no shadows cast, the moon at these times -would not show us the spots in question; and so it would be, now -more and now less, according to the changes in the position of the -sun to the moon, and of the moon to our eyes, as I have said above. - -905. - -OF THE SPOTS ON THE MOON. - -It has been asserted, that the spots on the moon result from the -moon being of varying thinness or density; but if this were so, when -there is an eclipse of the moon the solar rays would pierce through -the portions which were thin as is alleged [Footnote 3-5: _Eclissi_. -This word, as it seems to me, here means eclipses of the sun; and -the sense of the passage, as I understand it, is that by the -foregoing hypothesis the moon, when it comes between the sun and the -earth must appear as if pierced,--we may say like a sieve.]. But as -we do not see this effect the opinion must be false. - -Others say that the surface of the moon is smooth and polished and -that, like a mirror, it reflects in itself the image of our earth. -This view is also false, inasmuch as the land, where it is not -covered with water, presents various aspects and forms. Hence when -the moon is in the East it would reflect different spots from those -it would show when it is above us or in the West; now the spots on -the moon, as they are seen at full moon, never vary in the course of -its motion over our hemisphere. A second reason is that an object -reflected in a convex body takes up but a small portion of that -body, as is proved in perspective [Footnote 18: _come e provato_. -This alludes to the accompanying diagram.]. The third reason is that -when the moon is full, it only faces half the hemisphere of the -illuminated earth, on which only the ocean and other waters reflect -bright light, while the land makes spots on that brightness; thus -half of our earth would be seen girt round with the brightness of -the sea lighted up by the sun, and in the moon this reflection would -be the smallest part of that moon. Fourthly, a radiant body cannot -be reflected from another equally radiant; therefore the sea, since -it borrows its brightness from the sun,--as the moon does--, could -not cause the earth to be reflected in it, nor indeed could the body -of the sun be seen reflected in it, nor indeed any star opposite to -it. - -906. - -If you keep the details of the spots of the moon under observation -you will often find great variation in them, and this I myself have -proved by drawing them. And this is caused by the clouds that rise -from the waters in the moon, which come between the sun and those -waters, and by their shadow deprive these waters of the sun's rays. -Thus those waters remain dark, not being able to reflect the solar -body. - -907. - -How the spots on the moon must have varied from what they formerly -were, by reason of the course of its waters. - -On the moon's halo. - -908. - -OF HALOS ROUND THE MOON. - -I have found, that the circles which at night seem to surround the -moon, of various sizes, and degrees of density are caused by various -gradations in the densities of the vapours which exist at different -altitudes between the moon and our eyes. And of these halos the -largest and least red is caused by the lowest of these vapours; the -second, smaller one, is higher up, and looks redder because it is -seen through two vapours. And so on, as they are higher they will -appear smaller and redder, because, between the eye and them, there -is thicker vapour. Whence it is proved that where they are seen to -be reddest, the vapours are most dense. - -On instruments for observing the moon (909. 910). - -909. - -If you want to prove why the moon appears larger than it is, when it -reaches the horizon; take a lens which is highly convex on one -surface and concave on the opposite, and place the concave side next -the eye, and look at the object beyond the convex surface; by this -means you will have produced an exact imitation of the atmosphere -included beneath the sphere of fire and outside that of water; for -this atmosphere is concave on the side next the earth, and convex -towards the fire. - -910. - -Construct glasses to see the moon magnified. - -[Footnote: See the Introduction, p. 136, Fracastoro says in his work -Homocentres: "_Per dua specilla ocularla si quis perspiciat, alteri -altero superposito, majora multo et propinquiora videbit -omnia.--Quin imo quaedam specilla ocularia fiunt tantae densitatis, -ut si per ea quis aut lunam, aut aliud siderum spectet, adeo -propinqua illa iudicet, ut ne turres ipsas excedant_" (sect. II c. 8 -and sect. III, c. 23).] - -I. -THE STARS. -On the light of the stars (911-913). -911. -The stars are visible by night and not by day, because we are -eneath the dense atmosphere, which is full of innumerable -articles of moisture, each of which independently, when the -ays of the sun fall upon it, reflects a radiance, and so these -umberless bright particles conceal the stars; and if it were not -or this atmosphere the sky would always display the stars against -ts darkness. -[Footnote: See No. 296, which also refers to starlight.] -912. -Whether the stars have their light from the sun or in themselves. -Some say that they shine of themselves, alledging that if Venus -nd Mercury had not a light of their own, when they come between -ur eye and the sun they would darken so much of the sun as they -ould cover from our eye. But this is false, for it is proved that - dark object against a luminous body is enveloped and entirely -oncealed by the lateral rays of the rest of that luminous body -nd so remains invisible. As may be seen when the sun is seen -hrough the boughs of trees bare of their leaves, at some distance -he branches do not conceal any portion of the sun from our eye. -he same thing happens with the above mentioned planets which, -hough they have no light of their own, do not--as has been said-- -onceal any part of the sun from our eye -[18]. - -SECOND ARGUMENT. - -Some say that the stars appear most brilliant at night in proportion -as they are higher up; and that if they had no light of their own, -the shadow of the earth which comes between them and the sun, would -darken them, since they would not face nor be faced by the solar -body. But those persons have not considered that the conical shadow -of the earth cannot reach many of the stars; and even as to those it -does reach, the cone is so much diminished that it covers very -little of the star's mass, and all the rest is illuminated by the -sun. - -Footnote: From this and other remarks (see No. 902) it is clear -hat Leonardo was familiar with the phenomena of Irradiation.] - -13. - -Why the planets appear larger in the East than they do overhead, -whereas the contrary should be the case, as they are 3500 miles -nearer to us when in mid sky than when on the horizon. - -All the degrees of the elements, through which the images of the -celestial bodies pass to reach the eye, are equal curves and the -angles by which the central line of those images passes through -them, are unequal angles [Footnote 13: _inequali_, here and -elsewhere does not mean unequal in the sense of not being equal to -each other, but angles which are not right angles.]; and the -distance is greater, as is shown by the excess of _a b_ beyond _a -d_; and the enlargement of these celestial bodies on the horizon is -shown by the 9th of the 7th. - -Observations on the stars. - -914. - -To see the real nature of the planets open the covering and note at -the base [Footnote 4: _basa_. This probably alludes to some -instrument, perhaps the Camera obscura.] one single planet, and the -reflected movement of this base will show the nature of the said -planet; but arrange that the base may face only one at the time. - -On history of astronomy. - -915. - -Cicero says in [his book] De Divinatione that Astrology has been -practised five hundred seventy thousand years before the Trojan war. - -57000. - -[Footnote: The statement that CICERO, _De Divin._ ascribes the -discovery of astrology to a period 57000 years before the Trojan war -I believe to be quite erroneous. According to ERNESTI, _Clavis -Ciceroniana,_ CH. G. SCHULZ (_Lexic. Cicer._) and the edition of _De -Divin._ by GIESE the word Astrologia occurs only twice in CICERO: -_De Divin. II_, 42. _Ad Chaldaeorum monstra veniamus, de quibus -Eudoxus, Platonis auditor, in astrologia judicio doctissimorum -hominum facile princeps, sic opinatur (id quod scriptum reliquit): -Chaldaeis in praedictione et in notatione cujusque vitae ex natali -die minime esse credendum._" He then quotes the condemnatory verdict -of other philosophers as to the teaching of the Chaldaeans but says -nothing as to the antiquity and origin of astronomy. CICERO further -notes _De oratore_ I, 16 that Aratus was "_ignarus astrologiae_" but -that is all. So far as I know the word occurs nowhere else in -CICERO; and the word _Astronomia_ he does not seem to have used at -all. (H. MULLER-STRUBING.)] - -Of time and its divisions (916-918). - -916. - -Although time is included in the class of Continuous Quantities, -being indivisible and immaterial, it does not come entirely under -the head of Geometry, which represents its divisions by means of -figures and bodies of infinite variety, such as are seen to be -continuous in their visible and material properties. But only with -its first principles does it agree, that is with the Point and the -Line; the point may be compared to an instant of time, and the line -may be likened to the length of a certain quantity of time, and just -as a line begins and terminates in a point, so such a space of time. -begins and terminates in an instant. And whereas a line is -infinitely divisible, the divisibility of a space of time is of the -same nature; and as the divisions of the line may bear a certain -proportion to each other, so may the divisions of time. - -[Footnote: This passage is repeated word for word on page 190b of -the same manuscript and this is accounted for by the text in Vol. I, -No. 4. Compare also No. 1216.] - -917. - -Describe the nature of Time as distinguished from the Geometrical -definitions. - -918. - -Divide an hour into 3000 parts, and this you can do with a clock by -making the pendulum lighter or heavier. - -_XVI. - -Physical Geography. - -Leonardo's researches as to the structure of the earth and sea were -made at a time, when the extended voyages of the Spaniards and -Portuguese had also excited a special interest in geographical -questions in Italy, and particularly in Tuscany. Still, it need -scarcely surprise us to find that in deeper questions, as to the -structure of the globe, the primitive state of the earth's surface, -and the like, he was far in advance of his time. - -The number of passages which treat of such matters is relatively -considerable; like almost all Leonardo's scientific notes they deal -partly with theoretical and partly with practical questions. Some of -his theoretical views of the motion of water were collected in a -copied manuscript volume by an early transcriber, but without any -acknowledgment of the source whence they were derived. This copy is -now in the Library of the Barberini palace at Rome and was published -under the title: "De moto e misura dell'acqua," by FRANCESCO -CARDINALI, Bologna_ 1828. _In this work the texts are arranged under -the following titles:_ Libr. I. Della spera dell'acqua; Libr. II. -Del moto dell'acqua; Libr. III. Dell'onda dell'acqua; Libr. IV. Dei -retrosi d'acqua; Libr. V. Dell'acqua cadente; Libr. VI. Delle -rotture fatte dall'acqua; Libr. VII Delle cose portate dall'acqua; -Libr. VIII. Dell'oncia dell'acqua e delle canne; Libr. IX. De molini -e d'altri ordigni d'acqua. - -_The large number of isolated observations scattered through the -manuscripts, accounts for our so frequently finding notes of new -schemes for the arrangement of those relating to water and its -motions, particularly in the Codex Atlanticus: I have printed -several of these plans as an introduction to the Physical Geography, -and I have actually arranged the texts in accordance with the clue -afforded by one of them which is undoubtedly one of the latest notes -referring to the subject (No._ 920_). The text given as No._ 930 -_which is also taken from a late note-book of Leonardo's, served as -a basis for the arrangement of the first of the seven books--or -sections--, bearing the title: Of the Nature of Water_ (Dell'acque -in se). - -_As I have not made it any part of this undertaking to print the -passages which refer to purely physical principles, it has also been -necessary to exclude those practical researches which, in accordance -with indications given in_ 920, _ought to come in as Books_ 13, 14 -_and_ 15. _I can only incidentally mention here that Leonardo--as it -seems to me, especially in his youth--devoted a great deal of -attention to the construction of mills. This is proved by a number -of drawings of very careful and minute execution, which are to be -found in the Codex Atlanticus. Nor was it possible to include his -considerations on the regulation of rivers, the making of canals and -so forth (No._ 920, _Books_ 10, 11 _and_ 12_); but those passages in -which the structure of a canal is directly connected with notices of -particular places will be found duly inserted under section XVII -(Topographical notes). In Vol. I, No._ 5 _the text refers to -canal-making in general._ - -_On one point only can the collection of passages included under the -general heading of Physical Geography claim to be complete. When -comparing and sorting the materials for this work I took particular -care not to exclude or omit any text in which a geographical name -was mentioned even incidentally, since in all such researches the -chief interest, as it appeared to me, attached to the question -whether these acute observations on the various local -characteristics of mountains, rivers or seas, had been made by -Leonardo himself, and on the spot. It is self-evident that the few -general and somewhat superficial observations on the Rhine and the -Danube, on England and Flanders, must have been obtained from maps -or from some informants, and in the case of Flanders Leonardo -himself acknowledges this (see No._ 1008_). But that most of the -other and more exact observations were made, on the spot, by -Leonardo himself, may be safely assumed from their method and the -style in which he writes of them; and we should bear it in mind that -in all investigations, of whatever kind, experience is always spoken -of as the only basis on which he relies. Incidentally, as in No._ -984, _he thinks it necessary to allude to the total absence of all -recorded observations._ - -I. - -INTRODUCTION. - -Schemes for the arrangement of the materials (919-928). - -919. - -These books contain in the beginning: Of the nature of water itself -in its motions; the others treat of the effects of its currents, -which change the world in its centre and its shape. - -920. - -DIVISIONS OF THE BOOK. - -Book 1 of water in itself. - -Book 2 of the sea. - -Book 3 of subterranean rivers. - -Book 4 of rivers. - -Book 5 of the nature of the abyss. - -Book 6 of the obstacles. - -Book 7 of gravels. - -Book 8 of the surface of water. - -Book 9 of the things placed therein. - -Book 10 of the repairing of rivers. - -Book 11 of conduits. - -Book 12 of canals. - -Book 13 of machines turned by water. - -Book 14 of raising water. - -Book 15 of matters worn away by water. - -921. - -First you shall make a book treating of places occupied by fresh -waters, and the second by salt waters, and the third, how by the -disappearance of these, our parts of the world were made lighter and -in consequence more remote from the centre of the world. - -922. - -First write of all water, in each of its motions; then describe all -its bottoms and their various materials, always referring to the -propositions concerning the said waters; and let the order be good, -for otherwise the work will be confused. - -Describe all the forms taken by water from its greatest to its -smallest wave, and their causes. - -923. - -Book 9, of accidental risings of water. - -924. - -THE ORDER OF THE BOOK. - -Place at the beginning what a river can effect. - -925. - -A book of driving back armies by the force of a flood made by -releasing waters. - -A book showing how the waters safely bring down timber cut in the -mountains. - -A book of boats driven against the impetus of rivers. - -A book of raising large bridges higher. Simply by the swelling of -the waters. - -A book of guarding against the impetus of rivers so that towns may -not be damaged by them. - -926. - -A book of the ordering of rivers so as to preserve their banks. - -A book of the mountains, which would stand forth and become land, if -our hemisphere were to be uncovered by the water. - -A book of the earth carried down by the waters to fill up the great -abyss of the seas. - -A book of the ways in which a tempest may of itself clear out filled -up sea-ports. - -A book of the shores of rivers and of their permanency. - -A book of how to deal with rivers, so that they may keep their -bottom scoured by their own flow near the cities they pass. - -A book of how to make or to repair the foundations for bridges over -the rivers. - -A book of the repairs which ought to be made in walls and banks of -rivers where the water strikes them. - -A book of the formation of hills of sand or gravel at great depths -in water. - -927. - -Water gives the first impetus to its motion. - -A book of the levelling of waters by various means, - -A book of diverting rivers from places where they do mischief. - -A book of guiding rivers which occupy too much ground. - -A book of parting rivers into several branches and making them -fordable. - -A book of the waters which with various currents pass through seas. - -A book of deepening the beds of rivers by means of currents of -water. - -A book of controlling rivers so that the little beginnings of -mischief, caused by them, may not increase. - -A book of the various movements of waters passing through channels -of different forms. - -A book of preventing small rivers from diverting the larger one into -which their waters run. - -A book of the lowest level which can be found in the current of the -surface of rivers. - -A book of the origin of rivers which flow from the high tops of -mountains. - -A book of the various motions of waters in their rivers. - -928. - -[1] Of inequality in the concavity of a ship. [Footnote 1: The first -line of this passage was added subsequently, evidently as a -correction of the following line.] - -[1] A book of the inequality in the curve of the sides of ships. - -[1] A book of the inequality in the position of the tiller. - -[1] A book of the inequality in the keel of ships. - -[2] A book of various forms of apertures by which water flows out. - -[3] A book of water contained in vessels with air, and of its -movements. - -[4] A book of the motion of water through a syphon. [Footnote 7: -_cicognole_, see No. 966, 11, 17.] - -[5] A book of the meetings and union of waters coming from different -directions. - -[6] A book of the various forms of the banks through which rivers -pass. - -[7] A book of the various forms of shoals formed under the sluices -of rivers. - -[8] A book of the windings and meanderings of the currents of -rivers. - -[9] A book of the various places whence the waters of rivers are -derived. - -[10] A book of the configuration of the shores of rivers and of -their permanency. - -[11] A book of the perpendicular fall of water on various objects. - -[12] Abook of the course of water when it is impeded in various -places. - -[12] A book of the various forms of the obstacles which impede the -course of waters. - -[13] A book of the concavity and globosity formed round various -objects at the bottom. - -[14] Abook of conducting navigable canals above or beneath the -rivers which intersect them. - -[15] A book of the soils which absorb water in canals and of -repairing them. - -[16] Abook of creating currents for rivers, which quit their beds, -[and] for rivers choked with soil. - -General introduction. - -929. - -THE BEGINNING OF THE TREATISE ON WATER. - -By the ancients man has been called the world in miniature; and -certainly this name is well bestowed, because, inasmuch as man is -composed of earth, water, air and fire, his body resembles that of -the earth; and as man has in him bones the supports and framework of -his flesh, the world has its rocks the supports of the earth; as man -has in him a pool of blood in which the lungs rise and fall in -breathing, so the body of the earth has its ocean tide which -likewise rises and falls every six hours, as if the world breathed; -as in that pool of blood veins have their origin, which ramify all -over the human body, so likewise the ocean sea fills the body of the -earth with infinite springs of water. The body of the earth lacks -sinews and this is, because the sinews are made expressely for -movements and, the world being perpetually stable, no movement takes -place, and no movement taking place, muscles are not necessary. ---But in all other points they are much alike. - -I. - -OF THE NATURE OF WATER. - -The arrangement of Book I. - -930. - -THE ORDER OF THE FIRST BOOK ON WATER. - -Define first what is meant by height and depth; also how the -elements are situated one inside another. Then, what is meant by -solid weight and by liquid weight; but first what weight and -lightness are in themselves. Then describe why water moves, and why -its motion ceases; then why it becomes slower or more rapid; besides -this, how it always falls, being in contact with the air but lower -than the air. And how water rises in the air by means of the heat of -the sun, and then falls again in rain; again, why water springs -forth from the tops of mountains; and if the water of any spring -higher than the ocean can pour forth water higher than the surface -of that ocean. And how all the water that returns to the ocean is -higher than the sphere of waters. And how the waters of the -equatorial seas are higher than the waters of the North, and higher -beneath the body of the sun than in any part of the equatorial -circle; for experiment shows that under the heat of a burning brand -the water near the brand boils, and the water surrounding this -ebullition always sinks with a circular eddy. And how the waters of -the North are lower than the other seas, and more so as they become -colder, until they are converted into ice. - -Definitions (931. 932). - -931. - -OF WHAT IS WATER. - -Among the four elements water is the second both in weight and in -instability. - -932. - -THE BEGINNING OF THE BOOK ON WATER. - -Sea is the name given to that water which is wide and deep, in which -the waters have not much motion. - -[Footnote: Only the beginning of this passage is here given, the -remainder consists of definitions which have no direct bearing on -the subject.] - -Of the surface of the water in relation to the globe (933-936). - -933. - -The centres of the sphere of water are two, one universal and common -to all water, the other particular. The universal one is that which -is common to all waters not in motion, which exist in great -quantities. As canals, ditches, ponds, fountains, wells, dead -rivers, lakes, stagnant pools and seas, which, although they are at -various levels, have each in itself the limits of their superficies -equally distant from the centre of the earth, such as lakes placed -at the tops of high mountains; as the lake near Pietra Pana and the -lake of the Sybil near Norcia; and all the lakes that give rise to -great rivers, as the Ticino from Lago Maggiore, the Adda from the -lake of Como, the Mincio from the lake of Garda, the Rhine from the -lakes of Constance and of Chur, and from the lake of Lucerne, like -the Tigris which passes through Asia Minor carrying with it the -waters of three lakes, one above the other at different heights of -which the highest is Munace, the middle one Pallas, and the lowest -Triton; the Nile again flows from three very high lakes in Ethiopia. - -[Footnote 5: _Pietra Pana_, a mountain near Florence. If for Norcia, -we may read Norchia, the remains of the Etruscan city near Viterbo, -there can be no doubt that by '_Lago della Sibilla_'--a name not -known elsewhere, so far as I can learn--Leonardo meant _Lago di -Vico_ (Lacus Ciminus, Aen. 7).] - -934. - -OF THE CENTRE OF THE OCEAN. - -The centre of the sphere of waters is the true centre of the globe -of our world, which is composed of water and earth, having the shape -of a sphere. But, if you want to find the centre of the element of -the earth, this is placed at a point equidistant from the surface of -the ocean, and not equidistant from the surface of the earth; for it -is evident that this globe of earth has nowhere any perfect -rotundity, excepting in places where the sea is, or marshes or other -still waters. And every part of the earth that rises above the water -is farther from the centre. - -935. - -OF THE SEA WHICH CHANGES THE WEIGHT OF THE EARTH. - -The shells, oysters, and other similar animals, which originate in -sea-mud, bear witness to the changes of the earth round the centre -of our elements. This is proved thus: Great rivers always run -turbid, being coloured by the earth, which is stirred by the -friction of their waters at the bottom and on their shores; and this -wearing disturbs the face of the strata made by the layers of -shells, which lie on the surface of the marine mud, and which were -produced there when the salt waters covered them; and these strata -were covered over again from time to time, with mud of various -thickness, or carried down to the sea by the rivers and floods of -more or less extent; and thus these layers of mud became raised to -such a height, that they came up from the bottom to the air. At the -present time these bottoms are so high that they form hills or high -mountains, and the rivers, which wear away the sides of these -mountains, uncover the strata of these shells, and thus the softened -side of the earth continually rises and the antipodes sink closer to -the centre of the earth, and the ancient bottoms of the seas have -become mountain ridges. - -936. - -Let the earth make whatever changes it may in its weight, the -surface of the sphere of waters can never vary in its equal distance -from the centre of the world. - -Of the proportion of the mass of water to that of the earth (937. -938). - -937. - -WHETHER THE EARTH IS LESS THAN THE WATER. - -Some assert that it is true that the earth, which is not covered by -water is much less than that covered by water. But considering the -size of 7000 miles in diameter which is that of this earth, we may -conclude the water to be of small depth. - -938. - -OF THE EARTH. - -The great elevations of the peaks of the mountains above the sphere -of the water may have resulted from this that: a very large portion -of the earth which was filled with water that is to say the vast -cavern inside the earth may have fallen in a vast part of its vault -towards the centre of the earth, being pierced by means of the -course of the springs which continually wear away the place where -they pass. - -Sinking in of countries like the Dead Sea in Syria, that is Sodom -and Gomorrah. - -It is of necessity that there should be more water than land, and -the visible portion of the sea does not show this; so that there -must be a great deal of water inside the earth, besides that which -rises into the lower air and which flows through rivers and springs. - -[Footnote: The small sketch below on the left, is placed in the -original close to the text referring to the Dead Sea.] - -The theory of Plato. - -939. - -THE FIGURES OF THE ELEMENTS. - -Of the figures of the elements; and first as against those who deny -the opinions of Plato, and who say that if the elements include one -another in the forms attributed to them by Plato they would cause a -vacuum one within the other. I say it is not true, and I here prove -it, but first I desire to propound some conclusions. It is not -necessary that the elements which include each other should be of -corresponding magnitude in all the parts, of that which includes and -of that which is included. We see that the sphere of the waters -varies conspicuously in mass from the surface to the bottom, and -that, far from investing the earth when that was in the form of a -cube that is of 8 angles as Plato will have it, that it invests the -earth which has innumerable angles of rock covered by the water and -various prominences and concavities, and yet no vacuum is generated -between the earth and water; again, the air invests the sphere of -waters together with the mountains and valleys, which rise above -that sphere, and no vacuum remains between the earth and the air, so -that any one who says a vacuum is generated, speaks foolishly. - -But to Plato I would reply that the surface of the figures which -according to him the elements would have, could not exist. - -That the flow of rivers proves the slope of the land. - -940. - -PROVES HOW THE EARTH IS NOT GLOBULAR AND NOT BEING GLOBULAR CANNOT -HAVE A COMMON CENTRE. - -We see the Nile come from Southern regions and traverse various -provinces, running towards the North for a distance of 3000 miles -and flow into the Mediterranean by the shores of Egypt; and if we -will give to this a fall of ten braccia a mile, as is usually -allowed to the course of rivers in general, we shall find that the -Nile must have its mouth ten miles lower than its source. Again, we -see the Rhine, the Rhone and the Danube starting from the German -parts, almost the centre of Europe, and having a course one to the -East, the other to the North, and the last to Southern seas. And if -you consider all this you will see that the plains of Europe in -their aggregate are much higher than the high peaks of the maritime -mountains; think then how much their tops must be above the sea -shores. - -Theory of the elevation of water within the mountains. - -941. - -OF THE HEAT THAT IS IN THE WORLD. - -Where there is life there is heat, and where vital heat is, there is -movement of vapour. This is proved, inasmuch as we see that the -element of fire by its heat always draws to itself damp vapours and -thick mists as opaque clouds, which it raises from seas as well as -lakes and rivers and damp valleys; and these being drawn by degrees -as far as the cold region, the first portion stops, because heat and -moisture cannot exist with cold and dryness; and where the first -portion stops the rest settle, and thus one portion after another -being added, thick and dark clouds are formed. They are often wafted -about and borne by the winds from one region to another, where by -their density they become so heavy that they fall in thick rain; and -if the heat of the sun is added to the power of the element of fire, -the clouds are drawn up higher still and find a greater degree of -cold, in which they form ice and fall in storms of hail. Now the -same heat which holds up so great a weight of water as is seen to -rain from the clouds, draws them from below upwards, from the foot -of the mountains, and leads and holds them within the summits of the -mountains, and these, finding some fissure, issue continuously and -cause rivers. - -The relative height of the surface of the sea to that of the land -(942-945). - -942. - -OF THE SEA, WHICH TO MANY FOOLS APPEARS TO BE HIGHER THAN THE EARTH -WHICH FORMS ITS SHORE. - -_b d_ is a plain through which a river flows to the sea; this plain -ends at the sea, and since in fact the dry land that is uncovered is -not perfectly level--for, if it were, the river would have no -motion--as the river does move, this place is a slope rather than a -plain; hence this plain _d b_ so ends where the sphere of water -begins that if it were extended in a continuous line to _b a_ it -would go down beneath the sea, whence it follows that the sea _a c -b_ looks higher than the dry land. - -Obviously no portions of dry land left uncovered by water can ever -be lower than the surface of the watery sphere. - -943. - -OF CERTAIN PERSONS WHO SAY THE WATERS WERE HIGHER THAN THE DRY LAND. - -Certainly I wonder not a little at the common opinion which is -contrary to truth, but held by the universal consent of the judgment -of men. And this is that all are agreed that the surface of the sea -is higher than the highest peaks of the mountains; and they allege -many vain and childish reasons, against which I will allege only one -simple and short reason; We see plainly that if we could remove the -shores of the sea, it would invest the whole earth and make it a -perfect sphere. Now, consider how much earth would be carried away -to enable the waves of the sea to cover the world; therefore that -which would be carried away must be higher than the sea-shore. - -944. - -THE OPINION OF SOME PERSONS WHO SAY THAT THE WATER OF SOME SEAS IS -HIGHER THAN THE HIGHEST SUMMITS OF MOUNTAINS; AND NEVERTHELESS THE -WATER WAS FORCED UP TO THESE SUMMITS. - -Water would not move from place to place if it were not that it -seeks the lowest level and by a natural consequence it never can -return to a height like that of the place where it first on issuing -from the mountain came to light. And that portion of the sea which, -in your vain imagining, you say was so high that it flowed over the -summits of the high mountains, for so many centuries would be -swallowed up and poured out again through the issue from these -mountains. You can well imagine that all the time that Tigris and -Euphrates - -945. - -have flowed from the summits of the mountains of Armenia, it must be -believed that all the water of the ocean has passed very many times -through these mouths. And do you not believe that the Nile must have -sent more water into the sea than at present exists of all the -element of water? Undoubtedly, yes. And if all this water had fallen -away from this body of the earth, this terrestrial machine would -long since have been without water. Whence we may conclude that the -water goes from the rivers to the sea, and from the sea to the -rivers, thus constantly circulating and returning, and that all the -sea and the rivers have passed through the mouth of the Nile an -infinite number of times [Footnote: _Moti Armeni, Ermini_ in the -original, in M. RAVAISSON'S transcript _"monti ernini [le loro -ruine?]"_. He renders this _"Le Tigre et l'Euphrate se sont deverses -par les sommets des montagnes [avec leurs eaux destructives?] on -pent cro're" &c. Leonardo always writes _Ermini, Erminia_, for -_Armeni, Armenia_ (Arabic: _Irminiah_). M. RAVAISSON also deviates -from the original in his translation of the following passage: "_Or -tu ne crois pas que le Nil ait mis plus d'eau dans la mer qu'il n'y -en a a present dans tout l'element de l'eau. Il est certain que si -cette eau etait tombee_" &c.] - -II. - -ON THE OCEAN. - -Refutation of Pliny's theory as to the saltness of the sea (946. -947). - -946. - -WHY WATER IS SALT. - -Pliny says in his second book, chapter 103, that the water of the -sea is salt because the heat of the sun dries up the moisture and -drinks it up; and this gives to the wide stretching sea the savour -of salt. But this cannot be admitted, because if the saltness of the -sea were caused by the heat of the sun, there can be no doubt that -lakes, pools and marshes would be so much the more salt, as their -waters have less motion and are of less depth; but experience shows -us, on the contrary, that these lakes have their waters quite free -from salt. Again it is stated by Pliny in the same chapter that this -saltness might originate, because all the sweet and subtle portions -which the heat attracts easily being taken away, the more bitter and -coarser part will remain, and thus the water on the surface is -fresher than at the bottom [Footnote 22: Compare No. 948.]; but this -is contradicted by the same reason given above, which is, that the -same thing would happen in marshes and other waters, which are dried -up by the heat. Again, it has been said that the saltness of the sea -is the sweat of the earth; to this it may be answered that all the -springs of water which penetrate through the earth, would then be -salt. But the conclusion is, that the saltness of the sea must -proceed from the many springs of water which, as they penetrate into -the earth, find mines of salt and these they dissolve in part, and -carry with them to the ocean and the other seas, whence the clouds, -the begetters of rivers, never carry it up. And the sea would be -salter in our times than ever it was at any time; and if the -adversary were to say that in infinite time the sea would dry up or -congeal into salt, to this I answer that this salt is restored to -the earth by the setting free of that part of the earth which rises -out of the sea with the salt it has acquired, and the rivers return -it to the earth under the sea. - -[Footnote: See PLINY, Hist. Nat. II, CIII [C]. _Itaque Solis ardore -siccatur liquor: et hoc esse masculum sidus accepimus, torrens -cuncta sorbensque._ (cp. CIV.) _Sic mari late patenti saporem -incoqui salis, aut quia exhausto inde dulci tenuique, quod facillime -trahat vis ignea, omne asperius crassiusque linquatur: ideo summa -aequorum aqua dulciorem profundam; hanc esse veriorem causam, quam -quod mare terrae sudor sit aeternus: aut quia plurimum ex arido -misceatur illi vapore: aut quia terrae natura sicut medicatas aquas -inficiat_ ... (cp. CV): _altissimum mare XV. stadiorum Fabianus -tradit. Alii n Ponto coadverso Coraxorum gentis (vocant B Ponti) -trecentis fere a continenti stadiis immensam altitudinem maris -tradunt, vadis nunquam repertis._ (cp. CVI [CIII]) _Mirabilius id -faciunt aquae dulces, juxta mare, ut fistulis emicantes. Nam nec -aquarum natura a miraculis cessat. Dulces mari invehuntur, leviores -haud dubie. Ideo et marinae, quarum natura gravior, magis invecta -sustinent. Quaedam vero et dulces inter se supermeant alias._] - -947. - -For the third and last reason we will say that salt is in all -created things; and this we learn from water passed over the ashes -and cinders of burnt things; and the urine of every animal, and the -superfluities issuing from their bodies, and the earth into which -all things are converted by corruption. - -But,--to put it better,--given that the world is everlasting, it -must be admitted that its population will also be eternal; hence the -human species has eternally been and would be consumers of salt; and -if all the mass of the earth were to be turned into salt, it would -not suffice for all human food [Footnote 27: That is, on the -supposition that salt, once consumed, disappears for ever.]; whence -we are forced to admit, either that the species of salt must be -everlasting like the world, or that it dies and is born again like -the men who devour it. But as experience teaches us that it does not -die, as is evident by fire, which does not consume it, and by water -which becomes salt in proportion to the quantity dissolved in -it,--and when it is evaporated the salt always remains in the -original quantity--it must pass through the bodies of men either in -the urine or the sweat or other excretions where it is found again; -and as much salt is thus got rid of as is carried every year into -towns; therefore salt is dug in places where there is urine.-- Sea -hogs and sea winds are salt. - -We will say that the rains which penetrate the earth are what is -under the foundations of cities with their inhabitants, and are what -restore through the internal passages of the earth the saltness -taken from the sea; and that the change in the place of the sea, -which has been over all the mountains, caused it to be left there in -the mines found in those mountains, &c. - -The characteristics of sea water (948. 949). - -948. - -The waters of the salt sea are fresh at the greatest depths. - -949. - -THAT THE OCEAN DOES NOT PENETRATE UNDER THE EARTH. - -The ocean does not penetrate under the earth, and this we learn from -the many and various springs of fresh water which, in many parts of -the ocean make their way up from the bottom to the surface. The same -thing is farther proved by wells dug beyond the distance of a mile -from the said ocean, which fill with fresh water; and this happens -because the fresh water is lighter than salt water and consequently -more penetrating. - -Which weighs most, water when frozen or when not frozen? - -FRESH WATER PENETRATES MORE AGAINST SALT WATER THAN SALT WATER -AGAINST FRESH WATER. - -That fresh water penetrates more against salt water, than salt water -against fresh is proved by a thin cloth dry and old, hanging with -the two opposite ends equally low in the two different waters, the -surfaces of which are at an equal level; and it will then be seen -how much higher the fresh water will rise in this piece of linen -than the salt; by so much is the fresh lighter than the salt. - -On the formation of Gulfs (950. 951). - -950. - -All inland seas and the gulfs of those seas, are made by rivers -which flow into the sea. - -951. - -HERE THE REASON IS GIVEN OF THE EFFECTS PRODUCED BY THE WATERS IN -THE ABOVE MENTIONED PLACE. - -All the lakes and all the gulfs of the sea and all inland seas are -due to rivers which distribute their waters into them, and from -impediments in their downfall into the Mediterranean --which divides -Africa from Europe and Europe from Asia by means of the Nile and the -Don which pour their waters into it. It is asked what impediment is -great enough to stop the course of the waters which do not reach the -ocean. - -On the encroachments of the sea on the land and vice versa -(952-954). - -952. - -OF WAVES. - -A wave of the sea always breaks in front of its base, and that -portion of the crest will then be lowest which before was highest. - -[Footnote: The page of FRANCESCO DI GIORGIO'S _Trattato_, on which -Leonardo has written this remark, contains some notes on the -construction of dams, harbours &c.] - -953. - -That the shores of the sea constantly acquire more soil towards the -middle of the sea; that the rocks and promontories of the sea are -constantly being ruined and worn away; that the Mediterranean seas -will in time discover their bottom to the air, and all that will be -left will be the channel of the greatest river that enters it; and -this will run to the ocean and pour its waters into that with those -of all the rivers that are its tributaries. - -954. - -How the river Po, in a short time might dry up the Adriatic sea in -the same way as it has dried up a large part of Lombardy. - -The ebb and flow of the tide (955-960). - -955. - -Where there is a larger quantity of water, there is a greater flow -and ebb, but the contrary in narrow waters. - -Look whether the sea is at its greatest flow when the moon is half -way over our hemisphere [on the meridian]. - -956. - -Whether the flow and ebb are caused by the moon or the sun, or are -the breathing of this terrestrial machine. That the flow and ebb are -different in different countries and seas. - -[Footnote: 1. Allusion may here be made to the mythological -explanation of the ebb and flow given in the Edda. Utgardloki says -to Thor (Gylfaginning 48): "When thou wert drinking out of the horn, -and it seemed to thee that it was slow in emptying a wonder befell, -which I should not have believed possible: the other end of the horn -lay in the sea, which thou sawest not; but when thou shalt go to the -sea, thou shalt see how much thou hast drunk out of it. And that men -now call the ebb tide." - -Several passages in various manuscripts treat of the ebb and flow. -In collecting them I have been guided by the rule only to transcribe -those which named some particular spot.] - -957. - -Book 9 of the meeting of rivers and their flow and ebb. The cause is -the same in the sea, where it is caused by the straits of Gibraltar. -And again it is caused by whirlpools. - -958. - -OF THE FLOW AND EBB. - -All seas have their flow and ebb in the same period, but they seem -to vary because the days do not begin at the same time throughout -the universe; in such wise as that when it is midday in our -hemisphere, it is midnight in the opposite hemisphere; and at the -Eastern boundary of the two hemispheres the night begins which -follows on the day, and at the Western boundary of these hemispheres -begins the day, which follows the night from the opposite side. -Hence it is to be inferred that the above mentioned swelling and -diminution in the height of the seas, although they take place in -one and the same space of time, are seen to vary from the above -mentioned causes. The waters are then withdrawn into the fissures -which start from the depths of the sea and which ramify inside the -body of the earth, corresponding to the sources of rivers, which are -constantly taking from the bottom of the sea the water which has -flowed into it. A sea of water is incessantly being drawn off from -the surface of the sea. And if you should think that the moon, -rising at the Eastern end of the Mediterranean sea must there begin -to attract to herself the waters of the sea, it would follow that we -must at once see the effect of it at the Eastern end of that sea. -Again, as the Mediterranean sea is about the eighth part of the -circumference of the aqueous sphere, being 3000 miles long, while -the flow and ebb only occur 4 times in 24 hours, these results would -not agree with the time of 24 hours, unless this Mediterranean sea -were six thousand miles in length; because if such a superabundance -of water had to pass through the straits of Gibraltar in running -behind the moon, the rush of the water through that strait would be -so great, and would rise to such a height, that beyond the straits -it would for many miles rush so violently into the ocean as to cause -floods and tremendous seething, so that it would be impossible to -pass through. This agitated ocean would afterwards return the waters -it had received with equal fury to the place they had come from, so -that no one ever could pass through those straits. Now experience -shows that at every hour they are passed in safety, but when the -wind sets in the same direction as the current, the strong ebb -increases [Footnote 23: In attempting to get out of the -Mediterranean, vessels are sometimes detained for a considerable -time; not merely by the causes mentioned by Leonardo but by the -constant current flowing eastwards through the middle of the straits -of Gibraltar.]. The sea does not raise the water that has issued -from the straits, but it checks them and this retards the tide; then -it makes up with furious haste for the time it has lost until the -end of the ebb movement. - -959. - -That the flow and ebb are not general; for on the shore at Genoa -there is none, at Venice two braccia, between England and Flanders -18 braccia. That in the straits of Sicily the current is very strong -because all the waters from the rivers that flow into the Adriatic -pass there. - -[Footnote: A few more recent data may be given here to facilitate -comparison. In the Adriatic the tide rises 2 and 1/2 feet, at -Terracina 1 1/4. In the English channel between Calais and Kent it -rises from 18 to 20 feet. In the straits of Messina it rises no more -than 2 1/2 feet, and that only in stormy weather, but the current is -all the stronger. When Leonardo accounts for this by the southward -flow of all the Italian rivers along the coasts, the explanation is -at least based on a correct observation; namely that a steady -current flows southwards along the coast of Calabria and another -northwards, along the shores of Sicily; he seems to infer, from the -direction of the fust, that the tide in the Adriatic is caused by -it.] - -960. - -In the West, near to Flanders, the sea rises and decreases every 6 -hours about 20 braccia, and 22 when the moon is in its favour; but -20 braccia is the general rule, and this rule, as it is evident, -cannot have the moon for its cause. This variation in the increase -and decrease of the sea every 6 hours may arise from the damming up -of the waters, which are poured into the Mediterranean by the -quantity of rivers from Africa, Asia and Europe, which flow into -that sea, and the waters which are given to it by those rivers; it -pours them to the ocean through the straits of Gibraltar, between -Abila and Calpe [Footnote 5: _Abila_, Lat. _Abyla_, Gr. , now -Sierra _Ximiera_ near Ceuta; _Calpe_, Lat. _Calpe_. Gr., now -Gibraltar. Leonardo here uses the ancient names of the rocks, which -were known as the Pillars of Hercules.]. That ocean extends to the -island of England and others farther North, and it becomes dammed up -and kept high in various gulfs. These, being seas of which the -surface is remote from the centre of the earth, have acquired a -weight, which as it is greater than the force of the incoming waters -which cause it, gives this water an impetus in the contrary -direction to that in which it came and it is borne back to meet the -waters coming out of the straits; and this it does most against the -straits of Gibraltar; these, so long as this goes on, remain dammed -up and all the water which is poured out meanwhile by the -aforementioned rivers, is pent up [in the Mediterranean]; and this -might be assigned as the cause of its flow and ebb, as is shown in -the 21st of the 4th of my theory. - -III. - -SUBTERRANEAN WATER COURSES. - -Theory of the circulation of the waters (961. 962). - -961. - -Very large rivers flow under ground. - -962. - -This is meant to represent the earth cut through in the middle, -showing the depths of the sea and of the earth; the waters start -from the bottom of the seas, and ramifying through the earth they -rise to the summits of the mountains, flowing back by the rivers and -returning to the sea. - -Observations in support of the hypothesis (963-969). - -963. - -The waters circulate with constant motion from the utmost depths of -the sea to the highest summits of the mountains, not obeying the -nature of heavy matter; and in this case it acts as does the blood -of animals which is always moving from the sea of the heart and -flows to the top of their heads; and here it is that veins burst--as -one may see when a vein bursts in the nose, that all the blood from -below rises to the level of the burst vein. When the water rushes -out of a burst vein in the earth it obeys the nature of other things -heavier than the air, whence it always seeks the lowest places. [7] -These waters traverse the body of the earth with infinite -ramifications. - -[Footnote: The greater part of this passage has been given as No. -849 in the section on Anatomy.] - -964. - -The same cause which stirs the humours in every species of animal -body and by which every injury is repaired, also moves the waters -from the utmost depth of the sea to the greatest heights. - -965. - -It is the property of water that it constitutes the vital human of -this arid earth; and the cause which moves it through its ramified -veins, against the natural course of heavy matters, is the same -property which moves the humours in every species of animal body. -But that which crowns our wonder in contemplating it is, that it -rises from the utmost depths of the sea to the highest tops of the -mountains, and flowing from the opened veins returns to the low -seas; then once more, and with extreme swiftness, it mounts again -and returns by the same descent, thus rising from the inside to the -outside, and going round from the lowest to the highest, from whence -it rushes down in a natural course. Thus by these two movements -combined in a constant circulation, it travels through the veins of -the earth. - -966. - -WHETHER WATER RISES FROM THE SEA TO THE TOPS OF MOUNTAINS. - -The water of the ocean cannot make its way from the bases to the -tops of the mountains which bound it, but only so much rises as the -dryness of the mountain attracts. And if, on the contrary, the rain, -which penetrates from the summit of the mountain to the base, which -is the boundary of the sea, descends and softens the slope opposite -to the said mountain and constantly draws the water, like a syphon -[Footnote 11: Cicognola, Syphon. See Vol. I, Pl. XXIV, No. 1.] which -pours through its longest side, it must be this which draws up the -water of the sea; thus if _s n_ were the surface of the sea, and the -rain descends from the top of the mountain _a_ to _n_ on one side, -and on the other sides it descends from _a_ to _m_, without a doubt -this would occur after the manner of distilling through felt, or as -happens through the tubes called syphons [Footnote 17: Cicognola, -Syphon. See Vol. I, Pl. XXIV, No. 1.]. And at all times the water -which has softened the mountain, by the great rain which runs down -the two opposite sides, would constantly attract the rain _a n_, on -its longest side together with the water from the sea, if that side -of the mountain _a m_ were longer than the other _a n_; but this -cannot be, because no part of the earth which is not submerged by -the ocean can be lower than that ocean. - -967. - -OF SPRINGS OF WATER ON THE TOPS OF MOUNTAINS. - -It is quite evident that the whole surface of the ocean--when there -is no storm--is at an equal distance from the centre of the earth, -and that the tops of the mountains are farther from this centre in -proportion as they rise above the surface of that sea; therefore if -the body of the earth were not like that of man, it would be -impossible that the waters of the sea--being so much lower than the -mountains--could by their nature rise up to the summits of these -mountains. Hence it is to be believed that the same cause which -keeps the blood at the top of the head in man keeps the water at the -summits of the mountains. - -[Footnote: This conception of the rising of the blood, which has -given rise to the comparison, was recognised as erroneous by -Leonardo himself at a later period. It must be remembered that the -MS. A, from which these passages are taken, was written about twenty -years earlier than the MS. Leic. (Nos. 963 and 849) and twenty-five -years before the MS. W. An. IV. - -There is, in the original a sketch with No. 968 which is not -reproduced. It represents a hill of the same shape as that shown at -No. 982. There are veins, or branched streams, on the side of the -hill, like those on the skull Pl. CVIII, No. 4] - -968. - -IN CONFIRMATION OF WHY THE WATER GOES TO THE TOPS OF MOUNTAINS. - -I say that just as the natural heat of the blood in the veins keeps -it in the head of man,--for when the man is dead the cold blood -sinks to the lower parts--and when the sun is hot on the head of a -man the blood increases and rises so much, with other humours, that -by pressure in the veins pains in the head are often caused; in the -same way veins ramify through the body of the earth, and by the -natural heat which is distributed throughout the containing body, -the water is raised through the veins to the tops of mountains. And -this water, which passes through a closed conduit inside the body of -the mountain like a dead thing, cannot come forth from its low place -unless it is warmed by the vital heat of the spring time. Again, the -heat of the element of fire and, by day, the heat of the sun, have -power to draw forth the moisture of the low parts of the mountains -and to draw them up, in the same way as it draws the clouds and -collects their moisture from the bed of the sea. - -969. - -That many springs of salt water are found at great distances from -the sea; this might happen because such springs pass through some -mine of salt, like that in Hungary where salt is hewn out of vast -caverns, just as stone is hewn. - -[Footnote: The great mine of Wieliczka in Galicia, out of which a -million cwt. of rock-salt are annually dug out, extends for 3000 -metres from West to East, and 1150 metres from North to South.] - -IV. - -OF RIVERS. - -On the way in which the sources of rivers are fed. - -970. - -OF THE ORIGIN OF RIVERS. - -The body of the earth, like the bodies of animals, is intersected -with ramifications of waters which are all in connection and are -constituted to give nutriment and life to the earth and to its -creatures. These come from the depth of the sea and, after many -revolutions, have to return to it by the rivers created by the -bursting of these springs; and if you chose to say that the rains of -the winter or the melting of the snows in summer were the cause of -the birth of rivers, I could mention the rivers which originate in -the torrid countries of Africa, where it never rains--and still less -snows--because the intense heat always melts into air all the clouds -which are borne thither by the winds. And if you chose to say that -such rivers, as increase in July and August, come from the snows -which melt in May and June from the sun's approach to the snows on -the mountains of Scythia [Footnote 9: Scythia means here, as in -Ancient Geography, the whole of the Northern part of Asia as far as -India.], and that such meltings come down into certain valleys and -form lakes, into which they enter by springs and subterranean caves -to issue forth again at the sources of the Nile, this is false; -because Scythia is lower than the sources of the Nile, and, besides, -Scythia is only 400 miles from the Black sea and the sources of the -Nile are 3000 miles distant from the sea of Egypt into which its -waters flow. - -The tide in estuaries. - -971. - -Book 9, of the meeting of rivers and of their ebb and flow. The -cause is the same in the sea, where it is caused by the straits of -Gibraltar; and again it is caused by whirlpools. - -[3] If two rivers meet together to form a straight line, and then -below two right angles take their course together, the flow and ebb -will happen now in one river and now in the other above their -confluence, and principally if the outlet for their united volume is -no swifter than when they were separate. Here occur 4 instances. - -[Footnote: The first two lines of this passage have already been -given as No. 957. In the margin, near line 3 of this passage, the -text given as No. 919 is written.] - -On the alterations, caused in the courses of rivers by their -confluence (972-974). - -972. - -When a smaller river pours its waters into a larger one, and that -larger one flows from the opposite direction, the course of the -smaller river will bend up against the approach of the larger river; -and this happens because, when the larger river fills up all its bed -with water, it makes an eddy in front of the mouth of the other -river, and so carries the water poured in by the smaller river with -its own. When the smaller river pours its waters into the larger -one, which runs across the current at the mouth of the smaller -river, its waters will bend with the downward movement of the larger -river. [Footnote: In the original sketches the word _Arno_ is -written at the spot here marked _A_, at _R. Rifredi_, and at _M. -Mugnone_.] - -973. - -When the fulness of rivers is diminished, then the acute angles -formed at the junction of their branches become shorter at the sides -and wider at the point; like the current _a n_ and the current _d -n_, which unite in _n_ when the river is at its greatest fulness. I -say, that when it is in this condition if, before the fullest time, -_d n_ was lower than _a n_, at the time of fulness _d n_ will be -full of sand and mud. When the water _d n_ falls, it will carry away -the mud and remain with a lower bottom, and the channel _a n_ -finding itself the higher, will fling its waters into the lower, _d -n_, and will wash away all the point of the sand-spit _b n c_, and -thus the angle _a c d_ will remain larger than the angle _a n d_ and -the sides shorter, as I said before. - -[Footnote: Above the first sketch we find, in the original, this -note: "_Sopra il pote rubaconte alla torricella_"; and by the -second, which represents a pier of a bridge, "_Sotto l'ospedal del -ceppo._"] - -974. - -WATER. - -OF THE MOVEMENT OF A SUDDEN RUSH MADE BY A RIVER IN ITS BED -PREVIOUSLY DRY. - -In proportion as the current of the water given forth by the -draining of the lake is slow or rapid in the dry river bed, so will -this river be wider or narrower, or shallower or deeper in one place -than another, according to this proposition: the flow and ebb of the -sea which enters the Mediterranean from the ocean, and of the rivers -which meet and struggle with it, will raise their waters more or -less in proportion as the sea is wider or narrower. - -[Footnote: In the margin is a sketch of a river which winds so as to -form islands.] - -Whirlpools. - -975. - -Whirlpools, that is to say caverns; that is to say places left by -precipitated waters. - -On the alterations in the channels of rivers. - -976. - -OF THE VIBRATION OF THE EARTH. - -The subterranean channels of waters, like those which exist between -the air and the earth, are those which unceasingly wear away and -deepen the beds of their currents. - -The origin of the sand in rivers (977. 978). - -977. - -A river that flows from mountains deposits a great quantity of large -stones in its bed, which still have some of their angles and sides, -and in the course of its flow it carries down smaller stones with -the angles more worn; that is to say the large stones become -smaller. And farther on it deposits coarse gravel and then smaller, -and as it proceeds this becomes coarse sand and then finer, and -going on thus the water, turbid with sand and gravel, joins the sea; -and the sand settles on the sea-shores, being cast up by the salt -waves; and there results the sand of so fine a nature as to seem -almost like water, and it will not stop on the shores of the sea but -returns by reason of its lightness, because it was originally formed -of rotten leaves and other very light things. Still, being -almost--as was said--of the nature of water itself, it afterwards, -when the weather is calm, settles and becomes solid at the bottom of -the sea, where by its fineness it becomes compact and by its -smoothness resists the waves which glide over it; and in this shells -are found; and this is white earth, fit for pottery. - -978. - -All the torrents of water flowing from the mountains to the sea -carry with them the stones from the hills to the sea, and by the -influx of the sea-water towards the mountains; these stones were -thrown back towards the mountains, and as the waters rose and -retired, the stones were tossed about by it and in rolling, their -angles hit together; then as the parts, which least resisted the -blows, were worn off, the stones ceased to be angular and became -round in form, as may be seen on the banks of the Elsa. And those -remained larger which were less removed from their native spot; and -they became smaller, the farther they were carried from that place, -so that in the process they were converted into small pebbles and -then into sand and at last into mud. After the sea had receded from -the mountains the brine left by the sea with other humours of the -earth made a concretion of these pebbles and this sand, so that the -pebbles were converted into rock and the sand into tufa. And of this -we see an example in the Adda where it issues from the mountains of -Como and in the Ticino, the Adige and the Oglio coming from the -German Alps, and in the Arno at Monte Albano [Footnote 13: At the -foot of _Monte Albano_ lies Vinci, the birth place of Leonardo. -Opposite, on the other bank of the Arno, is _Monte Lupo_.], near -Monte Lupo and Capraia where the rocks, which are very large, are -all of conglomerated pebbles of various kinds and colours. - -V. - -ON MOUNTAINS. - -The formation of mountains (979-983). - -979. - -Mountains are made by the currents of rivers. - -Mountains are destroyed by the currents of rivers. - -[Footnote: Compare 789.] - -980. - -That the Northern bases of some Alps are not yet petrified. And this -is plainly to be seen where the rivers, which cut through them, flow -towards the North; where they cut through the strata in the living -stone in the higher parts of the mountains; and, where they join the -plains, these strata are all of potter's clay; as is to be seen in -the valley of Lamona where the river Lamona, as it issues from the -Appenines, does these things on its banks. - -That the rivers have all cut and divided the mountains of the great -Alps one from the other. This is visible in the order of the -stratified rocks, because from the summits of the banks, down to the -river the correspondence of the strata in the rocks is visible on -either side of the river. That the stratified stones of the -mountains are all layers of clay, deposited one above the other by -the various floods of the rivers. That the different size of the -strata is caused by the difference in the floods--that is to say -greater or lesser floods. - -981. - -The summits of mountains for a long time rise constantly. - -The opposite sides of the mountains always approach each other -below; the depths of the valleys which are above the sphere of the -waters are in the course of time constantly getting nearer to the -centre of the world. - -In an equal period, the valleys sink much more than the mountains -rise. - -The bases of the mountains always come closer together. - -In proportion as the valleys become deeper, the more quickly are -their sides worn away. - -982. - -In every concavity at the summit of the mountains we shall always -find the divisions of the strata in the rocks. - -983. - -OF THE SEA WHICH ENCIRCLES THE EARTH. - -I find that of old, the state of the earth was that its plains were -all covered up and hidden by salt water. [Footnote: This passage has -already been published by Dr. M. JORDAN: _Das Malerbuch des L. da -Vinci, Leipzig_ 1873, p. 86. However, his reading of the text -differs from mine.] - -The authorities for the study of the structure of the earth. - -984. - -Since things are much more ancient than letters, it is no marvel if, -in our day, no records exist of these seas having covered so many -countries; and if, moreover, some records had existed, war and -conflagrations, the deluge of waters, the changes of languages and -of laws have consumed every thing ancient. But sufficient for us is -the testimony of things created in the salt waters, and found again -in high mountains far from the seas. - -VI. - -GEOLOGICAL PROBLEMS. - -985. - -In this work you have first to prove that the shells at a thousand -braccia of elevation were not carried there by the deluge, because -they are seen to be all at one level, and many mountains are seen to -be above that level; and to inquire whether the deluge was caused by -rain or by the swelling of the sea; and then you must show how, -neither by rain nor by swelling of the rivers, nor by the overflow -of this sea, could the shells--being heavy objects--be floated up -the mountains by the sea, nor have carried there by the rivers -against the course of their waters. - -Doubts about the deluge. - -986. - -A DOUBTFUL POINT. - -Here a doubt arises, and that is: whether the deluge, which happened -at the time of Noah, was universal or not. And it would seem not, -for the reasons now to be given: We have it in the Bible that this -deluge lasted 40 days and 40 nights of incessant and universal rain, -and that this rain rose to ten cubits above the highest mountains in -the world. And if it had been that the rain was universal, it would -have covered our globe which is spherical in form. And this -spherical surface is equally distant in every part, from the centre -of its sphere; hence the sphere of the waters being under the same -conditions, it is impossible that the water upon it should move, -because water, in itself, does not move unless it falls; therefore -how could the waters of such a deluge depart, if it is proved that -it has no motion? and if it departed how could it move unless it -went upwards? Here, then, natural reasons are wanting; hence to -remove this doubt it is necessary to call in a miracle to aid us, or -else to say that all this water was evaporated by the heat of the -sun. - -[Footnote: The passages, here given from the MS. Leic., have -hitherto remained unknown. Some preliminary notes on the subject are -to be found in MS. F 8oa and 8ob; but as compared with the fuller -treatment here given, they are, it seems to me, of secondary -interest. They contain nothing that is not repeated here more -clearly and fully. LIBRI, _Histoire des Sciences mathematiques III_, -pages 218--221, has printed the text of F 80a and 80b, therefore it -seemed desirable to give my reasons for not inserting it in this -work.] - -That marine shells could not go up the mountains. - -987. - -OF THE DELUGE AND OF MARINE SHELLS. - -If you were to say that the shells which are to be seen within the -confines of Italy now, in our days, far from the sea and at such -heights, had been brought there by the deluge which left them there, -I should answer that if you believe that this deluge rose 7 cubits -above the highest mountains-- as he who measured it has -written--these shells, which always live near the sea-shore, should -have been left on the mountains; and not such a little way from the -foot of the mountains; nor all at one level, nor in layers upon -layers. And if you were to say that these shells are desirous of -remaining near to the margin of the sea, and that, as it rose in -height, the shells quitted their first home, and followed the -increase of the waters up to their highest level; to this I answer, -that the cockle is an animal of not more rapid movement than the -snail is out of water, or even somewhat slower; because it does not -swim, on the contrary it makes a furrow in the sand by means of its -sides, and in this furrow it will travel each day from 3 to 4 -braccia; therefore this creature, with so slow a motion, could not -have travelled from the Adriatic sea as far as Monferrato in -Lombardy [Footnote: _Monferrato di Lombardia_. The range of hills of -Monferrato is in Piedmont, and Casale di Monferrato belonged, in -Leonardo's time, to the Marchese di Mantova.], which is 250 miles -distance, in 40 days; which he has said who took account of the -time. And if you say that the waves carried them there, by their -gravity they could not move, excepting at the bottom. And if you -will not grant me this, confess at least that they would have to -stay at the summits of the highest mountains, in the lakes which are -enclosed among the mountains, like the lakes of Lario, or of Como -and il Maggiore [Footnote: _Lago di Lario._ Lacus Larius was the -name given by the Romans to the lake of Como. It is evident that it -is here a slip of the pen since the the words in the MS. are: _"Come -Lago di Lario o'l Magare e di Como,"_ In the MS. after line 16 we -come upon a digression treating of the weight of water; this has -here been omitted. It is 11 lines long.] and of Fiesole, and of -Perugia, and others. - -And if you should say that the shells were carried by the waves, -being empty and dead, I say that where the dead went they were not -far removed from the living; for in these mountains living ones are -found, which are recognisable by the shells being in pairs; and they -are in a layer where there are no dead ones; and a little higher up -they are found, where they were thrown by the waves, all the dead -ones with their shells separated, near to where the rivers fell into -the sea, to a great depth; like the Arno which fell from the -Gonfolina near to Monte Lupo [Footnote: _Monte Lupo_, compare 970, -13; it is between Empoli and Florence.], where it left a deposit of -gravel which may still be seen, and which has agglomerated; and of -stones of various districts, natures, and colours and hardness, -making one single conglomerate. And a little beyond the sandstone -conglomerate a tufa has been formed, where it turned towards Castel -Florentino; farther on, the mud was deposited in which the shells -lived, and which rose in layers according to the levels at which the -turbid Arno flowed into that sea. And from time to time the bottom -of the sea was raised, depositing these shells in layers, as may be -seen in the cutting at Colle Gonzoli, laid open by the Arno which is -wearing away the base of it; in which cutting the said layers of -shells are very plainly to be seen in clay of a bluish colour, and -various marine objects are found there. And if the earth of our -hemisphere is indeed raised by so much higher than it used to be, it -must have become by so much lighter by the waters which it lost -through the rift between Gibraltar and Ceuta; and all the more the -higher it rose, because the weight of the waters which were thus -lost would be added to the earth in the other hemisphere. And if the -shells had been carried by the muddy deluge they would have been -mixed up, and separated from each other amidst the mud, and not in -regular steps and layers-- as we see them now in our time. - -The marine shells were not produced away from the sea. - -988. - -As to those who say that shells existed for a long time and were -born at a distance from the sea, from the nature of the place and of -the cycles, which can influence a place to produce such -creatures--to them it may be answered: such an influence could not -place the animals all on one line, except those of the same sort and -age; and not the old with the young, nor some with an operculum and -others without their operculum, nor some broken and others whole, -nor some filled with sea-sand and large and small fragments of other -shells inside the whole shells which remained open; nor the claws of -crabs without the rest of their bodies; nor the shells of other -species stuck on to them like animals which have moved about on -them; since the traces of their track still remain, on the outside, -after the manner of worms in the wood which they ate into. Nor would -there be found among them the bones and teeth of fish which some -call arrows and others serpents' tongues, nor would so many -[Footnote: I. Scilla argued against this hypothesis, which was still -accepted in his days; see: _La vana Speculazione, Napoli_ 1670.] -portions of various animals be found all together if they had not -been thrown on the sea shore. And the deluge cannot have carried -them there, because things that are heavier than water do not float -on the water. But these things could not be at so great a height if -they had not been carried there by the water, such a thing being -impossible from their weight. In places where the valleys have not -been filled with salt sea water shells are never to be seen; as is -plainly visible in the great valley of the Arno above Gonfolina; a -rock formerly united to Monte Albano, in the form of a very high -bank which kept the river pent up, in such a way that before it -could flow into the sea, which was afterwards at its foot, it formed -two great lakes; of which the first was where we now see the city of -Florence together with Prato and Pistoia, and Monte Albano. It -followed the rest of its bank as far as where Serravalle now stands. ->From the Val d'Arno upwards, as far as Arezzo, another lake was -formed, which discharged its waters into the former lake. It was -closed at about the spot where now we see Girone, and occupied the -whole of that valley above for a distance of 40 miles in length. -This valley received on its bottom all the soil brought down by the -turbid waters. And this is still to be seen at the foot of Prato -Magno; it there lies very high where the rivers have not worn it -away. Across this land are to be seen the deep cuts of the rivers -that have passed there, falling from the great mountain of Prato -Magno; in these cuts there are no vestiges of any shells or of -marine soil. This lake was joined with that of Perugia [Footnote: -See PI. CXIII.] - -A great quantity of shells are to be seen where the rivers flow into -the sea, because on such shores the waters are not so salt owing to -the admixture of the fresh water, which is poured into it. Evidence -of this is to be seen where, of old, the Appenines poured their -rivers into the Adriatic sea; for there in most places great -quantities of shells are to be found, among the mountains, together -with bluish marine clay; and all the rocks which are torn off in -such places are full of shells. The same may be observed to have -been done by the Arno when it fell from the rock of Gonfolina into -the sea, which was not so very far below; for at that time it was -higher than the top of San Miniato al Tedesco, since at the highest -summit of this the shores may be seen full of shells and oysters -within its flanks. The shells did not extend towards Val di Nievole, -because the fresh waters of the Arno did not extend so far. - -That the shells were not carried away from the sea by the deluge, -because the waters which came from the earth although they drew the -sea towards the earth, were those which struck its depths; because -the water which goes down from the earth, has a stronger current -than that of the sea, and in consequence is more powerful, and it -enters beneath the sea water and stirs the depths and carries with -it all sorts of movable objects which are to be found in the earth, -such as the above-mentioned shells and other similar things. And in -proportion as the water which comes from the land is muddier than -sea water it is stronger and heavier than this; therefore I see no -way of getting the said shells so far in land, unless they had been -born there. If you were to tell me that the river Loire [Footnote: -Leonardo has written Era instead of Loera or Loira--perhaps under -the mistaken idea that _Lo_ was an article.],which traverses France -covers when the sea rises more than eighty miles of country, because -it is a district of vast plains, and the sea rises about 20 braccia, -and shells are found in this plain at the distance of 80 miles from -the sea; here I answer that the flow and ebb in our Mediterranean -Sea does not vary so much; for at Genoa it does not rise at all, and -at Venice but little, and very little in Africa; and where it varies -little it covers but little of the country. - -The course of the water of a river always rises higher in a place -where the current is impeded; it behaves as it does where it is -reduced in width to pass under the arches of a bridge. - -Further researches (989-991). - -989. - -A CONFUTATION OF THOSE WHO SAY THAT SHELLS MAY HAVE BEEN CARRIED TO -A DISTANCE OF MANY DAYS' JOURNEY FROM THE SEA BY THE DELUGE, WHICH -WAS SO HIGH AS TO BE ABOVE THOSE HEIGHTS. - -I say that the deluge could not carry objects, native to the sea, up -to the mountains, unless the sea had already increased so as to -create inundations as high up as those places; and this increase -could not have occurred because it would cause a vacuum; and if you -were to say that the air would rush in there, we have already -concluded that what is heavy cannot remain above what is light, -whence of necessity we must conclude that this deluge was caused by -rain water, so that all these waters ran to the sea, and the sea did -not run up the mountains; and as they ran to the sea, they thrust -the shells from the shore of the sea and did not draw them to wards -themselves. And if you were then to say that the sea, raised by the -rain water, had carried these shells to such a height, we have -already said that things heavier than water cannot rise upon it, but -remain at the bottom of it, and do not move unless by the impact of -the waves. And if you were to say that the waves had carried them to -such high spots, we have proved that the waves in a great depth move -in a contrary direction at the bottom to the motion at the top, and -this is shown by the turbidity of the sea from the earth washed down -near its shores. Anything which is lighter than the water moves with -the waves, and is left on the highest level of the highest margin of -the waves. Anything which is heavier than the water moves, suspended -in it, between the surface and the bottom; and from these two -conclusions, which will be amply proved in their place, we infer -that the waves of the surface cannot convey shells, since they are -heavier than water. - -If the deluge had to carry shells three hundred and four hundred -miles from the sea, it would have carried them mixed with various -other natural objects heaped together; and we see at such distances -oysters all together, and sea-snails, and cuttlefish, and all the -other shells which congregate together, all to be found together and -dead; and the solitary shells are found wide apart from each other, -as we may see them on sea-shores every day. And if we find oysters -of very large shells joined together and among them very many which -still have the covering attached, indicating that they were left -here by the sea, and still living when the strait of Gibraltar was -cut through; there are to be seen, in the mountains of Parma and -Piacenza, a multitude of shells and corals, full of holes, and still -sticking to the rocks there. When I was making the great horse for -Milan, a large sack full was brought to me in my workshop by certain -peasants; these were found in that place and among them were many -preserved in their first freshness. - -Under ground, and under the foundations of buildings, timbers are -found of wrought beams and already black. Such were found in my time -in those diggings at Castel Fiorentino. And these had been in that -deep place before the sand carried by the Arno into the sea, then -covering the plain, had heen raised to such a height; and before the -plains of Casentino had been so much lowered, by the earth being -constantly carried down from them. - -[Footnote: These lines are written in the margin.] - -And if you were to say that these shells were created, and were -continually being created in such places by the nature of the spot, -and of the heavens which might have some influence there, such an -opinion cannot exist in a brain of much reason; because here are the -years of their growth, numbered on their shells, and there are large -and small ones to be seen which could not have grown without food, -and could not have fed without motion--and here they could not move -[Footnote: These lines are written in the margin.] - -990. - -That in the drifts, among one and another, there are still to be -found the traces of the worms which crawled upon them when they were -not yet dry. And all marine clays still contain shells, and the -shells are petrified together with the clay. From their firmness and -unity some persons will have it that these animals were carried up -to places remote from the sea by the deluge. Another sect of -ignorant persons declare that Nature or Heaven created them in these -places by celestial influences, as if in these places we did not -also find the bones of fishes which have taken a long time to grow; -and as if, we could not count, in the shells of cockles and snails, -the years and months of their life, as we do in the horns of bulls -and oxen, and in the branches of plants that have never been cut in -any part. Besides, having proved by these signs the length of their -lives, it is evident, and it must be admitted, that these animals -could not live without moving to fetch their food; and we find in -them no instrument for penetrating the earth or the rock where we -find them enclosed. But how could we find in a large snail shell the -fragments and portions of many other sorts of shells, of various -sorts, if they had not been thrown there, when dead, by the waves of -the sea like the other light objects which it throws on the earth? -Why do we find so many fragments and whole shells between layer and -layer of stone, if this had not formerly been covered on the shore -by a layer of earth thrown up by the sea, and which was afterwards -petrified? And if the deluge before mentioned had carried them to -these parts of the sea, you might find these shells at the boundary -of one drift but not at the boundary between many drifts. We must -also account for the winters of the years during which the sea -multiplied the drifts of sand and mud brought down by the -neighbouring rivers, by washing down the shores; and if you chose to -say that there were several deluges to produce these rifts and the -shells among them, you would also have to affirm that such a deluge -took place every year. Again, among the fragments of these shells, -it must be presumed that in those places there were sea coasts, -where all the shells were thrown up, broken, and divided, and never -in pairs, since they are found alive in the sea, with two valves, -each serving as a lid to the other; and in the drifts of rivers and -on the shores of the sea they are found in fragments. And within the -limits of the separate strata of rocks they are found, few in number -and in pairs like those which were left by the sea, buried alive in -the mud, which subsequently dried up and, in time, was petrified. - -991. - -And if you choose to say that it was the deluge which carried these -shells away from the sea for hundreds of miles, this cannot have -happened, since that deluge was caused by rain; because rain -naturally forces the rivers to rush towards the sea with all the -things they carry with them, and not to bear the dead things of the -sea shores to the mountains. And if you choose to say that the -deluge afterwards rose with its waters above the mountains, the -movement of the sea must have been so sluggish in its rise against -the currents of the rivers, that it could not have carried, floating -upon it, things heavier than itself; and even if it had supported -them, in its receding it would have left them strewn about, in -various spots. But how are we to account for the corals which are -found every day towards Monte Ferrato in Lombardy, with the holes of -the worms in them, sticking to rocks left uncovered by the currents -of rivers? These rocks are all covered with stocks and families of -oysters, which as we know, never move, but always remain with one of -their halves stuck to a rock, and the other they open to feed -themselves on the animalcules that swim in the water, which, hoping -to find good feeding ground, become the food of these shells. We do -not find that the sand mixed with seaweed has been petrified, -because the weed which was mingled with it has shrunk away, and this -the Po shows us every day in the debris of its banks. - -Other problems (992-994). - -992. - -Why do we find the bones of great fishes and oysters and corals and -various other shells and sea-snails on the high summits of mountains -by the sea, just as we find them in low seas? - -993. - -You now have to prove that the shells cannot have originated if not -in salt water, almost all being of that sort; and that the shells in -Lombardy are at four levels, and thus it is everywhere, having been -made at various times. And they all occur in valleys that open -towards the seas. - -994. - ->From the two lines of shells we are forced to say that the earth -indignantly submerged under the sea and so the first layer was made; -and then the deluge made the second. - -[Footnote: This note is in the early writing of about 1470--1480. On -the same sheet are the passages No. 1217 and 1219. Compare also No. -1339. All the foregoing chapters are from Manuscripts of about 1510. -This explains the want of connection and the contradiction between -this and the foregoing texts.] - -VII. - -ON THE ATMOSPHERE. - -Constituents of the atmosphere. - -995. - -That the brightness of the air is occasioned by the water which has -dissolved itself in it into imperceptible molecules. These, being -lighted by the sun from the opposite side, reflect the brightness -which is visible in the air; and the azure which is seen in it is -caused by the darkness that is hidden beyond the air. [Footnote: -Compare Vol. I, No. 300.] - -On the motion of air (996--999). - -996. - -That the return eddies of wind at the mouth of certain valleys -strike upon the waters and scoop them out in a great hollow, whirl -the water into the air in the form of a column, and of the colour of -a cloud. And I saw this thing happen on a sand bank in the Arno, -where the sand was hollowed out to a greater depth than the stature -of a man; and with it the gravel was whirled round and flung about -for a great space; it appeared in the air in the form of a great -bell-tower; and the top spread like the branches of a pine tree, and -then it bent at the contact of the direct wind, which passed over -from the mountains. - -997. - -The element of fire acts upon a wave of air in the same way as the -air does on water, or as water does on a mass of sand --that is -earth; and their motions are in the same proportions as those of the -motors acting upon them. - -998. - -OF MOTION. - -I ask whether the true motion of the clouds can be known by the -motion of their shadows; and in like manner of the motion of the -sun. - -999. - -To know better the direction of the winds. [Footnote: In connection -with this text I may here mention a hygrometer, drawn and probably -invented by Leonardo. A facsimile of this is given in Vol. I, p. 297 -with the note: _'Modi di pesare l'arie eddi sapere quando s'a -arrompere il tepo'_ (Mode of weighing the air and of knowing when -the weather will change); by the sponge _"Spugnea"_ is written.] - -The globe an organism. - -1000. - -Nothing originates in a spot where there is no sentient, vegetable -and rational life; feathers grow upon birds and are changed every -year; hairs grow upon animals and are changed every year, excepting -some parts, like the hairs of the beard in lions, cats and their -like. The grass grows in the fields, and the leaves on the trees, -and every year they are, in great part, renewed. So that we might -say that the earth has a spirit of growth; that its flesh is the -soil, its bones the arrangement and connection of the rocks of which -the mountains are composed, its cartilage the tufa, and its blood -the springs of water. The pool of blood which lies round the heart -is the ocean, and its breathing, and the increase and decrease of -the blood in the pulses, is represented in the earth by the flow and -ebb of the sea; and the heat of the spirit of the world is the fire -which pervades the earth, and the seat of the vegetative soul is in -the fires, which in many parts of the earth find vent in baths and -mines of sulphur, and in volcanoes, as at Mount Aetna in Sicily, and -in many other places. - -[Footnote: Compare No. 929.] - -_XVII._ - -_Topographical Notes._ - -_A large part of the texts published in this section might perhaps -have found their proper place in connection with the foregoing -chapters on Physical Geography. But these observations on Physical -Geography, of whatever kind they may be, as soon as they are -localised acquire a special interest and importance and particularly -as bearing on the question whether Leonardo himself made the -observations recorded at the places mentioned or merely noted the -statements from hearsay. In a few instances he himself tells us that -he writes at second hand. In some cases again, although the style -and expressions used make it seem highly probable that he has -derived his information from others-- though, as it seems to me, -these cases are not very numerous--we find, on the other hand, among -these topographical notes a great number of observations, about -which it is extremely difficult to form a decided opinion. Of what -the Master's life and travels may have been throughout his -sixty-seven years of life we know comparatively little; for a long -course of time, and particularly from about 1482 to 1486, we do not -even know with certainty that he was living in Italy. Thus, from a -biographical point of view a very great interest attaches to some of -the topographical notes, and for this reason it seemed that it would -add to their value to arrange them in a group by themselves. -Leonardo's intimate knowledge with places, some of which were -certainly remote from his native home, are of importance as -contributing to decide the still open question as to the extent of -Leonardo's travels. We shall find in these notes a confirmation of -the view, that the MSS. in which the Topographical Notes occur are -in only a very few instances such diaries as may have been in use -during a journey. These notes are mostly found in the MSS. books of -his later and quieter years, and it is certainly remarkable that -Leonardo is very reticent as to the authorities from whom he quotes -his facts and observations: For instance, as to the Straits of -Gibraltar, the Nile, the Taurus Mountains and the Tigris and -Euphrates. Is it likely that he, who declared that in all scientific -research, his own experience should be the foundation of his -statements (see XIX Philosophy No. 987--991,) should here have made -an exception to this rule without mentioning it?_ - -_As for instance in the discussion as to the equilibrium of the mass -of water in the Mediterranean Sea--a subject which, it may be -observed, had at that time attracted the interest and study of -hardly any other observer. The acute remarks, in Nos. 985--993, on -the presence of shells at the tops of mountains, suffice to -prove--as it seems to me--that it was not in his nature to allow -himself to be betrayed into wide generalisations, extending beyond -the limits of his own investigations, even by such brilliant results -of personal study._ - -_Most of these Topographical Notes, though suggesting very careful -and thorough research, do not however, as has been said, afford -necessarily indisputable evidence that that research was Leonardo's -own. But it must be granted that in more than one instance -probability is in favour of this idea._ - -_Among the passages which treat somewhat fully of the topography of -Eastern places by far the most interesting is a description of the -Taurus Mountains; but as this text is written in the style of a -formal report and, in the original, is associated with certain -letters which give us the history of its origin, I have thought it -best not to sever it from that connection. It will be found under -No. XXI (Letters)._ - -_That Florence, and its neighbourhood, where Leonardo spent his -early years, should be nowhere mentioned except in connection with -the projects for canals, which occupied his attention for some short -time during the first ten years of the XVIth century, need not -surprise us. The various passages relating to the construction of -canals in Tuscany, which are put together at the beginning, are -immediately followed by those which deal with schemes for canals in -Lombardy; and after these come notes on the city and vicinity of -Milan as well as on the lakes of North Italy._ - -_The notes on some towns of Central Italy which Leonardo visited in -1502, when in the service of Cesare Borgia, are reproduced here in -the same order as in the note book used during these travels (MS. -L., Institut de France). These notes have but little interest in -themselves excepting as suggesting his itinerary. The maps of the -districts drawn by Leonardo at the time are more valuable (see No. -1054 note). The names on these maps are not written from right to -left, but in the usual manner, and we are permitted to infer that -they were made in obedience to some command, possibly for the use of -Cesare Borgia himself; the fact that they remained nevertheless in -Leonardo's hands is not surprising when we remember the sudden -political changes and warlike events of the period. There can be no -doubt that these maps, which are here published for the first time, -are original in the strictest sense of the word, that is to say -drawn from observations of the places themselves; this is proved by -the fact--among others--that we find among his manuscripts not only -the finished maps themselves but the rough sketches and studies for -them. And it would perhaps be difficult to point out among the -abundant contributions to geographical knowledge published during -the XVIth century, any maps at all approaching these in accuracy and -finish._ - -_The interesting map of the world, so far as it was then known, -which is among the Leonardo MSS. at Windsor (published in the_ -'Archaeologia' _Vol. XI) cannot be attributed to the Master, as the -Marchese Girolamo d'Adda has sufficiently proved; it has not -therefore been reproduced here._ - -_Such of Leonardo's observations on places in Italy as were made -before or after his official travels as military engineer to Cesare -Borgia, have been arranged in alphabetical order, under Nos. -1034-1054. The most interesting are those which relate to the Alps -and the Appenines, Nos. 1057-1068._ - -_Most of the passages in which France is mentioned have hitherto -remained unknown, as well as those which treat of the countries -bordering on the Mediterranean, which come at the end of this -section. Though these may be regarded as of a more questionable -importance in their bearing on the biography of the Master than -those which mention places in France, it must be allowed that they -are interesting as showing the prominent place which the countries -of the East held in his geographical studies. He never once alludes -to the discovery of America._ - -I. - -ITALY. - -Canals in connection with the Arno (1001-1008). - -1001. - -CANAL OF FLORENCE. - -Sluices should be made in the valley of la Chiana at Arezzo, so that -when, in the summer, the Arno lacks water, the canal may not remain -dry: and let this canal be 20 braccia wide at the bottom, and at the -top 30, and 2 braccia deep, or 4, so that two of these braccia may -flow to the mills and the meadows, which will benefit the country; -and Prato, Pistoia and Pisa, as well as Florence, will gain two -hundred thousand ducats a year, and will lend a hand and money to -this useful work; and the Lucchese the same, for the lake of Sesto -will be navigable; I shall direct it to Prato and Pistoia, and cut -through Serravalle and make an issue into the lake; for there will -be no need of locks or supports, which are not lasting and so will -always be giving trouble in working at them and keeping them up. - -And know that in digging this canal where it is 4 braccia deep, it -will cost 4 dinari the square braccio; for twice the depth 6 dinari, -if you are making 4 braccia [Footnote: This passage is illustrated -by a slightly sketched map, on which these places are indicated from -West to East: Pisa, Luccha, Lago, Seravalle, Pistoja, Prato, -Firenze.] and there are but 2 banks; that is to say one from the -bottom of the trench to the surface of the edges of it, and the -other from these edges to the top of the ridge of earth which will -be raised on the margin of the bank. And if this bank were of double -the depth only the first bank will be increased, that is 4 braccia -increased by half the first cost; that is to say that if at first 4 -dinari were paid for 2 banks, for 3 it would come to 6, at 2 dinari -the bank, if the trench measured 16 braccia at the bottom; again, if -the trench were 16 braccia wide and 4 deep, coming to 4 lire for the -work, 4 Milan dinari the square braccio; a trench which was 32 -braccia at the bottom would come to 8 dinari the square braccio. - -1002. - ->From the wall of the Arno at [the gate of] la Giustizia to the bank -of the Arno at Sardigna where the walls are, to the mills, is 7400 -braccia, that is 2 miles and 1400 braccia and beyond the Arno is -5500 braccia. - -[Footnote: 2. _Giustizia_. By this the Porta della Giustizia seems -to be meant; from the XVth to the XVIth centuries it was also -commonly known as Porta Guelfa, Porta San Francesco del Renaio, -Porta Nuova, and Porta Reale. It was close to the Arno opposite to -the Porta San Niccolo, which still exists.] - -1003. - -By guiding the Arno above and below a treasure will be found in each -acre of ground by whomsoever will. - -1004. - -The wall of the old houses runs towards the gate of San Nicolo. - -[Footnote: By the side of this text there is an indistinct sketch, -resembling that given under No.973. On the bank is written the word -_Casace_. There then follows in the original a passage of 12 lines -in which the consequences of the windings of the river are -discussed. A larger but equally hasty diagram on the same page -represents the shores of the Arno inside Florence as in two parallel -lines. Four horizontal lines indicate the bridges. By the side these -measures are stated in figures: I. (at the Ponte alla Carraja): -_230--largho br. 12 e 2 di spoda e 14 di pile e a 4 pilastri;_ 2. -(at the Ponte S. Trinita); _l88--largho br. 15 e 2 di spode he 28 -di pilastri for delle spode e pilastri so 2;_ 3. (at the Ponte -vecchio); _pote lung br. 152 e largo;_ 4. (at the Ponte alle -Grazie): _290 ellargo 12 e 2 di spode e 6 di pili._ - -There is, in MS. W. L. 2l2b, a sketched plan of Florence, with the -following names of gates: -_Nicholo--Saminiato--Giorgo--Ghanolini--Porta San Fredian ---Prato--Faenza--Ghallo--Pinti--Giustitia_.] - -1005. - -The ruined wall is 640 braccia; 130 is the wall remaining with the -mill; 300 braccia were broken in 4 years by Bisarno. - -1006. - -They do not know why the Arno will never remain in a channel. It is -because the rivers which flow into it deposit earth where they -enter, and wear it away on the opposite side, bending the river in -that direction. The Arno flows for 6 miles between la Caprona and -Leghorn; and for 12 through the marshes, which extend 32 miles, and -16 from La Caprona up the river, which makes 48; by the Arno from -Florence beyond 16 miles; to Vico 16 miles, and the canal is 5; from -Florence to Fucechio it is 40 miles by the river Arno. - -56 miles by the Arno from Florence to Vico; by the Pistoia canal it -is 44 miles. Thus it is 12 miles shorter by the canal than by the -Arno. - -[Footnote: This passage is written by the side of a map washed in -Indian ink, of the course of the Arno; it is evidently a sketch for -a completer map. - -These investigations may possibly be connected with the following -documents. _Francesco Guiducci alla Balia di Firenze. Dal Campo -contro Pisa_ 24 _Luglio_ 1503 (_Archivio di Stato, Firenze, Lettere -alla Balia_; published by J. GAYE, _Carteggio inedito d'Artisti, -Firenze_ 1840, _Tom. II_, p. 62): _Ex Castris, Franciscus -Ghuiduccius,_ 24. _Jul._ 1503. _Appresso fu qui hieri con una di V. -Signoria Alexandro degli Albizi insieme con Leonardo da Vinci et -certi altri, et veduto el disegno insieme con el ghovernatore, doppo -molte discussioni et dubii conclusesi che l'opera fussi molto al -proposito, o si veramente Arno volgersi qui, o restarvi con un -canale, che almeno vieterebbe che le colline da nemici non -potrebbono essere offese; come tucto referiranno loro a bocha V. S._ - -And, _Archivio di Stato, Firenze, Libro d'Entrata e Uscita di cassa -de' Magnifici Signori di luglio e agosto_ - -1503 _a_ 51 _T.: Andata di Leonardo al Campo sotto Pisa. Spese -extraordinarie dieno dare a di XXVI di luglio L. LVI sol. XII per -loro a Giovanni Piffero; e sono per tanti, asegnia avere spexi in -vetture di sei chavalli a spese di vitto per andare chon Lionardo da -Vinci a livellare Arno in quello di Pisa per levallo del lilo suo._ -(Published by MILANESI, _Archivio Storico Italiano, Serie III, Tom. -XVI._} VASARI asserts: _(Leonardo) fu il primo ancora, che -giovanetto discorresse sopra il fiume d'Arno per metterlo in canale -da Pisa a Fiorenza_ (ed. SANSONI, IV, 20). - -The passage above is in some degree illustrated by the map on Pl. -CXII, where the course of the Arno westward from Empoli is shown.] - -1007. - -The eddy made by the Mensola, when the Arno is low and the Mensola -full. - -[Footnote: _Mensola_ is a mountain stream which falls into the Arno -about a mile and a half above Florence. - -A=Arno, I=Isola, M=Mvgone, P=Pesa, N=Mesola.] - -1008. - -That the river which is to be turned from one place to another must -be coaxed and not treated roughly or with violence; and to do this a -sort of floodgate should be made in the river, and then lower down -one in front of it and in like manner a third, fourth and fifth, so -that the river may discharge itself into the channel given to it, or -that by this means it may be diverted from the place it has damaged, -as was done in Flanders--as I was told by Niccolo di Forsore. - -How to protect and repair the banks washed by the water, as below -the island of Cocomeri. - -Ponte Rubaconte (Fig. 1); below [the palaces] Bisticci and Canigiani -(Fig. 2). Above the flood gate of la Giustizia (Fig. 3); _a b_ is a -sand bank opposite the end of the island of the Cocomeri in the -middle of the Arno (Fig. 4). [Footnote: The course of the river Arno -is also discussed in Nos. 987 and 988.] - -Canals in the Milanese (1009-1013). - -1009. - -The canal of San Cristofano at Milan made May 3rd 1509. [Footnote: -This observation is written above a washed pen and ink drawing which -has been published as Tav. VI in the _,,Saggio."_ The editors of -that work explain the drawing as _"uno Studio di bocche per -estrazione d'acqua."_] - -1010. - -OF THE CANAL OF MARTESANA. - -By making the canal of Martesana the water of the Adda is greatly -diminished by its distribution over many districts for the -irrigation of the fields. A remedy for this would be to make several -little channels, since the water drunk up by the earth is of no more -use to any one, nor mischief neither, because it is taken from no -one; and by making these channels the water which before was lost -returns again and is once more serviceable and useful to men. - -[Footnote: _"el navilio di Martagano"_ is also mentioned in a note -written in red chalk, MS. H2 17a Leonardo has, as it seems, little -to do with Lodovico il Moro's scheme to render this canal navigable. -The canal had been made in 1460 by Bertonino da Novara. Il Moro -issued his degree in 1493, but Leonardo's notes about this canal -were, with the exception of one (No. 1343), written about sixteen -years later.] - -1011. - -No canal which is fed by a river can be permanent if the river -whence it originates is not wholly closed up, like the canal of -Martesana which is fed by the Ticino. - -1012. - ->From the beginning of the canal to the mill. - ->From the beginning of the canal of Brivio to the mill of Travaglia -is 2794 trabochi, that is 11176 braccia, which is more than 3 miles -and two thirds; and here the canal is 57 braccia higher than the -surface of the water of the Adda, giving a fall of two inches in -every hundred trabochi; and at that spot we propose to take the -opening of our canal. - -[Footnote: The following are written on the sketches: At the place -marked _N: navilio da dacquiue_ (canal of running water); at _M: -molin del Travaglia_ (Mill of Travaglia); at _R: rochetta ssanta -maria_ (small rock of Santa Maria); at _A: Adda;_ at _L: Lagho di -Lecho ringorgato alli 3 corni in Adda,--Concha perpetua_ (lake of -Lecco overflowing at Tre Corni, in Adda,-- a permanent sluice). Near -the second sketch, referring to the sluice near _Q: qui la chatena -ttalie d'u peso_ (here the chain is in one piece). At _M_ in the -lower sketch: _mol del travaglia, nel cavare la concha il tereno -ara chotrapero co cassa d'acqua._ (Mill of Travaglia, in digging -out the sluice the soil will have as a counterpoise a vessel of -water).] - -1013. - -If it be not reported there that this is to be a public canal, it -will be necessary to pay for the land; [Footnote 3: _il re_. Louis -XII or Francis I of France. It is hardly possible to doubt that the -canals here spoken of were intended to be in the Milanese. Compare -with this passage the rough copy of a letter by Leonardo, to the -_"Presidente dell' Ufficio regolatore dell' acqua"_ on No. 1350. See -also the note to No. 745, 1. 12.] and the king will pay it by -remitting the taxes for a year. - -Estimates and preparatory studies for canals (1014. 1015). - -1014. - -CANAL. - -The canal which may be 16 braccia wide at the bottom and 20 at the -top, we may say is on the average 18 braccia wide, and if it is 4 -braccia deep, at 4 dinari the square braccia; it will only cost 900 -ducats, to excavate by the mile, if the square braccio is calculated -in ordinary braccia; but if the braccia are those used in measuring -land, of which every 4 are equal to 4 1/2 and if by the mile we -understand three thousand ordinary braccia; turned into land -braccia, these 3000 braccia will lack 1/4; there remain 2250 -braccia, which at 4 dinari the braccio will amount to 675 ducats a -mile. At 3 dinari the square braccio, the mile will amount to 506 -1/4 ducats so that the excavation of 30 miles of the canal will -amount to 15187 1/2 ducats. - -1015. - -To make the great canal, first make the smaller one and conduct into -it the waters which by a wheel will help to fill the great one. - -Notes on buildings in Milan (1016-1019) - -1016. - -Indicate the centre of Milan. - -Moforte--porta resa--porta nova--strada nova--navilio--porta -cumana--barco--porta giovia--porta vercellina--porta sco -Anbrogio--porta Tesinese--torre dell' Imperatore-- porta -Lodovica--acqua. - -[Footnote: See Pl. CIX. The original sketch is here reduced to about -half its size. The gates of the town are here named, beginning at -the right hand and following the curved line. In the bird's eye view -of Milan below, the cathedral is plainly recognisable in the middle; -to the right is the tower of San Gottardo. The square, above the -number 9147, is the Lazzaretto, which was begun in 1488. On the left -the group of buildings of the _'Castello'_ will be noticed. On the -sketched Plan of Florence (see No. 1004 note) Leonardo has written -on the margin the following names of gates of Milan: Vercellina ---Ticinese--Ludovica--Romana--Orientale-- -Nova--Beatrice--Cumana--Compare too No. 1448, 11. 5, 12.] - -1017. - -The moat of Milan. - -Canal 2 braccia wide. - -The castle with the moats full. - -The filling of the moats of the Castle of Milan. - -1018. - -THE BATH. - -To heat the water for the stove of the Duchess take four parts of -cold water to three parts of hot water. - -[Footnote: _Duchessa di Milano_, Beatrice d'Este, wife of Ludovico -il Moro to whom she was married, in 1491. She died in June 1497.] - -1019. - -In the Cathedral at the pulley of the nail of the cross. - -Item. - -To place the mass _v r_ in the... - -[Footnote: On this passage AMORETTI remarks _(Memorie Storiche_ -chap. IX): _Nell'anno stesso lo veggiamo formare un congegno di -carucole e di corde, con cui trasportare in piu venerabile e piu -sicuro luogo, cioe nell'ultima arcata della nave di mezzo della -metropolitana, la sacra reliquia del Santo Chiodo, che ivi ancor si -venera. Al fol. 15 del codice segnato Q. R. in 16, egli ci ha -lasciata di tal congegno una doppia figura, cioe una di quattro -carucole, e una di tre colle rispettive corde, soggiugnandovi: in -Domo alla carucola del Chiodo della Croce._ - -AMORETTI'S views as to the mark on the MS, and the date when it was -written are, it may be observed, wholly unfounded. The MS. L, in -which it occurs, is of the year 1502, and it is very unlikely that -Leonardo was in Milan at that time; this however would not prevent -the remark, which is somewhat obscure, from applying to the -Cathedral at Milan.] - -1020. - -OF THE FORCE OF THE VACUUM FORMED IN A MOMENT. - -I saw, at Milan, a thunderbolt fall on the tower della Credenza on -its Northern side, and it descended with a slow motion down that -side, and then at once parted from that tower and carried with it -and tore away from that wall a space of 3 braccia wide and two deep; -and this wall was 4 braccia thick and was built of thin and small -old bricks; and this was dragged out by the vacuum which the flame -of the thunderbolt had caused, &c. - -[Footnote: With reference to buildings at Milan see also Nos. 751 -and 756, and Pl. XCV, No. 2 (explained on p. 52), Pl. C (explained -on pages 60-62). See also pages 25, 39 and 40.] - -Remarks on natural phenomena in and near Milan (1021. 1022). - -1021. - -I have already been to see a great variety (of atmospheric effects). -And lately over Milan towards Lago Maggiore I saw a cloud in the -form of an immense mountain full of rifts of glowing light, because -the rays of the sun, which was already close to the horizon and red, -tinged the cloud with its own hue. And this cloud attracted to it -all the little clouds that were near while the large one did not -move from its place; thus it retained on its summit the reflection -of the sunlight till an hour and a half after sunset, so immensely -large was it; and about two hours after sunset such a violent wind -arose, that it was really tremendous and unheard of. - -[Footnote: _di arie_ is wanting in the original but may safely be -inserted in the context, as the formation of clouds is under -discussion before this text.] - -1022. - -On the 10th day of December at 9 o'clock a. m. fire was set to the -place. - -On the l8th day of December 1511 at 9 o'clock a. m. this second fire -was kindled by the Swiss at Milan at the place called DCXC. -[Footnote: With these two texts, (l. 1--2 and l. 3--5 are in the -original side by side) there are sketches of smoke wreaths in red -chalk.] - -Note on Pavia. - -1023. - -The chimneys of the castle of Pavia have 6 rows of openings and from -each to the other is one braccio. - -[Footnote: Other notes relating to Pavia occur on p. 43 and p. 53 -(Pl. XCVIII, No. 3). Compare No. 1448, 26.] - -Notes on the Sforzesca near Vigevano (1024-1028). - -1024. - -On the 2nd day of February 1494. At Sforzesca I drew twenty five -steps, 2/3 braccia to each, and 8 braccia wide. - -[Footnote: See Pl. CX, No. 2. The rest of the notes on this page -refer to the motion of water. On the lower sketch we read: 4 _br._ -(four braccia) and _giara_ (for _ghiaja_, sand, gravel).] - -1025. - -The vineyards of Vigevano on the 20th day of March 1494. - -[Footnote: On one side there is an effaced sketch in red chalk.] - -1026. - -To lock up a butteris at Vigevano. - -1027. - -Again if the lowest part of the bank which lies across the current -of the waters is made in deep and wide steps, after the manner of -stairs, the waters which, in their course usually fall -perpendicularly from the top of such a place to the bottom, and wear -away the foundations of this bank can no longer descend with a blow -of too great a force; and I find the example of this in the stairs -down which the water falls in the fields at Sforzesca at Vigevano -over which the running water falls for a height of 50 braccia. - -1028. - -Stair of Vigevano below La Sforzesca, 130 steps, 1/4 braccio high -and 1/2 braccio wide, down which the water falls, so as not to wear -away anything at the end of its fall; by these steps so much soil -has come down that it has dried up a pool; that is to say it has -filled it up and a pool of great depth has been turned into meadows. - -Notes on the North Italian lake. (1029-1033) - -1029. - -In many places there are streams of water which swell for six hours -and ebb for six hours; and I, for my part, have seen one above the -lake of Como called Fonte Pliniana, which increases and ebbs, as I -have said, in such a way as to turn the stones of two mills; and -when it fails it falls so low that it is like looking at water in a -deep pit. - -[Footnote: The fountain is known by this name to this day: it is -near Torno, on the Eastern shore of Como. The waters still rise and -fall with the flow and ebb of the tide as Pliny described it (Epist. -IV, 30; Hist. Nat. II, 206).] - -1030. - -LAKE OF COMO. VALLEY OF CHIAVENNA. - -Above the lake of Como towards Germany is the valley of Chiavenna -where the river Mera flows into this lake. Here are barren and very -high mountains, with huge rocks. Among these mountains are to be -found the water-birds called gulls. Here grow fir trees, larches and -pines. Deer, wildgoats, chamois, and terrible bears. It is -impossible to climb them without using hands and feet. The peasants -go there at the time of the snows with great snares to make the -bears fall down these rocks. These mountains which very closely -approach each other are parted by the river. They are to the right -and left for the distance of 20 miles throughout of the same nature. ->From mile to mile there are good inns. Above on the said river there -are waterfalls of 400 braccia in height, which are fine to see; and -there is good living at 4 soldi the reckoning. This river brings -down a great deal of timber. - -VAL SASINA. - -Val Sasina runs down towards Italy; this is almost the same form and -character. There grow here many _mappello_ and there are great ruins -and falls of water [Footnote 14: The meaning of _mappello_ is -unknown.]. - -VALLEY OF INTROZZO. - -This valley produces a great quantity of firs, pines and larches; -and from here Ambrogio Fereri has his timber brought down; at the -head of the Valtellina are the mountains of Bormio, terrible and -always covered with snow; marmots (?) are found there. - -BELLAGGIO. - -Opposite the castle Bellaggio there is the river Latte, which falls -from a height of more than 100 braccia from the source whence it -springs, perpendicularly, into the lake with an inconceivable roar -and noise. This spring flows only in August and September. - -VALTELLINA. - -Valtellina, as it is called, is a valley enclosed in high and -terrible mountains; it produces much strong wine, and there is so -much cattle that the natives conclude that more milk than wine grows -there. This is the valley through which the Adda passes, which first -runs more than 40 miles through Germany; this river breeds the fish -_temolo_ which live on silver, of which much is to be found in its -sands. In this country every one can sell bread and wine, and the -wine is worth at most one soldo the bottle and a pound of veal one -soldo, and salt ten dinari and butter the same and their pound is 30 -ounces, and eggs are one soldo the lot. - -1031. - -At BORMIO. - -At Bormio are the baths;--About eight miles above Como is the -Pliniana, which increases and ebbs every six hours, and its swell -supplies water for two mills; and its ebbing makes the spring dry -up; two miles higher up there is Nesso, a place where a river falls -with great violence into a vast rift in the mountain. These -excursions are to be made in the month of May. And the largest bare -rocks that are to be found in this part of the country are the -mountains of Mandello near to those of Lecco, and of Gravidona -towards Bellinzona, 30 miles from Lecco, and those of the valley of -Chiavenna; but the greatest of all is that of Mandello, which has at -its base an opening towards the lake, which goes down 200 steps, and -there at all times is ice and wind. - -IN VAL SASINA. - -In Val Sasina, between Vimognio and Introbbio, to the right hand, -going in by the road to Lecco, is the river Troggia which falls from -a very high rock, and as it falls it goes underground and the river -ends there. 3 miles farther we find the buildings of the mines of -copper and silver near a place called Pra' Santo Pietro, and mines -of iron and curious things. La Grigna is the highest mountain there -is in this part, and it is quite bare. - -[Footnote: 1030 and 1031. From the character of the handwriting we -may conclude that these observations were made in Leonardo's youth; -and I should infer from their contents, that they were notes made in -anticipation of a visit to the places here described, and derived -from some person (unknown to us) who had given him an account of -them.] - -1032. - -The lake of Pusiano flows into the lake of Segrino [Footnote 3: The -statement about the lake Segrino is incorrect; it is situated in the -Valle Assina, above the lake of Pusiano.] and of Annone and of Sala. -The lake of Annone is 22 braccia higher at the surface of its water -than the surface of the water of the lake of Lecco, and the lake of -Pusiano is 20 braccia higher than the lake of Annone, which added to -the afore said 22 braccia make 42 braccia and this is the greatest -height of the surface of the lake of Pusiano above the surface of -the lake of Lecco. - -[Footnote: This text has in the original a slight sketch to -illustrate it.] - -1033. - -At Santa Maria in the Valley of Ravagnate [Footnote 2: _Ravagnate_ -(Leonardo writes _Ravagna_) in the Brianza is between Oggiono and -Brivio, South of the lake of Como. M. Ravaisson avails himself of -this note to prove his hypothesis that Leonardo paid two visits to -France. See Gazette des Beaux Arts, 1881 pag. 528: - -_Au recto du meme feuillet, on lit encore une note relative a une -vallee "nemonti brigatia"; il me semble qu'il s'agit bien des monts -de Briancon, le Brigantio des anciens. Briancon est sur la route de -Lyon en Italie. Ce fut par le mont Viso que passerent, en aout 1515, -les troupes francaises qui allaient remporter la victoire de -Marignan. - -Leonard de Vinci, ingenieur de Francois Ier, comme il l'avait ete de -Louis XII, aurait-il ete pour quelque chose dans le plan du celebre -passage des Alpes, qui eut lieu en aout 1515, et a la suite duquel -on le vit accompagner partout le chevaleresque vainqueur? Auraitil -ete appele par le jeune roi, de Rome ou l'artiste etait alors, des -son avenement au trone?_] in the mountains of Brianza are the rods -of chestnuts of 9 braccia and one out of an average of 100 will be -14 braccia. - -At Varallo di Ponbia near to Sesto on the Ticino the quinces are -white, large and hard. - -[Footnote 5: Varallo di Ponbia, about ten miles South of Arona is -distinct from Varallo the chief town in the Val di Sesia.] - -Notes on places in Central Italy, visited in 1502 (1034-1054). - -1034. - -Pigeon-house at Urbino, the 30th day of July 1502. [Footnote: An -indistinct sketch is introduced with this text, in the original, in -which the word _Scolatoro_ (conduit) is written.] - -1035. - -Made by the sea at Piombino. [Footnote: Below the sketch there are -eleven lines of text referring to the motion of waves.] - -1036. - -Acquapendente is near Orvieto. [Footnote: _Acquapendente_ is about -10 miles West of Orvieto, and is to the right in the map on Pl. -CXIII, near the lake of Bolsena.] - -1037. - -The rock of Cesena. [Footnote: See Pl. XCIV No. 1, the lower sketch. -The explanation of the upper sketch is given on p. 29.] - -1038. - -Siena, _a b_ 4 braccia, _a c_ 10 braccia. Steps at [the castle of] -Urbino. [Footnote: See Pl. CX No. 3; compare also No. 765.] - -1039. - -The bell of Siena, that is the manner of its movement, and the place -of the attachment of the clapper. [Footnote: The text is accompanied -by an indistinct sketch.] - -1040. - -On St. Mary's day in the middle of August, at Cesena, 1502. -[Footnote: See Pl. CX, No. 4.] - -1041. - -Stairs of the [palace of the] Count of Urbino,--rough. [Footnote: -The text is accompanied by a slight sketch.] - -1042. - -At the fair of San Lorenzo at Cesena. 1502. - -1043. - -Windows at Cesena. [Footnote: There are four more lines of text -which refer to a slightly sketched diagram.] - -1044. - -At Porto Cesenatico, on the 6th of September 1502 at 9 o'clock a. m. - -The way in which bastions ought to project beyond the walls of the -towers to defend the outer talus; so that they may not be taken by -artillery. - -[Footnote: An indistinct sketch, accompanies this passage.] - -1045. - -The rock of the harbour of Cesena is four points towards the South -West from Cesena. - -1046. - -In Romagna, the realm of all stupidity, vehicles with four wheels -are used, of which O the two in front are small and two high ones -are behind; an arrangement which is very unfavourable to the motion, -because on the fore wheels more weight is laid than on those behind, -as I showed in the first of the 5th on "Elements". - -1047. - -Thus grapes are carried at Cesena. The number of the diggers of the -ditches is [arranged] pyramidically. [Footnote: A sketch, -representing a hook to which two bunches of grapes are hanging, -refers to these first two lines. Cesena is mentioned again Fol. 82a: -_Carro da Cesena_ (a cart from Cesena).] - -1048. - -There might be a harmony of the different falls of water as you saw -them at the fountain of Rimini on the 8th day of August, 1502. - -1049. - -The fortress at Urbino. [Footnote: 1049. In the original the text is -written inside the sketch in the place here marked _n_.] - -1050. - -Imola, as regards Bologna, is five points from the West, towards the -North West, at a distance of 20 miles. - -Castel San Piero is seen from Imola at four points from the West -towards the North West, at a distance of 7 miles. - -Faenza stands with regard to Imola between East and South East at a -distance of ten miles. Forli stands with regard to Faenza between -South East and East at a distance of 20 miles from Imola and ten -from Faenza. - -Forlimpopoli lies in the same direction at 25 miles from Imola. - -Bertinoro, as regards Imola, is five points from the East to wards -the South East, at 27 miles. - -1051. - -Imola as regards Bologna is five points from the West towards the -North West at a distance of 20 miles. - -Castel San Pietro lies exactly North West of Imola, at a distance of -7 miles. - -Faenza, as regards Imola lies exactly half way between the East and -South East at a distance of 10 miles; and Forli lies in the same -direction from Imola at a distance of 20 miles; and Forlimpopolo -lies in the same direction from Forli at a distance of 25 miles. - -Bertinoro is seen from Imola two points from the East towards the -South East at a distance of 27 miles. - -[Footnote: Leonardo inserted this passage on the margin of the -circular plan, in water colour, of Imola--see Pl. CXI No. 1.--In the -original the fields surrounding the town are light green; the moat, -which surrounds the fortifications and the windings of the river -Santerno, are light blue. The parts, which have come out blackish -close to the river are yellow ochre in the original. The dark groups -of houses inside the town are red. At the four points of the compass -drawn in the middle of the town Leonardo has written (from right to -left): _Mezzodi_ (South) at the top; to the left _Scirocho_ (South -east), _levante_ (East), _Greco_ (North East), _Septantrione_ -(North), _Maesstro_ (North West), _ponente_ (West) _Libecco_ (South -West). The arch in which the plan is drawn is, in the original, 42 -centimetres across. - -At the beginning of October 1502 Cesare Borgia was shut up in Imola -by a sudden revolt of the Condottieri, and it was some weeks before -he could release himself from this state of siege (see Gregorovius, -_Geschichte der Stadt Rom im Mittelalter_, Vol. VII, Book XIII, 5, -5). - -Besides this incident Imola plays no important part in the history -of the time. I therefore think myself fully justified in connecting -this map, which is at Windsor, with the siege of 1502 and with -Leonardo's engagements in the service of Cesare Borgia, because a -comparison of these texts, Nos. 1050 and 1051, raise, I believe, the -hypothesis to a certainty.] - -1052. - ->From Bonconventi to Casa Nova are 10 miles, from Casa Nova to Chiusi -9 miles, from Chiusi to Perugia, from, Perugia to Santa Maria degli -Angeli, and then to Fuligno. [Footnote: Most of the places here -described lie within the district shown in the maps on Pl. CXIII.] - -1053. - -On the first of August 1502, the library at Pesaro. - -1054. - -OF PAINTING. - -On the tops and sides of hills foreshorten the shape of the ground -and its divisions, but give its proper shape to what is turned -towards you. [Footnote: This passage evidently refers to the making -of maps, such as Pl. CXII, CXIII, and CXIV. There is no mention of -such works, it is true, excepting in this one passage of MS. L. But -this can scarcely be taken as evidence against my view that Leonardo -busied himself very extensively at that time in the construction of -maps; and all the less since the foregoing chapters clearly prove -that at a time so full of events Leonardo would only now and then -commit his observations to paper, in the MS. L. - -By the side of this text we find, in the original, a very indistinct -sketch, perhaps a plan of a position. Instead of this drawing I have -here inserted a much clearer sketch of a position from the same MS., -L. 82b and 83a. They are the only drawings of landscape, it may be -noted, which occur at all in that MS.] - -Alessandria in Piedmont (1055. 1056). - -1055. - -At Candia in Lombardy, near Alessandria della Paglia, in making a -well for Messer Gualtieri [Footnote 2: Messer Gualtieri, the same -probably as is mentioned in Nos. 672 and 1344.] of Candia, the -skeleton of a very large boat was found about 10 braccia -underground; and as the timber was black and fine, it seemed good to -the said Messer Gualtieri to have the mouth of the well lengthened -in such a way as that the ends of the boat should be uncovered. - -1056. - -At Alessandria della Paglia in Lombardy there are no stones for -making lime of, but such as are mixed up with an infinite variety of -things native to the sea, which is now more than 200 miles away. - -The Alps (1057-1062). - -1057. - -At Monbracco, above Saluzzo,--a mile above the Certosa, at the foot -of Monte Viso, there is a quarry of flakey stone, which is as white -as Carrara marble, without a spot, and as hard as porphyry or even -harder; of which my worthy gossip, Master Benedetto the sculptor, -has promised to give me a small slab, for the colours, the second -day of January 1511. - -[Footnote: Saluzzo at the foot of the Alps South of Turin.] - -[Footnote 9. 10.: _Maestro Benedetto scultore_; probably some native -of Northern Italy acquainted with the place here described. Hardly -the Florentine sculptor Benedetto da Majano. Amoretti had published -this passage, and M. Ravaisson who gave a French translation of it -in the _Gazette des Beaux Arts_ (1881, pag. 528), remarks as -follows: _Le maitre sculpteur que Leonard appelle son "compare" ne -serait-il pas Benedetto da Majano, un de ceux qui jugerent avec lui -de la place a donner au David de Michel-Ange, et de qui le Louvre a -acquis recemment un buste d'apres Philippe Strozzi?_ To this it may -be objected that Benedetto da Majano had already lain in his grave -fourteen years, in the year 1511, when he is supposed to have given -the promise to Leonardo. The colours may have been given to the -sculptor Benedetto and the stone may have been in payment for them. ->From the description of the stone here given we may conclude that it -is repeated from hearsay of the sculptor's account of it. I do not -understand how, from this observation, it is possible to conclude -that Leonardo was on the spot.] - -1058. - -That there are springs which suddenly break forth in earthquakes or -other convulsions and suddenly fail; and this happened in a mountain -in Savoy where certain forests sank in and left a very deep gap, and -about four miles from here the earth opened itself like a gulf in -the mountain, and threw out a sudden and immense flood of water -which scoured the whole of a little valley of the tilled soil, -vineyards and houses, and did the greatest mischief, wherever it -overflowed. - -1059. - -The river Arve, a quarter of a mile from Geneva in Savoy, where the -fair is held on midsummerday in the village of Saint Gervais. - -[Footnote: An indistinct sketch is to be seen by the text.] - -1060. - -And this may be seen, as I saw it, by any one going up Monbroso -[Footnote: I have vainly enquired of every available authority for a -solution of the mystery as to what mountain is intended by the name -Monboso (Comp. Vol. I Nos. 300 and 301). It seems most obvious to -refer it to Monte Rosa. ROSA derived from the Keltic ROS which -survives in Breton and in Gaelic, meaning, in its first sense, a -mountain spur, but which also--like HORN--means a very high peak; -thus Monte Rosa would mean literally the High Peak.], a peak of the -Alps which divide France from Italy. The base of this mountain gives -birth to the 4 rivers which flow in four different directions -through the whole of Europe. And no mountain has its base at so -great a height as this, which lifts itself above almost all the -clouds; and snow seldom falls there, but only hail in the summer, -when the clouds are highest. And this hail lies [unmelted] there, so -that if it were not for the absorption of the rising and falling -clouds, which does not happen more than twice in an age, an enormous -mass of ice would be piled up there by the layers of hail, and in -the middle of July I found it very considerable; and I saw the sky -above me quite dark, and the sun as it fell on the mountain was far -brighter here than in the plains below, because a smaller extent of -atmosphere lay between the summit of the mountain and the sun. -[Footnote 6: _in una eta._ This is perhaps a slip of the pen on -Leonardo's part and should be read _estate_ (summer).] - -Leic. 9b] - -1061. - -In the mountains of Verona the red marble is found all mixed with -cockle shells turned into stone; some of them have been filled at -the mouth with the cement which is the substance of the stone; and -in some parts they have remained separate from the mass of the rock -which enclosed them, because the outer covering of the shell had -interposed and had not allowed them to unite with it; while in other -places this cement had petrified those which were old and almost -stripped the outer skin. - -1062. - -Bridge of Goertz-Wilbach (?). - -[Footnote: There is a slight sketch with this text, Leonardo seems -to have intended to suggest, with a few pen-strokes, the course of -the Isonzo and of the Wipbach in the vicinity of Gorizia (Goerz). He -himself says in another place that he had been in Friuli (see No. -1077 1. 19).] - -The Appenins (1063-1068). - -1063. - -That part of the earth which was lightest remained farthest from the -centre of the world; and that part of the earth became the lightest -over which the greatest quantity of water flowed. And therefore that -part became lightest where the greatest number of rivers flow; like -the Alps which divide Germany and France from Italy; whence issue -the Rhone flowing Southwards, and the Rhine to the North. The Danube -or Tanoia towards the North East, and the Po to the East, with -innumerable rivers which join them, and which always run turbid with -the soil carried by them to the sea. - -The shores of the sea are constantly moving towards the middle of -the sea and displace it from its original position. The lowest -portion of the Mediterranean will be reserved for the bed and -current of the Nile, the largest river that flows into that sea. And -with it are grouped all its tributaries, which at first fell into -the sea; as may be seen with the Po and its tributaries, which first -fell into that sea, which between the Appenines and the German Alps -was united to the Adriatic sea. - -That the Gallic Alps are the highest part of Europe. - -1064. - -And of these I found some in the rocks of the high Appenines and -mostly at the rock of La Vernia. [Footnote 6: _Sasso della Vernia._ -The frowning rock between the sources of the Arno and the Tiber, as -Dante describes this mountain, which is 1269 metres in height. - -This note is written by the side of that given as No. 1020; but -their connection does not make it clear what Leonardo's purpose was -in writing it.] - -1065. - -At Parma, at 'La Campana' on the twenty-fifth of October 1514. -[Footnote 2: _Capano_, an Inn.] - -A note on the petrifactions, or fossils near Parma will be found -under No. 989.] - -1066. - -A method for drying the marsh of Piombino. [Footnote: There is a -slight sketch with this text in the original.--Piombino is also -mentioned in Nos. 609, l. 55-58 (compare Pl. XXXV, 3, below). Also -in No. 1035.] - -1067. - -The shepherds in the Romagna at the foot of the Apennines make -peculiar large cavities in the mountains in the form of a horn, and -on one side they fasten a horn. This little horn becomes one and the -same with the said cavity and thus they produce by blowing into it a -very loud noise. [Footnote: As to the Romagna see also No. 1046.] - -1068. - -A spring may be seen to rise in Sicily which at certain times of the -year throws out chesnut leaves in quantities; but in Sicily chesnuts -do not grow, hence it is evident that that spring must issue from -some abyss in Italy and then flow beneath the sea to break forth in -Sicily. [Footnote: The chesnut tree is very common in Sicily. In -writing _cicilia_ Leonardo meant perhaps Cilicia.] - -II. - -FRANCE. - -1069. - - GERMANY. FRANCE. - -a. Austria, a. Picardy. -b. Saxony. b. Normandy. -c. Nuremberg. c. Dauphine. -d. Flanders. - - SPAIN. - - a. Biscay. - b. Castille. - c. Galicia. - d. Portugal. - e. Taragona. - f. Granada. - -[Footnote: Two slightly sketched maps, one of Europe the other of -Spain, are at the side of these notes.] - -1070. - -Perpignan. Roanne. Lyons. Paris. Ghent. Bruges. Holland. - -[Footnote: _Roana_ does not seem to mean here Rouen in Normandy, but -is probably Roanne (Rodumna) on the upper Loire, Lyonnais (Dep. du -Loire). This town is now unimportant, but in Leonardo's time was -still a place of some consequence.] - -1071. - -At Bordeaux in Gascony the sea rises about 40 braccia before its -ebb, and the river there is filled with salt water for more than a -hundred and fifty miles; and the vessels which are repaired there -rest high and dry on a high hill above the sea at low tide. -[Footnote 2: This is obviously an exaggeration founded on inaccurate -information. Half of 150 miles would be nearer the mark.] - -1072. - -The Rhone issues from the lake of Geneva and flows first to the West -and then to the South, with a course of 400 miles and pours its -waters into the Mediterranean. - -1073. - -_c d_ is the garden at Blois; _a b_ is the conduit of Blois, made in -France by Fra Giocondo, _b c_ is what is wanting in the height of -that conduit, _c d_ is the height of the garden at Blois, _e f_ is -the siphon of the conduit, _b c_, _e f_, _f g_ is where the siphon -discharges into the river. [Footnote: The tenor of this note (see -lines 2 and 3) seems to me to indicate that this passage was not -written in France, but was written from oral information. We have no -evidence as to when this note may have been written beyond the -circumstance that Fra Giocondo the Veronese Architect left France -not before the year 1505. The greater part of the magnificent -Chateau of Blois has now disappeared. Whether this note was made for -a special purpose is uncertain. The original form and extent of the -Chateau is shown in Androvet, _Les plus excellents Bastiments de -France, Paris MDCVII,_ and it may be observed that there is in the -middle of the garden a Pavilion somewhat similar to that shown on -Pl. LXXXVIII No. 7. - -See S. DE LA SAUSSAYE, _Histoire du Chateau de Blois 4eme edition -Blois et Paris_ p. 175: _En mariant sa fille ainee a Francois, comte -d'Angouleme, Louis XII lui avait constitue en dot les comtes de -Blois, d'Asti, de Coucy, de Montfort, d'Etampes et de Vertus. Une -ordonnance de Francois I. lui laissa en_ 1516 _l'administration du -comte de Blois. - -Le roi fit commencer, dans la meme annee, les travaux de celle belle -partie du chateau, connue sous le nom d'aile de Francois I, et dont -nous avons donne la description au commencement de ce livre. Nous -trouvons en effet, dans les archives du Baron de Foursanvault, une -piece qui en fixe parfaitement la date. On y lit: "Je, Baymon -Philippeaux, commis par le Roy a tenir le compte et fair le payement -des bastiments, ediffices et reparacions que le dit seigneur fait -faire en son chastu de Blois, confesse avoir eu et receu ... la -somme de trois mille livres tournois ... le cinquieme jour de -juillet, l'an mil cinq cent et seize._ P. 24: _Les jardins avaient -ete decores avec beaucoup de luxe par les differents possesseurs du -chateau. Il ne reste de tous les batiments qu'ils y eleverent que -ceux des officiers charges de l'ad_ministration et de la culture des -jardins, et un pavilion carre en pierre et en brique flanque de -terrasses a chacun de ses angles. Quoique defigure par des mesures -elevees sur les terrasses, cet edifice est tris-digne d'interet par -l'originalite du plan, la decoration architecturale et le souvenir -d'Anne de Bretagne qui le fit construire._ Felibien describes the -garden as follows: _Le jardin haut etait fort bien dresse par grands -compartimens de toutes sortes de figures, avec des allees de -meuriers blancs et des palissades de coudriers. Deux grands berceaux -de charpenterie separoient toute la longueur et la largeur du -jardin, et dans les quatres angles des allees, ou ces berceaux se -croissent, il y auoit 4 cabinets, de mesme charpenterie ... Il y a -pas longtemps qu'il y auoit dans ce mesme jardin, a l'endroit ou se -croissent les allees du milieu, un edifice de figure octogone, de -plus de 7 thoises de diametre et de plus de neuf thoises de haut; -avec 4 enfoncements en forme de niches dans les 4 angles des allies. -Ce bastiment.... esloit de charpente mais d'un extraordinairement -bien travaille. On y voyait particulierement la cordiliere qui -regnati tout autour en forme de cordon. Car la Reyne affectait de la -mettre nonseulement a ses armes et a ses chiffres mais de la faire -representer en divers manieres dans tous les ouvrages qu'on lui -faisait pour elle ... le bastiment estati couvert en forme de dome -qui dans son milieu avait encore un plus petit dome, ou lanterne -vitree au-dessus de laquelle estait une figure doree representant -Saint Michel. Les deux domes estoient proprement couvert d'ardoise -et de plomb dore par dehors; par dedans ils esloient lambrissez -d'une menuiserie tres delicate. Au milieu de ce Salon il y avait un -grand bassin octogone de marbre blanc, dont toutes les faces -estoient enrichies de differentes sculptures, avec les armes et les -chiffres du Roy Louis XII et de la Reine Anne, Dans ce bassin il y -en avait un autre pose sur un piedestal lequel auoit sept piedz de -diametre. Il estait de figure ronde a godrons, avec des masques et -d'autres ornements tres scauamment taillez. Du milieu de ce -deuxiesme bassin s'y levoit un autre petit piedestal qui portait un -troisiesme bassin de trois pieds de diametre, aussy parfaitement -bien taille; c'estoit de ce dernier bassin que jallissoit l'eau qui -se rependoit en suitte dans les deux autres bassins. Les beaux -ouvrages faits d'un marbre esgalement blanc et poli, furent brisez -par la pesanteur de tout l'edifice, que les injures de l'air -renverserent de fond en comble.] - -1074. - -The river Loire at Amboise. - -The river is higher within the bank _b d_ than outside that bank. - -The island where there is a part of Amboise. - -This is the river that passes through Amboise; it passes at _a b c -d_, and when it has passed the bridge it turns back, against the -original current, by the channel _d e_, _b f_ in contact with the -bank which lies between the two contrary currents of the said river, -_a b_, _c d_, and _d e_, _b f_. It then turns down again by the -channel _f l_, _g h_, _n m_, and reunites with the river from which -it was at first separated, which passes by _k n_, which makes _k m_, -_r t_. But when the river is very full it flows all in one channel -passing over the bank _b d_. [Footnote: See Pl. CXV. Lines 1-7 are -above, lines 8-10 in the middle of the large island and the word -_Isola_ is written above _d_ in the smaller island; _a_ is written -on the margin on the bank of the river above 1. I; in the -reproduction it is not visible. As may be seen from the last -sentence, the observation was made after long study of the river's -course, when Leonardo had resided for some time at, or near, -Amboise.] - -1075. - -The water may be dammed up above the level of Romorantin to such a -height, that in its fall it may be used for numerous mills. - -1075. - -The river at Villefranche may be conducted to Romorantin which may -be done by the inhabitants; and the timber of which their houses are -built may be carried in boats to Romorantin [Footnote: Compare No. -744.]. The river may be dammed up at such a height that the waters -may be brought back to Romorantin with a convenient fall. - -1076. - -As to whether it is better that the water should all be raised in a -single turn or in two? - -The answer is that in one single turn the wheel could not support -all the water that it can raise in two turns, because at the half -turn of the wheel it would be raising 100 pounds and no more; and if -it had to raise the whole, 200 pounds in one turn, it could not -raise them unless the wheel were of double the diameter and if the -diameter were doubled, the time of its revolution would be doubled; -therefore it is better and a greater advantage in expense to make -such a wheel of half the size (?) the land which it would water and -would render the country fertile to supply food to the inhabitants, -and would make navigable canals for mercantile purposes. - -The way in which the river in its flow should scour its own channel. - -By the ninth of the third; the more rapid it is, the more it wears -away its channel; and, by the converse proposition, the slower the -water the more it deposits that which renders it turbid. - -And let the sluice be movable like the one I arranged in Friuli -[Footnote 19: This passage reveals to us the fact that Leonardo had -visited the country of Friuli and that he had stayed there for some -time. Nothing whatever was known of this previously.], where when -one sluice was opened the water which passed through it dug out the -bottom. Therefore when the rivers are flooded, the sluices of the -mills ought to be opened in order that the whole course of the river -may pass through falls to each mill; there should be many in order -to give a greater impetus, and so all the river will be scoured. And -below the site of each of the two mills there may be one of the said -sluice falls; one of them may be placed below each mill. - -1078. - -A trabocco is four braccia, and one mile is three thousand of the -said braccia. Each braccio is divided into 12 inches; and the water -in the canals has a fall in every hundred trabocchi of two of these -inches; therefore 14 inches of fall are necessary in two thousand -eight hundred braccia of flow in these canals; it follows that 15 -inches of fall give the required momentum to the currents of the -waters in the said canals, that is one braccio and a half in the -mile. And from this it may be concluded that the water taken from -the river of Ville-franche and lent to the river of Romorantin -will..... Where one river by reason of its low level cannot flow -into the other, it will be necessary to dam it up, so that it may -acquire a fall into the other, which was previously the higher. - -The eve of Saint Antony I returned from Romorantin to Amboise, and -the King went away two days before from Romorantin. - ->From Romorantin as far as the bridge at Saudre it is called the -Saudre, and from that bridge as far as Tours it is called the Cher. - -I would test the level of that channel which is to lead from the -Loire to Romorantin, with a channel one braccio wide and one braccio -deep. - -[Footnote: Lines 6-18 are partly reproduced in the facsimile on p. -254, and the whole of lines 19-25. - -The following names are written along the rivers on the larger -sketch, _era f_ (the Loire) _scier f_ (the Cher) three times. _Pote -Sodro_ (bridge of the Soudre). _Villa francha_ (Villefranche) -_banco_ (sandbank) _Sodro_ (Soudre). The circle below shows the -position of Romorantin. The words '_orologio del sole_' written -below do not belong to the map of the rivers. The following names -are written by the side of the smaller sketch-map:--_tors_ (Tours), -_Abosa_ (Amboise) _bres_--for Bles (Blois) _mo rica_ (Montrichard). -_Lione_ (Lyons). This map was also published in the 'Saggio' -(Milano, 1872) Pl. XXII, and the editors remark: _Forse la linia -retta che va da Amboise a Romorantin segna l'andamento proposto d'un -Canale, che poi rembra prolungarsi in giu fin dove sta scritto -Lione._ - -M. Ravaisson has enlarged on this idea in the Gazette des Beaux Arts -(1881 p. 530): _Les traces de Leonard permettent d'entrevoir que le -canal commencant soit aupres de Tours, soit aupres de Blois et -passant par Romorantin, avec port d'embarquement a Villefranche, -devait, au dela de Bourges, traverser l'Allier au-dessous des -affluents de la Dore et de la Sioule, aller par Moulins jusqu' a -Digoin; enfin, sur l'autre rive de la Loire, depasser les monts du -Charolais et rejoindre la Saone aupres de Macon._ It seems to me -rash, however, to found so elaborate an hypothesis on these sketches -of rivers. The slight stroke going to _Lione_ is perhaps only an -indication of the direction.--With regard to the Loire compare also -No. 988. l. 38.] - -1079. - -THE ROAD TO ORLEANS - -At 1/4 from the South to the South East. At 1/3 from the South to -the South East. At 1/4 from the South to the South East. At 1/5 from -the South to the South East. Between the South West and South, to -the East bearing to the South; from the South towards the East 1/8; -thence to the West, between the South and South West; at the South. - -[Footnote: The meaning is obscure; a more important passage -referring to France is to be found under No. 744] - -On the Germans (1080. 1081). - -1080. - -The way in which the Germans closing up together cross and -interweave their broad leather shields against the enemy, stooping -down and putting one of the ends on the ground while they hold the -rest in their hand. [Footnote: Above the text is a sketch of a few -lines crossing each other and the words _de ponderibus_. The meaning -of the passage is obscure.] - -1081. - -The Germans are wont to annoy a garrison with the smoke of feathers, -sulphur and realgar, and they make this smoke last 7 or 8 hours. -Likewise the husks of wheat make a great and lasting smoke; and also -dry dung; but this must be mixed with olive husks, that is olives -pressed for oil and from which the oil has been extracted. -[Footnote: There is with this passage a sketch of a round tower -shrouded in smoke.] - -The Danube. - -1082. - -That the valleys were formerly in great part covered by lakes the -soil of which always forms the banks of rivers,--and by seas, which -afterwards, by the persistent wearing of the rivers, cut through the -mountains and the wandering courses of the rivers carried away the -other plains enclosed by the mountains; and the cutting away of the -mountains is evident from the strata in the rocks, which correspond -in their sections as made by the courses of the rivers [Footnote 4: -_Emus_, the Balkan; _Dardania_, now Servia.], The Haemus mountains -which go along Thrace and Dardania and join the Sardonius mountains -which, going on to the westward change their name from Sardus to -Rebi, as they come near Dalmatia; then turning to the West cross -Illyria, now called Sclavonia, changing the name of Rebi to Albanus, -and going on still to the West, they change to Mount Ocra in the -North; and to the South above Istria they are named Caruancas; and -to the West above Italy they join the Adula, where the Danube rises -[8], which stretches to the East and has a course of 1500 miles; its -shortest line is about l000 miles, and the same or about the same is -that branch of the Adula mountains changed as to their name, as -before mentioned. To the North are the Carpathians, closing in the -breadth of the valley of the Danube, which, as I have said extends -eastward, a length of about 1000 miles, and is sometimes 200 and in -some places 300 miles wide; and in the midst flows the Danube, the -principal river of Europe as to size. The said Danube runs through -the middle of Austria and Albania and northwards through Bavaria, -Poland, Hungary, Wallachia and Bosnia and then the Danube or Donau -flows into the Black Sea, which formerly extended almost to Austria -and occupied the plains through which the Danube now courses; and -the evidence of this is in the oysters and cockle shells and -scollops and bones of great fishes which are still to be found in -many places on the sides of those mountains; and this sea was formed -by the filling up of the spurs of the Adula mountains which then -extended to the East joining the spurs of the Taurus which extend to -the West. And near Bithynia the waters of this Black Sea poured into -the Propontis [Marmora] falling into the Aegean Sea, that is the -Mediterranean, where, after a long course, the spurs of the Adula -mountains became separated from those of the Taurus. The Black Sea -sank lower and laid bare the valley of the Danube with the above -named countries, and the whole of Asia Minor beyond the Taurus range -to the North, and the plains from mount Caucasus to the Black Sea to -the West, and the plains of the Don this side--that is to say, at -the foot of the Ural mountains. And thus the Black Sea must have -sunk about 1000 braccia to uncover such vast plains. - -[Footnote 8: _Danubio_, in the original _Reno_; evidently a mistake -as we may infer from _come dissi_ l. 10 &c.] - -III. - -THE COUNTRIES OF THE WESTERN END OF THE MEDITERRANEAN. - -The straits of Gibraltar (1083-1085). - -1083. - -WHY THE SEA MAKES A STRONGER CURRENT IN THE STRAITS OF SPAIN THAN -ELSEWHERE. - -A river of equal depth runs with greater speed in a narrow space -than in a wide one, in proportion to the difference between the -wider and the narrower one. - -This proposition is clearly proved by reason confirmed by -experiment. Supposing that through a channel one mile wide there -flows one mile in length of water; where the river is five miles -wide each of the 5 square miles will require 1/5 of itself to be -equal to the square mile of water required in the sea, and where the -river is 3 miles wide each of these square miles will require the -third of its volume to make up the amount of the square mile of the -narrow part; as is demonstrated in _f g h_ at the mile marked _n_. - -[Footnote: In the place marked A in the diagram _Mare Mediterano_ -(Mediterranean Sea) is written in the original. And at B, _stretto -di Spugna_ (straits of Spain, _i.e._ Gibraltar). Compare No. 960.] - -1084. - -WHY THE CURRENT OF GIBRALTAR IS ALWAYS GREATER TO THE WEST THAN TO -THE EAST. - -The reason is that if you put together the mouths of the rivers -which discharge into the Mediterranean sea, you would find the sum -of water to be larger than that which this sea pours through the -straits into the ocean. You see Africa discharging its rivers that -run northwards into this sea, and among them the Nile which runs -through 3000 miles of Africa; there is also the Bagrada river and -the Schelif and others. [Footnote 5: _Bagrada_ (Leonardo writes -Bragada) in Tunis, now Medscherda; _Mavretano_, now Schelif.] -Likewise Europe pours into it the Don and the Danube, the Po, the -Rhone, the Arno, and the Tiber, so that evidently these rivers, with -an infinite number of others of less fame, make its great breadth -and depth and current; and the sea is not wider than 18 miles at the -most westerly point of land where it divides Europe from Africa. - -1085. - -The gulf of the Mediterranean, as an inland sea, received the -principal waters of Africa, Asia and Europe that flowed towards it; -and its waters came up to the foot of the mountains that surrounded -it and made its shores. And the summits of the Apennines stood up -out of this sea like islands, surrounded by salt water. Africa -again, behind its Atlas mountains did not expose uncovered to the -sky the surface of its vast plains about 3000 miles in length, and -Memphis [Footnote 6: _Mefi._ Leonardo can only mean here the citadel -of Cairo on the Mokattam hills.] was on the shores of this sea, and -above the plains of Italy, where now birds fly in flocks, fish were -wont to wander in large shoals. - -1086. - -Tunis. - -The greatest ebb made anywhere by the Mediterranean is above Tunis, -being about two and a half braccia and at Venice it falls two -braccia. In all the rest of the Mediterranean sea the fall is little -or none. - -1087. - -Libya. - -Describe the mountains of shifting deserts; that is to say the -formation of waves of sand borne by the wind, and of its mountains -and hills, such as occur in Libya. Examples may be seen on the wide -sands of the Po and the Ticino, and other large rivers. - -1088. - -Majorca. - -Circumfulgore is a naval machine. It was an invention of the men of -Majorca. [Footnote: The machine is fully described in the MS. and -shown in a sketch.] - -1089. - -The Tyrrhene Sea. - -Some at the Tyrrhene sea employ this method; that is to say they -fastened an anchor to one end of the yard, and to the other a cord, -of which the lower end was fastened to an anchor; and in battle they -flung this anchor on to the oars of the opponent's boat and by the -use of a capstan drew it to the side; and threw soft soap and tow, -daubed with pitch and set ablaze, on to that side where the anchor -hung; so that in order to escape that fire, the defenders of that -ship had to fly to the opposite side; and in doing this they aided -to the attack, because the galley was more easily drawn to the side -by reason of the counterpoise. [Footnote: This text is illustrated -in the original by a pen and ink sketch.] - -IV. - -THE LEVANT. - -The Levantine Sea. - -1090. - -On the shores of the Mediterranean 300 rivers flow, and 40, 200 -ports. And this sea is 3000 miles long. Many times has the increase -of its waters, heaped up by their backward flow and the blowing of -the West winds, caused the overflow of the Nile and of the rivers -which flow out through the Black Sea, and have so much raised the -seas that they have spread with vast floods over many countries. And -these floods take place at the time when the sun melts the snows on -the high mountains of Ethiopia that rise up into the cold regions of -the air; and in the same way the approach of the sun acts on the -mountains of Sarmatia in Asia and on those in Europe; so that the -gathering together of these three things are, and always have been, -the cause of tremendous floods: that is, the return flow of the sea -with the West wind and the melting of the snows. So every river will -overflow in Syria, in Samaria, in Judea between Sinai and the -Lebanon, and in the rest of Syria between the Lebanon and the Taurus -mountains, and in Cilicia, in the Armenian mountains, and in -Pamphilia and in Lycia within the hills, and in Egypt as far as the -Atlas mountains. The gulf of Persia which was formerly a vast lake -of the Tigris and discharged into the Indian Sea, has now worn away -the mountains which formed its banks and laid them even with the -level of the Indian ocean. And if the Mediterranean had continued -its flow through the gulf of Arabia, it would have done the same, -that is to say, would have reduced the level of the Mediterranean to -that of the Indian Sea. - -The Red Sea. (1091. 1092). - -1091. - -For a long time the water of the Mediterranean flowed out through -the Red Sea, which is 100 miles wide and 1500 long, and full of -reefs; and it has worn away the sides of Mount Sinai, a fact which -testifies, not to an inundation from the Indian sea beating on these -coasts, but to a deluge of water which carried with it all the -rivers which abound round the Mediterranean, and besides this there -is the reflux of the sea; and then, a cutting being made to the West -3000 miles away from this place, Gibraltar was separated from Ceuta, -which had been joined to it. And this passage was cut very low down, -in the plains between Gibraltar and the ocean at the foot of the -mountain, in the low part, aided by the hollowing out of some -valleys made by certain rivers, which might have flowed here. -Hercules [Footnote 9: Leonardo seems here to mention Hercules half -jestingly and only in order to suggest to the reader an allusion to -the legend of the pillars of Hercules.] came to open the sea to the -westward and then the sea waters began to pour into the Western -Ocean; and in consequence of this great fall, the Red Sea remained -the higher; whence the water, abandoning its course here, ever after -poured away through the Straits of Spain. - -1092. - -The surface of the Red Sea is on a level with the ocean. - -A mountain may have fallen and closed the mouth of the Red Sea and -prevented the outlet of the Mediterranean, and the Mediterranean Sea -thus overfilled had for outlet the passage below the mountains of -Gades; for, in our own times a similar thing has been seen [Footnote -6: Compare also No. 1336, ll. 30, 35 and 36.-- Paolo Giovio, the -celebrated historian (born at Como in 1483) reports that in 1513 at -the foot of the Alps, above Bellinzona, on the road to Switzerland, -a mountain fell with a very great noise, in consequence of an -earthquake, and that the mass of rocks, which fell on the left -(Western) side blocked the river Breno (T. I p. 218 and 345 of D. -Sauvage's French edition, quoted in ALEXIS PERCY, _Memoire des -tremblements de terre de la peninsule italique; Academie Royale de -Belgique._ T. XXII).--]; a mountain fell seven miles across a valley -and closed it up and made a lake. And thus most lakes have been made -by mountains, as the lake of Garda, the lakes of Como and Lugano, -and the Lago Maggiore. The Mediterranean fell but little on the -confines of Syria, in consequence of the Gaditanean passage, but a -great deal in this passage, because before this cutting was made the -Mediterranean sea flowed to the South East, and then the fall had to -be made by its run through the Straits of Gades. - -At _a_ the water of the Mediterranean fell into the ocean. - -All the plains which lie between the sea and mountains were formerly -covered with salt water. - -Every valley has been made by its own river; and the proportion -between valleys is the same as that between river and river. - -The greatest river in our world is the Mediterranean river, which -moves from the sources of the Nile to the Western ocean. - -And its greatest height is in Outer Mauritania and it has a course -of ten thousand miles before it reunites with its ocean, the father -of the waters. - -That is 3000 miles for the Mediterranean, 3000 for the Nile, as far -as discovered and 3000 for the Nile which flows to the East, &c. - -[Footnote: See Pl. CXI 2, a sketch of the shores of the -Mediterranean Sea, where lines 11 to 16 may be seen. The large -figures 158 are not in Leonardo's writing. The character of the -writing leads us to conclude that this text was written later than -the foregoing. A slight sketch of the Mediterranean is also to be -found in MS. I', 47a.] - -The Nile (1093-1098). - -1093. - -Therefore we must conclude those mountains to be of the greatest -height, above which the clouds falling in snow give rise to the -Nile. - -1094. - -The Egyptians, the Ethiopians, and the Arabs, in crossing the Nile -with camels, are accustomed to attach two bags on the sides of the -camel's bodies that is skins in the form shown underneath. - -In these four meshes of the net the camels for baggage place their -feet. - -[Footnote: Unfortunately both the sketches which accompany this -passage are too much effaced to be reproduced. The upper represents -the two sacks joined by ropes, as here described, the other shows -four camels with riders swimming through a river.] - -1095. - -The Tigris passes through Asia Minor and brings with it the water of -three lakes, one after the other of various elevations; the first -being Munace and the middle Pallas and the lowest Triton. And the -Nile again springs from three very high lakes in Ethiopia, and runs -northwards towards the sea of Egypt with a course of 4000 miles, and -by the shortest and straightest line it is 3000 miles. It is said -that it issues from the Mountains of the Moon, and has various -unknown sources. The said lakes are about 4000 braccia above the -surface of the sphere of water, that is 1 mile and 1/3, giving to -the Nile a fall of 1 braccia in every mile. - -[Footnote 5: _Incogniti principio._ The affluents of the lakes are -probably here intended. Compare, as to the Nile, Nos. 970, 1063 and -1084.] - -1096. - -Very many times the Nile and other very large rivers have poured out -their whole element of water and restored it to the sea. - -1097. - -Why does the inundation of the Nile occur in the summer, coming from -torrid countries? - -1098. - -It is not denied that the Nile is constantly muddy in entering the -Egyptian sea and that its turbidity is caused by soil that this -river is continually bringing from the places it passes; which soil -never returns in the sea which receives it, unless it throws it on -its shores. You see the sandy desert beyond Mount Atlas where -formerly it was covered with salt water. - -Customs of Asiatic Nations (1099. 1100). - -1099. - -The Assyrians and the people of Euboea accustom their horses to -carry sacks which they can at pleasure fill with air, and which in -case of need they carry instead of the girth of the saddle above and -at the side, and they are well covered with plates of cuir bouilli, -in order that they may not be perforated by flights of arrows. Thus -they have not on their minds their security in flight, when the -victory is uncertain; a horse thus equipped enables four or five men -to cross over at need. - -1100. - -SMALL BOATS. - -The small boats used by the Assyrians were made of thin laths of -willow plaited over rods also of willow, and bent into the form of a -boat. They were daubed with fine mud soaked with oil or with -turpentine, and reduced to a kind of mud which resisted the water -and because pine would split; and always remained fresh; and they -covered this sort of boats with the skins of oxen in safely crossing -the river Sicuris of Spain, as is reported by Lucant; [Footnote 7: -See Lucan's Pharsalia IV, 130: _Utque habuit ripas Sicoris camposque -reliquit, Primum cana salix madefacto vimine parvam Texitur in -puppim, calsoque inducto juvenco Vectoris patiens tumidum supernatat -amnem. Sic Venetus stagnante Pado, fusoque Britannus Navigat oceano, -sic cum tenet omnia Nilus, Conseritur bibula Memphitis cymbo papyro. -His ratibus transjecta manus festinat utrimque Succisam cavare nemus -] - -The Spaniards, the Scythians and the Arabs, when they want to make a -bridge in haste, fix hurdlework made of willows on bags of ox-hide, -and so cross in safety. - -Rhodes (1101. 1102). - -1101. - -In [fourteen hundred and] eighty nine there was an earthquake in the -sea of Atalia near Rhodes, which opened the sea--that is its -bottom--and into this opening such a torrent of water poured that -for more than three hours the bottom of the sea was uncovered by -reason of the water which was lost in it, and then it closed to the -former level. - -[Footnote: _Nello ottanto_ 9. It is scarcely likely that Leonardo -should here mean 89 AD. Dr. H. MULLER- STRUBING writes to me as -follows on this subject: "With reference to Rhodes Ross says (_Reise -auf den Griechischen Inseln, III_ 70 _ff_. 1840), that ancient -history affords instances of severe earthquakes at Rhodes, among -others one in the second year of the 138th Olympiad=270 B. C.; a -remarkably violent one under Antoninus Pius (A. D. 138-161) and -again under Constantine and later. But Leonardo expressly speaks of -an earthquake "_nel mar di Atalia presso a Rodi_", which is -singular. The town of Attalia, founded by Attalus, which is what he -no doubt means, was in Pamphylia and more than 150 English miles -East of Rhodes in a straight line. Leake and most other geographers -identify it with the present town of Adalia. Attalia is rarely -mentioned by the ancients, indeed only by Strabo and Pliny and no -earthquake is spoken of. I think therefore you are justified in -assuming that Leonardo means 1489". In the elaborate catalogue of -earthquakes in the East by Sciale Dshelal eddin Sayouthy (an -unpublished Arabic MS. in the possession of Prof. SCHEFER, (Membre -de l'Institut, Paris) mention is made of a terrible earthquake in -the year 867 of the Mohamedan Era corresponding to the year 1489, -and it is there stated that a hundred persons were killed by it in -the fortress of Kerak. There are three places of this name. Kerak on -the sea of Tiberias, Kerak near Tahle on the Libanon, which I -visited in the summer of l876--but neither of these is the place -alluded to. Possibly it may be the strongly fortified town of -Kerak=Kir Moab, to the West of the Dead Sea. There is no notice -about this in ALEXIS PERCY, _Memoire sur les tremblements de terres -ressentis dans la peninsule turco- hellenique et en Syrie (Memoires -couronnes et memoires des savants etrangers, Academie Royale de -Belgique, Tome XXIII)._] - -1102. - -Rhodes has in it 5000 houses. - -Cyprus (1103. 1104). - -1103. - -SITE FOR [A TEMPLE OF] VENUS. - -You must make steps on four sides, by which to mount to a meadow -formed by nature at the top of a rock which may be hollowed out and -supported in front by pilasters and open underneath in a large -portico, - -[Footnote: See Pl. LXXXIII. Compare also p. 33 of this Vol. The -standing male figure at the side is evidently suggested by Michael -Angelo's David. On the same place a slight sketch of horses seems to -have been drawn first; there is no reason for assuming that the text -and this sketch, which have no connection with each other, are of -the same date. - -_Sito di Venere._ By this heading Leonardo appears to mean Cyprus, -which was always considered by the ancients to be the home and birth -place of Aphrodite (Kirpic in Homer).] - -in which the water may fall into various vases of granite, -porphyryand serpentine, within semi-circular recesses; and the water -may overflow from these. And round this portico towards the North -there should be a lake with a little island in the midst of which -should be a thick and shady wood; the waters at the top of the -pilasters should pour into vases at their base, from whence they -should flow in little channels. - -Starting from the shore of Cilicia towards the South you discover -the beauties of the island of Cyprus. - -The Caspian Sea (1105. 1106). - -1104. - ->From the shore of the Southern coast of Cilicia may be seen to the -South the beautiful island of Cyprus, which was the realm of the -goddess Venus, and many navigators being attracted by her beauty, -had their ships and rigging broken amidst the reefs, surrounded by -the whirling waters. Here the beauty of delightful hills tempts -wandering mariners to refresh themselves amidst their flowery -verdure, where the winds are tempered and fill the island and the -surrounding seas with fragrant odours. Ah! how many a ship has here -been sunk. Ah! how many a vessel broken on these rocks. Here might -be seen barks without number, some wrecked and half covered by the -sand; others showing the poop and another the prow, here a keel and -there the ribs; and it seems like a day of judgment when there -should be a resurrection of dead ships, so great is the number of -them covering all the Northern shore; and while the North gale makes -various and fearful noises there. - -1105. - -Write to Bartolomeo the Turk as to the flow and ebb of the Black -sea, and whether he is aware if there be such a flow and ebb in the -Hyrcanean or Caspian sea. [Footnote: The handwriting of this note -points to a late date.] - -1106. - -WHY WATER IS FOUND AT THE TOP OF MOUNTAINS. - ->From the straits of Gibraltar to the Don is 3500 miles, that is one -mile and 1/6, giving a fall of one braccio in a mile to any water -that moves gently. The Caspian sea is a great deal higher; and none -of the mountains of Europe rise a mile above the surface of our -seas; therefore it might be said that the water which is on the -summits of our mountains might come from the height of those seas, -and of the rivers which flow into them, and which are still higher. - -The sea of Azov. - -1107. - -Hence it follows that the sea of Azov is the highest part of the -Mediterranean sea, being at a distance of 3500 miles from the -Straits of Gibraltar, as is shown by the map for navigation; and it -has 3500 braccia of descent, that is, one mile and 1/6; therefore it -is higher than any mountains which exist in the West. - -[Footnote: The passage before this, in the original, treats of the -exit of the waters from Lakes in general.] - -The Dardanelles. - -1108. - -In the Bosphorus the Black Sea flows always into the Egean sea, and -the Egean sea never flows into it. And this is because the Caspian, -which is 400 miles to the East, with the rivers which pour into it, -always flows through subterranean caves into this sea of Pontus; and -the Don does the same as well as the Danube, so that the waters of -Pontus are always higher than those of the Egean; for the higher -always fall towards the lower, and never the lower towards the -higher. - -Constantinople. - -1109. - -The bridge of Pera at Constantinople, 40 braccia wide, 70 braccia -high above the water, 600 braccia long; that is 400 over the sea and -200 on the land, thus making its own abutments. - -[Footnote: See Pl. CX No. 1. In 1453 by order of Sultan Mohamed II. -the Golden Horn was crossed by a pontoon bridge laid on barrels (see -Joh. Dukas' History of the Byzantine Empire XXXVIII p. 279). --The -biographers of Michelangelo, Vasari as well as Condivi, relate that -at the time when Michelangelo suddenly left Rome, in 1506, he -entertained some intention of going to Constantinople, there to -serve the Sultan, who sought to engage him, by means of certain -Franciscan Monks, for the purpose of constructing a bridge to -connect Constantinople with Pera. See VASARI, _Vite_ (ed. Sansoni -VII, 168): _Michelangelo, veduto questa furia del papa, dubitando di -lui, ebbe, secondo che si dice, voglia di andarsene in -Gostantinopoli a servire il Turco, per mezzo di certi frati di San -Francesco, che desiderava averlo per fare un ponte che passassi da -Gostantinopoli a Pera._ And CONDIVI, _Vita di M. Buonaroti chap._ -30_; Michelangelo allora vedendosi condotto a questo, temendo -dell'ira del papa, penso d'andarsene in Levante; massimamente -essendo stato dal Turco ricercato con grandissime promesse per mezzo -di certi frati di San Francesco, per volersene servire in fare un -ponte da Costantinopoli a Pera ed in altri affari._ Leonardo's plan -for this bridge was made in 1502. We may therefore conclude that at -about that time the Sultan Bajazet II. had either announced a -competition in this matter, or that through his agents Leonardo had -first been called upon to carry out the scheme.] - -The Euphrates. - -1110. - -If the river will turn to the rift farther on it will never return -to its bed, as the Euphrates does, and this may do at Bologna the -one who is disappointed for his rivers. - -Centrae Asia. - -1111. - -Mounts Caucasus, Comedorum, and Paropemisidae are joined together -between Bactria and India, and give birth to the river Oxus which -takes its rise in these mountains and flows 500 miles towards the -North and as many towards the West, and discharges its waters into -the Caspian sea; and is accompanied by the Oxus, Dargados, Arthamis, -Xariaspes, Dargamaim, Ocus and Margus, all very large rivers. From -the opposite side towards the South rises the great river Indus -which sends its waters for 600 miles Southwards and receives as -tributaries in this course the rivers Xaradrus, Hyphasis, Vadris, -Vandabal Bislaspus to the East, Suastes and Coe to the West, uniting -with these rivers, and with their waters it flows 800 miles to the -West; then, turning back by the Arbiti mountains makes an elbow and -turns Southwards, where after a course of about 100 miles it finds -the Indian Sea, in which it pours itself by seven branches. On the -side of the same mountains rises the great Ganges, which river flows -Southwards for 500 miles and to the Southwest a thousand ... and -Sarabas, Diarnuna, Soas and Scilo, Condranunda are its tributaries. -It flows into the Indian sea by many mouths. - -On the natives of hot countries. - -1112. - -Men born in hot countries love the night because it refreshes them -and have a horror of light because it burns them; and therefore they -are of the colour of night, that is black. And in cold countries it -is just the contrary. - -[Footnote: The sketch here inserted is in MS. H3 55b.] - -_XVIII._ - -_Naval Warfare.--Mechanical Appliances.--Music._ - -_Such theoretical questions, as have been laid before the reader in -Sections XVI and XVII, though they were the chief subjects of -Leonardo's studies of the sea, did not exclusively claim his -attention. A few passages have been collected at the beginning of -this section, which prove that he had turned his mind to the -practical problems of navigation, and more especially of naval -warfare. What we know for certain of his life gives us no data, it -is true, as to when or where these matters came under his -consideration; but the fact remains certain both from these notes in -his manuscripts, and from the well known letter to Ludovico il Moro -(No._ 1340_), in which he expressly states that he is as capable as -any man, in this very department._ - -_The numerous notes as to the laws and rationale of the flight of -birds, are scattered through several note-books. An account of these -is given in the Bibliography of the manuscripts at the end of this -work. It seems probable that the idea which led him to these -investigations was his desire to construct a flying or aerial -machine for man. At the same time it must be admitted that the notes -on the two subjects are quite unconnected in the manuscripts, and -that those on the flight of birds are by far the most numerous and -extensive. The two most important passages that treat of the -construction of a flying machine are those already published as Tav. -XVI, No._ 1 _and Tav. XVIII in the_ "Saggio delle opere di Leonardo -da Vinci" _(Milan_ 1872_). The passages--Nos._ 1120-1125--_here -printed for the first time and hitherto unknown--refer to the same -subject and, with the exception of one already published in the -Saggio-- No._ 1126--_they are, so far as I know, the only notes, -among the numerous observations on the flight of birds, in which the -phenomena are incidentally and expressly connected with the idea of -a flying machine._ - -_The notes on machines of war, the construction of fortifications, -and similar matters which fall within the department of the -Engineer, have not been included in this work, for the reasons given -on page_ 26 _of this Vol. An exception has been made in favour of -the passages Nos._ 1127 _and_ 1128, _because they have a more -general interest, as bearing on the important question: whence the -Master derived his knowledge of these matters. Though it would be -rash to assert that Leonardo was the first to introduce the science -of mining into Italy, it may be confidently said that he is one of -the earliest writers who can be proved to have known and understood -it; while, on the other hand, it is almost beyond doubt that in the -East at that time, the whole science of besieging towns and mining -in particular, was far more advanced than in Europe. This gives a -peculiar value to the expressions used in No._ 1127. - -_I have been unable to find in the manuscripts any passage whatever -which throws any light on Leonardo's great reputation as a musician. -Nothing therein illustrates VASARPS well-known statement:_ Avvenne -che morto Giovan Galeazze duca di Milano, e creato Lodovico Sforza -nel grado medesimo anno 1494, fu condotto a Milano con gran -riputazione Lionardo al duca, il quale molto si dilettava del suono -della lira, perche sonasse; e Lionardo porto quello strumento -ch'egli aveva di sua mano fabbricato d'argento gran parte, in forma -d'un teschio di cavallo, cosa bizzarra e nuova, acciocche l'armonia -fosse con maggior tuba e piu sonora di voce; laonde supero tutti i -musici che quivi erano concorsi a sonare. - -_The only notes on musical matters are those given as Nos._ 1129 -_and_ 1130, _which explain certain arrangements in instruments._ - -The ship's logs of Vitruvius, of Alberti and of Leonardo - -1113. - -ON MOVEMENTS;--TO KNOW HOW MUCH A SHIP ADVANCES IN AN HOUR. - -The ancients used various devices to ascertain the distance gone by -a ship each hour, among which Vitruvius [Footnote 6: See VITRUVIUS, -_De Architectura lib. X._ C. 14 (p. 264 in the edition of Rose and -Muller- Strubing). The German edition published at Bale in 1543 has, -on fol. 596, an illustration of the contrivance, as described by -Vitruvius.] gives one in his work on Architecture which is just as -fallacious as all the others; and this is a mill wheel which touches -the waves of the sea at one end and in each complete revolution -describes a straight line which represents the circumference of the -wheel extended to a straightness. But this invention is of no worth -excepting on the smooth and motionless surface of lakes. But if the -water moves together with the ship at an equal rate, then the wheel -remains motionless; and if the motion of the water is more or less -rapid than that of the ship, then neither has the wheel the same -motion as the ship so that this invention is of but little use. -There is another method tried by experiment with a known distance -between one island and another; and this is done by a board or under -the pressure of wind which strikes on it with more or less -swiftness. This is in Battista Alberti [Footnote 25: LEON BATTISTA -ALBERTI, _De Architectura lib. V._, c. 12 treats '_de le navi e -parti loro_', but there is no reference to the machine, mentioned by -Leonardo. Alberti says here: _Noi abbiamo trattato lungamente in -altro luogo de' modi de le navi, ma in questo luogo ne abbiamo detto -quel tanto che si bisogna_. To this the following note is added in -the most recent Italian edition: _Questo libro e tuttora inedito e -porta il titolo, secondo Gesnero di_ '_Liber navis_'.]. - -Battista Alberti's method which is made by experiment on a known -distance between one island and another. But such an invention does -not succeed excepting on a ship like the one on which the experiment -was made, and it must be of the same burden and have the same sails, -and the sails in the same places, and the size of the waves must be -the same. But my method will serve for any ship, whether with oars -or sails; and whether it be small or large, broad or long, or high -or low, it always serves [Footnote 52: Leonardo does not reveal the -method invented by him.]. - -Methods of staying and moving in water - -1114. - -How an army ought to cross rivers by swimming with air-bags ... How -fishes swim [Footnote 2: Compare No. 821.]; of the way in which they -jump out of the water, as may be seen with dolphins; and it seems a -wonderful thing to make a leap from a thing which does not resist -but slips away. Of the swimming of animals of a long form, such as -eels and the like. Of the mode of swimming against currents and in -the rapid falls of rivers. Of the mode of swimming of fishes of a -round form. How it is that animals which have not long hind quartres -cannot swim. How it is that all other animals which have feet with -toes, know by nature how to swim, excepting man. In what way man -ought to learn to swim. Of the way in which man may rest on the -water. How man may protect himself against whirlpools or eddies in -the water, which drag him down. How a man dragged to the bottom must -seek the reflux which will throw him up from the depths. How he -ought to move his arms. How to swim on his back. How he can and how -he cannot stay under water unless he can hold his breath [13]. How -by means of a certain machine many people may stay some time under -water. How and why I do not describe my method of remaining under -water, or how long I can stay without eating; and I do not publish -nor divulge these by reason of the evil nature of men who would use -them as means of destruction at the bottom of the sea, by sending -ships to the bottom, and sinking them together with the men in them. -And although I will impart others, there is no danger in them; -because the mouth of the tube, by which you breathe, is above the -water supported on bags or corks [19]. - -[Footnote: L. 13-19 will also be found in Vol. I No. 1.] - -On naval warfare (1115. 1116). - -1115. - -Supposing in a battle between ships and galleys that the ships are -victorious by reason of the high of heir tops, you must haul the -yard up almost to the top of the mast, and at the extremity of the -yard, that is the end which is turned towards the enemy, have a -small cage fastened, wrapped up below and all round in a great -mattress full of cotton so that it may not be injured by the bombs; -then, with the capstan, haul down the opposite end of this yard and -the top on the opposite side will go up so high, that it will be far -above the round-top of the ship, and you will easily drive out the -men that are in it. But it is necessary that the men who are in the -galley should go to the opposite side of it so as to afford a -counterpoise to the weight of the men placed inside the cage on the -yard. - -1116. - -If you want to build an armada for the sea employ these ships to ram -in the enemy's ships. That is, make ships 100 feet long and 8 feet -wide, but arranged so that the left hand rowers may have their oars -to the right side of the ship, and the right hand ones to the left -side, as is shown at M, so that the leverage of the oars may be -longer. And the said ship may be one foot and a half thick, that is -made with cross beams within and without, with planks in contrary -directions. And this ship must have attached to it, a foot below the -water, an iron-shod spike of about the weight and size of an anvil; -and this, by force of oars may, after it has given the first blow, -be drawn back, and driven forward again with fury give a second -blow, and then a third, and so many as to destroy the other ship. - -The use of swimming belts. - -1117. - -A METHOD OF ESCAPING IN A TEMPEST AND SHIPWRECK AT SEA. - -Have a coat made of leather, which must be double across the breast, -that is having a hem on each side of about a finger breadth. Thus it -will be double from the waist to the knee; and the leather must be -quite air-tight. When you want to leap into the sea, blow out the -skirt of your coat through the double hems of the breast; and jump -into the sea, and allow yourself to be carried by the waves; when -you see no shore near, give your attention to the sea you are in, -and always keep in your mouth the air-tube which leads down into the -coat; and if now and again you require to take a breath of fresh -air, and the foam prevents you, you may draw a breath of the air -within the coat. - -[Footnote: AMORETTI, _Memorie Storiche_, Tav. II. B. Fig. 5, gives -the same figure, somewhat altered. 6. _La canna dell' aria_. Compare -Vol. I. No. I. Note] - -On the gravity of water. - -1118. - -If the weight of the sea bears on its bottom, a man, lying on that -bottom and having l000 braccia of water on his back, would have -enough to crush him. - -Diving apparatus and Skating (1119-1121). - -1119. - -Of walking under water. Method of walking on water. - -[Footnote: The two sketches belonging to this passage are given by -AMORETTI, _Memorie Storiche_. Tav. II, Fig. 3 and 4.] - -1120. - -Just as on a frozen river a man may run without moving his feet, so -a car might be made that would slide by itself. - -[Footnote: The drawings of carts by the side of this text have no -direct connection with the problem as stated in words.--Compare No. -1448, l. 17.] - -1121. - -A definition as to why a man who slides on ice does not fall. -[Footnote: An indistinct sketch accompanies the passage, in the -original.] - -On Flying machines (1122-1126). - -1122. - -Man when flying must stand free from the waist upwards so as to be -able to balance himself as he does in a boat so that the centre of -gravity in himself and in the machine may counterbalance each other, -and be shifted as necessity demands for the changes of its centre of -resistance. - -1123. - -Remember that your flying machine must imitate no other than the -bat, because the web is what by its union gives the armour, or -strength to the wings. - -If you imitate the wings of feathered birds, you will find a much -stronger structure, because they are pervious; that is, their -feathers are separate and the air passes through them. But the bat -is aided by the web that connects the whole and is not pervious. - -1124. - -TO ESCAPE THE PERIL OF DESTRUCTION. - -Destruction to such a machine may occur in two ways; of which the -first is the breaking of the machine. The second would be when the -machine should turn on its edge or nearly on its edge, because it -ought always to descend in a highly oblique direction, and almost -exactly balanced on its centre. As regards the first--the breaking -of the machine--, that may be prevented by making it as strong as -possible; and in whichever direction it may tend to turn over, one -centre must be very far from the other; that is, in a machine 30 -braccia long the centres must be 4 braccia one from the other. - -[Footnote: Compare No. 1428.] - -1125. - -Bags by which a man falling from a height of 6 braccia may avoid -hurting himself, by a fall whether into water or on the ground; and -these bags, strung together like a rosary, are to be fixed on one's -back. - -1126. - -An object offers as much resistance to the air as the air does to -the object. You may see that the beating of its wings against the -air supports a heavy eagle in the highest and rarest atmosphere, -close to the sphere of elemental fire. Again you may see the air in -motion over the sea, fill the swelling sails and drive heavily laden -ships. From these instances, and the reasons given, a man with wings -large enough and duly connected might learn to overcome the -resistance of the air, and by conquering it, succeed in subjugating -it and rising above it. [Footnote: A parachute is here sketched, -with an explanatory remark. It is reproduced on Tav. XVI in the -Saggio, and in: _Leonardo da Vinci als Ingenieur etc., Ein Beitrag -zur Geschichte der Technik und der induktiven Wissenschaften, von -Dr. Hermann Grothe, Berlin_ 1874, p. 50.] - -Of mining. - -1127. - -If you want to know where a mine runs, place a drum over all the -places where you suspect that it is being made, and upon this drum -put a couple of dice, and when you are over the spot where they are -mining, the dice will jump a little on the drum at every blow which -is given underground in the mining. - -There are persons who, having the convenience of a river or a lake -in their lands, have made, close to the place where they suspect -that a mine is being made, a great reservoir of water, and have -countermined the enemy, and having found them, have turned the water -upon them and destroyed a great number in the mine. - -Of Greek fire. - -1128. - -GREEK FIRE. - -Take charcoal of willow, and saltpetre, and sulphuric acid, and -sulphur, and pitch, with frankincense and camphor, and Ethiopian -wool, and boil them all together. This fire is so ready to burn that -it clings to the timbers even under water. And add to this -composition liquid varnish, and bituminous oil, and turpentine and -strong vinegar, and mix all together and dry it in the sun, or in an -oven when the bread is taken out; and then stick it round hempen or -other tow, moulding it into a round form, and studding it all over -with very sharp nails. You must leave in this ball an opening to -serve as a fusee, and cover it with rosin and sulphur. - -Again, this fire, stuck at the top of a long plank which has one -braccio length of the end pointed with iron that it may not be burnt -by the said fire, is good for avoiding and keeping off the ships, so -as not to be overwhelmed by their onset. - -Again throw vessels of glass full of pitch on to the enemy's ships -when the men in them are intent on the battle; and then by throwing -similar burning balls upon them you have it in your power to burn -all their ships. - -[Footnote: Venturi has given another short text about the Greek fire -in a French translation (Essai Section XIV). He adds that the -original text is to be found in MS. B. 30 (?). Libri speaks of it in -a note as follows (_Histoire des sciences mathematiques en Italie -Vol. II_ p. 129): _La composition du feu gregeois est une des chases -qui ont ete les plus cherchees et qui sont encore les plus -douteuses. On dit qu'il fut invente au septieme siecle de l'ere -chretienne par l'architecte Callinique (Constantini Porphyrogenetae -opera, Lugd. Batav._ 1617,-- _in-_8vo; p. 172, _de admin, imper. -exp._ 48_), et il se trouve souvent mentionne par les Historiens -Byzantins. Tantot on le langait avec des machines, comme on -lancerait une banche, tantot on le soufflait avec de longs tubes, -comme on soufflerait un gaz ou un liquide enflamme (Annae Comnenae -Alexias_, p. 335, _lib. XI.--Aeliani et Leonis, imperatoris tactica, -Lugd.-Bat._ 1613, _in_-4. part. 2 a, p. 322, _Leonis tact. cap._ -l9.--_Joinville, histoire du Saint Louis collect. Petitot tom. II,_ -p. 235). _Les ecrivains contemporains disent que l'eau ne pouvait -pas eteindre ce feu, mais qu'avec du vinaigre et du sable on y -parvenait. Suivant quelques historiens le feu gregeois etait compose -de soufre et de resine. Marcus Graecus (Liber ignium, Paris,_ 1804, -_in_-40_) donne plusieurs manieres de le faire qui ne sont pas tres -intelligibles, mais parmi lesquelles on trouve la composition de la -poudre a canon. Leonard de Vinci (MSS. de Leonard de Vinci, vol. B. -f. 30,) dit qu'on le faisait avec du charbon de saule, du salpetre, -de l'eau de vie, de la resine, du soufre, de la poix et du camphre. -Mais il est probable que nous ne savons pas qu'elle etait sa -composition, surtout a cause du secret qu'en faisaient les Grecs. En -effet, l'empereur Constantin Porphyrogenete recommende a son fils de -ne jamais en donner aux Barbares, et de leur repondre, s'ils en -demandaient, qu'il avait ete apporti du ciel par un ange et que le -secret en avait ete confie aux Chretiens (Constantini -Porphyrogennetae opera,_ p. 26-27, _de admin. imper., cap. _12_)._] - -Of Music (1129. 1130). - -1129. - -A drum with cogs working by wheels with springs [2]. - -[Footnote: This chapter consists of explanations of the sketches -shown on Pl. CXXI. Lines 1 and 2 of the text are to be seen at the -top at the left hand side of the first sketch of a drum. Lines 3-5 -refer to the sketch immediately below this. Line 6 is written as the -side of the seventh sketch, and lines 7 and 8 at the side of the -eighth. Lines 9-16 are at the bottom in the middle. The remainder of -the text is at the side of the drawing at the bottom.] - -A square drum of which the parchment may be drawn tight or slackened -by the lever _a b_ [5]. - -A drum for harmony [6]. - -[7] A clapper for harmony; that is, three clappers together. - -[9] Just as one and the same drum makes a deep or acute sound -according as the parchments are more or less tightened, so these -parchments variously tightened on one and the same drum will make -various sounds [16]. - -Keys narrow and close together; (bicchi) far apart; these will be -right for the trumpet shown above. - -_a_ must enter in the place of the ordinary keys which have the ... -in the openings of a flute. - -1130. - -Tymbals to be played like the monochord, or the soft flute. - -[6] Here there is to be a cylinder of cane after the manner of -clappers with a musical round called a Canon, which is sung in four -parts; each singer singing the whole round. Therefore I here make a -wheel with 4 teeth so that each tooth takes by itself the part of a -singer. - -[Footnote: In the original there are some more sketches, to which -the text, from line 6, refers. They are studies for a contrivance -exactly like the cylinder in our musical boxes.] - -1131. - -Of decorations. - -White and sky-blue cloths, woven in checks to make a decoration. - -Cloths with the threads drawn at _a b c d e f g h i k_, to go round -the decoration. - -_XIX._ - -_Philosophical Maxims. Morals. Polemics and Speculations_. - -_Vasari indulges in severe strictures on Leonardo's religious views. -He speaks, among other things, of his_ "capricci nel filosofar delle -cose naturali" _and says on this point:_ "Per il che fece nell'animo -un concetto si eretico che e' non si accostava a qualsi voglia -religione, stimando per avventura assai piu lo esser filosofo che -cristiano" _(see the first edition of_ 'Le Vite'_). But this -accusation on the part of a writer in the days of the Inquisition is -not a very serious one--and the less so, since, throughout the -manuscripts, we find nothing to support it._ - -_Under the heading of "Philosophical Maxims" I have collected all -the passages which can give us a clear comprehension of Leonardo's -ideas of the world at large. It is scarcely necessary to observe -that there is absolutely nothing in them to lead to the inference -that he was an atheist. His views of nature and its laws are no -doubt very unlike those of his contemporaries, and have a much -closer affinity to those which find general acceptance at the -present day. On the other hand, it is obvious from Leonardo's will -(see No._ 1566_) that, in the year before his death, he had -professed to adhere to the fundamental doctrines of the Roman -Catholic faith, and this evidently from his own personal desire and -impulse._ - -_The incredible and demonstrably fictitious legend of Leonardo's -death in the arms of Francis the First, is given, with others, by -Vasari and further embellished by this odious comment:_ "Mostrava -tuttavia quanto avea offeso Dio e gli uomini del mondo, non avendo -operato nell'arte come si conveniva." _This last accusation, it may -be remarked, is above all evidence of the superficial character of -the information which Vasari was in a position to give about -Leonardo. It seems to imply that Leonardo was disdainful of diligent -labour. With regard to the second, referring to Leonardo's morality -and dealings with his fellow men, Vasari himself nullifies it by -asserting the very contrary in several passages. A further -refutation may be found in the following sentence from the letter in -which Melsi, the young Milanese nobleman, announces the Master's -death to Leonardo's brothers:_ Credo siate certificati della morte -di Maestro Lionardo fratello vostro, e mio quanto optimo padre, per -la cui morte sarebbe impossibile che io potesse esprimere il dolore -che io ho preso; e in mentre che queste mia membra si sosterranno -insieme, io possedero una perpetua infelicita, e meritamente perche -sviscerato et ardentissimo amore mi portava giornalmente. E dolto ad -ognuno la perdita di tal uomo, quale non e piu in podesta della -natura, ecc. - -_It is true that, in April_ 1476, _we find the names of Leonardo and -Verrocchio entered in the_ "Libro degli Uffiziali di notte e de' -Monasteri" _as breaking the laws; but we immediately after find the -note_ "Absoluti cum condizione ut retamburentur" (Tamburini _was the -name given to the warrant cases of the night police). The acquittal -therefore did not exclude the possibility of a repetition of the -charge. It was in fact repeated, two months later, and on this -occasion the Master and his pupil were again fully acquitted. -Verrocchio was at this time forty and Leonardo four-and-twenty. The -documents referring to this affair are in the State Archives of -Florence; they have been withheld from publication, but it seemed to -me desirable to give the reader this brief account of the leading -facts of the story, as the vague hints of it, which have recently -been made public, may have given to the incident an aspect which it -had not in reality, and which it does not deserve._ - -_The passages here classed under the head "Morals" reveal Leonardo -to us as a man whose life and conduct were unfailingly governed by -lofty principles and aims. He could scarcely have recorded his stern -reprobation and unmeasured contempt for men who do nothing useful -and strive only for riches, if his own life and ambitions had been -such as they have so often been misrepresented._ - -_At a period like that, when superstition still exercised unlimited -dominion over the minds not merely of the illiterate crowd, but of -the cultivated and learned classes, it was very natural that -Leonardo's views as to Alchemy, Ghosts, Magicians, and the like -should be met with stern reprobation whenever and wherever he may -have expressed them; this accounts for the argumentative tone of all -his utterances on such subjects which I have collected in -Subdivision III of this section. To these I have added some passages -which throw light on Leonardo's personal views on the Universe. They -are, without exception, characterised by a broad spirit of -naturalism of which the principles are more strictly applied in his -essays on Astronomy, and still more on Physical Geography._ - -_To avoid repetition, only such notes on Philosophy, Morals and -Polemics, have been included in this section as occur as independent -texts in the original MSS. Several moral reflections have already -been given in Vol. I, in section "Allegorical representations, -Mottoes and Emblems". Others will be found in the following section. -Nos._ 9 _to_ 12, _Vol. I, are also passages of an argumentative -character. It did not seem requisite to repeat here these and -similar passages, since their direct connection with the context is -far closer in places where they have appeared already, than it would -be here._ - -I. - -PHILOSOPHICAL MAXIMS. - -Prayers to God (1132. 1133). - -1132. - -I obey Thee Lord, first for the love I ought, in all reason to bear -Thee; secondly for that Thou canst shorten or prolong the lives of -men. - -1133. - -A PRAYER. - -Thou, O God, dost sell us all good things at the price of labour. - -The powers of Nature (1134-1139). - -1134. - -O admirable impartiality of Thine, Thou first Mover; Thou hast not -permitted that any force should fail of the order or quality of its -necessary results. - -1135. - -Necessity is the mistress and guide of nature. - -Necessity is the theme and the inventress, the eternal curb and law -of nature. - -1136. - -In many cases one and the same thing is attracted by two strong -forces, namely Necessity and Potency. Water falls in rain; the earth -absorbs it from the necessity for moisture; and the sun evaporates -it, not from necessity, but by its power. - -1137. - -Weight, force and casual impulse, together with resistance, are the -four external powers in which all the visible actions of mortals -have their being and their end. - -1138. - -Our body is dependant on heaven and heaven on the Spirit. - -1139. - -The motive power is the cause of all life. - -Psychology (1140-1147). - -1140. - -And you, O Man, who will discern in this work of mine the wonderful -works of Nature, if you think it would be a criminal thing to -destroy it, reflect how much more criminal it is to take the life of -a man; and if this, his external form, appears to thee marvellously -constructed, remember that it is nothing as compared with the soul -that dwells in that structure; for that indeed, be it what it may, -is a thing divine. Leave it then to dwell in His work at His good -will and pleasure, and let not your rage or malice destroy a -life--for indeed, he who does not value it, does not himself deserve -it [Footnote 19: In MS. II 15a is the note: _chi no stima la vita, -non la merita._]. - -[Footnote: This text is on the back of the drawings reproduced on -Pl. CVII. Compare No. 798, 35 note on p. 111: Compare also No. 837 -and 838.] - -1141. - -The soul can never be corrupted with the corruption of the body,, -but is in the body as it were the air which causes the sound of the -organ, where when a pipe bursts, the wind would cease to have any -good effect. [Footnote: Compare No. 845.] - -1142. - -The part always has a tendency to reunite with its whole in order to -escape from its imperfection. - -The spirit desires to remain with its body, because, without the -organic instruments of that body, it can neither act, nor feel -anything. - -1143. - -If any one wishes to see how the soul dwells in its body, let him -observe how this body uses its daily habitation; that is to say, if -this is devoid of order and confused, the body will be kept in -disorder and confusion by its soul. - -1144. - -Why does the eye see a thing more clearly in dreams than with the -imagination being awake? - -1145. - -The senses are of the earth; Reason, stands apart in contemplation. - -[Footnote: Compare No. 842.] - -1146. - -Every action needs to be prompted by a motive. - -To know and to will are two operations of the human mind. - -Discerning, judging, deliberating are acts of the human mind. - -1147. - -All our knowledge has its origin in our preceptions. - -Science, its principles and rules (1148--1161) - -1148. - -Science is the observation of things possible, whether present or -past; prescience is the knowledge of things which may come to pass, -though but slowly. - -1149. - -Experience, the interpreter between formative nature and the human -race, teaches how that nature acts among mortals; and being -constrained by necessity cannot act otherwise than as reason, which -is its helm, requires her to act. - -1150. - -Wisdom is the daughter of experience. - -1151. - -Nature is full of infinite causes that have never occured in -experience. - -1152. - -Truth was the only daughter of Time. - -1153. - -Experience never errs; it is only your judgments that err by -promising themselves effects such as are not caused by your -experiments. - -Experience does not err; only your judgments err by expecting from -her what is not in her power. Men wrongly complain of Experience; -with great abuse they accuse her of leading them astray but they set -Experience aside, turning from it with complaints as to our -ignorance causing us to be carried away by vain and foolish desires -to promise ourselves, in her name, things that are not in her power; -saying that she is fallacious. Men are unjust in complaining of -innocent Experience, constantly accusing her of error and of false -evidence. - -1154. - -Instrumental or mechanical science is of all the noblest and the -most useful, seeing that by means of this all animated bodies that -have movement perform all their actions; and these movements are -based on the centre of gravity which is placed in the middle -dividing unequal weights, and it has dearth and wealth of muscles -and also lever and counterlever. - -1155. - -OF MECHANICS. - -Mechanics are the Paradise of mathematical science, because here we -come to the fruits of mathematics. [Footnote: Compare No. 660, 11. -19--22 (Vol. I., p. 332). 1156. - -Every instrument requires to be made by experience. - -1157. - -The man who blames the supreme certainty of mathematics feeds on -confusion, and can never silence the contradictions of sophistical -sciences which lead to an eternal quackery. - -1158. - -There is no certainty in sciences where one of the mathematical -sciences cannot be applied, or which are not in relation with these -mathematics. - -1159. - -Any one who in discussion relies upon authority uses, not his -understanding, but rather his memory. Good culture is born of a good -disposition; and since the cause is more to be praised than the -effect, I will rather praise a good disposition without culture, -than good culture without the disposition. - -1160. - -Science is the captain, and practice the soldiers. - -1161. - -OF THE ERRORS OF THOSE WHO DEPEND ON PRACTICE WITHOUT SCIENCE. - -Those who fall in love with practice without science are like a -sailor who enters a ship without a helm or a compass, and who never -can be certain whither he is going. - -II. - -MORALS. - -What is life? (1162. 1163). - -1162. - -Now you see that the hope and the desire of returning home and to -one's former state is like the moth to the light, and that the man -who with constant longing awaits with joy each new spring time, each -new summer, each new month and new year--deeming that the things he -longs for are ever too late in coming--does not perceive that he is -longing for his own destruction. But this desire is the very -quintessence, the spirit of the elements, which finding itself -imprisoned with the soul is ever longing to return from the human -body to its giver. And you must know that this same longing is that -quintessence, inseparable from nature, and that man is the image of -the world. - -1163. - -O Time! consumer of all things; O envious age! thou dost destroy all -things and devour all things with the relentless teeth of years, -little by little in a slow death. Helen, when she looked in her -mirror, seeing the withered wrinkles made in her face by old age, -wept and wondered why she had twice been carried away. - -O Time! consumer of all things, and O envious age! by which all -things are all devoured. - -Death. - -1164. - -Every evil leaves behind a grief in our memory, except the supreme -evil, that is death, which destroys this memory together with life. - -How to spend life (1165-1170). - -1165. - -0 sleepers! what a thing is slumber! Sleep resembles death. Ah, why -then dost thou not work in such wise as that after death thou mayst -retain a resemblance to perfect life, when, during life, thou art in -sleep so like to the hapless dead? [Footnote: Compare No. 676, Vol. -I. p. 353.] - -1166. - -One pushes down the other. - -By these square-blocks are meant the life and the studies of men. - -1167. - -The knowledge of past times and of the places on the earth is both -an ornament and nutriment to the human mind. - -1168. - -To lie is so vile, that even if it were in speaking well of godly -things it would take off something from God's grace; and Truth is so -excellent, that if it praises but small things they become noble. - -Beyond a doubt truth bears the same relation to falsehood as light -to darkness; and this truth is in itself so excellent that, even -when it dwells on humble and lowly matters, it is still infinitely -above uncertainty and lies, disguised in high and lofty discourses; -because in our minds, even if lying should be their fifth element, -this does not prevent that the truth of things is the chief -nutriment of superior intellects, though not of wandering wits. - -But you who live in dreams are better pleased by the sophistical -reasons and frauds of wits in great and uncertain things, than by -those reasons which are certain and natural and not so far above us. - -1169. - -Avoid studies of which the result dies with the worker. - -1170. - -Men are in error when they lament the flight of time, accusing it of -being too swift, and not perceiving that it is sufficient as it -passes; but good memory, with which nature has endowed us, causes -things long past to seem present. - -1171. - -Learning acquired in youth arrests the evil of old age; and if you -understand that old age has wisdom for its food, you will so conduct -yourself in youth that your old age will not lack for nourishment. - -1172. - -The acquisition of any knowledge is always of use to the intellect, -because it may thus drive out useless things and retain the good. - -For nothing can be loved or hated unless it is first known. - -1173. - -As a day well spent procures a happy sleep, so a life well employed -procures a happy death. - -1174. - -The water you touch in a river is the last of that which has passed, -and the first of that which is coming. Thus it is with time present. - -Life if well spent, is long. - -1175. - -Just as food eaten without caring for it is turned into loathsome -nourishment, so study without a taste for it spoils memory, by -retaining nothing which it has taken in. - -1176. - -Just as eating against one's will is injurious to health, so study -without a liking for it spoils the memory, and it retains nothing it -takes in. - -1177. - -On Mount Etna the words freeze in your mouth and you may make ice of -them.[Footnote 2: There is no clue to explain this strange -sentence.] - -Just as iron rusts unless it is used, and water putrifies or, in -cold, turns to ice, so our intellect spoils unless it is kept in -use. - -You do ill if you praise, and still worse if you reprove in a matter -you do not understand. - -When Fortune comes, seize her in front with a sure hand, because -behind she is bald. - -1178. - -It seems to me that men of coarse and clumsy habits and of small -knowledge do not deserve such fine instruments nor so great a -variety of natural mechanism as men of speculation and of great -knowledge; but merely a sack in which their food may be stowed and -whence it may issue, since they cannot be judged to be any thing -else than vehicles for food; for it seems to me they have nothing -about them of the human species but the voice and the figure, and -for all the rest are much below beasts. - -1179. - -Some there are who are nothing else than a passage for food and -augmentors of excrement and fillers of privies, because through them -no other things in the world, nor any good effects are produced, -since nothing but full privies results from them. - -On foolishness and ignorance (1180--1182). - -1180. - -The greatest deception men suffer is from their own opinions. - -1181. - -Folly is the shield of shame, as unreadiness is that of poverty -glorified. - -1182. - -Blind ignorance misleads us thus and delights with the results of -lascivious joys. - -Because it does not know the true light. Because it does not know -what is the true light. - -Vain splendour takes from us the power of being .... behold! for its -vain splendour we go into the fire, thus blind ignorance does -mislead us. That is, blind ignorance so misleads us that ... - -O! wretched mortals, open your eyes. - -On riches (1183--1187). - -1183. - -That is not riches, which may be lost; virtue is our true good and -the true reward of its possessor. That cannot be lost; that never -deserts us, but when life leaves us. As to property and external -riches, hold them with trembling; they often leave their possessor -in contempt, and mocked at for having lost them. - -1184. - -Every man wishes to make money to give it to the doctors, destroyers -of life; they then ought to be rich. [Footnote 2: Compare No. 856.] - -Man has much power of discourse which for the most part is vain and -false; animals have but little, but it is useful and true, and a -small truth is better than a great lie. - -1185. - -He who possesses most must be most afraid of loss. - -1186. - -He who wishes to be rich in a day will be hanged in a year. - -1187. - -That man is of supreme folly who always wants for fear of wanting; -and his life flies away while he is still hoping to enjoy the good -things which he has with extreme labour acquired. - -Rules of Life (1188-1202). - -1188. - -If you governed your body by the rules of virtue you would not walk -on all fours in this world. - -You grow in reputation like bread in the hands of a child. -[Footnote: The first sentence is obscure. Compare Nos. 825, 826.] - -1189. - -Savage he is who saves himself. - -1190. diff --git a/docs/examples/kernel/davinci3.txt b/docs/examples/kernel/davinci3.txt deleted file mode 100644 index 7291d55..0000000 --- a/docs/examples/kernel/davinci3.txt +++ /dev/null @@ -1,7968 +0,0 @@ - -We ought not to desire the impossible. [Footnote: The writing of -this note, which is exceedingly minute, is reproduced in facsimile -on Pl. XLI No. 5 above the first diagram. - -1191. - -Ask counsel of him who rules himself well. - -Justice requires power, insight, and will; and it resembles the -queen-bee. - -He who does not punish evil commands it to be done. - -He who takes the snake by the tail will presently be bitten by it. - -The grave will fall in upon him who digs it. - -1192. - -The man who does not restrain wantonness, allies himself with -beasts. - -You can have no dominion greater or less than that over yourself. - -He who thinks little, errs much. - -It is easier to contend with evil at the first than at the last. - -No counsel is more loyal than that given on ships which are in -peril: He may expect loss who acts on the advice of an inexperienced -youth. - -1193. - -Where there is most feeling, there is the greatest martyrdom;--a -great martyr. - -1194. - -The memory of benefits is a frail defence against ingratitude. - -Reprove your friend in secret and praise him openly. - -Be not false about the past. - -1195. - -A SIMILE FOR PATIENCE. - -Patience serves us against insults precisely as clothes do against -the cold. For if you multiply your garments as the cold increases, -that cold cannot hurt you; in the same way increase your patience -under great offences, and they cannot hurt your feelings. - -1196. - -To speak well of a base man is much the same as speaking ill of a -good man. - -1197. - -Envy wounds with false accusations, that is with detraction, a thing -which scares virtue. - -1198. - -We are deceived by promises and time disappoints us ... [Footnote 2: -The rest of this passage may be rendered in various ways, but none -of them give a satisfactory meaning.] - -1199. - -Fear arises sooner than any thing else. - -1200. - -Just as courage imperils life, fear protects it. - -Threats alone are the weapons of the threatened man. - -Wherever good fortune enters, envy lays siege to the place and -attacks it; and when it departs, sorrow and repentance remain -behind. - -He who walks straight rarely falls. - -It is bad if you praise, and worse if you reprove a thing, I mean, -if you do not understand the matter well. - -It is ill to praise, and worse to reprimand in matters that you do -not understand. - -1201. - -Words which do not satisfy the ear of the hearer weary him or vex -him, and the symptoms of this you will often see in such hearers in -their frequent yawns; you therefore, who speak before men whose good -will you desire, when you see such an excess of fatigue, abridge -your speech, or change your discourse; and if you do otherwise, then -instead of the favour you desire, you will get dislike and -hostility. - -And if you would see in what a man takes pleasure, without hearing -him speak, change the subject of your discourse in talking to him, -and when you presently see him intent, without yawning or wrinkling -his brow or other actions of various kinds, you may be certain that -the matter of which you are speaking is such as is agreeable to him -&c. - -1202. - -The lover is moved by the beloved object as the senses are by -sensible objects; and they unite and become one and the same thing. -The work is the first thing born of this union; if the thing loved -is base the lover becomes base. - -When the thing taken into union is perfectly adapted to that which -receives it, the result is delight and pleasure and satisfaction. - -When that which loves is united to the thing beloved it can rest -there; when the burden is laid down it finds rest there. - -Politics (1203. 1204). - -1203. - -There will be eternal fame also for the inhabitants of that town, -constructed and enlarged by him. - -All communities obey and are led by their magnates, and these -magnates ally themselves with the lords and subjugate them in two -ways: either by consanguinity, or by fortune; by consanguinity, when -their children are, as it were, hostages, and a security and pledge -of their suspected fidelity; by property, when you make each of -these build a house or two inside your city which may yield some -revenue and he shall have...; 10 towns, five thousand houses with -thirty thousand inhabitants, and you will disperse this great -congregation of people which stand like goats one behind the other, -filling every place with fetid smells and sowing seeds of pestilence -and death; - -And the city will gain beauty worthy of its name and to you it will -be useful by its revenues, and the eternal fame of its -aggrandizement. - -[Footnote: These notes were possibly written in preparation for a -letter. The meaning is obscure.] - -1204. - -To preserve Nature's chiefest boon, that is freedom, I can find -means of offence and defence, when it is assailed by ambitious -tyrants, and first I will speak of the situation of the walls, and -also I shall show how communities can maintain their good and just -Lords. - -[Footnote: Compare No. 1266.] - -III. - -POLEMICS.--SPECULATION. - -Against Speculators (1205. 1206). - -1205. - -Oh! speculators on things, boast not of knowing the things that -nature ordinarily brings about; but rejoice if you know the end of -those things which you yourself devise. - -1206. - -Oh! speculators on perpetual motion how many vain projects of the -like character you have created! Go and be the companions of the -searchers for gold. [Footnote: Another short passage in MS. I, -referring also to speculators, is given by LIBRI (_Hist, des -Sciences math._ III, 228): _Sicche voi speculatori non vi fidate -delli autori che anno sol col immaginatione voluto farsi interpreti -tra la natura e l'omo, ma sol di quelli che non coi cienni della -natura, ma cogli effetti delle sue esperienze anno esercitati i loro -ingegni._] - -Against alchemists (1207. 1208). - -1207. - -The false interpreters of nature declare that quicksilver is the -common seed of every metal, not remembering that nature varies the -seed according to the variety of the things she desires to produce -in the world. - -1208. - -And many have made a trade of delusions and false miracles, -deceiving the stupid multitude. - -Against friars. - -1209. - -Pharisees--that is to say, friars. - -[Footnote: Compare No. 837, 11. 54-57, No. 1296 (p. 363 and 364), -and No. 1305 (p. 370).] - -Against writers of epitomes. - -1210. - -Abbreviators do harm to knowledge and to love, seeing that the love -of any thing is the offspring of this knowledge, the love being the -more fervent in proportion as the knowledge is more certain. And -this certainty is born of a complete knowledge of all the parts, -which, when combined, compose the totality of the thing which ought -to be loved. Of what use then is he who abridges the details of -those matters of which he professes to give thorough information, -while he leaves behind the chief part of the things of which the -whole is composed? It is true that impatience, the mother of -stupidity, praises brevity, as if such persons had not life long -enough to serve them to acquire a complete knowledge of one single -subject, such as the human body; and then they want to comprehend -the mind of God in which the universe is included, weighing it -minutely and mincing it into infinite parts, as if they had to -dissect it! - -Oh! human stupidity, do you not perceive that, though you have been -with yourself all your life, you are not yet aware of the thing you -possess most of, that is of your folly? and then, with the crowd of -sophists, you deceive yourselves and others, despising the -mathematical sciences, in which truth dwells and the knowledge of -the things included in them. And then you occupy yourself with -miracles, and write that you possess information of those things of -which the human mind is incapable and which cannot be proved by any -instance from nature. And you fancy you have wrought miracles when -you spoil a work of some speculative mind, and do not perceive that -you are falling into the same error as that of a man who strips a -tree of the ornament of its branches covered with leaves mingled -with the scented blossoms or fruit....... [Footnote 48: _Givstino_, -Marcus Junianus Justinus, a Roman historian of the second century, -who compiled an epitome from the general history written by Trogus -Pompeius, who lived in the time of Augustus. The work of the latter -writer no longer exist.] as Justinus did, in abridging the histories -written by Trogus Pompeius, who had written in an ornate style all -the worthy deeds of his forefathers, full of the most admirable and -ornamental passages; and so composed a bald work worthy only of -those impatient spirits, who fancy they are losing as much time as -that which they employ usefully in studying the works of nature and -the deeds of men. But these may remain in company of beasts; among -their associates should be dogs and other animals full of rapine and -they may hunt with them after...., and then follow helpless beasts, -which in time of great snows come near to your houses asking alms as -from their master.... - -On spirits (1211--1213). - -1211. - -O mathematicians shed light on this error. - -The spirit has no voice, because where there is a voice there is a -body, and where there is a body space is occupied, and this prevents -the eye from seeing what is placed behind that space; hence the -surrounding air is filled by the body, that is by its image. - -1212. - -There can be no voice where there is no motion or percussion of the -air; there can be no percussion of the air where there is no -instrument, there can be no instrument without a body; and this -being so, a spirit can have neither voice, nor form, nor strength. -And if it were to assume a body it could not penetrate nor enter -where the passages are closed. And if any one should say that by -air, compressed and compacted together, a spirit may take bodies of -various forms and by this means speak and move with strength--to him -I reply that when there are neither nerves nor bones there can be no -force exercised in any kind of movement made by such imaginary -spirits. - -Beware of the teaching of these speculators, because their reasoning -is not confirmed by experience. - -1213. - -Of all human opinions that is to be reputed the most foolish which -deals with the belief in Necromancy, the sister of Alchemy, which -gives birth to simple and natural things. But it is all the more -worthy of reprehension than alchemy, because it brings forth nothing -but what is like itself, that is, lies; this does not happen in -Alchemy which deals with simple products of nature and whose -function cannot be exercised by nature itself, because it has no -organic instruments with which it can work, as men do by means of -their hands, who have produced, for instance, glass &c. but this -Necromancy the flag and flying banner, blown by the winds, is the -guide of the stupid crowd which is constantly witness to the -dazzling and endless effects of this art; and there are books full, -declaring that enchantments and spirits can work and speak without -tongues and without organic instruments-- without which it is -impossible to speak-- and can carry heaviest weights and raise -storms and rain; and that men can be turned into cats and wolves and -other beasts, although indeed it is those who affirm these things -who first became beasts. - -And surely if this Necromancy did exist, as is believed by small -wits, there is nothing on the earth that would be of so much -importance alike for the detriment and service of men, if it were -true that there were in such an art a power to disturb the calm -serenity of the air, converting it into darkness and making -coruscations or winds, with terrific thunder and lightnings rushing -through the darkness, and with violent storms overthrowing high -buildings and rooting up forests; and thus to oppose armies, -crushing and annihilating them; and, besides these frightful storms -may deprive the peasants of the reward of their labours.--Now what -kind of warfare is there to hurt the enemy so much as to deprive him -of the harvest? What naval warfare could be compared with this? I -say, the man who has power to command the winds and to make ruinous -gales by which any fleet may be submerged, --surely a man who could -command such violent forces would be lord of the nations, and no -human ingenuity could resist his crushing force. The hidden -treasures and gems reposing in the body of the earth would all be -made manifest to him. No lock nor fortress, though impregnable, -would be able to save any one against the will of the necromancer. -He would have himself carried through the air from East to West and -through all the opposite sides of the universe. But why should I -enlarge further upon this? What is there that could not be done by -such a craftsman? Almost nothing, except to escape death. Hereby I -have explained in part the mischief and the usefulness, contained in -this art, if it is real; and if it is real why has it not remained -among men who desire it so much, having nothing to do with any -deity? For I know that there are numberless people who would, to -satisfy a whim, destroy God and all the universe; and if this -necromancy, being, as it were, so necessary to men, has not been -left among them, it can never have existed, nor will it ever exist -according to the definition of the spirit, which is invisible in -substance; for within the elements there are no incorporate things, -because where there is no body, there is a vacuum; and no vacuum can -exist in the elements because it would be immediately filled up. -Turn over. - -1214. - -OF SPIRITS. - -We have said, on the other side of this page, that the definition of -a spirit is a power conjoined to a body; because it cannot move of -its own accord, nor can it have any kind of motion in space; and if -you were to say that it moves itself, this cannot be within the -elements. For, if the spirit is an incorporeal quantity, this -quantity is called a vacuum, and a vacuum does not exist in nature; -and granting that one were formed, it would be immediately filled up -by the rushing in of the element in which the vacuum had been -generated. Therefore, from the definition of weight, which is -this--Gravity is an accidental power, created by one element being -drawn to or suspended in another--it follows that an element, not -weighing anything compared with itself, has weight in the element -above it and lighter than it; as we see that the parts of water have -no gravity or levity compared with other water, but if you draw it -up into the air, then it would acquire weight, and if you were to -draw the air beneath the water then the water which remains above -this air would acquire weight, which weight could not sustain itself -by itself, whence collapse is inevitable. And this happens in water; -wherever the vacuum may be in this water it will fall in; and this -would happen with a spirit amid the elements, where it would -continuously generate a vacuum in whatever element it might find -itself, whence it would be inevitable that it should be constantly -flying towards the sky until it had quitted these elements. - -AS TO WHETHER A SPIRIT HAS A BODY AMID THE ELEMENTS. - -We have proved that a spirit cannot exist of itself amid the -elements without a body, nor can it move of itself by voluntary -motion unless it be to rise upwards. But now we will say how such a -spirit taking an aerial body would be inevitably melt into air; -because if it remained united, it would be separated and fall to -form a vacuum, as is said above; therefore it is inevitable, if it -is to be able to remain suspended in the air, that it should absorb -a certain quantity of air; and if it were mingled with the air, two -difficulties arise; that is to say: It must rarefy that portion of -the air with which it mingles; and for this cause the rarefied air -must fly up of itself and will not remain among the air that is -heavier than itself; and besides this the subtle spiritual essence -disunites itself, and its nature is modified, by which that nature -loses some of its first virtue. Added to these there is a third -difficulty, and this is that such a body formed of air assumed by -the spirits is exposed to the penetrating winds, which are -incessantly sundering and dispersing the united portions of the air, -revolving and whirling amidst the rest of the atmosphere; therefore -the spirit which is infused in this - -1215. - -air would be dismembered or rent and broken up with the rending of -the air into which it was incorporated. - -AS TO WHETHER THE SPIRIT, HAVING TAKEN THIS BODY OF AIR, CAN MOVE OF -ITSELF OR NOT. - -It is impossible that the spirit infused into a certain quantity of -air, should move this air; and this is proved by the above passage -where it is said: the spirit rarefies that portion of the air in -which it incorporates itself; therefore this air will rise high -above the other air and there will be a motion of the air caused by -its lightness and not by a voluntary movement of the spirit, and if -this air is encountered by the wind, according to the 3rd of this, -the air will be moved by the wind and not by the spirit incorporated -in it. - -AS TO WHETHER THE SPIRIT CAN SPEAK OR NOT. - -In order to prove whether the spirit can speak or not, it is -necessary in the first place to define what a voice is and how it is -generated; and we will say that the voice is, as it were, the -movement of air in friction against a dense body, or a dense body in -friction against the air,--which is the same thing. And this -friction of the dense and the rare condenses the rare and causes -resistance; again, the rare, when in swift motion, and the rare in -slow motion condense each other when they come in contact and make a -noise and very great uproar; and the sound or murmur made by the -rare moving through the rare with only moderate swiftness, like a -great flame generating noises in the air; and the tremendous uproar -made by the rare mingling with the rare, and when that air which is -both swift and rare rushes into that which is itself rare and in -motion, it is like the flame of fire which issues from a big gun and -striking against the air; and again when a flame issues from the -cloud, there is a concussion in the air as the bolt is generated. -Therefore we may say that the spirit cannot produce a voice without -movement of the air, and air in it there is none, nor can it emit -what it has not; and if desires to move that air in which it is -incorporated, it is necessary that the spirit should multiply -itself, and that cannot multiply which has no quantity. And in the -4th place it is said that no rare body can move, if it has not a -stable spot, whence it may take its motion; much more is it so when -an element has to move within its own element, which does not move -of itself, excepting by uniform evaporation at the centre of the -thing evaporated; as occurs in a sponge squeezed in the hand held -under water; the water escapes in every direction with equal -movement through the openings between the fingers of the hand in -which it is squeezed. - -As to whether the spirit has an articulate voice, and whether the -spirit can be heard, and what hearing is, and seeing; the wave of -the voice passes through the air as the images of objects pass to -the eye. - -Nonentity. - -1216. - -Every quantity is intellectually conceivable as infinitely -divisible. - -[Amid the vastness of the things among which we live, the existence -of nothingness holds the first place; its function extends over all -things that have no existence, and its essence, as regards time, -lies precisely between the past and the future, and has nothing in -the present. This nothingness has the part equal to the whole, and -the whole to the part, the divisible to the indivisible; and the -product of the sum is the same whether we divide or multiply, and in -addition as in subtraction; as is proved by arithmeticians by their -tenth figure which represents zero; and its power has not extension -among the things of Nature.] - -[What is called Nothingness is to be found only in time and in -speech. In time it stands between the past and future and has no -existence in the present; and thus in speech it is one of the things -of which we say: They are not, or they are impossible.] - -With regard to time, nothingness lies between the past and the -future, and has nothing to do with the present, and as to its nature -it is to be classed among things impossible: hence, from what has -been said, it has no existence; because where there is nothing there -would necessarily be a vacuum. - -[Footnote: Compare No. 916.] - -Reflections on Nature (1217-1219). - -1217. - -EXAMPLE OF THE LIGHTNING IN CLOUDS. - -[O mighty and once living instrument of formative nature. Incapable -of availing thyself of thy vast strength thou hast to abandon a life -of stillness and to obey the law which God and time gave to -procreative nature.] - -Ah! how many a time the shoals of terrified dolphins and the huge -tunny-fish were seen to flee before thy cruel fury, to escape; -whilst thy fulminations raised in the sea a sudden tempest with -buffeting and submersion of ships in the great waves; and filling -the uncovered shores with the terrified and desperate fishes which -fled from thee, and left by the sea, remained in spots where they -became the abundant prey of the people in the neighbourhood. - -O time, swift robber of all created things, how many kings, how many -nations hast thou undone, and how many changes of states and of -various events have happened since the wondrous forms of this fish -perished here in this cavernous and winding recess. Now destroyed by -time thou liest patiently in this confined space with bones stripped -and bare; serving as a support and prop for the superimposed -mountain. - -[Footnote: The character of the handwriting points to an early -period of Leonardo's life. It has become very indistinct, and is at -present exceedingly difficult to decipher. Some passages remain -doubtful.] - -[Footnote: Compare No. 1339, written on the same sheet.] - -1218. - -The watery element was left enclosed between the raised banks of the -rivers, and the sea was seen between the uplifted earth and the -surrounding air which has to envelope and enclose the complicated -machine of the earth, and whose mass, standing between the water and -the element of fire, remained much restricted and deprived of its -indispensable moisture; the rivers will be deprived of their waters, -the fruitful earth will put forth no more her light verdure; the -fields will no more be decked with waving corn; all the animals, -finding no fresh grass for pasture, will die and food will then be -lacking to the lions and wolves and other beasts of prey, and to men -who after many efforts will be compelled to abandon their life, and -the human race will die out. In this way the fertile and fruitful -earth will remain deserted, arid and sterile from the water being -shut up in its interior, and from the activity of nature it will -continue a little time to increase until the cold and subtle air -being gone, it will be forced to end with the element of fire; and -then its surface will be left burnt up to cinder and this will be -the end of all terrestrial nature. [Footnote: Compare No. 1339, -written on the same sheet.] - -1219. - -Why did nature not ordain that one animal should not live by the -death of another? Nature, being inconstant and taking pleasure in -creating and making constantly new lives and forms, because she -knows that her terrestrial materials become thereby augmented, is -more ready and more swift in her creating, than time in his -destruction; and so she has ordained that many animals shall be food -for others. Nay, this not satisfying her desire, to the same end she -frequently sends forth certain poisonous and pestilential vapours -upon the vast increase and congregation of animals; and most of all -upon men, who increase vastly because other animals do not feed upon -them; and, the causes being removed, the effects would not follow. -This earth therefore seeks to lose its life, desiring only continual -reproduction; and as, by the argument you bring forward and -demonstrate, like effects always follow like causes, animals are the -image of the world. - -_XX._ - -_Humorous Writings._ - -_Just as Michaelangelo's occasional poems reflect his private life -as well as the general disposition of his mind, we may find in the -writings collected in this section, the transcript of Leonardo's -fanciful nature, and we should probably not be far wrong in -assuming, that he himself had recited these fables in the company of -his friends or at the court festivals of princes and patrons._ Era -tanto piacevole nella conversazione-- _so relates Vasari_--che -tirava a se gli animi delle genti. _And Paulus Jovius says in his -short biography of the artist:_ Fuit ingenio valde comi, nitido, -liberali, vultu autem longe venustissimo, et cum elegantiae omnis -deliciarumque maxime theatralium mirificus inventor ac arbiter -esset, ad lyramque scito caneret, cunctis per omnem aetatem -principibus mire placuit. _There can be no doubt that the fables are -the original offspring of Leonardo's brain, and not borrowed from -any foreign source; indeed the schemes and plans for the composition -of fables collected in division V seem to afford an external proof -of this, if the fables themselves did not render it self-evident. -Several of them-- for instance No._ l279--_are so strikingly -characteristic of Leonardo's views of natural science that we cannot -do them justice till we are acquainted with his theories on such -subjects; and this is equally true of the 'Prophecies'_. - -_I have prefixed to these quaint writings the 'Studies on the life -and habits of animals' which are singular from their peculiar -aphoristic style, and I have transcribed them in exactly the order -in which they are written in MS. H. This is one of the very rare -instances in which one subject is treated in a consecutive series of -notes, all in one MS., and Leonardo has also departed from his -ordinary habits, by occasionally not completing the text on the page -it is begun. These brief notes of a somewhat mysterious bearing have -been placed here, simply because they may possibly have been -intended to serve as hints for fables or allegories. They can -scarcely be regarded as preparatory for a natural history, rather -they would seem to be extracts. On the one hand the names of some of -the animals seem to prove that Leonardo could not here be recording -observations of his own; on the other hand the notes on their habits -and life appear to me to dwell precisely on what must have -interested him most--so far as it is possible to form any complete -estimate of his nature and tastes._ - -_In No._ 1293 _lines_ 1-10, _we have a sketch of a scheme for -grouping the Prophecies. I have not however availed myself of it as -a clue to their arrangement here because, in the first place, the -texts are not so numerous as to render the suggested classification -useful to the reader, and, also, because in reading the long series, -as they occur in the original, we may follow the author's mind; and -here and there it is not difficult to see how one theme suggested -another. I have however regarded Leonardo's scheme for the -classification of the Prophecies as available for that of the Fables -and Jests, and have adhered to it as far as possible._ - -_Among the humourous writings I might perhaps have included the_ -'Rebusses', _of which there are several in the collection of -Leonardo's drawings at Windsor; it seems to me not likely that many -or all of them could be solved at the present day and the MSS. throw -no light on them. Nor should I be justified if I intended to include -in the literary works the well-known caricatures of human faces -attributed to Leonardo-- of which, however, it may be incidentally -observed, the greater number are in my opinion undoubtedly spurious. -Two only have necessarily been given owing to their presence in -text, which it was desired to reproduce: Vol. I page_ 326, _and Pl. -CXXII. It can scarcely be doubted that some satirical intention is -conveyed by the drawing on Pl. LXIV (text No. _688_). - -My reason for not presenting Leonardo to the reader as a poet is the -fact that the maxims and morals in verse which have been ascribed to -him, are not to be found in the manuscripts, and Prof. Uzielli has -already proved that they cannot be by him. Hence it would seem that -only a few short verses can be attributed to him with any -certainty._ - -I. - -STUDIES ON THE LIFE AND HABITS OF ANIMALS. - -1220. - -THE LOVE OF VIRTUE. - -The gold-finch is a bird of which it is related that, when it is -carried into the presence of a sick person, if the sick man is going -to die, the bird turns away its head and never looks at him; but if -the sick man is to be saved the bird never loses sight of him but is -the cause of curing him of all his sickness. - -Like unto this is the love of virtue. It never looks at any vile or -base thing, but rather clings always to pure and virtuous things and -takes up its abode in a noble heart; as the birds do in green woods -on flowery branches. And this Love shows itself more in adversity -than in prosperity; as light does, which shines most where the place -is darkest. - -1221. - -ENVY. - -We read of the kite that, when it sees its young ones growing too -big in the nest, out of envy it pecks their sides, and keeps them -without food. - -CHEERFULNESS. - -Cheerfulness is proper to the cock, which rejoices over every little -thing, and crows with varied and lively movements. - -SADNESS. - -Sadness resembles the raven, which, when it sees its young ones born -white, departs in great grief, and abandons them with doleful -lamentations, and does not feed them until it sees in them some few -black feathers. - -1222. - -PEACE. - -We read of the beaver that when it is pursued, knowing that it is -for the virtue [contained] in its medicinal testicles and not being -able to escape, it stops; and to be at peace with its pursuers, it -bites off its testicles with its sharp teeth, and leaves them to its -enemies. - -RAGE. - -It is said of the bear that when it goes to the haunts of bees to -take their honey, the bees having begun to sting him he leaves the -honey and rushes to revenge himself. And as he seeks to be revenged -on all those that sting him, he is revenged on none; in such wise -that his rage is turned to madness, and he flings himself on the -ground, vainly exasperating, by his hands and feet, the foes against -which he is defending himself. - -1223. - -GRATITUDE. - -The virtue of gratitude is said to be more [developed] in the birds -called hoopoes which, knowing the benefits of life and food, they -have received from their father and their mother, when they see them -grow old, make a nest for them and brood over them and feed them, -and with their beaks pull out their old and shabby feathers; and -then, with a certain herb restore their sight so that they return to -a prosperous state. - -AVARICE. - -The toad feeds on earth and always remains lean; because it never -eats enough:-- it is so afraid lest it should want for earth. - -1224. - -INGRATITUDE. - -Pigeons are a symbol of ingratitude; for when they are old enough no -longer to need to be fed, they begin to fight with their father, and -this struggle does not end until the young one drives the father out -and takes the hen and makes her his own. - -CRUELTY. - -The basilisk is so utterly cruel that when it cannot kill animals by -its baleful gaze, it turns upon herbs and plants, and fixing its -gaze on them withers them up. - -1225. - -GENEROSITY. - -It is said of the eagle that it is never so hungry but that it will -leave a part of its prey for the birds that are round it, which, -being unable to provide their own food, are necessarily dependent on -the eagle, since it is thus that they obtain food. - -DISCIPLINE. - -When the wolf goes cunningly round some stable of cattle, and by -accident puts his foot in a trap, so that he makes a noise, he bites -his foot off to punish himself for his folly. - -1226. - -FLATTERERS OR SYRENS. - -The syren sings so sweetly that she lulls the mariners to sleep; -then she climbs upon the ships and kills the sleeping mariners. - -PRUDENCE. - -The ant, by her natural foresight provides in the summer for the -winter, killing the seeds she harvests that they may not germinate, -and on them, in due time she feeds. - -FOLLY. - -The wild bull having a horror of a red colour, the hunters dress up -the trunk of a tree with red and the bull runs at this with great -frenzy, thus fixing his horns, and forthwith the hunters kill him -there. - -1227. - -JUSTICE. - -We may liken the virtue of Justice to the king of the bees which -orders and arranges every thing with judgment. For some bees are -ordered to go to the flowers, others are ordered to labour, others -to fight with the wasps, others to clear away all dirt, others to -accompagny and escort the king; and when he is old and has no wings -they carry him. And if one of them fails in his duty, he is punished -without reprieve. - -TRUTH. - -Although partridges steal each other's eggs, nevertheless the young -born of these eggs always return to their true mother. - -1228. - -FIDELITY, OR LOYALTY. - -The cranes are so faithful and loyal to their king, that at night, -when he is sleeping, some of them go round the field to keep watch -at a distance; others remain near, each holding a stone in his foot, -so that if sleep should overcome them, this stone would fall and -make so much noise that they would wake up again. And there are -others which sleep together round the king; and this they do every -night, changing in turn so that their king may never find them -wanting. - -FALSEHOOD. - -The fox when it sees a flock of herons or magpies or birds of that -kind, suddenly flings himself on the ground with his mouth open to -look as he were dead; and these birds want to peck at his tongue, -and he bites off their heads. - -1229. - -LIES. - -The mole has very small eyes and it always lives under ground; and -it lives as long as it is in the dark but when it comes into the -light it dies immediately, because it becomes known;--and so it is -with lies. - -VALOUR. - -The lion is never afraid, but rather fights with a bold spirit and -savage onslaught against a multitude of hunters, always seeking to -injure the first that injures him. - -FEAR OR COWARDICE. - -The hare is always frightened; and the leaves that fall from the -trees in autumn always keep him in terror and generally put him to -flight. - -1230. - -MAGNANIMITY. - -The falcon never preys but on large birds; and it will let itself -die rather than feed on little ones, or eat stinking meat. - -VAIN GLORY. - -As regards this vice, we read that the peacock is more guilty of it -than any other animal. For it is always contemplating the beauty of -its tail, which it spreads in the form of a wheel, and by its cries -attracts to itself the gaze of the creatures that surround it. - -And this is the last vice to be conquered. - -1231. - -CONSTANCY. - -Constancy may be symbolised by the phoenix which, knowing that by -nature it must be resuscitated, has the constancy to endure the -burning flames which consume it, and then it rises anew. - -INCONSTANCY. - -The swallow may serve for Inconstancy, for it is always in movement, -since it cannot endure the smallest discomfort. - -CONTINENCE. - -The camel is the most lustful animal there is, and will follow the -female for a thousand miles. But if you keep it constantly with its -mother or sister it will leave them alone, so temperate is its -nature. - -1232. - -INCONTINENCE. - -The unicorn, through its intemperance and not knowing how to control -itself, for the love it bears to fair maidens forgets its ferocity -and wildness; and laying aside all fear it will go up to a seated -damsel and go to sleep in her lap, and thus the hunters take it. - -HUMILITY. - -We see the most striking example of humility in the lamb which will -submit to any animal; and when they are given for food to imprisoned -lions they are as gentle to them as to their own mother, so that -very often it has been seen that the lions forbear to kill them. - -1233. - -PRIDE. - -The falcon, by reason of its haughtiness and pride, is fain to lord -it and rule over all the other birds of prey, and longs to be sole -and supreme; and very often the falcon has been seen to assault the -eagle, the Queen of birds. - -ABSTINENCE. - -The wild ass, when it goes to the well to drink, and finds the water -troubled, is never so thirsty but that it will abstain from -drinking, and wait till the water is clear again. - -GLUTTONY. - -The vulture is so addicted to gluttony that it will go a thousand -miles to eat a carrion [carcase]; therefore is it that it follows -armies. - -1234. - -CHASTITY. - -The turtle-dove is never false to its mate; and if one dies the -other preserves perpetual chastity, and never again sits on a green -bough, nor ever again drinks of clear water. - -UNCHASTITY. - -The bat, owing to unbridled lust, observes no universal rule in -pairing, but males with males and females with females pair -promiscuously, as it may happen. - -MODERATION. - -The ermine out of moderation never eats but once in the day; it will -rather let itself be taken by the hunters than take refuge in a -dirty lair, in order not to stain its purity. - -1235. - -THE EAGLE. - -The eagle when it is old flies so high that it scorches its -feathers, and Nature allowing that it should renew its youth, it -falls into shallow water [Footnote 5: The meaning is obscure.]. And -if its young ones cannot bear to gaze on the sun [Footnote 6: The -meaning is obscure.]--; it does not feed them with any bird, that -does not wish to die. Animals which much fear it do not approach its -nest, although it does not hurt them. It always leaves part of its -prey uneaten. - -LUMERPA,--FAME. - -This is found in Asia Major, and shines so brightly that it absorbs -its own shadow, and when it dies it does not lose this light, and -its feathers never fall out, but a feather pulled out shines no -longer. - -1236. - -THE PELICAN. - -This bird has a great love for its young; and when it finds them in -its nest dead from a serpent's bite, it pierces itself to the heart, -and with its blood it bathes them till they return to life. - -THE SALAMANDER. - -This has no digestive organs, and gets no food but from the fire, in -which it constantly renews its scaly skin. - -The salamander, which renews its scaly skin in the fire,--for -virtue. - -THE CAMELEON. - -This lives on air, and there it is the prey of all the birds; so in -order to be safer it flies above the clouds and finds an air so -rarefied that it cannot support the bird that follows it. - -At that height nothing can go unless it has a gift from Heaven, and -that is where the chameleon flies. - -1237. - -THE ALEPO, A FISH. - -The fish _alepo_ does not live out of water. - -THE OSTRICH. - -This bird converts iron into nourishment, and hatches its eggs by -its gaze;--Armies under commanders. - -THE SWAN. - -The swan is white without any spot, and it sings sweetly as it dies, -its life ending with that song. - -THE STORK. - -This bird, by drinking saltwater purges itself of distempers. If the -male finds his mate unfaithful, he abandons her; and when it grows -old its young ones brood over it, and feed it till it dies. - -1238. - -THE GRASSHOPPER. - -This silences the cuckoo with its song. It dies in oil and revives -in vinegar. It sings in the greatest heats - -THE BAT. - -The more light there is the blinder this creature becomes; as those -who gaze most at the sun become most dazzled.--For Vice, that cannot -remain where Virtue appears. - -THE PARTRIDGE. - -This bird changes from the female into the male and forgets its -former sex; and out of envy it steals the eggs from others and -hatches them, but the young ones follow the true mother. - -THE SWALLOW. - -This bird gives sight to its blind young ones by means of celandine. - -1239. - -THE OYSTER.--FOR TREACHERY. - -This creature, when the moon is full opens itself wide, and when the -crab looks in he throws in a piece of rock or seaweed and the oyster -cannot close again, whereby it serves for food to that crab. This is -what happens to him who opens his mouth to tell his secret. He -becomes the prey of the treacherous hearer. - -THE BASILISK.--CRUELTY. - -All snakes flie from this creature; but the weasel attacks it by -means of rue and kills it. - -THE ASP. - -This carries instantaneous death in its fangs; and, that it may not -hear the charmer it stops its ears with its tail. - -1240. - -THE DRAGON. - -This creature entangles itself in the legs of the elephant which -falls upon it, and so both die, and in its death it is avenged. - -THE VIPER. - -She, in pairing opens her mouth and at last clenches her teeth and -kills her husband. Then the young ones, growing within her body rend -her open and kill their mother. - -THE SCORPION. - -Saliva, spit out when fasting will kill a scorpion. This may be -likened to abstinence from greediness, which removes and heals the -ills which result from that gluttony, and opens the path of virtue. - -1241. - -THE CROCODILE. HYPOCRISY. - -This animal catches a man and straightway kills him; after he is -dead, it weeps for him with a lamentable voice and many tears. Then, -having done lamenting, it cruelly devours him. It is thus with the -hypocrite, who, for the smallest matter, has his face bathed with -tears, but shows the heart of a tiger and rejoices in his heart at -the woes of others, while wearing a pitiful face. - -THE TOAD. - -The toad flies from the light of the sun, and if it is held there by -force it puffs itself out so much as to hide its head below and -shield itself from the rays. Thus does the foe of clear and radiant -virtue, who can only be constrainedly brought to face it with puffed -up courage. - -1242. - -THE CATERPILLAR.--FOR VIRTUE IN GENERAL. - -The caterpillar, which by means of assiduous care is able to weave -round itself a new dwelling place with marvellous artifice and fine -workmanship, comes out of it afterwards with painted and lovely -wings, with which it rises towards Heaven. - -THE SPIDER. - -The spider brings forth out of herself the delicate and ingenious -web, which makes her a return by the prey it takes. - -[Footnote: Two notes are underneath this text. The first: _'nessuna -chosa e da ttemere piu che lla sozza fama'_ is a repetition of the -first line of the text given in Vol. I No. 695. - -The second: _faticha fugga cholla fama in braccio quasi ochultata c_ -is written in red chalk and is evidently an incomplete sentence.] - -1243. - -THE LION. - -This animal, with his thundering roar, rouses his young the third -day after they are born, teaching them the use of all their dormant -senses and all the wild things which are in the wood flee away. - -This may be compared to the children of Virtue who are roused by the -sound of praise and grow up in honourable studies, by which they are -more and more elevated; while all that is base flies at the sound, -shunning those who are virtuous. - -Again, the lion covers over its foot tracks, so that the way it has -gone may not be known to its enemies. Thus it beseems a captain to -conceal the secrets of his mind so that the enemy may not know his -purpose. - -1244. - -THE TARANTULA. - -The bite of the tarantula fixes a man's mind on one idea; that is on -the thing he was thinking of when he was bitten. - -THE SCREECH-OWL AND THE OWL. - -These punish those who are scoffing at them by pecking out their -eyes; for nature has so ordered it, that they may thus be fed. - -1245. - -THE ELEPHANT. - -The huge elephant has by nature what is rarely found in man; that is -Honesty, Prudence, Justice, and the Observance of Religion; inasmuch -as when the moon is new, these beasts go down to the rivers, and -there, solemnly cleansing themselves, they bathe, and so, having -saluted the planet, return to the woods. And when they are ill, -being laid down, they fling up plants towards Heaven as though they -would offer sacrifice. --They bury their tusks when they fall out -from old age.--Of these two tusks they use one to dig up roots for -food; but they save the point of the other for fighting with; when -they are taken by hunters and when worn out by fatigue, they dig up -these buried tusks and ransom themselves. - -1246. - -They are merciful, and know the dangers, and if one finds a man -alone and lost, he kindly puts him back in the road he has missed, -if he finds the footprints of the man before the man himself. It -dreads betrayal, so it stops and blows, pointing it out to the other -elephants who form in a troop and go warily. - -These beasts always go in troops, and the oldest goes in front and -the second in age remains the last, and thus they enclose the troop. -Out of shame they pair only at night and secretly, nor do they then -rejoin the herd but first bathe in the river. The females do not -fight as with other animals; and it is so merciful that it is most -unwilling by nature ever to hurt those weaker than itself. And if it -meets in the middle of its way a flock of sheep - -1247. - -it puts them aside with its trunk, so as not to trample them under -foot; and it never hurts any thing unless when provoked. When one -has fallen into a pit the others fill up the pit with branches, -earth and stones, thus raising the bottom that he may easily get -out. They greatly dread the noise of swine and fly in confusion, -doing no less harm then, with their feet, to their own kind than to -the enemy. They delight in rivers and are always wandering about -near them, though on account of their great weight they cannot swim. -They devour stones, and the trunks of trees are their favourite -food. They have a horror of rats. Flies delight in their smell and -settle on their back, and the beast scrapes its skin making its -folds even and kills them. - -1248. - -When they cross rivers they send their young ones up against the -stream of the water; thus, being set towards the fall, they break -the united current of the water so that the current does not carry -them away. The dragon flings itself under the elephant's body, and -with its tail it ties its legs; with its wings and with its arms it -also clings round its ribs and cuts its throat with its teeth, and -the elephant falls upon it and the dragon is burst. Thus, in its -death it is revenged on its foe. - -THE DRAGON. - -These go in companies together, and they twine themselves after the -manner of roots, and with their heads raised they cross lakes, and -swim to where they find better pasture; and if they did not thus -combine - -1249. - -they would be drowned, therefore they combine. - -THE SERPENT. - -The serpent is a very large animal. When it sees a bird in the air -it draws in its breath so strongly that it draws the birds into its -mouth too. Marcus Regulus, the consul of the Roman army was -attacked, with his army, by such an animal and almost defeated. And -this animal, being killed by a catapult, measured 123 feet, that is -64 1/2 braccia and its head was high above all the trees in a wood. - -THE BOA(?) - -This is a very large snake which entangles itself round the legs of -the cow so that it cannot move and then sucks it, in such wise that -it almost dries it up. In the time of Claudius the Emperor, there -was killed, on the Vatican Hill, - -1250. - -one which had inside it a boy, entire, that it had swallowed. - -THE MACLI.--CAUGHT WHEN ASLEEP. - -This beast is born in Scandinavia. It has the shape of a great -horse, excepting that the great length of its neck and of its ears -make a difference. It feeds on grass, going backwards, for it has so -long an upper lip that if it went forwards it would cover up the -grass. Its legs are all in one piece; for this reason when it wants -to sleep it leans against a tree, and the hunters, spying out the -place where it is wont to sleep, saw the tree almost through, and -then, when it leans against it to sleep, in its sleep it falls, and -thus the hunters take it. And every other mode of taking it is in -vain, because it is incredibly swift in running. - -1251. - -THE BISON WHICH DOES INJURY IN ITS FLIGHT. - -This beast is a native of Paeonia and has a neck with a mane like a -horse. In all its other parts it is like a bull, excepting that its -horns are in a way bent inwards so that it cannot butt; hence it has -no safety but in flight, in which it flings out its excrement to a -distance of 400 braccia in its course, and this burns like fire -wherever it touches. - -LIONS, PARDS, PANTHERS, TIGERS. - -These keep their claws in the sheath, and never put them out unless -they are on the back of their prey or their enemy. - -THE LIONESS. - -When the lioness defends her young from the hand of the hunter, in -order not to be frightened by the spears she keeps her eyes on the -ground, to the end that she may not by her flight leave her young -ones prisoners. - -1252. - -THE LION. - -This animal, which is so terrible, fears nothing more than the noise -of empty carts, and likewise the crowing of cocks. And it is much -terrified at the sight of one, and looks at its comb with a -frightened aspect, and is strangely alarmed when its face is -covered. - -THE PANTHER IN AFRICA. - -This has the form of the lioness but it is taller on its legs and -slimmer and long bodied; and it is all white and marked with black -spots after the manner of rosettes; and all animals delight to look -upon these rosettes, and they would always be standing round it if -it were not for the terror of its face; - -1253. - -therefore knowing this, it hides its face, and the surrounding -animals grow bold and come close, the better to enjoy the sight of -so much beauty; when suddenly it seizes the nearest and at once -devours it. - -CAMELS. - -The Bactrian have two humps; the Arabian one only. They are swift in -battle and most useful to carry burdens. This animal is extremely -observant of rule and measure, for it will not move if it has a -greater weight than it is used to, and if it is taken too far it -does the same, and suddenly stops and so the merchants are obliged -to lodge there. - -1254. - -THE TIGER. - -This beast is a native of Hyrcania, and it is something like the -panther from the various spots on its skin. It is an animal of -terrible swiftness; the hunter when he finds its young ones carries -them off hastily, placing mirrors in the place whence he takes them, -and at once escapes on a swift horse. The panther returning finds -the mirrors fixed on the ground and looking into them believes it -sees its young; then scratching with its paws it discovers the -cheat. Forthwith, by means of the scent of its young, it follows the -hunter, and when this hunter sees the tigress he drops one of the -young ones and she takes it, and having carried it to the den she -immediately returns to the hunter and does - -1255. - -the same till he gets into his boat. - -CATOBLEPAS. - -It is found in Ethiopia near to the source Nigricapo. It is not a -very large animal, is sluggish in all its parts, and its head is so -large that it carries it with difficulty, in such wise that it -always droops towards the ground; otherwise it would be a great pest -to man, for any one on whom it fixes its eyes dies immediately. -[Footnote: Leonardo undoubtedly derived these remarks as to the -Catoblepas from Pliny, Hist. Nat. VIII. 21 (al. 32): _Apud Hesperios -Aethiopas fons est Nigris_ (different readings), _ut plerique -existimavere, Nili caput.-----Juxta hunc fera appellatur catoblepas, -modica alioquin, ceterisque membris iners, caput tantum praegrave -aegre ferens; alias internecio humani generis, omnibus qui oculos -ejus videre, confestim morientibus._ Aelian, _Hist. An._ gives a far -more minute description of the creature, but he says that it poisons -beasts not by its gaze, but by its venomous breath. Athenaeus 221 B, -mentions both. If Leonardo had known of these two passages, he would -scarcely have omitted the poisonous breath. (H. MULLER-STRUBING.)] - -THE BASILISK. - -This is found in the province of Cyrenaica and is not more than 12 -fingers long. It has on its head a white spot after the fashion of a -diadem. It scares all serpents with its whistling. It resembles a -snake, but does not move by wriggling but from the centre forwards -to the right. It is said that one - -1256. - -of these, being killed with a spear by one who was on horse-back, -and its venom flowing on the spear, not only the man but the horse -also died. It spoils the wheat and not only that which it touches, -but where it breathes the grass dries and the stones are split. - -THE WEASEL. - -This beast finding the lair of the basilisk kills it with the smell -of its urine, and this smell, indeed, often kills the weasel itself. - -THE CERASTES. - -This has four movable little horns; so, when it wants to feed, it -hides under leaves all of its body except these little horns which, -as they move, seem to the birds to be some small worms at play. Then -they immediately swoop down to pick them and the Cerastes suddenly -twines round them and encircles and devours them. - -1257. - -THE AMPHISBOENA. - -This has two heads, one in its proper place the other at the tail; -as if one place were not enough from which to fling its venom. - -THE IACULUS. - -This lies on trees, and flings itself down like a dart, and pierces -through the wild beast and kills them. - -THE ASP. - -The bite of this animal cannot be cured unless by immediately -cutting out the bitten part. This pestilential animal has such a -love for its mate that they always go in company. And if, by mishap, -one of them is killed the other, with incredible swiftness, follows -him who has killed it; and it is so determined and eager for -vengeance that it overcomes every difficulty, and passing by every -troop it seeks to hurt none but its enemy. And it will travel any -distance, and it is impossible to avoid it unless by crossing water -and by very swift flight. It has its eyes turned inwards, and large -ears and it hears better than it sees. - -1258. - -THE ICHNEUMON. - -This animal is the mortal enemy of the asp. It is a native of Egypt -and when it sees an asp near its place, it runs at once to the bed -or mud of the Nile and with this makes itself muddy all over, then -it dries itself in the sun, smears itself again with mud, and thus, -drying one after the other, it makes itself three or four coatings -like a coat of mail. Then it attacks the asp, and fights well with -him, so that, taking its time it catches him in the throat and -destroys him. - -THE CROCODILE. - -This is found in the Nile, it has four feet and lives on land and in -water. No other terrestrial creature but this is found to have no -tongue, and it only bites by moving its upper jaw. It grows to a -length of forty feet and has claws and is armed with a hide that -will take any blow. By day it is on land and at night in the water. -It feeds on fishes, and going to sleep on the bank of the Nile with -its mouth open, a bird called - -1259. - -trochilus, a very small bird, runs at once to its mouth and hops -among its teeth and goes pecking out the remains of the food, and so -inciting it with voluptuous delight tempts it to open the whole of -its mouth, and so it sleeps. This being observed by the ichneumon it -flings itself into its mouth and perforates its stomach and bowels, -and finally kills it. - -THE DOLPHIN. - -Nature has given such knowledge to animals, that besides the -consciousness of their own advantages they know the disadvantages of -their foes. Thus the dolphin understands what strength lies in a cut -from the fins placed on his chine, and how tender is the belly of -the crocodile; hence in fighting with him it thrusts at him from -beneath and rips up his belly and so kills him. - -The crocodile is a terror to those that flee, and a base coward to -those that pursue him. - -1260. - -THE HIPPOPOTAMUS. - -This beast when it feels itself over-full goes about seeking thorns, -or where there may be the remains of canes that have been split, and -it rubs against them till a vein is opened; then when the blood has -flowed as much as he needs, he plasters himself with mud and heals -the wound. In form he is something like a horse with long haunches, -a twisted tail and the teeth of a wild boar, his neck has a mane; -the skin cannot be pierced, unless when he is bathing; he feeds on -plants in the fields and goes into them backwards so that it may -seem, as though he had come out. - -THE IBIS. - -This bird resembles a crane, and when it feels itself ill it fills -its craw with water, and with its beak makes an injection of it. - -THE STAG. - -These creatures when they feel themselves bitten by the spider -called father-long-legs, eat crabs and free themselves of the venom. - -1261. - -THE LIZARD. - -This, when fighting with serpents eats the sow-thistle and is free. - -THE SWALLOW. - -This [bird] gives sight to its blind young ones, with the juice of -the celandine. - -THE WEASEL. - -This, when chasing rats first eats of rue. - -THE WILD BOAR. - -This beast cures its sickness by eating of ivy. - -THE SNAKE. - -This creature when it wants to renew itself casts its old skin, -beginning with the head, and changing in one day and one night. - -THE PANTHER. - -This beast after its bowels have fallen out will still fight with -the dogs and hunters. - -1262. - -THE CHAMELEON. - -This creature always takes the colour of the thing on which it is -resting, whence it is often devoured together with the leaves on -which the elephant feeds. - -THE RAVEN. - -When it has killed the Chameleon it takes laurel as a purge. - -1263. - -Moderation checks all the vices. The ermine will die rather than -besmirch itself. - -OF FORESIGHT. - -The cock does not crow till it has thrice flapped its wings; the -parrot in moving among boughs never puts its feet excepting where it -has first put its beak. Vows are not made till Hope is dead. - -Motion tends towards the centre of gravity. - -1264. - -MAGNANIMITY. - -The falcon never seizes any but large birds and will sooner die than -eat [tainted] meat of bad savour. - -II. - -FABLES. - -Fables on animals (1265-1270). - -1265. - -A FABLE. - -An oyster being turned out together with other fish in the house of -a fisherman near the sea, he entreated a rat to take him to the sea. -The rat purposing to eat him bid him open; but as he bit him the -oyster squeezed his head and closed; and the cat came and killed -him. - -1266. - -A FABLE. - -The thrushes rejoiced greatly at seeing a man take the owl and -deprive her of liberty, tying her feet with strong bonds. But this -owl was afterwards by means of bird-lime the cause of the thrushes -losing not only their liberty, but their life. This is said for -those countries which rejoice in seeing their governors lose their -liberty, when by that means they themselves lose all succour, and -remain in bondage in the power of their enemies, losing their -liberty and often their life. - -1267. - -A FABLE. - -A dog, lying asleep on the fur of a sheep, one of his fleas, -perceiving the odour of the greasy wool, judged that this must be a -land of better living, and also more secure from the teeth and nails -of the dog than where he fed on the dog; and without farther -reflection he left the dog and went into the thick wool. There he -began with great labour to try to pass among the roots of the hairs; -but after much sweating had to give up the task as vain, because -these hairs were so close that they almost touched each other, and -there was no space where fleas could taste the skin. Hence, after -much labour and fatigue, he began to wish to return to his dog, who -however had already departed; so he was constrained after long -repentance and bitter tears, to die of hunger. - -1268. - -A FABLE. - -The vain and wandering butterfly, not content with being able to fly -at its ease through the air, overcome by the tempting flame of the -candle, decided to fly into it; but its sportive impulse was the -cause of a sudden fall, for its delicate wings were burnt in the -flame. And the hapless butterfly having dropped, all scorched, at -the foot of the candlestick, after much lamentation and repentance, -dried the tears from its swimming eyes, and raising its face -exclaimed: O false light! how many must thou have miserably deceived -in the past, like me; or if I must indeed see light so near, ought I -not to have known the sun from the false glare of dirty tallow? - -A FABLE. - -The monkey, finding a nest of small birds, went up to it greatly -delighted. But they, being already fledged, he could only succeed in -taking the smallest; greatly delighted he took it in his hand and -went to his abode; and having begun to look at the little bird he -took to kissing it, and from excess of love he kissed it so much and -turned it about and squeezed it till he killed it. This is said for -those who by not punishing their children let them come to mischief. - -1269. - -A FABLE. - -A rat was besieged in his little dwelling by a weasel, which with -unwearied vigilance awaited his surrender, while watching his -imminent peril through a little hole. Meanwhile the cat came by and -suddenly seized the weasel and forthwith devoured it. Then the rat -offered up a sacrifice to Jove of some of his store of nuts, humbly -thanking His providence, and came out of his hole to enjoy his -lately lost liberty. But he was instantly deprived of it, together -with his life, by the cruel claws and teeth of the lurking cat. - -1270. - -A FABLE. - -The ant found a grain of millet. The seed feeling itself taken -prisoner cried out to her: "If you will do me the kindness to allow -me accomplish my function of reproduction, I will give you a hundred -such as I am." And so it was. - -A Spider found a bunch of grapes which for its sweetness was much -resorted to by bees and divers kinds of flies. It seemed to her that -she had found a most convenient spot to spread her snare, and having -settled herself on it with her delicate web, and entered into her -new habitation, there, every day placing herself in the openings -made by the spaces between the grapes, she fell like a thief on the -wretched creatures which were not aware of her. But, after a few -days had passed, the vintager came, and cut away the bunch of grapes -and put it with others, with which it was trodden; and thus the -grapes were a snare and pitfall both for the treacherous spider and -the betrayed flies. - -An ass having gone to sleep on the ice over a deep lake, his heat -dissolved the ice and the ass awoke under water to his great grief, -and was forthwith drowned. - -A falcon, unable to endure with patience the disappearance of a -duck, which, flying before him had plunged under water, wished to -follow it under water, and having soaked his feathers had to remain -in the water while the duck rising to the air mocked at the falcon -as he drowned. - -The spider wishing to take flies in her treacherous net, was cruelly -killed in it by the hornet. - -An eagle wanting to mock at the owl was caught by the wings in -bird-lime and was taken and killed by a man. - -Fables on lifeless objects (1271--1274). - -1271. - -The water finding that its element was the lordly ocean, was seized -with a desire to rise above the air, and being encouraged by the -element of fire and rising as a very subtle vapour, it seemed as -though it were really as thin as air. But having risen very high, it -reached the air that was still more rare and cold, where the fire -forsook it, and the minute particles, being brought together, united -and became heavy; whence its haughtiness deserting it, it betook -itself to flight and it fell from the sky, and was drunk up by the -dry earth, where, being imprisoned for a long time, it did penance -for its sin. - -1272. - -A FABLE. - -The razor having one day come forth from the handle which serves as -its sheath and having placed himself in the sun, saw the sun -reflected in his body, which filled him with great pride. And -turning it over in his thoughts he began to say to himself: "And -shall I return again to that shop from which I have just come? -Certainly not; such splendid beauty shall not, please God, be turned -to such base uses. What folly it would be that could lead me to -shave the lathered beards of rustic peasants and perform such menial -service! Is this body destined for such work? Certainly not. I will -hide myself in some retired spot and there pass my life in tranquil -repose." And having thus remained hidden for some months, one day he -came out into the air, and issuing from his sheath, saw himself -turned to the similitude of a rusty saw while his surface no longer -reflected the resplendent sun. With useless repentance he vainly -deplored the irreparable mischief saying to himself: "Oh! how far -better was it to employ at the barbers my lost edge of such -exquisite keenness! Where is that lustrous surface? It has been -consumed by this vexatious and unsightly rust." - -The same thing happens to those minds which instead of exercise give -themselves up to sloth. They are like the razor here spoken of, and -lose the keenness of their edge, while the rust of ignorance spoils -their form. - -A FABLE. - -A stone of some size recently uncovered by the water lay on a -certain spot somewhat raised, and just where a delightful grove -ended by a stony road; here it was surrounded by plants decorated by -various flowers of divers colours. And as it saw the great quantity -of stones collected together in the roadway below, it began to wish -it could let itself fall down there, saying to itself: "What have I -to do here with these plants? I want to live in the company of -those, my sisters." And letting itself fall, its rapid course ended -among these longed for companions. When it had been there sometime -it began to find itself constantly toiling under the wheels of the -carts the iron-shoed feet of horses and of travellers. This one -rolled it over, that one trod upon it; sometimes it lifted itself a -little and then it was covered with mud or the dung of some animal, -and it was in vain that it looked at the spot whence it had come as -a place of solitude and tranquil place. - -Thus it happens to those who choose to leave a life of solitary -comtemplation, and come to live in cities among people full of -infinite evil. - -1273. - -Some flames had already lasted in the furnace of a glass-blower, -when they saw a candle approaching in a beautiful and glittering -candlestick. With ardent longing they strove to reach it; and one of -them, quitting its natural course, writhed up to an unburnt brand on -which it fed and passed at the opposite end out by a narrow chink to -the candle which was near. It flung itself upon it, and with fierce -jealousy and greediness it devoured it, having reduced it almost to -death, and, wishing to procure the prolongation of its life, it -tried to return to the furnace whence it had come. But in vain, for -it was compelled to die, the wood perishing together with the -candle, being at last converted, with lamentation and repentance, -into foul smoke, while leaving all its sisters in brilliant and -enduring life and beauty. - -1274. - -A small patch of snow finding itself clinging to the top of a rock -which was lying on the topmost height of a very high mountain and -being left to its own imaginings, it began to reflect in this way, -saying to itself: "Now, shall not I be thought vain and proud for -having placed myself--such a small patch of snow--in so lofty a -spot, and for allowing that so large a quantity of snow as I have -seen here around me, should take a place lower than mine? Certainly -my small dimensions by no means merit this elevation. How easily may -I, in proof of my insignificance, experience the same fate as that -which the sun brought about yesterday to my companions, who were -all, in a few hours, destroyed by the sun. And this happened from -their having placed themselves higher than became them. I will flee -from the wrath of the sun, and humble myself and find a place -befitting my small importance." Thus, flinging itself down, it began -to descend, hurrying from its high home on to the other snow; but -the more it sought a low place the more its bulk increased, so that -when at last its course was ended on a hill, it found itself no less -in size than the hill which supported it; and it was the last of the -snow which was destroyed that summer by the sun. This is said for -those who, humbling themselves, become exalted. - -Fables on plants (1275-1279). - -1275. - -The cedar, being desirous of producing a fine and noble fruit at its -summit, set to work to form it with all the strength of its sap. But -this fruit, when grown, was the cause of the tall and upright -tree-top being bent over. - -The peach, being envious of the vast quantity of fruit which she saw -borne on the nut-tree, her neighbour, determined to do the same, and -loaded herself with her own in such a way that the weight of the -fruit pulled her up by the roots and broke her down to the ground. - -The nut-tree stood always by a road side displaying the wealth of -its fruit to the passers by, and every one cast stones at it. - -The fig-tree, having no fruit, no one looked at it; then, wishing to -produce fruits that it might be praised by men, it was bent and -broken down by them. - -The fig-tree, standing by the side of the elm and seeing that its -boughs were bare of fruit, yet that it had the audacity to keep the -Sun from its own unripe figs with its branches, said to it: "Oh elm! -art thou not ashamed to stand in front of me. But wait till my -offspring are fully grown and you will see where you are!" But when -her offspring were mature, a troop of soldiers coming by fell upon -the fig-tree and her figs were all torn off her, and her boughs cut -away and broken. Then, when she was thus maimed in all her limbs, -the elm asked her, saying: "O fig-tree! which was best, to be -without offspring, or to be brought by them into so miserable a -plight!" - -1276. - -The plant complains of the old and dry stick which stands by its -side and of the dry stakes that surround it. - -One keeps it upright, the other keeps it from low company. - -1277. - -A FABLE. - -A nut, having been carried by a crow to the top of a tall campanile -and released by falling into a chink from the mortal grip of its -beak, it prayed the wall by the grace bestowed on it by God in -allowing it to be so high and thick, and to own such fine bells and -of so noble a tone, that it would succour it, and that, as it had -not been able to fall under the verdurous boughs of its venerable -father and lie in the fat earth covered up by his fallen leaves it -would not abandon it; because, finding itself in the beak of the -cruel crow, it had there made a vow that if it escaped from her it -would end its life in a little hole. At these words the wall, moved -to compassion, was content to shelter it in the spot where it had -fallen; and after a short time the nut began to split open and put -forth roots between the rifts of the stones and push them apart, and -to throw out shoots from its hollow shell; and, to be brief, these -rose above the building and the twisted roots, growing thicker, -began to thrust the walls apart, and tear out the ancient stones -from their old places. Then the wall too late and in vain bewailed -the cause of its destruction and in a short time, it wrought the -ruin of a great part of it. - -1278. - -A FABLE. - -The privet feeling its tender boughs loaded with young fruit, -pricked by the sharp claws and beak of the insolent blackbird, -complained to the blackbird with pitious remonstrance entreating her -that since she stole its delicious fruits she should not deprive it -of the leaves with which it preserved them from the burning rays of -the sun, and that she should not divest it of its tender bark by -scratching it with her sharp claws. To which the blackbird replied -with angry upbraiding: "O, be silent, uncultured shrub! Do you not -know that Nature made you produce these fruits for my nourishment; -do you not see that you are in the world [only] to serve me as food; -do you not know, base creature, that next winter you will be food -and prey for the Fire?" To which words the tree listened patiently, -and not without tears. After a short time the blackbird was taken in -a net and boughs were cut to make a cage, in which to imprison her. -Branches were cut, among others from the pliant privet, to serve for -the small rods of the cage; and seeing herself to be the cause of -the Blackbird's loss of liberty it rejoiced and spoke as follows: "O -Blackbird, I am here, and not yet burnt by fire as you said. I shall -see you in prison before you see me burnt." - -A FABLE. - -The laurel and the myrtle seeing the pear tree cut down cried out -with a loud voice: "O pear-tree! whither are you going? Where is the -pride you had when you were covered with ripe fruits? Now you will -no longer shade us with your mass of leaves." Then the pear-tree -replied: "I am going with the husbandman who has cut me down and who -will take me to the workshop of a good sculptor who by his art will -make me take the form of Jove the god; and I shall be dedicated in a -temple and adored by men in the place of Jove, while you are bound -always to remain maimed and stripped of your boughs, which will be -placed round me to do me honour. - -A FABLE. - -The chesnut, seeing a man upon the fig-tree, bending its boughs down -and pulling off the ripe fruits, which he put into his open mouth -destroying and crushing them with his hard teeth, it tossed its long -boughs and with a noisy rustle exclaimed: "O fig! how much less are -you protected by nature than I. See how in me my sweet offspring are -set in close array; first clothed in soft wrappers over which is the -hard but softly lined husk; and not content with taking this care of -me, and having given them so strong a shelter, on this she has -placed sharp and close-set spines so that the hand of man cannot -hurt me." Then the fig-tree and her offspring began to laugh and -having laughed she said: "I know man to be of such ingenuity that -with rods and stones and stakes flung up among your branches he will -bereave you of your fruits; and when they are fallen, he will -trample them with his feet or with stones, so that your offspring -will come out of their armour, crushed and maimed; while I am -touched carefully by their hands, and not like you with sticks and -stones." - -1279. - -The hapless willow, finding that she could not enjoy the pleasure of -seeing her slender branches grow or attain to the height she wished, -or point to the sky, by reason of the vine and whatever other trees -that grew near, but was always maimed and lopped and spoiled, -brought all her spirits together and gave and devoted itself -entirely to imagination, standing plunged in long meditation and -seeking, in all the world of plants, with which of them she might -ally herself and which could not need the help of her withes. Having -stood for some time in this prolific imagination, with a sudden -flash the gourd presented itself to her thoughts and tossing all her -branches with extreme delight, it seemed to her that she had found -the companion suited to her purpose, because the gourd is more apt -to bind others than to need binding; having come to this conclusion -she awaited eagerly some friendly bird who should be the mediator of -her wishes. Presently seeing near her the magpie she said to him: "O -gentle bird! by the memory of the refuge which you found this -morning among my branches, when the hungry cruel, and rapacious -falcon wanted to devour you, and by that repose which you have -always found in me when your wings craved rest, and by the pleasure -you have enjoyed among my boughs, when playing with your companions -or making love--I entreat you find the gourd and obtain from her -some of her seeds, and tell her that those that are born of them I -will treat exactly as though they were my own flesh and blood; and -in this way use all the words you can think of, which are of the -same persuasive purport; though, indeed, since you are a master of -language, I need not teach you. And if you will do me this service I -shall be happy to have your nest in the fork of my boughs, and all -your family without payment of any rent." Then the magpie, having -made and confirmed certain new stipulations with the willow,--and -principally that she should never admit upon her any snake or -polecat, cocked his tail, and put down his head, and flung himself -from the bough, throwing his weight upon his wings; and these, -beating the fleeting air, now here, now there, bearing about -inquisitively, while his tail served as a rudder to steer him, he -came to a gourd; then with a handsome bow and a few polite words, he -obtained the required seeds, and carried them to the willow, who -received him with a cheerful face. And when he had scraped away with -his foot a small quantity of the earth near the willow, describing a -circle, with his beak he planted the grains, which in a short time -began to grow, and by their growth and the branches to take up all -the boughs of the willow, while their broad leaves deprived it of -the beauty of the sun and sky. And not content with so much evil, -the gourds next began, by their rude hold, to drag the ends of the -tender shoots down towards the earth, with strange twisting and -distortion. - -Then, being much annoyed, it shook itself in vain to throw off the -gourd. After raving for some days in such plans vainly, because the -firm union forbade it, seeing the wind come by it commended itself -to him. The wind flew hard and opened the old and hollow stem of the -willow in two down to the roots, so that it fell into two parts. In -vain did it bewail itself recognising that it was born to no good -end. - -III. - -JESTS AND TALES. - -1280. - -A JEST. - -A priest, making the rounds of his parish on Easter Eve, and -sprinkling holy water in the houses as is customary, came to a -painter's room, where he sprinkled the water on some of his -pictures. The painter turned round, somewhat angered, and asked him -why this sprinkling had been bestowed on his pictures; then said the -priest, that it was the custom and his duty to do so, and that he -was doing good; and that he who did good might look for good in -return, and, indeed, for better, since God had promised that every -good deed that was done on earth should be rewarded a hundred-fold -from above. Then the painter, waiting till he went out, went to an -upper window and flung a large pail of water on the priest's back, -saying: "Here is the reward a hundred-fold from above, which you -said would come from the good you had done me with your holy water, -by which you have damaged my pictures." - -1281. - -When wine is drunk by a drunkard, that wine is revenged on the -drinker. - -1282. - -Wine, the divine juice of the grape, finding itself in a golden and -richly wrought cup, on the table of Mahomet, was puffed up with -pride at so much honour; when suddenly it was struck by a contrary -reflection, saying to itself: "What am I about, that I should -rejoice, and not perceive that I am now near to my death and shall -leave my golden abode in this cup to enter into the foul and fetid -caverns of the human body, and to be transmuted from a fragrant and -delicious liquor into a foul and base one. Nay, and as though so -much evil as this were not enough, I must for a long time lie in -hideous receptacles, together with other fetid and corrupt matter, -cast out from human intestines." And it cried to Heaven, imploring -vengeance for so much insult, and that an end might henceforth be -put to such contempt; and that, since that country produced the -finest and best grapes in the whole world, at least they should not -be turned into wine. Then Jove made that wine drunk by Mahomet to -rise in spirit to his brain; and that in so deleterious a manner -that it made him mad, and gave birth to so many follies that when he -had recovered himself, he made a law that no Asiatic should drink -wine, and henceforth the vine and its fruit were left free. - -As soon as wine has entered the stomach it begins to ferment and -swell; then the spirit of that man begins to abandon his body, -rising as it were skywards, and the brain finds itself parting from -the body. Then it begins to degrade him, and make him rave like a -madman, and then he does irreparable evil, killing his friends. - -1283. - -An artizan often going to visit a great gentleman without any -definite purpose, the gentleman asked him what he did this for. The -other said that he came there to have a pleasure which his lordship -could not have; since to him it was a satisfaction to see men -greater than himself, as is the way with the populace; while the -gentleman could only see men of less consequence than himself; and -so lords and great men were deprived of that pleasure. - -1284. - -Franciscan begging Friars are wont, at certain times, to keep fasts, -when they do not eat meat in their convents. But on journeys, as -they live on charity, they have license to eat whatever is set -before them. Now a couple of these friars on their travels, stopped -at an inn, in company with a certain merchant, and sat down with him -at the same table, where, from the poverty of the inn, nothing was -served to them but a small roast chicken. The merchant, seeing this -to be but little even for himself, turned to the friars and said: -"If my memory serves me, you do not eat any kind of flesh in your -convents at this season." At these words the friars were compelled -by their rule to admit, without cavil, that this was the truth; so -the merchant had his wish, and eat the chicken and the friars did -the best they could. After dinner the messmates departed, all three -together, and after travelling some distance they came to a river of -some width and depth. All three being on foot--the friars by reason -of their poverty, and the other from avarice--it was necessary by -the custom of company that one of the friars, being barefoot, should -carry the merchant on his shoulders: so having given his wooden -shoes into his keeping, he took up his man. But it so happened that -when the friar had got to the middle of the river, he again -remembered a rule of his order, and stopping short, he looked up, -like Saint Christopher, to the burden on his back and said: "Tell -me, have you any money about you?"--"You know I have", answered the -other, "How do you suppose that a Merchant like me should go about -otherwise?" "Alack!" cried the friar, "our rules forbid as to carry -any money on our persons," and forthwith he dropped him into the -water, which the merchant perceived was a facetious way of being -revenged on the indignity he had done them; so, with a smiling face, -and blushing somewhat with shame, he peaceably endured the revenge. - -1285. - -A JEST. - -A man wishing to prove, by the authority of Pythagoras, that he had -formerly been in the world, while another would not let him finish -his argument, the first speaker said to the second: "It is by this -token that I was formerly here, I remember that you were a miller." -The other one, feeling himself stung by these words, agreed that it -was true, and that by the same token he remembered that the speaker -had been the ass that carried the flour. - -A JEST. - -It was asked of a painter why, since he made such beautiful figures, -which were but dead things, his children were so ugly; to which the -painter replied that he made his pictures by day, and his children -by night. - -1286. - -A man saw a large sword which another one wore at his side. Said he -"Poor fellow, for a long time I have seen you tied to that weapon; -why do you not release yourself as your hands are untied, and set -yourself free?" To which the other replied: "This is none of yours, -on the contrary it is an old story." The former speaker, feeling -stung, replied: "I know that you are acquainted with so few things -in this world, that I thought anything I could tell you would be new -to you." - -1287. - -A man gave up his intimacy with one of his friends because he often -spoke ill of his other friends. The neglected friend one day -lamenting to this former friend, after much complaining, entreated -him to say what might be the cause that had made him forget so much -friendship. To which he answered: "I will no longer be intimate with -you because I love you, and I do not choose that you, by speaking -ill of me, your friend, to others, should produce in others, as in -me, a bad impression of yourself, by speaking evil to them of me, -your friend. Therefore, being no longer intimate together, it will -seem as though we had become enemies; and in speaking evil of me, as -is your wont, you will not be blamed so much as if we continued -intimate. - -1288. - -A man was arguing and boasting that he knew many and various tricks. -Another among the bystanders said: "I know how to play a trick which -will make whomsoever I like pull off his breeches." The first man-- -the boaster--said: "You won't make me pull off mine, and I bet you a -pair of hose on it." He who proposed the game, having accepted the -offer, produced breeches and drew them across the face of him who -bet the pair of hose and won the bet [4]. - -A man said to an acquaintance: "Your eyes are changed to a strange -colour." The other replied: "It often happens, but you have not -noticed it." "When does it happen?" said the former. "Every time -that my eyes see your ugly face, from the shock of so unpleasing a -sight they suddenly turn pale and change to a strange colour." - -A man said to another: "Your eyes are changed to a strange colour." -The other replied: "It is because my eyes behold your strange ugly -face." - -A man said that in his country were the strangest things in the -world. Another answered: "You, who were born there, confirm this as -true, by the strangeness of your ugly face." - -[Footnote: The joke turns, it appears, on two meanings of trarre and -is not easily translated.] - -1289. - -An old man was publicly casting contempt on a young one, and boldly -showing that he did not fear him; on which the young man replied -that his advanced age served him better as a shield than either his -tongue or his strength. - -1290. - -A JEST. - -A sick man finding himself in _articulo mortis_ heard a knock at the -door, and asking one of his servants who was knocking, the servant -went out, and answered that it was a woman calling herself Madonna -Bona. Then the sick man lifting his arms to Heaven thanked God with -a loud voice, and told the servants that they were to let her come -in at once, so that he might see one good woman before he died, -since in all his life he had never yet seen one. - -1291. - -A JEST. - -A man was desired to rise from bed, because the sun was already -risen. To which he replied: "If I had as far to go, and as much to -do as he has, I should be risen by now; but having but a little way -to go, I shall not rise yet." - -1292. - -A man, seeing a woman ready to hold up the target for a jousting -match, exclaimed, looking at the shield, and considering his spear: -"Alack! this is too small a workman for so great a business." - -IV. - -PROPHECIES. - -1293. - -THE DIVISION OF THE PROPHECIES. - -First, of things relating to animals; secondly, of irrational -creatures; thirdly of plants; fourthly, of ceremonies; fifthly, of -manners; sixthly, of cases or edicts or quarrels; seventhly, of -cases that are impossible in nature [paradoxes], as, for instance, -of those things which, the more is taken from them, the more they -grow. And reserve the great matters till the end, and the small -matters give at the beginning. And first show the evils and then the -punishment of philosophical things. - -(Of Ants.) - -These creatures will form many communities, which will hide -themselves and their young ones and victuals in dark caverns, and -they will feed themselves and their families in dark places for many -months without any light, artificial or natural. - -[Footnote: Lines 1--5l are in the original written in one column, -beginning with the text of line 11. At the end of the column is the -programme for the arrangement of the prophecies, placed here at the -head: Lines 56--79 form a second column, lines 80--97 a third one -(see the reproduction of the text on the facsimile PI. CXVIII). - -Another suggestion for the arrangement of the prophecies is to be -found among the notes 55--57 on page 357.] - -(Of Bees.) - -And many others will be deprived of their store and their food, and -will be cruelly submerged and drowned by folks devoid of reason. Oh -Justice of God! Why dost thou not wake and behold thy creatures thus -ill used? - -(Of Sheep, Cows, Goats and the like.) - -Endless multitudes of these will have their little children taken -from them ripped open and flayed and most barbarously quartered. - -(Of Nuts, and Olives, and Acorns, and Chesnuts, and such like.) - -Many offspring shall be snatched by cruel thrashing from the very -arms of their mothers, and flung on the ground, and crushed. - -(Of Children bound in Bundles.) - -O cities of the Sea! In you I see your citizens--both females and -males--tightly bound, arms and legs, with strong withes by folks who -will not understand your language. And you will only be able to -assuage your sorrows and lost liberty by means of tearful complaints -and sighing and lamentation among yourselves; for those who will -bind you will not understand you, nor will you understand them. - -(Of Cats that eat Rats.) - -In you, O cities of Africa your children will be seen quartered in -their own houses by most cruel and rapacious beasts of your own -country. - -(Of Asses that are beaten.) - -[Footnote 48: Compare No. 845.] O Nature! Wherefore art thou so -partial; being to some of thy children a tender and benign mother, -and to others a most cruel and pitiless stepmother? I see children -of thine given up to slavery to others, without any sort of -advantage, and instead of remuneration for the good they do, they -are paid with the severest suffering, and spend their whole life in -benefitting those who ill treat them. - -(Of Men who sleep on boards of Trees.) - -Men shall sleep, and eat, and dwell among trees, in the forests and -open country. - -(Of Dreaming.) - -Men will seem to see new destructions in the sky. The flames that -fall from it will seem to rise in it and to fly from it with terror. -They will hear every kind of animals speak in human language. They -will instantaneously run in person in various parts of the world, -without motion. They will see the greatest splendour in the midst of -darkness. O! marvel of the human race! What madness has led you -thus! You will speak with animals of every species and they with you -in human speech. You will see yourself fall from great heights -without any harm and torrents will accompany you, and will mingle -with their rapid course. - -(Of Christians.) - -Many who hold the faith of the Son only build temples in the name of -the Mother. - -(Of Food which has been alive.) - -[84] A great portion of bodies that have been alive will pass into -the bodies of other animals; which is as much as to say, that the -deserted tenements will pass piecemeal into the inhabited ones, -furnishing them with good things, and carrying with them their -evils. That is to say the life of man is formed from things eaten, -and these carry with them that part of man which dies . . . - -1294. - -(Of Funeral Rites, and Processions, and Lights, and Bells, and -Followers.) - -The greatest honours will be paid to men, and much pomp, without -their knowledge. - -[Footnote: A facsimile of this text is on PI. CXVI below on the -right, but the writing is larger than the other notes on the same -sheet and of a somewhat different style. The ink is also of a -different hue, as may be seen on the original sheet at Milan.] - -1295. - -(Of the Avaricious.) - -There will be many who will eagerly and with great care and -solicitude follow up a thing, which, if they only knew its -malignity, would always terrify them. - -(Of those men, who, the older they grow, the more avaricious they -become, whereas, having but little time to stay, they should become -more liberal.) - -We see those who are regarded as being most experienced and -judicious, when they least need a thing, seek and cherish it with -most avidity. - -(Of the Ditch.) - -Many will be busied in taking away from a thing, which will grow in -proportion as it is diminished. - -(Of a Weight placed on a Feather-pillow.) - -And it will be seen in many bodies that by raising the head they -swell visibly; and by laying the raised head down again, their size -will immediately be diminished. - -(Of catching Lice.) - -And many will be hunters of animals, which, the fewer there are the -more will be taken; and conversely, the more there are, the fewer -will be taken. - -(Of Drawing Water in two Buckets with a single Rope.) - -And many will be busily occupied, though the more of the thing they -draw up, the more will escape at the other end. - -(Of the Tongues of Pigs and Calves in Sausage-skins.) - -Oh! how foul a thing, that we should see the tongue of one animal in -the guts of another. - -(Of Sieves made of the Hair of Animals.) - -We shall see the food of animals pass through their skin everyway -excepting through their mouths, and penetrate from the outside -downwards to the ground. - -(Of Lanterns.) - -[Footnote 35: Lanterns were in Italy formerly made of horn.] The -cruel horns of powerful bulls will screen the lights of night -against the wild fury of the winds. - -(Of Feather-beds.) - -Flying creatures will give their very feathers to support men. - -(Of Animals which walk on Trees--wearing wooden Shoes.) - -The mire will be so great that men will walk on the trees of their -country. - -(Of the Soles of Shoes, which are made from the Ox.) - -And in many parts of the country men will be seen walking on the -skins of large beasts. - -(Of Sailing in Ships.) - -There will be great winds by reason of which things of the East will -become things of the West; and those of the South, being involved in -the course of the winds, will follow them to distant lands. - -(Of Worshipping the Pictures of Saints.) - -Men will speak to men who hear not; having their eyes open, they -will not see; they will speak to these, and they will not be -answered. They will implore favours of those who have ears and hear -not; they will make light for the blind. - -(Of Sawyers.) - -There will be many men who will move one against another, holding in -their hands a cutting tool. But these will not do each other any -injury beyond tiring each other; for, when one pushes forward the -other will draw back. But woe to him who comes between them! For he -will end by being cut in pieces. - -(Of Silk-spinning.) - -Dismal cries will be heard loud, shrieking with anguish, and the -hoarse and smothered tones of those who will be despoiled, and at -last left naked and motionless; and this by reason of the mover, -which makes every thing turn round. - -(Of putting Bread into the Mouth of the Oven and taking it out -again.) - -In every city, land, castle and house, men shall be seen, who for -want of food will take it out of the mouths of others, who will not -be able to resist in any way. - -(Of tilled Land.) - -The Earth will be seen turned up side down and facing the opposite -hemispheres, uncovering the lurking holes of the fiercest animals. - -(Of Sowing Seed.) - -Then many of the men who will remain alive, will throw the victuals -they have preserved out of their houses, a free prey to the birds -and beasts of the earth, without taking any care of them at all. - -(Of the Rains, which, by making the Rivers muddy, wash away the -Land.) - -[Footnote 81: Compare No. 945.] Something will fall from the sky -which will transport a large part of Africa which lies under that -sky towards Europe, and that of Europe towards Africa, and that of -the Scythian countries will meet with tremendous revolutions -[Footnote 84: Compare No. 945.]. - -(Of Wood that burns.) - -The trees and shrubs in the great forests will be converted into -cinder. - -(Of Kilns for Bricks and Lime.) - -Finally the earth will turn red from a conflagration of many days -and the stones will be turned to cinders. - -(Of boiled Fish.) - -The natives of the waters will die in the boiling flood. - -(Of the Olives which fall from the Olive trees, shedding oil which -makes light.) - -And things will fall with great force from above, which will give us -nourishment and light. - -(Of Owls and screech owls and what will happen to certain birds.) - -Many will perish of dashing their heads in pieces, and the eyes of -many will jump out of their heads by reason of fearful creatures -come out of the darkness. - -(Of flax which works the cure of men.) - -That which was at first bound, cast out and rent by many and various -beaters will be respected and honoured, and its precepts will be -listened to with reverence and love. - -(Of Books which teach Precepts.) - -Bodies without souls will, by their contents give us precepts by -which to die well. - -(Of Flagellants.) - -Men will hide themselves under the bark of trees, and, screaming, -they will make themselves martyrs, by striking their own limbs. - -(Of the Handles of Knives made of the Horns of Sheep.) - -We shall see the horns of certain beasts fitted to iron tools, which -will take the lives of many of their kind. - -(Of Night when no Colour can be discerned.) - -There will come a time when no difference can be discerned between -colours, on the contrary, everything will be black alike. - -(Of Swords and Spears which by themselves never hurt any one.) - -One who by himself is mild enough and void of all offence will -become terrible and fierce by being in bad company, and will most -cruelly take the life of many men, and would kill many more if they -were not hindered by bodies having no soul, that have come out of -caverns--that is, breastplates of iron. - -(Of Snares and Traps.) - -Many dead things will move furiously, and will take and bind the -living, and will ensnare them for the enemies who seek their death -and destruction. - -(Of Metals.) - -That shall be brought forth out of dark and obscure caves, which -will put the whole human race in great anxiety, peril and death. To -many that seek them, after many sorrows they will give delight, and -to those who are not in their company, death with want and -misfortune. This will lead to the commission of endless crimes; this -will increase and persuade bad men to assassinations, robberies and -treachery, and by reason of it each will be suspicious of his -partner. This will deprive free cities of their happy condition; -this will take away the lives of many; this will make men torment -each other with many artifices deceptions and treasons. O monstrous -creature! How much better would it be for men that every thing -should return to Hell! For this the vast forests will be devastated -of their trees; for this endless animals will lose their lives. - -(Of Fire.) - -One shall be born from small beginnings which will rapidly become -vast. This will respect no created thing, rather will it, by its -power, transform almost every thing from its own nature into -another. - -(Of Ships which sink.) - -Huge bodies will be seen, devoid of life, carrying, in fierce haste, -a multitude of men to the destruction of their lives. - -(Of Oxen, which are eaten.) - -The masters of estates will eat their own labourers. - -(Of beating Beds to renew them.) - -Men will be seen so deeply ungrateful that they will turn upon that -which has harboured them, for nothing at all; they will so load it -with blows that a great part of its inside will come out of its -place, and will be turned over and over in its body. - -(Of Things which are eaten and which first are killed.) - -Those who nourish them will be killed by them and afflicted by -merciless deaths. - -(Of the Reflection of Walls of Cities in the Water of their -Ditches.) - -The high walls of great cities will be seen up side down in their -ditches. - -(Of Water, which flows turbid and mixed with Soil and Dust; and of -Mist, which is mixed with the Air; and of Fire which is mixed with -its own, and each with each.) - -All the elements will be seen mixed together in a great whirling -mass, now borne towards the centre of the world, now towards the -sky; and now furiously rushing from the South towards the frozen -North, and sometimes from the East towards the West, and then again -from this hemisphere to the other. - -(The World may be divided into two Hemispheres at any Point.) - -All men will suddenly be transferred into opposite hemispheres. - -(The division of the East from the West may be made at any point.) - -All living creatures will be moved from the East to the West; and in -the same way from North to South, and vice versa. - -(Of the Motion of Water which carries wood, which is dead.) - -Bodies devoid of life will move by themselves and carry with them -endless generations of the dead, taking the wealth from the -bystanders. - -(Of Eggs which being eaten cannot form Chickens.) - -Oh! how many will they be that never come to the birth! - -(Of Fishes which are eaten unborn.) - -Endless generations will be lost by the death of the pregnant. - -(Of the Lamentation on Good Friday.) - -Throughout Europe there will be a lamentation of great nations over -the death of one man who died in the East. - -(Of Dreaming.) - -Men will walk and not stir, they will talk to those who are not -present, and hear those who do not speak. - -(Of a Man's Shadow which moves with him.) - -Shapes and figures of men and animals will be seen following these -animals and men wherever they flee. And exactly as the one moves the -other moves; but what seems so wonderful is the variety of height -they assume. - -(Of our Shadow cast by the Sun, and our Reflection in the Water at -one and the same time.) - -Many a time will one man be seen as three and all three move -together, and often the most real one quits him. - -(Of wooden Chests which contain great Treasures.) - -Within walnuts and trees and other plants vast treasures will be -found, which lie hidden there and well guarded. - -(Of putting out the Light when going to Bed.) - -Many persons puffing out a breath with too much haste, will thereby -lose their sight, and soon after all consciousness. - -(Of the Bells of Mules, which are close to their Ears.) - -In many parts of Europe instruments of various sizes will be heard -making divers harmonies, with great labour to those who hear them -most closely. - -(Of Asses.) - -The severest labour will be repaid with hunger and thirst, and -discomfort, and blows, and goadings, and curses, and great abuse. - -(Of Soldiers on horseback.) - -Many men will be seen carried by large animals, swift of pace, to -the loss of their lives and immediate death. - -In the air and on earth animals will be seen of divers colours -furiously carrying men to the destruction of their lives. - -(Of the Stars of Spurs.) - -By the aid of the stars men will be seen who will be as swift as any -swift animal. - -(Of a Stick, which is dead.) - -The motions of a dead thing will make many living ones flee with -pain and lamentation and cries. - -(Of Tinder.) - -With a stone and with iron things will be made visible which before -were not seen. - -1296. - -(Of going in Ships.) - -We shall see the trees of the great forests of Taurus and of Sinai -and of the Appenines and others, rush by means of the air, from East -to West and from North to South; and carry, by means of the air, -great multitudes of men. Oh! how many vows! Oh! how many deaths! Oh! -how many partings of friends and relations! Oh! how many will those -be who will never again see their own country nor their native land, -and who will die unburied, with their bones strewn in various parts -of the world! - -(Of moving on All Saints' Day.) - -Many will forsake their own dwellings and carry with them all their -belongings and will go to live in other parts. - -(Of All Souls' Day.) - -How many will they be who will bewail their deceased forefathers, -carrying lights to them. - -(Of Friars, who spending nothing but words, receive great gifts and -bestow Paradise.) - -Invisible money will procure the triumph of many who will spend it. - -(Of Bows made of the Horns of Oxen.) - -Many will there be who will die a painful death by means of the -horns of cattle. - -(Of writing Letters from one Country to another.) - -Men will speak with each other from the most remote countries, and -reply. - -(Of Hemispheres, which are infinite; and which are divided by an -infinite number of Lines, so that every Man always has one of these -Lines between his Feet.) - -Men standing in opposite hemispheres will converse and deride each -other and embrace each other, and understand each other's language. - -(Of Priests who say Mass.) - -There will be many men who, when they go to their labour will put on -the richest clothes, and these will be made after the fashion of -aprons [petticoats]. - -(Of Friars who are Confessors.) - -And unhappy women will, of their own free will, reveal to men all -their sins and shameful and most secret deeds. - -(Of Churches and the Habitations of Friars.) - -Many will there be who will give up work and labour and poverty of -life and goods, and will go to live among wealth in splendid -buildings, declaring that this is the way to make themselves -acceptable to God. - -(Of Selling Paradise.) - -An infinite number of men will sell publicly and unhindered things -of the very highest price, without leave from the Master of it; -while it never was theirs nor in their power; and human justice will -not prevent it. - -(Of the Dead which are carried to be buried.) - -The simple folks will carry vast quantities of lights to light up -the road for those who have entirely lost the power of sight. - -(Of Dowries for Maidens.) - -And whereas, at first, maidens could not be protected against the -violence of Men, neither by the watchfulness of parents nor by -strong walls, the time will come when the fathers and parents of -those girls will pay a large price to a man who wants to marry them, -even if they are rich, noble and most handsome. Certainly this seems -as though nature wished to eradicate the human race as being useless -to the world, and as spoiling all created things. - -(Of the Cruelty of Man.) - -Animals will be seen on the earth who will always be fighting -against each other with the greatest loss and frequent deaths on -each side. And there will be no end to their malignity; by their -strong limbs we shall see a great portion of the trees of the vast -forests laid low throughout the universe; and, when they are filled -with food the satisfaction of their desires will be to deal death -and grief and labour and wars and fury to every living thing; and -from their immoderate pride they will desire to rise towards heaven, -but the too great weight of their limbs will keep them down. Nothing -will remain on earth, or under the earth or in the waters which will -not be persecuted, disturbed and spoiled, and those of one country -removed into another. And their bodies will become the sepulture and -means of transit of all they have killed. - -O Earth! why dost thou not open and engulf them in the fissures of -thy vast abyss and caverns, and no longer display in the sight of -heaven such a cruel and horrible monster. - -1297. - -PROPHECIES. - -There will be many which will increase in their destruction. - -(The Ball of Snow rolling over Snow.) - -There will be many who, forgetting their existence and their name, -will lie as dead on the spoils of other dead creatures. - -(Sleeping on the Feathers of Birds.) - -The East will be seen to rush to the West and the South to the North -in confusion round and about the universe, with great noise and -trembling or fury. - -(In the East wind which rushes to the West.) - -The solar rays will kindle fire on the earth, by which a thing that -is under the sky will be set on fire, and, being reflected by some -obstacle, it will bend downwards. - -(The Concave Mirror kindles a Fire, with which we heat the oven, and -this has its foundation beneath its roof.) - -A great part of the sea will fly towards heaven and for a long time -will not return. (That is, in Clouds.) - -There remains the motion which divides the mover from the thing -moved. - -Those who give light for divine service will be destroyed.(The Bees -which make the Wax for Candles) - -Dead things will come from underground and by their fierce movements -will send numberless human beings out of the world. (Iron, which -comes from under ground is dead but the Weapons are made of it which -kill so many Men.) - -The greatest mountains, even those which are remote from the sea -shore, will drive the sea from its place. - -(This is by Rivers which carry the Earth they wash away from the -Mountains and bear it to the Sea-shore; and where the Earth comes -the sea must retire.) - -The water dropped from the clouds still in motion on the flanks of -mountains will lie still for a long period of time without any -motion whatever; and this will happen in many and divers lands. - -(Snow, which falls in flakes and is Water.) - -The great rocks of the mountains will throw out fire; so that they -will burn the timber of many vast forests, and many beasts both wild -and tame. - -(The Flint in the Tinder-box which makes a Fire that consumes all -the loads of Wood of which the Forests are despoiled and with this -the flesh of Beasts is cooked.) - -Oh! how many great buildings will be ruined by reason of Fire. - -(The Fire of great Guns.) - -Oxen will be to a great extent the cause of the destruction of -cities, and in the same way horses and buffaloes. - -(By drawing Guns.) - -1298. - -The Lion tribe will be seen tearing open the earth with their clawed -paws and in the caves thus made, burying themselves together with -the other animals that are beneath them. - -Animals will come forth from the earth in gloomy vesture, which will -attack the human species with astonishing assaults, and which by -their ferocious bites will make confusion of blood among those they -devour. - -Again the air will be filled with a mischievous winged race which -will assail men and beasts and feed upon them with much noise-- -filling themselves with scarlet blood. - -1299. - -Blood will be seen issuing from the torn flesh of men, and trickling -down the surface. - -Men will have such cruel maladies that they will tear their flesh -with their own nails. (The Itch.) - -Plants will be seen left without leaves, and the rivers standing -still in their channels. - -The waters of the sea will rise above the high peaks of the -mountains towards heaven and fall again on to the dwellings of men. -(That is, in Clouds.) - -The largest trees of the forest will be seen carried by the fury of -the winds from East to West. (That is across the Sea.) - -Men will cast away their own victuals. (That is, in Sowing.) - -1300. - -Human beings will be seen who will not understand each other's -speech; that is, a German with a Turk. - -Fathers will be seen giving their daughters into the power of man -and giving up all their former care in guarding them. (When Girls -are married.) - -Men will come out their graves turned into flying creatures; and -they will attack other men, taking their food from their very hand -or table. (As Flies.) - -Many will there be who, flaying their mother, will tear the skin -from her back. (Husbandmen tilling the Earth.) - -Happy will they be who lend ear to the words of the Dead. (Who read -good works and obey them.) - -1031. - -Feathers will raise men, as they do birds, towards heaven (that is, -by the letters which are written with quills.) - -The works of men's hands will occasion their death. (Swords and -Spears.) - -Men out of fear will cling to the thing they most fear. (That is -they will be miserable lest they should fall into misery.) - -Things that are separate shall be united and acquire such virtue -that they will restore to man his lost memory; that is papyrus -[sheets] which are made of separate strips and have preserved the -memory of the things and acts of men. - -The bones of the Dead will be seen to govern the fortunes of him who -moves them. (By Dice.) - -Cattle with their horns protect the Flame from its death. (In a -Lantern [Footnote 13: See note page 357.].) - -The Forests will bring forth young which will be the cause of their -death. (The handle of the hatchet.) - -1302. - -Men will deal bitter blows to that which is the cause of their life. -(In thrashing Grain.) - -The skins of animals will rouse men from their silence with great -outcries and curses. (Balls for playing Games.) - -Very often a thing that is itself broken is the occasion of much -union. (That is the Comb made of split Cane which unites the threads -of Silk.) - -The wind passing through the skins of animals will make men dance. -(That is the Bag-pipe, which makes people dance.) - -1303. - -(Of Walnut trees, that are beaten.) - -Those which have done best will be most beaten, and their offspring -taken and flayed or peeled, and their bones broken or crushed. - -(Of Sculpture.) - -Alas! what do I see? The Saviour cru- cified anew. - -(Of the Mouth of Man, which is a Sepulchre.) - -Great noise will issue from the sepulchres of those who died evil -and violent deaths. - -(Of the Skins of Animals which have the sense of feeling what is in -the things written.) - -The more you converse with skins covered with sentiments, the more -wisdom will you acquire. - -(Of Priests who bear the Host in their body.) - -Then almost all the tabernacles in which dwells the Corpus Domini, -will be plainly seen walking about of themselves on the various -roads of the world. - -1304. - -And those who feed on grass will turn night into day (Tallow.) - -And many creatures of land and water will go up among the stars -(that is Planets.) - -The dead will be seen carrying the living (in Carts and Ships in -various places.) - -Food shall be taken out of the mouth of many ( the oven's mouth.) - -And those which will have their food in their mouth will be deprived -of it by the hands of others (the oven.) - -1305. - -(Of Crucifixes which are sold.) - -I see Christ sold and crucified afresh, and his Saints suffering -Martyrdom. - -(Of Physicians, who live by sickness.) - -Men will come into so wretched a plight that they will be glad that -others will derive profit from their sufferings or from the loss of -their real wealth, that is health. - -(Of the Religion of Friars, who live by the Saints who have been -dead a great while.) - -Those who are dead will, after a thou- sand years be those who will -give a livelihood to many who are living. - -(Of Stones converted into Lime, with which prison walls are made.) - -Many things that have been before that time destroyed by fire will -deprive many men of liberty. - -1306. - -(Of Children who are suckled.) - -Many Franciscans, Dominicans and Benedictines will eat that which at -other times was eaten by others, who for some months to come will -not be able to speak. - -(Of Cockles and Sea Snails which are thrown up by the sea and which -rot inside their shells.) - -How many will there be who, after they are dead, will putrefy inside -their own houses, filling all the surrounding air with a fetid -smell. - -1307. - -(Of Mules which have on them rich burdens of silver and gold.) - -Much treasure and great riches will be laid upon four-footed beasts, -which will convey them to divers places. - -1308. - -(Of the Shadow cast by a man at night with a light.) - -Huge figures will appear in human shape, and the nearer you get to -them, the more will their immense size diminish. - -[Footnote page 1307: It seems to me probable that this note, which -occurs in the note book used in 1502, when Leonardo, in the service -of Cesare Borgia, visited Urbino, was suggested by the famous -pillage of the riches of the palace of Guidobaldo, whose treasures -Cesare Borgia at once had carried to Cesena (see GREGOROVIUS, -_Geschichte der Stadt Rom im Mittelalter_. XIII, 5, 4). ] - -1309. - -(Of Snakes, carried by Storks.) - -Serpents of great length will be seen at a great height in the air, -fighting with birds. - -(Of great guns, which come out of a pit and a mould.) - -Creatures will come from underground which with their terrific noise -will stun all who are near; and with their breath will kill men and -destroy cities and castles. - -1310. - -(Of Grain and other Seeds.) - -Men will fling out of their houses those victuals which were -intended to sustain their life. - -(Of Trees, which nourish grafted shoots.) - -Fathers and mothers will be seen to take much more delight in their -step-children then in their own children. - -(Of the Censer.) - -Some will go about in white garments with arrogant gestures -threatening others with metal and fire which will do no harm at all -to them. - -1311. - -(Of drying Fodder.) - -Innumerable lives will be destroyed and innumerable vacant spaces -will be made on the earth. - -(Of the Life of Men, who every year change their bodily substance.) - -Men, when dead, will pass through their own bowels. - -1312. - -(Shoemakers.) - -Men will take pleasure in seeing their own work destroyed and -injured. - -1313. - -(Of Kids.) - -The time of Herod will come again, for the little innocent children -will be taken from their nurses, and will die of terrible wounds -inflicted by cruel men. - -V. - -DRAUGHTS AND SCHEMES FOR THE HUMOROUS WRITINGS. - -Schemes for fables, etc. (1314-1323). - -1314. - -A FABLE. - -The crab standing under the rock to catch the fish which crept under -it, it came to pass that the rock fell with a ruinous downfall of -stones, and by their fall the crab was crushed. - -THE SAME. - -The spider, being among the grapes, caught the flies which were -feeding on those grapes. Then came the vintage, and the spider was -cut down with the grapes. - -The vine that has grown old on an old tree falls with the ruin of -that tree, and through that bad companionship must perish with it. - -The torrent carried so much earth and stones into its bed, that it -was then constrained to change its course. - -The net that was wont to take the fish was seized and carried away -by the rush of fish. - -The ball of snow when, as it rolls, it descends from the snowy -mountains, increases in size as it falls. - -The willow, which by its long shoots hopes as it grows, to outstrip -every other plant, from having associated itself with the vine which -is pruned every year was always crippled. - -1315. - -Fable of the tongue bitten by the teeth. - -The cedar puffed up with pride of its beauty, separated itself from -the trees around it and in so doing it turned away towards the wind, -which not being broken in its fury, flung it uprooted on the earth. - -The traveller's joy, not content in its hedge, began to fling its -branches out over the high road, and cling to the opposite hedge, -and for this it was broken away by the passers by. - -1316. - -The goldfinch gives victuals to its caged young. Death rather than -loss of liberty. [Footnote: Above this text is another note, also -referring to liberty; see No. 694.] - -1317. - -(Of Bags.) - -Goats will convey the wine to the city. - -1318. - -All those things which in winter are hidden under the snow, will be -uncovered and laid bare in summer. (for Falsehood, which cannot -remain hidden). - -1319. - -A FABLE. - -The lily set itself down by the shores of the Ticino, and the -current carried away bank and the lily with it. - -1320. - -A JEST. - -Why Hungarian ducats have a double cross on them. - -1321. - -A SIMILE. - -A vase of unbaked clay, when broken, may be remoulded, but not a -baked one. - -1322. - -Seeing the paper all stained with the deep blackness of ink, it he -deeply regrets it; and this proves to the paper that the words, -composed upon it were the cause of its being preserved. - -1323. - -The pen must necessarily have the penknife for a companion, and it -is a useful companionship, for one is not good for much without the -other. - -Schemes for prophecies (1324-1329). - -1324. - -The knife, which is an artificial weapon, deprives man of his nails, -his natural weapons. - -The mirror conducts itself haughtily holding mirrored in itself the -Queen. When she departs the mirror remains there ... - -1325. - -Flax is dedicated to death, and to the corruption of mortals. To -death, by being used for snares and nets for birds, animals and -fish; to corruption, by the flaxen sheets in which the dead are -wrapped when they are buried, and who become corrupt in these -winding sheets.-- And again, this flax does not separate its fibre -till it has begun to steep and putrefy, and this is the flower with -which garlands and decorations for funerals should be made. - -1326. - -(Of Peasants who work in shirts) - -Shadows will come from the East which will blacken with great colour -darkness the sky that covers Italy. - -(Of the Barbers.) - -All men will take refuge in Africa. - -1327. - -The cloth which is held in the hand in the current of a running -stream, in the waters of which the cloth leaves all its foulness and -dirt, is meant to signify this &c. - -By the thorn with inoculated good fruit is signified those natures -which of themselves were not disposed towards virtue, but by the aid -of their preceptors they have the repudation of it. - -1328. - -A COMMON THING. - -A wretched person will be flattered, and these flatterers are always -the deceivers, robbers and murderers of the wretched person. - -The image of the sun where it falls appears as a thing which covers -the person who attempts to cover it. - -(Money and Gold.) - -Out of cavernous pits a thing shall come forth which will make all -the nations of the world toil and sweat with the greatest torments, -anxiety and labour, that they may gain its aid. - -(Of the Dread of Poverty.) - -The malicious and terrible [monster] will cause so much terror of -itself in men that they will rush together, with a rapid motion, -like madmen, thinking they are escaping her boundless force. - -(Of Advice.) - -The man who may be most necessary to him who needs him, will be -repaid with ingratitude, that is greatly contemned. - -1329. - -(Of Bees.) - -They live together in communities, they are destroyed that we may -take the honey from them. Many and very great nations will be -destroyed in their own dwellings. - -1330. - -WHY DOGS TAKE PLEASURE IN SMELLING AT EACH OTHER. - -This animal has a horror of the poor, because they eat poor food, -and it loves the rich, because they have good living and especially -meat. And the excrement of animals always retains some virtue of its -origin as is shown by the faeces ... - -Now dogs have so keen a smell, that they can discern by their nose -the virtue remaining in these faeces, and if they find them in the -streets, smell them and if they smell in them the virtue of meat or -of other things, they take them, and if not, they leave them: And to -return to the question, I say that if by means of this smell they -know that dog to be well fed, they respect him, because they judge -that he has a powerful and rich master; and if they discover no such -smell with the virtue of meet, they judge that dog to be of small -account and to have a poor and humble master, and therefore they -bite that dog as they would his master. - -1331. - -The circular plans of carrying earth are very useful, inasmuch as -men never stop in their work; and it is done in many ways. By one of -these ways men carry the earth on their shoulders, by another in -chests and others on wheelbarrows. The man who carries it on his -shoulders first fills the tub on the ground, and he loses time in -hoisting it on to his shoulders. He with the chests loses no time. -[Footnote: The subject of this text has apparently no connection -with the other texts of this section.] - -Irony (1332). - -1332. - -If Petrarch was so fond of bay, it was because it is of a good taste -in sausages and with tunny; I cannot put any value on their foolery. -[Footnote: Conte Porro has published these lines in the _Archivio -Stor. Lombarda_ VIII, IV; he reads the concluding line thus: _I no -posso di loro gia (sic) co' far tesauro._--This is known to be by a -contemporary poet, as Senatore Morelli informs me.] - -Tricks (1333-1335). - -1333. - -We are two brothers, each of us has a brother. Here the way of -saying it makes it appear that the two brothers have become four. - -1334. - -TRICKS OF DIVIDING. - -Take in each hand an equal number; put 4 from the right hand into -the left; cast away the remainder; cast away an equal number from -the left hand; add 5, and now you will find 13 in this [left] hand; -that is-I made you put 4 from the right hand into the left, and cast -away the remainder; now your right hand has 4 more; then I make you -throw away as many from the right as you threw away from the left; -so, throwing from each hand a quantity of which the remainder may be -equal, you now have 4 and 4, which make 8, and that the trick may -not be detec- ted I made you put 5 more, which made 13. - -TRICKS OF DIVIDING. - -Take any number less than 12 that you please; then take of mine -enough to make up the number 12, and that which remains to me is the -number which you at first had; because when I said, take any number -less than 12 as you please, I took 12 into my hand, and of that 12 -you took such a number as made up your number of 12; and what you -added to your number, you took from mine; that is, if you had 8 to -go as far as to 12, you took of my 12, 4; hence this 4 transferred -from me to you reduced my 12 to a remainder of 8, and your 8 became -12; so that my 8 is equal to your 8, before it was made 12. - -[Footnote 1334: G. Govi _says in the_ 'Saggio' p. 22: _Si dilett -Leonarda, di giuochi di prestigi e molti (?) ne descrisse, che si -leggono poi riportati dal Paciolo nel suo libro:_ de Viribus -Quantitatis, _e che, se non tutti, sono certo in gran parte -invenzioni del Vinci._] - -1335. - -If you want to teach someone a subject you do not know yourself, let -him measure the length of an object unknown to you, and he will -learn the measure you did not know before;--Master Giovanni da Lodi. - -_XXI._ - -_Letters. Personal Records. Dated Notes._ - -_When we consider how superficial and imperfect are the accounts of -Leonardo's life written some time after his death by Vasari and -others, any notes or letters which can throw more light on his -personal circumstances cannot fail to be in the highest degree -interesting. The texts here given as Nos._ 1351--1353, _set his -residence in Rome in quite a new aspect; nay, the picture which -irresistibly dwells in our minds after reading these details of his -life in the Vatican, forms a striking contrast to the contemporary -life of Raphael at Rome._ - -_I have placed foremost of these documents the very remarkable -letters to the Defterdar of Syria. In these Leonardo speaks of -himself as having staid among the mountains of Armenia, and as the -biographies of the master tell nothing of any such distant journeys, -it would seem most obvious to treat this passage as fiction, and so -spare ourselves the onus of proof and discussion. But on close -examination no one can doubt that these documents, with the -accompanying sketches, are the work of Leonardo's own hand. Not -merely is the character of the handwriting his, but the spelling and -the language are his also. In one respect only does the writing -betray any marked deviation from the rest of the notes, especially -those treating on scientific questions; namely, in these -observations he seems to have taken particular pains to give the -most distinct and best form of expression to all he had to say; we -find erasures and emendations in almost every line. He proceeded, as -we shall see, in the same way in the sketches for letters to -Giuliano de' Medici, and what can be more natural, I may ask, than -to find the draft of a letter thus altered and improved when it is -to contain an account of a definite subject, and when personal -interests are in the scale? The finished copies as sent off are not -known to exist; if we had these instead of the rough drafts, we -might unhesitatingly have declared that some unknown Italian -engineer must have been, at that time, engaged in Armenia in the -service of the Egyptian Sultan, and that Leonardo had copied his -documents. Under this hypothesis however we should have to state -that this unknown writer must have been so far one in mind with -Leonardo as to use the same style of language and even the same -lines of thought. This explanation might--as I say--have been -possible, if only we had the finished letters. But why should these -rough drafts of letters be regarded as anything else than what they -actually and obviously are? If Leonardo had been a man of our own -time, we might perhaps have attempted to account for the facts by -saying that Leonardo, without having been in the East himself, might -have undertaken to write a Romance of which the scene was laid in -Armenia, and at the desire of his publisher had made sketches of -landscape to illustrate the text. - -I feel bound to mention this singular hypothesis as it has actually -been put forward (see No. 1336 note 5); and it would certainly seem -as though there were no other possible way of evading the conclusion -to which these letters point, and their bearing on the life of the -master,--absurd as the alternative is. But, if, on a question of -such importance, we are justified in suggesting theories that have -no foundation in probability, I could suggest another which, as -compared with that of a Fiction by Leonardo, would be neither more -nor less plausible; it is, moreover the only other hypothesis, -perhaps, which can be devised to account for these passages, if it -were possible to prove that the interpretation that the documents -themselves suggest, must be rejected a priori; viz may not Leonardo -have written them with the intention of mystifying those who, after -his death, should try to decipher these manuscripts with a view to -publishing them? But if, in fact, no objection that will stand the -test of criticism can be brought against the simple and direct -interpretation of the words as they stand, we are bound to regard -Leonardo's travels in the East as an established fact. There is, I -believe nothing in what we know of his biography to negative such a -fact, especially as the details of his life for some few years are -wholly unknown; nor need we be at a loss for evidence which may -serve to explain--at any rate to some extent--the strangeness of his -undertaking such a journey. We have no information as to Leonardo's -history between 1482 and 1486; it cannot be proved that he was -either in Milan or in Florence. On the other hand the tenor of this -letter does not require us to assume a longer absence than a year or -two. For, even if his appointment_ (offitio) _as Engineer in Syria -had been a permanent one, it might have become untenable--by the -death perhaps of the Defterdar, his patron, or by his removal from -office--, and Leonardo on his return home may have kept silence on -the subject of an episode which probably had ended in failure and -disappointment. - -From the text of No. 1379 we can hardly doubt that Leonardo intended -to make an excursion secretly from Rome to Naples, although so far -as has hitherto been known, his biographers never allude to it. In -another place (No. 1077) he says that he had worked as an Engineer -in Friuli. Are we to doubt this statement too, merely because no -biographer has hitherto given us any information on the matter? In -the geographical notes Leonardo frequently speaks of the East, and -though such passages afford no direct proof of his having been -there, they show beyond a doubt that, next to the Nile, the -Euphrates, the Tigris and the Taurus mountains had a special -interest in his eyes. As a still further proof of the futility of -the argument that there is nothing in his drawings to show that he -had travelled in the East, we find on Pl. CXX a study of oriental -heads of Armenian type,--though of course this may have been made in -Italy. - -If the style of these letters were less sober, and the expressions -less strictly to the point throughout, it miglit be possible to -regard them as a romantic fiction instead of a narrative of fact. -Nay, we have only to compare them with such obviously fanciful -passages as No. 1354, Nos. 670-673, and the Fables and Prophecies. -It is unnecessary to discuss the subject any further here; such -explanations as the letter needs are given in the foot notes. - -The drafts of letters to Lodovico il Moro are very remarkable. -Leonardo and this prince were certainly far less closely connected, -than has hitherto been supposed. It is impossible that Leonardo can -have remained so long in the service of this prince, because the -salary was good, as is commonly stated. On the contrary, it would -seem, that what kept him there, in spite of his sore need of the -money owed him by the prince, was the hope of some day being able to -carry out the project of casting the_ 'gran cavallo'. - -Drafts of Letters and Reports referring to Armenia (1336. 1337). - -1336. - -To THE DEVATDAR OF SYRIA, LIEUTENANT OF THE SACRED SULTAN OF -BABYLON. - -[3] The recent disaster in our Northern parts which I am certain -will terrify not you alone but the whole world, which - -[Footnote: Lines 1-52 are reproduced in facsimile on Pl. CXVI. - -1. _Diodario._ This word is not to be found in any Italian -dictionary, and for a long time I vainly sought an explanation of -it. The youthful reminiscences of my wife afforded the desired clue. -The chief town of each Turkish Villayet, or province --such as -Broussa, for instance, in Asia Minor, is the residence of a -Defterdar, who presides over the financial affairs of the province. -_Defterdar hane_ was, in former times, the name given to the -Ministry of Finance at Constantinople; the Minister of Finance to -the Porte is now known as the _Mallie-Nazri_ and the _Defterdars_ -are his subordinates. A _Defterdar_, at the present day is merely -the head of the finance department in each Provincial district. With -regard to my suggestion that Leonardo's _Diodario_ might be -identical with the Defterdar of former times, the late M. C. -DEFREMERIE, Arabic Professor, and Membre de l'Institut de France -wrote to me as follows: _Votre conjecture est parfaitement fondee; -diodario est Vequivalent de devadar ou plus exactement devatdar, -titre d'une importante dignite en Egypt'e, sous les Mamlouks._ - -The word however is not of Turkish, but of Perso-Arabie derivation. -[Defter written in arab?] literally _Defter_ (Arabic) meaning -_folio_; for _dar_ (Persian) Bookkeeper or holder is the English -equivalent; and the idea is that of a deputy in command. During the -Mamelook supremacy over Syria, which corresponded in date with -Leonardo's time, the office of Defterdar was the third in importance -in the State. - -_Soltano di Babilonia_. The name of Babylon was commonly applied to -Cairo in the middle ages. For instance BREIDENBACH, _Itinerarium -Hierosolyma_ p. 218 says: "At last we reached Babylon. But this is -not that Babylon which stood on the further shore of the river -Chober, but that which is called the Egyptian Babylon. It is close -by Cairo and the twain are but one and not two towns; one half is -called Cairo and the other Babylon, whence they are called together -Cairo-Babylon; originally the town is said to have been named -Memphis and then Babylon, but now it is called Cairo." Compare No. -1085, 6. - -Egypt was governed from 1382 till 1517 by the Borgite or -Tcherkessian dynasty of the Mamelook Sultans. One of the most famous -of these, Sultan Kait Bey, ruled from 1468-1496 during whose reign -the Gama (or Mosque) of Kait Bey and tomb of Kait Bey near the -Okella Kait Bey were erected in Cairo, which preserve his name to -this day. Under the rule of this great and wise prince many -foreigners, particularly Italians, found occupation in Egypt, as may -be seen in the 'Viaggio di Josaphat Barbaro', among other -travellers. "Next to Leonardo (so I learn from Prof. Jac. Burckhardt -of Bale) Kait Bey's most helpful engineer was a German who in about -1487, superintended the construction of the Mole at Alexandria. -Felix Fabri knew him and mentions him in his _Historia Suevorum_, -written in 1488." - -3. _Il nuovo accidente accaduto_, or as Leonardo first wrote and -then erased, _e accaduto un nuovo accidente_. From the sequel this -must refer to an earthquake, and indeed these were frequent at that -period, particularly in Asia Minor, where they caused immense -mischief. See No. 1101 note.] - -shall be related to you in due order, showing first the effect and -then the cause. [Footnote 4: The text here breaks off. The following -lines are a fresh beginning of a letter, evidently addressed to the -same person, but, as it would seem, written at a later date than the -previous text. The numerous corrections and amendments amply prove -that it is not a copy from any account of a journey by some unknown -person; but, on the contrary, that Leonardo was particularly anxious -to choose such words and phrases as might best express his own -ideas.] - -Finding myself in this part of Armenia [Footnote 5: _Parti -d'Erminia_. See No. 945, note. The extent of Armenia in Leonardo's -time is only approximately known. In the XVth century the Persians -governed the Eastern, and the Arabs the Southern portions. Arabic -authors--as, for instance Abulfeda--include Cilicia and a part of -Cappadocia in Armenia, and Greater Armenia was the tract of that -country known later as Turcomania, while Armenia Minor was the -territory between Cappadocia and the Euphrates. It was not till -1522, or even 1574 that the whole country came under the dominion of -the Ottoman Turks, in the reign of Selim I. - -The Mamelook Sultans of Egypt seem to have taken a particular -interest in this, the most Northern province of their empire, which -was even then in danger of being conquered by the Turks. In the -autumn of 1477 Sultan Kait Bey made a journey of inspection, -visiting Antioch and the valleys of the Tigris and Euphrates with a -numerous and brilliant escort. This tour is briefly alluded to by -_Moodshireddin_ p. 561; and by WEIL, _Geschichte der Abbasiden_ V, -p. 358. An anonymous member of the suite wrote a diary of the -expedition in Arabic, which has been published by R. V. LONZONE -(_'Viaggio in Palestina e Soria di Kaid Ba XVIII sultano della II -dinastia mamelucca, fatto nel 1477. Testo arabo. Torino 1878'_, -without notes or commentary). Compare the critique on this edition, -by J. GILDEMEISTER in _Zeitschrift des Deutschen Palaestina Vereins_ -(Vol. Ill p. 246--249). Lanzone's edition seems to be no more than -an abridged copy of the original. I owe to Professor Sche'fer, -Membre de l'Institut, the information that he is in possession of a -manuscript in which the text is fuller, and more correctly given. -The Mamelook dynasty was, as is well known, of Circassian origin, -and a large proportion of the Egyptian Army was recruited in -Circassia even so late as in the XVth century. That was a period of -political storms in Syria and Asia Minor and it is easy to suppose -that the Sultan's minister, to whom Leonardo addresses his report as -his superior, had a special interest in the welfare of those -frontier provinces. Only to mention a few historical events of -Sultan Kait Bey's reign, we find that in 1488 he assisted the -Circassians to resist the encroachments of Alaeddoulet, an Asiatic -prince who had allied himself with the Osmanli to threaten the -province; the consequence was a war in Cilicia by sea and land, -which broke out in the following year between the contending powers. -Only a few years earlier the same province had been the scene of the -so-called Caramenian war in which the united Venetian, Neapolitan -and Sclavonic fleets had been engaged. (See CORIALANO CIPPICO, -_Della guerra dei Veneziani nell' Asia dal_ 1469--1474. Venezia -1796, p. 54) and we learn incidentally that a certain Leonardo -Boldo, Governor of Scutari under Sultan Mahmoud,--as his name would -indicate, one of the numerous renegades of Italian birth--played an -important part in the negotiations for peace. - -_Tu mi mandasti_. The address _tu_ to a personage so high in office -is singular and suggests personal intimacy; Leonardo seems to have -been a favourite with the Diodario. Compare lines 54 and 55. - -I have endeavoured to show, and I believe that I am also in a -position to prove with regard to these texts, that they are draughts -of letters actually written by Leonardo; at the same time I must not -omit to mention that shortly after I had discovered - -these texts in the Codex Atlanticus and published a paper on the -subject in the _Zeitschrift fur bildende Kunst (Vol. XVI)_, Prof. -Govi put forward this hypothesis to account for their origin: - -_"Quanto alle notizie sul monte Tauro, sull'Armenia e sull' Asia -minore che si contengono negli altri frammenti, esse vennero prese -da qualche geografro o viaggiatore contemporaneo. Dall'indice -imperfetto che accompagna quei frammenti, si potrebbe dedurre che -Leonardo volesse farne un libro, che poi non venne compiuto. A ogni -modo, non e possibile di trovare in questi brani nessun indizio di -un viaggio di Leonardo in oriente, ne della sua conversione alla -religione di Maometto, come qualcuno pretenderebbe. Leonardo amava -con passione gli studi geografici, e nel suoi scritti s'incontran -spesso itinerart, indicazioni, o descrizioni di luoghi, schizzi di -carte e abbozzi topografici di varie regioni, non e quindi strano -che egli, abile narratore com'era, si fosse proposto di scrivere una -specie di Romanzo in forma epistolare svolgendone Pintreccio -nell'Asia Minore, intorno alla quale i libri d'allora, e forse -qualche viaggiatore amico suo, gli avevano somministrato alcuni -elementi piu o meno_ fantastici. (See Transunti della Reale -Accademia dei Lincei Voi. V Ser. 3). - -It is hardly necessary to point out that Prof. Govi omits to name -the sources from which Leonardo could be supposed to have drawn his -information, and I may leave it to the reader to pronounce judgment -on the anomaly which is involved in the hypothesis that we have here -a fragment of a Romance, cast in the form of a correspondence. At -the same time, I cannot but admit that the solution of the -difficulties proposed by Prof. Govi is, under the circumstances, -certainly the easiest way of dealing with the question. But we -should then be equally justified in supposing some more of -Leonardo's letters to be fragments of such romances; particularly -those of which the addresses can no longer be named. Still, as -regards these drafts of letters to the Diodario, if we accept the -Romance theory, as pro- posed by Prof. Govi, we are also compelled -to assume that Leonardo purposed from the first to illustrate his -tale; for it needs only a glance at the sketches on PI. CXVI to CXIX -to perceive that they are connected with the texts; and of course -the rest of Leonardo's numerous notes on matters pertaining to the -East, the greater part of which are here published for the first -time, may also be somehow connected with this strange romance. - -7. _Citta de Calindra (Chalindra)_. The position of this city is so -exactly determined, between the valley of the Euphrates and the -Taurus range that it ought to be possible to identify it. But it can -hardly be the same as the sea port of Cilicia with a somewhat -similar name Celenderis, Kelandria, Celendria, Kilindria, now the -Turkish Gulnar. In two Catalonian Portulans in the Bibliotheque -Natio- nale in Paris-one dating from the XV'h century, by Wilhelm -von Soler, the other by Olivez de Majorca, in l584-I find this place -called Calandra. But Leonardo's Calindra must certainly have lain -more to the North West, probably somewhere in Kurdistan. The fact -that the geographical position is so care- fully determined by -Leonardo seems to prove that it was a place of no great importance -and little known. It is singular that the words first written in 1. -8 were divisa dal lago (Lake Van?), altered afterwards to -dall'Eitfrates. - -Nostri confini, and in 1. 6 proposito nostro. These refer to the -frontier and to the affairs of the Mamelook Sultan, Lines 65 and 66 -throw some light on the purpose of Leonardo's mission. - -8. _I_ corni del gra mote Tauro. Compare the sketches PI. -CXVI-CXVIII. So long as it is im- possible to identify the situation -of Calindra it is most difficult to decide with any certainty which -peak of the Taurus is here meant; and I greatly regret that I had no -foreknowledge of this puzzling topographical question when, in 1876, -I was pursuing archaeological enquiries in the Provinces of Aleppo -and Cilicia, and had to travel for some time in view of the imposing -snow-peaks of Bulghar Dagh and Ala Tepessi. - -9-10. The opinion here expressed as to the height of the mountain -would be unmeaning, unless it had been written before Leonardo moved -to Milan, where Monte Rosa is so conspicuous an object in the -landscape. 4 _ore inanzi_ seems to mean, four hours before the sun's -rays penetrate to the bottom of the valleys.] - -to carry into effect with due love and care the task for which you -sent me [Footnote: ][6]; and to make a beginning in a place which -seemed to me to be most to our purpose, I entered into the city of -Calindrafy[7], near to our frontiers. This city is situated at the -base of that part of the Taurus mountains which is divided from the -Euphrates and looks towards the peaks of the great Mount Taurus [8] -to the West [9]. These peaks are of such a height that they seem to -touch the sky, and in all the world there is no part of the earth, -higher than its summit[10], and the rays of the sun always fall upon -it on its East side, four hours before day-time, and being of the -whitest stone [Footnote 11:_Pietra bianchissima_. The Taurus -Mountains consist in great part of limestone.] it shines -resplendently and fulfils the function to these Armenians which a -bright moon-light would in the midst of the darkness; and by its -great height it outreaches the utmost level of the clouds by a space -of four miles in a straight line. This peak is seen in many places -towards the West, illuminated by the sun after its setting the third -part of the night. This it is, which with you [Footnote 14: -_Appresso di voi_. Leonardo had at first written _noi_ as though his -meaning had,been: This peak appeared to us to be a comet when you -and I observed it in North Syria (at Aleppo? at Aintas?). The -description of the curious reflection in the evening, resembling the -"Alpine-glow" is certainly not an invented fiction, for in the next -lines an explanation of the phenomenon is offered, or at least -attempted.] we formerly in calm weather had supposed to be a comet, -and appears to us in the darkness of night, to change its form, -being sometimes divided in two or three parts, and sometimes long -and sometimes short. And this is caused by the clouds on the horizon -of the sky which interpose between part of this mountain and the -sun, and by cutting off some of the solar rays the light on the -mountain is intercepted by various intervals of clouds, and -therefore varies in the form of its brightness. - -THE DIVISIONS OF THE BOOK [Footnote 19: The next 33 lines are -evidently the contents of a connected Report or Book, but not of one -which he had at hand; more probably, indeed, of one he purposed -writing.]. - -The praise and confession of the faith [Footnote 20: _Persuasione di -fede_, of the Christian or the Mohammedan faith? We must suppose the -latter, at the beginning of a document addressed to so high a -Mohammedan official. _Predica_ probably stands as an abbreviation -for _predicazione_ (lat. _praedicatio_) in the sense of praise or -glorification; very probably it may mean some such initial doxology -as we find in Mohammedan works. (Comp. 1. 40.)]. - -The sudden inundation, to its end. - -[23] The destruction of the city. - -[24]The death of the people and their despair. - -The preacher's search, his release and benevolence [Footnote 28: The -phraseology of this is too general for any conjecture as to its -meaning to be worth hazarding.] - -Description of the cause of this fall of the mountain [Footnote 30: -_Ruina del monte_. Of course by an earthquake. In a catalogue of -earthquakes, entitled _kechf aussalssaleb an auasf ezzel-zeleh_, and -written by Djelal eddin]. - -The mischief it did. - -[32] Fall of snow. - -The finding of the prophet [33]. - -His prophesy. - -[35] The inundation of the lower portion of Eastern Armenia, the -draining of which was effected by the cutting through the Taurus -Mountains. - -How the new prophet showed [Footnote 40:_Nova profeta, 1. 33, -profeta_. Mohammed. Leonardo here refers to the Koran: - -In the name of the most merciful God.--When the earth shall be -shaken by an earthquake; and the earth shall cast forth her burdens; -and a man shall say, what aileth her? On that day the earth shall -declare her tidings, for that thy Lord will inspire her. On that day -men shall go forward in distinct classes, that they may behold their -works. And whoever shall have wrought good of the weight of an ant, -shall behold the same. And whoever shall have wrought evil of the -weight of an ant, shall behold the same. (The Koran, translated by -G. Sale, Chapter XCIX, p. 452).] that this destruction would happen -as he had foretold. - -Description of the Taurus Mountains [43] and the river Euphrates. - -Why the mountain shines at the top, from half to a third of the -night, and looks like a comet to the inhabitants of the West after -the sunset, and before day to those of the East. - -Why this comet appears of variable forms, so that it is now round -and now long, and now again divided into two or three parts, and now -in one piece, and when it is to be seen again. - -OF THE SHAPE OF THE TAURUS MOUNTAINS [Footnote 53-94: The facsimile -of this passage is given on Pl. CXVII.]. - -I am not to be accused, Oh Devatdar, of idleness, as your chidings -seem to hint; but your excessive love for me, which gave rise to the -benefits you have conferred on me [Footnote 55] is that which has -also compelled me to the utmost painstaking in seeking out and -diligently investigating the cause of so great and stupendous an -effect. And this could not be done without time; now, in order to -satisfy you fully as to the cause of so great an effect, it is -requisite that I should explain to you the form of the place, and -then I will proceed to the effect, by which I believe you will be -amply satisfied. - -[Footnote 36: _Tagliata di Monte Tauro_. The Euphrates flows through -the Taurus range near the influx of the Kura Shai; it rushes through -a rift in the wildest cliffs from 2000 to 3000 feet high and runs on -for 90 miles in 300 falls or rapids till it reaches Telek, near -which at a spot called Gleikash, or the Hart's leap, it measures -only 35 paces across. Compare the map on Pl. CXIX and the -explanation for it on p. 391.] - -[Footnote 54: The foregoing sketch of a letter, lines 5. 18, appears -to have remained a fragment when Leonardo received pressing orders -which caused him to write immediately and fully on the subject -mentioned in line 43.] - -[Footnote 59: This passage was evidently intended as an improvement -on that immediately preceding it. The purport of both is essentially -the same, but the first is pitched in a key of ill-disguised -annoyance which is absent from the second. I do not see how these -two versions can be reconciled with the romance-theory held by Prof. -Govi.] Do not be aggrieved, O Devatdar, by my delay in responding to -your pressing request, for those things which you require of me are -of such a nature that they cannot be well expressed without some -lapse of time; particularly because, in order to explain the cause -of so great an effect, it is necessary to describe with accuracy the -nature of the place; and by this means I can afterwards easily -satisfy your above-mentioned request. [Footnote 62: This passage was -evidently intended as an improvement on that immediately preceding -it. The purport of both is essentially the same, but the first is -pitched in a key of ill-disguised annoyance which is absent from the -second. I do not see how these two versions can be reconciled with -the romance-theory held by Prof. Govi.] - -I will pass over any description of the form of Asia Minor, or as to -what seas or lands form the limits of its outline and extent, -because I know that by your own diligence and carefulness in your -studies you have not remained in ignorance of these matters [65]; -and I will go on to describe the true form of the Taurus Mountain -which is the cause of this stupendous and harmful marvel, and which -will serve to advance us in our purpose [66]. This Taurus is that -mountain which, with many others is said to be the ridge of Mount -Caucasus; but wishing to be very clear about it, I desired to speak -to some of the inhabitants of the shores of the Caspian sea, who -give evidence that this must be the true Caucasus, and that though -their mountains bear the same name, yet these are higher; and to -confirm this in the Scythian tongue Caucasus means a very high -[Footnote 68: Caucasus; Herodot Kaoxaais; Armen. Kaukaz.] peak, and -in fact we have no information of there being, in the East or in the -West, any mountain so high. And the proof of this is that the -inhabitants of the countries to the West see the rays of the sun -illuminating a great part of its summit for as much as a quarter of -the longest night. And in the same way, in those countries which lie -to the East. - -OF THE STRUCTURE AND SIZE OF MOUNT TAURUS. - -[Footnote 73: The statements are of course founded on those of the -'inhabitants' spoken of in 1. 67.] The shadow of this ridge of the -Taurus is of such a height that when, in the middle of June, the Sun -is at its meridian, its shadow extends as far as the borders of -Sarmatia, twelve days off; and in the middle of December it extends -as far as the Hyperborean mountains, which are at a month's journey -to the North [75]. And the side which faces the wind is always free -from clouds and mists, because the wind which is parted in beating -on the rock, closes again on the further side of that rock, and in -its motion carries with it the clouds from all quarters and leaves -them where it strikes. And it is always full of thunderbolts from -the great quantity of clouds which accumulate there, whence the rock -is all riven and full of huge debris [Footnote 77: Sudden storms are -equally common on the heights of Ararat. It is hardly necessary to -observe that Ararat cannot be meant here. Its summit is formed like -the crater of Vesuvius. The peaks sketched on Pl. CXVI-CXVIII are -probably views of the same mountain, taken from different sides. -Near the solitary peak, Pl. CXVIII these three names are written -_goba, arnigasar, caruda_, names most likely of different peaks. Pl. -CXVI and CXVII are in the original on a single sheet folded down the -middle, 30 centimetres high and 43 1/2 wide. On the reverse of one -half of the sheet are notes on _peso_ and _bilancia_ (weight and -balance), on the other are the 'prophecies' printed under Nos. 1293 -and 1294. It is evident from the arrangement that these were written -subsequently, on the space which had been left blank. These pages -are facsimiled on Pl. CXVIII. In Pl. CXVI-CXVIII the size is smaller -than in the original; the map of Armenia, Pl. CXVIII, is on Pl. CXIX -slightly enlarged. On this map we find the following names, -beginning from the right hand at the top: _pariardes mo_ (for -Paryadres Mons, Arm. Parchar, now Barchal or Kolai Dagh; Trebizond -is on its slope). - -_Aquilone_ --North, _Antitaurus Antitaurus psis mo_ (probably meant -for Thospitis = Lake Van, Arm. Dgov Vanai, Tospoi, and the Mountain -range to the South); _Gordis mo_ (Mountains of Gordyaea), the birth -place of the Tigris; _Oriente_ --East; _Tigris_, and then, to the -left, _Eufrates_. Then, above to the left _Argeo mo_ (now Erdshigas, -an extinct volcano, 12000 feet high); _Celeno mo_ (no doubt Sultan -Dagh in Pisidia). Celeno is the Greek town of KeAouvat-- see Arian -I, 29, I--now the ruins of Dineir); _oriente_ --East; _africo -libezco_ (for libeccio--South West). In the middle of the Euphrates -river on this small map we see a shaded portion surrounded by -mountains, perhaps to indicate the inundation mentioned in l. 35. -The affluent to the Euphrates shown as coming with many windings -from the high land of 'Argeo' on the West, is the Tochma Su, which -joins the main river at Malatie. I have not been able to discover -any map of Armenia of the XVth or XVIth century in which the course -of the Euphrates is laid down with any thing like the correctness -displayed in this sketch. The best I have seen is the Catalonian -Portulan of Olivez de Majorca, executed in 1584, and it is far -behind Leonardo's.]. This mountain, at its base, is inhabited by a -very rich population and is full of most beautiful springs and -rivers, and is fertile and abounding in all good produce, -particularly in those parts which face to the South. But after -mounting about three miles we begin to find forests of great fir -trees, and beech and other similar trees; after this, for a space of -three more miles, there are meadows and vast pastures; and all the -rest, as far as the beginning of the Taurus, is eternal snows which -never disappear at any time, and extend to a height of about -fourteen miles in all. From this beginning of the Taurus up to the -height of a mile the clouds never pass away; thus we have fifteen -miles, that is, a height of about five miles in a straight line; and -the summit of the peaks of the Taurus are as much, or about that. -There, half way up, we begin to find a scorching air and never feel -a breath of wind; but nothing can live long there; there nothing is -brought forth save a few birds of prey which breed in the high -fissures of Taurus and descend below the clouds to seek their prey. -Above the wooded hills all is bare rock, that is, from the clouds -upwards; and the rock is the purest white. And it is impossible to -walk to the high summit on account of the rough and perilous ascent. - -1337. - -[Footnote: 1337. On comparing this commencement of a letter l. 1-2 -with that in l. 3 and 4 of No. 1336 it is quite evident that both -refer to the same event. (Compare also No. 1337 l. 10-l2 and 17 with -No. 1336 l. 23, 24 and 32.) But the text No. 1336, including the -fragment l. 3-4, was obviously written later than the draft here -reproduced. The _Diodario_ is not directly addressed--the person -addressed indeed is not known--and it seems to me highly probable -that it was written to some other patron and friend whose name and -position are not mentioned.] - -Having often made you, by my letters, acquainted with the things -which have happened, I think I ought not to be silent as to the -events of the last few days, which--[2]... - -Having several times-- - -Having many times rejoiced with you by letters over your prosperous -fortunes, I know now that, as a friend you will be sad with me over -the miserable state in which I find myself; and this is, that during -the last few days I have been in so much trouble, fear, peril and -loss, besides the miseries of the people here, that we have been -envious of the dead; and certainly I do not believe that since the -elements by their separation reduced the vast chaos to order, they -have ever combined their force and fury to do so much mischief to -man. As far as regards us here, what we have seen and gone through -is such that I could not imagine that things could ever rise to such -an amount of mischief, as we experienced in the space of ten hours. -In the first place we were assailed and attacked by the violence and -fury of the winds [10]; to this was added the falling of great -mountains of snow which filled up all this valley, thus destroying a -great part of our city [Footnote 11: _Della nostra citta_ (Leonardo -first wrote _di questa citta_). From this we may infer that he had -at some time lived in the place in question wherever it might be.]. -And not content with this the tempest sent a sudden flood of water -to submerge all the low part of this city [12]; added to which there -came a sudden rain, or rather a ruinous torrent and flood of water, -sand, mud, and stones, entangled with roots, and stems and fragments -of various trees; and every kind of thing flying through the air -fell upon us; finally a great fire broke out, not brought by the -wind, but carried as it would seem, by ten thousand devils, which -completely burnt up all this neighbourhood and it has not yet -ceased. And those few who remain unhurt are in such dejection and -such terror that they hardly have courage to speak to each other, as -if they were stunned. Having abandoned all our business, we stay -here together in the ruins of some churches, men and women mingled -together, small and great [Footnote 17: _Certe ruine di chiese_. -Either of Armenian churches or of Mosques, which it was not unusual -to speak of as churches. - -_Maschi e femmini insieme unite_, implies an infringement of the -usually strict rule of the separation of the sexes.], just like -herds of goats. The neighbours out of pity succoured us with -victuals, and they had previously been our enemies. And if - -[Footnote 18: _I vicini, nostri nimici_. The town must then have -stood quite close to the frontier of the country. Compare 1336. L. -7. _vicini ai nostri confini_. Dr. M. JORDAN has already published -lines 4-13 (see _Das Malerbuch, Leipzig_, 1873, p. 90:--his reading -differs from mine) under the title of "Description of a landscape -near Lake Como". We do in fact find, among other loose sheets in the -Codex Atlanticus, certain texts referring to valleys of the Alps -(see Nos. 1030, 1031 and note p. 237) and in the arrangement of the -loose sheets, of which the Codex Atlanticus has been formed, these -happen to be placed close to this text. The compiler stuck both on -the same folio sheet; and if this is not the reason for Dr. JORDAN'S -choosing such a title (Description &c.) I cannot imagine what it can -have been. It is, at any rate, a merely hypothetical statement. The -designation of the population of the country round a city as "the -enemy" (_nemici_) is hardly appropriate to Italy in the time of -Leonardo.] - -it had not been for certain people who succoured us with victuals, -all would have died of hunger. Now you see the state we are in. And -all these evils are as nothing compared with those which are -promised to us shortly. - -I know that as a friend you will grieve for my misfortunes, as I, in -former letters have shown my joy at your prosperity ... - -Notes about events observed abroad (1338-1339). - -1338. - -BOOK 43. OF THE MOVEMENT OF AIR ENCLOSED IN WATER. - -I have seen motions of the air so furious that they have carried, -mixed up in their course, the largest trees of the forest and whole -roofs of great palaces, and I have seen the same fury bore a hole -with a whirling movement digging out a gravel pit, and carrying -gravel, sand and water more than half a mile through the air. - -[Footnote: The first sixteen lines of this passage which treat of -the subject as indicated on the title line have no place in this -connexion and have been omitted.] - -[Footnote 2: _Ho veduto movimenti_ &c. Nothing of the kind happened -in Italy during Leonardo's lifetime, and it is therefore extremely -probable that this refers to the natural phenomena which are so -fully described in the foregoing passage. (Compare too, No. 1021.) -There can be no doubt that the descriptions of the Deluge in the -Libro di Pittura (Vol. I, No. 607-611), and that of the fall of a -mountain No. 610, l. 17-30 were written from the vivid impressions -derived from personal experience. Compare also Pl. XXXIV-XL.] - -1339. - -[Footnote: It may be inferred from the character of the writing, -which is in the style of the note in facsimile Vol. I, p. 297, that -this passage was written between 1470 and 1480. As the figure 6 at -the end of the text indicates, it was continued on another page, but -I have searched in vain for it. The reverse of this leaf is coloured -red for drawing in silver point, but has not been used for that -purpose but for writing on, and at about the same date. The passages -are given as Nos. 1217, 1218, 1219, 1162 and No. 994 (see note page -218). The text given above is obviously not a fragment of a letter, -but a record of some personal experience. No. 1379 also seems to -refer to Leonardo's journeys in Southern Italy.] - -Like a whirling wind which rushes down a sandy and hollow valley, -and which, in its hasty course, drives to its centre every thing -that opposes its furious course ... - -No otherwise does the Northern blast whirl round in its tempestuous -progress ... - -Nor does the tempestuous sea bellow so loud, when the Northern blast -dashes it, with its foaming waves between Scylla and Charybdis; nor -Stromboli, nor Mount Etna, when their sulphurous flames, having been -forcibly confined, rend, and burst open the mountain, fulminating -stones and earth through the air together with the flames they -vomit. - -Nor when the inflamed caverns of Mount Etna [Footnote 13: Mongibello -is a name commonly given in Sicily to Mount Etna (from Djebel, -Arab.=mountain). Fr. FERRARA, _Descrizione dell' Etna con la storia -delle eruzioni_ (Palermo, 1818, p. 88) tells us, on the authority of -the _Cronaca del Monastero Benedettino di Licordia_ of an eruption -of the Volcano with a great flow of lava on Sept. 21, 1447. The next -records of the mountain are from the years 1533 and 1536. A. Percy -neither does mention any eruptions of Etna during the years to which -this note must probably refer _Memoire des tremblements de terre de -la peninsule italique, Vol. XXII des Memoires couronnees et Memoires -des savants etrangers. Academie Royal de Belgique_). - -A literal interpretation of the passage would not, however, indicate -an allusion to any great eruption; particularly in the connection -with Stromboli, where the periodical outbreaks in very short -intervals are very striking to any observer, especially at night -time, when passing the island on the way from Naples to Messina.], -rejecting the ill-restained element vomit it forth, back to its own -region, driving furiously before it every obstacle that comes in the -way of its impetuous rage ... - -Unable to resist my eager desire and wanting to see the great ... of -the various and strange shapes made by formative nature, and having -wandered some distance among gloomy rocks, I came to the entrance of -a great cavern, in front of which I stood some time, astonished and -unaware of such a thing. Bending my back into an arch I rested my -left hand on my knee and held my right hand over my down-cast and -contracted eye brows: often bending first one way and then the -other, to see whether I could discover anything inside, and this -being forbidden by the deep darkness within, and after having -remained there some time, two contrary emotions arose in me, fear -and desire--fear of the threatening dark cavern, desire to see -whether there were any marvellous thing within it ... - -Drafts of Letters to Lodovico il Moro (1340-1345). - -1340. - -[Footnote: The numerous corrections, the alterations in the figures -(l. 18) and the absence of any signature prove that this is merely -the rough draft of a letter to Lodovico il Moro. It is one of the -very few manuscripts which are written from left to right--see the -facsimile of the beginning as here reproduced. This is probably the -final sketch of a document the clean of which copy was written in -the usual manner. Leonardo no doubt very rarely wrote so, and this -is probably the reason of the conspicuous dissimilarity in the -handwriting, when he did. (Compare Pl. XXXVIII.) It is noteworthy -too that here the orthography and abbreviations are also -exceptional. But such superficial peculiarities are not enough to -stamp the document as altogether spurious. It is neither a forgery -nor the production of any artist but Leonardo himself. As to this -point the contents leave us no doubt as to its authenticity, -particularly l. 32 (see No. 719, where this passage is repeated). -But whether the fragment, as we here see it, was written from -Leonardo's dictation--a theory favoured by the orthography, the -erasures and corrections--or whether it may be a copy made for or by -Melzi or Mazenta is comparatively unimportant. There are in the -Codex Atlanticus a few other documents not written by Leonardo -himself, but the notes in his own hand found on the reverse pages of -these leaves amply prove that they were certainly in Leonardo's -possession. This mark of ownership is wanting to the text in -question, but the compilers of the Codex Atlanticus, at any rate, -accepted it as a genuine document. - -With regard to the probable date of this projected letter see Vol. -II, p. 3.] - -Most illustrious Lord, Having now sufficiently considered the -specimens of all those who proclaim themselves skilled contrivers of -instruments of war, and that the invention and operation of the said -instruments are nothing different to those in common use: I shall -endeavour, without prejudice to any one else, to explain myself to -your Excellency showing your Lordship my secrets, and then offering -them to your best pleasure and approbation to work with effect at -opportune moments as well as all those things which, in part, shall -be briefly noted below. - -1) I have a sort of extremely light and strong bridges, adapted to -be most easily carried, and with them you may pursue, and at any -time flee from the enemy; and others, secure and indestructible by -fire and battle, easy and convenient to lift and place. Also methods -of burning and destroying those of the enemy. - -2) I know how, when a place is besieged, to take the water out of -the trenches, and make endless variety of bridges, and covered ways -and ladders, and other machines pertaining to such expeditions. - -3) Item. If, by reason of the height of the banks, or the strength -of the place and its position, it is impossible, when besieging a -place, to avail oneself of the plan of bombardment, I have methods -for destroying every rock or other fortress, even if it were founded -on a rock, &c. - -4) Again I have kinds of mortars; most convenient and easy to carry; -and with these can fling small stones almost resembling a storm; and -with the smoke of these causing great terror to the enemy, to his -great detriment and confusion. - -9) [8] And when the fight should be at sea I have kinds of many -machines most efficient for offence and defence; and vessels which -will resist the attack of the largest guns and powder and fumes. - -5) Item. I have means by secret and tortuous mines and ways, made -without noise to reach a designated [spot], even if it were needed -to pass under a trench or a river. - -6) Item. I will make covered chariots, safe and unattackable which, -entering among the enemy with their artillery, there is no body of -men so great but they would break them. And behind these, infantry -could follow quite unhurt and without any hindrance. - -7) Item. In case of need I will make big guns, mortars and light -ordnance of fine and useful forms, out of the common type. - -8) Where the operation of bombardment should fail, I would contrive -catapults, mangonels, _trabocchi_ and other machines of marvellous -efficacy and not in common use. And in short, according to the -variety of cases, I can contrive various and endless means of -offence and defence. - -10) In time of peace I believe I can give perfect satisfaction and -to the equal of any other in architecture and the composition of -buildings public and private; and in guiding water from one place to -another. - -Item: I can carry out sculpture in marble, bronze or clay, and also -in painting whatever may be done, and as well as any other, be he -whom he may. - -[32] Again, the bronze horse may be taken in hand, which is to be to -the immortal glory and eternal honour of the prince your father of -happy memory, and of the illustrious house of Sforza. - -And if any one of the above-named things seem to any one to be -impossible or not feasible, I am most ready to make the experiment -in your park, or in whatever place may please your Excellency--to -whom I commend myself with the utmost humility &c. - -1341. - -To my illustrious Lord, Lodovico, Duke of Bari, Leonardo da Vinci of -Florence-- Leonardo. - -[Footnote: Evidently a note of the superscription of a letter to the -Duke, and written, like the foregoing from left to right. The -manuscript containing it is of the year 1493. Lodovico was not -proclaimed and styled Duke of Milan till September 1494. The Dukedom -of Bari belonged to the Sforza family till 1499.] - -1342. - -You would like to see a model which will prove useful to you and to -me, also it will be of use to those who will be the cause of our -usefulness. - -[Footnote: 1342. 1343. These two notes occur in the same not very -voluminous MS. as the former one and it is possible that they are -fragments of the same letter. By the _Modello_, the equestrian -statue is probably meant, particularly as the model of this statue -was publicly exhibited in this very year, 1493, on tne occasion of -the marriage of the Emperor Maximilian with Bianca Maria Sforza.] - -1343. - -There are here, my Lord, many gentlemen who will undertake this -expense among them, if they are allowed to enjoy the use of -admission to the waters, the mills, and the passage of vessels and -when it is sold to them the price will be repaid to them by the -canal of Martesana. - -1344. - -I am greatly vexed to be in necessity, but I still more regret that -this should be the cause of the hindrance of my wish which is always -disposed to obey your Excellency. - -Perhaps your Excellency did not give further orders to Messer -Gualtieri, believing that I had money enough. - -I am greatly annoyed that you should have found me in necessity, and -that my having to earn my living should have hindered me ... - -[12] It vexes me greatly that having to earn my living has forced me -to interrupt the work and to attend to small matters, instead of -following up the work which your Lordship entrusted to me. But I -hope in a short time to have earned so much that I may carry it out -quietly to the satisfaction of your Excellency, to whom I commend -myself; and if your Lordship thought that I had money, your Lordship -was deceived. I had to feed 6 men for 56 months, and have had 50 -ducats. - -1345. - -And if any other comission is given me - by any ... -of the reward of my service. Because I am - not [able] to be ... -things assigned because meanwhile they - have ... to them ... -... which they well may settle rather than I ... -not my art which I wish to change and ... -given some clothing if I dare a sum ... - - -My Lord, I knowing your Excellency's - mind to be occupied ... -to remind your Lordship of my small matters - and the arts put to silence -that my silence might be the cause of making - your Lordship scorn ... -my life in your service. I hold myself ever - in readiness to obey ... - -[Footnote 11: See No. 723, where this passage is repeated.] - -Of the horse I will say nothing because - I know the times [are bad] -to your Lordship how I had still to receive - two years' salary of the ... -with the two skilled workmen who are constantly -in my pay and at my cost -that at last I found myself advanced the - said sum about 15 lire ... -works of fame by which I could show to - those who shall see it that I have been -everywhere, but I do not know where I -could bestow my work [more] ... - -[Footnote 17: See No. 1344 l. 12.] -I, having been working to gain my - living ... - -I not having been informed what it is, I find - myself ... - -[Footnote 19: In April, 1498, Leonardo was engaged in -painting the Saletta Nigra of the Castello at Milan. -(See G. MONGERI, _l'Arte in Milano_, 1872, p. 417.)] - -remember the commission to paint the - rooms ... - -I conveyed to your Lordship only requesting - you ... - - -[Footnote: The paper on which this is written is torn down the -middle; about half of each line remains.] - -Draft of letter to be sent to Piacenza (1346. 1347). - -[Footnote: 1346. 1347. Piacenza belonged to Milan. The Lord spoken -of in this letter, is no doubt Lodovico il Moro. One may infer from -the concluding sentence (No. 1346, l. 33. 34 and No. 1347), that -Leonardo, who no doubt compiled this letter, did not forward it to -Piacenza himself, but gave it to some influential patron, under -whose name and signature a copy of it was sent to the Commission.] - -1346. - -Magnificent Commissioners of Buildings I, understanding that your -Magnificencies have made up your minds to make certain great works -in bronze, will remind you of certain things: first that you should -not be so hasty or so quick to give the commission, lest by this -haste it should become impossible to select a good model and a good -master; and some man of small merit may be chosen, who by his -insufficiency may cause you to be abused by your descendants, -judging that this age was but ill supplied with men of good counsel -and with good masters; seeing that other cities, and chiefly the -city of the Florentines, has been as it were in these very days, -endowed with beautiful and grand works in bronze; among which are -the doors of their Baptistery. And this town of Florence, like -Piacenza, is a place of intercourse, through which many foreigners -pass; who, seeing that the works are fine and of good quality, carry -away a good impression, and will say that that city is well filled -with worthy inhabitants, seeing the works which bear witness to -their opinion; and on the other hand, I say seeing so much metal -expended and so badly wrought, it were less shame to the city if the -doors had been of plain wood; because, the material, costing so -little, would not seem to merit any great outlay of skill... - -Now the principal parts which are sought for in cities are their -cathedrals, and of these the first things which strike the eye are -the doors, by which one passes into these churches. - -Beware, gentlemen of the Commission, lest too great speed in your -determination, and so much haste to expedite the entrusting of so -great a work as that which I hear you have ordered, be the cause -that that which was intended for the honour of God and of men should -be turned to great dishonour of your judgments, and of your city, -which, being a place of mark, is the resort and gathering-place of -innumerable foreigners. And this dishonour would result if by your -lack of diligence you were to put your trust in some vaunter, who by -his tricks or by favour shown to him here should obtain such work -from you, by which lasting and very great shame would result to him -and to you. Thus I cannot help being angry when I consider what men -those are who have conferred with you as wishing to undertake this -great work without thinking of their sufficiency for it, not to say -more. This one is a potter, that one a maker of cuirasses, this one -is a bell-founder, another a bell ringer, and one is even a -bombardier; and among them one in his Lordship's service, who -boasted that he was the gossip of Messer Ambrosio Ferrere [Footnote -26: Messer Ambrogio Ferrere was Farmer of the Customs under the -Duke. Piacenza at that time belonged to Milan.], who has some power -and who has made him some promises; and if this were not enough he -would mount on horseback, and go to his Lord and obtain such letters -that you could never refuse [to give] him the work. But consider -where masters of real talent and fit for such work are brought when -they have to compete with such men as these. Open your eyes and look -carefully lest your money should be spent in buying your own -disgrace. I can declare to you that from that place you will procure -none but average works of inferior and coarse masters. There is no -capable man,--[33] and you may believe me,--except Leonardo the -Florentine, who is making the equestrian statue in bronze of the -Duke Francesco and who has no need to bring himself into notice, -because he has work for all his life time; and I doubt, whether -being so great a work, he will ever finish it [34]. - -The miserable painstakers ... with what hope may they expect a -reward of their merit? - -1347. - -There is one whom his Lordship invited from Florence to do this work -and who is a worthy master, but with so very much business he will -never finish it; and you may imagine that a difference there is to -be seen between a beautiful object and an ugly one. Quote Pliny. - -Letter to the Cardinal Ippolito d' Este. - -1348. - -[Footnote: This letter addressed to the Cardinal Ippolito d'Este is -here given from Marchese G. CAMPORI'S publication: _Nuovi documenti -per la Vita di Leonardo da Vinci. Atti e Memorie delle R. R. -Deputazioni di Storia patria per la provincie modenesi e parmenesi, -Vol. III._ It is the only text throughout this work which I have not -myself examined and copied from the original. The learned discoverer -of this letter--the only letter from Leonardo hitherto known as -having been sent--adds these interesting remarks: _Codesto Cardinale -nato ad Ercole I. nel 1470, arcivescovo di Strigonia a sette anni, -poi d'Agra, aveva conseguito nel 1497 la pingue ed ambita cattedra -di Milano, la dove avra conosciuto il Vinci, sebbene il poco amore -ch'ei professava alle arti lasci credere che le proteste di servitu -di Leonardo piu che a gratitudine per favori ricevuti e per opere a -lui allogate, accennino a speranza per un favore che si aspetta. -Notabile e ancora in questo prezioso documento la ripetuta signatura -del grande artista 'che si scrive Vincio e Vincius, non da Vinci -come si tiene comunemente, sebbene l'una e l'altra possano valere a -significare cosi il casato come il paese; restando a sapere se il -nome del paese di Vinci fosse assunto a cognome della famiglia di -Leonardo nel qual supposto piu propriamento avrebbe a chiamarsi -Leonardo Vinci, o Vincio (latinamente Vincius) com'egli stesso amo -segnarsi in questa lettera, e come scrissero parecchi contenporanei -di lui, il Casio, il Cesariano, Geoffrey Tory, il Gaurico, il -Bandello, Raffaelle Maffei, il Paciolo. Per ultimo non lascero -d'avvertire come la lettera del Vinci e assai ben conservata, di -nitida e larga scrittura in forma pienemente corrispondente a quella -dei suoi manoscritti, vergata all'uso comune da sinistra a destra, -anziche contrariamente come fu suo costume; ma indubbiamente -autentica e fornita della menzione e del suggello che fresca ancora -conserva l'impronta di una testa di profilo da un picciolo antico -cammeo._ (Compare No. 1368, note.)] - -Most Illustrious and most Reverend Lord. - The Lord Ippolito, Cardinal of Este - at Ferrare. - -Most Illustrious and most Reverend Lord. - -I arrived from Milan but a few days since and finding that my elder -brother refuses to - -carry into effect a will, made three years ago when my father -died--as also, and no less, because I would not fail in a matter I -esteem most important--I cannot forbear to crave of your most -Reverend Highness a letter of recommendation and favour to Ser -Raphaello Hieronymo, at present one of the illustrious members of -the Signoria before whom my cause is being argued; and more -particularly it has been laid by his Excellency the Gonfaloniere -into the hands of the said Ser Raphaello, that his Worship may have -to decide and end it before the festival of All Saints. And -therefore, my Lord, I entreat you, as urgently as I know how and am -able, that your Highness will write a letter to the said Ser -Raphaello in that admirable and pressing manner which your Highness -can use, recommending to him Leonardo Vincio, your most humble -servant as I am, and shall always be; requesting him and pressing -him not only to do me justice but to do so with despatch; and I have -not the least doubt, from many things that I hear, that Ser -Raphaello, being most affectionately devoted to your Highness, the -matter will issue _ad votum_. And this I shall attribute to your -most Reverend Highness' letter, to whom I once more humbly commend -myself. _Et bene valeat_. - -Florence XVIIIa 7bris 1507. -E. V. R. D. - -your humble servant -Leonardus Vincius, pictor. - -Draft of Letter to the Governor of Milan. - -1349. - -I am afraid lest the small return I have made for the great -benefits, I have received from your Excellency, have not made you -somewhat angry with me, and that this is why to so many letters -which I have written to your Lordship I have never had an answer. I -now send Salai to explain to your Lordship that I am almost at an -end of the litigation I had with my brother; that I hope to find -myself with you this Easter, and to carry with me two pictures of -two Madonnas of different sizes. These were done for our most -Christian King, or for whomsoever your Lordship may please. I should -be very glad to know on my return thence where I may have to reside, -for I would not give any more trouble to your Lordship. Also, as I -have worked for the most Christian King, whether my salary is to -continue or not. I wrote to the President as to that water which the -king granted me, and which I was not put in possession of because at -that time there was a dearth in the canal by reason of the great -droughts and because [Footnote:Compare Nos. 1009 and 1010. Leonardo -has noted the payment of the pension from the king in 1505.] its -outlets were not regulated; but he certainly promised me that when -this was done I should be put in possession. Thus I pray your -Lordship that you will take so much trouble, now that these outlets -are regulated, as to remind the President of my matter; that is, to -give me possession of this water, because on my return I hope to -make there instruments and other things which will greatly please -our most Christian King. Nothing else occurs to me. I am always -yours to command. [Footnote:1349. Charles d'Amboise, Marechal de -Chaumont, was Governor of Milan under Louis XII. Leonardo was in -personal communication with him so early as in 1503. He was absent -from Milan in the autumn of 1506 and from October l5l0--when he -besieged Pope Julius II. in Bologna--till his death, which took -place at Correggio, February 11, 1511. Francesco Vinci, Leonardo's -uncle, died--as Amoretti tells us--in the winter of l5l0-11 (or -according to Uzielli in 1506?), and Leonardo remained in Florence -for business connected with his estate. The letter written with -reference to this affair, No. 1348, is undoubtedly earlier than the -letters Nos. 1349 and 1350. Amoretti tells us, _Memorie Storiche_, -ch. II, that the following note existed on the same leaf in MS. C. -A. I have not however succeeded in finding it. The passage runs -thus: _Jo sono quasi al fine del mio letizio che io o con mie -fratetgli ... Ancora ricordo a V. Excia la facenda che o cum Ser -Juliana mio Fratello capo delli altri fratelli ricordandoli come se -offerse di conciar le cose nostre fra noi fratelli del comune della -eredita de mio Zio, e quelli costringa alla expeditione, quale -conteneva la lettera che lui me mando._] - -Drafts of Letters to the Superintendent of Canals and to Fr. Melzi. - -1350. - -Magnificent President, I am sending thither Salai, my pupil, who is -the bearer of this, and from him you will hear by word of mouth the -cause of my... - -Magnificent President, I... - -Magnificent President:--Having ofttimes remembered the proposals -made many times to me by your Excellency, I take the liberty of -writing to remind your Lordship of the promise made to me at my last -departure, that is the possession of the twelve inches of water -granted to me by the most Christian King. Your Lordship knows that I -did not enter into possession, because at that time when it was -given to me there was a dearth of water in the canal, as well by -reason of the great drought as also because the outlets were not -regulated; but your Excellency promised me that as soon as this was -done, I should have my rights. Afterwards hearing that the canal was -complete I wrote several times to your Lordship and to Messer -Girolamo da Cusano,who has in his keeping the deed of this gift; and -so also I wrote to Corigero and never had a reply. I now send -thither Salai, my pupil, the bearer of this, to whom your Lordship -may tell by word of mouth all that happened in the matter about -which I petition your Excellency. I expect to go thither this Easter -since I am nearly at the end of my lawsuit, and I will take with me -two pictures of our Lady which I have begun, and at the present time -have brought them on to a very good end; nothing else occurs to me. - -My Lord the love which your Excellency has always shown me and the -benefits that I have constantly received from you I have hitherto... - -I am fearful lest the small return I have made for the great -benefits I have received from your Excellency may not have made you -somewhat annoyed with me. And this is why, to many letters which I -have written to your Excellency I have never had an answer. I now -send to you Salai to explain to your Excellency that I am almost at -the end of my litigation with my brothers, and that I hope to be -with you this Easter and carry with me two pictures on which are two -Madonnas of different sizes which I began for the most Christian -King, or for whomsoever you please. I should be very glad to know -where, on my return from this place, I shall have to reside, because -I do not wish to give more trouble to your Lordship; and then, -having worked for the most Christian King, whether my salary is to -be continued or not. I write to the President as to the water that -the king granted me of which I had not been put in possession by -reason of the dearth in the canal, caused by the great drought and -because its outlets were not regulated; but he promised me certainly -that as soon as the regulation was made, I should be put in -possession of it; I therefore pray you that, if you should meet the -said President, you would be good enough, now that the outlets are -regulated, to remind the said President to cause me to be put in -possession of that water, since I understand it is in great measure -in his power. Nothing else occurs to me; always yours to command. - -Good day to you Messer Francesco. Why, in God's name, of all the -letters I have written to you, have you never answered one. Now wait -till I come, by God, and I shall make you write so much that perhaps -you will become sick of it. - -Dear Messer Francesco. I am sending thither Salai to learn from His -Magnificence the President to what end the regulation of the water -has come since, at my departure this regulation of the outlets of -the canal had been ordered, because His Magnificence the President -promised me that as soon as this was done I should be satisfied. It -is now some time since I heard that the canal was in order, as also -its outlets, and I immediately wrote to the President and to you, -and then I repeated it, and never had an answer. So you will have -the goodness to answer me as to that which happened, and as I am not -to hurry the matter, would you take the trouble, for the love of me, -to urge the President a little, and also Messer Girolamo Cusano, to -whom you will commend me and offer my duty to his Magnificence. - -[Footnote: 1350. 28-36. Draft of a letter to Francesco Melzi, born -l493--a youth therefore of about 17 in 1510. Leonardo addresses his -young friend as "Messer", as being the son of a noble house. Melzi -practised art under Leonardo as a dilettante and not as a pupil, -like Cesare da Sesto and others (See LERMOLIEFF, _Die Galerien_ &c., -p. 476).] - -Drafts of a letter to Giuliano de' Medici (1351-1352). - -135l. - -[Most illustrious Lord. I greatly rejoice most Illustrious Lord at -your...] - -I was so greatly rejoiced, most illustrious Lord, by the desired -restoration of your health, that it almost had the effect that [my -own health recovered]--[I have got through my illness]--my own -illness left me-- --of your Excellency's almost restored health. But -I am extremely vexed that I have not been able completely to satisfy -the wishes of your Excellency, by reason of the wickedness of that -deceiver, for whom I left nothing undone which could be done for him -by me and by which I might be of use to him; and in the first place -his allowances were paid to him before the time, which I believe he -would willingly deny, if I had not the writing signed by myself and -the interpreter. And I, seeing that he did not work for me unless he -had no work to do for others, which he was very careful in -solliciting, invited him to dine with me, and to work afterwards -near me, because, besides the saving of expense, he - -[Footnote 1351. 1353: It is clear from the contents of this notes -that they refer to Leonardo's residence in Rome in 1513-1515. Nor -can there be any doubt that they were addressed to Leonardo's patron -at the time: Giuliano de' Medici, third son of Lorenzo the -Magnificent and brother of Pope Leo X (born 1478). In 1512 he became -the head of the Florentine Republic. The Pope invited him to Rome, -where he settled; in 1513 he was named patrician with much splendid -ceremonial. The medal struck in honour of the event bears the words -MAG. IVLIAN. MEDICES. Leonardo too uses the style "Magnifico", in -his letter. Compare also No. 1377. - -GlNO CAPPONI (_Storia della Repubblica di Firenze_, Vol. III, p. -139) thus describes the character of Giuliano de' Medici, who died -in 1516: _Era il migliore della famiglia, di vita placida, grande -spenditore, tenendo intorno a se uomini ingegnosi, ed ogni nuova -cosa voleva provare._ - -See too GREGOROVIUS, _Geschichte der Stadi Rom_, VIII (book XIV. -III, 2): _Die Luftschlosser furstlicher Grosse, wozu ihn der Papst -hatte erheben wollen zerfielen. Julian war der edelste aller -damaligen Medici, ein Mensch von innerlicher Richtung, unbefriedigt -durch das Leben, mitten im Sonnenglanz der Herrlichkeit Leo's X. -eine dunkle Gestalt die wie ein Schatten voruberzog._ Giuliano lived -in the Vatican, and it may be safely inferred from No. 1352 l. 2, -and No. 1353 l. 4, that Leonardo did the same. - -From the following unpublished notice in the Vatican archives, which -M. Eug. Muntz, librarian of the Ecole des Beaux arts, Paris, has -done me the favour to communicate to me, we get a more accurate view -of Leonardo's relation to the often named GIORGIO TEDESCO: - -_Nota delle provisione_ (sic) _a da pagare per me in nome del nostro -ill. S. Bernardo Bini e chompa di Roma, e prima della illma sua -chonsorte ogni mese d. 800. - -A Ldo da Vinci per sua provisione d. XXXIII, e piu d. VII al detto -per la provisione di Giorgio tedescho, che sono in tutto d. 40. - -From this we learn, that seven ducats formed the German's monthly -wages, but according to No. 1353 l. 7 he pretended that eight ducats -had been agreed upon.] - -would acquire the Italian language. He always promised, but would -never do so. And this I did also, because that Giovanni, the German -who makes the mirrors, was there always in the workshop, and wanted -to see and to know all that was being done there and made it known -outside ... strongly criticising it; and because he dined with those -of the Pope's guard, and then they went out with guns killing birds -among the ruins; and this went on from after dinner till the -evening; and when I sent Lorenzo to urge him to work he said that he -would not have so many masters over him, and that his work was for -your Excellency's Wardrobe; and thus two months passed and so it -went on; and one day finding Gian Niccolo of the Wardrobe and asking -whether the German had finished the work for your Magnificence, he -told me this was not true, but only that he had given him two guns -to clean. Afterwards, when I had urged him farther, be left the -workshop and began to work in his room, and lost much time in making -another pair of pincers and files and other tools with screws; and -there he worked at mills for twisting silk which he hid when any one -of my people went in, and with a thousand oaths and mutterings, so -that none of them would go there any more. - -I was so greatly rejoiced, most Illustrious Lord, by the desired -restoration of your health, that my own illness almost left me. But -I am greatly vexed at not having been able to completely satisfy -your Excellency's wishes by reason of the wickedness of that German -deceiver, for whom I left nothing undone by which I could have hope -to please him; and secondly I invited him to lodge and board with -me, by which means I should constantly see the work he was doing and -with greater ease correct his errors while, besides this, he would -learn the Italian tongue, by means of which be could with more ease -talk without an interpreter; his moneys were always given him in -advance of the time when due. Afterwards he wanted to have the -models finished in wood, just as they were to be in iron, and wished -to carry them away to his own country. But this I refused him, -telling him that I would give him, in drawing, the breadth, length, -height and form of what he had to do; and so we remained in -ill-will. - -The next thing was that he made himself another workshop and pincers -and tools in his room where he slept, and there he worked for -others; afterwards he went to dine with the Swiss of the guard, -where there are idle fellows, in which he beat them all; and most -times they went two or three together with guns, to shoot birds -among the ruins, and this went on till evening. - -At last I found how this master Giovanni the mirror-maker was he who -had done it all, for two reasons; the first because he had said that -my coming here had deprived him of the countenance and favour of -your Lordship which always... The other is that he said that his -iron-workers' rooms suited him for working at his mirrors, and of -this he gave proof; for besides making him my enemy, he made him -sell all he had and leave his workshop to him, where he works with a -number of workmen making numerous mirrors to send to the fairs. - -1352. - -I was so greatly rejoiced, most Illustrious Lord, by the wished for -recovery of your health, that my own ills have almost left me; and I -say God be praised for it. But it vexes me greatly that I have not -been able completely to satisfy your Excellency's wishes by reason -of the wickedness of that German deceiver, for whom I left nothing -undone by which I could hope to please him; and secondly I invited -him to lodge and board with me, by which means I should see -constantly the work he was doing, for which purpose I would have a -table fixed at the foot of one of these windows, where he could work -with the file and finish the things made below; and so I should -constantly see the work he might do, and it could be corrected with -greater ease. - -Draft of letter written at Rome. - -1353. - -This other hindered me in anatomy, blaming it before the Pope; and -likewise at the hospital; and he has filled [4] this whole Belvedere -with workshops for mirrors; and he did the same thing in Maestro -Giorgio's room. He said that he had been promised [7] eight ducats -every month, beginning with the first day, when he set out, or at -latest when he spoke with you; and that you agreed. - -Seeing that he seldom stayed in the workshop, and that he ate a -great deal, I sent him word that, if he liked I could deal with him -separately for each thing that he might make, and would give him -what we might agree to be a fair valuation. He took counsel with his -neighbour and gave up his room, selling every thing, and went to -find... - -Miscellaneous Records (1354. 1355). - -1354. - -[Footnote: A puzzling passage, meant, as it would seem, for a jest. -Compare the description of Giants in Dante, _Inf_. XXI and XXII. -Perhaps Leonardo had the Giant Antaeus in his mind. Of him the myth -relates that he was a son of Ge, that he fed on lions; that he -hunted in Libya and killed the inhabitants. He enjoyed the -peculiarity of renewing his strength whenever he fell and came in -contact with his mother earth; but that Hercules lifted him up and -so conquered and strangled him. Lucan gives a full account of the -struggle. Pharsalia IV, 617. The reading of this passage, which is -very indistinctly written, is in many places doubtful.] - -Dear Benedetto de' Pertarti. When the proud giant fell because of -the bloody and miry state of the ground it was as though a mountain -had fallen so that the country shook as with an earthquake, and -terror fell on Pluto in hell. From the violence of the shock he lay -as stunned on the level ground. Suddenly the people, seeing him as -one killed by a thunderbolt, turned back; like ants running wildly -over the body of the fallen oak, so these rushing over his ample -limbs.......... them with frequent wounds; by which, the giant being -roused and feeling himself almost covered by the multitude, he -suddenly perceives the smarting of the stabs, and sent forth a roar -which sounded like a terrific clap of thunder; and placing his hands -on the ground he raised his terrible face: and having lifted one -hand to his head he found it full of men and rabble sticking to it -like the minute creatures which not unfrequently are found there; -wherefore with a shake of his head he sends the men flying through -the air just as hail does when driven by the fury of the winds. Many -of these men were found to be dead; stamping with his feet. - -And clinging to his hair, and striving to hide in it, they behaved -like sailors in a storm, who run up the ropes to lessen the force of -the wind [by taking in sail]. - -News of things from the East. - -Be it known to you that in the month of June there appeared a Giant, -who came from the Lybian desert... mad with rage like ants.... -struck down by the rude. - -This great Giant was born in Mount Atlas and was a hero ... and had -to fight against the Egyptians and Arabs, Medes and Persians. He -lived in the sea on whales, grampuses and ships. - -Mars fearing for his life took refuge under the... of Jove. - -And at the great fall it seemed as though the whole province quaked. - -1355. - -This spirit returns to the brain whence it had departed, with a loud -voice and with these words, it moved... - -And if any man though he may have wisdom or goodness ......... - -[Footnote: This passage, very difficult to decipher, is on the -reverse of a drawing at Windsor, Pl. CXXII, which possibly has some -connection with it. The drawing is slightly reduced in this -reproduction; the original being 25 cm. high by 19 cm. wide.] - -O blessed and happy spirit whence comest thou? Well have I known -this man, much against my will. This one is a receptacle of -villainy; he is a perfect heap of the utmost ingratitude combined -with every vice. But of what use is it to fatigue myself with vain -words? Nothing is to be found in them but every form of sin ... And -if there should be found among them any that possesses any good, -they will not be treated differently to myself by other men; and in -fine, I come to the conclusion that it is bad if they are hostile, -and worse if they are friendly. - -Miscellaneous drafts of letters and personal records (1356--1368). - -1356. - -All the ills that are or ever were, if they could be set to work by -him, would not satisfy the desires of his iniquitous soul; and I -could not in any length of time describe his nature to you, but I -conclude... - -1357. - -I know one who, having promised me much, less than my due, being -disappointed of his presumptuous desires, has tried to deprive me of -all my friends; and as he has found them wise and not pliable to his -will, he has menaced me that, having found means of denouncing me, -he would deprive me of my benefactors. Hence I have informed your -Lordship of this, to the end [that this man who wishes to sow the -usual scandals, may find no soil fit for sowing the thoughts and -deeds of his evil nature] so that he, trying to make your Lordship, -the instrument of his iniquitous and maliceous nature may be -disappointed of his desire. - -1358. - -[Footnote: Below this text we read gusstino--Giustino and in another -passage on the same page Justin is quoted (No. 1210, 1. 48). The two -have however no real connection.] - -And in this case I know that I shall make few enemies seeing that no -one will believe what I can say of him; for they are but few whom -his vices have disgusted, and he only dislikes those men whose -natures are contrary to those vices. And many hate their fathers, -and break off friendship with those who reprove their vices; and he -will not permit any examples against them, nor any advice. - -If you meet with any one who is virtuous do not drive him from you; -do him honour, so that he may not have to flee from you and be -reduced to hiding in hermitages, or caves or other solitary places -to escape from your treachery; if there is such an one among you do -him honour, for these are our Saints upon earth; these are they who -deserve statues from us, and images; but remember that their images -are not to be eaten by you, as is still done in some parts of India -[Footnote 15: In explanation of this passage I have received the -following communication from Dr. G. W. LEITNER of Lahore: "So far as -Indian customs are known to us, this practice spoken of by Leonardo -as 'still existing in some parts of India' is perfectly unknown; and -it is equally opposed to the spirit of Hinduism, Mohammedanism and -Sikhism. In central Thibet the ashes of the dead, when burnt, are -mixed with dough, and small figures--usually of Buddha--are stamped -out of them and some are laid in the grave while others are -distributed among the relations. The custom spoken of by Leonardo -may have prevailed there but I never heard of it." Possibly Leonardo -refers here to customs of nations of America.] where, when the -images have according to them, performed some miracle, the priests -cut them in pieces, being of wood, and give them to all the people -of the country, not without payment; and each one grates his portion -very fine, and puts it upon the first food he eats; and thus -believes that by faith he has eaten his saint who then preserves him -from all perils. What do you think here, Man, of your own species? -Are you so wise as you believe yourselves to be? Are these things to -be done by men? - -1359. - -As I told you in past days, you know that I am without any.... -Francesco d'Antonio. Bernardo di Maestro Jacopo. - -1360. - -Tell me how the things happened. - -1361. - -j lorezo\\\ 2 inbiadali\\\ 3 inferri de\\\ 4in lorezo\\\ 5[inno -abuil]\\ 6 in acocatu\\\ 7 per la sella\\\ 8colte di lor\\\ 9v -cavallott\\\ I0el uiagg\\\ IIal\\\ I2a lurez\\\ 13in biada\\\ -14inferri\\\ 15abuss\\\ 16in viagg\\\ 17alorz\\\ [Footnote: This -seems to be the beginning of a letter, but only the first words of -the lines have been preserved, the leaf being torn down the middle. -No translation is possible.] - -1362. - -And so may it please our great Author that I may demonstrate the -nature of man and his customs, in the way I describe his figure. - -[Footnote: A preparatory note for the passage given as No. 798, 11. -41--42.] - -1363. - -This writing distinctly about the kite seems to be my destiny, -because among the first recollections of my infancy, it seemed to me -that, as I was in my cradle, a kite came to me and opened my mouth -with its tail, and struck me several times with its tail inside my -lips. - -[Footnote: This note probably refers to the text No. 1221.] - -1364. - -[When I did well, as a boy you used to put me in prison. Now if I do -it being grown up, you will do worse to me.] - -1365. - -Tell me if anything was ever done. - -1366. - -Tell me if ever I did a thing which me .... - -1367. - -Do not reveal, if liberty is precious to you; my face is the prison -of love. - -[Footnote: This note seems to be a quotation.] - -1368. - -Maestro Leonardo of Florence. - -[Footnote: So Leonardo writes his name on a sheet with sundry short -notes, evidently to try a pen. Compare the signature with those in -Nos. 1341, 1348 and 1374 (see also No. 1346, l. 33). The form -"Lionardo" does not occur in the autographs. The Portrait of the -Master in the Royal Library at Turin, which is reproduced--slightly -diminished--on Pl. I, has in the original two lines of writing -underneath; one in red chalk of two or three words is partly -effaced: _lionardo it... lm_ (or _lai_?); the second written in -pencil is as follows: _fatto da lui stesso assai vecchio_. In both -of these the writing is very like the Master's, but is certainly -only an imitation.] - -Notes bearing Dates (1369--1378). - -1369. - -The day of Santa Maria _della Neve_ [of the Snows] August the 2nd -1473. [Footnote: W. An. I. 1368. 1369. This date is on a drawing of -a rocky landscape. See _Chronique des Arts_ 1881 no. 23: _Leonard de -Vinci a-t-il ete au Righi le 5 aout 1473_? letter by H. de -Geymuller. The next following date in the MSS. is 1478 (see No. -663). - -1370. - -On the 2nd of April 1489, book entitled 'Of the human figure'. -[Footnote: While the letters in the MS. notes of 1473 and 1478 are -very ornate, this note and the texts on anatomy on the same sheet -(for instance No. 805) are in the same simple hand as we see on Pl. -CXVI and CXIX. No 1370 is the only dated note of the years between -1480 and 1489, and the characters are in all essential points -identical with those that we see in the latest manuscripts written -in France (compare the facsimiles on Pl. CXV and p. 254), so that it -is hardly possible to determine exactly the date of a manuscript -from the style of the handwriting, if it does not betray the -peculiarities of style as displayed in the few notes dated previous -to l480.--Compare the facsimile of the manuscripts 1479 on Pl.LXII, -No. 2; No. 664, note, Vol. I p. 346. This shows already a marked -simplicity as compared with the calligraphy of I478. - -The text No. 720 belongs to the year 1490; No. 1510 to the year -1492; No. 1459, No. 1384 and No. 1460 to the year 1493; No. 1463, -No. 1517, No. 1024, 1025 and 1461 to the year 1494; Nos. 1523 and -1524 to the year 1497. - -1371. - -On the 1st of August 1499, I wrote here of motion and of weight. - -[Footnote:1371. _Scrissi qui_. Leonardo does not say where; still we -may assume that it was not in Milan. Amoretti writes, _Memorie -Storiche_, chap. XIX: _Sembra pertanto che non nel 1499 ma nel 1500, -dopo il ritorno e la prigionia del duca, sia da qui partito Lionardo -per andare a Firenze; ed e quindi probabile, che i mesi di governo -nuovo e incerto abbia passati coll' amico suo Francesco Melzi a -Vaprio, ove meglio che altrove studiar potea la natura, e -soprattutta le acque, e l'Adda specialmente, che gia era stato -l'ogetto delle sue idrostatiche ricerche_. At that time Melzi was -only six years of age. The next date is 1502; to this year belong -No. 1034, 1040, 1042, 1048 and 1053. The note No. 1525 belongs to -the year 1503.] - -1372. - -On the 9th of July 1504, Wednesday, at seven o'clock, died Ser Piero -da Vinci, notary at the Palazzo del Podesta, my father, --at seven -o'clock, being eighty years old, leaving behind ten sons and two -daughters. - -[Footnote: This statement of Ser Piero's age contradicts that of the -_Riassunto della portata di Antonio da Vinci_ (Leonardo's -grandfather), who speaks of Ser Piero as being thirty years old in -1457; and that of the _Riassunto della portata di Ser Piero e -Francesco_, sons of Antonia da Vinci, where Ser Piero is mentioned -as being forty in 1469. These documents were published by G. -UZIELLI, _Ricerche intorno a L. da Vinci, Firenze_, 1872, pp. 144 -and 146. Leonardo was, as is well known, a natural son. His mother -'La Catarina' was married in 1457 to Acchattabriga di Piero del -Vaccha da Vinci. She died in 1519. Leonardo never mentions her in -the Manuscripts. In the year of Leonardo's birth Ser Piero married -Albiera di Giovanni Amadoci, and after her death at the age of -thirty eight he again married, Francesca, daughter of Ser Giovanni -Lanfredi, then only fifteen. Their children were Leonardo's -halfbrothers, Antonio (b. 1476), Ser Giuliano (b. 1479), Lorenzo (b. -1484), a girl, Violante (b. 1485), and another boy Domenico (b. -1486); Domenico's descendants still exist as a family. Ser Piero -married for the third time Lucrezia di Guglielmo Cortigiani by whom -he had six children: Margherita (b. 1491), Benedetto (b. 1492), -Pandolfo (b. 1494), Guglielmo (b. 1496), Bartolommeo (b. 1497), and -Giovanni) date of birth unknown). Pierino da Vinci the sculptor -(about 1520-1554) was the son of Bartolommeo, the fifth of these -children. The dates of their deaths are not known, but we may infer -from the above passage that they were all still living in 1505.] - -1373. - -On Wednesday at seven o'clock died Ser Piero da Vinci on the 9th of -July 1504. - -[Footnote: This and the previous text it may be remarked are the -only mention made by Leonardo of his father; Nos. 1526, 1527 and No. -1463 are of the year 1504.] - -1374. - -Begun by me, Leonardo da Vinci, on the l2th of July 1505. - -[Footnote: Thus he writes on the first page of the MS. The title is -on the foregoing coversheet as follows: _Libro titolato -disstrafformatione coe_ (cioe) _d'un corpo nvn_ (in un) _altro sanza -diminuitione e acresscemento di materia._] - -1375. - -Begun at Milan on the l2th of September 1508. - -[Footnote: No. 1528 and No. 1529 belong to the same year. The text -Vol. I, No. 4 belongs to the following year 1509 (1508 old style); -so also does No. 1009.-- Nos. 1022, 1057 and 1464 belong to 1511.] - -1376. - -On the 9th of January 1513. - -[Footnote: No. 1465 belongs to the same year. No. 1065 has the next -date 1514.] - -1377. - -The Magnifico Giuliano de' Medici left Rome on the 9th of January -1515, just at daybreak, to take a wife in Savoy; and on the same day -fell the death of the king of France. - -[Footnote: Giuliano de Medici, brother to Pope Leo X.; see note to -Nos. 1351-1353. In February, 1515, he was married to Filiberta, -daughter of Filippo, Duke of Savoy, and aunt to Francis I, Louis -XII's successor on the throne of France. Louis XII died on Jan. 1st, -and not on Jan. 9th as is here stated.-- This addition is written in -paler ink and evidently at a later date.] - -1378. - -On the 24th of June, St John's day, 1518 at Amboise, in the palace -of... - -[Footnote: _Castello del clli_. The meaning of this word is obscure; -it is perhaps not written at full length.] - -_XXII._ - -_Miscellaneous Notes._ - -_The incidental memoranda scattered here and there throughout the -MSS. can have been for the most part intelligible to the writer -only; in many cases their meaning and connection are all the more -obscure because we are in ignorance about the persons with whom -Leonardo used to converse nor can we say what part he may have -played in the various events of his time. Vasari and other early -biographers give us a very superficial and far from accurate picture -of Leonardo's private life. Though his own memoranda, referring for -the most part to incidents of no permanent interest, do not go far -towards supplying this deficiency, they are nevertheless of some -importance and interest as helping us to solve the numerous -mysteries in which the history of Leonardo's long life remains -involved. We may at any rate assume, from Leonardo's having -committed to paper notes on more or less trivial matters on his -pupils, on his house-keeping, on various known and unknown -personages, and a hundred other trifies--that at the time they must -have been in some way important to him._ - -_I have endeavoured to make these 'Miscellaneous Notes' as complete -as possible, for in many cases an incidental memorandum will help to -explain the meaning of some other note of a similar kind. The first -portion of these notes (Nos. l379--l457), as well as those referring -to his pupils and to other artists and artificers who lived in his -house (1458--1468,) are arranged in chronological order. A -considerable proportion of these notes belong to the period between -1490 and 1500, when Leonardo was living at Milan under the patronage -of Lodovico il Moro, a time concerning which we have otherwise only -very scanty information. If Leonardo did really--as has always been -supposed,--spend also the greater part of the preceding decade in -Milan, it seems hardly likely that we should not find a single note -indicative of the fact, or referring to any event of that period, on -the numerous loose leaves in his writing that exist. Leonardo's life -in Milan between 1489 and 1500 must have been comparatively -uneventful. The MSS. and memoranda of those years seem to prove that -it was a tranquil period of intellectual and artistic labour rather -than of bustling court life. Whatever may have been the fate of the -MSS. and note books of the foregoing years--whether they were -destroyed by Leonardo himself or have been lost--it is certainly -strange that nothing whatever exists to inform us as to his life and -doings in Milan earlier than the consecutive series of manuscripts -which begin in the year 1489._ - -_There is nothing surprising in the fact that the notes regarding -his pupils are few and meagre. Excepting for the record of money -transactions only very exceptional circumstances would have prompted -him to make any written observations on the persons with whom he was -in daily intercourse, among whom, of course, were his pupils. Of -them all none is so frequently mentioned as Salai, but the character -of the notes does not--as it seems to me--justify us in supposing -that he was any thing more than a sort of factotum of Leonardo's -(see 1519, note)._ - -_Leonardo's quotations from books and his lists of titles supply -nothing more than a hint as to his occasional literary studies or -recreations. It was evidently no part of his ambition to be deeply -read (see Nrs. 10, 11, 1159) and he more than once expressly states -(in various passages which will be found in the foregoing sections) -that he did not recognise the authority of the Ancients, on -scientific questions, which in his day was held paramount. -Archimedes is the sole exception, and Leonardo frankly owns his -admiration for the illustrious Greek to whose genius his own was so -much akin (see No. 1476). All his notes on various authors, -excepting those which have already been inserted in the previous -section, have been arranged alphabetically for the sake of -convenience (1469--1508)._ - -_The passages next in order contain accounts and inventories -principally of household property. The publication of these--often -very trivial entries--is only justifiable as proving that the -wealth, the splendid mode of life and lavish expenditure which have -been attributed to Leonardo are altogether mythical; unless we put -forward the very improbable hypothesis that these notes as to money -in hand, outlay and receipts, refer throughout to an exceptional -state of his affairs, viz. when he was short of money._ - -_The memoranda collected at the end (No. 1505--1565) are, in the -original, in the usual writing, from left to right. Besides, the -style of the handwriting is at variance with what we should expect -it to be, if really Leonardo himself had written these notes. Most -of them are to be found in juxtaposition with undoubtedly authentic -writing of his. But this may be easily explained, if we take into -account the fact, that Leonardo frequently wrote on loose sheets. He -may therefore have occasionally used paper on which others had made -short memoranda, for the most part as it would seem, for his use. At -the end of all I have given Leonardo's will from the copy of it -preserved in the Melzi Library. It has already been printed by -Amoretti and by Uzielli. It is not known what has become of the -original document._ - -Memoranda before 1500 (1379-l413). - -1379. - -Find Longhi and tell him that you wait for him at Rome and will go -with him to Naples; make you pay the donation [Footnote 2: _Libro di -Vitolone_ see No. 1506 note.] and take the book by Vitolone, and the -measurements of the public buildings. [3] Have two covered boxes -made to be carried on mules, but bed-covers will be best; this makes -three, of which you will leave one at Vinci. [4] Obtain -the.............. from Giovanni Lombardo the linen draper of Verona. -Buy handkerchiefs and towels,.... and shoes, 4 pairs of hose, a -jerkin of... and skins, to make new ones; the lake of Alessandro. -[Footnote: 7 and fol. It would seem from the text that Leonardo -intended to have instructions in painting on paper. It is hardly -necessary to point out that the Art of illuminating was quite -separate from that of painting.] - -Sell what you cannot take with you. Get from Jean de Paris the -method of painting in tempera and the way of making white [Footnote: -The mysterious looking words, quite distinctly written, in line 1: -_ingol, amor a, ilopan a_ and on line 2: _enoiganod al_ are -obviously in cipher and the solution is a simple one; by reading -them backwards we find for _ingol_: logni-probably _longi_, -evidently the name of a person; for _amor a_: _a Roma_, for _ilopan -a_: _a Napoli_. Leonardo has done the same in two passages treating -on some secrets of his art Nos. 641 and 729, the only other places -in which we find this cipher employed; we may therefore conclude -that it was for the sake of secrecy that he used it. - -There can be no doubt, from the tenor of this passage, that Leonardo -projected a secret excursion to Naples. Nothing has hitherto been -known of this journey, but the significance of the passage will be -easily understood by a reference to the following notes, from which -we may infer that Leonardo really had at the time plans for -travelling further than Naples. From lines 3, 4 and 7 it is evident -that he purposed, after selling every thing that was not easily -portable, to leave a chest in the care of his relations at Vinci. -His luggage was to be packed into two trunks especially adapted for -transport by mules. The exact meaning of many sentences in the -following notes must necessarily remain obscure. These brief remarks -on small and irrelevant affairs and so forth are however of no -historical value. The notes referring to the preparations for his -journey are more intelligible.] - -salt, and how to make tinted paper; sheets of paper folded up; and -his box of colours; learn to work flesh colours in tempera, learn to -dissolve gum lac, linseed ... white, of the garlic of Piacenza; take -'de Ponderibus'; take the works of Leonardo of Cremona. Remove the -small furnace ... seed of lilies and of... Sell the boards of the -support. Make him who stole it, give you the ... learn levelling and -how much soil a man can dig out in a day. - -1380. - -This was done by Leone in the piazza of the castle with a chain and -an arrow. [Footnote: This note must have been made in Milan; as we -know from the date of the MS.] - -1381. - -NAMES OF ENGINEERS. - -Callias of Rhodes, Epimachus the Athenian, Diogenes, a philosopher, -of Rhodes, Calcedonius of Thrace, Febar of Tyre, Callimachus the -architect, a master of fires. [Footnote: Callias, Architect of -Aradus, mentioned by Vitruvius (X, 16, 5).--Epimachus, of Athens, -invented a battering-enginee for Demetrius Poliorketes (Vitruvius X, -16, 4).--Callimachus, the inventor of the Corinthian capital (Vitr. -IV, I, 9), and of the method of boring marble (Paus. I, 26, 7), was -also famous for his casts in bronze (Plin. XXXIV, 8, 19). He -invented a lamp for the temple of Athene Polias, on the Acropolis of -Athens (Paus. I, 26, 7)--The other names, here mentioned, cannot be -identified.] - -1382. - -Ask maestro Lodovico for 'the conduits of water'. [Footnote: -Condotti d'acqua. Possibly a book, a MS. or a map.] - -1383. - -... at Pistoja, Fioravante di Domenico at Florence is my most -beloved friend, as though he were my [brother]. [Footnote: On the -same sheet is the text No. 663.] - -1384. - -On the 16th day of July. - -Caterina came on 16th day of July, 1493. - -Messer Mariolo's Morel the Florentin, has a big horse with a fine -neck and a beautiful head. - -The white stallion belonging to the falconer has fine hind quarters; -it is behind the Comasina Gate. - -The big horse of Cermonino, of Signor Giulio. [Footnote: Compare -Nos. 1522 and 1517. Caterina seems to have been his housekeeper.] - -1385. - -OF THE INSTRUMENT. - -Any one who spends one ducat may take the instrument; and he will -not pay more than half a ducat as a premium to the inventor of the -instrument and one grosso to the workman every year. I do not want -sub-officials. [Footnote: Refers perhaps to the regulation of the -water in the canals.] - -1386. - -Maestro Giuliano da Marliano has a fine herbal. He lives opposite to -Strami the Carpenters. [Footnote: Compare No. 616, note. 4. -legnamiere (milanese dialect) = legnajuolo.] - -1387. - -Christofano da Castiglione who lives at the Pieta has a fine head. - -1388. - -Work of ... of the stable of Galeazzo; by the road of Brera -[Footnote 4: Brera, see No. 1448, II, 13]; benefice of Stanghe -[Footnote 5:Stanghe, see No. 1509.]; benefice of Porta Nuova; -benefice of Monza; Indaco's mistake; give first the benefices; then -the works; then ingratitude, indignity and lamentations. - -1389. - -Chiliarch--captain of 1000. - -Prefects--captains. - -A legion, six thousand and sixty three men. - -1390. - -A nun lives at La Colomba at Cremona; she works good straw plait, -and a friar of Saint Francis. [Footnote: _La Colomba_ is to this day -the name of a small house at Cremona, decorated with frescoes.] - -1391. - -Needle,--Niccolao,--thread,--Ferrando, -lacopo -Andrea,--canvas,--stone,--colours, --brushes,--pallet,--sponge,--the -panel of the Duke. - -1392. - -Messer Gian Domenico Mezzabarba and Messer Giovanni Franceso -Mezzabarba. By the side of Messer Piero d'Anghiera. - -1393. - -Conte Francesco Torello. - -1394. - -Giuliano Trombetta,--Antonio di Ferrara, --Oil of .... [Footnote: -Near this text is the sketch of a head drawn in red chalk.] - -1395. - -Paul was snatched up to heaven. [Footnote: See the facsimile of this -note on Pl. XXIII No. 2.] - -1396. - -Giuliano da Maria, physician, has a steward without hands. - -1397. - -Have some ears of corn of large size sent from Florence. - -1398. - -See the bedstead at Santa Maria. Secret. - -1399. - -Arrigo is to have 11 gold Ducats. Arrigo is to have 4 gold ducats in -the middle of August. - -1400. - -Give your master the instance of a captain who does not himself win -the victory, but the soldiers do by his counsels; and so he still -deserves the reward. - -1401. - -Messer Pier Antonio. - -1402. - -Oil,--yellow,--Ambrosio,--the mouth, --the farmhouse. - -1403. - -My dear Alessandro from Parma, by the hand of ... - -1404. - -Giovannina, has a fantastic face,--is at Santa Caterina, at the -Hospital. [Footnote: Compare the text on the same page: No. 667.] - -1405. - -24 tavole make 1 perch. 4 trabochi make 1 tavola. 4 braccia and a -half make a trabocco. A perch contains 1936 square braccia, or 1944. - -1406. - -The road of Messer Mariolo is 13 1/4 braccia wide; the House of -Evangelista is 75. - -It enters 7 1/2 braccia in the house of Mariolo. [Footnote: On this -page and that which faces it, MS.I2 7la, are two diagrams with -numerous reference numbers, evidently relating to the measurements -of a street.] - -1407. - -I ask at what part of its curved motion the moving cause will leave -the thing moved and moveable. - -Speak to Pietro Monti of these methods of throwing spears. - -1408. - -Antonio de' Risi is at the council of Justice. - -1409. - -Paolo said that no machine that moves another .... [Footnote: The -passage, of which the beginning is here given, deals with questions -in mechanics. The instances in which Leonardo quotes the opinions of -his contemporaries on scientific matters are so rare as to be worth -noticing. Compare No. 901. ] - -1410. - -Caravaggio. [Footnote: _Caravaggio_, a village not far from the Adda -between Milan and Brescia, where Polidoro and Michelangelo da -Caravaggio were born. This note is given in facsimile on Pl. XIII, -No. I (above, to the left). On Pl. XIII, No. 2 above to the right we -read _cerovazo_.] - -1411. - -Pulleys,--nails,--rope,--mercury,--cloth, Monday. - -1412. - -MEMORANDUM. - -Maghino, Speculus of Master Giovanni the Frenchman; Galenus on -utility. - -1413. - -Near to Cordusio is Pier Antonio da Tossano and his brother -Serafino. [Footnote: This note is written between lines 23 and 24 of -the text No. 710. Corduso, Cordusio (_curia ducis_) = Cordus in the -Milanese dialect, is the name of a Piazza between the Via del -Broletto and the Piazza de' Mercanti at Milan.. In the time of il -Moro it was the centre of the town. The persons here named were -members of the noble Milanese family de'Fossani; Ambrogio da -Possano, the contemporary painter, had no connection with them.] - -1414. - -Memoranda after 1500 (1414--1434) - -1414. - -Paul of Vannochio at Siena ... The upper chamber for the apostles. - -[4] Buildings by Bramante. - -The governor of the castle made a prisoner. - -[6] Visconti carried away and his son killed. [Footnote 6: Visconti. -_Chi fosse quel Visconte non sapremmo indovinare fra tanti di questo -nome. Arluno narra che allora atterrate furono le case de' Viconti, -de' Castiglioni, de' Sanseverini, e de' Botta e non e improbabile -che ne fossero insultati e morti i padroni. Molti Visconti annovera -lo stesso Cronista che per essersi rallegrati del ritorno del duca -in Milano furono da' Francesi arrestati, e strascinati in Francia -come prigionieri di stato; e fra questi Messer Francesco Visconti, e -suo figliuolo Battista_. (AMORETTI, Mem. Stor. XIX.).] - -Giovanni della Rosa deprived of his money. - -Borgonzio began ....; and moreover his fortunes fled. [Footnote 8: -Borgonzio o Brugonzio Botta fu regolatore delle ducali entrate sotto -il Moro, alla cui fuga la casa sua fu pur messa a sacco da' -partitanti francesi. (AMORETTI, l. c.)] - -The Duke has lost the state, property and liberty and none of his -entreprises was carried out by him. - -[Footnote: l. 4--10 This passage evidently refers to events in Milan -at the time of the overthrow of Ludovico il Moro. Amoretti published -it in the '_Memorie Storiche_' and added copious notes.] - -1415. - -Ambrosio Petri, St. Mark, 4 boards for the window, 2 ..., 3 the -saints of chapels, 5 the Genoese at home. - -1416. - -Piece of tapestry,--pair of compasses,-- Tommaso's book,--the book -of Giovanni Benci,--the box in the custom-house,--to cut the -cloth,--the sword-belt,--to sole the boots, --a light hat,--the cane -from the ruined houses,--the debt for the table linen, ---swimming-belt,--a book of white paper for drawing,--charcoal.--How -much is a florin ...., a leather bodice. - -1417. - -Borges shall get for you the Archimedes from the bishop of Padua, -and Vitellozzo the one from Borgo a San Sepolcro [Footnote 3: Borgo -a San Sepolcro, where Luca Paciolo, Leonardo's friend, was born.] - -[Footnote: Borges. A Spanish name.] - -1418. - -Marzocco's tablet. - -1419. - -Marcello lives in the house of Giacomo da Mengardino. - -1420. - -Where is Valentino?--boots,--boxes in the -custom-house,...,--[Footnote 5: Carmine. A church and monastery at -Florence.] the monk at the Carmine,--squares,--[Footnotes 7 and 8: -Martelli, Borgherini; names of Florentine families. See No. 4.] -Piero Martelli,--[8] Salvi Borgherini,--send back the bags,--a -support for the spectacles,--[Footnote 11: San Gallo; possibly -Giuliano da San Gallo, the Florentine architect.] the nude study of -San Gallo,--the cloak. Porphyry,--groups,--square,--[Footnote 16: -Pandolfini, see No. 1544 note.] Pandolfino. [Footnote: Valentino. -Cesare Borgia is probably meant. After being made Archbishop of -Valence by Alexander VI he was commonly called Valentinus or -Valentino. With reference to Leonardo's engagements by him see pp. -224 and 243, note.] - -1421. - -Concave mirrors; philosophy of Aristotle;[Footnote 2: _Avicenna_ -(Leonardo here writes it Avinega) the Arab philosopher, 980-1037, -for centuries the unimpeachable authority on all medical questions. -Leonardo possibly points here to a printed edition: _Avicennae -canonum libri V, latine_ 1476 _Patavis._ Other editions are, Padua -1479, and Venice 1490.] the books of Avicenna Italian and Latin -vocabulary; Messer Ottaviano Palavicino or his Vitruvius [Footnote -3: _Vitruvius._ See Vol. I, No. 343 note.]. bohemian knives; -Vitruvius[Footnote 6: _Vitruvius._ See Vol. I, No. 343 note.]; go -every Saturday to the hot bath where you will see naked men; - -'Meteora' [Footnote 7: _Meteora._ See No. 1448, 25.], - -Archimedes, on the centre of gravity; [Footnote 9: The works of -Archimedes were not printed during Leonardo's life-time.] anatomy -[Footnote 10: Compare No. 1494.] Alessandro Benedetto; The Dante of -Niccolo della Croce; Inflate the lungs of a pig and observe whether -they increase in width and in length, or in width diminishing in -length. - -[Footnote 14: _Johannes Marliani sua etate philosophorum et -medicorum principis et ducalis phisic. primi de proportione motuum -velocitate questio subtilissima incipit ex ejusdem Marliani -originali feliciter extracta, M(ilano)_ 1482. - -Another work by him has the title: _Marlianus mediolanensis. Questio -de caliditate corporum humanorum tempore hiemis ed estatis et de -antiparistasi ad celebrem philosophorum et medicorum universitatem -ticinensem._ 1474.] Marliano, on Calculation, to Bertuccio. -Albertus, on heaven and earth [Footnote 15: See No. 1469, 1. 7.], -[from the monk Bernardino]. Horace has written on the movements of -the heavens. - -[Footnote: _Filosofia d'Aristotele_ see No. 1481 note.] - -1422. - -Of the three regular bodies as opposed to some commentators who -disparage the Ancients, who were the originators of grammar and the -sciences and ... - -1423. - -The room in the tower of Vaneri. - -[Footnote: This note is written inside the sketch of a plan of a -house. On the same page is the date 1513 (see No. 1376).] - -1424. - -The figures you will have to reserve for the last book on shadows -that they may appear in the study of Gerardo the illuminator at San -Marco at Florence. - -[Go to see Melzo, and the Ambassador, and Maestro Bernardo]. - -[Footnote: L. 1-3 are in the original written between lines 3 and 4 -of No. 292. But the sense is not clear in this connection. It is -scarcely possible to devine the meaning of the following sentence. - -2. 3. _Gherardo_ Miniatore, a famous illuminator, 1445-1497, to whom -Vasari dedicated a section of his Lives (Vol. II pp. 237-243, ed. -Sansoni 1879). - -5. _Bernardo_, possibly the painter Bernardo Zenale.] - -1425. - -Hermes the philosopher. - -1426. - -Suisset, viz. calculator,--Tisber, --Angelo Fossobron,--Alberto. - -1427. - -The structure of the drawbridge shown me by Donnino, and why _c_ and -_d_ thrust downwards. - -[Footnote: The sketch on the same page as this text represents two -poles one across the other. At the ends of the longest are the -letter _c_ and _d_. The sense of the passage is not rendered any -clearer.] - -1428. - -The great bird will take its first flight;-- on the back of his -great swan,--filling the universe with wonders; filling all writings -with his fame and bringing eternal glory to his birthplace. - -[Footnote: This seems to be a speculation about the flying machine -(compare p. 271).] - -1429. - -This stratagem was used by the Gauls against the Romans, and so -great a mortality ensued that all Rome was dressed in mourning. - -[Footnote: Leonardo perhaps alludes to the Gauls under Brennus, who -laid his sword in the scale when the tribute was weighed.] - -1430. - -Alberto da Imola;--Algebra, that is, the demonstration of the -equality of one thing to another. - -1431. - -Johannes Rubicissa e Robbia. - -1432. - -Ask the wife of Biagio Crivelli how the capon nurtures and hatches -the eggs of the hen,--he being drunk. - -1433. - -The book on Water to Messer Marco Antonio. - -[Footnote: Possibly Marc-Antonio della Torre, see p. 97.] - -1434. - -Have Avicenna's work on useful inventions translated; spectacles -with the case, steel and fork and...., charcoal, boards, and paper, -and chalk and white, and wax;.... .... for glass, a saw for bones -with fine teeth, a chisel, inkstand ........ three herbs, and Agnolo -Benedetto. Get a skull, nut,--mustard. - -Boots,--gloves, socks, combs, papers, towels, shirts,.... -shoe-tapes,--..... shoes, penknife, pens. A skin for the chest. - -[Footnote: 4. Lapis. Compare Condivi, _Vita di Michelagnolo -Buonarotti_, Chap. XVIII.: _Ma egli_ (Michelangelo) _non avendo che -mostrare, prese una penna (percioche in quel tempo il lapis non era -in uso) e con tal leggiadria gli dipinse una mano ecc._ The incident -is of the year l496.--Lapis means pencil, and chalk (_matita_). -Between lines 7 and 8 are the texts given as Nos. 819 and No. 7.] - -Undated memoranda (1435-1457). - -1435. - -The book of Piero Crescenze,--studies from the nude by Giovanni -Ambrosio,--compasses, --the book of Giovanni Giacomo. - -1436. - -MEMORARDUM. - -To make some provisions for my garden, --Giordano, _De -Ponderibus_[Footnote 3: _Giordano_. Jordanus Nemorarius, a -mathematician of the beginning of the XIIIth century. No particulars -of his life are known. The title of his principal work is: -_Arithmetica decem libris demonstrata_, first published at Paris -1496. In 1523 appeared at Nuremberg: _Liber Jordani Nemorarii de -ponderibus, propositiones XIII et earundem demonstrationes, -multarumque rerum rationes sane pulcherrimas complectens, nunc in -lucem editus._],--the peacemaker, the flow and ebb of the sea,--have -two baggage trunks made, look to Beltraffio's [Footnote 6: -_Beltraffio_, see No. 465, note 2. - -There are sketches by the side of lines 8 and 10.] lathe and have -taken the stone,--out leave the books belonging to Messer Andrea the -German,-- make scales of a long reed and weigh the substance when -hot and again when cold. The mirror of Master Luigi; _A b_ the flow -and ebb of the water is shown at the mill of Vaprio,--a cap. - -1437. - -Giovanni Fabre,--Lazaro del Volpe,-- the common,--Ser Piero. - -[Footnote: These names are inserted on a plan of plots of land -adjoining the Arno.] - -1438. - -[Lactantius], [the book of Benozzo], groups,--to bind the book,--a -lantern,--Ser Pecantino,--Pandolfino.--[Rosso]--a square, --small -knives,--carriages,--curry combs-- cup. - -1439. - -Quadrant of Carlo Marmocchi,--Messer Francesco Araldo,--Ser -Benedetto d'Accie perello,--Benedetto on arithmetic,--Maestro Paulo, -physician,--Domenico di Michelino,-- ...... of the Alberti,--Messer -Giovanni Argimboldi. - -1440. - -Colours, formula,--Archimedes,--Marcantonio. - -Tinned iron,--pierced iron. - -1441. - -See the shop that was formerly Bartolommeo's, the stationer. - -[Footnote: 6. _Marc Antonio_, see No. 1433.] - -1442. - -The first book is by Michele di Francesco Nabini; it treats on -science. - -1443. - -Messer Francesco, physician of Lucca, with the Cardinal Farnese. - -[Footnote: _Alessandro Farnese_, afterwards Pope Paul III was -created in 1493 Cardinal di San Cosimo e San Damiano, by Alexander -VI.] - -1444. - -Pandolfino's book [Footnote 1: _Pandolfino, Agnolo_, of Florence. It -is to this day doubtful whether he or L. B. Alberti was the author -of the famous work '_Del Governo della Famiglia_'. It is the more -probable that Leonardo should have meant this work by the words _il -libro_, because no other book is known to have been written by -Pandolfino. This being the case this allusion of Leonardo's is an -important evidence in favour of Pandolfino's authorship (compare No. -1454, line 3).],--knives,--a pen for ruling,--to have the vest -dyed,--The library at St.-Mark's,--The library at Santo -Spirito,--Lactantius of the Daldi [Footnote 7: The works of -Lactantius were published very often in Italy during Leonardo's -lifetime. The first edition published in 1465 "_in monastero -sublacensi_" was also the first book printed in Italy.],--Antonio -Covoni,--A book by Maestro Paolo Infermieri, --Boots, shoes and -hose,--(Shell)lac, --An apprentice to do the models for me. Grammar, -by Lorenzo de Medici,--Giovanni del Sodo,--Sansovino, [Footnote 15: -_Sansovino_, Andrea--the _sculptor_; 1460-1529.]--a ruler,--a very -sharp knife,--Spectacles,--fractions...., ---repair.........,--Tomaso's book,-- Michelagnolo's little chain; -Learn the multiplication of roots from Maestro Luca;--my map of the -world which Giovanni Benci has [Footnote 25: Leonardo here probably -alludes to the map, not executed by him (See p. 224), which is with -the collection of his MSS. at Windsor, and was published in the -_Archaeologia_ Vol. XI (see p. 224).];-Socks,--clothes from the -customhouse-officier,--Red Cordova leather,--The map of the world, -of Giovanni Benci,--a print, the districts about Milan--Market book. - -Get the Friar di Brera to show you [the book] '_de Ponderibus_' -[Footnote 11: _Brera_, now _Palazzo delle Scienze ed Arti. Until -1571 it was the monastery of the order of the Umiliati and -afterwards of the Jesuits. - -_De ponderibus_, compare No. 1436, 3.],-- - -Of the measurement of San Lorenzo,-- - -I lent certain groups to Fra Filippo de Brera, [Footnote 13: -_Brera_, now _Palazzo delle Scienze ed Arti. Until 1571 it was the -monastery of the order of the Umiliati and afterwards of the -Jesuits. - -_De ponderibus_, compare No. 1436, 3.]-- - -Memorandum: to ask Maestro Giovannino as to the mode in which the -tower of Ferrara is walled without loopholes,-- - -Ask Maestro Antonio how mortars are placed on bastions by day or by -night,-- - -Ask Benedetto Portinari how the people go on the ice in Flanders,-- - -On proportions by Alchino, with notes by Marliano, from Messer -Fazio,-- - -The measurement of the sun, promised me by Maestro Giovanni, the -Frenchman,-- - -The cross bow of Maestro Gianetto,-- - -The book by Giovanni Taverna that Messer Fazio,-- - -You will draw Milan [21],-- - -The measurement of the canal, locks and supports, and large boats; -and the expense,-- - -Plan of Milan [Footnote 23: _Fondamento_ is commonly used by -Leonardo to mean ground-plan. See for instance p. 53.],-- - -Groups by Bramante [Footnote 24: _Gruppi_. See Vol. I p. 355, No. -600, note 9.],-- - -The book on celestial phenomena by Aristoteles, in Italian [Footnote -25: _Meteora_. By this Leonardo means no doubt the four books. He -must refer here to a MS. translation, as no Italian translation is -known to have been published (see No. 1477 note).],-- - -Try to get Vitolone, which is in the library at Pavia [Footnote 26: -_Vitolone_ see No. 1506, note. - -_Libreria di Pavia_. One of the most famous of Italian libraries. -After the victory of Novara in April 1500, Louis XII had it conveyed -to France, '_come trofeo di vittoria_'!] and which treats of -Mathematics,--He had a master [learned] in waterworks and get him to -explain the repairs and the costs, and a lock and a canal and a mill -in the Lombard fashion. - -A grandson of Gian Angelo's, the painter has a book on water which -was his fathers. - -Paolino Scarpellino, called Assiolo has great knowledge of water -works. - -[Footnote 12: _Sco Lorenzo_. A church at Milan, see pp. 39, 40 and -50.] - -[Footnote 13. 24: _Gruppi_. See Vol. I p. 355, No. 600, note 9.] - -[Footnote 16: The _Portinari_ were one of the great merchant- -families of Florence.] - -1449. - -Francesco d'Antonio at Florence. - -1450. - -Giuliano Condi[1],--Tomaso Ridolfi,-- Tomaso Paganelli,--Nicolo del -Nero,--Simone Zasti,--Nasi,--the heir of Lionardo Manelli, ---Guglielmo di Ser Martino,--Bartolomeo del Tovaglia,--Andrea -Arrigucci,-- Nicolo Capponi,--Giovanni Portinari. - -[Footnote: I. _Guiliano Gondi_. Ser Piero da Vinci, Leonardo's -father, lived till 1480, in a house belonging to Giuliano Gondi. In -1498 this was pulled down to make room for the fine Palazzo built on -the Piazza San Firenze by Giuliano di San Gallo, which still exists. -In the _Riassunto del Catasto di Ser Piero da Vinci_, 1480, Leonardo -is not mentioned; it is evident therefore that he was living -elsewhere. It may be noticed incidentally that in the _Catasto di -Giuliano Gondi_ of the same year the following mention is made of -his four eldest sons: - -_Lionardo mio figliuolo d'eta d'anni 29, non fa nulla, Giovambatista -d'eta d'anni 28 in Ghostantinopoli, Billichozo d'eta d'anni 24 a -Napoli, Simone d'eta d'anni 23 in Ungheria._ - -He himself was a merchant of gold filigree (_facciamo lavorare una -bottegha d'arte di seta ... facciamo un pocho di trafico a Napoli_}. -As he was 59 years old in 1480, he certainly would not have been -alive at the time of Leonardo's death. But Leonardo must have been -on intimate terms with the family till the end of his life, for in a -letter dated June 1. 1519, in which Fr. Melzi, writing from Amboise, -announces Leonardo's death to Giuliano da Vinci at Florence (see p. -284), he says at the end "_Datemene risposta per i Gondi_" (see -UZIELLI, _Ricerche_, passim). - -Most of the other names on the list are those of well-known -Florentine families.] - -1451. - -Pandolfino. - -1452. - -Vespuccio will give me a book of Geometry. - -[Footnote: See No. 844, note, p. 130.] - -1453. - -Marcantonio Colonna at Santi Apostoli. - -[Footnote: In July 1506 Pope Julius II gave Donna Lucrezia della -Rovere, the daughter of his sister Lucchina, in marriage to the -youthful Marcantonio Colonna, who, like his brothers Prospero and -Fabrizio, became one of the most famous Captains of his family. He -gave to him Frascati and made him a present of the palazzo he had -built, when Cardinal, near the church of Santi Apostoli which is now -known as the Palazzo Colonna (see GREGOROVIUS, _Gesch. der Stadt -Rom._ Vol. VIII, book XIV I, 3. And COPPI, _Mem. Colonnesi_ p. -251).] - -1454. - -A box, a cage,-- A square, to make the bird [Footnote 2: Vasari -states that Leonardo invented mechanical birds which moved through -the air. Compare No. 703.],-- Pandolfino's book, mortar [?],-- Small -knives, Venieri for the - -[Footnote: Much of No. 1444 is repeated in this memorandum.] - -Pen for ruling, stone,--star,-- - -To have the vest dyed, Alfieri's tazza,-- - -The Libraries, the book on celestial - phenomena,-- - -Lactantius of the go to the house of -Daldi,-- the Pazzi, - -Book from Maestro small box,-- -Paolo Infermieri,-- - -Boots, shoes and small gimlet,-- -hose, - -Lac, .......,-- - -An apprentice for .....,-- -models, - -Grammar of Lo- the amount of the -renzo de' Medici, ... - -Giovanni del Sodo ..... -for...,--the broken - -Sansovino, the.... - -Piero di Cosino the wings,-- - -[Footnote 16: _Pier di Cosimo_ the well known Florentine painter -1462-1521. See VASARI, _Vite_ (Vol. IV, p. 134 ed. Sansoni 1880) -about Leonardo's influence on Piero di Cosimo's style of painting.] - -Filippo and Lorenzo [Footnote 17: _Filippo e Lorenzo_; probably the -painters Filippino Lippi and Lorenzo di Credi. L. di Credi's -pictures and Vasari's history of that painter bear ample evidence to -his intimate relations with Leonardo.],--A ruler-,-- Spectacles,--to -do the..... again,--Tomaso's book,--Michelagnolo's chain,--The -multiplication of roots,--Of the bow and strinch,--The map of the -world from Benci,-- Socks,--The clothes from the custom-house -officier,--Cordova leather,--Market books, --waters of -Cronaca,--waters of Tanaglino..., --the caps,--Rosso's mirror; to -see him make it,--1/3 of which I have 5/6,--on the celestial -phenomena, by Aristotle [Footnote 36: _Meteora_. See No. 1448, -25.],--boxes of Lorenzo di Pier Francesco [Footnote 37: _Lorenzo di -Pier Francesco_ and his brother _Giovanni_ were a lateral branch of -the _Medici_ family and changed their name for that of -Popolani.],--Maestro Piero of the Borgo,--To have my book -bound,--Show the book to Serigatto,-- and get the rule of the clock -[Footnote 41: Possibly this refers to the clock on the tower of the -Palazzo Vecchio at Florence. In February 1512 it had been repaired, -and so arranged as to indicate the hours after the French manner -(twelve hours a. m. and as many p. m.).],-- -ring,--nutmeg,--gum,--the square,--Giovan' Batista at the piazza, -de' Mozzi,--Giovanni Benci has my book and jaspers,--brass for the -spectacles. - -1455. - -Search in Florence for...... - -1456. - -Bernardo da Ponte ... Val di Lugano ... many veins for anatomical -demonstration. - -[Footnote: This fragmentary note is written on the margin of a -drawing of two legs.] - -1457. - -Paolo of Tavechia, to see the marks in the German stones. - -[Footnote: This note occurs on a pen and ink drawing made by -Leonardo as a sketch for the celebrated large cartoon in the -possession of the Royal Academy of Arts, in London. This cartoon is -commonly supposed to be identical with that described and lauded by -Vasari, which was exhibited in Florence at the time and which now -seems to be lost. Mr. Alfred Marks, of Long Ditton, in his valuable -paper (read before the Royal Soc. of Literature, June 28, 1882) "On -the St. Anne of Leonardo da Vinci", has adduced proof that the -cartoon now in the Royal Academy was executed earlier at Milan. The -note here given, which is written on the sheet containing the study -for the said cartoon, has evidently no reference to the drawing on -which it is written but is obviously of the same date. Though I have -not any opening here for discussing this question of the cartoon, it -seemed to me important to point out that the character of the -writing in this note does not confirm the opinion hitherto held that -the Royal Academy cartoon was the one described by Vasari, but, on -the contrary, supports the hypothesis put forward by Mr. Marks.] - -Notes on pupils (1458-1468.) - -1458. - -Giacomo came to live with me on St.-Mary Magdalen's[Footnote: _Il di -della Maddalena._ July 22.] day, 1490, aged 10 years. The second day -I had two shirts cut out for him, a pair of hose, and a jerkin, and -when I put aside some money to pay for these things he stole 4 -_lire_ the money out of the purse; and I could never make him -confess, though I was quite certain of the fact.--Thief, liar, -obstinate, glutton. - -The day after, I went to sup with Giacomo Andrea, and the said -Giacomo supped for two and did mischief for four; for he brake 3 -cruets, spilled the wine, and after this came to sup where I .... - -Item: on the 7th day of September he stole a silver point of the -value of 22 soldi from Marco[Footnote 6: _Marco_, probably -Leonardo's pupil Marco d'Oggionno; 1470 is supposed to be the date -of his birth and 1540 of his death. - -_Che stava con meco._ We may infer from this that he left the master -shortly after this, his term of study having perhaps expired.] who -was living with me, 4 _lire_ this being of silver; and he took it -from his studio, and when the said Marco had searched for it a long -while he found it hidden in the said Giacomo's box 4 _lire_. - -Item: on the 26th January following, I, being in the house of Messer -Galeazzo da San Severino [Footnote 9: Galeazzo. See No. 718 note.], -was arranging the festival for his jousting, and certain footmen -having undressed to try on some costumes of wild men for the said -festival, Giacomo went to the purse of one of them which lay on the -bed with other clothes, 2 lire 4 S, and took out such money as was -in it. - -Item: when I was in the same house, Maestro Agostino da Pavia gave -to me a Turkish hide to have (2 lire.) a pair of short boots made of -it; this Giacomo stole it of me within a month and sold it to a -cobbler for 20 soldi, with which money, by his own confession, he -bought anise comfits. - -Item: again, on the 2nd April, Giovan Antonio [Footnote 16: Giovan -Antonio, probably Beltraffio, 1467 to 1516.] having left a silver -point on a drawing of his, Giacomo stole it, and this was of the -value of 24 soldi (1 lira 4 S.) - -The first year- - -A cloak, 2 lire, -6 shirts, 4 lire, -3 jerkins, 6 lire, -4 pairs of hose, 7 lire 8 soldi, -1 lined doublet, 5 lire, -24 pairs of shoes, 6 lire 5 soldi, -A cap, 1 lira, -laces, 1 lira. - -[Footnote: Leonardo here gives a detailed account not only of the -loss he and others incurred through Giacomo but of the wild tricks -of the youth, and we may therefore assume that the note was not made -merely as a record for his own use, but as a report to be forwarded -to the lad's father or other responsible guardian.] - -1459. - -On the last day but one of September; - -Thursday the 27th day of September Maestro Tommaso came back and -worked for himself until the last day but one of February. On the -18th day of March, 1493, Giulio, a German, came to live with -me,--Lucia, Piero, Leonardo. - -On the 6th day of October. - -1460. - -1493. On the 1st day of November we settled accounts. Giulio had to -pay 4 months; and Maestro Tommaso 9 months; Maestro Tommaso -afterwards made 6 candlesticks, 10 days' work; Giulio some -fire-tongs 15 days work. Then he worked for himself till the 27th -May, and worked for me at a lever till the 18th July; then for -himself till the 7th of August, and for one day, on the fifteenth, -for a lady. Then again for me at 2 locks until the 20th of August. - -1461. - -On the 23rd day of August, 12 lire from Pulisona. On the 14th of -March 1494, Galeazzo came to live with me, agreeing to pay 5 lire a -month for his cost paying on the l4th day of each month. - -His father gave me 2 Rhenish florins. - -On the l4th of July, I had from Galeazzo 2 Rhenish florins. - -1462. - -On the 15th day of September Giulio began the lock of my studio -1494. - -1463. - -Saturday morning the 3rd of August 1504 Jacopo the German came to -live with me in the house, and agreed with me that I should charge -him a carlino a day. - -1464. - -1511. On the 26th of September Antonio broke his leg; he must rest -40 days. - -[Footnote: This note refers possibly to Beltraffio.] - -1465. - -I left Milan for Rome on the 24th day of September, 1513, with -Giovanni [Footnote 2: _Giovan;_ it is not likely that Leonardo -should have called Giovan' Antonio Beltraffio at one time Giovanni, -as in this note and another time Antonio, as in No. 1464 while in -No. 1458 l. 16 we find _Giovan'Antonio_, and in No. 1436, l.6 -_Beltraffio_. Possibly the Giovanni here spoken of is Leonardo's -less known pupil Giovan Pietrino (see No. 1467, 5).], Francesco di -Melzi [Footnote 2,3: _Francesco de' Melzi_ is often mentioned, see -Nos. 1350.], Salai [Footnote 3: _Salai_. See No. 1519 note.], -Lorenzo and il Fanfoia. - -[Footnote 4: _Lorenzo_. See No. 1351, l. 10 (p. 408). Amoretti gives -the following note in _Mem. Stor. XXIII:_ 1505. _Martedi--sera a di -14 d'aprile. Venne Lorenzo a stare con mecho: disse essere d'eta -d'anni 17 .. a di 15 del detto aprile ebbi scudi 25 d'oro dal -chamerlingo di Santa Maria nuova._ This, he asserts is derived from -a MS. marked S, in quarto. This MS. seems to have vanished and left -no trace behind; Amoretti himself had not seen it, but copied from a -selection of extracts made by Oltrocchi before the Leonardo MSS. -were conveyed to Paris on the responsibility of the first French -Republic. Lorenzo, by this, must have been born in 1487. The -sculptor Lorenzetto was born in 1490. Amoretti has been led by the -above passage to make the following absurd observations: - -_Cotesto Lorenzo, che poi gli fu sempre compagno, almeno sin che -stette in Italia, sarebb' egli Lorenzo Lotto bergamasco? Sappiamo -essere stato questo valente dipintore uno de'bravi scolari del -Vinci_ (?). - -_Il Fafoia_, perhaps a nickname. Cesare da Sesto, Leonardo's pupil, -seems to have been in Rome in these years, as we learn from a -drawing by him in the Louvre. - -1466. - -On the 3rd day of January. - -Benedetto came on the 17th of October; he stayed with me two months -and 13 days of last year, in which time he earned 38 lire, 18 soldi -and 8 dinari; he had of this 26 lire and 8 soldi, and there remains -to be paid for the past year 12 lire 10 soldi. - -Giodatti (?) came on the 8th day of September, at 4 soldi a month, -and stayed with me 3 months and 24 days, and earned 59 lire 14 soldi -and 8 dinari; he has had 43 lire, 4 soldi, there remains to pay 16 -lire, 10 soldi and 8 dinari. - -Benedetto, 24 grossoni. - -[Footnote: This seems to be an account for two assistants. The name -of the second is scarcely legible. The year is not given. The note -is nevertheless of chronological value. The first line tells us the -date when the note was registered, January 3d, and the observations -that follow refer to events of the previous month 'of last year' -_(dell'anno passato)_. Leonardo cannot therefore have written thus -in Florence where the year was, at that period, calculated as -beginning in the month of March (see Vol. I, No. 4, note 2). He must -then have been in Milan. What is more important is that we thus -learn how to date the beginning of the year in all the notes written -at Milan. This clears up Uzielli's doubts: _A Milano facevasi -cominciar l'anno ab incarnatione, cioe il 25 Marzo e a nativitate, -cioe il 25 Decembre. Ci sembra probabile che Leonardo dovesse -prescegliere lo stile che era in uso a Firenze._ (_Ricerche_, p. 84, -note.)] - -1467. - -Gian Maria 4, -Benedetto 4, -Gian Pietro [5] 3, -Salai 3, -Bartolomeo 3, -Gherardo 4. - -1468. - -Salai, 20 lire, -Bonifacio, 2 lire, -Bartolomeo, 4 lire, -Arrigo [Harry], 15 lire. - -Quotations and notes on books and authors (1469-1508). - -1469. - -Book on Arithmetic [Footnote 1: _"La nobel opera de arithmethica ne -la qual se tracta tute cosse amercantia pertinente facta & compilata -per Piero borgi da Veniesia", in-40. In fine: "Nela inclita cita di -Venetia a corni. 2 augusto. 1484. fu imposto fine ala presente -opera." Segn. a--p. quaderni. V'ha pero un' altra opera simile di -Filippo Calandro, 1491. E da consultarsi su quest' ultimo, Federici: -Memorie Trevigiane, Fiore di virtu: pag. 73. "Libricciuolo composto -di bello stile verso il 1320 e piu volte impresso nel secolo XV -(ristampato poi anche piu tardi). Gli accademici della Crusca lo -ammettono nella serie dei testi di lingua. Vedasi Gamba, Razzolini, -Panzer, Brunet, Lechi, ecc._ (G. D'A.)], 'Flowers of Virtue', - -Pliny [Footnote 2: _"Historia naturale di C. Plinio Secondo, -tradocta di lingua latina in fiorentina per Christophoro Laudino & -Opus Nicolai Jansonis gallici imp. anno salutis M.CCCC.LXXVI. -Venetiis" in-fol.--Diogene Laertio. Incomincia: "El libro de la vita -de philosophi etc.: Impressum Venetiis" per Bernardinum Celerium de -Luere, 1480", in-40_ (G. D'A.).], 'Lives of the Philosophers', - -The Bible [Footnote 3: _"La Bibia volgare historiata (per Nicolo di -Mallermi) Venecia ... M.CCCC.LXXI in kalende di Augusto (per -Vindelino de Spira)" 2 vol. in-fol. a 2 col. di 50 lin,; od altra -ediz. della stessa versione del Mallermi, Venetia 1471, e sempre: -"Venecia per Gabriel de Piero 1477," in-fol.; 2 vol.; Ottavio Scotto -da Modoetia 1481," "Venetia 1487 per Joan Rosso Vercellese," "1490 -Giovanni Ragazo di Monteferato a instantia di Luchanthonio di -Giunta, ecc."--Lapidario Teofrasto? Mandebille: "Le grand -lapidaire," versione italiana ms.?... Giorgio Agricola non puo -essere, perche nato nel 1494, forse Alberto Magno: de mineralibus. -Potrebbe essere una traduzione del poema latino (Liber lapidum seu -de gemmis) di Marbordio Veterio di Rennes (morto nel 1123 da lui -stesso tradotto in francese dal greco di Evao re d'Arabia celebre -medico che l'aveva composto per l'imperatore Tiberio. Marbodio -scrisse il suo prima per Filippo Augusto re di Francia. Vi sono -anche traduzioni in prosa. "Il lapidario o la forza e la virtu delle -pietre preziose, delle Erbe e degli Animali."_ (G. D'A.)], -'Lapidary', - -'On warfare' [Footnote 4: _Il Vegezio? ... Il Frontino? ... Il -Cornazzano?... Noi crediamo piuttosto il Valturio. Questo libro -doveva essere uno de'favoriti di Leonardo poiche libro di scienza e -d'arte nel tempo stesso._], 'Epistles of Filelfo', - -[Footnote: The late Marchese Girolamo d'Adda published a highly -valuable and interesting disquisition on this passage under the -title: _Leonardo da Vinci e la sua Libreria, note di un bibliofilo -(Milano 1873. Ed. di soli 75 esemplari_; privately printed). In the -autumn of 1880 the Marchese d'Adda showed me a considerable mass of -additional notes prepared for a second edition. This, as he then -intended, was to come out after the publication of this work of -mine. After the much regretted death of the elder Marchese, his son, -the Marchese Gioachino d'Adda was so liberal as to place these MS. -materials at my disposal for the present work, through the kind -intervention of Signor Gustavo Frizzoni. The following passages, -with the initials G. d'A. are prints from the valuable notes in that -publication, the MS. additions I have marked. I did not however -think myself justified in reproducing here the acute and interesting -observations on the contents of most of the rare books here -enumerated.] - -[Footnote: 1467. 5. See No. 1465, 2.] - -The first decade, [5] 'On the preservation of health', The third -decade, [6] Ciecho d'Ascoli, The fourth decade, [7] Albertus Magnus, -Guido, [8] New treatise on rhetorics, Piero Crescentio, [9] -Cibaldone, 'Quadriregio', [10] Aesop, - -Donato, [Footnote 11: "_Donatus latine & italice: Impressum Venetiis -impensis Johannis Baptistae de Sessa anno_ 1499, _in_-4deg.".-- "_El -Psalterio de David in lingua volgare (da Malermi Venetia nel -M.CCCC.LXXVI,_" in-fol. s. n._ (G. D'A.)] Psalms, - -Justinus, [Footnote 12: Compare No. 1210, 48.--_La versione di -Girolamo Squarzafico:_ "_Il libro di Justino posto diligentemente in -materna lingua. Venetia ale spesse (sic) di Johane de Colonia & -Johane Gheretze_ ... l477," _in-fol._--"_Marsilii Ficini, Theologia -platonica, sive de animarum immortalitate, Florentine, per Ant. -Misconimum_ 1482," _in-fol., ovvero qualche versione italiana di -questo stesso libro, ms._ (G. D'A.)] 'On the immortality of the -soul, - -Guido [Footnote 13: _Forse_ "_la Historia Trojana Guidonis_" _od il -_"_manipulus_" _di_ "_Guido da Monterocherii_"_ ma piu probabilmente -_"_Guido d'Arezzo_"_ il di cui libro: _"_Micrologus, seu disciplina -artis musicae_"_ poteva da Leonardo aversi ms.; di questi ne -esistono in molto biblioteche, e fu poi impresso nel 1784 dal -Gerbert._ - -_Molte sono le edizione dei sonetti di Burchiello Fiorentino, -impresse nel secolo XV. La prima e piu rara e recercata:_ -"_Incominciano li sonetti, ecc. (per Christoforo Arnaldo)_"_, in_-4deg. -_senza numeri, richiami o segnature, del_ 1475, _e fors' anche del_ -1472, _secondo Morelli e Dibdin, ecc._ (G. D'A.)] Burchiello, - -'Doctrinale' [Footnote 14: _Versione italiana det "Doctrinal de -Sapience" di Guy de Roy, e foris'anche l'originale in lingua -francese.--_ - -_Di Pulci Luigi, benche nell' edizione:_ "_Florentiae_ 1479" _in_-4deg. -si dica: _"_Il Driadeo composto in rima octava per Lucio Pulcro_"_ -Altre ediz, del secolo XV, _"_Florentie Miscomini_ 1481, _in_-40, -_Firenze, apud S. Jacob, de Ripoli,_ 1483,_" _in_-4deg. _e "Antoni de -Francesco,_ 1487," _in_-4deg. _e Francesco di Jacopo_ 1489,_in_-4deg. _ed -altre ancora di Venezia e senza alcuna nota ecc._ (G. D'A.)] -Driadeo, - -Morgante [Footnote 15: _Una delle edizioni del Morgante impresse nel -secolo XV, ecc.--_ - -_Quale delle opere di Francesco Petrarca, sarebbe malagevole -l'indovinare, ma probabilmente il Canzoniere._ (G. D'A.)] Petrarch. - -John de Mandeville [Footnote 16: _Sono i viaggi del cavaliere_ -"_Mandeville_" _gentiluomo inglese. Scrisse il suo libro in lingua -francese. Fu stampato replicatamente nel secolo XV in francese, in -inglese ed in italiano ed in tedesco; del secolo XV ne annoverano -forse piu di 27 edizioni, di cui ne conosciamo_ 8 _in francese, -quattro in latino, sei in tedesco e molte altre in volgare._ (G. -D'A.)] - -'On honest recreation' [Footnote 17: _Il Platina (Bartolomeo Sacchi) -la versione italiana_ "_de la honesta voluptate, & valetudine (& de -li obsonnii) Venetia (senza nome di tipografo)_ 1487," _piccolo -in_-4deg. _gotico._ (G. D'A.)--Compare No. 844, 21.] - -Manganello, [Footnote 18: _Il Manganello: Satira eccessivamente -vivace contro le donne ad imitazione della Sesta di Giovenale. -Manganello non e soltanto il titolo del libricino, sua ben anche il -nome dell'autore ch'era un_ "_milanese_". _Di questo libercolo -rarissimo, che sembra impresso a Venezia dallo Zoppino (Nicolo -d'Aristotile detto il), senza data, ma dei primissimi anni del -secolo XVI, e forse piu antico, come vedremo in appresso, non se ne -conoscono fra biblioteche pubbliche e private che due soli esemplari -in Europa._ (G. D'A.)] - -The Chronicle of Isidoro, [Footnote 19: "_Cronica desidero_", -_sembra si deggia leggere piuttosto_ "_cronico disidoro_"_; ed in -questo caso s'intenderebbe la_ "_cronica d'Isidoro_" _tanto in voga -a quel tempo_ "_Comenza la Cronica di Sancto Isidoro menore con -alchune additione cavate del testo & istorie de la Bibia & del libro -di Paulo Oroso .... Impresso in Ascoli in casa del reverendo misser -Pascale ..... per mano di Guglielmo de Linis de Alamania -M.CCCC.LXXVII_" _in_-4deg. _di_ 157 _ff. E il primo libro impresso ad -Ascoli e l'edizione principe di questa cronica in oggi assai rara. -Non lo e meno l'edizione di Cividal del Friuli_, 1480, _e quella ben -anche di Aquila_, 1482, _sempre in-_4deg.. _Vedasi Panzer, Hain, Brunet -e P. Dechamps._ (G. D'A.)] - -The Epistles of Ovid, [Footnote 20: "_Le pistole di Ovidio tradotte -in prosa. Napoli Sixt. Riessinger_", _in_-4deg., _oppure:_ "_Epistole -volgarizzate_ 1489," _in_-4deg. _a due col._ "_impresse ne la cita -(sic) di Bressa per pre: Baptista de Farfengo,_" _(in ottave) o:_ -"_El libro dele Epistole di Ovidio in rima volgare per messere -Dominico de Monticelli toschano. Brescia Farfengo_," _in_-4deg. _got. -(in rima volgare)_, 1491, _ed anche la versione di Luca Pulci. -Firenze, Mischomini_, 1481, _in_-4deg.. (G. D'A.) ] - -Epistles of Filelfo, [Footnote 21: See l. 4.] - -Sphere, [Footnote 22: "_Jo: de Sacrobusto_," _o_ "_Goro Dati_," _o_ -"_Tolosano da Colle_" _di cui molteplici edizioni del secolo XV._ -(G. D'A.)] - -The Jests of Poggio, [Footnote 23: _Tre edizioni delle facezie del -Poggio abbiamo in lingua italiana della fine del secolo XV, tutte -senza data. "Facetie de Poggio fiorentino traducte de latino in -vulgare ornatissimo," in-40, segn. a--e in caratteri romani; -l'altra: "Facetie traducte de latino in vulgare," in-40, caratteri -gotici, ecc._ (G. D'A.)] Chiromancy, [Footnote 24: "_Die Kunst -Cyromantia etc, in tedesco. 26 ff. di testo e figure il tutte -eseguito su tavole di legno verso la fine del secolo XV da Giorgio -Schapff". Dibdin, Heinecken, Sotheby e Chatto ne diedero una lunga -descrizione; i primi tre accompagnati da fac-simili. La data 1448 -che si legge alla fine del titolo si riferisce al periodo della -composizione del testo, non a quello della stampa del volume benche -tabellario. Altri molti libri di Chiromanzia si conoscono di quel -tempo e sarebbe opera vana il citarli tutti._ (G. D'A.)] - -Formulary of letters, [Footnote 25: _Miniatore Bartolomeo. -"Formulario de epistole vulgare missive e responsive, & altri fiori -de ornali parlamenti al principe Hercule d'Esti ecc. composto ecc. -Bologna per Ugo di Rugerii," in-40, del secolo XV. Altra edizione di -"Venetia Bernardino di Novara, 1487" e "Milano per Joanne Angelo -Scinzenzeler 1500," in-40._ (G. D'A.) - -Five books out of this list are noted by Leonardo in another MS. -(Tr. 3): _donato, -- lapidario, -- plinio, -- abacho, -- morgante._] - -1470. - -Nonius Marcellus, Festus Pompeius, Marcus Varro. - -[Footnote: Nonius Marcellus and Sextus Pompeius Festus were Roman -grammarians of about the fourth century A. D. Early publications of -the works of Marcellus are: _De proprietate sermonis, Romae_ (about -1470), and 1471 (place of publication unknown). _Compendiosa -doctrina, ad filium, de proprietate sermonum._ Venice, 1476. BRUNET, -_Manuel du libraire_ (IV, p. 97) notes: _Le texte de cet ancien -grammairien a ete reimprime plusieurs fois a la fin du XVe siecle, -avec ceux de Pomponius Festus et de Terentius Varro. La plus -ancienne edition qui reunisse ces trois auteurs est celle de Parme, -1480 ... Celles de Venise, 1483, 1490, 1498, et de Milan, 1500, -toutes in-fol., ont peu de valeur._] - -1471. - -Map of Elephanta in India which Antonello Merciaio has from maestro -Maffeo;--there for seven years the earth rises and for seven years -it sinks;--Enquire at the stationers about Vitruvius. - -1472. - -See 'On Ships' Messer Battista, and Frontinus 'On Acqueducts' -[Footnote 2: 2. _Vitruvius de Arch., et Frontinus de Aquedoctibus._ -Florence, 1513.--This is the earliest edition of Frontinus.--The -note referring to this author thus suggests a solution of the -problem of the date of the Leicester Manuscript.]. - -[Footnote: Compare No. 1113, 25.] - -1473. - -Anaxagoras: Every thing proceeds from every thing, and every thing -becomes every thing, and every thing can be turned into every thing -else, because that which exists in the elements is composed of those -elements. - -1474. - -The Archimedes belonging to the Bishop of Padua. - -[Footnote: See No. 1421, 1. 3, 6 and Vol. I, No. 343.] - -1475. - -Archimedes gave the quadrature of a polygonal figure, but not of the -circle. Hence Archimedes never squared any figure with curved sides. -He squared the circle minus the smallest portion that the intellect -can conceive, that is the smallest point visible. - -[Footnote: Compare No. 1504.] - -1476. - -If any man could have discovered the utmost powers of the cannon, in -all its various forms and have given such a secret to the Romans, -with what rapidity would they have conquered every country and have -vanquished every army, and what reward could have been great enough -for such a service! Archimedes indeed, although he had greatly -damaged the Romans in the siege of Syracuse, nevertheless did not -fail of being offered great rewards from these very Romans; and when -Syracuse was taken, diligent search was made for Archimedes; and he -being found dead greater lamentation was made for him by the Senate -and people of Rome than if they had lost all their army; and they -did not fail to honour him with burial and with a statue. At their -head was Marcus Marcellus. And after the second destruction of -Syracuse, the sepulchre of Archimedes was found again by Cato[25], -in the ruins of a temple. So Cato had the temple restored and the -sepulchre he so highly honoured.... Whence it is written that Cato -said that he was not so proud of any thing he had done as of having -paid such honour to Archimedes. - -[Footnote: Where Leonardo found the statement that Cato had found -and restored the tomb of Archimedes, I do not know. It is a merit -that Cicero claims as his own (Tusc. V, 23) and certainly with a -full right to it. None of Archimedes' biographers --not even the -diligent Mazzucchelli, mentions any version in which Cato is named. -It is evidently a slip of the memory on Leonardo's part. Besides, -according to the passage in Cicero, the grave was not found _'nelle -ruine d'un tempio'_--which is highly improbable as relating to a -Greek--but in an open spot (H. MULLER-STRUBING).--See too, as to -Archimedes, No. 1417. - -Leonardo says somewhere in MS. C.A.: _Architronito e una macchina di -fino rame, invenzlon d' Archimede_ (see _'Saggio'_, p. 20).] - -1477. - -Aristotle, Book 3 of the Physics, and Albertus Magnus, and Thomas -Aquinas and the others on the rebound of bodies, in the 7th on -Physics, on heaven and earth. - -1478. - -Aristotle says that if a force can move a body a given distance in a -given time, the same force will move half the same body twice as far -in the same time. - -1479. - -Aristotle in Book 3 of the Ethics: Man merits praise or blame solely -in such matters as lie within his option to do or not to do. - -1480. - -Aristotle says that every body tends to maintain its nature. - -1481. - -On the increase of the Nile, a small book by Aristotle. [Footnote: -_De inundatione Nili_, is quoted here and by others as a work of -Aristotle. The Greek original is lost, but a Latin version of the -beginning exists (Arist. Opp. IV p. 213 ed. Did. Par.). - -In his quotations from Aristotle Leonardo possibly refers to one of -the following editions: _Aristotelis libri IV de coelo et mundo; de -anima libri III; libri VIII physi- corum; libri de generatione et -corruptione; de sensu et sensato... omnia latine, interprete -Averroe, Venetiis 1483_ (first Latin edition). There is also a -separate edition of _Liber de coelo et mundo_, dated 1473.] - -1482. - -Avicenna will have it that soul gives birth to soul as body to body, -and each member to itself. - -[Footnote: Avicenna, see too No. 1421, 1. 2.] - -1483. - -Avicenna on liquids. - -1484. - -Roger Bacon, done in print. [Footnote: The earliest printed edition -known to Brunet of the works of Roger Bacon, is a French -translation, which appeared about fourty years after Leonardo's -death.] - -1485. - -Cleomedes the philosopher. - -[Footnote: Cleomede. A Greek mathematician of the IVth century B. C. -We have a Cyclic theory of Meteorica by him. His works were not -published before Leonardo's death.] - -1486. - -CORNELIUS CELSUS. - -The highest good is wisdom, the chief evil is suffering in the body. -Because, as we are composed of two things, that is soul and body, of -which the first is the better, the body is the inferior; wisdom -belongs to the better part, and the chief evil belongs to the worse -part and is the worst of all. As the best thing of all in the soul -is wisdom, so the worst in the body is suffering. Therefore just as -bodily pain is the chief evil, wisdom is the chief good of the soul, -that is with the wise man; and nothing else can be compared with it. - -[Footnote: _Aulus Cornelius Celsus_, a Roman physician, known as the -Roman Hippocrates, probably contemporary with Augustus. Only his -eight Books 'De Medicina', are preserved. The earliest editions are: -_Cornelius Celsus, de medicina libr. VIII._, Milan 1481 Venice 1493 -and 1497.] - -1487. - -Demetrius was wont to say that there was no difference between the -speech and words of the foolish and ignorant, and the noises and -rumblings of the wind in an inflated stomach. Nor did he say so -without reason, for he saw no difference between the parts whence -the noise issued; whether their lower parts or their mouth, since -one and the other were of equal use and importance. - -[Footnote: Compare Vol. I, No. 10.] - -1488. - -Maestro Stefano Caponi, a physician, lives at the piscina, and has -Euclid _De Ponderibus_. - -1489. - -5th Book of Euclid. First definition: a part is a quantity of less -magnitude than the greater magnitude when the less is contained a -certain number of times in the greater. - -A part properly speaking is that which may be multiplied, that is -when, being multiplied by a certain number, it forms exactly the -whole. A common aggregate part ... - -Second definition. A greater magnitude is said to be a multiple of a -less, when the greater is measured by the less. - -By the first we define the lesser [magnitude] and by the second the -greater is defined. A part is spoken - -1490. - -of in relation to the whole; and all their relations lie between -these two extremes, and are called multiples. - -1491. - -Hippocrates says that the origin of men's sperm derives from the -brain, and from the lungs and testicles of our parents, where the -final decocture is made, and all the other limbs transmit their -substance to this sperm by means of expiration, because there are no -channels through which they might come to the sperm. - -[Footnote: The works of Hippocrates were printed first after -Leonardo's death.] - -1492. - -Lucretius in his third [book] 'De Rerum Natura'. The hands, nails -and teeth were (165) the weapons of ancient man. - -They also use for a standard a bunch of grass tied to a pole (167). - -[Footnote: _Lucretius, de rerum natura libri VI_ were printed first -about 1473, at Verona in 1486, at Brescia in 1495, at Venice in 1500 -and in 1515, and at Florence in 1515. The numbers 165 and 167 noted -by Leonardo at the end of the two passages seem to indicate pages, -but if so, none of the editions just mentioned can here be meant, -nor do these numbers refer to the verses in the poems of Lucretius.] - -1493. - -Ammianus Marcellinus asserts that seven hundred thousand volumes of -books were burnt in the siege of Alexandria in the time of Julius -Cesar. - -[Footnote: _Ammiani Marcellini historiarum libri qui extant XIII_, -published at Rome in 1474.] - -1494. - -Mondino says that the muscles which raise the toes are in the -outward side of the thigh, and he adds that there are no muscles in -the back [upper side] of the feet, because nature desired to make -them light, so as to move with ease; and if they had been fleshy -they would be heavier; and here experience shows ... - -[Footnote: _"Mundini anatomia. Mundinus, Anothomia (sic). Mundini -praestantissimorum doctorum almi studii ticiensis (sic) cura -diligentissime emendata. Impressa Papiae per magistrum Antonium de -Carfano 1478," in-fol.; ristampata: "Bononiae Johan. de Noerdlingen, -1482," in-fol.; "Padova per Mattheum Cerdonis de Vuindischgretz, -1484," in-40; "Lipsia, 1493," in-40; "Venezia, 1494," in-40 e ivi -"1498," con fig. Queste figure per altro non sono, come si e -preteso, le prime che fossero introdotte in un trattato di Notamia. -Nel 'fasciculus Medicinae' di Giovanni Ketham, che riproduce -l''Anatomia' del Mundinus, impresso pure a Venezia da J. e G. de -Gregoriis, 1491, in-fol., contengonsi intagli in legno (si vogliono -disegnati non gia incisi da Andrea Mantegna) di grande dimensione, e -che furono piu volte riprodotti negli anni successivi. Quest' -edizione del "fasciculus" del 1491, sta fra nostri libri e potrebbe -benissimo essere il volume d'Anatomia notato da Leonardo._ (G. -D'A.)] - -1495. - -Of the error of those who practice without knowledge;--[3] See first -the 'Ars poetica' of Horace [5]. - -[Footnote: A 3-5 are written on the margin at the side of the title -line of the text given, entire as No. 19] - -1496. - -The heirs of Maestro Giovanni Ghiringallo have the works of -Pelacano. - -1497. - -The catapult, as we are told by Nonius and Pliny, is a machine -devised by those &c. - -[Footnote: _Plinius_, see No. 946.] - -1498. - -I have found in a history of the Spaniards that in their wars with -the English Archimedes of Syracuse who at that time was living at -the court of Ecliderides, King of the Cirodastri. And in maritime -warfare he ordered that the ships should have tall masts, and that -on their tops there should be a spar fixed [Footnote 6: Compare No. -1115.] of 40 feet long and one third of a foot thick. At one end of -this was a small grappling iron and at the other a counterpoise; and -there was also attached 12 feet of chain; and, at the end of this -chain, as much rope as would reach from the chain to the base of the -top, where it was fixed with a small rope; from this base it ran -down to the bottom of the mast where a very strong spar was attached -and to this was fastened the end of the rope. But to go on to the -use of his machine; I say that below this grappling iron was a fire -[Footnote 14: Compare No. 1128.] which, with tremendous noise, threw -down its rays and a shower of burning pitch; which, pouring down on -the [enemy's] top, compelled the men who were in it to abandon the -top to which the grappling-iron had clung. This was hooked on to the -edges of the top and then suddenly the cord attached at the base of -the top to support the cord which went from the grappling iron, was -cut, giving way and drawing in the enemy's ship; and if the -anchor--was cast ... - -[Footnote: Archimedes never visited Spain, and the names here -mentioned cannot be explained. Leonardo seems to quote here from a -book, perhaps by some questionable mediaeval writer. Prof. C. Justi -writes to me from Madrid, that Spanish savants have no knowledge of -the sources from which this story may have been derived.] - -1499. - -Theophrastus on the ebb and flow of the tide, and of eddies, and on -water. [Footnote: The Greek philosophers had no opportunity to study -the phenomenon of the ebb and flow of the tide and none of them -wrote about it. The movement of the waters in the Euripus however -was to a few of them a puzzling problem.] - -1500. - -Tryphon of Alexandria, who spent his life at Apollonia, a city of -Albania (163). [Footnote: Tryphon of Alexandria, a Greek Grammarian -of the time of Augustus. His treatise TtaOY Aeijecu appeared first -at Milan in 1476, in Constantin Laskaris's Greek Grammar.] - -1501. - -Messer Vincenzio Aliprando, who lives near the Inn of the Bear, has -Giacomo Andrea's Vitruvius. - -1502. - -Vitruvius says that small models are of no avail for ascertaining -the effects of large ones; and I here propose to prove that this -conclusion is a false one. And chiefly by bringing forward the very -same argument which led him to this conclusion; that is, by an -experiment with an auger. For he proves that if a man, by a certain -exertion of strength, makes a hole of a given diameter, and -afterwards another hole of double the diameter, this cannot be made -with only double the exertion of the man's strength, but needs much -more. To this it may very well be answered that an auger - -1503. - -of double the diameter cannot be moved by double the exertion, be- -cause the superficies of a body of the same form but twice as large -has four times the extent of the superficies of the smaller, as is -shown in the two figures a and n. - -1504. - -OF SQUARING THE CIRCLE, AND WHO IT WAS THAT FIRST DISCOVERED IT BY -ACCIDENT. - -Vitruvius, measuring miles by means of the repeated revolutions of -the wheels which move vehicles, extended over many Stadia the lines -of the circumferences of the circles of these wheels. He became -aware of them by the animals that moved the vehicles. But he did not -discern that this was a means of finding a square equal to a circle. -This was first done by Archimedes of Syracuse, who by multiplying -the second diameter of a circle by half its circumference produced a -rectangular quadrilateral equal figure to the circle [Footnote 10: -Compare No. 1475.]. - -[Footnote: _Vitruvius_, see also Nos. 1113 and 343.] - -1505. - -Virgil says that a blank shield is devoid of merit because among the -people of Athens the true recognition confirmed by testimonies ... - -[Footnote: The end of the text cannot be deciphered.] - -1506. - -In Vitolone there are 805 conclusions [problems] in perspective. - -[Footnote: _(Witelo, Vitellion, Vitellon) Vitellione. E da vedersi -su questo ottico prospettico del secolo XIII Luca Pacioli, Paolo -Lomazzo, Leonardo da Vinci, ecc. e fra i moderni il Graesse, il -Libri, il Brunet, e le Memorie pubblicate dal principe Boncompagni, -e 'Sur l' orthographe du nom et sur la patrie de Witelo (Vitellion) -note de Maximilien Curtze, professeur a Thorn', ove sono descritti i -molti codici esistenti nelle biblioteche d' Europa. Bernardino Baldi -nelle sue 'Vite de'matematici', manoscritto presso il principe -Boncompagni, ha una biografia del Vitellione. Questo scritto del -Baldi reca la data 25 agosto 1588. Discorsero poi di lui Federigo -Risnerio e Giovanni di Monteregio nella prefazione dell' Alfagrano, -Giovanni Boteone, Girolamo Cardano, 'De subtilitate', che nota gli -errori di Vitellione. Visse, secondo il Baldi, intorno all' anno -1269, ma secondo il Reinoldo fioriva nel 1299, avendo dedicata la -sua opera ad un frate Guglielmo di Monteca, che visse di que' tempi. - -Intorno ad un manoscritto dell' ottica di Vitellione, citato da Luca -Pacioli v'ha un secondo esemplare del Kurlz, con aggiunte del -principe Boncompagni, e le illustrazioni del cav. Enrico Narducci. -Nel 'Catalogo di manoscritti' posseduti da D. Baldassare de' -principi Boncompagni, compilato da esso Narducci, Roma, 1862, sotto -al n. 358, troviamo citato: Vitellio, 'Perspectiva', manoscritto del -secolo XIV. La 'Prospettiva di Vitelleone' (sic) Thuringo-poloni e -citata due volte da Paolo Lomazzo nel Trattato dell' arte della -pittura. Vitellio o Vitello o Witelo. Il suo libro fu impresso in -foglio a Norimberga nel 1535; la secondo edizione e del 1551, sempre -di Norimberga, ed una terza di Basilea, 1572._ (See _Indagini -Storiche ... sulla Libreria-Visconteo-Sforzesca del Castello di -Pavia ... per cura di_ G. D'A., _Milano 1879. P. I. Appendice p. -113. 114)._] - -1507. - -Vitolone, at Saint Mark's. - -[Footnote: _Altro codice di cotesta 'Prospettiva' del Vitolone -troviamo notato nel 'Canone bibliographico di Nicolo V', conservato -alla, Magliabecchiana, in copia dell' originale verosimilmente -inviato dal Parentucelli a Cosimo de' Medici (Magliab. cod. segn. 1 -VII, 30 carte da 193 a 198). Proviene dal Convento di San Marco e lo -aveva trascritto frate Leonardo Scruberti fiorentino, dell' ordine -dei predicatori che fu anche bibliotecario della Medicea pubblica in -San Marco_ (See _Indagini Storiche ... per cura di_ G. D'A. _Parte -I, p. 97)._] - -1508. - -How this proposition of Xenophon is false. - -If you take away unequal quantities from unequal quantities, but in -the same proportion, &c. [Footnote: Xenophon's works were published -several times during Leonardo's lifetime.] - -Inventories and accounts (1509--1545). - -1509. - -On the 28th day of April I received from the Marchesino 103 lire and -12 dinari. [Footnote: Instead of the indication of the year there is -a blank space after _d'aprile_.--Marchesino Stange was one of -Lodovico il Moro's officials.--Compare No. 1388.] - -1510. - -On the 10th day of July 1492 in 135 -Rhenish florins 1. 445 -in dinari of 6 soldi 1. 112 S 16 -in dinari of 5 1/2 soldi 1. 29 S 13 -9 in gold and 3 scudi 1. 53 - ----------------------------- - 1. 811 in all - -1511. - -On the first day of February, lire 1200. - -1512. - -The hall towards the court is 126 paces long and 27 braccia wide. - -1513. - -The narrow cornice above the hall lire 30. - -The cornice beneath that, being one for each picture, lire 7, and -for the cost of blue, gold, white, plaster, indigo and glue 3 lire; -time 3 days. - -The pictures below these mouldings with their pilasters, 12 lire -each. - -I calculate the cost for smalt, blue and gold and other colours at 1 -1/2 lire. - -The days I calculate at 3, for the invention of the composition, -pilasters and other things. - -1514. - -Item for each vault 7 lire - -outlay for blue and gold 3 1/2 - -time, 4 days - -for the windows 1 1/2 - -The cornice below the windows 16 soldi per braccio - -item for 24 pictures of Roman history 14 lire each - -The philosophers 10 lire - -the pilasters, one ounce of blue 10 soldi - -for gold 15 soldi - -Total 2 and 1/2 lire. - -1515. - -The cornice above lire 30 - -The cornice below lire 7 - -The compositions, one with another lire 13 - -1516. - -Salai, 6 lire ... 4 soldi ... 10 soldi for a chain;-- - -On the l4th of March I had 13 lire S. 4; 16 lire remain. - -1517. - -How many braccia high is the level of the walls?-- - -123 braccia - -How large is the hall? - -How large is the garland? - -30 ducats. - -On the 29th day of January, 1494 - -cloth for hose lire 4 S 3 - -lining S 16 - -making S 8 - -to Salai S 3 - -a jasper ring S 13 - -a sparkling stone S 11 - -to Caterina S 10 - -to Caterina S 10 - -1518. - -The wheel lire 7 - -the tire lire 10 - -the shield lire 4 - -the cushion lire 8 - -the ends of the axle-tree lire 2 - -bed and frame lire 30 - -conduit lire 10 - -S.K.M.II.2 4a] - -1519. - -Parsley 10 parts - -mint 1 part - -thyme 1 part - -Vinegar ... and a little salt two pieces of canvas for Salai. - -[Footnote: This note, of about the year 1494, is the earliest -mention of Salai, and the last is of the year 1513 (see No. 1465, -3). From the various notes in the MSS. he seems to have been -Leonardo's assistant and keeper only, and scarcely himself a -painter. At any rate no signed or otherwise authenticated picture by -him is known to exist. Vasari speaks somewhat doubtfully on this -point.] - -1520. - -On Tuesday I bought wine for morning [drinking]; on Friday the 4th -day of September the same. - -[Footnote: This note enables us to fix the date of the Manuscript, -in which it is to be found. In 1495 the 4th of September fell on a -Friday; the contents of the Manuscript do not permit us to assign it -to a much earlier or later date (Compare No. 1522, and Note).] - -1521. - -The cistern ... at the Hospital, --2 ducats, --beans, --white maize, ---red maize, --millet, --buckwheat, --kidney beans, --beans, --peas. - -1522. - -EXPENSES OF THE INTERMENT OF CATERINA. - -For the 3 lbs of tapers 27 S -For the bier 8 S -A pall over the bier 12 S -For bearing and placing the cross 4 S -For bearing the body 8 S -For 4 priests and 4 clerks 20 S -Bell, book and sponge 2 S -For the gravediggers 16 S -To the senior 8 S -For a license from the authorities 1 S -106 S - -The doctor 2 S -Sugar and candles 12 S -120 S - -[Footnote: See Nos. 1384 and 1517.] - -1523. - -Salai's cloak, the 4th of April 1497. -4 braccia of silver cloth l. 15 S 4 -green velvet to trim it l. 9 S -- -binding l.-- S 9 -loops l.-- S 12 -the making l. 1 S 5 -binding for the front l.-- S 5 -stitching _________ -here are 13 grossoni of his l. 26 S 5 -Salai stole the soldi. - -1524. - -On Monday I bought 4 braccia of cloth lire 13 S 14 1/2 on the 17th -of, October 1497. - -1525. - -Memorandum. That on the 8th day of April 1503, I, Leonardo da Vinci, -lent to Vante, miniature painter 4 gold ducats, in gold. Salai -carried them to him and gave them into his own hand, and he said he -would repay within the space of 40 days. - -Memorandum. That on the same day I paid to Salai 3 gold ducats which -he said he wanted for a pair of rose-coloured hose with their -trimming; and there remain 9 ducats due to him--excepting that he -owes me 20 ducats, that is 17 I lent him at Milan, and 3 at Venice. - -Memorandum. That I gave Salai 21 braccia of cloth to make a shirt, -at 10 soldi the braccio, which I gave him on the 20th day of April -1503. - -[Footnote: With regard to Vante or Attavante, the miniature painter -(not Nanni as I formerly deciphered this name, which is difficult to -read; see _Zeitschrift fur Bild. Kunst_, 1879, p. 155), and Vasari, -Lives of Frate Giovanni da Fiesole, of Bartolommeo della Gatta, and -of Gherardo, _miniatore._ He, like Leonardo, was one of the -committee of artists who, in 1503, considered the erection and -placing of Michel Angelo's David. The date of his death is not -known; he was of the same age as Leonardo. Further details will be -found in '_Notizie di Attavante miniatore, e di alcuni suoi lavori_' -(Milanese's ed. of Vasari, III, 231-235).] - -1526. - -On the morning of San Peter's day, June 29th, 1504, I took io -ducats, of which I gave one to Tommaso my servant to spend. - -On Monday morning 1 florin to Salai to spend on the house. - -On Thursday I took 1 florin for my own spending. - -Wednesday evening 1 florin to Tommaso, before supper. - -Saturday morning 1 florin to Tommaso. - -Monday morning 1 florin less 10 soldi. - -Thursday to Salai 1 florin less 10 soldi. - -For a jerkin, 1 florin. - -For a jerkin And a cap 2 florins. - -To the hosier, 1 florin. - -To Salai, 1 florin. - -Friday morning, the 19th of July, 1 florin, less 6 soldi. I have 7 -fl. left, and 22 in the box. - -Tuesday, the 23th day of July, 1 florin to Tommaso. - -Monday morning, to Tommaso 1 florin. - -[Wednesday morning 1 fl. to Tommaso.] - -Thursday morning the 1st day of August 1 fl. to Tommaso. - -Sunday, the 4th of August, 1 florin. - -Friday, the 9th day of August 1504, I took 10 ducats out of the box. - -1527. - -1504. On the 9th day of August, 1504, I took 10 florins in gold[2] -... [3] on Friday the 9th day of August fifteen grossoni that is fl. -5 S 5 ... given to me 1 florin in gold on the 12th day of August [4] -... on the 14th of August, 32 grossoni to Tommaso. On the 18th of -the same 5 grossoni to Salai. On the 8th of September 6 grossoni to -the workman to spend; that is on the day of our Lady's birth. On the -16th day of September I gave 4 grossoni to Tommaso: on a Sunday. - -[Footnote: In the original, the passage given as No. 1463 is written -between lines 2 and 3 of this text, and it is possible that the -entries in lines 3 and 4 refer to the payments of Jacopo Tedesco, -who is there mentioned. The first words of these lines are very -illegible.] - -[Footnote 7: _Al fattore._ Il Fattore, was, as is well known, the -nick-name of Giovanni Franceso Penni, born in Florence in 1486, and -subsequently a pupil of Raphael's. According to Vasari he was known -by it even as a boy. Whether he is spoken of in this passage, or -whether the word Fattore should be translated literally, I will not -undertake to decide. The latter seems to me more probably right.] - -1528. - -On the day of October, 1508, I had 30 scudi; 13 I lent to Salai to -make up his sister's dowry, and 17 I have left. - -1529. - -Memorandum of the money I have had from the King as my salary from -July 1508 till April next 1509. First 100 scudi, then 70, then 50, -then 20 and then 200 florins at 48 soldi the florin. [Footnote: -Compare No. 1350 and 1561.] - -1530. - -Saturday the 2nd day of March I had from Santa Maria Novella 5 gold -ducats, leaving 450. Of these I gave 2 the same day to Salai, who -had lent them to me. [Footnote: See '_Conto corrente di Leonardo da -Vinci con lo Spedale di S. Maria Nuova_' [1500 a 1507, 1513-1520] -published by G. UZIELLI, _Ricerche intorno a Leonardo da Vinci, -Firenze,_ 1872, pp. 164, 165, 218 and 219. The date here given by -Leonardo does not occur in either of the accounts.] - -1531. - -Thursday, the eighth day of June, I took 17 grossoni, 18 soldi; on -the same Thursday in the morning I gave to Salai 22 soldi for the -expenses. - -1532. - -To Salai 4 grossoni, and for one braccio of velvet, 5 lire, and 1/2; -viz. 10 soldi for loops of silver; Salai 14 soldi for binding, the -making of the cloak 25 soldi. [Footnote: Compare No. 1523.] - -1533. - -I gave to Salai 93 lire 6 soldi, of which I have had 67 lire and -there remain 26 lire 6 soldi. - -1534. - -To Salai S 42 - -2 dozen of laces S 8 - -for papers S 3 d 8 - -a pair of shoes S 14 - -for velvet S 14 - -a sword and knife S 21 - -to the barber S 11 - -to Paolo for a ... S 20 - -For having his fortune told S 6 - -1535. - -On Friday morning, -one florin to Salai to -spend; 3 soldi received - -bread S.. d - -wine S.. d - -grapes S.. d - -mushrooms S.. d - -fruit S.. d - -[Footnote 6: Compare Nos. 1545, l. 4 and 5, -with similar entries for horse's fodder.] -bran S.. d - -at the barber's S.. d - -for shoes S.. d - -1536. - -On Thursday morning one florin. - -1537. - -On Saint Ambrose's day from the morning to Thursday 36 soldi. - -1538. - -The moneys I have had from Ser Matteo; -first 20 grassoni, then on 13 occasions 3 f. -and then 61 grassoni, then 3, and then 33; -46 soldi 12 grossoni. - -1539. - -For paper S 18 - -for canvas S 30 - -for paper S 10 d 19 - -Total S 73 - -1540. - -20 pounds of German -blue, at one ducat the pound lire 80 S d - -60 pounds of white, S.. -the pound lire 15 S d - -1 1/2 pound at 4 S the pound lire 6 S d - -2 pounds of cinnabar at -S 18 the pound lire 1 S 16 d - -6 pounds of green at S 12 -the pound lire 3 S 12 d - -4 pounds of yellow at S 12 -the pound lire 2 S 8 d - -1 pound of minium at S 8 -the pound lire 0 S 8 d - -4 pounds of ... at S 2 -the pound lire 0 S 8 d - -6 pounds of ochre at S 1 -the pound lire 0 S 6 d - -black ... at S 2 the pound -for 20 lire 2 S 0 d - -wax to make the stars -29 pounds at S--the pound lire 0 S 0 d - -40 pounds of oil for painting -at 5 soldi the pound lire 10 S 0 d - -Altogether lire 120 d 18 -without the gold. 18 - -tin for putting on the gold 120 18 - -58 - -1541. - -Two large hatchets and one very small one, 8 brass spoons, 4 -tablecloths, 2 towels, 15 small napkins, 2 coarse napkins, 2 coarse -cloths, 2 wrappers, 3 pairs of sheets, 2 pairs new and 1 old. - -1542. - -Bed 7 0 S - -ring 7 0 - -crockery 2 5 - -gardener 1 2 - -..... 2 8 - -porters 2 1 - -glasses 1 - -fuel 3 6 - -a lock 1 - -Section title: Miscellaneous Notes. - -1543. - -New tin-ware 3 pairs of sheets -6 small bowls, each of 4 breadths, -6 bowls, 2 small sheets, -2 large dishes, 2 tablecloths and 1/2, -2 dishes medium size, 16 coarse cloths, -2 small ones 8 shirts, - Old tin-ware 9 napkins, -3 small bowls, 2 hand-towels. -4 bowls, -3 square stones, -2 small bowls, -1 large bowl, -1 platter, -4 candlesticks, -1 small candlestick. - -1544. - -Hose S 40 -straw S 60 -wheat S 42 -wine S 54 -bread S 18 -meat S 54 -eggs S 5 -salad S 3 -the Barber S 2 d 6 -horses S 1 - -1545. - - Sunday - -meat S 10 d -wine S 12 d -bran S 5 d 4 -herbs S 10 d -buttermilk S 4 d 4 -melon S 3 d -bread S 3 d 1 -____________________ - Monday S 9 8 -____________________ -..... S 6 d -wine S 12 d -bran S 9 d 4 -buttermilk S 4 d 4 -herbs S 8 d -____________________ - Tuesday S d -_____________________ -meat S 0 d 8 -wine S 12 d -bread S 3 d -meal S 5 d 4 -herbs S 8 d -_____________________ - Wednesday -_____________________ -wine S 5 d -melon S 2 d -meal S 5 d 4 -vegetables S 8 - -Notes by unknown persons among the MSS. (1546-1565). - -1546. - -Miseracione divina sacro sancte Romane ecclesie tituli n cardinalis -2wulgariter nuncupatus venerabili religioso fratri Johanni Mair -d'Nustorf 3ordinis praedicatorum provintie teutonie (?) conventus -Wiennensis capellano 4 nostro commensali salutem in dno sempiternam -Religione zelus rite ac in [ferite?] 5honestas aliarumque -laudabilium probitatis et virtutum merita quibus apud nos fide -6digno commendationis testimonio Magistri videlicet ordinis felicis -recordacionis Leonardi de 7Mansuetis de Perusio sigillo suo ... us -dans tibi ad ... opera virtutum comen(salem)? 8 locum et tempus -success(ores) cujus similiter officium ministratus qui -praedecessoris sui donum (?) 9confirmavit et de novo dedit -aliorumque plurima [laudatis] qui opera tua laudant 10nos inducunt -ut tibi (?) reddamus ad gratiam liberalem hinc est quod nos -cupientes. [Footnote: The meaning of this document, which is very -difficult to decipher, and is written in unintelligible Latin, is, -that Leonardo di Mansuetis recommends the Rev. Mair of Nusdorf, -chaplain at Vienna, to some third person; and says also that -something, which had to be proved, has been proved. The rest of the -passages on the same leaf are undoubtedly in Leonardo's hand. (Nos. -483, 661, 519, 578, 392, 582, 887 and 894.)] - -1547. - -Johannes Antonius di Johannes Ambrosius de Bolate. He who lets time -pass and does not grow in virtue, the more I think of it the more I -grieve. No man has it in him to be virtuous who will give up honour -for gain. Good fortune is valueless to him who knows not toil. The -man becomes happy who follows Christ. There is no perfect gift -without great suffering. Our glories and our triumphs pass away. -Foul lust, and dreams, and luxury, and sloth have banished every -virtue from the world; so that our Nature, wandering and perplexed, -has almost lost the old and better track. Henceforth it were well to -rouse thyself from sleep. The master said that lying in down will -not bring thee to Fame; nor staying beneath the quilts. He who, -without Fame, burns his life to waste, leaves no more vestige of -himself on earth than wind-blown smoke, or the foam upon the sea. -[Footnote: From the last sentence we may infer that this text is by -the hand of a pupil of Leonardo's.-- On the same sheet are the notes -Nos.1175 and 715 in Leonardo's own handwriting.] - -1548. - -On the morning of Santo Zanobio the -29th of May 1504, I had from Lionardo Vinci -15 gold ducats and began to spend them. -to Mona Margarita S 62 d 4 -to remake the ring S 19 d 8 -clothes S 13 -good beef S 4 -eggs S 6 -debt at the bank S 7 -velvet S 12 -wine S 6 d 4 -meat S 4 -mulberries S 2 d 4 -mushrooms S 3 d 4 -salad S 1 -fruit S 1 d 4 -candles S 3 -... S 1 -flour S 2 - - Sunday 198 8 - -bread S 6 -wine S 9 d 4 -meat S 7 -soup S 2 -fruit S 3 d 4 -candles S 3 d - -Monday 31 - -bread S 6 d 4 -meat S 10 d 8 -wine S 9 d 4 -fruit S 4 -soup S 1 d 8 - - 32 - -1549. - -Tuesday - -bread S 6 -meat S 11 -wine S 7 -fruit S 9 -soup S 2 -salad S 1 - -[Footnote 1548 and 1549: On the same sheet is the text No. 1015 in Leonardo's own handwriting.] - -1550. - -To Monna Margarita S 5 -to Tomaso S 14 -to Monna Margarita d 5 S 2 -on the day of San Zanobi -left ... after -payment d 13 S 2 d 4 -of Monna Margarita - - altogether d 14 S 5 d 4 - -1551. - -On Monday, the l3th of February, I lent lire S 7 to Lionardo to -spend, Friday d 7. - -[Footnote: This note is followed by an account very like the one -given as No. 1549.] - -1552. - -Stephano Chigi, Canonico ..., servant of the honorable Count Grimani -at S. Apostoli. - -[Footnote: Compare No. 674, 21-23.] - -1553. - -Having become anxious ... Bernardo di Simone, Silvestro di Stefano, -Bernardo di Jacopo, Francesco di Matteo Bonciani, Antonio di -Giovanni Ruberti, Antonio da Pistoia.... Antonio; He who has time -and waits for time, will lose his friends and his money. - -1554. - -Reverend Maestro, Domino Giovanni, I spoke to Maestro Zacaria as a -brother about this business, and I made him satisfied with the -arrangement that I had wished; that is, as regards the commission -that I had from the parties and I say that between us there is no -need to pay money down, as regard the pictures of the ... - -1555. - -Of things seen through a mist that which is nearest its farthest -limit will be least visible, and all the more so as they are more -remote. - -1556. - -Theodoricus Rex Semper Augustus. - -1557. - -Either you say Hesperia alone, and it will mean Italy, or you add -ultima, and it will mean Spain. Umbria, part of Tuscany. - -[Footnote: The notes in Greek, Nos. 1557, 1558 and 1562 stand in -close connection with each other, but the meaning of some words is -very doubtful, and a translation is thus rendered impossible.] - -1558. - -[Footnote: Greek Characters] - -1559. - -Canonica of ... on the 5th of July 1507; my dearly beloved mother, -sisters and cousin I herewith inform you that thanks to God I am ... -about the sword which I ... bring it to Maso at the piazza ... and I -will settle the business of Piero so that ... - -[Footnote: AMORETTI, _Mem. Stor. XXIV_, quotes the first three lines -of this letter as by Leonardo. The character of the writing however -does not favour this hypothesis, and still less the contents. I -should regard it rather a rough draft of a letter by young Melzi. I -have not succeeded in deciphering completely the 13 lines of this -text. Amoretti reads at the beginning _Canonica di Vaprio_, but -_Vaprio_ seems to me a very doubtful reading.] - -1560. - - Ut bene respondet Naturae ars docta! dedisset - Vincius, ut tribuit cetera - sic animam - - Noluit ut similis magis haec foret: altera sic est: - Possidet illius Maurus amans animam. - -[Footnote: These three epigrams on the portrait of Lucrezia -Crivelli, a picture by Leonardo which must have been lost at a very -early date, seem to have been dedicated to Leonardo by the poet. -Leonardo used the reverse of the sheet for notes on geometry.] - -Hujus quam cernis nomen Lucretia, Divi Omnia cui larga contribuere -manu. Rara huic forma data est; pinxit Leonardos, amavit Maurus, -pictorum primus hic, ille ducum. - -Naturam, ac superas hac laesit imagine Divas Pictor: tantum hominis -posse manum haec doluit, Illae longa dari tam magnae tempera formae, -Quae spatio fuerat deperitura brevi. - -1561. - -Egidius Romanus on the formation of the human body in the mother's -womb [Footnote 1: _Liber magistri Egidii de pulsibus matrice -conipositus (cum commentario Gentilis de Fulgineo)_ published in -1484 at Padova, in 1494 and in 1514 at Venice, and in 1505 at -Lyons.]. - -[Footnote 2:2. This text appears to be in a handwriting different -from that in the note, l. 1. Here the reading is not so simple as -AMORETTI gave it, _Mem. Star. XXV: A Monsieur Lyonard Peintre du Roy -pour Amboyse_. He says too that this address is of the year 1509, -and Mr. Ravaisson remarks: "_De cette suscription il semble qu'on -peut inferer que Leonard etait alors en France, a la cour de Louis -XII ... Pour conclure je crois qu'il n'est pas prouve que Leonard de -Vinci n'ait pas fait un voyage de quelques mois en France sous Louis -XII, entre le printemps de 1509 et l'automne de_ 1510."--I must -confess that I myself have not succeeded in deciphering completely -this French writing of which two words remain to me doubtful. But so -much seems to be quite evident that this is not an address of a -letter at all, but a certificate or note. _Amboise_[l. 6] I believe -to be the signature of Charles d'Amboise the Governor of Milan. If -this explanation is the right one, it can be easily explained by the -contents of Nos. 1350 and 1529. The note, line 1, was perhaps added -later by another hand; and Leonardo himself wrote afterwards on the -same sheet some geometrical explanations. I must also point out that -the statement that this sheet belongs to the year 1509 has -absolutely no foundation in fact. There is no clue whatever for -giving a precise date to this note.] To Monsieur le Vinci,--the -horses of the king's equerry.... Continue the payment to Ms. -Lyonard, Painter to the King. - -[6] Amboise. - -1562. - -[Footnote: Greek Characters] - -1563. - -Memorandum to Maestro Lionardo to have ... the state of Florence. - -1564. - -To remind your Excellency that Ridolfo Manini brought to Florence a -quantity of crystal besides other stones such as are ... - -1565. - -XVI C. 6 de Ciuitate Dei, se Antipodes. - -[Footnote: A facsimile of this note, which refers to a well known -book by St. Augustin, is given on page 254.] - -1566. - -Leonardo's Will. - -Be it known to all persons, present and to come that at the court of -our Lord the King at Amboise before ourselves in person, Messer -Leonardo da Vinci painter to the King, at present staying at the -place known as Cloux near Amboise, duly considering the certainty of -death and the uncertainty of its time, has acknowledged and declared -in the said court and before us that he has made, according to the -tenor of these presents, his testament and the declaration of his -last will, as follows. And first he commends his soul to our Lord, -Almighty God, and to the Glorious Virgin Mary, and to our lord Saint -Michael, to all the blessed Angels and Saints male and female in -Paradise. - -Item. The said Testator desires to be buried within the church of -Saint Florentin at Amboise, and that his body shall be borne thither -by the chaplains of the church. - -Item. That his body may be followed from the said place to the said -church of Saint Florentin by the _collegium_ of the said church, -that is to say by the rector and the prior, or by their vicars and -chaplains of the church of Saint Denis of Amboise, also the lesser -friars of the place, and before his body shall be carried to the -said church this Testator desires, that in the said church of Saint -Florentin three grand masses shall be celebrated by the deacon and -sub-deacon and that on the day when these three high masses are -celebrated, thirty low masses shall also be performed at Saint -Gregoire. - -Item. That in the said church of Saint Denis similar services shall -be performed, as above. - -Item. That the same shall be done in the church of the said friars -and lesser brethren. - -Item. The aforesaid Testator gives and bequeaths to Messer Francesco -da Melzo, nobleman, of Milan, in remuneration for services and -favours done to him in the past, each - -[Footnote: See page 420.] - -and all of the books the Testator is at present possessed of, and -the instruments and portraits appertaining to his art and calling as -a painter. - -Item. The same Testator gives and bequeaths henceforth for ever to -Battista de Vilanis his servant one half, that is the moity, of his -garden which is outside the walls of Milan, and the other half of -the same garden to Salai his servant; in which garden aforesaid -Salai has built and constructed a house which shall be and remain -henceforth in all perpetuity the property of the said Salai, his -heirs and successors; and this is in remuneration for the good and -kind services which the said de Vilanis and Salai, his servants have -done him in past times until now. - -Item. The said Testator gives to Maturina his waiting woman a cloak -of good black cloth lined with fur, a ... of cloth and two ducats -paid once only; and this likewise is in remuneration for good -service rendered to him in past times by the said Maturina. - -Item. He desires that at his funeral sixty tapers shall be carried -which shall be borne by sixty poor men, to whom shall be given money -for carrying them; at the discretion of the said Melzo, and these -tapers shall be distributed among the four above mentioned churches. - -Item. The said Testator gives to each of the said churches ten lbs. -of wax in thick tapers, which shall be placed in the said churches -to be used on the day when those said services are celebrated. - -Item. That alms shall be given to the poor of the Hotel-Dieu, to the -poor of Saint Lazare d'Amboise and, to that end, there shall be -given and paid to the treasurers of that same fraternity the sum and -amount of seventy soldi of Tours. - -Item. The said Testator gives and bequeaths to the said Messer -Francesco Melzo, being present and agreeing, the remainder of his -pension and the sums of money which are owing to him from the past -time till the day of his death by the receiver or treasurer-general -M. Johan Sapin, and each and every sum of money that he has already -received from the aforesaid Sapin of his said pension, and in case -he should die before the said Melzo and not otherwise; which moneys -are at present in the possession of the said Testator in the said -place called Cloux, as he says. And he likewise gives and bequeaths -to the said Melzo all and each of his clothes which he at present -possesses at the said place of Cloux, and all in remuneration for -the good and kind services done by him in past times till now, as -well as in payment for the trouble and annoyance he may incur with -regard to the execution of this present testament, which however, -shall all be at the expense of the said Testator. - -And he orders and desires that the sum of four hundred scudi del -Sole, which he has deposited in the hands of the treasurer of Santa -Maria Nuova in the city of Florence, may be given to his brothers -now living in Florence with all the interest and usufruct that may -have accrued up to the present time, and be due from the aforesaid -treasurer to the aforesaid Testator on account of the said four -hundred crowns, since they were given and consigned by the Testator -to the said treasurers. - -Item. He desires and orders that the said Messer Francesco de Melzo -shall be and remain the sole and only executor of the said will of -the said Testator; and that the said testament shall be executed in -its full and complete meaning and according to that which is here -narrated and said, to have, hold, keep and observe, the said Messer -Leonardo da Vinci, constituted Testator, has obliged and obliges by -these presents the said his heirs and successors with all his goods -moveable and immoveable present and to come, and has renounced and -expressly renounces by these presents all and each of the things -which to that are contrary. Given at the said place of Cloux in the -presence of Magister Spirito Fieri vicar, of the church of Saint -Denis at Amboise, of M. Guglielmo Croysant priest and chaplain, of -Magister Cipriane Fulchin, Brother Francesco de Corion, and of -Francesco da Milano, a brother of the Convent of the Minorites at -Amboise, witnesses summoned and required to that end by the -indictment of the said court in the presence of the aforesaid M. -Francesco de Melze who accepting and agreeing to the same has -promised by his faith and his oath which he has administered to us -personally and has sworn to us never to do nor say nor act in any -way to the contrary. And it is sealed by his request with the royal -seal apposed to legal contracts at Amboise, and in token of good -faith. - -Given on the XXIIIrd day of April MDXVIII, before Easter. - -And on the XXIIIrd day of this month of April MDXVIII, in the -presence of M. Guglielmo Borian, Royal notary in the court of the -bailiwick of Amboise, the aforesaid M. Leonardo de Vinci gave and -bequeathed, by his last will and testament, as aforesaid, to the -said M. Baptista de Vilanis, being present and agreeing, the right -of water which the King Louis XII, of pious memory lately deceased -gave to this same de Vinci, the stream of the canal of Santo -Cristoforo in the duchy of Milan, to belong to the said Vilanis for -ever in such wise and manner that the said gentleman made him this -gift in the presence of M. Francesco da Melzo, gentleman, of Milan -and in mine. - -And on the aforesaid day in the said month of April in the said year -MDXVIII the same M. Leonardo de Vinci by his last will and testament -gave to the aforesaid M. Baptista de Vilanis, being present and -agreeing, each and all of the articles of furniture and utensils of -his house at present at the said place of Cloux, in the event of the -said de Vilanis surviving the aforesaid M. Leonardo de Vinci, in the -presence of the said M. Francesco Melzo and of me Notary &c. 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Before running this script start the IPython controller -and some engines using something like:: - - ipcluster -n 4 -""" -from twisted.python.failure import Failure -from IPython.kernel import client -import time - -fetchParse = """ -from twisted.web import microdom -import urllib2 -import urlparse - -def fetchAndParse(url, data=None): - links = [] - try: - page = urllib2.urlopen(url, data=data) - except Exception: - return links - else: - if page.headers.type == 'text/html': - doc = microdom.parseString(page.read(), beExtremelyLenient=True) - for node in doc.getElementsByTagName('a'): - if node.getAttribute('href'): - links.append(urlparse.urljoin(url, node.getAttribute('href'))) - return links -""" - -class DistributedSpider(object): - - # Time to wait between polling for task results. - pollingDelay = 0.5 - - def __init__(self, site): - self.tc = client.TaskClient() - self.rc = client.MultiEngineClient() - self.rc.execute(fetchParse) - - self.allLinks = [] - self.linksWorking = {} - self.linksDone = {} - - self.site = site - - def visitLink(self, url): - if url not in self.allLinks: - self.allLinks.append(url) - if url.startswith(self.site): - print ' ', url - self.linksWorking[url] = self.tc.run(client.StringTask('links = fetchAndParse(url)', pull=['links'], push={'url': url})) - - def onVisitDone(self, result, url): - print url, ':' - self.linksDone[url] = None - del self.linksWorking[url] - if isinstance(result.failure, Failure): - txt = result.failure.getTraceback() - for line in txt.split('\n'): - print ' ', line - else: - for link in result.ns.links: - self.visitLink(link) - - def run(self): - self.visitLink(self.site) - while self.linksWorking: - print len(self.linksWorking), 'pending...' - self.synchronize() - time.sleep(self.pollingDelay) - - def synchronize(self): - for url, taskId in self.linksWorking.items(): - # Calling get_task_result with block=False will return None if the - # task is not done yet. This provides a simple way of polling. - result = self.tc.get_task_result(taskId, block=False) - if result is not None: - self.onVisitDone(result, url) - -def main(): - distributedSpider = DistributedSpider(raw_input('Enter site to crawl: ')) - distributedSpider.run() - -if __name__ == '__main__': - main() diff --git a/docs/examples/kernel/helloworld.py b/docs/examples/kernel/helloworld.py deleted file mode 100644 index ce18244..0000000 --- a/docs/examples/kernel/helloworld.py +++ /dev/null @@ -1,14 +0,0 @@ -""" -A Distributed Hello world -Ken Kinder -""" -from IPython.kernel import client - -tc = client.TaskClient() -mec = client.MultiEngineClient() - -mec.execute('import time') -hello_taskid = tc.run(client.StringTask('time.sleep(3) ; word = "Hello,"', pull=('word'))) -world_taskid = tc.run(client.StringTask('time.sleep(3) ; word = "World!"', pull=('word'))) -print "Submitted tasks:", hello_taskid, world_taskid -print tc.get_task_result(hello_taskid,block=True).ns.word, tc.get_task_result(world_taskid,block=True).ns.word diff --git a/docs/examples/kernel/mcdriver.py b/docs/examples/kernel/mcdriver.py deleted file mode 100644 index fe5f6b7..0000000 --- a/docs/examples/kernel/mcdriver.py +++ /dev/null @@ -1,148 +0,0 @@ -#!/usr/bin/env python -"""Run a Monte-Carlo options pricer in parallel.""" - -#----------------------------------------------------------------------------- -# Imports -#----------------------------------------------------------------------------- - -import sys -import time -from IPython.kernel import client -import numpy as np -from mcpricer import price_options -from matplotlib import pyplot as plt - -#----------------------------------------------------------------------------- -# Setup parameters for the run -#----------------------------------------------------------------------------- - -def ask_question(text, the_type, default): - s = '%s [%r]: ' % (text, the_type(default)) - result = raw_input(s) - if result: - return the_type(result) - else: - return the_type(default) - -cluster_profile = ask_question("Cluster profile", str, "default") -price = ask_question("Initial price", float, 100.0) -rate = ask_question("Interest rate", float, 0.05) -days = ask_question("Days to expiration", int, 260) -paths = ask_question("Number of MC paths", int, 10000) -n_strikes = ask_question("Number of strike values", int, 5) -min_strike = ask_question("Min strike price", float, 90.0) -max_strike = ask_question("Max strike price", float, 110.0) -n_sigmas = ask_question("Number of volatility values", int, 5) -min_sigma = ask_question("Min volatility", float, 0.1) -max_sigma = ask_question("Max volatility", float, 0.4) - -strike_vals = np.linspace(min_strike, max_strike, n_strikes) -sigma_vals = np.linspace(min_sigma, max_sigma, n_sigmas) - -#----------------------------------------------------------------------------- -# Setup for parallel calculation -#----------------------------------------------------------------------------- - -# The MultiEngineClient is used to setup the calculation and works with all -# engine. -mec = client.MultiEngineClient(profile=cluster_profile) - -# The TaskClient is an interface to the engines that provides dynamic load -# balancing at the expense of not knowing which engine will execute the code. -tc = client.TaskClient(profile=cluster_profile) - -# Initialize the common code on the engines. This Python module has the -# price_options function that prices the options. -mec.run('mcpricer.py') - -#----------------------------------------------------------------------------- -# Perform parallel calculation -#----------------------------------------------------------------------------- - -print "Running parallel calculation over strike prices and volatilities..." -print "Strike prices: ", strike_vals -print "Volatilities: ", sigma_vals -sys.stdout.flush() - -# Submit tasks to the TaskClient for each (strike, sigma) pair as a MapTask. -t1 = time.time() -taskids = [] -for strike in strike_vals: - for sigma in sigma_vals: - t = client.MapTask( - price_options, - args=(price, strike, sigma, rate, days, paths) - ) - taskids.append(tc.run(t)) - -print "Submitted tasks: ", len(taskids) -sys.stdout.flush() - -# Block until all tasks are completed. -tc.barrier(taskids) -t2 = time.time() -t = t2-t1 - -print "Parallel calculation completed, time = %s s" % t -print "Collecting results..." - -# Get the results using TaskClient.get_task_result. -results = [tc.get_task_result(tid) for tid in taskids] - -# Assemble the result into a structured NumPy array. -prices = np.empty(n_strikes*n_sigmas, - dtype=[('ecall',float),('eput',float),('acall',float),('aput',float)] -) - -for i, price_tuple in enumerate(results): - prices[i] = price_tuple - -prices.shape = (n_strikes, n_sigmas) -strike_mesh, sigma_mesh = np.meshgrid(strike_vals, sigma_vals) - -print "Results are available: strike_mesh, sigma_mesh, prices" -print "To plot results type 'plot_options(sigma_mesh, strike_mesh, prices)'" - -#----------------------------------------------------------------------------- -# Utilities -#----------------------------------------------------------------------------- - -def plot_options(sigma_mesh, strike_mesh, prices): - """ - Make a contour plot of the option price in (sigma, strike) space. - """ - plt.figure(1) - - plt.subplot(221) - plt.contourf(sigma_mesh, strike_mesh, prices['ecall']) - plt.axis('tight') - plt.colorbar() - plt.title('European Call') - plt.ylabel("Strike Price") - - plt.subplot(222) - plt.contourf(sigma_mesh, strike_mesh, prices['acall']) - plt.axis('tight') - plt.colorbar() - plt.title("Asian Call") - - plt.subplot(223) - plt.contourf(sigma_mesh, strike_mesh, prices['eput']) - plt.axis('tight') - plt.colorbar() - plt.title("European Put") - plt.xlabel("Volatility") - plt.ylabel("Strike Price") - - plt.subplot(224) - plt.contourf(sigma_mesh, strike_mesh, prices['aput']) - plt.axis('tight') - plt.colorbar() - plt.title("Asian Put") - plt.xlabel("Volatility") - - - - - - diff --git a/docs/examples/kernel/mcpricer.py b/docs/examples/kernel/mcpricer.py deleted file mode 100644 index 29772ff..0000000 --- a/docs/examples/kernel/mcpricer.py +++ /dev/null @@ -1,45 +0,0 @@ -import numpy as np -from math import * - - -def price_options(S=100.0, K=100.0, sigma=0.25, r=0.05, days=260, paths=10000): - """ - Price European and Asian options using a Monte Carlo method. - - Parameters - ---------- - S : float - The initial price of the stock. - K : float - The strike price of the option. - sigma : float - The volatility of the stock. - r : float - The risk free interest rate. - days : int - The number of days until the option expires. - paths : int - The number of Monte Carlo paths used to price the option. - - Returns - ------- - A tuple of (E. call, E. put, A. call, A. put) option prices. - """ - h = 1.0/days - const1 = exp((r-0.5*sigma**2)*h) - const2 = sigma*sqrt(h) - stock_price = S*np.ones(paths, dtype='float64') - stock_price_sum = np.zeros(paths, dtype='float64') - for j in range(days): - growth_factor = const1*np.exp(const2*np.random.standard_normal(paths)) - stock_price = stock_price*growth_factor - stock_price_sum = stock_price_sum + stock_price - stock_price_avg = stock_price_sum/days - zeros = np.zeros(paths, dtype='float64') - r_factor = exp(-r*h*days) - euro_put = r_factor*np.mean(np.maximum(zeros, K-stock_price)) - asian_put = r_factor*np.mean(np.maximum(zeros, K-stock_price_avg)) - euro_call = r_factor*np.mean(np.maximum(zeros, stock_price-K)) - asian_call = r_factor*np.mean(np.maximum(zeros, stock_price_avg-K)) - return (euro_call, euro_put, asian_call, asian_put) - diff --git a/docs/examples/kernel/multienginemap.py b/docs/examples/kernel/multienginemap.py deleted file mode 100644 index 016e0a8..0000000 --- a/docs/examples/kernel/multienginemap.py +++ /dev/null @@ -1,18 +0,0 @@ -from IPython.kernel import client - -mec = client.MultiEngineClient() - -result = mec.map(lambda x: 2*x, range(10)) -print "Simple, default map: ", result - -m = mec.mapper(block=False) -pr = m.map(lambda x: 2*x, range(10)) -print "Submitted map, got PendingResult: ", pr -result = pr.r -print "Using a mapper: ", result - -@mec.parallel() -def f(x): return 2*x - -result = f(range(10)) -print "Using a parallel function: ", result \ No newline at end of file diff --git a/docs/examples/kernel/nwmerge.py b/docs/examples/kernel/nwmerge.py deleted file mode 100644 index 4723501..0000000 --- a/docs/examples/kernel/nwmerge.py +++ /dev/null @@ -1,123 +0,0 @@ -"""Example showing how to merge multiple remote data streams. -""" -# Slightly modified version of: -# http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/511509 - -import heapq -from IPython.kernel.error import CompositeError - -def mergesort(list_of_lists, key=None): - """ Perform an N-way merge operation on sorted lists. - - @param list_of_lists: (really iterable of iterable) of sorted elements - (either by naturally or by C{key}) - @param key: specify sort key function (like C{sort()}, C{sorted()}) - - Yields tuples of the form C{(item, iterator)}, where the iterator is the - built-in list iterator or something you pass in, if you pre-generate the - iterators. - - This is a stable merge; complexity O(N lg N) - - Examples:: - - >>> print list(mergesort([[1,2,3,4], - ... [2,3.25,3.75,4.5,6,7], - ... [2.625,3.625,6.625,9]])) - [1, 2, 2, 2.625, 3, 3.25, 3.625, 3.75, 4, 4.5, 6, 6.625, 7, 9] - - # note stability - >>> print list(mergesort([[1,2,3,4], - ... [2,3.25,3.75,4.5,6,7], - ... [2.625,3.625,6.625,9]], - ... key=int)) - [1, 2, 2, 2.625, 3, 3.25, 3.75, 3.625, 4, 4.5, 6, 6.625, 7, 9] - - - >>> print list(mergesort([[4, 3, 2, 1], - ... [7, 6, 4.5, 3.75, 3.25, 2], - ... [9, 6.625, 3.625, 2.625]], - ... key=lambda x: -x)) - [9, 7, 6.625, 6, 4.5, 4, 3.75, 3.625, 3.25, 3, 2.625, 2, 2, 1] - """ - - heap = [] - for i, itr in enumerate(iter(pl) for pl in list_of_lists): - try: - item = itr.next() - if key: - toadd = (key(item), i, item, itr) - else: - toadd = (item, i, itr) - heap.append(toadd) - except StopIteration: - pass - heapq.heapify(heap) - - if key: - while heap: - _, idx, item, itr = heap[0] - yield item - try: - item = itr.next() - heapq.heapreplace(heap, (key(item), idx, item, itr) ) - except StopIteration: - heapq.heappop(heap) - - else: - while heap: - item, idx, itr = heap[0] - yield item - try: - heapq.heapreplace(heap, (itr.next(), idx, itr)) - except StopIteration: - heapq.heappop(heap) - - -def remote_iterator(rc,engine,name): - """Return an iterator on an object living on a remote engine. - """ - # Check that the object exists on the engine and pin a reference to it - iter_name = '_%s_rmt_iter_' % name - rc.execute('%s = iter(%s)' % (iter_name,name), targets=engine) - tpl = '_tmp = %s.next()' % iter_name - while True: - try: - rc.execute(tpl, targets=engine) - result = rc.pull('_tmp', targets=engine)[0] - # This causes the StopIteration exception to be raised. - except CompositeError, e: - e.raise_exception() - else: - yield result - -# Main, interactive testing -if __name__ == '__main__': - - from IPython.kernel import client - ipc = client.MultiEngineClient() - print 'Engine IDs:',ipc.get_ids() - - # Make a set of 'sorted datasets' - a0 = range(5,20) - a1 = range(10) - a2 = range(15,25) - - # Now, imagine these had been created in the remote engines by some long - # computation. In this simple example, we just send them over into the - # remote engines. They will all be called 'a' in each engine. - ipc.push(dict(a=a0), targets=0) - ipc.push(dict(a=a1), targets=1) - ipc.push(dict(a=a2), targets=2) - - # And we now make a local object which represents the remote iterator - aa0 = remote_iterator(ipc,0,'a') - aa1 = remote_iterator(ipc,1,'a') - aa2 = remote_iterator(ipc,2,'a') - - # Let's merge them, both locally and remotely: - print 'Merge the local datasets:' - print list(mergesort([a0,a1,a2])) - - print 'Locally merge the remote sets:' - print list(mergesort([aa0,aa1,aa2])) diff --git a/docs/examples/kernel/parallelpi.py b/docs/examples/kernel/parallelpi.py deleted file mode 100644 index 1254407..0000000 --- a/docs/examples/kernel/parallelpi.py +++ /dev/null @@ -1,54 +0,0 @@ -"""Calculate statistics on the digits of pi in parallel. - -This program uses the functions in :file:`pidigits.py` to calculate -the frequencies of 2 digit sequences in the digits of pi. The -results are plotted using matplotlib. - -To run, text files from http://www.super-computing.org/ -must be installed in the working directory of the IPython engines. -The actual filenames to be used can be set with the ``filestring`` -variable below. - -The dataset we have been using for this is the 200 million digit one here: -ftp://pi.super-computing.org/.2/pi200m/ -""" - -from IPython.kernel import client -from matplotlib import pyplot as plt -import numpy as np -from pidigits import * -from timeit import default_timer as clock - - -# Files with digits of pi (10m digits each) -filestring = 'pi200m-ascii-%(i)02dof20.txt' -files = [filestring % {'i':i} for i in range(1,16)] - - -# Connect to the IPython cluster -mec = client.MultiEngineClient(profile='mycluster') -mec.run('pidigits.py') - - -# Run 10m digits on 1 engine -mapper = mec.mapper(targets=0) -t1 = clock() -freqs10m = mapper.map(compute_two_digit_freqs, files[:1])[0] -t2 = clock() -digits_per_second1 = 10.0e6/(t2-t1) -print "Digits per second (1 core, 10m digits): ", digits_per_second1 - - -# Run 150m digits on 15 engines (8 cores) -t1 = clock() -freqs_all = mec.map(compute_two_digit_freqs, files[:len(mec)]) -freqs150m = reduce_freqs(freqs_all) -t2 = clock() -digits_per_second8 = 150.0e6/(t2-t1) -print "Digits per second (8 cores, 150m digits): ", digits_per_second8 - -print "Speedup: ", digits_per_second8/digits_per_second1 - -plot_two_digit_freqs(freqs150m) -plt.title("2 digit sequences in 150m digits of pi") - diff --git a/docs/examples/kernel/phistogram.py b/docs/examples/kernel/phistogram.py deleted file mode 100644 index 2401db0..0000000 --- a/docs/examples/kernel/phistogram.py +++ /dev/null @@ -1,33 +0,0 @@ -"""Parallel histogram function""" -import numpy - -def phistogram(rc, a, bins=10, rng=None, normed=False): - """Compute the histogram of a remote array a. - - :Parameters: - rc - IPython RemoteController instance - a : str - String name of the remote array - bins : int - Number of histogram bins - rng : (float, float) - Tuple of min, max of the range to histogram - normed : boolean - Should the histogram counts be normalized to 1 - """ - nengines = len(rc) - rc.push(dict(bins=bins, rng=rng)) - rc.execute('import numpy') - rc.execute('hist, lower_edges = numpy.histogram(%s, bins, rng)' % a) - lower_edges = rc.pull('lower_edges', targets=0) - hist_array = rc.gather('hist') - hist_array.shape = (nengines,-1) - total_hist = numpy.sum(hist_array, 0) - if normed: - total_hist = total_hist/numpy.sum(total_hist,dtype=float) - return total_hist, lower_edges - - - - diff --git a/docs/examples/kernel/pidigits.py b/docs/examples/kernel/pidigits.py deleted file mode 100644 index 7234d50..0000000 --- a/docs/examples/kernel/pidigits.py +++ /dev/null @@ -1,144 +0,0 @@ -"""Compute statistics on the digits of pi. - -This uses precomputed digits of pi from the website -of Professor Yasumasa Kanada at the University of -Tokoyo: http://www.super-computing.org/ - -Currently, there are only functions to read the -.txt (non-compressed, non-binary) files, but adding -support for compression and binary files would be -straightforward. - -This focuses on computing the number of times that -all 1, 2, n digits sequences occur in the digits of pi. -If the digits of pi are truly random, these frequencies -should be equal. -""" - -# Import statements - -from __future__ import division, with_statement -import numpy as np -from matplotlib import pyplot as plt - -# Top-level functions - -def compute_one_digit_freqs(filename): - """ - Read digits of pi from a file and compute the 1 digit frequencies. - """ - d = txt_file_to_digits(filename) - freqs = one_digit_freqs(d) - return freqs - -def compute_two_digit_freqs(filename): - """ - Read digits of pi from a file and compute the 2 digit frequencies. - """ - d = txt_file_to_digits(filename) - freqs = two_digit_freqs(d) - return freqs - -def reduce_freqs(freqlist): - """ - Add up a list of freq counts to get the total counts. - """ - allfreqs = np.zeros_like(freqlist[0]) - for f in freqlist: - allfreqs += f - return allfreqs - -def compute_n_digit_freqs(filename, n): - """ - Read digits of pi from a file and compute the n digit frequencies. - """ - d = txt_file_to_digits(filename) - freqs = n_digit_freqs(d, n) - return freqs - -# Read digits from a txt file - -def txt_file_to_digits(filename, the_type=str): - """ - Yield the digits of pi read from a .txt file. - """ - with open(filename, 'r') as f: - for line in f.readlines(): - for c in line: - if c != '\n' and c!= ' ': - yield the_type(c) - -# Actual counting functions - -def one_digit_freqs(digits, normalize=False): - """ - Consume digits of pi and compute 1 digit freq. counts. - """ - freqs = np.zeros(10, dtype='i4') - for d in digits: - freqs[int(d)] += 1 - if normalize: - freqs = freqs/freqs.sum() - return freqs - -def two_digit_freqs(digits, normalize=False): - """ - Consume digits of pi and compute 2 digits freq. counts. - """ - freqs = np.zeros(100, dtype='i4') - last = digits.next() - this = digits.next() - for d in digits: - index = int(last + this) - freqs[index] += 1 - last = this - this = d - if normalize: - freqs = freqs/freqs.sum() - return freqs - -def n_digit_freqs(digits, n, normalize=False): - """ - Consume digits of pi and compute n digits freq. counts. - - This should only be used for 1-6 digits. - """ - freqs = np.zeros(pow(10,n), dtype='i4') - current = np.zeros(n, dtype=int) - for i in range(n): - current[i] = digits.next() - for d in digits: - index = int(''.join(map(str, current))) - freqs[index] += 1 - current[0:-1] = current[1:] - current[-1] = d - if normalize: - freqs = freqs/freqs.sum() - return freqs - -# Plotting functions - -def plot_two_digit_freqs(f2): - """ - Plot two digits frequency counts using matplotlib. - """ - f2_copy = f2.copy() - f2_copy.shape = (10,10) - ax = plt.matshow(f2_copy) - plt.colorbar() - for i in range(10): - for j in range(10): - plt.text(i-0.2, j+0.2, str(j)+str(i)) - plt.ylabel('First digit') - plt.xlabel('Second digit') - return ax - -def plot_one_digit_freqs(f1): - """ - Plot one digit frequency counts using matplotlib. - """ - ax = plt.plot(f1,'bo-') - plt.title('Single digit counts in pi') - plt.xlabel('Digit') - plt.ylabel('Count') - return ax diff --git a/docs/examples/kernel/plotting_backend.py b/docs/examples/kernel/plotting_backend.py deleted file mode 100644 index 22fc3c2..0000000 --- a/docs/examples/kernel/plotting_backend.py +++ /dev/null @@ -1,57 +0,0 @@ -"""An example of how to use IPython1 for plotting remote parallel data - -The two files plotting_frontend.ipy and plotting_backend.py go together. - -This file (plotting_backend.py) performs the actual computation. For this -example, the computation just generates a set of random numbers that -look like a distribution of particles with 2D position (x,y) and -momentum (px,py). In a real situation, this file would do some time -consuming and complicated calculation, and could possibly make calls -to MPI. - -One important feature is that this script can also be run standalone without -IPython. This is nice as it allows it to be run in more traditional -settings where IPython isn't being used. - -When used with IPython1, this code is run on the engines. Because this -code doesn't make any plots, the engines don't have to have any plotting -packages installed. -""" - -# Imports -import numpy as N -import time -import random - -# Functions -def compute_particles(number): - x = N.random.standard_normal(number) - y = N.random.standard_normal(number) - px = N.random.standard_normal(number) - py = N.random.standard_normal(number) - return x, y, px, py - -def downsample(array, k): - """Choose k random elements of array.""" - length = array.shape[0] - indices = random.sample(xrange(length), k) - return array[indices] - -# Parameters of the run -number = 100000 -d_number = 1000 - -# The actual run - -time.sleep(0) # Pretend it took a while -x, y, px, py = compute_particles(number) -# Now downsample the data -downx = downsample(x, d_number) -downy = downsample(x, d_number) -downpx = downsample(px, d_number) -downpy = downsample(py, d_number) - -print "downx: ", downx[:10] -print "downy: ", downy[:10] -print "downpx: ", downpx[:10] -print "downpy: ", downpy[:10] \ No newline at end of file diff --git a/docs/examples/kernel/plotting_frontend.py b/docs/examples/kernel/plotting_frontend.py deleted file mode 100644 index 87a2fa3..0000000 --- a/docs/examples/kernel/plotting_frontend.py +++ /dev/null @@ -1,52 +0,0 @@ -"""An example of how to use IPython1 for plotting remote parallel data - -The two files plotting_frontend.ipy and plotting_backend.py go together. - -To run this example, first start the IPython controller and 4 -engines:: - - ipcluster -n 4 - -Then start ipython in pylab mode:: - - ipython -pylab - -Then a simple "run plotting_frontend.ipy" in IPython will run the -example. When this is done, all the variables (such as number, downx, etc.) -are available in IPython, so for example you can make additional plots. -""" - -import numpy as N -from pylab import * -from IPython.kernel import client - -# Get an IPython1 client -rc = client.MultiEngineClient() -rc.get_ids() - -# Run the simulation on all the engines -rc.run('plotting_backend.py') - -# Bring back the data -number = rc.pull('number') -d_number = rc.pull('d_number') -downx = rc.gather('downx') -downy = rc.gather('downy') -downpx = rc.gather('downpx') -downpy = rc.gather('downpy') - -print "number: ", sum(number) -print "downsampled number: ", sum(d_number) - -# Make a scatter plot of the gathered data -# These calls to matplotlib could be replaced by calls to pygist or -# another plotting package. -figure(1) -scatter(downx, downy) -xlabel('x') -ylabel('y') -figure(2) -scatter(downpx, downpy) -xlabel('px') -ylabel('py') -show() \ No newline at end of file diff --git a/docs/examples/kernel/pwordfreq.py b/docs/examples/kernel/pwordfreq.py deleted file mode 100644 index f96423b..0000000 --- a/docs/examples/kernel/pwordfreq.py +++ /dev/null @@ -1,46 +0,0 @@ -#!/usr/bin/env python -"""Parallel word frequency counter.""" - - -from itertools import repeat -from wordfreq import print_wordfreq, wordfreq - -def pwordfreq(rc, text): - """Parallel word frequency counter. - - rc - An IPython RemoteController - text - The name of a string on the engines to do the freq count on. - """ - - rc.execute('freqs = wordfreq(%s)' %text) - freqs_list = rc.pull('freqs') - word_set = set() - for f in freqs_list: - word_set.update(f.keys()) - freqs = dict(zip(word_set, repeat(0))) - for f in freqs_list: - for word, count in f.iteritems(): - freqs[word] += count - return freqs - -if __name__ == '__main__': - # Create a MultiEngineClient - from IPython.kernel import client - ipc = client.MultiEngineClient() - - # Run the wordfreq script on the engines. - ipc.run('wordfreq.py') - - # Run the serial version - print "Serial word frequency count:" - text = open('davinci.txt').read() - freqs = wordfreq(text) - print_wordfreq(freqs, 10) - - # The parallel version - print "\nParallel word frequency count:" - files = ['davinci%i.txt' % i for i in range(4)] - ipc.scatter('textfile', files) - ipc.execute('text = open(textfile[0]).read()') - pfreqs = pwordfreq(ipc,'text') - print_wordfreq(freqs) diff --git a/docs/examples/kernel/pwordfreq_skel.py b/docs/examples/kernel/pwordfreq_skel.py deleted file mode 100644 index e5a5357..0000000 --- a/docs/examples/kernel/pwordfreq_skel.py +++ /dev/null @@ -1,35 +0,0 @@ -#!/usr/bin/env python -"""Parallel word frequency counter.""" - - -from itertools import repeat -from wordfreq import print_wordfreq, wordfreq - -def pwordfreq(rc, text): - """Parallel word frequency counter. - - rc - An IPython RemoteController - text - The name of a string on the engines to do the freq count on. - """ - -if __name__ == '__main__': - # Create a MultiEngineClient - from IPython.kernel import client - ipc = client.MultiEngineClient() - - # Run the wordfreq script on the engines. - ipc.run('wordfreq.py') - - # Run the serial version - print "Serial word frequency count:" - text = open('davinci.txt').read() - freqs = wordfreq(text) - print_wordfreq(freqs, 10) - - # The parallel version - print "\nParallel word frequency count:" - files = ['davinci%i.txt' % i for i in range(4)] - ipc.scatter('textfile', files) - ipc.execute('text = open(textfile[0]).read()') - pfreqs = pwordfreq(ipc,'text') - print_wordfreq(freqs) diff --git a/docs/examples/kernel/rmt.ipy b/docs/examples/kernel/rmt.ipy deleted file mode 100644 index ab47c5e..0000000 --- a/docs/examples/kernel/rmt.ipy +++ /dev/null @@ -1,57 +0,0 @@ -#------------------------------------------------------------------------------- -# Driver code that the client runs. -#------------------------------------------------------------------------------- -# To run this code start a controller and engines using: -# ipcluster -n 2 -# Then run the scripts by doing irunner rmt.ipy or by starting ipython and -# doing run rmt.ipy. - -from rmtkernel import * -from IPython.kernel import client - - -def wignerDistribution(s): - """Returns (s, rho(s)) for the Wigner GOE distribution.""" - return (numpy.pi*s/2.0) * numpy.exp(-numpy.pi*s**2/4.) - - -def generateWignerData(): - s = numpy.linspace(0.0,4.0,400) - rhos = wignerDistribution(s) - return s, rhos - - -def serialDiffs(num, N): - diffs = ensembleDiffs(num, N) - normalizedDiffs = normalizeDiffs(diffs) - return normalizedDiffs - - -def parallelDiffs(rc, num, N): - nengines = len(rc.get_ids()) - num_per_engine = num/nengines - print "Running with", num_per_engine, "per engine." - rc.push(dict(num_per_engine=num_per_engine, N=N)) - rc.execute('diffs = ensembleDiffs(num_per_engine, N)') - # gather blocks always for now - pr = rc.gather('diffs') - return pr.r - - -# Main code -if __name__ == '__main__': - rc = client.MultiEngineClient() - print "Distributing code to engines..." - r = rc.run('rmtkernel.py') - rc.block = False - - # Simulation parameters - nmats = 100 - matsize = 30 - - %timeit -n1 -r1 serialDiffs(nmats,matsize) - %timeit -n1 -r1 parallelDiffs(rc, nmats, matsize) - - # Uncomment these to plot the histogram - # import pylab - # pylab.hist(parallelDiffs(rc,matsize,matsize)) diff --git a/docs/examples/kernel/rmtkernel.py b/docs/examples/kernel/rmtkernel.py deleted file mode 100644 index 2c913e2..0000000 --- a/docs/examples/kernel/rmtkernel.py +++ /dev/null @@ -1,44 +0,0 @@ -#------------------------------------------------------------------------------- -# Core routines for computing properties of symmetric random matrices. -#------------------------------------------------------------------------------- - -import numpy -ra = numpy.random -la = numpy.linalg - -def GOE(N): - """Creates an NxN element of the Gaussian Orthogonal Ensemble""" - m = ra.standard_normal((N,N)) - m += m.T - return m - - -def centerEigenvalueDiff(mat): - """Compute the eigvals of mat and then find the center eigval difference.""" - N = len(mat) - evals = numpy.sort(la.eigvals(mat)) - diff = evals[N/2] - evals[N/2-1] - return diff.real - - -def ensembleDiffs(num, N): - """Return an array of num eigenvalue differences for the NxN GOE - ensemble.""" - diffs = numpy.empty(num) - for i in xrange(num): - mat = GOE(N) - diffs[i] = centerEigenvalueDiff(mat) - return diffs - - -def normalizeDiffs(diffs): - """Normalize an array of eigenvalue diffs.""" - return diffs/diffs.mean() - - -def normalizedEnsembleDiffs(num, N): - """Return an array of num *normalized eigenvalue differences for the NxN - GOE ensemble.""" - diffs = ensembleDiffs(num, N) - return normalizeDiffs(diffs) - diff --git a/docs/examples/kernel/task_profiler.py b/docs/examples/kernel/task_profiler.py deleted file mode 100644 index 139e8ca..0000000 --- a/docs/examples/kernel/task_profiler.py +++ /dev/null @@ -1,77 +0,0 @@ -#!/usr/bin/env python -"""Test the performance of the task farming system. - -This script submits a set of tasks to the TaskClient. The tasks -are basically just a time.sleep(t), where t is a random number between -two limits that can be configured at the command line. To run -the script there must first be an IPython controller and engines running:: - - ipcluster -n 16 - -A good test to run with 16 engines is:: - - python task_profiler.py -n 128 -t 0.01 -T 1.0 - -This should show a speedup of 13-14x. The limitation here is that the -overhead of a single task is about 0.001-0.01 seconds. -""" -import random, sys -from optparse import OptionParser - -from IPython.utils.timing import time -from IPython.kernel import client - -def main(): - parser = OptionParser() - parser.set_defaults(n=100) - parser.set_defaults(tmin=1) - parser.set_defaults(tmax=60) - parser.set_defaults(controller='localhost') - parser.set_defaults(meport=10105) - parser.set_defaults(tport=10113) - - parser.add_option("-n", type='int', dest='n', - help='the number of tasks to run') - parser.add_option("-t", type='float', dest='tmin', - help='the minimum task length in seconds') - parser.add_option("-T", type='float', dest='tmax', - help='the maximum task length in seconds') - parser.add_option("-c", type='string', dest='controller', - help='the address of the controller') - parser.add_option("-p", type='int', dest='meport', - help="the port on which the controller listens for the MultiEngine/RemoteController client") - parser.add_option("-P", type='int', dest='tport', - help="the port on which the controller listens for the TaskClient client") - - (opts, args) = parser.parse_args() - assert opts.tmax >= opts.tmin, "tmax must not be smaller than tmin" - - rc = client.MultiEngineClient() - tc = client.TaskClient() - print tc.task_controller - rc.block=True - nengines = len(rc.get_ids()) - rc.execute('from IPython.utils.timing import time') - - # the jobs should take a random time within a range - times = [random.random()*(opts.tmax-opts.tmin)+opts.tmin for i in range(opts.n)] - tasks = [client.StringTask("time.sleep(%f)"%t) for t in times] - stime = sum(times) - - print "executing %i tasks, totalling %.1f secs on %i engines"%(opts.n, stime, nengines) - time.sleep(1) - start = time.time() - taskids = [tc.run(t) for t in tasks] - tc.barrier(taskids) - stop = time.time() - - ptime = stop-start - scale = stime/ptime - - print "executed %.1f secs in %.1f secs"%(stime, ptime) - print "%.3fx parallel performance on %i engines"%(scale, nengines) - print "%.1f%% of theoretical max"%(100*scale/nengines) - - -if __name__ == '__main__': - main() diff --git a/docs/examples/kernel/wordfreq.py b/docs/examples/kernel/wordfreq.py deleted file mode 100644 index d762f18..0000000 --- a/docs/examples/kernel/wordfreq.py +++ /dev/null @@ -1,66 +0,0 @@ -"""Count the frequencies of words in a string""" - -from __future__ import division - -import cmath as math - - -def wordfreq(text): - """Return a dictionary of words and word counts in a string.""" - - freqs = {} - for word in text.split(): - lword = word.lower() - freqs[lword] = freqs.get(lword, 0) + 1 - return freqs - - -def print_wordfreq(freqs, n=10): - """Print the n most common words and counts in the freqs dict.""" - - words, counts = freqs.keys(), freqs.values() - items = zip(counts, words) - items.sort(reverse=True) - for (count, word) in items[:n]: - print word, count - - -def wordfreq_to_weightsize(worddict, minsize=25, maxsize=50, minalpha=0.5, maxalpha=1.0): - mincount = min(worddict.itervalues()) - maxcount = max(worddict.itervalues()) - weights = {} - for k, v in worddict.iteritems(): - w = (v-mincount)/(maxcount-mincount) - alpha = minalpha + (maxalpha-minalpha)*w - size = minsize + (maxsize-minsize)*w - weights[k] = (alpha, size) - return weights - - -def tagcloud(worddict, n=10, minsize=25, maxsize=50, minalpha=0.5, maxalpha=1.0): - from matplotlib import pyplot as plt - import random - - worddict = wordfreq_to_weightsize(worddict, minsize, maxsize, minalpha, maxalpha) - - fig = plt.figure() - ax = fig.add_subplot(111) - ax.set_position([0.0,0.0,1.0,1.0]) - plt.xticks([]) - plt.yticks([]) - - words = worddict.keys() - alphas = [v[0] for v in worddict.values()] - sizes = [v[1] for v in worddict.values()] - items = zip(alphas, sizes, words) - items.sort(reverse=True) - for alpha, size, word in items[:n]: - # xpos = random.normalvariate(0.5, 0.3) - # ypos = random.normalvariate(0.5, 0.3) - xpos = random.uniform(0.0,1.0) - ypos = random.uniform(0.0,1.0) - ax.text(xpos, ypos, word.lower(), alpha=alpha, fontsize=size) - ax.autoscale_view() - return ax - - \ No newline at end of file diff --git a/docs/examples/kernel/wordfreq_skel.py b/docs/examples/kernel/wordfreq_skel.py deleted file mode 100644 index 691ccdf..0000000 --- a/docs/examples/kernel/wordfreq_skel.py +++ /dev/null @@ -1,18 +0,0 @@ -"""Count the frequencies of words in a string""" - -def wordfreq(text): - """Return a dictionary of words and word counts in a string.""" - - -def print_wordfreq(freqs, n=10): - """Print the n most common words and counts in the freqs dict.""" - words, counts = freqs.keys(), freqs.values() - items = zip(counts, words) - items.sort(reverse=True) - for (count, word) in items[:n]: - print word, count - -if __name__ == '__main__': - import gzip - text = gzip.open('HISTORY.gz').read() - freqs = wordfreq(text) \ No newline at end of file