upstream/ipython Files · docs/examples/kernel/davinci2.txt

Darren Dale

r3218

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.

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