docs/examples/kernel/davinci2.txt

strata; and in this shaft, on the side from which the hill slopes,
smooth and flatten a space one palm wide from the top to the bottom;
and after some time this smooth portion made on the side of the
shaft, will show plainly which part of the hill is moving.

[Footnote: See Pl. CIV.]

771.

The cracks in walls will never be parallel unless the part of the
wall that separates from the remainder does not slip down.

WHAT IS THE LAW BY WHICH BUILDINGS HAVE STABILITY.

The stability of buildings is the result of the contrary law to the
two former cases. That is to say that the walls must be all built up
equally, and by degrees, to equal heights all round the building,
and the whole thickness at once, whatever kind of walls they may be.
And although a thin wall dries more quickly than a thick one it will
not necessarily give way under the added weight day by day and thus,
[16] although a thin wall dries more quickly than a thick one, it
will not give way under the weight which the latter may acquire from
day to day. Because if double the amount of it dries in one day, one
of double the thickness will dry in two days or thereabouts; thus
the small addition of weight will be balanced by the smaller
difference of time [18].

The adversary says that _a_ which projects, slips down.

And here the adversary says that _r_ slips and not _c_.

HOW TO PROGNOSTICATE THE CAUSES OF CRACKS IN ANY SORT OF WALL.

The part of the wall which does not slip is that in which the
obliquity projects and overhangs the portion which has parted from
it and slipped down.

ON THE SITUATION OF FOUNDATIONS AND IN WHAT PLACES THEY ARE A CAUSE
OF RUIN.

When the crevice in the wall is wider at the top than at the bottom,
it is a manifest sign, that the cause of the fissure in the wall is
remote from the perpendicular line through the crevice.

[Footnote: Lines 1-5 refer to Pl. CV, No. 2. Line 9 _alle due
anteciedete_, see on the same page.

Lines 16-18. The translation of this is doubtful, and the meaning in
any case very obscure.

Lines 19-23 are on the right hand margin close to the two sketches
on Pl. CII, No. 3.]

772.

OF CRACKS IN WALLS, WHICH ARE WIDE AT THE BOTTOM AND NARROW AT THE
TOP AND OF THEIR CAUSES.

That wall which does not dry uniformly in an equal time, always
cracks.

A wall though of equal thickness will not dry with equal quickness
if it is not everywhere in contact with the same medium. Thus, if
one side of a wall were in contact with a damp slope and the other
were in contact with the air, then this latter side would remain of
the same size as before; that side which dries in the air will
shrink or diminish and the side which is kept damp will not dry. And
the dry portion will break away readily from the damp portion
because the damp part not shrinking in the same proportion does not
cohere and follow the movement of the part which dries continuously.

OF ARCHED CRACKS, WIDE AT THE TOP, AND NARROW BELOW.

Arched cracks, wide at the top and narrow below are found in
walled-up doors, which shrink more in their height than in their
breadth, and in proportion as their height is greater than their
width, and as the joints of the mortar are more numerous in the
height than in the width.

The crack diminishes less in _r o_ than in _m n_, in proportion as
there is less material between _r_ and _o_ than between _n_ and _m_.

Any crack made in a concave wall is wide below and narrow at the
top; and this originates, as is here shown at _b c d_, in the side
figure.

1. That which gets wet increases in proportion to the moisture it
imbibes.

2. And a wet object shrinks, while drying, in proportion to the
amount of moisture which evaporates from it.

[Footnote: The text of this passage is reproduced in facsimile on
Pl. CVI to the left. L. 36-40 are written inside the sketch No. 2.
L. 41-46 are partly written over the sketch No. 3 to which they
refer.]

773.

OF THE CAUSES OF FISSURES IN [THE WALLS OF] PUBLIC AND PRIVATE
BUILDINGS.

The walls give way in cracks, some of which are more or less
vertical and others are oblique. The cracks which are in a vertical
direction are caused by the joining of new walls, with old walls,
whether straight or with indentations fitting on to those of the old
wall; for, as these indentations cannot bear the too great weight of
the wall added on to them, it is inevitable that they should break,
and give way to the settling of the new wall, which will shrink one
braccia in every ten, more or less, according to the greater or
smaller quantity of mortar used between the stones of the masonry,
and whether this mortar is more or less liquid. And observe, that
the walls should always be built first and then faced with the
stones intended to face them. For, if you do not proceed thus, since
the wall settles more than the stone facing, the projections left on
the sides of the wall must inevitably give way; because the stones
used for facing the wall being larger than those over which they are
laid, they will necessarily have less mortar laid between the
joints, and consequently they settle less; and this cannot happen if
the facing is added after the wall is dry.

_a b_ the new wall, _c_ the old wall, which has already settled; and
the part _a b_ settles afterwards, although _a_, being founded on
_c_, the old wall, cannot possibly break, having a stable foundation
on the old wall. But only the remainder _b_ of the new wall will
break away, because it is built from top to bottom of the building;
and the remainder of the new wall will overhang the gap above the
wall that has sunk.

774.

A new tower founded partly on old masonry.

775.

OF STONES WHICH DISJOIN THEMSELVES FROM THEIR MORTAR.

Stones laid in regular courses from bottom to top and built up with
an equal quantity of mortar settle equally throughout, when the
moisture that made the mortar soft evaporates.

By what is said above it is proved that the small extent of the new
wall between _A_ and _n_ will settle but little, in proportion to
the extent of the same wall between _c_ and _d_. The proportion will
in fact be that of the thinness of the mortar in relation to the
number of courses or to the quantity of mortar laid between the
stones above the different levels of the old wall.

[Footnote: See Pl. CV, No. 1. The top of the tower is wanting in
this reproduction, and with it the letter _n_ which, in the
original, stands above the letter _A_ over the top of the tower,
while _c_ stands perpendicularly over _d_.]

776.

This wall will break under the arch _e f_, because the seven whole
square bricks are not sufficient to sustain the spring of the arch
placed on them. And these seven bricks will give way in their middle
exactly as appears in _a b_. The reason is, that the brick _a_ has
above it only the weight _a k_, whilst the last brick under the arch
has above it the weight _c d x a_.

_c d_ seems to press on the arch towards the abutment at the point
_p_ but the weight _p o_ opposes resistence to it, whence the whole
pressure is transmitted to the root of the arch. Therefore the foot
of the arch acts like 7 6, which is more than double of _x z_.

II.

ON FISSURES IN NICHES.

777.

ON FISSURES IN NICHES.

An arch constructed on a semicircle and bearing weights on the two
opposite thirds of its curve will give way at five points of the
curve. To prove this let the weights be at _n m_ which will break
the arch _a_, _b_, _f_. I say that, by the foregoing, as the
extremities _c_ and _a_ are equally pressed upon by the thrust _n_,
it follows, by the 5th, that the arch will give way at the point
which is furthest from the two forces acting on them and that is the
middle _e_. The same is to be understood of the opposite curve, _d g
b_; hence the weights _n m_ must sink, but they cannot sink by the
7th, without coming closer together, and they cannot come together
unless the extremities of the arch between them come closer, and if
these draw together the crown of the arch must break; and thus the
arch will give way in two places as was at first said &c.

I ask, given a weight at _a_ what counteracts it in the direction
_n_ _f_ and by what weight must the weight at _f_ be counteracted.

778.

ON THE SHRINKING OF DAMP BODIES OF DIFFERENT THICKNESS AND WIDTH.

The window _a_ is the cause of the crack at _b_; and this crack is
increased by the pressure of _n_ and _m_ which sink or penetrate
into the soil in which foundations are built more than the lighter
portion at _b_. Besides, the old foundation under _b_ has already
settled, and this the piers _n_ and _m_ have not yet done. Hence the
part _b_ does not settle down perpendicularly; on the contrary, it
is thrown outwards obliquely, and it cannot on the contrary be
thrown inwards, because a portion like this, separated from the main
wall, is larger outside than inside and the main wall, where it is
broken, is of the same shape and is also larger outside than inside;
therefore, if this separate portion were to fall inwards the larger
would have to pass through the smaller--which is impossible. Hence
it is evident that the portion of the semicircular wall when
disunited from the main wall will be thrust outwards, and not
inwards as the adversary says.

When a dome or a half-dome is crushed from above by an excess of
weight the vault will give way, forming a crack which diminishes
towards the top and is wide below, narrow on the inner side and wide
outside; as is the case with the outer husk of a pomegranate,
divided into many parts lengthwise; for the more it is pressed in
the direction of its length, that part of the joints will open most,
which is most distant from the cause of the pressure; and for that
reason the arches of the vaults of any apse should never be more
loaded than the arches of the principal building. Because that which
weighs most, presses most on the parts below, and they sink into the
foundations; but this cannot happen to lighter structures like the
said apses.

[Footnote: The figure on Pl. CV, No. 4 belongs to the first
paragraph of this passage, lines 1-14; fig. 5 is sketched by the
side of lines l5--and following. The sketch below of a pomegranate
refers to line 22. The drawing fig. 6 is, in the original, over line
37 and fig. 7 over line 54.]

Which of these two cubes will shrink the more uniformly: the cube
_A_ resting on the pavement, or the cube _b_ suspended in the air,
when both cubes are equal in weight and bulk, and of clay mixed with
equal quantities of water?

The cube placed on the pavement diminishes more in height than in
breadth, which the cube above, hanging in the air, cannot do. Thus
it is proved. The cube shown above is better shown here below.

The final result of the two cylinders of damp clay that is _a_ and
_b_ will be the pyramidal figures below _c_ and _d_. This is proved
thus: The cylinder _a_ resting on block of stone being made of clay
mixed with a great deal of water will sink by its weight, which
presses on its base, and in proportion as it settles and spreads all
the parts will be somewhat nearer to the base because that is
charged with the whole weight.

III.

ON THE NATURE OF THE ARCH.

779.

WHAT IS AN ARCH?

The arch is nothing else than a force originated by two weaknesses,
for the arch in buildings is composed of two segments of a circle,
each of which being very weak in itself tends to fall; but as each
opposes this tendency in the other, the two weaknesses combine to
form one strength.

OF THE KIND OF PRESSURE IN ARCHES.

As the arch is a composite force it remains in equilibrium because
the thrust is equal from both sides; and if one of the segments
weighs more than the other the stability is lost, because the
greater pressure will outweigh the lesser.

OF DISTRIBUTING THE PRESSURE ABOVE AN ARCH.

Next to giving the segments of the circle equal weight it is
necessary to load them equally, or you will fall into the same
defect as before.

WHERE AN ARCH BREAKS.

An arch breaks at the part which lies below half way from the
centre.

SECOND RUPTURE OF THE ARCH.

If the excess of weight be placed in the middle of the arch at the
point _a_, that weight tends to fall towards _b_, and the arch
breaks at 2/3 of its height at _c e_; and _g e_ is as many times
stronger than _e a_, as _m o_ goes into _m n_.

ON ANOTHER CAUSE OF RUIN.

The arch will likewise give way under a transversal thrust, for when
the charge is not thrown directly on the foot of the arch, the arch
lasts but a short time.

780.

ON THE STRENGTH OF THE ARCH.

The way to give stability to the arch is to fill the spandrils with
good masonry up to the level of its summit.

ON THE LOADING OF ROUND ARCHES.

ON THE PROPER MANNER OF LOADING THE POINTED ARCH.

ON THE EVIL EFFECTS OF LOADING THE POINTED ARCH DIRECTLY ABOVE ITS
CROWN.

ON THE DAMAGE DONE TO THE POINTED ARCH BY THROWING THE PRESSURE ON
THE FLANKS.

An arch of small curve is safe in itself, but if it be heavily
charged, it is necessary to strengthen the flanks well. An arch of a
very large curve is weak in itself, and stronger if it be charged,
and will do little harm to its abutments, and its places of giving
way are _o p_.

[Footnote: Inside the large figure on the righi is the note: _Da
pesare la forza dell' archo_.]

781.

ON THE REMEDY FOR EARTHQUAKES.

The arch which throws its pressure perpendicularly on the abutments
will fulfil its function whatever be its direction, upside down,
sideways or upright.

The arch will not break if the chord of the outer arch does not
touch the inner arch. This is manifest by experience, because
whenever the chord _a o n_ of the outer arch _n r a_ approaches the
inner arch _x b y_ the arch will be weak, and it will be weaker in
proportion as the inner arch passes beyond that chord. When an arch
is loaded only on one side the thrust will press on the top of the
other side and be transmitted to the spring of the arch on that
side; and it will break at a point half way between its two
extremes, where it is farthest from the chord.

782.

A continuous body which has been forcibly bent into an arch, thrusts
in the direction of the straight line, which it tends to recover.

783.

In an arch judiciously weighted the thrust is oblique, so that the
triangle _c n b_ has no weight upon it.

784.

I here ask what weight will be needed to counterpoise and resist the
tendency of each of these arches to give way?

[Footnote: The two lower sketches are taken from the MS. S. K. M.
III, 10a; they have there no explanatory text.]

785.

ON THE STRENGTH OF THE ARCH IN ARCHITECTURE.

The stability of the arch built by an architect resides in the tie
and in the flanks.

ON THE POSITION OF THE TIE IN THE ABOVE NAMED ARCH.

The position of the tie is of the same importance at the beginning
of the arch and at the top of the perpendicular pier on which it
rests. This is proved by the 2nd "of supports" which says: that part
of a support has least resistance which is farthest from its solid
attachment; hence, as the top of the pier is farthest from the
middle of its true foundation and the same being the case at the
opposite extremities of the arch which are the points farthest from
the middle, which is really its [upper] attachment, we have
concluded that the tie _a b_ requires to be in such a position as
that its opposite ends are between the four above-mentioned
extremes.

The adversary says that this arch must be more than half a circle,
and that then it will not need a tie, because then the ends will not
thrust outwards but inwards, as is seen in the excess at _a c_, _b
d_. To this it must be answered that this would be a very poor
device, for three reasons. The first refers to the strength of the
arch, since it is proved that the circular parallel being composed
of two semicircles will only break where these semicircles cross
each other, as is seen in the figure _n m;_ besides this it follows
that there is a wider space between the extremes of the semicircle
than between the plane of the walls; the third reason is that the
weight placed to counterbalance the strength of the arch diminishes
in proportion as the piers of the arch are wider than the space
between the piers. Fourthly in proportion as the parts at _c a b d_
turn outwards, the piers are weaker to support the arch above them.
The 5th is that all the material and weight of the arch which are in
excess of the semicircle are useless and indeed mischievous; and
here it is to be noted that the weight placed above the arch will be
more likely to break the arch at _a b_, where the curve of the
excess begins that is added to the semicircle, than if the pier were
straight up to its junction with the semicircle [spring of the
arch].

AN ARCH LOADED OVER THE CROWN WILL GIVE WAY AT THE LEFT HAND AND
RIGHT HAND QUARTERS.

This is proved by the 7th of this which says: The opposite ends of
the support are equally pressed upon by the weight suspended to
them; hence the weight shown at _f_ is felt at _b c_, that is half
at each extremity; and by the third which says: in a support of
equal strength [throughout] that portion will give way soonest which
is farthest from its attachment; whence it follows that _d_ being
equally distant from _f, e_ .....

If the centering of the arch does not settle as the arch settles,
the mortar, as it dries, will shrink and detach itself from the
bricks between which it was laid to keep them together; and as it
thus leaves them disjoined the vault will remain loosely built, and
the rains will soon destroy it.

786.

ON THE STRENGTH AND NATURE OF ARCHES, AND WHERE THEY ARE STRONG OR
WEAK; AND THE SAME AS TO COLUMNS.

That part of the arch which is nearer to the horizontal offers least
resistance to the weight placed on it.

When the triangle _a z n_, by settling, drives backwards the 2/3 of
each 1/2 circle that is _a s_ and in the same way _z m_, the reason
is that _a_ is perpendicularly over _b_ and so likewise _z_ is above
_f_.

Either half of an arch, if overweighted, will break at 2/3 of its
height, the point which corresponds to the perpendicular line above
the middle of its bases, as is seen at _a b_; and this happens
because the weight tends to fall past the point _r_.--And if,
against its nature it should tend to fall towards the point _s_ the
arch _n s_ would break precisely in its middle. If the arch _n s_
were of a single piece of timber, if the weight placed at _n_ should
tend to fall in the line _n m_, the arch would break in the middle
of the arch _e m_, otherwise it will break at one third from the top
at the point a because from _a_ to _n_ the arch is nearer to the
horizontal than from _a_ to _o_ and from _o_ to _s_, in proportion
as _p t_ is greater than _t n_, _a o_ will be stronger than _a n_
and likewise in proportion as _s o_ is stronger than _o a_, _r p_
will be greater than _p t_.

The arch which is doubled to four times of its thickness will bear
four times the weight that the single arch could carry, and more in
proportion as the diameter of its thickness goes a smaller number of
times into its length. That is to say that if the thickness of the
single arch goes ten times into its length, the thickness of the
doubled arch will go five times into its length. Hence as the
thickness of the double arch goes only half as many times into its
length as that of the single arch does, it is reasonable that it
should carry half as much more weight as it would have to carry if
it were in direct proportion to the single arch. Hence as this
double arch has 4 times the thickness of the single arch, it would
seem that it ought to bear 4 times the weight; but by the above rule
it is shown that it will bear exactly 8 times as much.

THAT PIER, WHICH is CHARGED MOST UNEQUALLY, WILL SOONEST GIVE WAY.

The column _c b_, being charged with an equal weight, [on each side]
will be most durable, and the other two outward columns require on
the part outside of their centre as much pressure as there is inside
of their centre, that is, from the centre of the column, towards the
middle of the arch.

Arches which depend on chains for their support will not be very
durable.

THAT ARCH WILL BE OF LONGER DURATION WHICH HAS A GOOD ABUTMENT
OPPOSED TO ITS THRUST.

The arch itself tends to fall. If the arch be 30 braccia and the
interval between the walls which carry it be 20, we know that 30
cannot pass through the 20 unless 20 becomes likewise 30. Hence the
arch being crushed by the excess of weight, and the walls offering
insufficient resistance, part, and afford room between them, for the
fall of the arch.

But if you do not wish to strengthen the arch with an iron tie you
must give it such abutments as can resist the thrust; and you can do
this thus: fill up the spandrels _m n_ with stones, and direct the
lines of the joints between them to the centre of the circle of the
arch, and the reason why this makes the arch durable is this. We
know very well that if the arch is loaded with an excess of weight
above its quarter as _a b_, the wall _f g_ will be thrust outwards
because the arch would yield in that direction; if the other quarter
_b c_ were loaded, the wall _f g_ would be thrust inwards, if it
were not for the line of stones _x y_ which resists this.

787.

PLAN.

Here it is shown how the arches made in the side of the octagon
thrust the piers of the angles outwards, as is shown by the line _h
c_ and by the line _t d_ which thrust out the pier _m_; that is they
tend to force it away from the centre of such an octagon.

788.

An Experiment to show that a weight placed on an arch does not
discharge itself entirely on its columns; on the contrary the
greater the weight placed on the arches, the less the arch transmits
the weight to the columns. The experiment is the following. Let a
man be placed on a steel yard in the middle of the shaft of a well,
then let him spread out his hands and feet between the walls of the
well, and you will see him weigh much less on the steel yard; give
him a weight on the shoulders, you will see by experiment, that the
greater the weight you give him the greater effort he will make in
spreading his arms and legs, and in pressing against the wall and
the less weight will be thrown on the steel yard.

IV.

ON FOUNDATIONS, THE NATURE OF THE GROUND AND SUPPORTS.

789.

The first and most important thing is stability.

As to the foundations of the component parts of temples and other
public buildings, the depths of the foundations must bear the same
proportions to each other as the weight of material which is to be
placed upon them.

Every part of the depth of earth in a given space is composed of
layers, and each layer is composed of heavier or lighter materials,
the lowest being the heaviest. And this can be proved, because these
layers have been formed by the sediment from water carried down to
the sea, by the current of rivers which flow into it. The heaviest
part of this sediment was that which was first thrown down, and so
on by degrees; and this is the action of water when it becomes
stagnant, having first brought down the mud whence it first flowed.
And such layers of soil are seen in the banks of rivers, where their
constant flow has cut through them and divided one slope from the
other to a great depth; where in gravelly strata the waters have run
off, the materials have, in consequence, dried and been converted
into hard stone, and this happened most in what was the finest mud;
whence we conclude that every portion of the surface of the earth
was once at the centre of the earth, and _vice_versa_ &c.

790.

The heaviest part of the foundations of buildings settles most, and
leaves the lighter part above it separated from it.

And the soil which is most pressed, if it be porous yields most.

You should always make the foundations project equally beyond the
weight of the walls and piers, as shown at _m a b_. If you do as
many do, that is to say if you make a foundation of equal width from
the bottom up to the surface of the ground, and charge it above with
unequal weights, as shown at _b e_ and at _e o_, at the part of the
foundation at _b e_, the pier of the angle will weigh most and
thrust its foundation downwards, which the wall at _e o_ will not
do; since it does not cover the whole of its foundation, and
therefore thrusts less heavily and settles less. Hence, the pier _b
e_ in settling cracks and parts from the wall _e o_. This may be
seen in most buildings which are cracked round the piers.

791.

The window _a_ is well placed under the window _c_, and the window
_b_ is badly placed under the pier _d_, because this latter is
without support and foundation; mind therefore never to make a break
under the piers between the windows.

792.

OF THE SUPPORTS.

A pillar of which the thickness is increased will gain more than its
due strength, in direct proportion to what its loses in relative
height.

EXAMPLE.

If a pillar should be nine times as high as it is broad--that is to
say, if it is one braccio thick, according to rule it should be nine
braccia high--then, if you place 100 such pillars together in a mass
this will be ten braccia broad and 9 high; and if the first pillar
could carry 10000 pounds the second being only about as high as it
is wide, and thus lacking 8 parts of its proper length, it, that is
to say, each pillar thus united, will bear eight times more than
when disconnected; that is to say, that if at first it would carry
ten thousand pounds, it would now carry 90 thousand.

V.

ON THE RESISTANCE OF BEAMS.

793.

That angle will offer the greatest resistance which is most acute,
and the most obtuse will be the weakest.

[Footnote: The three smaller sketches accompany the text in the
original, but the larger one is not directly connected with it. It
is to be found on fol. 89a of the same Manuscript and there we read
in a note, written underneath, _coverchio della perdicha del
castello_ (roof of the flagstaff of the castle),--Compare also Pl.
XCIII, No. 1.]

794.

If the beams and the weight _o_ are 100 pounds, how much weight will
be wanted at _ae_ to resist such a weight, that it may not fall
down?

795.

ON THE LENGTH OF BEAMS.

That beam which is more than 20 times as long as its greatest
thickness will be of brief duration and will break in half; and
remember, that the part built into the wall should be steeped in hot
pitch and filleted with oak boards likewise so steeped. Each beam
must pass through its walls and be secured beyond the walls with
sufficient chaining, because in consequence of earthquakes the beams
are often seen to come out of the walls and bring down the walls and
floors; whilst if they are chained they will hold the walls strongly
together and the walls will hold the floors. Again I remind you
never to put plaster over timber. Since by expansion and shrinking
of the timber produced by damp and dryness such floors often crack,
and once cracked their divisions gradually produce dust and an ugly
effect. Again remember not to lay a floor on beams supported on
arches; for, in time the floor which is made on beams settles
somewhat in the middle while that part of the floor which rests on
the arches remains in its place; hence, floors laid over two kinds
of supports look, in time, as if they were made in hills [Footnote:
19 M. RAVAISSON, in his edition of MS. A gives a very different
rendering of this passage translating it thus: _Les planchers qui
sont soutenus par deux differentes natures de supports paraissent
avec le temps faits en voute a cholli_.]

Remarks on the style of Leonardo's architecture.

A few remarks may here be added on the style of Leonardo's
architectural studies. However incomplete, however small in scale,
they allow us to establish a certain number of facts and
probabilities, well worthy of consideration.

When Leonardo began his studies the great name of Brunellesco was
still the inspiration of all Florence, and we cannot doubt that
Leonardo was open to it, since we find among his sketches the plan
of the church of Santo Spirito[Footnote 1: See Pl. XCIV, No. 2. Then
only in course of erection after the designs of Brunellesco, though
he was already dead; finished in 1481.] and a lateral view of San
Lorenzo (Pl. XCIV No. 1), a plan almost identical with the chapel
Degli Angeli, only begun by him (Pl. XCIV, No. 3) while among
Leonardo's designs for domes several clearly betray the influence of
Brunellesco's Cupola and the lantern of Santa Maria del
Fiore[Footnote 2: A small sketch of the tower of the Palazzo della
Signoria (MS. C.A. 309) proves that he also studied mediaeval
monuments.]

The beginning of the second period of modern Italian architecture
falls during the first twenty years of Leonardo's life. However the
new impetus given by Leon Battista Alberti either was not generally
understood by his contemporaries, or those who appreciated it, had
no opportunity of showing that they did so. It was only when taken
up by Bramante and developed by him to the highest rank of modern
architecture that this new influence was generally felt. Now the
peculiar feature of Leonardo's sketches is that, like the works of
Bramante, they appear to be the development and continuation of
Alberti's.

_But a question here occurs which is difficult to answer. Did
Leonardo, till he quitted Florence, follow the direction given by
the dominant school of Brunellesco, which would then have given rise
to his "First manner", or had he, even before he left Florence, felt
Alberti's influence--either through his works (Palazzo Ruccellai,
and the front of Santa Maria Novella) or through personal
intercourse? Or was it not till he went to Milan that Alberti's work
began to impress him through Bramante, who probably had known
Alberti at Mantua about 1470 and who not only carried out Alberti's
views and ideas, but, by his designs for St. Peter's at Rome, proved
himself the greatest of modern architects. When Leonardo went to
Milan Bramante had already been living there for many years. One of
his earliest works in Milan was the church of Santa Maria presso San
Satiro, Via del Falcone[Footnote 1: Evidence of this I intend to
give later on in a Life of Bramante, which I have in preparation.].

Now we find among Leonardos studies of Cupolas on Plates LXXXIV and
LXXXV and in Pl. LXXX several sketches which seem to me to have been
suggested by Bramante's dome of this church.

The MSS. B and Ash. II contain the plans of S. Sepolcro, the
pavilion in the garden of the duke of Milan, and two churches,
evidently inspired by the church of San Lorenzo at Milan.

MS. B. contains besides two notes relating to Pavia, one of them a
design for the sacristy of the Cathedral at Pavia, which cannot be
supposed to be dated later than 1492, and it has probably some
relation to Leonardo's call to Pavia June 21, 1490[Footnote 2: The
sketch of the plan of Brunellesco's church of Santo Spirito at
Florence, which occurs in the same Manuscript, may have been done
from memory.]. These and other considerations justify us in
concluding, that Leonardo made his studies of cupolas at Milan,
probably between the years 1487 and 1492 in anticipation of the
erection of one of the grandest churches of Italy, the Cathedral of
Pavia. This may explain the decidedly Lombardo-Bramantesque tendency
in the style of these studies, among which only a few remind us of
the forms of the cupolas of S. Maria del Fiore and of the Baptistery
of Florence. Thus, although when compared with Bramante's work,
several of these sketches plainly reveal that master's influence, we
find, among the sketches of domes, some, which show already
Bramante's classic style, of which the Tempietto of San Pietro in
Montorio, his first building executed at Rome, is the foremost
example[Footnote 3: It may be mentioned here, that in 1494 Bramante
made a similar design for the lantern of the Cupola of the Church of
Santa Maria delle Grazie.].

On Plate LXXXIV is a sketch of the plan of a similar circular
building; and the Mausoleum on Pl. XCVIII, no less than one of the
pedestals for the statue of Francesco Sforza (Pl. LXV), is of the
same type.

The drawings Pl. LXXXIV No. 2, Pl. LXXXVI No. 1 and 2 and the ground
flour ("flour" sic but should be "floor" ?) of the building in the
drawing Pl. XCI No. 2, with the interesting decoration by gigantic
statues in large niches, are also, I believe, more in the style
Bramante adopted at Rome, than in the Lombard style. Are we to
conclude from this that Leonardo on his part influenced Bramante in
the sense of simplifying his style and rendering it more congenial
to antique art? The answer to this important question seems at first
difficult to give, for we are here in presence of Bramante, the
greatest of modern architects, and with Leonardo, the man comparable
with no other. We have no knowledge of any buildings erected by
Leonardo, and unless we admit personal intercourse--which seems
probable, but of which there is no proof--, it would be difficult to
understand how Leonardo could have affected Bramante's style. The
converse is more easily to be admitted, since Bramante, as we have
proved elsewhere, drew and built simultaneously in different
manners, and though in Lombardy there is no building by him in his
classic style, the use of brick for building, in that part of Italy,
may easily account for it._

_Bramante's name is incidentally mentioned in Leonardo's manuscripts
in two passages (Nos. 1414 and 1448). On each occasion it is only a
slight passing allusion, and the nature of the context gives us no
due information as to any close connection between the two artists._

_It might be supposed, on the ground of Leonardo's relations with
the East given in sections XVII and XXI of this volume, that some
evidence of oriental influence might be detected in his
architectural drawings. I do not however think that any such traces
can be pointed out with certainty unless perhaps the drawing for a
Mausoleum, Pl. XC VIII._

_Among several studies for the construction of cupolas above a Greek
cross there are some in which the forms are decidedly monotonous.
These, it is clear, were not designed as models of taste; they must
be regarded as the results of certain investigations into the laws
of proportion, harmony and contrast._

_The designs for churches, on the plan of a Latin cross are
evidently intended to depart as little as possible from the form of
a Greek cross; and they also show a preference for a nave surrounded
with outer porticos._

_The architectural forms preferred by Leonardo are pilasters coupled
(Pl. LXXXII No. 1; or grouped (Pl. LXXX No. 5 and XCIV No. 4), often
combined with niches. We often meet with orders superposed, one in
each story, or two small orders on one story, in combination with
one great order (Pl. XCVI No. 2)._

The drum (tamburo) of these cupolas is generally octagonal, as in
the cathedral of Florence, and with similar round windows in its
sides. In Pl. LXXXVII No. 2 it is circular like the model actually
carried out by Michael Angelo at St. Peter's.

The cupola itself is either hidden under a pyramidal roof, as in the
Baptistery of Florence, San Lorenzo of Milan and most of the Lombard
churches (Pl. XCI No. 1 and Pl. XCII No. 1); but it more generally
suggests the curve of Sta Maria del Fiore (Pl. LXXXVIII No. 5; Pl.
XC No. 2; Pl. LXXXIX, M; Pl XC No. 4, Pl. XCVI No. 2). In other
cases (Pl. LXXX No. 4; Pl. LXXXIX; Pl. XC No. 2) it shows the sides
of the octagon crowned by semicircular pediments, as in
Brunellesco's lantern of the Cathedral and in the model for the
Cathedral of Pavia.

Finally, in some sketches the cupola is either semicircular, or as
in Pl. LXXXVII No. 2, shows the beautiful line, adopted sixty years
later by Michael Angelo for the existing dome of St. Peter's.

It is worth noticing that for all these domes Leonardo is not
satisfied to decorate the exterior merely with ascending ribs or
mouldings, but employs also a system of horizontal parallels to
complete the architectural system. Not the least interesting are the
designs for the tiburio (cupola) of the Milan Cathedral. They show
some of the forms, just mentioned, adapted to the peculiar gothic
style of that monument.

The few examples of interiors of churches recall the style employed
in Lombardy by Bramante, for instance in S. Maria di Canepanuova at
Pavia, or by Dolcebuono in the Monastero Maggiore at Milan (see Pl.
CI No. 1 [C. A. 181b; 546b]; Pl. LXXXIV No. 10).

The few indications concerning palaces seem to prove that Leonardo
followed Alberti's example of decorating the walls with pilasters
and a flat rustica, either in stone or by graffitti (Pl. CII No. 1
and Pl. LXXXV No. 14).

By pointing out the analogies between Leonardo's architecture and
that of other masters we in no way pretend to depreciate his
individual and original inventive power. These are at all events
beyond dispute. The project for the Mausoleum (Pl. XCVIII) would
alone suffice to rank him among the greatest architects who ever
lived. The peculiar shape of the tower (Pl. LXXX), of the churches
for preaching (Pl. XCVII No. 1 and pages 56 and 57, Fig. 1-4), his
curious plan for a city with high and low level streets (Pl. LXXVII
and LXXVIII No. 2 and No. 3), his Loggia with fountains (Pl. LXXXII
No. 4) reveal an originality, a power and facility of invention for
almost any given problem, which are quite wonderful.

_In addition to all these qualities he propably stood alone in his
day in one department of architectural study,--his investigations,
namely, as to the resistance of vaults, foundations, walls and
arches._

_As an application of these studies the plan of a semicircular vault
(Pl. CIII No. 2) may be mentioned here, disposed so as to produce no
thrust on the columns on which it rests:_ volta i botte e non
ispignie ifori le colone. _Above the geometrical patterns on the
same sheet, close to a circle inscribed in a square is the note:_ la
ragio d'una volta cioe il terzo del diamitro della sua ... del
tedesco in domo.

_There are few data by which to judge of Leonardo's style in the
treatment of detail. On Pl. LXXXV No. 10 and Pl. CIII No. 3, we find
some details of pillars; on Pl. CI No. 3 slender pillars designed
for a fountain and on Pl. CIII No. 1 MS. B, is a pen and ink drawing
of a vase which also seems intended for a fountain. Three handles
seem to have been intended to connect the upper parts with the base.
There can be no doubt that Leonardo, like Bramante, but unlike
Michael Angelo, brought infinite delicacy of motive and execution to
bear on the details of his work._

_XIV._

_Anatomy, Zoology and Physiology._

_Leonardo's eminent place in the history of medicine, as a pioneer
in the sciences of Anatomy and Physiology, will never be appreciated
till it is possible to publish the mass of manuscripts in which he
largely treated of these two branches of learning. In the present
work I must necessarily limit myself to giving the reader a general
view of these labours, by publishing his introductory notes to the
various books on anatomical subjects. I have added some extracts,
and such observations as are scattered incidentally through these
treatises, as serving to throw a light on Leonardo's scientific
attitude, besides having an interest for a wider circle than that of
specialists only._

_VASARI expressly mentions Leonardo's anatomical studies, having had
occasion to examine the manuscript books which refer to them.
According to him Leonardo studied Anatomy in the companionship of
Marc Antonio della Torre_ "aiutato e scambievolmente
aiutando."_--This learned Anatomist taught the science in the
universities first of Padua and then of Pavia, and at Pavia he and
Leonardo may have worked and studied together. We have no clue to
any exact dates, but in the year 1506 Marc Antonio della Torre seems
to have not yet left Padua. He was scarcely thirty years old when he
died in 1512, and his writings on anatomy have not only never been
published, but no manuscript copy of them is known to exist._

_This is not the place to enlarge on the connection between Leonardo
and Marc Antonio della Torre. I may however observe that I have not
been able to discover in Leonardo's manuscripts on anatomy any
mention of his younger contemporary. The few quotations which occur
from writers on medicine--either of antiquity or of the middle ages
are printed in Section XXII. Here and there in the manuscripts
mention is made of an anonymous "adversary"_ (avversario) _whose
views are opposed and refuted by Leonardo, but there is no ground
for supposing that Marc Antonio della Torre should have been this
"adversary"._

_Only a very small selection from the mass of anatomical drawings
left by Leonardo have been published here in facsimile, but to form
any adequate idea of their scientific merit they should be compared
with the coarse and inadequate figures given in the published books
of the early part of the XVI. century.

William Hunter, the great surgeon--a competent judge--who had an
opportunity in the time of George III. of seeing the originals in
the King's Library, has thus recorded his opinion: "I expected to
see little more than such designs in Anatomy as might be useful to a
painter in his own profession. But I saw, and indeed with
astonishment, that Leonardo had been a general and deep student.
When I consider what pains he has taken upon every part of the body,
the superiority of his universal genius, his particular excellence
in mechanics and hydraulics, and the attention with which such a man
would examine and see objects which he has to draw, I am fully
persuaded that Leonardo was the best Anatomist, at that time, in the
world ... Leonardo was certainly the first man, we know of, who
introduced the practice of making anatomical drawings" (Two
introductory letters. London 1784, pages 37 and 39).

The illustrious German Naturalist Johan Friedrich Blumenback
esteemed them no less highly; he was one of the privileged few who,
after Hunter, had the chance of seeing these Manuscripts. He writes:
_Der Scharfblick dieses grossen Forschers und Darstellers der Natur
hat schon auf Dinge geachtet, die noch Jahrhunderte nachher
unbemerkt geblieben sind_" (see _Blumenbach's medicinische
Bibliothek_, Vol. 3, St. 4, 1795. page 728).

These opinions were founded on the drawings alone. Up to the present
day hardly anything has been made known of the text, and, for the
reasons I have given, it is my intention to reproduce here no more
than a selection of extracts which I have made from the originals at
Windsor Castle and elsewhere. In the Bibliography of the
Manuscripts, at the end of this volume a short review is given of
the valuable contents of these Anatomical note books which are at
present almost all in the possession of her Majesty the Queen of
England. It is, I believe, possible to assign the date with
approximate accuracy to almost all the fragments, and I am thus led
to conclude that the greater part of Leonardo's anatomical
investigations were carried out after the death of della Torre.

Merely in reading the introductory notes to his various books on
Anatomy which are here printed it is impossible to resist the
impression that the Master's anatomical studies bear to a very great
extent the stamp of originality and independent thought.

I.

ANATOMY.

796.

A general introduction

I wish to work miracles;--it may be that I shall possess less than
other men of more peaceful lives, or than those who want to grow
rich in a day. I may live for a long time in great poverty, as
always happens, and to all eternity will happen, to alchemists, the
would-be creators of gold and silver, and to engineers who would
have dead water stir itself into life and perpetual motion, and to
those supreme fools, the necromancer and the enchanter.

[Footnote 23: The following seems to be directed against students of
painting and young artists rather than against medical men and
anatomists.]

And you, who say that it would be better to watch an anatomist at
work than to see these drawings, you would be right, if it were
possible to observe all the things which are demonstrated in such
drawings in a single figure, in which you, with all your cleverness,
will not see nor obtain knowledge of more than some few veins, to
obtain a true and perfect knowledge of which I have dissected more
than ten human bodies, destroying all the other members, and
removing the very minutest particles of the flesh by which these
veins are surrounded, without causing them to bleed, excepting the
insensible bleeding of the capillary veins; and as one single body
would not last so long, since it was necessary to proceed with
several bodies by degrees, until I came to an end and had a complete
knowledge; this I repeated twice, to learn the differences [59].

[Footnote: Lines 1-59 and 60-89 are written in two parallel columns.
When we here find Leonardo putting himself in the same category as
the Alchemists and Necromancers, whom he elsewhere mocks at so
bitterly, it is evidently meant ironically. In the same way
Leonardo, in the introduction to the Books on Perspective sets
himself with transparent satire on a level with other writers on the
subject.]

And if you should have a love for such things you might be prevented
by loathing, and if that did not prevent you, you might be deterred
by the fear of living in the night hours in the company of those
corpses, quartered and flayed and horrible to see. And if this did
not prevent you, perhaps you might not be able to draw so well as is
necessary for such a demonstration; or, if you had the skill in
drawing, it might not be combined with knowledge of perspective; and
if it were so, you might not understand the methods of geometrical
demonstration and the method of the calculation of forces and of the
strength of the muscles; patience also may be wanting, so that you
lack perseverance. As to whether all these things were found in me
or not [Footnote 84: Leonardo frequently, and perhaps habitually,
wrote in note books of a very small size and only moderately thick;
in most of those which have been preserved undivided, each contains
less than fifty leaves. Thus a considerable number of such volumes
must have gone to make up a volume of the bulk of the '_Codex
Atlanticus_' which now contains nearly 1200 detached leaves. In the
passage under consideration, which was evidently written at a late
period of his life, Leonardo speaks of his Manuscript note-books as
numbering 12O; but we should hardly be justified in concluding from
this passage that the greater part of his Manuscripts were now
missing (see _Prolegomena_, Vol. I, pp. 5-7).], the hundred and
twenty books composed by me will give verdict Yes or No. In these I
have been hindered neither by avarice nor negligence, but simply by
want of time. Farewell [89].

Plans and suggestions for the arrangement of materials (797-802).

797.

OF THE ORDER OF THE BOOK.

This work must begin with the conception of man, and describe the
nature of the womb and how the foetus lives in it, up to what stage
it resides there, and in what way it quickens into life and feeds.
Also its growth and what interval there is between one stage of
growth and another. What it is that forces it out from the body of
the mother, and for what reasons it sometimes comes out of the
mother's womb before the due time.

Then I will describe which are the members, which, after the boy is
born, grow more than the others, and determine the proportions of a
boy of one year.

Then describe the fully grown man and woman, with their proportions,
and the nature of their complexions, colour, and physiognomy.

Then how they are composed of veins, tendons, muscles and bones.
This I shall do at the end of the book. Then, in four drawings,
represent four universal conditions of men. That is, Mirth, with
various acts of laughter, and describe the cause of laughter.
Weeping in various aspects with its causes. Contention, with various
acts of killing; flight, fear, ferocity, boldness, murder and every
thing pertaining to such cases. Then represent Labour, with pulling,
thrusting, carrying, stopping, supporting and such like things.

Further I would describe attitudes and movements. Then perspective,
concerning the functions and effects of the eye; and of
hearing--here I will speak of music--, and treat of the other
senses.

And then describe the nature of the senses.

This mechanism of man we will demonstrate in ... figures; of which
the three first will show the ramification of the bones; that is:
first one to show their height and position and shape: the second
will be seen in profile and will show the depth of the whole and of
the parts, and their position. The third figure will be a
demonstration of the bones of the backparts. Then I will make three
other figures from the same point of view, with the bones sawn
across, in which will be shown their thickness and hollowness. Three
other figures of the bones complete, and of the nerves which rise
from the nape of the neck, and in what limbs they ramify. And three
others of the bones and veins, and where they ramify. Then three
figures with the muscles and three with the skin, and their proper
proportions; and three of woman, to illustrate the womb and the
menstrual veins which go to the breasts.

[Footnote: The meaning of the word _nervo_ varies in different
passages, being sometimes used for _muscolo_ (muscle).]

798.

THE ORDER OF THE BOOK.

This depicting of mine of the human body will be as clear to you as
if you had the natural man before you; and the reason is that if you
wish thoroughly to know the parts of man, anatomically, you--or your
eye--require to see it from different aspects, considering it from
below and from above and from its sides, turning it about and
seeking the origin of each member; and in this way the natural
anatomy is sufficient for your comprehension. But you must
understand that this amount of knowledge will not continue to
satisfy you; seeing the very great confusion that must result from
the combination of tissues, with veins, arteries, nerves, sinews,
muscles, bones, and blood which, of itself, tinges every part the
same colour. And the veins, which discharge this blood, are not
discerned by reason of their smallness. Moreover integrity of the
tissues, in the process of the investigating the parts within them,
is inevitably destroyed, and their transparent substance being
tinged with blood does not allow you to recognise the parts covered
by them, from the similarity of their blood-stained hue; and you
cannot know everything of the one without confusing and destroying
the other. Hence, some further anatomy drawings become necessary. Of
which you want three to give full knowledge of the veins and
arteries, everything else being destroyed with the greatest care.
And three others to display the tissues; and three for the sinews
and muscles and ligaments; and three for the bones and cartilages;
and three for the anatomy of the bones, which have to be sawn to
show which are hollow and which are not, which have marrow and which
are spongy, and which are thick from the outside inwards, and which
are thin. And some are extremely thin in some parts and thick in
others, and in some parts hollow or filled up with bone, or full of
marrow, or spongy. And all these conditions are sometimes found in
one and the same bone, and in some bones none of them. And three you
must have for the woman, in which there is much that is mysterious
by reason of the womb and the foetus. Therefore by my drawings every
part will be known to you, and all by means of demonstrations from
three different points of view of each part; for when you have seen
a limb from the front, with any muscles, sinews, or veins which take
their rise from the opposite side, the same limb will be shown to
you in a side view or from behind, exactly as if you had that same
limb in your hand and were turning it from side to side until you
had acquired a full comprehension of all you wished to know. In the
same way there will be put before you three or four demonstrations
of each limb, from various points of view, so that you will be left
with a true and complete knowledge of all you wish to learn of the
human figure[Footnote 35: Compare Pl. CVII. The original drawing at
Windsor is 28 1/2 X 19 1/2 centimetres. The upper figures are
slightly washed with Indian ink. On the back of this drawing is the
text No. 1140.].

Thus, in twelve entire figures, you will have set before you the
cosmography of this lesser world on the same plan as, before me, was
adopted by Ptolemy in his cosmography; and so I will afterwards
divide them into limbs as he divided the whole world into provinces;
then I will speak of the function of each part in every direction,
putting before your eyes a description of the whole form and
substance of man, as regards his movements from place to place, by
means of his different parts. And thus, if it please our great
Author, I may demonstrate the nature of men, and their customs in
the way I describe his figure.

And remember that the anatomy of the nerves will not give the
position of their ramifications, nor show you which muscles they
branch into, by means of bodies dissected in running water or in
lime water; though indeed their origin and starting point may be
seen without such water as well as with it. But their ramifications,
when under running water, cling and unite--just like flat or hemp
carded for spinning--all into a skein, in a way which makes it
impossible to trace in which muscles or by what ramification the
nerves are distributed among those muscles.

799.

THE ARRANGEMENT OF ANATOMY

First draw the bones, let us say, of the arm, and put in the motor
muscle from the shoulder to the elbow with all its lines. Then
proceed in the same way from the elbow to the wrist. Then from the
wrist to the hand and from the hand to the fingers.

And in the arm you will put the motors of the fingers which open,
and these you will show separately in their demonstration. In the
second demonstration you will clothe these muscles with the
secondary motors of the fingers and so proceed by degrees to avoid
confusion. But first lay on the bones those muscles which lie close
to the said bones, without confusion of other muscles; and with
these you may put the nerves and veins which supply their
nourishment, after having first drawn the tree of veins and nerves
over the simple bones.

800.

Begin the anatomy at the head and finish at the sole of the foot.

801.

3 men complete, 3 with bones and nerves, 3 with the bones only. Here
we have 12 demonstrations of entire figures.

802.

When you have finished building up the man, you will make the statue
with all its superficial measurements.

[Footnote: _Cresciere l'omo_. The meaning of this expression appears
to be different here and in the passage C.A. 157a, 468a (see No.
526, Note 1. 2). Here it can hardly mean anything else than
modelling, since the sculptor forms the figure by degrees, by adding
wet clay and the figure consequently increases or grows. _Tu farai
la statua_ would then mean, you must work out the figure in marble.
If this interpretation is the correct one, this passage would have
no right to find a place in the series on anatomical studies. I may
say that it was originally inserted in this connection under the
impression that _di cresciere_ should be read _descrivere_.]

Plans for the representation of muscles by drawings (803-809).

803.

You must show all the motions of the bones with their joints to
follow the demonstration of the first three figures of the bones,
and this should be done in the first book.

804.

Remember that to be certain of the point of origin of any muscle,
you must pull the sinew from which the muscle springs in such a way
as to see that muscle move, and where it is attached to the
ligaments of the bones.

NOTE.

You will never get any thing but confusion in demonstrating the
muscles and their positions, origin, and termination, unless you
first make a demonstration of thin muscles after the manner of linen
threads; and thus you can represent them, one over another as nature
has placed them; and thus, too, you can name them according to the
limb they serve; for instance the motor of the point of the great
toe, of its middle bone, of its first bone, &c. And when you have
the knowledge you will draw, by the side of this, the true form and
size and position of each muscle. But remember to give the threads
which explain the situation of the muscles in the position which
corresponds to the central line of each muscle; and so these threads
will demonstrate the form of the leg and their distance in a plain
and clear manner.

I have removed the skin from a man who was so shrunk by illness that
the muscles were worn down and remained in a state like thin
membrane, in such a way that the sinews instead of merging in
muscles ended in wide membrane; and where the bones were covered by
the skin they had very little over their natural size.

[Footnote: The photograph No. 41 of Grosvenor Gallery Publications:
a drawing of the muscles of the foot, includes a complete facsimile
of the text of this passage.]

805.

Which nerve causes the motion of the eye so that the motion of one
eye moves the other?

Of frowning the brows, of raising the brows, of lowering the
brows,--of closing the eyes, of opening the eyes,--of raising the
nostrils, of opening the lips, with the teeth shut, of pouting with
the lips, of smiling, of astonishment.--

Describe the beginning of man when it is caused in the womb and why
an eight months child does not live. What sneezing is. What yawning
is. Falling sickness, spasms, paralysis, shivering with cold,
sweating, fatigue, hunger, sleepiness, thirst, lust.

Of the nerve which is the cause of movement from the shoulder to the
elbow, of the movement from the elbow to the hand, from the joint of
the hand to the springing of the fingers. From the springing of the
fingers to the middle joints, and from the middle joints to the
last.

Of the nerve which causes the movement of the thigh, and from the
knee to the foot, and from the joint of the foot to the toes, and
then to the middle of the toes and of the rotary motion of the leg.

806.

ANATOMY.

Which nerves or sinews of the hand are those which close and part
the fingers and toes latteraly?

807.

Remove by degrees all the parts of the front of a man in making your
dissection, till you come to the bones. Description of the parts of
the bust and of their motions.

808.

Give the anatomy of the leg up to the hip, in all views and in every
action and in every state; veins, arteries, nerves, sinews and
muscles, skin and bones; then the bones in sections to show the
thickness of the bones.

[Footnote: A straightened leg in profile is sketched by the side of
this text.]

On corpulency and leanness (809-811).

809.

Make the rule and give the measurement of each muscle, and give the
reasons of all their functions, and in which way they work and what
makes them work &c.

[4] First draw the spine of the back; then clothe it by degrees, one
after the other, with each of its muscles and put in the nerves and
arteries and veins to each muscle by itself; and besides these note
the vertebrae to which they are attached; which of the intestines
come in contact with them; and which bones and other organs &c.

The most prominent parts of lean people are most prominent in the
muscular, and equally so in fat persons. But concerning the
difference in the forms of the muscles in fat persons as compared
with muscular persons, it shall be described below.

[Footnote: The two drawings given on Pl. CVIII no. 1 come between
lines 3 and 4. A good and very early copy of this drawing without
the written text exists in the collection of drawings belonging to
Christ's College Oxford, where it is attributed to Leonardo.]

810.

Describe which muscles disappear in growing fat, and which become
visible in growing lean.

And observe that that part which on the surface of a fat person is
most concave, when he grows lean becomes more prominent.

Where the muscles separate one from another you must give profiles
and where they coalesce ...

811.

OF THE HUMAN FIGURE.

Which is the part in man, which, as he grows fatter, never gains
flesh?

Or what part which as a man grows lean never falls away with a too
perceptible diminution? And among the parts which grow fat which is
that which grows fattest?

Among those which grow lean which is that which grows leanest?

In very strong men which are the muscles which are thickest and most
prominent?

In your anatomy you must represent all the stages of the limbs from
man's creation to his death, and then till the death of the bone;
and which part of him is first decayed and which is preserved the
longest.

And in the same way of extreme leanness and extreme fatness.

The divisions of the head (812. 813).

812.

ANATOMY.

There are eleven elementary tissues:-- Cartilage, bones, nerves,
veins, arteries, fascia, ligament and sinews, skin, muscle and fat.

OF THE HEAD.

The divisions of the head are 10, viz. 5 external and 5 internal,
the external are the hair, skin, muscle, fascia and the skull; the
internal are the dura mater, the pia mater, [which enclose] the
brain. The pia mater and the dura mater come again underneath and
enclose the brain; then the rete mirabile, and the occipital bone,
which supports the brain from which the nerves spring.

813.

_a_. hair

_n_. skin

_c_. muscle

_m_. fascia

_o_. skull _i.e._ bone

_b_. dura mater

_d_. pia mater

_f_. brain

_r_. pia mater, below

_t_. dura mater

_l_. rete mirablile

_s_. the occipitul bone.

[Footnote: See Pl. CVIII, No. 3.]

Physiological problems (814. 815).

814.

Of the cause of breathing, of the cause of the motion of the heart,
of the cause of vomiting, of the cause of the descent of food from
the stomach, of the cause of emptying the intestines.

Of the cause of the movement of the superfluous matter through the
intestines.

Of the cause of swallowing, of the cause of coughing, of the cause
of yawning, of the cause of sneezing, of the cause of limbs getting
asleep.

Of the cause of losing sensibility in any limb.

Of the cause of tickling.

Of the cause of lust and other appetites of the body, of the cause
of urine and also of all the natural excretions of the body.

[Footnote: By the side of this text stands the pen and ink drawing
reproduced on Pl. CVIII, No. 4; a skull with indications of the
veins in the fleshy covering.]

815.

The tears come from the heart and not from the brain.

Define all the parts, of which the body is composed, beginning with
the skin with its outer cuticle which is often chapped by the
influence of the sun.

II.

ZOOLOGY AND COMPARATIVE ANATOMY.

The divisions of the animal kingdom (816. 817).

816.

_Man_. The description of man, which includes that of such creatures
as are of almost the same species, as Apes, Monkeys and the like,
which are many,

_The Lion_ and its kindred, as Panthers. [Footnote 3: _Leonza_--wild
cat? "_Secondo alcuni, lo stesso che Leonessa; e secondo altri con
piu certezza, lo stesso che Pantera_" FANFANI, _Vocabolario_ page
858.] Wildcats (?) Tigers, Leopards, Wolfs, Lynxes, Spanish cats,
common cats and the like.

_The Horse_ and its kindred, as Mule, Ass and the like, with incisor
teeth above and below.

_The Bull_ and its allies with horns and without upper incisors as
the Buffalo, Stag Fallow Deer, Wild Goat, Swine, Goat, wild Goats
Muskdeers, Chamois, Giraffe.

817.

Describe the various forms of the intestines of the human species,
of apes and such like. Then, in what way the leonine species differ,
and then the bovine, and finally birds; and arrange this description
after the manner of a disquisition.

Miscellaneous notes on the study of Zoology (818-821).

818.

Procure the placenta of a calf when it is born and observe the form
of the cotyledons, if their cotyledons are male or female.

819.

Describe the tongue of the woodpecker and the jaw of the crocodile.

820.

Of the flight of the 4th kind of butterflies that consume winged
ants. Of the three principal positions of the wings of birds in
downward flight.

[Footnote: A passing allusion is all I can here permit myself to
Leonardo's elaborate researches into the flight of birds. Compare
the observations on this subject in the Introduction to section
XVIII and in the Bibliography of Manuscripts at the end of the
work.]

821.

Of the way in which the tail of a fish acts in propelling the fish;
as in the eel, snake and leech.

[Footnote: A sketch of a fish, swimming upwards is in the original,
inserted above this text.--Compare No. 1114.]

Comparative study of the structure of bones and of the action of
muscles (822-826).

822.

OF THE PALM OF THE HAND.

Then I will discourse of the hands of each animal to show in what
they vary; as in the bear, which has the ligatures of the sinews of
the toes joined above the instep.

823.

A second demonstration inserted between anatomy and [the treatise
on] the living being.

You will represent here for a comparison, the legs of a frog, which
have a great resemblance to the legs of man, both in the bones and
in the muscles. Then, in continuation, the hind legs of the hare,
which are very muscular, with strong active muscles, because they
are not encumbered with fat.

[Footnote: This text is written by the side of a drawing in black
chalk of a nude male figure, but there is no connection between the
sketch and the text.]

824.

Here I make a note to demonstrate the difference there is between
man and the horse and in the same way with other animals. And first
I will begin with the bones, and then will go on to all the muscles
which spring from the bones without tendons and end in them in the
same way, and then go on to those which start with a single tendon
at one end.

[Footnote: See Pl. CVIII, No. 2.]

825.

Note on the bendings of joints and in what way the flesh grows upon
them in their flexions or extensions; and of this most important
study write a separate treatise: in the description of the movements
of animals with four feet; among which is man, who likewise in his
infancy crawls on all fours.

826.

OF THE WAY OF WALKING IN MAN.

The walking of man is always after the universal manner of walking
in animals with 4 legs, inasmuch as just as they move their feet
crosswise after the manner of a horse in trotting, so man moves his
4 limbs crosswise; that is, if he puts forward his right foot in
walking he puts forward, with it, his left arm and vice versa,
invariably.

III.

PHYSIOLOGY.

Comparative study of the organs of sense in men and animals.

827.

I have found that in the composition of the human body as compared
with the bodies of animals the organs of sense are duller and
coarser. Thus it is composed of less ingenious instruments, and of
spaces less capacious for receiving the faculties of sense. I have
seen in the Lion tribe that the sense of smell is connected with
part of the substance of the brain which comes down the nostrils,
which form a spacious receptacle for the sense of smell, which
enters by a great number of cartilaginous vesicles with several
passages leading up to where the brain, as before said, comes down.

The eyes in the Lion tribe have a large part of the head for their
sockets and the optic nerves communicate at once with the brain; but
the contrary is to be seen in man, for the sockets of the eyes are
but a small part of the head, and the optic nerves are very fine and
long and weak, and by the weakness of their action we see by day but
badly at night, while these animals can see as well at night as by
day. The proof that they can see is that they prowl for prey at
night and sleep by day, as nocturnal birds do also.

Advantages in the structure of the eye in certain animals (828-831).

828.

Every object we see will appear larger at midnight than at midday,
and larger in the morning than at midday.

This happens because the pupil of the eye is much smaller at midday
than at any other time.

In proportion as the eye or the pupil of the owl is larger in
proportion to the animal than that of man, so much the more light
can it see at night than man can; hence at midday it can see nothing
if its pupil does not diminish; and, in the same way, at night
things look larger to it than by day.

829.

OF THE EYES IN ANIMALS.

The eyes of all animals have their pupils adapted to dilate and
diminish of their own accord in proportion to the greater or less
light of the sun or other luminary. But in birds the variation is
much greater; and particularly in nocturnal birds, such as horned
owls, and in the eyes of one species of owl; in these the pupil
dilates in such away as to occupy nearly the whole eye, or
diminishes to the size of a grain of millet, and always preserves
the circular form. But in the Lion tribe, as panthers, pards,
ounces, tigers, lynxes, Spanish cats and other similar animals the
pupil diminishes from the perfect circle to the figure of a pointed
oval such as is shown in the margin. But man having a weaker sight
than any other animal is less hurt by a very strong light and his
pupil increases but little in dark places; but in the eyes of these
nocturnal animals, the horned owl--a bird which is the largest of
all nocturnal birds--the power of vision increases so much that in
the faintest nocturnal light (which we call darkness) it sees with
much more distinctness than we do in the splendour of noon day, at
which time these birds remain hidden in dark holes; or if indeed
they are compelled to come out into the open air lighted up by the
sun, they contract their pupils so much that their power of sight
diminishes together with the quantity of light admitted.

Study the anatomy of various eyes and see which are the muscles
which open and close the said pupils of the eyes of animals.

[Footnote: Compare No. 24, lines 8 and fol.]

830.

_a b n_ is the membrane which closes the eye from below, upwards,
with an opaque film, _c n b_ encloses the eye in front and behind
with a transparent membrane.

It closes from below, upwards, because it [the eye] comes downwards.

When the eye of a bird closes with its two lids, the first to close
is the nictitating membrane which closes from the lacrymal duct over
to the outer corner of the eye; and the outer lid closes from below
upwards, and these two intersecting motions begin first from the
lacrymatory duct, because we have already seen that in front and
below birds are protected and use only the upper portion of the eye
from fear of birds of prey which come down from above and behind;
and they uncover first the membrane from the outer corner, because
if the enemy comes from behind, they have the power of escaping to
the front; and again the muscle called the nictitating membrane is
transparent, because, if the eye had not such a screen, they could
not keep it open against the wind which strikes against the eye in
the rush of their rapid flight. And the pupil of the eye dilates and
contracts as it sees a less or greater light, that is to say intense
brilliancy.

831.

If at night your eye is placed between the light and the eye of a
cat, it will see the eye look like fire.

Remarks on the organs of speech

(832. 833).

832.

_a  e  i  o  u
ba be bi bo bu
ca ce ci co cu
da de di do du
fa fe fi fo fu
ga ge gi go gu
la le li lo lu
ma me mi mo mu
na ne ni no nu
pa pe pi po pu
qa qe qi qo qu
ra re ri ro ru
sa se si so su
ta te ti to tu_

The tongue is found to have 24 muscles which correspond to the six
muscles which compose the portion of the tongue which moves in the
mouth.

And when _a o u_ are spoken with a clear and rapid pronunciation, it
is necessary, in order to pronounce continuously, without any pause
between, that the opening of the lips should close by degrees; that
is, they are wide apart in saying _a_, closer in saying _o_, and
much closer still to pronounce _u_.

It may be shown how all the vowels are pronounced with the farthest
portion of the false palate which is above the epiglottis.

833.

If you draw in breath by the nose and send it out by the mouth you
will hear the sound made by the division that is the membrane in
[Footnote 5: The text here breaks off.]...

On the conditions of sight (834. 835).

834.

OF THE NATURE OF SIGHT.

I say that sight is exercised by all animals, by the medium of
light; and if any one adduces, as against this, the sight of
nocturnal animals, I must say that this in the same way is subject
to the very same natural laws. For it will easily be understood that
the senses which receive the images of things do not project from
themselves any visual virtue [Footnote 4: Compare No. 68.]. On the
contrary the atmospheric medium which exists between the object and
the sense incorporates in itself the figure of things, and by its
contact with the sense transmits the object to it. If the
object--whether by sound or by odour--presents its spiritual force
to the ear or the nose, then light is not required and does not act.
The forms of objects do not send their images into the air if they
are not illuminated [8]; and the eye being thus constituted cannot
receive that from the air, which the air does not possess, although
it touches its surface. If you choose to say that there are many
animals that prey at night, I answer that when the little light
which suffices the nature of their eyes is wanting, they direct
themselves by their strong sense of hearing and of smell, which are
not impeded by the darkness, and in which they are very far superior
to man. If you make a cat leap, by daylight, among a quantity of
jars and crocks you will see them remain unbroken, but if you do the
same at night, many will be broken. Night birds do not fly about
unless the moon shines full or in part; rather do they feed between
sun-down and the total darkness of the night.

[Footnote 8: See No. 58-67.]

No body can be apprehended without light and shade, and light and
shade are caused by light.

835.

WHY MEN ADVANCED IN AGE SEE BETTER AT A DISTANCE.

Sight is better from a distance than near in those men who are
advancing in age, because the same object transmits a smaller
impression of itself to the eye when it is distant than when it is
near.

The seat of the common sense.

836.

The Common Sense, is that which judges of things offered to it by
the other senses. The ancient speculators have concluded that that
part of man which constitutes his judgment is caused by a central
organ to which the other five senses refer everything by means of
impressibility; and to this centre they have given the name Common
Sense. And they say that this Sense is situated in the centre of the
head between Sensation and Memory. And this name of Common Sense is
given to it solely because it is the common judge of all the other
five senses _i.e._ Seeing, Hearing, Touch, Taste and Smell. This
Common Sense is acted upon by means of Sensation which is placed as
a medium between it and the senses. Sensation is acted upon by means
of the images of things presented to it by the external instruments,
that is to say the senses which are the medium between external
things and Sensation. In the same way the senses are acted upon by
objects. Surrounding things transmit their images to the senses and
the senses transfer them to the Sensation. Sensation sends them to
the Common Sense, and by it they are stamped upon the memory and are
there more or less retained according to the importance or force of
the impression. That sense is most rapid in its function which is
nearest to the sensitive medium and the eye, being the highest is
the chief of the others. Of this then only we will speak, and the
others we will leave in order not to make our matter too long.
Experience tells us that the eye apprehends ten different natures of
things, that is: Light and Darkness, one being the cause of the
perception of the nine others, and the other its absence:-- Colour
and substance, form and place, distance and nearness, motion and
stillness [Footnote 15: Compare No. 23.].

On the origin of the soul.

837.

Though human ingenuity may make various inventions which, by the
help of various machines answering the same end, it will never
devise any inventions more beautiful, nor more simple, nor more to
the purpose than Nature does; because in her inventions nothing is
wanting, and nothing is superfluous, and she needs no counterpoise
when she makes limbs proper for motion in the bodies of animals. But
she puts into them the soul of the body, which forms them that is
the soul of the mother which first constructs in the womb the form
of the man and in due time awakens the soul that is to inhabit it.
And this at first lies dormant and under the tutelage of the soul of
the mother, who nourishes and vivifies it by the umbilical vein,
with all its spiritual parts, and this happens because this
umbilicus is joined to the placenta and the cotyledons, by which the
child is attached to the mother. And these are the reason why a
wish, a strong craving or a fright or any other mental suffering in
the mother, has more influence on the child than on the mother; for
there are many cases when the child loses its life from them, &c.

This discourse is not in its place here, but will be wanted for the
one on the composition of animated bodies--and the rest of the
definition of the soul I leave to the imaginations of friars, those
fathers of the people who know all secrets by inspiration.

[Footnote 57: _lettere incoronate_. By this term Leonardo probably
understands not the Bible only, but the works of the early Fathers,
and all the books recognised as sacred by the Roman Church.] I leave
alone the sacred books; for they are supreme truth.

On the relations of the soul to the organs of sense.

838.

HOW THE FIVE SENSES ARE THE MINISTERS OF THE SOUL.

The soul seems to reside in the judgment, and the judgment would
seem to be seated in that part where all the senses meet; and this
is called the Common Sense and is not all-pervading throughout the
body, as many have thought. Rather is it entirely in one part.
Because, if it were all-pervading and the same in every part, there
would have been no need to make the instruments of the senses meet
in one centre and in one single spot; on the contrary it would have
sufficed that the eye should fulfil the function of its sensation on
its surface only, and not transmit the image of the things seen, to
the sense, by means of the optic nerves, so that the soul--for the
reason given above-- may perceive it in the surface of the eye. In
the same way as to the sense of hearing, it would have sufficed if
the voice had merely sounded in the porous cavity of the indurated
portion of the temporal bone which lies within the ear, without
making any farther transit from this bone to the common sense, where
the voice confers with and discourses to the common judgment. The
sense of smell, again, is compelled by necessity to refer itself to
that same judgment. Feeling passes through the perforated cords and
is conveyed to this common sense. These cords diverge with infinite
ramifications into the skin which encloses the members of the body
and the viscera. The perforated cords convey volition and sensation
to the subordinate limbs. These cords and the nerves direct the
motions of the muscles and sinews, between which they are placed;
these obey, and this obedience takes effect by reducing their
thickness; for in swelling, their length is reduced, and the nerves
shrink which are interwoven among the particles of the limbs; being
extended to the tips of the fingers, they transmit to the sense the
object which they touch.

The nerves with their muscles obey the tendons as soldiers obey the
officers, and the tendons obey the Common [central] Sense as the
officers obey the general. [27] Thus the joint of the bones obeys
the nerve, and the nerve the muscle, and the muscle the tendon and
the tendon the Common Sense. And the Common Sense is the seat of the
soul [28], and memory is its ammunition, and the impressibility is
its referendary since the sense waits on the soul and not the soul
on the sense. And where the sense that ministers to the soul is not
at the service of the soul, all the functions of that sense are also
wanting in that man's life, as is seen in those born mute and blind.

[Footnote: The peculiar use of the words _nervo_, _muscolo_,
_corda_, _senso comune_, which are here literally rendered by nerve,
muscle cord or tendon and Common Sense may be understood from lines
27 and 28.]

On involuntary muscular action.

839.

HOW THE NERVES SOMETIMES ACT OF THEMSELVES WITHOUT ANY COMMANDS FROM
THE OTHER FUNCTIONS OF THE SOUL.

This is most plainly seen; for you will see palsied and shivering
persons move, and their trembling limbs, as their head and hands,
quake without leave from their soul and their soul with all its
power cannot prevent their members from trembling. The same thing
happens in falling sickness, or in parts that have been cut off, as
in the tails of lizards. The idea or imagination is the helm and
guiding-rein of the senses, because the thing conceived of moves the
sense. Pre-imagining, is imagining the things that are to be.
Post-imagining, is imagining the things that are past.

Miscellaneous physiological observations (840-842).

840.

There are four Powers: memory and intellect, desire and
covetousness. The two first are mental and the others sensual. The
three senses: sight, hearing and smell cannot well be prevented;
touch and taste not at all. Smell is connected with taste in dogs
and other gluttonous animals.

841.

I reveal to men the origin of the first, or perhaps second cause of
their existence.

842.

Lust is the cause of generation.

Appetite is the support of life. Fear or timidity is the
prolongation of life and preservation of its instruments.

The laws of nutrition and the support of life (843-848).

843.

HOW THE BODY OF ANIMALS IS CONSTANTLY DYING AND BEING RENEWED.

The body of any thing whatever that takes nourishment constantly
dies and is constantly renewed; because nourishment can only enter
into places where the former nourishment has expired, and if it has
expired it no longer has life. And if you do not supply nourishment
equal to the nourishment which is gone, life will fail in vigour,
and if you take away this nourishment, the life is entirely
destroyed. But if you restore as much is destroyed day by day, then
as much of the life is renewed as is consumed, just as the flame of
the candle is fed by the nourishment afforded by the liquid of this
candle, which flame continually with a rapid supply restores to it
from below as much as is consumed in dying above: and from a
brilliant light is converted in dying into murky smoke; and this
death is continuous, as the smoke is continuous; and the continuance
of the smoke is equal to the continuance of the nourishment, and in
the same instant all the flame is dead and all regenerated,
simultaneously with the movement of its own nourishment.

844.

King of the animals--as thou hast described him--I should rather say
king of the beasts, thou being the greatest--because thou hast
spared slaying them, in order that they may give thee their children
for the benefit of the gullet, of which thou hast attempted to make
a sepulchre for all animals; and I would say still more, if it were
allowed me to speak the entire truth [5]. But we do not go outside
human matters in telling of one supreme wickedness, which does not
happen among the animals of the earth, inasmuch as among them are
found none who eat their own kind, unless through want of sense (few
indeed among them, and those being mothers, as with men, albeit they
be not many in number); and this happens only among the rapacious
animals, as with the leonine species, and leopards, panthers lynxes,
cats and the like, who sometimes eat their children; but thou,
besides thy children devourest father, mother, brothers and friends;
nor is this enough for thee, but thou goest to the chase on the
islands of others, taking other men and these half-naked, the ...
and the ... thou fattenest, and chasest them down thy own
throat[18]; now does not nature produce enough simples, for thee to
satisfy thyself? and if thou art not content with simples, canst
thou not by the mixture of them make infinite compounds, as Platina
wrote[Footnote 21: _Come scrisse il Platina_ (Bartolomeo Sacchi, a
famous humanist). The Italian edition of his treatise _De arte
coquinaria_, was published under the title _De la honestra
voluptate, e valetudine, Venezia_ 1487.], and other authors on
feeding?

[Footnote: We are led to believe that Leonardo himself was a
vegetarian from the following interesting passage in the first of
Andrea Corsali's letters to Giuliano de'Medici: _Alcuni gentili
chiamati Guzzarati non si cibano di cosa, alcuna che tenga sangue,
ne fra essi loro consentono che si noccia ad alcuna cosa animata,
come il nostro Leonardo da Vinci_.

5-18. Amerigo Vespucci, with whom Leonardo was personally
acquainted, writes in his second letter to Pietro Soderini, about
the inhabitants of the Canary Islands after having stayed there in
1503: "_Hanno una scelerata liberta di viuere; ... si cibano di
carne humana, di maniera che il padre magia il figliuolo, et
all'incontro il figliuolo il padre secondo che a caso e per sorte
auiene. Io viddi un certo huomo sceleratissimo che si vantaua, et si
teneua a non piccola gloria di hauer mangiato piu di trecento
huomini. Viddi anche vna certa citta, nella quale io dimorai forse
ventisette giorni, doue le carni humane, hauendole salate, eran
appicate alli traui, si come noi alli traui di cucina_ _appicchiamo
le carni di cinghali secche al sole o al fumo, et massimamente
salsiccie, et altre simil cose: anzi si marauigliauano gradem ete
che noi non magiaissimo della carne de nemici, le quali dicono
muouere appetito, et essere di marauiglioso sapore, et le lodano
come cibi soaui et delicati (Lettere due di Amerigo Vespucci
Fiorentino drizzate al magnifico Pietro Soderini, Gonfaloniere della
eccelsa Republica di Firenze_; various editions).]

845.

Our life is made by the death of others.

In dead matter insensible life remains, which, reunited to the
stomachs of living beings, resumes life, both sensual and
intellectual.

846.

Here nature appears with many animals to have been rather a cruel
stepmother than a mother, and with others not a stepmother, but a
most tender mother.

847.

Man and animals are really the passage and the conduit of food, the
sepulchre of animals and resting place of the dead, one causing the
death of the other, making themselves the covering for the
corruption of other dead [bodies].

On the circulation of the blood (848-850).

848.

Death in old men, when not from fever, is caused by the veins which
go from the spleen to the valve of the liver, and which thicken so
much in the walls that they become closed up and leave no passage
for the blood that nourishes it.

[6]The incessant current of the blood through the veins makes these
veins thicken and become callous, so that at last they close up and
prevent the passage of the blood.

849.

The waters return with constant motion from the lowest depths of the
sea to the utmost height of the mountains, not obeying the nature of
heavier bodies; and in this they resemble the blood of animated
beings which always moves from the sea of the heart and flows
towards the top of the head; and here it may burst a vein, as may be
seen when a vein bursts in the nose; all the blood rises from below
to the level of the burst vein. When the water rushes out from the
burst vein in the earth, it obeys the law of other bodies that are
heavier than the air since it always seeks low places.

[Footnote: From this passage it is quite plain that Leonardo had not
merely a general suspicion of the circulation of the blood but a
very clear conception of it. Leonardo's studies on the muscles of
the heart are to be found in the MS. W. An. III. but no information
about them has hitherto been made public. The limits of my plan in
this work exclude all purely anatomical writings, therefore only a
very brief excerpt from this note book can be given here. WILLIAM
HARVEY (born 1578 and Professor of Anatomy at Cambridge from 1615)
is always considered to have been the discoverer of the circulation
of the blood. He studied medicine at Padua in 1598, and in 1628
brought out his memorable and important work: _De motu cordis et
sanguinis_.]

850.

That the blood which returns when the heart opens again is not the
same as that which closes the valves of the heart.

Some notes on medicine (851-855).

851.

Make them give you the definition and remedies for the case ... and
you will see that men are selected to be doctors for diseases they
do not know.

852.

A remedy for scratches taught me by the Herald to the King of
France. 4 ounces of virgin wax, 4 ounces of colophony, 2 ounces of
incense. Keep each thing separate; and melt the wax, and then put in
the incense and then the colophony, make a mixture of it and put it
on the sore place.

853.

Medicine is the restoration of discordant elements; sickness is the
discord of the elements infused into the living body.

854.

Those who are annoyed by sickness at sea should drink extract of
wormwood.

855.

To keep in health, this rule is wise: Eat only when you want and
relish food. Chew thoroughly that it may do you good. Have it well
cooked, unspiced and undisguised. He who takes medicine is ill
advised.

[Footnote: This appears to be a sketch for a poem.]

856.

I teach you to preserve your health; and in this you will succed
better in proportion as you shun physicians, because their medicines
are the work of alchemists.

[Footnote: This passage is written on the back of the drawing Pl.
CVIII. Compare also No. 1184.]

_XV_.

_Astronomy_.

_Ever since the publication by Venturi in_ 1797 _and Libri in_ 1840
_of some few passages of Leonardo's astronomical notes, scientific
astronomers have frequently expressed the opinion, that they must
have been based on very important discoveries, and that the great
painter also deserved a conspicuous place in the history of this
science. In the passages here printed, a connected view is given of
his astronomical studies as they lie scattered through the
manuscripts, which have come down to us. Unlike his other purely
scientific labours, Leonardo devotes here a good deal of attention
to the opinions of the ancients, though he does not follow the
practice universal in his day of relying on them as authorities; he
only quotes them, as we shall see, in order to refute their
arguments. His researches throughout have the stamp of independent
thought. There is nothing in these writings to lead us to suppose
that they were merely an epitome of the general learning common to
the astronomers of the period. As early as in the XIVth century
there were chairs of astronomy in the universities of Padua and
Bologna, but so late as during the entire XVIth century Astronomy
and Astrology were still closely allied._

_It is impossible now to decide whether Leonardo, when living in
Florence, became acquainted in his youth with the doctrines of Paolo
Toscanelli the great astronomer and mathematician (died_ 1482_), of
whose influence and teaching but little is now known, beyond the
fact that he advised and encouraged Columbus to carry out his
project of sailing round the world. His name is nowhere mentioned by
Leonardo, and from the dates of the manuscripts from which the texts
on astronomy are taken, it seems highly probable that Leonardo
devoted his attention to astronomical studies less in his youth than
in his later years. It was evidently his purpose to treat of
Astronomy in a connected form and in a separate work (see the
beginning of Nos._ 866 _and_ 892_; compare also No._ 1167_). It is
quite in accordance with his general scientific thoroughness that he
should propose to write a special treatise on Optics as an
introduction to Astronomy (see Nos._ 867 _and_ 877_). Some of the
chapters belonging to this Section bear the title "Prospettiva"
_(see Nos._ 869 _and_ 870_), this being the term universally applied
at the time to Optics as well as Perspective (see Vol. I, p._ 10,
_note to No._ 13, _l._ 10_)_.

_At the beginning of the XVIth century the Ptolemaic theory of the
universe was still universally accepted as the true one, and
Leonardo conceives of the earth as fixed, with the moon and sun
revolving round it, as they are represented in the diagram to No._
897. _He does not go into any theory of the motions of the planets;
with regard to these and the fixed stars he only investigates the
phenomena of their luminosity. The spherical form of the earth he
takes for granted as an axiom from the first, and he anticipates
Newton by pointing out the universality of Gravitation not merely in
the earth, but even in the moon. Although his acute research into
the nature of the moon's light and the spots on the moon did not
bring to light many results of lasting importance beyond making it
evident that they were a refutation of the errors of his
contemporaries, they contain various explanations of facts which
modern science need not modify in any essential point, and
discoveries which history has hitherto assigned to a very much later
date_.

_The ingenious theory by which he tries to explain the nature of
what is known as earth shine, the reflection of the sun's rays by
the earth towards the moon, saying that it is a peculiar refraction,
originating in the innumerable curved surfaces of the waves of the
sea may be regarded as absurd; but it must not be forgotten that he
had no means of detecting the fundamental error on which he based
it, namely: the assumption that the moon was at a relatively short
distance from the earth. So long as the motion of the earth round
the sun remained unknown, it was of course impossible to form any
estimate of the moon's distance from the earth by a calculation of
its parallax_.

_Before the discovery of the telescope accurate astronomical
observations were only possible to a very limited extent. It would
appear however from certain passages in the notes here printed for
the first time, that Leonardo was in a position to study the spots
in the moon more closely than he could have done with the unaided
eye. So far as can be gathered from the mysterious language in which
the description of his instrument is wrapped, he made use of
magnifying glasses; these do not however seem to have been
constructed like a telescope--telescopes were first made about_
1600. _As LIBRI pointed out_ (Histoire des Sciences mathematiques
III, 101) _Fracastoro of Verona_ (1473-1553) _succeeded in
magnifying the moon's face by an arrangement of lenses (compare No._
910, _note), and this gives probability to Leonardo's invention at a
not much earlier date._

I.

THE EARTH AS A PLANET.

The earth's place in the universe (857. 858).

857.

The equator, the line of the horizon, the ecliptic, the meridian:

These lines are those which in all their parts are equidistant from
the centre of the globe.

858.

The earth is not in the centre of the Sun's orbit nor at the centre
of the universe, but in the centre of its companion elements, and
united with them. And any one standing on the moon, when it and the
sun are both beneath us, would see this our earth and the element of
water upon it just as we see the moon, and the earth would light it
as it lights us.

The fundamental laws of the solar system (859-864).

859.

Force arises from dearth or abundance; it is the child of physical
motion, and the grand-child of spiritual motion, and the mother and
origin of gravity. Gravity is limited to the elements of water and
earth; but this force is unlimited, and by it infinite worlds might
be moved if instruments could be made by which the force could be
generated.

Force, with physical motion, and gravity, with resistance are the
four external powers on which all actions of mortals depend.

Force has its origin in spiritual motion; and this motion, flowing
through the limbs of sentient animals, enlarges their muscles. Being
enlarged by this current the muscles are shrunk in length and
contract the tendons which are connected with them, and this is the
cause of the force of the limbs in man.

The quality and quantity of the force of a man are able to give
birth to other forces, which will be proportionally greater as the
motions produced by them last longer.

[Footnote: Only part of this passage belongs, strictly speaking, to
this section. The principle laid down in the second paragraph is
more directly connected with the notes given in the preceding
section on Physiology.]

860.

Why does not the weight _o_ remain in its place? It does not remain
because it has no resistance. Where will it move to? It will move
towards the centre [of gravity]. And why by no other line? Because a
weight which has no support falls by the shortest road to the lowest
point which is the centre of the world. And why does the weight know
how to find it by so short a line? Because it is not independant and
does not move about in various directions.

[Footnote: This text and the sketch belonging to it, are reproduced
on Pl. CXXI.]

861.

Let the earth turn on which side it may the surface of the waters
will never move from its spherical form, but will always remain
equidistant from the centre of the globe.

Granting that the earth might be removed from the centre of the
globe, what would happen to the water?

It would remain in a sphere round that centre equally thick, but the
sphere would have a smaller diameter than when it enclosed the
earth.

[Footnote: Compare No. 896, lines 48-64; and No. 936.]

862.

Supposing the earth at our antipodes which supports the ocean were
to rise and stand uncovered, far out of the sea, but remaining
almost level, by what means afterwards, in the course of time, would
mountains and vallies be formed?

And the rocks with their various strata?

863.

Each man is always in the middle of the surface of the earth and
under the zenith of his own hemisphere, and over the centre of the
earth.

864.

Mem.: That I must first show the distance of the sun from the earth;
and, by means of a ray passing through a small hole into a dark
chamber, detect its real size; and besides this, by means of the
aqueous sphere calculate the size of the globe ...

Here it will be shown, that when the sun is in the meridian of our
hemisphere [Footnote 10: _Antipodi orientali cogli occidentali_. The
word _Antipodes_ does not here bear its literal sense, but--as we
may infer from the simultaneous reference to inhabitants of the
North and South-- is used as meaning men living at a distance of 90
degrees from the zenith of the rational horizon of each observer.],
the antipodes to the East and to the West, alike, and at the same
time, see the sun mirrored in their waters; and the same is equally
true of the arctic and antarctic poles, if indeed they are
inhabited.

How to prove that the earth is a planet (865-867).

865.

That the earth is a star.

866.

In your discourse you must prove that the earth is a star much like
the moon, and the glory of our universe; and then you must treat of
the size of various stars, according to the authors.

867.

THE METHOD OF PROVING THAT THE EARTH IS A STAR.

First describe the eye; then show how the twinkling of a star is
really in the eye and why one star should twinkle more than another,
and how the rays from the stars originate in the eye; and add, that
if the twinkling of the stars were really in the stars --as it seems
to be--that this twinkling appears to be an extension as great as
the diameter of the body of the star; therefore, the star being
larger than the earth, this motion effected in an instant would be a
rapid doubling of the size of the star. Then prove that the surface
of the air where it lies contiguous to fire, and the surface of the
fire where it ends are those into which the solar rays penetrate,
and transmit the images of the heavenly bodies, large when they
rise, and small, when they are on the meridian. Let _a_ be the earth
and _n d m_ the surface of the air in contact with the sphere of
fire; _h f g_ is the orbit of the moon or, if you please, of the
sun; then I say that when the sun appears on the horizon _g_, its
rays are seen passing through the surface of the air at a slanting
angle, that is _o m_; this is not the case at _d k_. And so it
passes through a greater mass of air; all of _e m_ is a denser
atmosphere.

868.

Beyond the sun and us there is darkness and so the air appears blue.

[Footnote: Compare Vol. I, No. 301.]

869.

PERSPECTIVE.

It is possible to find means by which the eye shall not see remote
objects as much diminished as in natural perspective, which
diminishes them by reason of the convexity of the eye which
necessarily intersects, at its surface, the pyramid of every image
conveyed to the eye at a right angle on its spherical surface. But
by the method I here teach in the margin [9] these pyramids are
intersected at right angles close to the surface of the pupil. The
convex pupil of the eye can take in the whole of our hemisphere,
while this will show only a single star; but where many small stars
transmit their images to the surface of the pupil those stars are
extremely small; here only one star is seen but it will be large.
And so the moon will be seen larger and its spots of a more defined
form [Footnote 20 and fol.: Telescopes were not in use till a century
later. Compare No. 910 and page 136.]. You must place close to the
eye a glass filled with the water of which mention is made in number
4 of Book 113 "On natural substances" [Footnote 23: _libro_ 113.
This is perhaps the number of a book in some library catalogue. But
it may refer, on the other hand, to one of the 120 Books mentioned
in No. 796. l. 84.]; for this water makes objects which are enclosed
in balls of crystalline glass appear free from the glass.

OF THE EYE.

Among the smaller objects presented to the pupil of the eye, that
which is closest to it, will be least appreciable to the eye. And at
the same time, the experiments here made with the power of sight,
show that it is not reduced to speck if the &c. [32][Footnote 32:
Compare with this the passage in Vol. I, No. 52, written about
twenty years earlier.].

Read in the margin.

[34]Those objects are seen largest which come to the eye at the
largest angles.

But the images of the objects conveyed to the pupil of the eye are
distributed to the pupil exactly as they are distributed in the air:
and the proof of this is in what follows; that when we look at the
starry sky, without gazing more fixedly at one star than another,
the sky appears all strewn with stars; and their proportions to the
eye are the same as in the sky and likewise the spaces between them
[61].

[Footnote: 9. 32. _in margine:_ lines 34-61 are, in the original,
written on the margin and above them is the diagram to which
Leonardo seems to refer here.]

870.

PERSPECTIVE.

Among objects moved from the eye at equal distance, that undergoes
least diminution which at first was most remote.

When various objects are removed at equal distances farther from
their original position, that which was at first the farthest from
the eye will diminish least. And the proportion of the diminution
will be in proportion to the relative distance of the objects from
the eye before they were removed.

That is to say in the object _t_ and the object _e_ the proportion
of their distances from the eye _a_ is quintuple. I remove each from
its place and set it farther from the eye by one of the 5 parts into
which the proposition is divided. Hence it happens that the nearest
to the eye has doubled the distance and according to the last
proposition but one of this, is diminished by the half of its whole
size; and the body _e_, by the same motion, is diminished 1/5 of its
whole size. Therefore, by that same last proposition but one, that
which is said in this last proposition is true; and this I say of
the motions of the celestial bodies which are more distant by 3500
miles when setting than when overhead, and yet do not increase or
diminish in any sensible degree.

871.

_a b_ is the aperture through which the sun passes, and if you could
measure the size of the solar rays at _n m_, you could accurately
trace the real lines of the convergence of the solar rays, the
mirror being at _a b_, and then show the reflected rays at equal
angles to _n m_; but, as you want to have them at _n m_, take them
at the. inner side of the aperture at cd, where they maybe measured
at the spot where the solar rays fall. Then place your mirror at the
distance _a b_, making the rays _d b_, _c a_ fall and then be
reflected at equal angles towards _c d_; and this is the best
method, but you must use this mirror always in the same month, and
the same day, and hour and instant, and this will be better than at
no fixed time because when the sun is at a certain distance it
produces a certain pyramid of rays.

872.

_a_, the side of the body in light and shade _b_, faces the whole
portion of the hemisphere bed _e f_, and does not face any part of
the darkness of the earth. And the same occurs at the point _o_;
therefore the space a _o_ is throughout of one and the same
brightness, and s faces only four degrees of the hemisphere _d e f g
h_, and also the whole of the earth _s h_, which will render it
darker; and how much must be demonstrated by calculation. [Footnote:
This passage, which has perhaps a doubtful right to its place in
this connection, stands in the Manuscript between those given in
Vol. I as No. 117 and No. 427.]

873.

THE REASON OF THE INCREASED SIZE OF THE SUN IN THE WEST.

Some mathematicians explain that the sun looks larger as it sets,
because the eye always sees it through a denser atmosphere, alleging
that objects seen through mist or through water appear larger. To
these I reply: No; because objects seen through a mist are similar
in colour to those at a distance; but not being similarly diminished
they appear larger. Again, nothing increases in size in smooth
water; and the proof of this may be seen by throwing a light on a
board placed half under water. But the reason why the sun looks
larger is that every luminous body appears larger in proportion as
it is more remote. [Footnote: Lines 5 and 6 are thus rendered by M.
RAVAISSON in his edition of MS. A. "_De meme, aucune chose ne croit
dans l'eau plane, et tu en feras l'experience_ en calquant un ais
sous l'eau."--Compare the diagrams in Vol. I, p. 114.]

On the luminosity of the Earth in the universal space (874-878).

874.

In my book I propose to show, how the ocean and the other seas must,
by means of the sun, make our world shine with the appearance of a
moon, and to the remoter worlds it looks like a star; and this I
shall prove.

Show, first that every light at a distance from the eye throws out
rays which appear to increase the size of the luminous body; and
from this it follows that 2 ...[Footnote 10: Here the text breaks
off; lines 11 and fol. are written in the margin.].

[11]The moon is cold and moist. Water is cold and moist. Thus our
seas must appear to the moon as the moon does to us.

875.

The waves in water magnify the image of an object reflected in it.

Let _a_ be the sun, and _n m_ the ruffled water, _b_ the image of
the sun when the water is smooth. Let _f_ be the eye which sees the
image in all the waves included within the base of the triangle _c e
f_. Now the sun reflected in the unruffled surface occupied the
space _c d_, while in the ruffled surface it covers all the watery
space _c e_ (as is proved in the 4th of my "Perspective") [Footnote
9: _Nel quarto della mia prospettiva_. If this reference is to the
diagrams accompanying the text--as is usual with Leonardo--and not
to some particular work, the largest of the diagrams here given must
be meant. It is the lowest and actually the fifth, but he would have
called it the fourth, for the text here given is preceded on the
same page of the manuscript by a passage on whirlpools, with the
diagram belonging to it also reproduced here. The words _della mia
prospettiva_ may therefore indicate that the diagram to the
preceding chapter treating on a heterogeneal subject is to be
excluded. It is a further difficulty that this diagram belongs
properly to lines 9-10 and not to the preceding sentence. The
reflection of the sun in water is also discussed in the Theoretical
part of the Book on Painting; see Vol. I, No. 206, 207.] and it will
cover more of the water in proportion as the reflected image is
remote from the eye [10].

[Footnote: In the original sketch, inside the circle in the first
diagram, is written _Sole_ (sun), and to the right of it _luna_
(moon). Thus either of these heavenly bodies may be supposed to fill
that space. Within the lower circle is written _simulacro_ (image).
In the two next diagrams at the spot here marked _L_ the word _Luna_
is written, and in the last _sole_ is written in the top circle at
_a_.]

The image of the sun will be more brightly shown in small waves than
in large ones--and this is because the reflections or images of the
sun are more numerous in the small waves than in large ones, and the
more numerous reflections of its radiance give a larger light than
the fewer.

Waves which intersect like the scales of a fir cone reflect the
image of the sun with the greatest splendour; and this is the case
because the images are as many as the ridges of the waves on which
the sun shines, and the shadows between these waves are small and
not very dark; and the radiance of so many reflections together
becomes united in the image which is transmitted to the eye, so that
these shadows are imperceptible.

That reflection of the sun will cover most space on the surface of
the water which is most remote from the eye which sees it.

Let _a_ be the sun, _p q_ the reflection of the sun; _a b_ is the
surface of the water, in which the sun is mirrored, and _r_ the eye
which sees this reflection on the surface of the water occupying the
space _o m_. _c_ is the eye at a greater distance from the surface
of the water and also from the reflection; hence this reflection
covers a larger space of water, by the distance between _n_ and _o_.

876.

It is impossible that the side of a spherical mirror, illuminated by
the sun, should reflect its radiance unless this mirror were
undulating or filled with bubbles.

You see here the sun which lights up the moon, a spherical mirror,
and all of its surface, which faces the sun is rendered radiant.

Whence it may be concluded that what shines in the moon is water
like that of our seas, and in waves as that is; and that portion
which does not shine consists of islands and terra firma.

This diagram, of several spherical bodies interposed between the eye
and the sun, is given to show that, just as the reflection of the
sun is seen in each of these bodies, in the same way that image may
be seen in each curve of the waves of the sea; and as in these many
spheres many reflections of the sun are seen, so in many waves there
are many images, each of which at a great distance is much magnified
to the eye. And, as this happens with each wave, the spaces
interposed between the waves are concealed; and, for this reason, it
looks as though the many suns mirrored in the many waves were but
one continuous sun; and the shadows,, mixed up with the luminous
images, render this radiance less brilliant than that of the sun
mirrored in these waves.

[Footnote: In the original, at letter _A_ in the diagram "_Sole_"
(the sun) is written, and at _o_ "_occhio_" (the eye).]

877.

This will have before it the treatise on light and shade.

The edges in the moon will be most strongly lighted and reflect most
light, because, there, nothing will be visible but the tops of the
waves of the water [Footnote 5: I have thought it unnecessary to
reproduce the detailed explanation of the theory of reflection on
waves contained in the passage which follows this.].

878.

The sun will appear larger in moving water or on waves than in still
water; an example is the light reflected on the strings of a
monochord.

II.

THE SUN.

The question of the true and of the apparent size of the sun
(879-884).

879.

IN PRAISE OF THE SUN.

If you look at the stars, cutting off the rays (as may be done by
looking through a very small hole made with the extreme point of a
very fine needle, placed so as almost to touch the eye), you will
see those stars so minute that it would seem as though nothing could
be smaller; it is in fact their great distance which is the reason
of their diminution, for many of them are very many times larger
than the star which is the earth with water. Now reflect what this
our star must look like at such a distance, and then consider how
many stars might be added--both in longitude and latitude--between
those stars which are scattered over the darkened sky. But I cannot
forbear to condemn many of the ancients, who said that the sun was
no larger than it appears; among these was Epicurus, and I believe
that he founded his reason on the effects of a light placed in our
atmosphere equidistant from the centre of the earth. Any one looking
at it never sees it diminished in size at whatever distance; and the
rea-

[Footnote 879-882: What Leonardo says of Epicurus-- who according to
LEWIS, _The Astronomy of the ancients_, and MADLER, _Geschichte der
Himmelskunde_, did not devote much attention to the study of
celestial phenomena--, he probably derived from Book X of Diogenes
Laertius, whose _Vitae Philosophorum_ was not printed in Greek till
1533, but the Latin translation appeared in 1475.]

880.

sons of its size and power I shall reserve for Book 4. But I wonder
greatly that Socrates

[Footnote 2: _Socrates;_ I have little light to throw on this
reference. Plato's Socrates himself declares on more than one
occasion that in his youth he had turned his mind to the study of
celestial phenomena (METEWPA) but not in his later years (see G. C.
LEWIS, _The Astronomy of the ancients_, page 109; MADLER,
_Geschichte der Himmelskunde_, page 41). Here and there in Plato's
writings we find incidental notes on the sun and other heavenly
bodies. Leonardo may very well have known of these, since the Latin
version by Ficinus was printed as early as 1491; indeed an undated
edition exists which may very likely have appeared between 1480--90.

There is but one passage in Plato, Epinomis (p. 983) where he speaks
of the physical properties of the sun and says that it is larger
than the earth.

Aristotle who goes very fully into the subject says the same. A
complete edition of Aristotele's works was first printed in Venice
1495-98, but a Latin version of the Books _De Coelo et Mundo_ and
_De Physica_ had been printed in Venice as early as in 1483 (H.
MULLER-STRUBING).]

should have depreciated that solar body, saying that it was of the
nature of incandescent stone, and the one who opposed him as to that
error was not far wrong. But I only wish I had words to serve me to
blame those who are fain to extol the worship of men more than that
of the sun; for in the whole universe there is nowhere to be seen a
body of greater magnitude and power than the sun. Its light gives
light to all the celestial bodies which are distributed throughout
the universe; and from it descends all vital force, for the heat
that is in living beings comes from the soul [vital spark]; and
there is no other centre of heat and light in the universe as will
be shown in Book 4; and certainly those who have chosen to worship
men as gods--as Jove, Saturn, Mars and the like--have fallen into
the gravest error, seeing that even if a man were as large as our
earth, he would look no bigger than a little star which appears but
as a speck in the universe; and seeing again that these men are
mortal, and putrid and corrupt in their sepulchres.

Marcellus [Footnote 23: I have no means of identifying _Marcello_
who is named in the margin. It may be Nonius Marcellus, an obscure
Roman Grammarian of uncertain date (between the IInd and Vth
centuries A. C.) the author of the treatise _De compendiosa doctrina
per litteras ad filium_ in which he treats _de rebus omnibus et
quibusdam aliis_. This was much read in the middle ages. The _editto
princeps_ is dated 1470 (H. MULLER-STRUBING).] and many others
praise the sun.

881.

Epicurus perhaps saw the shadows cast by columns on the walls in
front of them equal in diameter to the columns from which the
shadows were cast; and the breadth of the shadows being parallel
from beginning to end, he thought he might infer that the sun also
was directly opposite to this parallel and that consequently its
breadth was not greater than that of the column; not perceiving that
the diminution in the shadow was insensibly slight by reason of the
remoteness of the sun. If the sun were smaller than the earth, the
stars on a great portion of our hemisphere would have no light,
which is evidence against Epicurus who says the sun is only as large
as it appears.

[Footnote: In the original the writing is across the diagram.]

882.

Epicurus says the sun is the size it looks. Hence as it looks about
a foot across we must consider that to be its size; it would follow
that when the moon eclipses the sun, the sun ought not to appear the
larger, as it does. Then, the moon being smaller than the sun, the
moon must be less than a foot, and consequently when our world
eclipses the moon, it must be less than a foot by a finger's
breadth; inasmuch as if the sun is a foot across, and our earth
casts a conical shadow on the moon, it is inevitable that the
luminous cause of the cone of shadow must be larger than the opaque
body which casts the cone of shadow.

883.

To measure how many times the diameter of the sun will go into its
course in 24 hours.

Make a circle and place it to face the south, after the manner of a
sundial, and place a rod in the middle in such a way as that its
length points to the centre of this circle, and mark the shadow cast
in the sunshine by this rod on the circumference of the circle, and
this shadow will be--let us say-- as broad as from _a_ to _n_. Now
measure how many times this shadow will go into this circumference
of a circle, and that will give you the number of times that the
solar body will go into its orbit in 24 hours. Thus you may see
whether Epicurus was [right in] saying that the sun was only as
large as it looked; for, as the apparent diameter of the sun is
about a foot, and as that sun would go a thousand times into the
length of its course in 24 hours, it would have gone a thousand
feet, that is 300 braccia, which is the sixth of a mile. Whence it
would follow that the course of the sun during the day would be the
sixth part of a mile and that this venerable snail, the sun will
have travelled 25 braccia an hour.

884.

Posidonius composed books on the size of the sun. [Footnote:
Poseidonius of Apamea, commonly called the Rhodian, because he
taught in Rhodes, was a Stoic philosopher, a contemporary and friend
of Cicero's, and the author of numerous works on natural science,
among them.

Strabo quotes no doubt from one of his works, when he says that
Poseidonius explained how it was that the sun looked larger when it
was rising or setting than during the rest of its course (III, p.
135). Kleomedes, a later Greek Naturalist also mentions this
observation of Poseidonius' without naming the title of his work;
however, as Kleomedes' Cyclia Theorica was not printed till 1535,
Leonardo must have derived his quotation from Strabo. He probably
wrote this note in 1508, and as the original Greek was first printed
in Venice in 1516, we must suppose him to quote here from the
translation by Guarinus Veronensis, which was printed as early as
1471, also at Venice (H. MULLER-STRUBING).]

Of the nature of Sunlight.

885.

OF THE PROOF THAT THE SUN IS HOT BY NATURE AND NOT BY VIRTUE.

Of the nature of Sunlight.

That the heat of the sun resides in its nature and not in its virtue
[or mode of action] is abundantly proved by the radiance of the
solar body on which the human eye cannot dwell and besides this no
less manifestly by the rays reflected from a concave mirror,
which--when they strike the eye with such splendour that the eye
cannot bear them--have a brilliancy equal to the sun in its own
place. And that this is true I prove by the fact that if the mirror
has its concavity formed exactly as is requisite for the collecting
and reflecting of these rays, no created being could endure the
heat that strikes from the reflected rays of such a mirror. And if
you argue that the mirror itself is cold and yet send forth hot
rays, I should reply that those rays come really from the sun and
that it is the ray of the concave mirror after having passed through
the window.

Considerations as to the size of the sun (886-891).

886.

The sun does not move. [Footnote: This sentence occurs incidentally
among mathematical notes, and is written in unusually large
letters.]

887.

PROOF THAT THE NEARER YOU ARE TO THE SOURCE OF THE SOLAR RAYS, THE
LARGER WILL THE REFLECTION OF THE SUN FROM THE SEA APPEAR TO YOU.

[Footnote: Lines 4 and fol. Compare Vol. I, Nos. 130, 131.] If it is
from the centre that the sun employs its radiance to intensify the
power of its whole mass, it is evident that the farther its rays
extend, the more widely they will be divided; and this being so,
you, whose eye is near the water that mirrors the sun, see but a
small portion of the rays of the sun strike the surface of the
water, and reflecting the form of the sun. But if you were near to
the sun--as would be the case when the sun is on the meridian and
the sea to the westward--you would see the sun, mirrored in the sea,
of a very great size; because, as you are nearer to the sun, your
eye taking in the rays nearer to the point of radiation takes more
of them in, and a great splendour is the result. And in this way it
can be proved that the moon must have seas which reflect the sun,
and that the parts which do not shine are land.

888.

Take the measure of the sun at the solstice in mid-June.

889.

WHY THE SUN APPEARS LARGER WHEN SETTING THAN AT NOON, WHEN IT IS
NEAR TO US.

Every object seen through a curved medium seems to be of larger size
than it is.

[Footnote: At A is written _sole_ (the sun), at B _terra_ (the
earth).]

890.

Because the eye is small it can only see the image of the sun as of
a small size. If the eye were as large as the sun it would see the
image of the sun in water of the same size as the real body of the
sun, so long as the water is smooth.

891.

A METHOD OF SEEING THE SUN ECLIPSED WITHOUT PAIN TO THE EYE.

Take a piece of paper and pierce holes in it with a needle, and look
at the sun through these holes.

III.

THE MOON.

On the luminousity of the moon (892-901).

892.

OF THE MOON.

As I propose to treat of the nature of the moon, it is necessary
that first I should describe the perspective of mirrors, whether
plane, concave or convex; and first what is meant by a luminous ray,
and how it is refracted by various kinds of media; then, when a
reflected ray is most powerful, whether when the angle of incidence
is acute, right, or obtuse, or from a convex, a plane, or a concave
surface; or from an opaque or a transparent body. Besides this, how
it is that the solar rays which fall on the waves of the sea, are
seen by the eye of the same width at the angle nearest to the eye,
as at the highest line of the waves on the horizon; but
notwithstanding this the solar rays reflected from the waves of the
sea assume the pyramidal form and consequently, at each degree of
distance increase proportionally in size, although to our sight,
they appear as parallel.

1st. Nothing that has very little weight is opaque.

2dly. Nothing that is excessively weighty can remain beneath that
which is heavier.

3dly. As to whether the moon is situated in the centre of its
elements or not.

And, if it has no proper place of its own, like the earth, in the
midst of its elements, why does it not fall to the centre of our
elements? [Footnote 26: The problem here propounded by Leonardo was
not satisfactorily answered till Newton in 1682 formulated the law
of universal attraction and gravitation. Compare No. 902, lines
5-15.]

And, if the moon is not in the centre of its own elements and yet
does not fall, it must then be lighter than any other element.

And, if the moon is lighter than the other elements why is it opaque
and not transparent?

When objects of various sizes, being placed at various distances,
look of equal size, there must be the same relative proportion in
the distances as in the magnitudes of the objects.

[Footnote: In the diagram Leonardo wrote _sole_ at the place marked
_A_.]

893.

OF THE MOON AND WHETHER IT IS POLISHED AND SPHERICAL.

The image of the sun in the moon is powerfully luminous, and is only
on a small portion of its surface. And the proof may be seen by
taking a ball of burnished gold and placing it in the dark with a
light at some distance from it; and then, although it will
illuminate about half of the ball, the eye will perceive its
reflection only in a small part of its surface, and all the rest of
the surface reflects the darkness which surrounds it; so that it is
only in that spot that the image of the light is seen, and all the
rest remains invisible, the eye being at a distance from the ball.
The same thing would happen on the surface of the moon if it were
polished, lustrous and opaque, like all bodies with a reflecting
surface.

Show how, if you were standing on the moon or on a star, our earth
would seem to reflect the sun as the moon does.

And show that the image of the sun in the sea cannot appear one and
undivided, as it appears in a perfectly plane mirror.

894.

How shadows are lost at great distances, as is shown by the shadow
side of the moon which is never seen. [Footnote: Compare also Vol.
I, Nos. 175-179.]

895.

Either the moon has intrinsic luminosity or not. If it has, why does
it not shine without the aid of the sun? But if it has not any light
in itself it must of necessity be a spherical mirror; and if it is a
mirror, is it not proved in Perspective that the image of a luminous
object will never be equal to the extent of surface of the
reflecting body that it illuminates? And if it be thus [Footnote 13:
At A, in the diagram, Leonardo wrote "_sole_" (the sun), and at B
"_luna o noi terra_" (the moon or our earth). Compare also the text
of No. 876.], as is here shown at _r s_ in the figure, whence comes
so great an extent of radiance as that of the full moon as we see
it, at the fifteenth day of the moon?

896.

OF THE MOON.

The moon has no light in itself; but so much of it as faces the sun
is illuminated, and of that illumined portion we see so much as
faces the earth. And the moon's night receives just as much light as
is lent it by our waters as they reflect the image of the sun, which
is mirrored in all those waters which are on the side towards the
sun. The outside or surface of the waters forming the seas of the
moon and of the seas of our globe is always ruffled little or much,
or more or less--and this roughness causes an extension of the
numberless images of the sun which are repeated in the ridges and
hollows, the sides and fronts of the innumerable waves; that is to
say in as many different spots on each wave as our eyes find
different positions to view them from. This could not happen, if the
aqueous sphere which covers a great part of the moon were uniformly
spherical, for then the images of the sun would be one to each
spectator, and its reflections would be separate and independent and
its radiance would always appear circular; as is plainly to be seen
in the gilt balls placed on the tops of high buildings. But if those
gilt balls were rugged or composed of several little balls, like
mulberries, which are a black fruit composed of minute round
globules, then each portion of these little balls, when seen in the
sun, would display to the eye the lustre resulting from the
reflection of the sun, and thus, in one and the same body many tiny
suns would be seen; and these often combine at a long distance and
appear as one. The lustre of the new moon is brighter and stronger,
than when the moon is full; and the reason of this is that the angle
of incidence is more obtuse in the new than in the full moon, in
which the angles [of incidence and reflection] are highly acute. The
waves of the moon therefore mirror the sun in the hollows of the
waves as well as on the ridges, and the sides remain in shadow. But
at the sides of the moon the hollows of the waves do not catch the
sunlight, but only their crests; and thus the images are fewer and
more mixed up with the shadows in the hollows; and this
intermingling of the shaded and illuminated spots comes to the eye
with a mitigated splendour, so that the edges will be darker,
because the curves of the sides of the waves are insufficient to
reflect to the eye the rays that fall upon them. Now the new moon
naturally reflects the solar rays more directly towards the eye from
the crests of the waves than from any other part, as is shown by the
form of the moon, whose rays a strike the waves _b_ and are
reflected in the line _b d_, the eye being situated at _d_. This
cannot happen at the full moon, when the solar rays, being in the
west, fall on the extreme waters of the moon to the East from _n_ to
_m_, and are not reflected to the eye in the West, but are thrown
back eastwards, with but slight deflection from the straight course
of the solar ray; and thus the angle of incidence is very wide
indeed.

The moon is an opaque and solid body and if, on the contrary, it
were transparent, it would not receive the light of the sun.

The yellow or yolk of an egg remains in the middle of the albumen,
without moving on either side; now it is either lighter or heavier
than this albumen, or equal to it; if it is lighter, it ought to
rise above all the albumen and stop in contact with the shell of the
egg; and if it is heavier, it ought to sink, and if it is equal, it
might just as well be at one of the ends, as in the middle or below
[54].

[Footnote 48-64: Compare No. 861.]

The innumerable images of the solar rays reflected from the
innumerable waves of the sea, as they fall upon those waves, are
what cause us to see the very broad and continuous radiance on the
surface of the sea.

897.

That the sun could not be mirrored in the body of the moon, which is
a convex mirror, in such a way as that so much of its surface as is
illuminated by the sun, should reflect the sun unless the moon had a
surface adapted to reflect it--in waves and ridges, like the surface
of the sea when its surface is moved by the wind.

[Footnote: In the original diagrams _sole_ is written at the place
marked _A; luna_ at _C,_ and _terra_ at the two spots marked _B_.]

The waves in water multiply the image of the object reflected in it.

These waves reflect light, each by its own line, as the surface of
the fir cone does [Footnote 14: See the diagram p. 145.]

These are 2 figures one different from the other; one with
undulating water and the other with smooth water.

It is impossible that at any distance the image of the sun cast on
the surface of a spherical body should occupy the half of the
sphere.

Here you must prove that the earth produces all the same effects
with regard to the moon, as the moon with regard to the earth.

The moon, with its reflected light, does not shine like the sun,
because the light of the moon is not a continuous reflection of that
of the sun on its whole surface, but only on the crests and hollows
of the waves of its waters; and thus the sun being confusedly
reflected, from the admixture of the shadows that lie between the
lustrous waves, its light is not pure and clear as the sun is.

[Footnote 38: This refers to the small diagram placed between _B_
and _B_.--]. The earth between the moon on the fifteenth day and the
sun. [Footnote 39: See the diagram below the one referred to in the
preceding note.] Here the sun is in the East and the moon on the
fifteenth day in the West. [Footnote 40.41: Refers to the diagram
below the others.] The moon on the fifteenth [day] between the earth
and the sun. [41]Here it is the moon which has the sun to the West
and the earth to the East.

898.

WHAT SORT OF THING THE MOON IS.

The moon is not of itself luminous, but is highly fitted to
assimilate the character of light after the manner of a mirror, or
of water, or of any other reflecting body; and it grows larger in
the East and in the West, like the sun and the other planets. And
the reason is that every luminous body looks larger in proportion as
it is remote. It is easy to understand that every planet and star is
farther from us when in the West than when it is overhead, by about
3500 miles, as is proved on the margin [Footnote 7: refers to the
first diagram.--A = _sole_ (the sun), B = _terra_ (the earth), C =
_luna_ (the moon).], and if you see the sun or moon mirrored in the
water near to you, it looks to you of the same size in the water as
in the sky. But if you recede to the distance of a mile, it will
look 100 times larger; and if you see the sun reflected in the sea
at sunset, its image would look to you more than 10 miles long;
because that reflected image extends over more than 10 miles of sea.
And if you could stand where the moon is, the sun would look to you,
as if it were reflected from all the sea that it illuminates by day;
and the land amid the water would appear just like the dark spots
that are on the moon, which, when looked at from our earth, appears
to men the same as our earth would appear to any men who might dwell
in the moon.

[Footnote: This text has already been published by LIBRI: _Histoire
des Sciences,_ III, pp. 224, 225.]

OF THE NATURE OF THE MOON.

When the moon is entirely lighted up to our sight, we see its full
daylight; and at that time, owing to the reflection of the solar
rays which fall on it and are thrown off towards us, its ocean casts
off less moisture towards us; and the less light it gives the more
injurious it is.

899.

OF THE MOON.

I say that as the moon has no light in itself and yet is luminous,
it is inevitable but that its light is caused by some other body.

900.

OF THE MOON.

All my opponent's arguments to say that there is no water in the
moon. [Footnote: The objections are very minutely noted down in the
manuscript, but they hardly seem to have a place here.]

901.

Answer to Maestro Andrea da Imola, who said that the solar rays
reflected from a convex mirror are mingled and lost at a short
distance; whereby it is altogether denied that the luminous side of
the moon is of the nature of a mirror, and that consequently the
light is not produced by the innumerable multitude of the waves of
that sea, which I declared to be the portion of the moon which is
illuminated by the solar rays.

Let _o p_ be the body of the sun, _c n s_ the moon, and _b_ the eye
which, above the base _c n_ of the cathetus _c n m_, sees the body
of the sun reflected at equal angles _c n_; and the same again on
moving the eye from _b_ to _a_. [Footnote: The large diagram on the
margin of page 161 belongs to this chapter.]

Explanation of the lumen cinereum in the moon.

902.

OF THE MOON.

No solid body is less heavy than the atmosphere.

[Footnote: 1. On the margin are the words _tola romantina,
tola--ferro stagnato_ (tinned iron); _romantina_ is some special
kind of sheet-iron no longer known by that name.]

Having proved that the part of the moon that shines consists of
water, which mirrors the body of the sun and reflects the radiance
it receives from it; and that, if these waters were devoid of waves,
it would appear small, but of a radiance almost like the sun; --[5]
It must now be shown whether the moon is a heavy or a light body:
for, if it were a heavy body--admitting that at every grade of
distance from the earth greater levity must prevail, so that water
is lighter than the earth, and air than water, and fire than air and
so on successively--it would seem that if the moon had density as it
really has, it would have weight, and having weight, that it could
not be sustained in the space where it is, and consequently that it
would fall towards the centre of the universe and become united to
the earth; or if not the moon itself, at least its waters would fall
away and be lost from it, and descend towards the centre, leaving
the moon without any and so devoid of lustre. But as this does not
happen, as might in reason be expected, it is a manifest sign that
the moon is surrounded by its own elements: that is to say water,
air and fire; and thus is, of itself and by itself, suspended in
that part of space, as our earth with its element is in this part of
space; and that heavy bodies act in the midst of its elements just
as other heavy bodies do in ours [Footnote 15: This passage would
certainly seem to establish Leonardo's claim to be regarded as the
original discoverer of the cause of the ashy colour of the new moon
(_lumen cinereum_). His observations however, having hitherto
remained unknown to astronomers, Moestlin and Kepler have been
credited with the discoveries which they made independently a
century later.

Some disconnected notes treat of the same subject in MS. C. A. 239b;
718b and 719b; "_Perche la luna cinta della parte alluminata dal
sole in ponente, tra maggior splendore in mezzo a tal cerchio, che
quando essa eclissava il sole. Questo accade perche nell' eclissare
il sole ella ombrava il nostro oceano, il qual caso non accade
essendo in ponente, quando il sole alluma esso oceano_." The editors
of the "_Saggio_" who first published this passage (page 12) add
another short one about the seasons in the moon which I confess not
to have seen in the original manuscript: "_La luna ha ogni mese un
verno e una state, e ha maggiori freddi e maggiori caldi, e i suoi
equinozii son piu freddi de' nostri._"]

When the eye is in the East and sees the moon in the West near to
the setting sun, it sees it with its shaded portion surrounded by
luminous portions; and the lateral and upper portion of this light
is derived from the sun, and the lower portion from the ocean in the
West, which receives the solar rays and reflects them on the lower
waters of the moon, and indeed affords the part of the moon that is
in shadow as much radiance as the moon gives the earth at midnight.
Therefore it is not totally dark, and hence some have believed that
the moon must in parts have a light of its own besides that which is
given it by the sun; and this light is due, as has been said, to the
above- mentioned cause,--that our seas are illuminated by the sun.

Again, it might be said that the circle of radiance shown by the
moon when it and the sun are both in the West is wholly borrowed
from the sun, when it, and the sun, and the eye are situated as is
shown above.

[Footnote 23. 24: The larger of the two diagrams reproduced above
stands between these two lines, and the smaller one is sketched in
the margin. At the spot marked _A_ Leonardo wrote _corpo solare_
(solar body) in the larger diagram and _Sole_ (sun) in the smaller
one. At _C luna_ (moon) is written and at _B terra_ (the earth).]

Some might say that the air surrounding the moon as an element,
catches the light of the sun as our atmosphere does, and that it is
this which completes the luminous circle on the body of the moon.

Some have thought that the moon has a light of its own, but this
opinion is false, because they have founded it on that dim light
seen between the hornes of the new moon, which looks dark where it
is close to the bright part, while against the darkness of the
background it looks so light that many have taken it to be a ring of
new radiance completing the circle where the tips of the horns
illuminated by the sun cease to shine [Footnote 34: See Pl. CVIII,
No. 5.]. And this difference of background arises from the fact that
the portion of that background which is conterminous with the bright
part of the moon, by comparison with that brightness looks darker
than it is; while at the upper part, where a portion of the luminous
circle is to be seen of uniform width, the result is that the moon,
being brighter there than the medium or background on which it is
seen by comparison with that darkness it looks more luminous at that
edge than it is. And that brightness at such a time itself is
derived from our ocean and other inland-seas. These are, at that
time, illuminated by the sun which is already setting in such a way
as that the sea then fulfils the same function to the dark side of
the moon as the moon at its fifteenth day does to us when the sun is
set. And the small amount of light which the dark side of the moon
receives bears the same proportion to the light of that side which
is illuminated, as that... [Footnote 42: Here the text breaks off;
lines 43-52 are written on the margin.].

If you want to see how much brighter the shaded portion of the moon
is than the background on which it is seen, conceal the luminous
portion of the moon with your hand or with some other more distant
object.

On the spots in the moon (903-907).

903.

THE SPOTS ON THE MOON.

Some have said that vapours rise from the moon, after the manner of
clouds and are interposed between the moon and our eyes. But, if
this were the case, these spots would never be permanent, either as
to position or form; and, seeing the moon from various aspects, even
if these spots did not move they would change in form, as objects do
which are seen from different sides.

904.

OF THE SPOTS ON THE MOON.

Others say that the moon is composed of more or less transparent
parts; as though one part were something like alabaster and others
like crystal or glass. It would follow from this that the sun
casting its rays on the less transparent portions, the light would
remain on the surface, and so the denser part would be illuminated,
and the transparent portions would display the shadow of their
darker depths; and this is their account of the structure and nature
of the moon. And this opinion has found favour with many
philosophers, and particularly with Aristotle, and yet it is a false
view--for, in the various phases and frequent changes of the moon
and sun to our eyes, we should see these spots vary, at one time
looking dark and at another light: they would be dark when the sun
is in the West and the moon in the middle of the sky; for then the
transparent hollows would be in shadow as far as the tops of the
edges of those transparent hollows, because the sun could not then
fling his rays into the mouth of the hollows, which however, at full
moon, would be seen in bright light, at which time the moon is in
the East and faces the sun in the West; then the sun would
illuminate even the lowest depths of these transparent places and
thus, as there would be no shadows cast, the moon at these times
would not show us the spots in question; and so it would be, now
more and now less, according to the changes in the position of the
sun to the moon, and of the moon to our eyes, as I have said above.

905.

OF THE SPOTS ON THE MOON.

It has been asserted, that the spots on the moon result from the
moon being of varying thinness or density; but if this were so, when
there is an eclipse of the moon the solar rays would pierce through
the portions which were thin as is alleged [Footnote 3-5: _Eclissi_.
This word, as it seems to me, here means eclipses of the sun; and
the sense of the passage, as I understand it, is that by the
foregoing hypothesis the moon, when it comes between the sun and the
earth must appear as if pierced,--we may say like a sieve.]. But as
we do not see this effect the opinion must be false.

Others say that the surface of the moon is smooth and polished and
that, like a mirror, it reflects in itself the image of our earth.
This view is also false, inasmuch as the land, where it is not
covered with water, presents various aspects and forms. Hence when
the moon is in the East it would reflect different spots from those
it would show when it is above us or in the West; now the spots on
the moon, as they are seen at full moon, never vary in the course of
its motion over our hemisphere. A second reason is that an object
reflected in a convex body takes up but a small portion of that
body, as is proved in perspective [Footnote 18: _come e provato_.
This alludes to the accompanying diagram.]. The third reason is that
when the moon is full, it only faces half the hemisphere of the
illuminated earth, on which only the ocean and other waters reflect
bright light, while the land makes spots on that brightness; thus
half of our earth would be seen girt round with the brightness of
the sea lighted up by the sun, and in the moon this reflection would
be the smallest part of that moon. Fourthly, a radiant body cannot
be reflected from another equally radiant; therefore the sea, since
it borrows its brightness from the sun,--as the moon does--, could
not cause the earth to be reflected in it, nor indeed could the body
of the sun be seen reflected in it, nor indeed any star opposite to
it.

906.

If you keep the details of the spots of the moon under observation
you will often find great variation in them, and this I myself have
proved by drawing them. And this is caused by the clouds that rise
from the waters in the moon, which come between the sun and those
waters, and by their shadow deprive these waters of the sun's rays.
Thus those waters remain dark, not being able to reflect the solar
body.

907.

How the spots on the moon must have varied from what they formerly
were, by reason of the course of its waters.

On the moon's halo.

908.

OF HALOS ROUND THE MOON.

I have found, that the circles which at night seem to surround the
moon, of various sizes, and degrees of density are caused by various
gradations in the densities of the vapours which exist at different
altitudes between the moon and our eyes. And of these halos the
largest and least red is caused by the lowest of these vapours; the
second, smaller one, is higher up, and looks redder because it is
seen through two vapours. And so on, as they are higher they will
appear smaller and redder, because, between the eye and them, there
is thicker vapour. Whence it is proved that where they are seen to
be reddest, the vapours are most dense.

On instruments for observing the moon (909. 910).

909.

If you want to prove why the moon appears larger than it is, when it
reaches the horizon; take a lens which is highly convex on one
surface and concave on the opposite, and place the concave side next
the eye, and look at the object beyond the convex surface; by this
means you will have produced an exact imitation of the atmosphere
included beneath the sphere of fire and outside that of water; for
this atmosphere is concave on the side next the earth, and convex
towards the fire.

910.

Construct glasses to see the moon magnified.

[Footnote: See the Introduction, p. 136, Fracastoro says in his work
Homocentres: "_Per dua specilla ocularla si quis perspiciat, alteri
altero superposito, majora multo et propinquiora videbit
omnia.--Quin imo quaedam specilla ocularia fiunt tantae densitatis,
ut si per ea quis aut lunam, aut aliud siderum spectet, adeo
propinqua illa iudicet, ut ne turres ipsas excedant_" (sect. II c. 8
and sect. III, c. 23).]

I.
THE STARS.
On the light of the stars (911-913).
911.
The stars are visible by night and not by day, because we are
eneath the dense atmosphere, which is full of innumerable
articles of moisture, each of which independently, when the
ays of the sun fall upon it, reflects a radiance, and so these
umberless bright particles conceal the stars; and if it were not
or this atmosphere the sky would always display the stars against
ts darkness.
[Footnote: See No. 296, which also refers to starlight.]
912.
Whether the stars have their light from the sun or in themselves.
Some say that they shine of themselves, alledging that if Venus
nd Mercury had not a light of their own, when they come between
ur eye and the sun they would darken so much of the sun as they
ould cover from our eye. But this is false, for it is proved that
 dark object against a luminous body is enveloped and entirely
oncealed by the lateral rays of the rest of that luminous body
nd so remains invisible. As may be seen when the sun is seen
hrough the boughs of trees bare of their leaves, at some distance
he branches do not conceal any portion of the sun from our eye.
he same thing happens with the above mentioned planets which,
hough they have no light of their own, do not--as has been said--
onceal any part of the sun from our eye
[18].

SECOND ARGUMENT.

Some say that the stars appear most brilliant at night in proportion
as they are higher up; and that if they had no light of their own,
the shadow of the earth which comes between them and the sun, would
darken them, since they would not face nor be faced by the solar
body. But those persons have not considered that the conical shadow
of the earth cannot reach many of the stars; and even as to those it
does reach, the cone is so much diminished that it covers very
little of the star's mass, and all the rest is illuminated by the
sun.

Footnote: From this and other remarks (see No. 902) it is clear
hat Leonardo was familiar with the phenomena of Irradiation.]

13.

Why the planets appear larger in the East than they do overhead,
whereas the contrary should be the case, as they are 3500 miles
nearer to us when in mid sky than when on the horizon.

All the degrees of the elements, through which the images of the
celestial bodies pass to reach the eye, are equal curves and the
angles by which the central line of those images passes through
them, are unequal angles [Footnote 13: _inequali_, here and
elsewhere does not mean unequal in the sense of not being equal to
each other, but angles which are not right angles.]; and the
distance is greater, as is shown by the excess of _a b_ beyond _a
d_; and the enlargement of these celestial bodies on the horizon is
shown by the 9th of the 7th.

Observations on the stars.

914.

To see the real nature of the planets open the covering and note at
the base [Footnote 4: _basa_. This probably alludes to some
instrument, perhaps the Camera obscura.] one single planet, and the
reflected movement of this base will show the nature of the said
planet; but arrange that the base may face only one at the time.

On history of astronomy.

915.

Cicero says in [his book] De Divinatione that Astrology has been
practised five hundred seventy thousand years before the Trojan war.

57000.

[Footnote: The statement that CICERO, _De Divin._ ascribes the
discovery of astrology to a period 57000 years before the Trojan war
I believe to be quite erroneous. According to ERNESTI, _Clavis
Ciceroniana,_ CH. G. SCHULZ (_Lexic. Cicer._) and the edition of _De
Divin._ by GIESE the word Astrologia occurs only twice in CICERO:
_De Divin. II_, 42. _Ad Chaldaeorum monstra veniamus, de quibus
Eudoxus, Platonis auditor, in astrologia judicio doctissimorum
hominum facile princeps, sic opinatur (id quod scriptum reliquit):
Chaldaeis in praedictione et in notatione cujusque vitae ex natali
die minime esse credendum._" He then quotes the condemnatory verdict
of other philosophers as to the teaching of the Chaldaeans but says
nothing as to the antiquity and origin of astronomy. CICERO further
notes _De oratore_ I, 16 that Aratus was "_ignarus astrologiae_" but
that is all. So far as I know the word occurs nowhere else in
CICERO; and the word _Astronomia_ he does not seem to have used at
all. (H. MULLER-STRUBING.)]

Of time and its divisions (916-918).

916.

Although time is included in the class of Continuous Quantities,
being indivisible and immaterial, it does not come entirely under
the head of Geometry, which represents its divisions by means of
figures and bodies of infinite variety, such as are seen to be
continuous in their visible and material properties. But only with
its first principles does it agree, that is with the Point and the
Line; the point may be compared to an instant of time, and the line
may be likened to the length of a certain quantity of time, and just
as a line begins and terminates in a point, so such a space of time.
begins and terminates in an instant. And whereas a line is
infinitely divisible, the divisibility of a space of time is of the
same nature; and as the divisions of the line may bear a certain
proportion to each other, so may the divisions of time.

[Footnote: This passage is repeated word for word on page 190b of
the same manuscript and this is accounted for by the text in Vol. I,
No. 4. Compare also No. 1216.]

917.

Describe the nature of Time as distinguished from the Geometrical
definitions.

918.

Divide an hour into 3000 parts, and this you can do with a clock by
making the pendulum lighter or heavier.

_XVI.

Physical Geography.

Leonardo's researches as to the structure of the earth and sea were
made at a time, when the extended voyages of the Spaniards and
Portuguese had also excited a special interest in geographical
questions in Italy, and particularly in Tuscany. Still, it need
scarcely surprise us to find that in deeper questions, as to the
structure of the globe, the primitive state of the earth's surface,
and the like, he was far in advance of his time.

The number of passages which treat of such matters is relatively
considerable; like almost all Leonardo's scientific notes they deal
partly with theoretical and partly with practical questions. Some of
his theoretical views of the motion of water were collected in a
copied manuscript volume by an early transcriber, but without any
acknowledgment of the source whence they were derived. This copy is
now in the Library of the Barberini palace at Rome and was published
under the title: "De moto e misura dell'acqua," by FRANCESCO
CARDINALI, Bologna_ 1828. _In this work the texts are arranged under
the following titles:_ Libr. I. Della spera dell'acqua; Libr. II.
Del moto dell'acqua; Libr. III. Dell'onda dell'acqua; Libr. IV. Dei
retrosi d'acqua; Libr. V. Dell'acqua cadente; Libr. VI. Delle
rotture fatte dall'acqua; Libr. VII Delle cose portate dall'acqua;
Libr. VIII. Dell'oncia dell'acqua e delle canne; Libr. IX. De molini
e d'altri ordigni d'acqua.

_The large number of isolated observations scattered through the
manuscripts, accounts for our so frequently finding notes of new
schemes for the arrangement of those relating to water and its
motions, particularly in the Codex Atlanticus: I have printed
several of these plans as an introduction to the Physical Geography,
and I have actually arranged the texts in accordance with the clue
afforded by one of them which is undoubtedly one of the latest notes
referring to the subject (No._ 920_). The text given as No._ 930
_which is also taken from a late note-book of Leonardo's, served as
a basis for the arrangement of the first of the seven books--or
sections--, bearing the title: Of the Nature of Water_ (Dell'acque
in se).

_As I have not made it any part of this undertaking to print the
passages which refer to purely physical principles, it has also been
necessary to exclude those practical researches which, in accordance
with indications given in_ 920, _ought to come in as Books_ 13, 14
_and_ 15. _I can only incidentally mention here that Leonardo--as it
seems to me, especially in his youth--devoted a great deal of
attention to the construction of mills. This is proved by a number
of drawings of very careful and minute execution, which are to be
found in the Codex Atlanticus. Nor was it possible to include his
considerations on the regulation of rivers, the making of canals and
so forth (No._ 920, _Books_ 10, 11 _and_ 12_); but those passages in
which the structure of a canal is directly connected with notices of
particular places will be found duly inserted under section XVII
(Topographical notes). In Vol. I, No._ 5 _the text refers to
canal-making in general._

_On one point only can the collection of passages included under the
general heading of Physical Geography claim to be complete. When
comparing and sorting the materials for this work I took particular
care not to exclude or omit any text in which a geographical name
was mentioned even incidentally, since in all such researches the
chief interest, as it appeared to me, attached to the question
whether these acute observations on the various local
characteristics of mountains, rivers or seas, had been made by
Leonardo himself, and on the spot. It is self-evident that the few
general and somewhat superficial observations on the Rhine and the
Danube, on England and Flanders, must have been obtained from maps
or from some informants, and in the case of Flanders Leonardo
himself acknowledges this (see No._ 1008_). But that most of the
other and more exact observations were made, on the spot, by
Leonardo himself, may be safely assumed from their method and the
style in which he writes of them; and we should bear it in mind that
in all investigations, of whatever kind, experience is always spoken
of as the only basis on which he relies. Incidentally, as in No._
984, _he thinks it necessary to allude to the total absence of all
recorded observations._

I.

INTRODUCTION.

Schemes for the arrangement of the materials (919-928).

919.

These books contain in the beginning: Of the nature of water itself
in its motions; the others treat of the effects of its currents,
which change the world in its centre and its shape.

920.

DIVISIONS OF THE BOOK.

Book 1 of water in itself.

Book 2 of the sea.

Book 3 of subterranean rivers.

Book 4 of rivers.

Book 5 of the nature of the abyss.

Book 6 of the obstacles.

Book 7 of gravels.

Book 8 of the surface of water.

Book 9 of the things placed therein.

Book 10 of the repairing of rivers.

Book 11 of conduits.

Book 12 of canals.

Book 13 of machines turned by water.

Book 14 of raising water.

Book 15 of matters worn away by water.

921.

First you shall make a book treating of places occupied by fresh
waters, and the second by salt waters, and the third, how by the
disappearance of these, our parts of the world were made lighter and
in consequence more remote from the centre of the world.

922.

First write of all water, in each of its motions; then describe all
its bottoms and their various materials, always referring to the
propositions concerning the said waters; and let the order be good,
for otherwise the work will be confused.

Describe all the forms taken by water from its greatest to its
smallest wave, and their causes.

923.

Book 9, of accidental risings of water.

924.

THE ORDER OF THE BOOK.

Place at the beginning what a river can effect.

925.

A book of driving back armies by the force of a flood made by
releasing waters.

A book showing how the waters safely bring down timber cut in the
mountains.

A book of boats driven against the impetus of rivers.

A book of raising large bridges higher. Simply by the swelling of
the waters.

A book of guarding against the impetus of rivers so that towns may
not be damaged by them.

926.

A book of the ordering of rivers so as to preserve their banks.

A book of the mountains, which would stand forth and become land, if
our hemisphere were to be uncovered by the water.

A book of the earth carried down by the waters to fill up the great
abyss of the seas.

A book of the ways in which a tempest may of itself clear out filled
up sea-ports.

A book of the shores of rivers and of their permanency.

A book of how to deal with rivers, so that they may keep their
bottom scoured by their own flow near the cities they pass.

A book of how to make or to repair the foundations for bridges over
the rivers.

A book of the repairs which ought to be made in walls and banks of
rivers where the water strikes them.

A book of the formation of hills of sand or gravel at great depths
in water.

927.

Water gives the first impetus to its motion.

A book of the levelling of waters by various means,

A book of diverting rivers from places where they do mischief.

A book of guiding rivers which occupy too much ground.

A book of parting rivers into several branches and making them
fordable.

A book of the waters which with various currents pass through seas.

A book of deepening the beds of rivers by means of currents of
water.

A book of controlling rivers so that the little beginnings of
mischief, caused by them, may not increase.

A book of the various movements of waters passing through channels
of different forms.

A book of preventing small rivers from diverting the larger one into
which their waters run.

A book of the lowest level which can be found in the current of the
surface of rivers.

A book of the origin of rivers which flow from the high tops of
mountains.

A book of the various motions of waters in their rivers.

928.

[1] Of inequality in the concavity of a ship. [Footnote 1: The first
line of this passage was added subsequently, evidently as a
correction of the following line.]

[1] A book of the inequality in the curve of the sides of ships.

[1] A book of the inequality in the position of the tiller.

[1] A book of the inequality in the keel of ships.

[2] A book of various forms of apertures by which water flows out.

[3] A book of water contained in vessels with air, and of its
movements.

[4] A book of the motion of water through a syphon. [Footnote 7:
_cicognole_, see No. 966, 11, 17.]

[5] A book of the meetings and union of waters coming from different
directions.

[6] A book of the various forms of the banks through which rivers
pass.

[7] A book of the various forms of shoals formed under the sluices
of rivers.

[8] A book of the windings and meanderings of the currents of
rivers.

[9] A book of the various places whence the waters of rivers are
derived.

[10] A book of the configuration of the shores of rivers and of
their permanency.

[11] A book of the perpendicular fall of water on various objects.

[12] Abook of the course of water when it is impeded in various
places.

[12] A book of the various forms of the obstacles which impede the
course of waters.

[13] A book of the concavity and globosity formed round various
objects at the bottom.

[14] Abook of conducting navigable canals above or beneath the
rivers which intersect them.

[15] A book of the soils which absorb water in canals and of
repairing them.

[16] Abook of creating currents for rivers, which quit their beds,
[and] for rivers choked with soil.

General introduction.

929.

THE BEGINNING OF THE TREATISE ON WATER.

By the ancients man has been called the world in miniature; and
certainly this name is well bestowed, because, inasmuch as man is
composed of earth, water, air and fire, his body resembles that of
the earth; and as man has in him bones the supports and framework of
his flesh, the world has its rocks the supports of the earth; as man
has in him a pool of blood in which the lungs rise and fall in
breathing, so the body of the earth has its ocean tide which
likewise rises and falls every six hours, as if the world breathed;
as in that pool of blood veins have their origin, which ramify all
over the human body, so likewise the ocean sea fills the body of the
earth with infinite springs of water. The body of the earth lacks
sinews and this is, because the sinews are made expressely for
movements and, the world being perpetually stable, no movement takes
place, and no movement taking place, muscles are not necessary.
--But in all other points they are much alike.

I.

OF THE NATURE OF WATER.

The arrangement of Book I.

930.

THE ORDER OF THE FIRST BOOK ON WATER.

Define first what is meant by height and depth; also how the
elements are situated one inside another. Then, what is meant by
solid weight and by liquid weight; but first what weight and
lightness are in themselves. Then describe why water moves, and why
its motion ceases; then why it becomes slower or more rapid; besides
this, how it always falls, being in contact with the air but lower
than the air. And how water rises in the air by means of the heat of
the sun, and then falls again in rain; again, why water springs
forth from the tops of mountains; and if the water of any spring
higher than the ocean can pour forth water higher than the surface
of that ocean. And how all the water that returns to the ocean is
higher than the sphere of waters. And how the waters of the
equatorial seas are higher than the waters of the North, and higher
beneath the body of the sun than in any part of the equatorial
circle; for experiment shows that under the heat of a burning brand
the water near the brand boils, and the water surrounding this
ebullition always sinks with a circular eddy. And how the waters of
the North are lower than the other seas, and more so as they become
colder, until they are converted into ice.

Definitions (931. 932).

931.

OF WHAT IS WATER.

Among the four elements water is the second both in weight and in
instability.

932.

THE BEGINNING OF THE BOOK ON WATER.

Sea is the name given to that water which is wide and deep, in which
the waters have not much motion.

[Footnote: Only the beginning of this passage is here given, the
remainder consists of definitions which have no direct bearing on
the subject.]

Of the surface of the water in relation to the globe (933-936).

933.

The centres of the sphere of water are two, one universal and common
to all water, the other particular. The universal one is that which
is common to all waters not in motion, which exist in great
quantities. As canals, ditches, ponds, fountains, wells, dead
rivers, lakes, stagnant pools and seas, which, although they are at
various levels, have each in itself the limits of their superficies
equally distant from the centre of the earth, such as lakes placed
at the tops of high mountains; as the lake near Pietra Pana and the
lake of the Sybil near Norcia; and all the lakes that give rise to
great rivers, as the Ticino from Lago Maggiore, the Adda from the
lake of Como, the Mincio from the lake of Garda, the Rhine from the
lakes of Constance and of Chur, and from the lake of Lucerne, like
the Tigris which passes through Asia Minor carrying with it the
waters of three lakes, one above the other at different heights of
which the highest is Munace, the middle one Pallas, and the lowest
Triton; the Nile again flows from three very high lakes in Ethiopia.

[Footnote 5: _Pietra Pana_, a mountain near Florence. If for Norcia,
we may read Norchia, the remains of the Etruscan city near Viterbo,
there can be no doubt that by '_Lago della Sibilla_'--a name not
known elsewhere, so far as I can learn--Leonardo meant _Lago di
Vico_ (Lacus Ciminus, Aen. 7).]

934.

OF THE CENTRE OF THE OCEAN.

The centre of the sphere of waters is the true centre of the globe
of our world, which is composed of water and earth, having the shape
of a sphere. But, if you want to find the centre of the element of
the earth, this is placed at a point equidistant from the surface of
the ocean, and not equidistant from the surface of the earth; for it
is evident that this globe of earth has nowhere any perfect
rotundity, excepting in places where the sea is, or marshes or other
still waters. And every part of the earth that rises above the water
is farther from the centre.

935.

OF THE SEA WHICH CHANGES THE WEIGHT OF THE EARTH.

The shells, oysters, and other similar animals, which originate in
sea-mud, bear witness to the changes of the earth round the centre
of our elements. This is proved thus: Great rivers always run
turbid, being coloured by the earth, which is stirred by the
friction of their waters at the bottom and on their shores; and this
wearing disturbs the face of the strata made by the layers of
shells, which lie on the surface of the marine mud, and which were
produced there when the salt waters covered them; and these strata
were covered over again from time to time, with mud of various
thickness, or carried down to the sea by the rivers and floods of
more or less extent; and thus these layers of mud became raised to
such a height, that they came up from the bottom to the air. At the
present time these bottoms are so high that they form hills or high
mountains, and the rivers, which wear away the sides of these
mountains, uncover the strata of these shells, and thus the softened
side of the earth continually rises and the antipodes sink closer to
the centre of the earth, and the ancient bottoms of the seas have
become mountain ridges.

936.

Let the earth make whatever changes it may in its weight, the
surface of the sphere of waters can never vary in its equal distance
from the centre of the world.

Of the proportion of the mass of water to that of the earth (937.
938).

937.

WHETHER THE EARTH IS LESS THAN THE WATER.

Some assert that it is true that the earth, which is not covered by
water is much less than that covered by water. But considering the
size of 7000 miles in diameter which is that of this earth, we may
conclude the water to be of small depth.

938.

OF THE EARTH.

The great elevations of the peaks of the mountains above the sphere
of the water may have resulted from this that: a very large portion
of the earth which was filled with water that is to say the vast
cavern inside the earth may have fallen in a vast part of its vault
towards the centre of the earth, being pierced by means of the
course of the springs which continually wear away the place where
they pass.

Sinking in of countries like the Dead Sea in Syria, that is Sodom
and Gomorrah.

It is of necessity that there should be more water than land, and
the visible portion of the sea does not show this; so that there
must be a great deal of water inside the earth, besides that which
rises into the lower air and which flows through rivers and springs.

[Footnote: The small sketch below on the left, is placed in the
original close to the text referring to the Dead Sea.]

The theory of Plato.

939.

THE FIGURES OF THE ELEMENTS.

Of the figures of the elements; and first as against those who deny
the opinions of Plato, and who say that if the elements include one
another in the forms attributed to them by Plato they would cause a
vacuum one within the other. I say it is not true, and I here prove
it, but first I desire to propound some conclusions. It is not
necessary that the elements which include each other should be of
corresponding magnitude in all the parts, of that which includes and
of that which is included. We see that the sphere of the waters
varies conspicuously in mass from the surface to the bottom, and
that, far from investing the earth when that was in the form of a
cube that is of 8 angles as Plato will have it, that it invests the
earth which has innumerable angles of rock covered by the water and
various prominences and concavities, and yet no vacuum is generated
between the earth and water; again, the air invests the sphere of
waters together with the mountains and valleys, which rise above
that sphere, and no vacuum remains between the earth and the air, so
that any one who says a vacuum is generated, speaks foolishly.

But to Plato I would reply that the surface of the figures which
according to him the elements would have, could not exist.

That the flow of rivers proves the slope of the land.

940.

PROVES HOW THE EARTH IS NOT GLOBULAR AND NOT BEING GLOBULAR CANNOT
HAVE A COMMON CENTRE.

We see the Nile come from Southern regions and traverse various
provinces, running towards the North for a distance of 3000 miles
and flow into the Mediterranean by the shores of Egypt; and if we
will give to this a fall of ten braccia a mile, as is usually
allowed to the course of rivers in general, we shall find that the
Nile must have its mouth ten miles lower than its source. Again, we
see the Rhine, the Rhone and the Danube starting from the German
parts, almost the centre of Europe, and having a course one to the
East, the other to the North, and the last to Southern seas. And if
you consider all this you will see that the plains of Europe in
their aggregate are much higher than the high peaks of the maritime
mountains; think then how much their tops must be above the sea
shores.

Theory of the elevation of water within the mountains.

941.

OF THE HEAT THAT IS IN THE WORLD.

Where there is life there is heat, and where vital heat is, there is
movement of vapour. This is proved, inasmuch as we see that the
element of fire by its heat always draws to itself damp vapours and
thick mists as opaque clouds, which it raises from seas as well as
lakes and rivers and damp valleys; and these being drawn by degrees
as far as the cold region, the first portion stops, because heat and
moisture cannot exist with cold and dryness; and where the first
portion stops the rest settle, and thus one portion after another
being added, thick and dark clouds are formed. They are often wafted
about and borne by the winds from one region to another, where by
their density they become so heavy that they fall in thick rain; and
if the heat of the sun is added to the power of the element of fire,
the clouds are drawn up higher still and find a greater degree of
cold, in which they form ice and fall in storms of hail. Now the
same heat which holds up so great a weight of water as is seen to
rain from the clouds, draws them from below upwards, from the foot
of the mountains, and leads and holds them within the summits of the
mountains, and these, finding some fissure, issue continuously and
cause rivers.

The relative height of the surface of the sea to that of the land
(942-945).

942.

OF THE SEA, WHICH TO MANY FOOLS APPEARS TO BE HIGHER THAN THE EARTH
WHICH FORMS ITS SHORE.

_b d_ is a plain through which a river flows to the sea; this plain
ends at the sea, and since in fact the dry land that is uncovered is
not perfectly level--for, if it were, the river would have no
motion--as the river does move, this place is a slope rather than a
plain; hence this plain _d b_ so ends where the sphere of water
begins that if it were extended in a continuous line to _b a_ it
would go down beneath the sea, whence it follows that the sea _a c
b_ looks higher than the dry land.

Obviously no portions of dry land left uncovered by water can ever
be lower than the surface of the watery sphere.

943.

OF CERTAIN PERSONS WHO SAY THE WATERS WERE HIGHER THAN THE DRY LAND.

Certainly I wonder not a little at the common opinion which is
contrary to truth, but held by the universal consent of the judgment
of men. And this is that all are agreed that the surface of the sea
is higher than the highest peaks of the mountains; and they allege
many vain and childish reasons, against which I will allege only one
simple and short reason; We see plainly that if we could remove the
shores of the sea, it would invest the whole earth and make it a
perfect sphere. Now, consider how much earth would be carried away
to enable the waves of the sea to cover the world; therefore that
which would be carried away must be higher than the sea-shore.

944.

THE OPINION OF SOME PERSONS WHO SAY THAT THE WATER OF SOME SEAS IS
HIGHER THAN THE HIGHEST SUMMITS OF MOUNTAINS; AND NEVERTHELESS THE
WATER WAS FORCED UP TO THESE SUMMITS.

Water would not move from place to place if it were not that it
seeks the lowest level and by a natural consequence it never can
return to a height like that of the place where it first on issuing
from the mountain came to light. And that portion of the sea which,
in your vain imagining, you say was so high that it flowed over the
summits of the high mountains, for so many centuries would be
swallowed up and poured out again through the issue from these
mountains. You can well imagine that all the time that Tigris and
Euphrates

945.

have flowed from the summits of the mountains of Armenia, it must be
believed that all the water of the ocean has passed very many times
through these mouths. And do you not believe that the Nile must have
sent more water into the sea than at present exists of all the
element of water? Undoubtedly, yes. And if all this water had fallen
away from this body of the earth, this terrestrial machine would
long since have been without water. Whence we may conclude that the
water goes from the rivers to the sea, and from the sea to the
rivers, thus constantly circulating and returning, and that all the
sea and the rivers have passed through the mouth of the Nile an
infinite number of times [Footnote: _Moti Armeni, Ermini_ in the
original, in M. RAVAISSON'S transcript _"monti ernini [le loro
ruine?]"_. He renders this _"Le Tigre et l'Euphrate se sont deverses
par les sommets des montagnes [avec leurs eaux destructives?] on
pent cro're" &c. Leonardo always writes _Ermini, Erminia_, for
_Armeni, Armenia_ (Arabic: _Irminiah_). M. RAVAISSON also deviates
from the original in his translation of the following passage: "_Or
tu ne crois pas que le Nil ait mis plus d'eau dans la mer qu'il n'y
en a a present dans tout l'element de l'eau. Il est certain que si
cette eau etait tombee_" &c.]

II.

ON THE OCEAN.

Refutation of Pliny's theory as to the saltness of the sea (946.
947).

946.

WHY WATER IS SALT.

Pliny says in his second book, chapter 103, that the water of the
sea is salt because the heat of the sun dries up the moisture and
drinks it up; and this gives to the wide stretching sea the savour
of salt. But this cannot be admitted, because if the saltness of the
sea were caused by the heat of the sun, there can be no doubt that
lakes, pools and marshes would be so much the more salt, as their
waters have less motion and are of less depth; but experience shows
us, on the contrary, that these lakes have their waters quite free
from salt. Again it is stated by Pliny in the same chapter that this
saltness might originate, because all the sweet and subtle portions
which the heat attracts easily being taken away, the more bitter and
coarser part will remain, and thus the water on the surface is
fresher than at the bottom [Footnote 22: Compare No. 948.]; but this
is contradicted by the same reason given above, which is, that the
same thing would happen in marshes and other waters, which are dried
up by the heat. Again, it has been said that the saltness of the sea
is the sweat of the earth; to this it may be answered that all the
springs of water which penetrate through the earth, would then be
salt. But the conclusion is, that the saltness of the sea must
proceed from the many springs of water which, as they penetrate into
the earth, find mines of salt and these they dissolve in part, and
carry with them to the ocean and the other seas, whence the clouds,
the begetters of rivers, never carry it up. And the sea would be
salter in our times than ever it was at any time; and if the
adversary were to say that in infinite time the sea would dry up or
congeal into salt, to this I answer that this salt is restored to
the earth by the setting free of that part of the earth which rises
out of the sea with the salt it has acquired, and the rivers return
it to the earth under the sea.

[Footnote: See PLINY, Hist. Nat. II, CIII [C]. _Itaque Solis ardore
siccatur liquor: et hoc esse masculum sidus accepimus, torrens
cuncta sorbensque._ (cp. CIV.) _Sic mari late patenti saporem
incoqui salis, aut quia exhausto inde dulci tenuique, quod facillime
trahat vis ignea, omne asperius crassiusque linquatur: ideo summa
aequorum aqua dulciorem profundam; hanc esse veriorem causam, quam
quod mare terrae sudor sit aeternus: aut quia plurimum ex arido
misceatur illi vapore: aut quia terrae natura sicut medicatas aquas
inficiat_ ... (cp. CV): _altissimum mare XV. stadiorum Fabianus
tradit. Alii n Ponto coadverso Coraxorum gentis (vocant B Ponti)
trecentis fere a continenti stadiis immensam altitudinem maris
tradunt, vadis nunquam repertis._ (cp. CVI [CIII]) _Mirabilius id
faciunt aquae dulces, juxta mare, ut fistulis emicantes. Nam nec
aquarum natura a miraculis cessat. Dulces mari invehuntur, leviores
haud dubie. Ideo et marinae, quarum natura gravior, magis invecta
sustinent. Quaedam vero et dulces inter se supermeant alias._]

947.

For the third and last reason we will say that salt is in all
created things; and this we learn from water passed over the ashes
and cinders of burnt things; and the urine of every animal, and the
superfluities issuing from their bodies, and the earth into which
all things are converted by corruption.

But,--to put it better,--given that the world is everlasting, it
must be admitted that its population will also be eternal; hence the
human species has eternally been and would be consumers of salt; and
if all the mass of the earth were to be turned into salt, it would
not suffice for all human food [Footnote 27: That is, on the
supposition that salt, once consumed, disappears for ever.]; whence
we are forced to admit, either that the species of salt must be
everlasting like the world, or that it dies and is born again like
the men who devour it. But as experience teaches us that it does not
die, as is evident by fire, which does not consume it, and by water
which becomes salt in proportion to the quantity dissolved in
it,--and when it is evaporated the salt always remains in the
original quantity--it must pass through the bodies of men either in
the urine or the sweat or other excretions where it is found again;
and as much salt is thus got rid of as is carried every year into
towns; therefore salt is dug in places where there is urine.-- Sea
hogs and sea winds are salt.

We will say that the rains which penetrate the earth are what is
under the foundations of cities with their inhabitants, and are what
restore through the internal passages of the earth the saltness
taken from the sea; and that the change in the place of the sea,
which has been over all the mountains, caused it to be left there in
the mines found in those mountains, &c.

The characteristics of sea water (948. 949).

948.

The waters of the salt sea are fresh at the greatest depths.

949.

THAT THE OCEAN DOES NOT PENETRATE UNDER THE EARTH.

The ocean does not penetrate under the earth, and this we learn from
the many and various springs of fresh water which, in many parts of
the ocean make their way up from the bottom to the surface. The same
thing is farther proved by wells dug beyond the distance of a mile
from the said ocean, which fill with fresh water; and this happens
because the fresh water is lighter than salt water and consequently
more penetrating.

Which weighs most, water when frozen or when not frozen?

FRESH WATER PENETRATES MORE AGAINST SALT WATER THAN SALT WATER
AGAINST FRESH WATER.

That fresh water penetrates more against salt water, than salt water
against fresh is proved by a thin cloth dry and old, hanging with
the two opposite ends equally low in the two different waters, the
surfaces of which are at an equal level; and it will then be seen
how much higher the fresh water will rise in this piece of linen
than the salt; by so much is the fresh lighter than the salt.

On the formation of Gulfs (950. 951).

950.

All inland seas and the gulfs of those seas, are made by rivers
which flow into the sea.

951.

HERE THE REASON IS GIVEN OF THE EFFECTS PRODUCED BY THE WATERS IN
THE ABOVE MENTIONED PLACE.

All the lakes and all the gulfs of the sea and all inland seas are
due to rivers which distribute their waters into them, and from
impediments in their downfall into the Mediterranean --which divides
Africa from Europe and Europe from Asia by means of the Nile and the
Don which pour their waters into it. It is asked what impediment is
great enough to stop the course of the waters which do not reach the
ocean.

On the encroachments of the sea on the land and vice versa
(952-954).

952.

OF WAVES.

A wave of the sea always breaks in front of its base, and that
portion of the crest will then be lowest which before was highest.

[Footnote: The page of FRANCESCO DI GIORGIO'S _Trattato_, on which
Leonardo has written this remark, contains some notes on the
construction of dams, harbours &c.]

953.

That the shores of the sea constantly acquire more soil towards the
middle of the sea; that the rocks and promontories of the sea are
constantly being ruined and worn away; that the Mediterranean seas
will in time discover their bottom to the air, and all that will be
left will be the channel of the greatest river that enters it; and
this will run to the ocean and pour its waters into that with those
of all the rivers that are its tributaries.

954.

How the river Po, in a short time might dry up the Adriatic sea in
the same way as it has dried up a large part of Lombardy.

The ebb and flow of the tide (955-960).

955.

Where there is a larger quantity of water, there is a greater flow
and ebb, but the contrary in narrow waters.

Look whether the sea is at its greatest flow when the moon is half
way over our hemisphere [on the meridian].

956.

Whether the flow and ebb are caused by the moon or the sun, or are
the breathing of this terrestrial machine. That the flow and ebb are
different in different countries and seas.

[Footnote: 1. Allusion may here be made to the mythological
explanation of the ebb and flow given in the Edda. Utgardloki says
to Thor (Gylfaginning 48): "When thou wert drinking out of the horn,
and it seemed to thee that it was slow in emptying a wonder befell,
which I should not have believed possible: the other end of the horn
lay in the sea, which thou sawest not; but when thou shalt go to the
sea, thou shalt see how much thou hast drunk out of it. And that men
now call the ebb tide."

Several passages in various manuscripts treat of the ebb and flow.
In collecting them I have been guided by the rule only to transcribe
those which named some particular spot.]

957.

Book 9 of the meeting of rivers and their flow and ebb. The cause is
the same in the sea, where it is caused by the straits of Gibraltar.
And again it is caused by whirlpools.

958.

OF THE FLOW AND EBB.

All seas have their flow and ebb in the same period, but they seem
to vary because the days do not begin at the same time throughout
the universe; in such wise as that when it is midday in our
hemisphere, it is midnight in the opposite hemisphere; and at the
Eastern boundary of the two hemispheres the night begins which
follows on the day, and at the Western boundary of these hemispheres
begins the day, which follows the night from the opposite side.
Hence it is to be inferred that the above mentioned swelling and
diminution in the height of the seas, although they take place in
one and the same space of time, are seen to vary from the above
mentioned causes. The waters are then withdrawn into the fissures
which start from the depths of the sea and which ramify inside the
body of the earth, corresponding to the sources of rivers, which are
constantly taking from the bottom of the sea the water which has
flowed into it. A sea of water is incessantly being drawn off from
the surface of the sea. And if you should think that the moon,
rising at the Eastern end of the Mediterranean sea must there begin
to attract to herself the waters of the sea, it would follow that we
must at once see the effect of it at the Eastern end of that sea.
Again, as the Mediterranean sea is about the eighth part of the
circumference of the aqueous sphere, being 3000 miles long, while
the flow and ebb only occur 4 times in 24 hours, these results would
not agree with the time of 24 hours, unless this Mediterranean sea
were six thousand miles in length; because if such a superabundance
of water had to pass through the straits of Gibraltar in running
behind the moon, the rush of the water through that strait would be
so great, and would rise to such a height, that beyond the straits
it would for many miles rush so violently into the ocean as to cause
floods and tremendous seething, so that it would be impossible to
pass through. This agitated ocean would afterwards return the waters
it had received with equal fury to the place they had come from, so
that no one ever could pass through those straits. Now experience
shows that at every hour they are passed in safety, but when the
wind sets in the same direction as the current, the strong ebb
increases [Footnote 23: In attempting to get out of the
Mediterranean, vessels are sometimes detained for a considerable
time; not merely by the causes mentioned by Leonardo but by the
constant current flowing eastwards through the middle of the straits
of Gibraltar.]. The sea does not raise the water that has issued
from the straits, but it checks them and this retards the tide; then
it makes up with furious haste for the time it has lost until the
end of the ebb movement.

959.

That the flow and ebb are not general; for on the shore at Genoa
there is none, at Venice two braccia, between England and Flanders
18 braccia. That in the straits of Sicily the current is very strong
because all the waters from the rivers that flow into the Adriatic
pass there.

[Footnote: A few more recent data may be given here to facilitate
comparison. In the Adriatic the tide rises 2 and 1/2 feet, at
Terracina 1 1/4. In the English channel between Calais and Kent it
rises from 18 to 20 feet. In the straits of Messina it rises no more
than 2 1/2 feet, and that only in stormy weather, but the current is
all the stronger. When Leonardo accounts for this by the southward
flow of all the Italian rivers along the coasts, the explanation is
at least based on a correct observation; namely that a steady
current flows southwards along the coast of Calabria and another
northwards, along the shores of Sicily; he seems to infer, from the
direction of the fust, that the tide in the Adriatic is caused by
it.]

960.

In the West, near to Flanders, the sea rises and decreases every 6
hours about 20 braccia, and 22 when the moon is in its favour; but
20 braccia is the general rule, and this rule, as it is evident,
cannot have the moon for its cause. This variation in the increase
and decrease of the sea every 6 hours may arise from the damming up
of the waters, which are poured into the Mediterranean by the
quantity of rivers from Africa, Asia and Europe, which flow into
that sea, and the waters which are given to it by those rivers; it
pours them to the ocean through the straits of Gibraltar, between
Abila and Calpe [Footnote 5: _Abila_, Lat. _Abyla_, Gr. , now
Sierra _Ximiera_ near Ceuta; _Calpe_, Lat. _Calpe_. Gr., now
Gibraltar. Leonardo here uses the ancient names of the rocks, which
were known as the Pillars of Hercules.]. That ocean extends to the
island of England and others farther North, and it becomes dammed up
and kept high in various gulfs. These, being seas of which the
surface is remote from the centre of the earth, have acquired a
weight, which as it is greater than the force of the incoming waters
which cause it, gives this water an impetus in the contrary
direction to that in which it came and it is borne back to meet the
waters coming out of the straits; and this it does most against the
straits of Gibraltar; these, so long as this goes on, remain dammed
up and all the water which is poured out meanwhile by the
aforementioned rivers, is pent up [in the Mediterranean]; and this
might be assigned as the cause of its flow and ebb, as is shown in
the 21st of the 4th of my theory.

III.

SUBTERRANEAN WATER COURSES.

Theory of the circulation of the waters (961. 962).

961.

Very large rivers flow under ground.

962.

This is meant to represent the earth cut through in the middle,
showing the depths of the sea and of the earth; the waters start
from the bottom of the seas, and ramifying through the earth they
rise to the summits of the mountains, flowing back by the rivers and
returning to the sea.

Observations in support of the hypothesis (963-969).

963.

The waters circulate with constant motion from the utmost depths of
the sea to the highest summits of the mountains, not obeying the
nature of heavy matter; and in this case it acts as does the blood
of animals which is always moving from the sea of the heart and
flows to the top of their heads; and here it is that veins burst--as
one may see when a vein bursts in the nose, that all the blood from
below rises to the level of the burst vein. When the water rushes
out of a burst vein in the earth it obeys the nature of other things
heavier than the air, whence it always seeks the lowest places. [7]
These waters traverse the body of the earth with infinite
ramifications.

[Footnote: The greater part of this passage has been given as No.
849 in the section on Anatomy.]

964.

The same cause which stirs the humours in every species of animal
body and by which every injury is repaired, also moves the waters
from the utmost depth of the sea to the greatest heights.

965.

It is the property of water that it constitutes the vital human of
this arid earth; and the cause which moves it through its ramified
veins, against the natural course of heavy matters, is the same
property which moves the humours in every species of animal body.
But that which crowns our wonder in contemplating it is, that it
rises from the utmost depths of the sea to the highest tops of the
mountains, and flowing from the opened veins returns to the low
seas; then once more, and with extreme swiftness, it mounts again
and returns by the same descent, thus rising from the inside to the
outside, and going round from the lowest to the highest, from whence
it rushes down in a natural course. Thus by these two movements
combined in a constant circulation, it travels through the veins of
the earth.

966.

WHETHER WATER RISES FROM THE SEA TO THE TOPS OF MOUNTAINS.

The water of the ocean cannot make its way from the bases to the
tops of the mountains which bound it, but only so much rises as the
dryness of the mountain attracts. And if, on the contrary, the rain,
which penetrates from the summit of the mountain to the base, which
is the boundary of the sea, descends and softens the slope opposite
to the said mountain and constantly draws the water, like a syphon
[Footnote 11: Cicognola, Syphon. See Vol. I, Pl. XXIV, No. 1.] which
pours through its longest side, it must be this which draws up the
water of the sea; thus if _s n_ were the surface of the sea, and the
rain descends from the top of the mountain _a_ to _n_ on one side,
and on the other sides it descends from _a_ to _m_, without a doubt
this would occur after the manner of distilling through felt, or as
happens through the tubes called syphons [Footnote 17: Cicognola,
Syphon. See Vol. I, Pl. XXIV, No. 1.]. And at all times the water
which has softened the mountain, by the great rain which runs down
the two opposite sides, would constantly attract the rain _a n_, on
its longest side together with the water from the sea, if that side
of the mountain _a m_ were longer than the other _a n_; but this
cannot be, because no part of the earth which is not submerged by
the ocean can be lower than that ocean.

967.

OF SPRINGS OF WATER ON THE TOPS OF MOUNTAINS.

It is quite evident that the whole surface of the ocean--when there
is no storm--is at an equal distance from the centre of the earth,
and that the tops of the mountains are farther from this centre in
proportion as they rise above the surface of that sea; therefore if
the body of the earth were not like that of man, it would be
impossible that the waters of the sea--being so much lower than the
mountains--could by their nature rise up to the summits of these
mountains. Hence it is to be believed that the same cause which
keeps the blood at the top of the head in man keeps the water at the
summits of the mountains.

[Footnote: This conception of the rising of the blood, which has
given rise to the comparison, was recognised as erroneous by
Leonardo himself at a later period. It must be remembered that the
MS. A, from which these passages are taken, was written about twenty
years earlier than the MS. Leic. (Nos. 963 and 849) and twenty-five
years before the MS. W. An. IV.

There is, in the original a sketch with No. 968 which is not
reproduced. It represents a hill of the same shape as that shown at
No. 982. There are veins, or branched streams, on the side of the
hill, like those on the skull Pl. CVIII, No. 4]

968.

IN CONFIRMATION OF WHY THE WATER GOES TO THE TOPS OF MOUNTAINS.

I say that just as the natural heat of the blood in the veins keeps
it in the head of man,--for when the man is dead the cold blood
sinks to the lower parts--and when the sun is hot on the head of a
man the blood increases and rises so much, with other humours, that
by pressure in the veins pains in the head are often caused; in the
same way veins ramify through the body of the earth, and by the
natural heat which is distributed throughout the containing body,
the water is raised through the veins to the tops of mountains. And
this water, which passes through a closed conduit inside the body of
the mountain like a dead thing, cannot come forth from its low place
unless it is warmed by the vital heat of the spring time. Again, the
heat of the element of fire and, by day, the heat of the sun, have
power to draw forth the moisture of the low parts of the mountains
and to draw them up, in the same way as it draws the clouds and
collects their moisture from the bed of the sea.

969.

That many springs of salt water are found at great distances from
the sea; this might happen because such springs pass through some
mine of salt, like that in Hungary where salt is hewn out of vast
caverns, just as stone is hewn.

[Footnote: The great mine of Wieliczka in Galicia, out of which a
million cwt. of rock-salt are annually dug out, extends for 3000
metres from West to East, and 1150 metres from North to South.]

IV.

OF RIVERS.

On the way in which the sources of rivers are fed.

970.

OF THE ORIGIN OF RIVERS.

The body of the earth, like the bodies of animals, is intersected
with ramifications of waters which are all in connection and are
constituted to give nutriment and life to the earth and to its
creatures. These come from the depth of the sea and, after many
revolutions, have to return to it by the rivers created by the
bursting of these springs; and if you chose to say that the rains of
the winter or the melting of the snows in summer were the cause of
the birth of rivers, I could mention the rivers which originate in
the torrid countries of Africa, where it never rains--and still less
snows--because the intense heat always melts into air all the clouds
which are borne thither by the winds. And if you chose to say that
such rivers, as increase in July and August, come from the snows
which melt in May and June from the sun's approach to the snows on
the mountains of Scythia [Footnote 9: Scythia means here, as in
Ancient Geography, the whole of the Northern part of Asia as far as
India.], and that such meltings come down into certain valleys and
form lakes, into which they enter by springs and subterranean caves
to issue forth again at the sources of the Nile, this is false;
because Scythia is lower than the sources of the Nile, and, besides,
Scythia is only 400 miles from the Black sea and the sources of the
Nile are 3000 miles distant from the sea of Egypt into which its
waters flow.

The tide in estuaries.

971.

Book 9, of the meeting of rivers and of their ebb and flow. The
cause is the same in the sea, where it is caused by the straits of
Gibraltar; and again it is caused by whirlpools.

[3] If two rivers meet together to form a straight line, and then
below two right angles take their course together, the flow and ebb
will happen now in one river and now in the other above their
confluence, and principally if the outlet for their united volume is
no swifter than when they were separate. Here occur 4 instances.

[Footnote: The first two lines of this passage have already been
given as No. 957. In the margin, near line 3 of this passage, the
text given as No. 919 is written.]

On the alterations, caused in the courses of rivers by their
confluence (972-974).

972.

When a smaller river pours its waters into a larger one, and that
larger one flows from the opposite direction, the course of the
smaller river will bend up against the approach of the larger river;
and this happens because, when the larger river fills up all its bed
with water, it makes an eddy in front of the mouth of the other
river, and so carries the water poured in by the smaller river with
its own. When the smaller river pours its waters into the larger
one, which runs across the current at the mouth of the smaller
river, its waters will bend with the downward movement of the larger
river. [Footnote: In the original sketches the word _Arno_ is
written at the spot here marked _A_, at _R. Rifredi_, and at _M.
Mugnone_.]

973.

When the fulness of rivers is diminished, then the acute angles
formed at the junction of their branches become shorter at the sides
and wider at the point; like the current _a n_ and the current _d
n_, which unite in _n_ when the river is at its greatest fulness. I
say, that when it is in this condition if, before the fullest time,
_d n_ was lower than _a n_, at the time of fulness _d n_ will be
full of sand and mud. When the water _d n_ falls, it will carry away
the mud and remain with a lower bottom, and the channel _a n_
finding itself the higher, will fling its waters into the lower, _d
n_, and will wash away all the point of the sand-spit _b n c_, and
thus the angle _a c d_ will remain larger than the angle _a n d_ and
the sides shorter, as I said before.

[Footnote: Above the first sketch we find, in the original, this
note: "_Sopra il pote rubaconte alla torricella_"; and by the
second, which represents a pier of a bridge, "_Sotto l'ospedal del
ceppo._"]

974.

WATER.

OF THE MOVEMENT OF A SUDDEN RUSH MADE BY A RIVER IN ITS BED
PREVIOUSLY DRY.

In proportion as the current of the water given forth by the
draining of the lake is slow or rapid in the dry river bed, so will
this river be wider or narrower, or shallower or deeper in one place
than another, according to this proposition: the flow and ebb of the
sea which enters the Mediterranean from the ocean, and of the rivers
which meet and struggle with it, will raise their waters more or
less in proportion as the sea is wider or narrower.

[Footnote: In the margin is a sketch of a river which winds so as to
form islands.]

Whirlpools.

975.

Whirlpools, that is to say caverns; that is to say places left by
precipitated waters.

On the alterations in the channels of rivers.

976.

OF THE VIBRATION OF THE EARTH.

The subterranean channels of waters, like those which exist between
the air and the earth, are those which unceasingly wear away and
deepen the beds of their currents.

The origin of the sand in rivers (977. 978).

977.

A river that flows from mountains deposits a great quantity of large
stones in its bed, which still have some of their angles and sides,
and in the course of its flow it carries down smaller stones with
the angles more worn; that is to say the large stones become
smaller. And farther on it deposits coarse gravel and then smaller,
and as it proceeds this becomes coarse sand and then finer, and
going on thus the water, turbid with sand and gravel, joins the sea;
and the sand settles on the sea-shores, being cast up by the salt
waves; and there results the sand of so fine a nature as to seem
almost like water, and it will not stop on the shores of the sea but
returns by reason of its lightness, because it was originally formed
of rotten leaves and other very light things. Still, being
almost--as was said--of the nature of water itself, it afterwards,
when the weather is calm, settles and becomes solid at the bottom of
the sea, where by its fineness it becomes compact and by its
smoothness resists the waves which glide over it; and in this shells
are found; and this is white earth, fit for pottery.

978.

All the torrents of water flowing from the mountains to the sea
carry with them the stones from the hills to the sea, and by the
influx of the sea-water towards the mountains; these stones were
thrown back towards the mountains, and as the waters rose and
retired, the stones were tossed about by it and in rolling, their
angles hit together; then as the parts, which least resisted the
blows, were worn off, the stones ceased to be angular and became
round in form, as may be seen on the banks of the Elsa. And those
remained larger which were less removed from their native spot; and
they became smaller, the farther they were carried from that place,
so that in the process they were converted into small pebbles and
then into sand and at last into mud. After the sea had receded from
the mountains the brine left by the sea with other humours of the
earth made a concretion of these pebbles and this sand, so that the
pebbles were converted into rock and the sand into tufa. And of this
we see an example in the Adda where it issues from the mountains of
Como and in the Ticino, the Adige and the Oglio coming from the
German Alps, and in the Arno at Monte Albano [Footnote 13: At the
foot of _Monte Albano_ lies Vinci, the birth place of Leonardo.
Opposite, on the other bank of the Arno, is _Monte Lupo_.], near
Monte Lupo and Capraia where the rocks, which are very large, are
all of conglomerated pebbles of various kinds and colours.

V.

ON MOUNTAINS.

The formation of mountains (979-983).

979.

Mountains are made by the currents of rivers.

Mountains are destroyed by the currents of rivers.

[Footnote: Compare 789.]

980.

That the Northern bases of some Alps are not yet petrified. And this
is plainly to be seen where the rivers, which cut through them, flow
towards the North; where they cut through the strata in the living
stone in the higher parts of the mountains; and, where they join the
plains, these strata are all of potter's clay; as is to be seen in
the valley of Lamona where the river Lamona, as it issues from the
Appenines, does these things on its banks.

That the rivers have all cut and divided the mountains of the great
Alps one from the other. This is visible in the order of the
stratified rocks, because from the summits of the banks, down to the
river the correspondence of the strata in the rocks is visible on
either side of the river. That the stratified stones of the
mountains are all layers of clay, deposited one above the other by
the various floods of the rivers. That the different size of the
strata is caused by the difference in the floods--that is to say
greater or lesser floods.

981.

The summits of mountains for a long time rise constantly.

The opposite sides of the mountains always approach each other
below; the depths of the valleys which are above the sphere of the
waters are in the course of time constantly getting nearer to the
centre of the world.

In an equal period, the valleys sink much more than the mountains
rise.

The bases of the mountains always come closer together.

In proportion as the valleys become deeper, the more quickly are
their sides worn away.

982.

In every concavity at the summit of the mountains we shall always
find the divisions of the strata in the rocks.

983.

OF THE SEA WHICH ENCIRCLES THE EARTH.

I find that of old, the state of the earth was that its plains were
all covered up and hidden by salt water. [Footnote: This passage has
already been published by Dr. M. JORDAN: _Das Malerbuch des L. da
Vinci, Leipzig_ 1873, p. 86. However, his reading of the text
differs from mine.]

The authorities for the study of the structure of the earth.

984.

Since things are much more ancient than letters, it is no marvel if,
in our day, no records exist of these seas having covered so many
countries; and if, moreover, some records had existed, war and
conflagrations, the deluge of waters, the changes of languages and
of laws have consumed every thing ancient. But sufficient for us is
the testimony of things created in the salt waters, and found again
in high mountains far from the seas.

VI.

GEOLOGICAL PROBLEMS.

985.

In this work you have first to prove that the shells at a thousand
braccia of elevation were not carried there by the deluge, because
they are seen to be all at one level, and many mountains are seen to
be above that level; and to inquire whether the deluge was caused by
rain or by the swelling of the sea; and then you must show how,
neither by rain nor by swelling of the rivers, nor by the overflow
of this sea, could the shells--being heavy objects--be floated up
the mountains by the sea, nor have carried there by the rivers
against the course of their waters.

Doubts about the deluge.

986.

A DOUBTFUL POINT.

Here a doubt arises, and that is: whether the deluge, which happened
at the time of Noah, was universal or not. And it would seem not,
for the reasons now to be given: We have it in the Bible that this
deluge lasted 40 days and 40 nights of incessant and universal rain,
and that this rain rose to ten cubits above the highest mountains in
the world. And if it had been that the rain was universal, it would
have covered our globe which is spherical in form. And this
spherical surface is equally distant in every part, from the centre
of its sphere; hence the sphere of the waters being under the same
conditions, it is impossible that the water upon it should move,
because water, in itself, does not move unless it falls; therefore
how could the waters of such a deluge depart, if it is proved that
it has no motion? and if it departed how could it move unless it
went upwards? Here, then, natural reasons are wanting; hence to
remove this doubt it is necessary to call in a miracle to aid us, or
else to say that all this water was evaporated by the heat of the
sun.

[Footnote: The passages, here given from the MS. Leic., have
hitherto remained unknown. Some preliminary notes on the subject are
to be found in MS. F 8oa and 8ob; but as compared with the fuller
treatment here given, they are, it seems to me, of secondary
interest. They contain nothing that is not repeated here more
clearly and fully. LIBRI, _Histoire des Sciences mathematiques III_,
pages 218--221, has printed the text of F 80a and 80b, therefore it
seemed desirable to give my reasons for not inserting it in this
work.]

That marine shells could not go up the mountains.

987.

OF THE DELUGE AND OF MARINE SHELLS.

If you were to say that the shells which are to be seen within the
confines of Italy now, in our days, far from the sea and at such
heights, had been brought there by the deluge which left them there,
I should answer that if you believe that this deluge rose 7 cubits
above the highest mountains-- as he who measured it has
written--these shells, which always live near the sea-shore, should
have been left on the mountains; and not such a little way from the
foot of the mountains; nor all at one level, nor in layers upon
layers. And if you were to say that these shells are desirous of
remaining near to the margin of the sea, and that, as it rose in
height, the shells quitted their first home, and followed the
increase of the waters up to their highest level; to this I answer,
that the cockle is an animal of not more rapid movement than the
snail is out of water, or even somewhat slower; because it does not
swim, on the contrary it makes a furrow in the sand by means of its
sides, and in this furrow it will travel each day from 3 to 4
braccia; therefore this creature, with so slow a motion, could not
have travelled from the Adriatic sea as far as Monferrato in
Lombardy [Footnote: _Monferrato di Lombardia_. The range of hills of
Monferrato is in Piedmont, and Casale di Monferrato belonged, in
Leonardo's time, to the Marchese di Mantova.], which is 250 miles
distance, in 40 days; which he has said who took account of the
time. And if you say that the waves carried them there, by their
gravity they could not move, excepting at the bottom. And if you
will not grant me this, confess at least that they would have to
stay at the summits of the highest mountains, in the lakes which are
enclosed among the mountains, like the lakes of Lario, or of Como
and il Maggiore [Footnote: _Lago di Lario._ Lacus Larius was the
name given by the Romans to the lake of Como. It is evident that it
is here a slip of the pen since the the words in the MS. are: _"Come
Lago di Lario o'l Magare e di Como,"_ In the MS. after line 16 we
come upon a digression treating of the weight of water; this has
here been omitted. It is 11 lines long.] and of Fiesole, and of
Perugia, and others.

And if you should say that the shells were carried by the waves,
being empty and dead, I say that where the dead went they were not
far removed from the living; for in these mountains living ones are
found, which are recognisable by the shells being in pairs; and they
are in a layer where there are no dead ones; and a little higher up
they are found, where they were thrown by the waves, all the dead
ones with their shells separated, near to where the rivers fell into
the sea, to a great depth; like the Arno which fell from the
Gonfolina near to Monte Lupo [Footnote: _Monte Lupo_, compare 970,
13; it is between Empoli and Florence.], where it left a deposit of
gravel which may still be seen, and which has agglomerated; and of
stones of various districts, natures, and colours and hardness,
making one single conglomerate. And a little beyond the sandstone
conglomerate a tufa has been formed, where it turned towards Castel
Florentino; farther on, the mud was deposited in which the shells
lived, and which rose in layers according to the levels at which the
turbid Arno flowed into that sea. And from time to time the bottom
of the sea was raised, depositing these shells in layers, as may be
seen in the cutting at Colle Gonzoli, laid open by the Arno which is
wearing away the base of it; in which cutting the said layers of
shells are very plainly to be seen in clay of a bluish colour, and
various marine objects are found there. And if the earth of our
hemisphere is indeed raised by so much higher than it used to be, it
must have become by so much lighter by the waters which it lost
through the rift between Gibraltar and Ceuta; and all the more the
higher it rose, because the weight of the waters which were thus
lost would be added to the earth in the other hemisphere. And if the
shells had been carried by the muddy deluge they would have been
mixed up, and separated from each other amidst the mud, and not in
regular steps and layers-- as we see them now in our time.

The marine shells were not produced away from the sea.

988.

As to those who say that shells existed for a long time and were
born at a distance from the sea, from the nature of the place and of
the cycles, which can influence a place to produce such
creatures--to them it may be answered: such an influence could not
place the animals all on one line, except those of the same sort and
age; and not the old with the young, nor some with an operculum and
others without their operculum, nor some broken and others whole,
nor some filled with sea-sand and large and small fragments of other
shells inside the whole shells which remained open; nor the claws of
crabs without the rest of their bodies; nor the shells of other
species stuck on to them like animals which have moved about on
them; since the traces of their track still remain, on the outside,
after the manner of worms in the wood which they ate into. Nor would
there be found among them the bones and teeth of fish which some
call arrows and others serpents' tongues, nor would so many
[Footnote: I. Scilla argued against this hypothesis, which was still
accepted in his days; see: _La vana Speculazione, Napoli_ 1670.]
portions of various animals be found all together if they had not
been thrown on the sea shore. And the deluge cannot have carried
them there, because things that are heavier than water do not float
on the water. But these things could not be at so great a height if
they had not been carried there by the water, such a thing being
impossible from their weight. In places where the valleys have not
been filled with salt sea water shells are never to be seen; as is
plainly visible in the great valley of the Arno above Gonfolina; a
rock formerly united to Monte Albano, in the form of a very high
bank which kept the river pent up, in such a way that before it
could flow into the sea, which was afterwards at its foot, it formed
two great lakes; of which the first was where we now see the city of
Florence together with Prato and Pistoia, and Monte Albano. It
followed the rest of its bank as far as where Serravalle now stands.
>From the Val d'Arno upwards, as far as Arezzo, another lake was
formed, which discharged its waters into the former lake. It was
closed at about the spot where now we see Girone, and occupied the
whole of that valley above for a distance of 40 miles in length.
This valley received on its bottom all the soil brought down by the
turbid waters. And this is still to be seen at the foot of Prato
Magno; it there lies very high where the rivers have not worn it
away. Across this land are to be seen the deep cuts of the rivers
that have passed there, falling from the great mountain of Prato
Magno; in these cuts there are no vestiges of any shells or of
marine soil. This lake was joined with that of Perugia [Footnote:
See PI. CXIII.]

A great quantity of shells are to be seen where the rivers flow into
the sea, because on such shores the waters are not so salt owing to
the admixture of the fresh water, which is poured into it. Evidence
of this is to be seen where, of old, the Appenines poured their
rivers into the Adriatic sea; for there in most places great
quantities of shells are to be found, among the mountains, together
with bluish marine clay; and all the rocks which are torn off in
such places are full of shells. The same may be observed to have
been done by the Arno when it fell from the rock of Gonfolina into
the sea, which was not so very far below; for at that time it was
higher than the top of San Miniato al Tedesco, since at the highest
summit of this the shores may be seen full of shells and oysters
within its flanks. The shells did not extend towards Val di Nievole,
because the fresh waters of the Arno did not extend so far.

That the shells were not carried away from the sea by the deluge,
because the waters which came from the earth although they drew the
sea towards the earth, were those which struck its depths; because
the water which goes down from the earth, has a stronger current
than that of the sea, and in consequence is more powerful, and it
enters beneath the sea water and stirs the depths and carries with
it all sorts of movable objects which are to be found in the earth,
such as the above-mentioned shells and other similar things. And in
proportion as the water which comes from the land is muddier than
sea water it is stronger and heavier than this; therefore I see no
way of getting the said shells so far in land, unless they had been
born there. If you were to tell me that the river Loire [Footnote:
Leonardo has written Era instead of Loera or Loira--perhaps under
the mistaken idea that _Lo_ was an article.],which traverses France
covers when the sea rises more than eighty miles of country, because
it is a district of vast plains, and the sea rises about 20 braccia,
and shells are found in this plain at the distance of 80 miles from
the sea; here I answer that the flow and ebb in our Mediterranean
Sea does not vary so much; for at Genoa it does not rise at all, and
at Venice but little, and very little in Africa; and where it varies
little it covers but little of the country.

The course of the water of a river always rises higher in a place
where the current is impeded; it behaves as it does where it is
reduced in width to pass under the arches of a bridge.

Further researches (989-991).

989.

A CONFUTATION OF THOSE WHO SAY THAT SHELLS MAY HAVE BEEN CARRIED TO
A DISTANCE OF MANY DAYS' JOURNEY FROM THE SEA BY THE DELUGE, WHICH
WAS SO HIGH AS TO BE ABOVE THOSE HEIGHTS.

I say that the deluge could not carry objects, native to the sea, up
to the mountains, unless the sea had already increased so as to
create inundations as high up as those places; and this increase
could not have occurred because it would cause a vacuum; and if you
were to say that the air would rush in there, we have already
concluded that what is heavy cannot remain above what is light,
whence of necessity we must conclude that this deluge was caused by
rain water, so that all these waters ran to the sea, and the sea did
not run up the mountains; and as they ran to the sea, they thrust
the shells from the shore of the sea and did not draw them to wards
themselves. And if you were then to say that the sea, raised by the
rain water, had carried these shells to such a height, we have
already said that things heavier than water cannot rise upon it, but
remain at the bottom of it, and do not move unless by the impact of
the waves. And if you were to say that the waves had carried them to
such high spots, we have proved that the waves in a great depth move
in a contrary direction at the bottom to the motion at the top, and
this is shown by the turbidity of the sea from the earth washed down
near its shores. Anything which is lighter than the water moves with
the waves, and is left on the highest level of the highest margin of
the waves. Anything which is heavier than the water moves, suspended
in it, between the surface and the bottom; and from these two
conclusions, which will be amply proved in their place, we infer
that the waves of the surface cannot convey shells, since they are
heavier than water.

If the deluge had to carry shells three hundred and four hundred
miles from the sea, it would have carried them mixed with various
other natural objects heaped together; and we see at such distances
oysters all together, and sea-snails, and cuttlefish, and all the
other shells which congregate together, all to be found together and
dead; and the solitary shells are found wide apart from each other,
as we may see them on sea-shores every day. And if we find oysters
of very large shells joined together and among them very many which
still have the covering attached, indicating that they were left
here by the sea, and still living when the strait of Gibraltar was
cut through; there are to be seen, in the mountains of Parma and
Piacenza, a multitude of shells and corals, full of holes, and still
sticking to the rocks there. When I was making the great horse for
Milan, a large sack full was brought to me in my workshop by certain
peasants; these were found in that place and among them were many
preserved in their first freshness.

Under ground, and under the foundations of buildings, timbers are
found of wrought beams and already black. Such were found in my time
in those diggings at Castel Fiorentino. And these had been in that
deep place before the sand carried by the Arno into the sea, then
covering the plain, had heen raised to such a height; and before the
plains of Casentino had been so much lowered, by the earth being
constantly carried down from them.

[Footnote: These lines are written in the margin.]

And if you were to say that these shells were created, and were
continually being created in such places by the nature of the spot,
and of the heavens which might have some influence there, such an
opinion cannot exist in a brain of much reason; because here are the
years of their growth, numbered on their shells, and there are large
and small ones to be seen which could not have grown without food,
and could not have fed without motion--and here they could not move
[Footnote: These lines are written in the margin.]

990.

That in the drifts, among one and another, there are still to be
found the traces of the worms which crawled upon them when they were
not yet dry. And all marine clays still contain shells, and the
shells are petrified together with the clay. From their firmness and
unity some persons will have it that these animals were carried up
to places remote from the sea by the deluge. Another sect of
ignorant persons declare that Nature or Heaven created them in these
places by celestial influences, as if in these places we did not
also find the bones of fishes which have taken a long time to grow;
and as if, we could not count, in the shells of cockles and snails,
the years and months of their life, as we do in the horns of bulls
and oxen, and in the branches of plants that have never been cut in
any part. Besides, having proved by these signs the length of their
lives, it is evident, and it must be admitted, that these animals
could not live without moving to fetch their food; and we find in
them no instrument for penetrating the earth or the rock where we
find them enclosed. But how could we find in a large snail shell the
fragments and portions of many other sorts of shells, of various
sorts, if they had not been thrown there, when dead, by the waves of
the sea like the other light objects which it throws on the earth?
Why do we find so many fragments and whole shells between layer and
layer of stone, if this had not formerly been covered on the shore
by a layer of earth thrown up by the sea, and which was afterwards
petrified? And if the deluge before mentioned had carried them to
these parts of the sea, you might find these shells at the boundary
of one drift but not at the boundary between many drifts. We must
also account for the winters of the years during which the sea
multiplied the drifts of sand and mud brought down by the
neighbouring rivers, by washing down the shores; and if you chose to
say that there were several deluges to produce these rifts and the
shells among them, you would also have to affirm that such a deluge
took place every year. Again, among the fragments of these shells,
it must be presumed that in those places there were sea coasts,
where all the shells were thrown up, broken, and divided, and never
in pairs, since they are found alive in the sea, with two valves,
each serving as a lid to the other; and in the drifts of rivers and
on the shores of the sea they are found in fragments. And within the
limits of the separate strata of rocks they are found, few in number
and in pairs like those which were left by the sea, buried alive in
the mud, which subsequently dried up and, in time, was petrified.

991.

And if you choose to say that it was the deluge which carried these
shells away from the sea for hundreds of miles, this cannot have
happened, since that deluge was caused by rain; because rain
naturally forces the rivers to rush towards the sea with all the
things they carry with them, and not to bear the dead things of the
sea shores to the mountains. And if you choose to say that the
deluge afterwards rose with its waters above the mountains, the
movement of the sea must have been so sluggish in its rise against
the currents of the rivers, that it could not have carried, floating
upon it, things heavier than itself; and even if it had supported
them, in its receding it would have left them strewn about, in
various spots. But how are we to account for the corals which are
found every day towards Monte Ferrato in Lombardy, with the holes of
the worms in them, sticking to rocks left uncovered by the currents
of rivers? These rocks are all covered with stocks and families of
oysters, which as we know, never move, but always remain with one of
their halves stuck to a rock, and the other they open to feed
themselves on the animalcules that swim in the water, which, hoping
to find good feeding ground, become the food of these shells. We do
not find that the sand mixed with seaweed has been petrified,
because the weed which was mingled with it has shrunk away, and this
the Po shows us every day in the debris of its banks.

Other problems (992-994).

992.

Why do we find the bones of great fishes and oysters and corals and
various other shells and sea-snails on the high summits of mountains
by the sea, just as we find them in low seas?

993.

You now have to prove that the shells cannot have originated if not
in salt water, almost all being of that sort; and that the shells in
Lombardy are at four levels, and thus it is everywhere, having been
made at various times. And they all occur in valleys that open
towards the seas.

994.

>From the two lines of shells we are forced to say that the earth
indignantly submerged under the sea and so the first layer was made;
and then the deluge made the second.

[Footnote: This note is in the early writing of about 1470--1480. On
the same sheet are the passages No. 1217 and 1219. Compare also No.
1339. All the foregoing chapters are from Manuscripts of about 1510.
This explains the want of connection and the contradiction between
this and the foregoing texts.]

VII.

ON THE ATMOSPHERE.

Constituents of the atmosphere.

995.

That the brightness of the air is occasioned by the water which has
dissolved itself in it into imperceptible molecules. These, being
lighted by the sun from the opposite side, reflect the brightness
which is visible in the air; and the azure which is seen in it is
caused by the darkness that is hidden beyond the air. [Footnote:
Compare Vol. I, No. 300.]

On the motion of air (996--999).

996.

That the return eddies of wind at the mouth of certain valleys
strike upon the waters and scoop them out in a great hollow, whirl
the water into the air in the form of a column, and of the colour of
a cloud. And I saw this thing happen on a sand bank in the Arno,
where the sand was hollowed out to a greater depth than the stature
of a man; and with it the gravel was whirled round and flung about
for a great space; it appeared in the air in the form of a great
bell-tower; and the top spread like the branches of a pine tree, and
then it bent at the contact of the direct wind, which passed over
from the mountains.

997.

The element of fire acts upon a wave of air in the same way as the
air does on water, or as water does on a mass of sand --that is
earth; and their motions are in the same proportions as those of the
motors acting upon them.

998.

OF MOTION.

I ask whether the true motion of the clouds can be known by the
motion of their shadows; and in like manner of the motion of the
sun.

999.

To know better the direction of the winds. [Footnote: In connection
with this text I may here mention a hygrometer, drawn and probably
invented by Leonardo. A facsimile of this is given in Vol. I, p. 297
with the note: _'Modi di pesare l'arie eddi sapere quando s'a
arrompere il tepo'_ (Mode of weighing the air and of knowing when
the weather will change); by the sponge _"Spugnea"_ is written.]

The globe an organism.

1000.

Nothing originates in a spot where there is no sentient, vegetable
and rational life; feathers grow upon birds and are changed every
year; hairs grow upon animals and are changed every year, excepting
some parts, like the hairs of the beard in lions, cats and their
like. The grass grows in the fields, and the leaves on the trees,
and every year they are, in great part, renewed. So that we might
say that the earth has a spirit of growth; that its flesh is the
soil, its bones the arrangement and connection of the rocks of which
the mountains are composed, its cartilage the tufa, and its blood
the springs of water. The pool of blood which lies round the heart
is the ocean, and its breathing, and the increase and decrease of
the blood in the pulses, is represented in the earth by the flow and
ebb of the sea; and the heat of the spirit of the world is the fire
which pervades the earth, and the seat of the vegetative soul is in
the fires, which in many parts of the earth find vent in baths and
mines of sulphur, and in volcanoes, as at Mount Aetna in Sicily, and
in many other places.

[Footnote: Compare No. 929.]

_XVII._

_Topographical Notes._

_A large part of the texts published in this section might perhaps
have found their proper place in connection with the foregoing
chapters on Physical Geography. But these observations on Physical
Geography, of whatever kind they may be, as soon as they are
localised acquire a special interest and importance and particularly
as bearing on the question whether Leonardo himself made the
observations recorded at the places mentioned or merely noted the
statements from hearsay. In a few instances he himself tells us that
he writes at second hand. In some cases again, although the style
and expressions used make it seem highly probable that he has
derived his information from others-- though, as it seems to me,
these cases are not very numerous--we find, on the other hand, among
these topographical notes a great number of observations, about
which it is extremely difficult to form a decided opinion. Of what
the Master's life and travels may have been throughout his
sixty-seven years of life we know comparatively little; for a long
course of time, and particularly from about 1482 to 1486, we do not
even know with certainty that he was living in Italy. Thus, from a
biographical point of view a very great interest attaches to some of
the topographical notes, and for this reason it seemed that it would
add to their value to arrange them in a group by themselves.
Leonardo's intimate knowledge with places, some of which were
certainly remote from his native home, are of importance as
contributing to decide the still open question as to the extent of
Leonardo's travels. We shall find in these notes a confirmation of
the view, that the MSS. in which the Topographical Notes occur are
in only a very few instances such diaries as may have been in use
during a journey. These notes are mostly found in the MSS. books of
his later and quieter years, and it is certainly remarkable that
Leonardo is very reticent as to the authorities from whom he quotes
his facts and observations: For instance, as to the Straits of
Gibraltar, the Nile, the Taurus Mountains and the Tigris and
Euphrates. Is it likely that he, who declared that in all scientific
research, his own experience should be the foundation of his
statements (see XIX Philosophy No. 987--991,) should here have made
an exception to this rule without mentioning it?_

_As for instance in the discussion as to the equilibrium of the mass
of water in the Mediterranean Sea--a subject which, it may be
observed, had at that time attracted the interest and study of
hardly any other observer. The acute remarks, in Nos. 985--993, on
the presence of shells at the tops of mountains, suffice to
prove--as it seems to me--that it was not in his nature to allow
himself to be betrayed into wide generalisations, extending beyond
the limits of his own investigations, even by such brilliant results
of personal study._

_Most of these Topographical Notes, though suggesting very careful
and thorough research, do not however, as has been said, afford
necessarily indisputable evidence that that research was Leonardo's
own. But it must be granted that in more than one instance
probability is in favour of this idea._

_Among the passages which treat somewhat fully of the topography of
Eastern places by far the most interesting is a description of the
Taurus Mountains; but as this text is written in the style of a
formal report and, in the original, is associated with certain
letters which give us the history of its origin, I have thought it
best not to sever it from that connection. It will be found under
No. XXI (Letters)._

_That Florence, and its neighbourhood, where Leonardo spent his
early years, should be nowhere mentioned except in connection with
the projects for canals, which occupied his attention for some short
time during the first ten years of the XVIth century, need not
surprise us. The various passages relating to the construction of
canals in Tuscany, which are put together at the beginning, are
immediately followed by those which deal with schemes for canals in
Lombardy; and after these come notes on the city and vicinity of
Milan as well as on the lakes of North Italy._

_The notes on some towns of Central Italy which Leonardo visited in
1502, when in the service of Cesare Borgia, are reproduced here in
the same order as in the note book used during these travels (MS.
L., Institut de France). These notes have but little interest in
themselves excepting as suggesting his itinerary. The maps of the
districts drawn by Leonardo at the time are more valuable (see No.
1054 note). The names on these maps are not written from right to
left, but in the usual manner, and we are permitted to infer that
they were made in obedience to some command, possibly for the use of
Cesare Borgia himself; the fact that they remained nevertheless in
Leonardo's hands is not surprising when we remember the sudden
political changes and warlike events of the period. There can be no
doubt that these maps, which are here published for the first time,
are original in the strictest sense of the word, that is to say
drawn from observations of the places themselves; this is proved by
the fact--among others--that we find among his manuscripts not only
the finished maps themselves but the rough sketches and studies for
them. And it would perhaps be difficult to point out among the
abundant contributions to geographical knowledge published during
the XVIth century, any maps at all approaching these in accuracy and
finish._

_The interesting map of the world, so far as it was then known,
which is among the Leonardo MSS. at Windsor (published in the_
'Archaeologia' _Vol. XI) cannot be attributed to the Master, as the
Marchese Girolamo d'Adda has sufficiently proved; it has not
therefore been reproduced here._

_Such of Leonardo's observations on places in Italy as were made
before or after his official travels as military engineer to Cesare
Borgia, have been arranged in alphabetical order, under Nos.
1034-1054. The most interesting are those which relate to the Alps
and the Appenines, Nos. 1057-1068._

_Most of the passages in which France is mentioned have hitherto
remained unknown, as well as those which treat of the countries
bordering on the Mediterranean, which come at the end of this
section. Though these may be regarded as of a more questionable
importance in their bearing on the biography of the Master than
those which mention places in France, it must be allowed that they
are interesting as showing the prominent place which the countries
of the East held in his geographical studies. He never once alludes
to the discovery of America._

I.

ITALY.

Canals in connection with the Arno (1001-1008).

1001.

CANAL OF FLORENCE.

Sluices should be made in the valley of la Chiana at Arezzo, so that
when, in the summer, the Arno lacks water, the canal may not remain
dry: and let this canal be 20 braccia wide at the bottom, and at the
top 30, and 2 braccia deep, or 4, so that two of these braccia may
flow to the mills and the meadows, which will benefit the country;
and Prato, Pistoia and Pisa, as well as Florence, will gain two
hundred thousand ducats a year, and will lend a hand and money to
this useful work; and the Lucchese the same, for the lake of Sesto
will be navigable; I shall direct it to Prato and Pistoia, and cut
through Serravalle and make an issue into the lake; for there will
be no need of locks or supports, which are not lasting and so will
always be giving trouble in working at them and keeping them up.

And know that in digging this canal where it is 4 braccia deep, it
will cost 4 dinari the square braccio; for twice the depth 6 dinari,
if you are making 4 braccia [Footnote: This passage is illustrated
by a slightly sketched map, on which these places are indicated from
West to East: Pisa, Luccha, Lago, Seravalle, Pistoja, Prato,
Firenze.] and there are but 2 banks; that is to say one from the
bottom of the trench to the surface of the edges of it, and the
other from these edges to the top of the ridge of earth which will
be raised on the margin of the bank. And if this bank were of double
the depth only the first bank will be increased, that is 4 braccia
increased by half the first cost; that is to say that if at first 4
dinari were paid for 2 banks, for 3 it would come to 6, at 2 dinari
the bank, if the trench measured 16 braccia at the bottom; again, if
the trench were 16 braccia wide and 4 deep, coming to 4 lire for the
work, 4 Milan dinari the square braccio; a trench which was 32
braccia at the bottom would come to 8 dinari the square braccio.

1002.

>From the wall of the Arno at [the gate of] la Giustizia to the bank
of the Arno at Sardigna where the walls are, to the mills, is 7400
braccia, that is 2 miles and 1400 braccia and beyond the Arno is
5500 braccia.

[Footnote: 2. _Giustizia_. By this the Porta della Giustizia seems
to be meant; from the XVth to the XVIth centuries it was also
commonly known as Porta Guelfa, Porta San Francesco del Renaio,
Porta Nuova, and Porta Reale. It was close to the Arno opposite to
the Porta San Niccolo, which still exists.]

1003.

By guiding the Arno above and below a treasure will be found in each
acre of ground by whomsoever will.

1004.

The wall of the old houses runs towards the gate of San Nicolo.

[Footnote: By the side of this text there is an indistinct sketch,
resembling that given under No.973. On the bank is written the word
_Casace_. There then follows in the original a passage of 12 lines
in which the consequences of the windings of the river are
discussed. A larger but equally hasty diagram on the same page
represents the shores of the Arno inside Florence as in two parallel
lines. Four horizontal lines indicate the bridges. By the side these
measures are stated in figures: I. (at the Ponte alla Carraja):
_230--largho br. 12 e 2 di spoda e 14 di pile e a 4 pilastri;_ 2.
(at the Ponte S. Trinita); _l88--largho br. 15 e 2 di spode he 28
di pilastri for delle spode e pilastri so 2;_ 3. (at the Ponte
vecchio); _pote lung br. 152 e largo;_ 4. (at the Ponte alle
Grazie): _290 ellargo 12 e 2 di spode e 6 di pili._

There is, in MS. W. L. 2l2b, a sketched plan of Florence, with the
following names of gates:
_Nicholo--Saminiato--Giorgo--Ghanolini--Porta San Fredian
--Prato--Faenza--Ghallo--Pinti--Giustitia_.]

1005.

The ruined wall is 640 braccia; 130 is the wall remaining with the
mill; 300 braccia were broken in 4 years by Bisarno.

1006.

They do not know why the Arno will never remain in a channel. It is
because the rivers which flow into it deposit earth where they
enter, and wear it away on the opposite side, bending the river in
that direction. The Arno flows for 6 miles between la Caprona and
Leghorn; and for 12 through the marshes, which extend 32 miles, and
16 from La Caprona up the river, which makes 48; by the Arno from
Florence beyond 16 miles; to Vico 16 miles, and the canal is 5; from
Florence to Fucechio it is 40 miles by the river Arno.

56 miles by the Arno from Florence to Vico; by the Pistoia canal it
is 44 miles. Thus it is 12 miles shorter by the canal than by the
Arno.

[Footnote: This passage is written by the side of a map washed in
Indian ink, of the course of the Arno; it is evidently a sketch for
a completer map.

These investigations may possibly be connected with the following
documents. _Francesco Guiducci alla Balia di Firenze. Dal Campo
contro Pisa_ 24 _Luglio_ 1503 (_Archivio di Stato, Firenze, Lettere
alla Balia_; published by J. GAYE, _Carteggio inedito d'Artisti,
Firenze_ 1840, _Tom. II_, p. 62): _Ex Castris, Franciscus
Ghuiduccius,_ 24. _Jul._ 1503. _Appresso fu qui hieri con una di V.
Signoria Alexandro degli Albizi insieme con Leonardo da Vinci et
certi altri, et veduto el disegno insieme con el ghovernatore, doppo
molte discussioni et dubii conclusesi che l'opera fussi molto al
proposito, o si veramente Arno volgersi qui, o restarvi con un
canale, che almeno vieterebbe che le colline da nemici non
potrebbono essere offese; come tucto referiranno loro a bocha V. S._

And, _Archivio di Stato, Firenze, Libro d'Entrata e Uscita di cassa
de' Magnifici Signori di luglio e agosto_

1503 _a_ 51 _T.: Andata di Leonardo al Campo sotto Pisa. Spese
extraordinarie dieno dare a di XXVI di luglio L. LVI sol. XII per
loro a Giovanni Piffero; e sono per tanti, asegnia avere spexi in
vetture di sei chavalli a spese di vitto per andare chon Lionardo da
Vinci a livellare Arno in quello di Pisa per levallo del lilo suo._
(Published by MILANESI, _Archivio Storico Italiano, Serie III, Tom.
XVI._} VASARI asserts: _(Leonardo) fu il primo ancora, che
giovanetto discorresse sopra il fiume d'Arno per metterlo in canale
da Pisa a Fiorenza_ (ed. SANSONI, IV, 20).

The passage above is in some degree illustrated by the map on Pl.
CXII, where the course of the Arno westward from Empoli is shown.]

1007.

The eddy made by the Mensola, when the Arno is low and the Mensola
full.

[Footnote: _Mensola_ is a mountain stream which falls into the Arno
about a mile and a half above Florence.

A=Arno, I=Isola, M=Mvgone, P=Pesa, N=Mesola.]

1008.

That the river which is to be turned from one place to another must
be coaxed and not treated roughly or with violence; and to do this a
sort of floodgate should be made in the river, and then lower down
one in front of it and in like manner a third, fourth and fifth, so
that the river may discharge itself into the channel given to it, or
that by this means it may be diverted from the place it has damaged,
as was done in Flanders--as I was told by Niccolo di Forsore.

How to protect and repair the banks washed by the water, as below
the island of Cocomeri.

Ponte Rubaconte (Fig. 1); below [the palaces] Bisticci and Canigiani
(Fig. 2). Above the flood gate of la Giustizia (Fig. 3); _a b_ is a
sand bank opposite the end of the island of the Cocomeri in the
middle of the Arno (Fig. 4). [Footnote: The course of the river Arno
is also discussed in Nos. 987 and 988.]

Canals in the Milanese (1009-1013).

1009.

The canal of San Cristofano at Milan made May 3rd 1509. [Footnote:
This observation is written above a washed pen and ink drawing which
has been published as Tav. VI in the _,,Saggio."_ The editors of
that work explain the drawing as _"uno Studio di bocche per
estrazione d'acqua."_]

1010.

OF THE CANAL OF MARTESANA.

By making the canal of Martesana the water of the Adda is greatly
diminished by its distribution over many districts for the
irrigation of the fields. A remedy for this would be to make several
little channels, since the water drunk up by the earth is of no more
use to any one, nor mischief neither, because it is taken from no
one; and by making these channels the water which before was lost
returns again and is once more serviceable and useful to men.

[Footnote: _"el navilio di Martagano"_ is also mentioned in a note
written in red chalk, MS. H2 17a Leonardo has, as it seems, little
to do with Lodovico il Moro's scheme to render this canal navigable.
The canal had been made in 1460 by Bertonino da Novara. Il Moro
issued his degree in 1493, but Leonardo's notes about this canal
were, with the exception of one (No. 1343), written about sixteen
years later.]

1011.

No canal which is fed by a river can be permanent if the river
whence it originates is not wholly closed up, like the canal of
Martesana which is fed by the Ticino.

1012.

>From the beginning of the canal to the mill.

>From the beginning of the canal of Brivio to the mill of Travaglia
is 2794 trabochi, that is 11176 braccia, which is more than 3 miles
and two thirds; and here the canal is 57 braccia higher than the
surface of the water of the Adda, giving a fall of two inches in
every hundred trabochi; and at that spot we propose to take the
opening of our canal.

[Footnote: The following are written on the sketches: At the place
marked _N: navilio da dacquiue_ (canal of running water); at _M:
molin del Travaglia_ (Mill of Travaglia); at _R: rochetta ssanta
maria_ (small rock of Santa Maria); at _A: Adda;_ at _L: Lagho di
Lecho ringorgato alli 3 corni in Adda,--Concha perpetua_ (lake of
Lecco overflowing at Tre Corni, in Adda,-- a permanent sluice). Near
the second sketch, referring to the sluice near _Q: qui la chatena
ttalie d'u peso_ (here the chain is in one piece). At _M_ in the
lower sketch: _mol del travaglia, nel cavare la concha il tereno
ara chotrapero co cassa d'acqua._ (Mill of Travaglia, in digging
out the sluice the soil will have as a counterpoise a vessel of
water).]

1013.

If it be not reported there that this is to be a public canal, it
will be necessary to pay for the land; [Footnote 3: _il re_. Louis
XII or Francis I of France. It is hardly possible to doubt that the
canals here spoken of were intended to be in the Milanese. Compare
with this passage the rough copy of a letter by Leonardo, to the
_"Presidente dell' Ufficio regolatore dell' acqua"_ on No. 1350. See
also the note to No. 745, 1. 12.] and the king will pay it by
remitting the taxes for a year.

Estimates and preparatory studies for canals (1014. 1015).

1014.

CANAL.

The canal which may be 16 braccia wide at the bottom and 20 at the
top, we may say is on the average 18 braccia wide, and if it is 4
braccia deep, at 4 dinari the square braccia; it will only cost 900
ducats, to excavate by the mile, if the square braccio is calculated
in ordinary braccia; but if the braccia are those used in measuring
land, of which every 4 are equal to 4 1/2 and if by the mile we
understand three thousand ordinary braccia; turned into land
braccia, these 3000 braccia will lack 1/4; there remain 2250
braccia, which at 4 dinari the braccio will amount to 675 ducats a
mile. At 3 dinari the square braccio, the mile will amount to 506
1/4 ducats so that the excavation of 30 miles of the canal will
amount to 15187 1/2 ducats.

1015.

To make the great canal, first make the smaller one and conduct into
it the waters which by a wheel will help to fill the great one.

Notes on buildings in Milan (1016-1019)

1016.

Indicate the centre of Milan.

Moforte--porta resa--porta nova--strada nova--navilio--porta
cumana--barco--porta giovia--porta vercellina--porta sco
Anbrogio--porta Tesinese--torre dell' Imperatore-- porta
Lodovica--acqua.

[Footnote: See Pl. CIX. The original sketch is here reduced to about
half its size. The gates of the town are here named, beginning at
the right hand and following the curved line. In the bird's eye view
of Milan below, the cathedral is plainly recognisable in the middle;
to the right is the tower of San Gottardo. The square, above the
number 9147, is the Lazzaretto, which was begun in 1488. On the left
the group of buildings of the _'Castello'_ will be noticed. On the
sketched Plan of Florence (see No. 1004 note) Leonardo has written
on the margin the following names of gates of Milan: Vercellina
--Ticinese--Ludovica--Romana--Orientale--
Nova--Beatrice--Cumana--Compare too No. 1448, 11. 5, 12.]

1017.

The moat of Milan.

Canal 2 braccia wide.

The castle with the moats full.

The filling of the moats of the Castle of Milan.

1018.

THE BATH.

To heat the water for the stove of the Duchess take four parts of
cold water to three parts of hot water.

[Footnote: _Duchessa di Milano_, Beatrice d'Este, wife of Ludovico
il Moro to whom she was married, in 1491. She died in June 1497.]

1019.

In the Cathedral at the pulley of the nail of the cross.

Item.

To place the mass _v r_ in the...

[Footnote: On this passage AMORETTI remarks _(Memorie Storiche_
chap. IX): _Nell'anno stesso lo veggiamo formare un congegno di
carucole e di corde, con cui trasportare in piu venerabile e piu
sicuro luogo, cioe nell'ultima arcata della nave di mezzo della
metropolitana, la sacra reliquia del Santo Chiodo, che ivi ancor si
venera. Al fol. 15 del codice segnato Q. R. in 16, egli ci ha
lasciata di tal congegno una doppia figura, cioe una di quattro
carucole, e una di tre colle rispettive corde, soggiugnandovi: in
Domo alla carucola del Chiodo della Croce._

AMORETTI'S views as to the mark on the MS, and the date when it was
written are, it may be observed, wholly unfounded. The MS. L, in
which it occurs, is of the year 1502, and it is very unlikely that
Leonardo was in Milan at that time; this however would not prevent
the remark, which is somewhat obscure, from applying to the
Cathedral at Milan.]

1020.

OF THE FORCE OF THE VACUUM FORMED IN A MOMENT.

I saw, at Milan, a thunderbolt fall on the tower della Credenza on
its Northern side, and it descended with a slow motion down that
side, and then at once parted from that tower and carried with it
and tore away from that wall a space of 3 braccia wide and two deep;
and this wall was 4 braccia thick and was built of thin and small
old bricks; and this was dragged out by the vacuum which the flame
of the thunderbolt had caused, &c.

[Footnote: With reference to buildings at Milan see also Nos. 751
and 756, and Pl. XCV, No. 2 (explained on p. 52), Pl. C (explained
on pages 60-62). See also pages 25, 39 and 40.]

Remarks on natural phenomena in and near Milan (1021. 1022).

1021.

I have already been to see a great variety (of atmospheric effects).
And lately over Milan towards Lago Maggiore I saw a cloud in the
form of an immense mountain full of rifts of glowing light, because
the rays of the sun, which was already close to the horizon and red,
tinged the cloud with its own hue. And this cloud attracted to it
all the little clouds that were near while the large one did not
move from its place; thus it retained on its summit the reflection
of the sunlight till an hour and a half after sunset, so immensely
large was it; and about two hours after sunset such a violent wind
arose, that it was really tremendous and unheard of.

[Footnote: _di arie_ is wanting in the original but may safely be
inserted in the context, as the formation of clouds is under
discussion before this text.]

1022.

On the 10th day of December at 9 o'clock a. m. fire was set to the
place.

On the l8th day of December 1511 at 9 o'clock a. m. this second fire
was kindled by the Swiss at Milan at the place called DCXC.
[Footnote: With these two texts, (l. 1--2 and l. 3--5 are in the
original side by side) there are sketches of smoke wreaths in red
chalk.]

Note on Pavia.

1023.

The chimneys of the castle of Pavia have 6 rows of openings and from
each to the other is one braccio.

[Footnote: Other notes relating to Pavia occur on p. 43 and p. 53
(Pl. XCVIII, No. 3). Compare No. 1448, 26.]

Notes on the Sforzesca near Vigevano (1024-1028).

1024.

On the 2nd day of February 1494. At Sforzesca I drew twenty five
steps, 2/3 braccia to each, and 8 braccia wide.

[Footnote: See Pl. CX, No. 2. The rest of the notes on this page
refer to the motion of water. On the lower sketch we read: 4 _br._
(four braccia) and _giara_ (for _ghiaja_, sand, gravel).]

1025.

The vineyards of Vigevano on the 20th day of March 1494.

[Footnote: On one side there is an effaced sketch in red chalk.]

1026.

To lock up a butteris at Vigevano.

1027.

Again if the lowest part of the bank which lies across the current
of the waters is made in deep and wide steps, after the manner of
stairs, the waters which, in their course usually fall
perpendicularly from the top of such a place to the bottom, and wear
away the foundations of this bank can no longer descend with a blow
of too great a force; and I find the example of this in the stairs
down which the water falls in the fields at Sforzesca at Vigevano
over which the running water falls for a height of 50 braccia.

1028.

Stair of Vigevano below La Sforzesca, 130 steps, 1/4 braccio high
and 1/2 braccio wide, down which the water falls, so as not to wear
away anything at the end of its fall; by these steps so much soil
has come down that it has dried up a pool; that is to say it has
filled it up and a pool of great depth has been turned into meadows.

Notes on the North Italian lake. (1029-1033)

1029.

In many places there are streams of water which swell for six hours
and ebb for six hours; and I, for my part, have seen one above the
lake of Como called Fonte Pliniana, which increases and ebbs, as I
have said, in such a way as to turn the stones of two mills; and
when it fails it falls so low that it is like looking at water in a
deep pit.

[Footnote: The fountain is known by this name to this day: it is
near Torno, on the Eastern shore of Como. The waters still rise and
fall with the flow and ebb of the tide as Pliny described it (Epist.
IV, 30; Hist. Nat. II, 206).]

1030.

LAKE OF COMO. VALLEY OF CHIAVENNA.

Above the lake of Como towards Germany is the valley of Chiavenna
where the river Mera flows into this lake. Here are barren and very
high mountains, with huge rocks. Among these mountains are to be
found the water-birds called gulls. Here grow fir trees, larches and
pines. Deer, wildgoats, chamois, and terrible bears. It is
impossible to climb them without using hands and feet. The peasants
go there at the time of the snows with great snares to make the
bears fall down these rocks. These mountains which very closely
approach each other are parted by the river. They are to the right
and left for the distance of 20 miles throughout of the same nature.
>From mile to mile there are good inns. Above on the said river there
are waterfalls of 400 braccia in height, which are fine to see; and
there is good living at 4 soldi the reckoning. This river brings
down a great deal of timber.

VAL SASINA.

Val Sasina runs down towards Italy; this is almost the same form and
character. There grow here many _mappello_ and there are great ruins
and falls of water [Footnote 14: The meaning of _mappello_ is
unknown.].

VALLEY OF INTROZZO.

This valley produces a great quantity of firs, pines and larches;
and from here Ambrogio Fereri has his timber brought down; at the
head of the Valtellina are the mountains of Bormio, terrible and
always covered with snow; marmots (?) are found there.

BELLAGGIO.

Opposite the castle Bellaggio there is the river Latte, which falls
from a height of more than 100 braccia from the source whence it
springs, perpendicularly, into the lake with an inconceivable roar
and noise. This spring flows only in August and September.

VALTELLINA.

Valtellina, as it is called, is a valley enclosed in high and
terrible mountains; it produces much strong wine, and there is so
much cattle that the natives conclude that more milk than wine grows
there. This is the valley through which the Adda passes, which first
runs more than 40 miles through Germany; this river breeds the fish
_temolo_ which live on silver, of which much is to be found in its
sands. In this country every one can sell bread and wine, and the
wine is worth at most one soldo the bottle and a pound of veal one
soldo, and salt ten dinari and butter the same and their pound is 30
ounces, and eggs are one soldo the lot.

1031.

At BORMIO.

At Bormio are the baths;--About eight miles above Como is the
Pliniana, which increases and ebbs every six hours, and its swell
supplies water for two mills; and its ebbing makes the spring dry
up; two miles higher up there is Nesso, a place where a river falls
with great violence into a vast rift in the mountain. These
excursions are to be made in the month of May. And the largest bare
rocks that are to be found in this part of the country are the
mountains of Mandello near to those of Lecco, and of Gravidona
towards Bellinzona, 30 miles from Lecco, and those of the valley of
Chiavenna; but the greatest of all is that of Mandello, which has at
its base an opening towards the lake, which goes down 200 steps, and
there at all times is ice and wind.

IN VAL SASINA.

In Val Sasina, between Vimognio and Introbbio, to the right hand,
going in by the road to Lecco, is the river Troggia which falls from
a very high rock, and as it falls it goes underground and the river
ends there. 3 miles farther we find the buildings of the mines of
copper and silver near a place called Pra' Santo Pietro, and mines
of iron and curious things. La Grigna is the highest mountain there
is in this part, and it is quite bare.

[Footnote: 1030 and 1031. From the character of the handwriting we
may conclude that these observations were made in Leonardo's youth;
and I should infer from their contents, that they were notes made in
anticipation of a visit to the places here described, and derived
from some person (unknown to us) who had given him an account of
them.]

1032.

The lake of Pusiano flows into the lake of Segrino [Footnote 3: The
statement about the lake Segrino is incorrect; it is situated in the
Valle Assina, above the lake of Pusiano.] and of Annone and of Sala.
The lake of Annone is 22 braccia higher at the surface of its water
than the surface of the water of the lake of Lecco, and the lake of
Pusiano is 20 braccia higher than the lake of Annone, which added to
the afore said 22 braccia make 42 braccia and this is the greatest
height of the surface of the lake of Pusiano above the surface of
the lake of Lecco.

[Footnote: This text has in the original a slight sketch to
illustrate it.]

1033.

At Santa Maria in the Valley of Ravagnate [Footnote 2: _Ravagnate_
(Leonardo writes _Ravagna_) in the Brianza is between Oggiono and
Brivio, South of the lake of Como. M. Ravaisson avails himself of
this note to prove his hypothesis that Leonardo paid two visits to
France. See Gazette des Beaux Arts, 1881 pag. 528:

_Au recto du meme feuillet, on lit encore une note relative a une
vallee "nemonti brigatia"; il me semble qu'il s'agit bien des monts
de Briancon, le Brigantio des anciens. Briancon est sur la route de
Lyon en Italie. Ce fut par le mont Viso que passerent, en aout 1515,
les troupes francaises qui allaient remporter la victoire de
Marignan.

Leonard de Vinci, ingenieur de Francois Ier, comme il l'avait ete de
Louis XII, aurait-il ete pour quelque chose dans le plan du celebre
passage des Alpes, qui eut lieu en aout 1515, et a la suite duquel
on le vit accompagner partout le chevaleresque vainqueur? Auraitil
ete appele par le jeune roi, de Rome ou l'artiste etait alors, des
son avenement au trone?_] in the mountains of Brianza are the rods
of chestnuts of 9 braccia and one out of an average of 100 will be
14 braccia.

At Varallo di Ponbia near to Sesto on the Ticino the quinces are
white, large and hard.

[Footnote 5: Varallo di Ponbia, about ten miles South of Arona is
distinct from Varallo the chief town in the Val di Sesia.]

Notes on places in Central Italy, visited in 1502 (1034-1054).

1034.

Pigeon-house at Urbino, the 30th day of July 1502. [Footnote: An
indistinct sketch is introduced with this text, in the original, in
which the word _Scolatoro_ (conduit) is written.]

1035.

Made by the sea at Piombino. [Footnote: Below the sketch there are
eleven lines of text referring to the motion of waves.]

1036.

Acquapendente is near Orvieto. [Footnote: _Acquapendente_ is about
10 miles West of Orvieto, and is to the right in the map on Pl.
CXIII, near the lake of Bolsena.]

1037.

The rock of Cesena. [Footnote: See Pl. XCIV No. 1, the lower sketch.
The explanation of the upper sketch is given on p. 29.]

1038.

Siena, _a b_ 4 braccia, _a c_ 10 braccia. Steps at [the castle of]
Urbino. [Footnote: See Pl. CX No. 3; compare also No. 765.]

1039.

The bell of Siena, that is the manner of its movement, and the place
of the attachment of the clapper. [Footnote: The text is accompanied
by an indistinct sketch.]

1040.

On St. Mary's day in the middle of August, at Cesena, 1502.
[Footnote: See Pl. CX, No. 4.]

1041.

Stairs of the [palace of the] Count of Urbino,--rough. [Footnote:
The text is accompanied by a slight sketch.]

1042.

At the fair of San Lorenzo at Cesena. 1502.

1043.

Windows at Cesena. [Footnote: There are four more lines of text
which refer to a slightly sketched diagram.]

1044.

At Porto Cesenatico, on the 6th of September 1502 at 9 o'clock a. m.

The way in which bastions ought to project beyond the walls of the
towers to defend the outer talus; so that they may not be taken by
artillery.

[Footnote: An indistinct sketch, accompanies this passage.]

1045.

The rock of the harbour of Cesena is four points towards the South
West from Cesena.

1046.

In Romagna, the realm of all stupidity, vehicles with four wheels
are used, of which O the two in front are small and two high ones
are behind; an arrangement which is very unfavourable to the motion,
because on the fore wheels more weight is laid than on those behind,
as I showed in the first of the 5th on "Elements".

1047.

Thus grapes are carried at Cesena. The number of the diggers of the
ditches is [arranged] pyramidically. [Footnote: A sketch,
representing a hook to which two bunches of grapes are hanging,
refers to these first two lines. Cesena is mentioned again Fol. 82a:
_Carro da Cesena_ (a cart from Cesena).]

1048.

There might be a harmony of the different falls of water as you saw
them at the fountain of Rimini on the 8th day of August, 1502.

1049.

The fortress at Urbino. [Footnote: 1049. In the original the text is
written inside the sketch in the place here marked _n_.]

1050.

Imola, as regards Bologna, is five points from the West, towards the
North West, at a distance of 20 miles.

Castel San Piero is seen from Imola at four points from the West
towards the North West, at a distance of 7 miles.

Faenza stands with regard to Imola between East and South East at a
distance of ten miles. Forli stands with regard to Faenza between
South East and East at a distance of 20 miles from Imola and ten
from Faenza.

Forlimpopoli lies in the same direction at 25 miles from Imola.

Bertinoro, as regards Imola, is five points from the East to wards
the South East, at 27 miles.

1051.

Imola as regards Bologna is five points from the West towards the
North West at a distance of 20 miles.

Castel San Pietro lies exactly North West of Imola, at a distance of
7 miles.

Faenza, as regards Imola lies exactly half way between the East and
South East at a distance of 10 miles; and Forli lies in the same
direction from Imola at a distance of 20 miles; and Forlimpopolo
lies in the same direction from Forli at a distance of 25 miles.

Bertinoro is seen from Imola two points from the East towards the
South East at a distance of 27 miles.

[Footnote: Leonardo inserted this passage on the margin of the
circular plan, in water colour, of Imola--see Pl. CXI No. 1.--In the
original the fields surrounding the town are light green; the moat,
which surrounds the fortifications and the windings of the river
Santerno, are light blue. The parts, which have come out blackish
close to the river are yellow ochre in the original. The dark groups
of houses inside the town are red. At the four points of the compass
drawn in the middle of the town Leonardo has written (from right to
left): _Mezzodi_ (South) at the top; to the left _Scirocho_ (South
east), _levante_ (East), _Greco_ (North East), _Septantrione_
(North), _Maesstro_ (North West), _ponente_ (West) _Libecco_ (South
West). The arch in which the plan is drawn is, in the original, 42
centimetres across.

At the beginning of October 1502 Cesare Borgia was shut up in Imola
by a sudden revolt of the Condottieri, and it was some weeks before
he could release himself from this state of siege (see Gregorovius,
_Geschichte der Stadt Rom im Mittelalter_, Vol. VII, Book XIII, 5,
5).

Besides this incident Imola plays no important part in the history
of the time. I therefore think myself fully justified in connecting
this map, which is at Windsor, with the siege of 1502 and with
Leonardo's engagements in the service of Cesare Borgia, because a
comparison of these texts, Nos. 1050 and 1051, raise, I believe, the
hypothesis to a certainty.]

1052.

>From Bonconventi to Casa Nova are 10 miles, from Casa Nova to Chiusi
9 miles, from Chiusi to Perugia, from, Perugia to Santa Maria degli
Angeli, and then to Fuligno. [Footnote: Most of the places here
described lie within the district shown in the maps on Pl. CXIII.]

1053.

On the first of August 1502, the library at Pesaro.

1054.

OF PAINTING.

On the tops and sides of hills foreshorten the shape of the ground
and its divisions, but give its proper shape to what is turned
towards you. [Footnote: This passage evidently refers to the making
of maps, such as Pl. CXII, CXIII, and CXIV. There is no mention of
such works, it is true, excepting in this one passage of MS. L. But
this can scarcely be taken as evidence against my view that Leonardo
busied himself very extensively at that time in the construction of
maps; and all the less since the foregoing chapters clearly prove
that at a time so full of events Leonardo would only now and then
commit his observations to paper, in the MS. L.

By the side of this text we find, in the original, a very indistinct
sketch, perhaps a plan of a position. Instead of this drawing I have
here inserted a much clearer sketch of a position from the same MS.,
L. 82b and 83a. They are the only drawings of landscape, it may be
noted, which occur at all in that MS.]

Alessandria in Piedmont (1055. 1056).

1055.

At Candia in Lombardy, near Alessandria della Paglia, in making a
well for Messer Gualtieri [Footnote 2: Messer Gualtieri, the same
probably as is mentioned in Nos. 672 and 1344.] of Candia, the
skeleton of a very large boat was found about 10 braccia
underground; and as the timber was black and fine, it seemed good to
the said Messer Gualtieri to have the mouth of the well lengthened
in such a way as that the ends of the boat should be uncovered.

1056.

At Alessandria della Paglia in Lombardy there are no stones for
making lime of, but such as are mixed up with an infinite variety of
things native to the sea, which is now more than 200 miles away.

The Alps (1057-1062).

1057.

At Monbracco, above Saluzzo,--a mile above the Certosa, at the foot
of Monte Viso, there is a quarry of flakey stone, which is as white
as Carrara marble, without a spot, and as hard as porphyry or even
harder; of which my worthy gossip, Master Benedetto the sculptor,
has promised to give me a small slab, for the colours, the second
day of January 1511.

[Footnote: Saluzzo at the foot of the Alps South of Turin.]

[Footnote 9. 10.: _Maestro Benedetto scultore_; probably some native
of Northern Italy acquainted with the place here described. Hardly
the Florentine sculptor Benedetto da Majano. Amoretti had published
this passage, and M. Ravaisson who gave a French translation of it
in the _Gazette des Beaux Arts_ (1881, pag. 528), remarks as
follows: _Le maitre sculpteur que Leonard appelle son "compare" ne
serait-il pas Benedetto da Majano, un de ceux qui jugerent avec lui
de la place a donner au David de Michel-Ange, et de qui le Louvre a
acquis recemment un buste d'apres Philippe Strozzi?_ To this it may
be objected that Benedetto da Majano had already lain in his grave
fourteen years, in the year 1511, when he is supposed to have given
the promise to Leonardo. The colours may have been given to the
sculptor Benedetto and the stone may have been in payment for them.
>From the description of the stone here given we may conclude that it
is repeated from hearsay of the sculptor's account of it. I do not
understand how, from this observation, it is possible to conclude
that Leonardo was on the spot.]

1058.

That there are springs which suddenly break forth in earthquakes or
other convulsions and suddenly fail; and this happened in a mountain
in Savoy where certain forests sank in and left a very deep gap, and
about four miles from here the earth opened itself like a gulf in
the mountain, and threw out a sudden and immense flood of water
which scoured the whole of a little valley of the tilled soil,
vineyards and houses, and did the greatest mischief, wherever it
overflowed.

1059.

The river Arve, a quarter of a mile from Geneva in Savoy, where the
fair is held on midsummerday in the village of Saint Gervais.

[Footnote: An indistinct sketch is to be seen by the text.]

1060.

And this may be seen, as I saw it, by any one going up Monbroso
[Footnote: I have vainly enquired of every available authority for a
solution of the mystery as to what mountain is intended by the name
Monboso (Comp. Vol. I Nos. 300 and 301). It seems most obvious to
refer it to Monte Rosa. ROSA derived from the Keltic ROS which
survives in Breton and in Gaelic, meaning, in its first sense, a
mountain spur, but which also--like HORN--means a very high peak;
thus Monte Rosa would mean literally the High Peak.], a peak of the
Alps which divide France from Italy. The base of this mountain gives
birth to the 4 rivers which flow in four different directions
through the whole of Europe. And no mountain has its base at so
great a height as this, which lifts itself above almost all the
clouds; and snow seldom falls there, but only hail in the summer,
when the clouds are highest. And this hail lies [unmelted] there, so
that if it were not for the absorption of the rising and falling
clouds, which does not happen more than twice in an age, an enormous
mass of ice would be piled up there by the layers of hail, and in
the middle of July I found it very considerable; and I saw the sky
above me quite dark, and the sun as it fell on the mountain was far
brighter here than in the plains below, because a smaller extent of
atmosphere lay between the summit of the mountain and the sun.
[Footnote 6: _in una eta._ This is perhaps a slip of the pen on
Leonardo's part and should be read _estate_ (summer).]

Leic. 9b]

1061.

In the mountains of Verona the red marble is found all mixed with
cockle shells turned into stone; some of them have been filled at
the mouth with the cement which is the substance of the stone; and
in some parts they have remained separate from the mass of the rock
which enclosed them, because the outer covering of the shell had
interposed and had not allowed them to unite with it; while in other
places this cement had petrified those which were old and almost
stripped the outer skin.

1062.

Bridge of Goertz-Wilbach (?).

[Footnote: There is a slight sketch with this text, Leonardo seems
to have intended to suggest, with a few pen-strokes, the course of
the Isonzo and of the Wipbach in the vicinity of Gorizia (Goerz). He
himself says in another place that he had been in Friuli (see No.
1077 1. 19).]

The Appenins (1063-1068).

1063.

That part of the earth which was lightest remained farthest from the
centre of the world; and that part of the earth became the lightest
over which the greatest quantity of water flowed. And therefore that
part became lightest where the greatest number of rivers flow; like
the Alps which divide Germany and France from Italy; whence issue
the Rhone flowing Southwards, and the Rhine to the North. The Danube
or Tanoia towards the North East, and the Po to the East, with
innumerable rivers which join them, and which always run turbid with
the soil carried by them to the sea.

The shores of the sea are constantly moving towards the middle of
the sea and displace it from its original position. The lowest
portion of the Mediterranean will be reserved for the bed and
current of the Nile, the largest river that flows into that sea. And
with it are grouped all its tributaries, which at first fell into
the sea; as may be seen with the Po and its tributaries, which first
fell into that sea, which between the Appenines and the German Alps
was united to the Adriatic sea.

That the Gallic Alps are the highest part of Europe.

1064.

And of these I found some in the rocks of the high Appenines and
mostly at the rock of La Vernia. [Footnote 6: _Sasso della Vernia._
The frowning rock between the sources of the Arno and the Tiber, as
Dante describes this mountain, which is 1269 metres in height.

This note is written by the side of that given as No. 1020; but
their connection does not make it clear what Leonardo's purpose was
in writing it.]

1065.

At Parma, at 'La Campana' on the twenty-fifth of October 1514.
[Footnote 2: _Capano_, an Inn.]

A note on the petrifactions, or fossils near Parma will be found
under No. 989.]

1066.

A method for drying the marsh of Piombino. [Footnote: There is a
slight sketch with this text in the original.--Piombino is also
mentioned in Nos. 609, l. 55-58 (compare Pl. XXXV, 3, below). Also
in No. 1035.]

1067.

The shepherds in the Romagna at the foot of the Apennines make
peculiar large cavities in the mountains in the form of a horn, and
on one side they fasten a horn. This little horn becomes one and the
same with the said cavity and thus they produce by blowing into it a
very loud noise. [Footnote: As to the Romagna see also No. 1046.]

1068.

A spring may be seen to rise in Sicily which at certain times of the
year throws out chesnut leaves in quantities; but in Sicily chesnuts
do not grow, hence it is evident that that spring must issue from
some abyss in Italy and then flow beneath the sea to break forth in
Sicily. [Footnote: The chesnut tree is very common in Sicily. In
writing _cicilia_ Leonardo meant perhaps Cilicia.]

II.

FRANCE.

1069.

   GERMANY.                     FRANCE.

a. Austria,                 a. Picardy.
b. Saxony.                  b. Normandy.
c. Nuremberg.               c. Dauphine.
d. Flanders.

               SPAIN.

            a. Biscay.
            b. Castille.
            c. Galicia.
            d. Portugal.
            e. Taragona.
            f. Granada.

[Footnote: Two slightly sketched maps, one of Europe the other of
Spain, are at the side of these notes.]

1070.

Perpignan. Roanne. Lyons. Paris. Ghent. Bruges. Holland.

[Footnote: _Roana_ does not seem to mean here Rouen in Normandy, but
is probably Roanne (Rodumna) on the upper Loire, Lyonnais (Dep. du
Loire). This town is now unimportant, but in Leonardo's time was
still a place of some consequence.]

1071.

At Bordeaux in Gascony the sea rises about 40 braccia before its
ebb, and the river there is filled with salt water for more than a
hundred and fifty miles; and the vessels which are repaired there
rest high and dry on a high hill above the sea at low tide.
[Footnote 2: This is obviously an exaggeration founded on inaccurate
information. Half of 150 miles would be nearer the mark.]

1072.

The Rhone issues from the lake of Geneva and flows first to the West
and then to the South, with a course of 400 miles and pours its
waters into the Mediterranean.

1073.

_c d_ is the garden at Blois; _a b_ is the conduit of Blois, made in
France by Fra Giocondo, _b c_ is what is wanting in the height of
that conduit, _c d_ is the height of the garden at Blois, _e f_ is
the siphon of the conduit, _b c_, _e f_, _f g_ is where the siphon
discharges into the river. [Footnote: The tenor of this note (see
lines 2 and 3) seems to me to indicate that this passage was not
written in France, but was written from oral information. We have no
evidence as to when this note may have been written beyond the
circumstance that Fra Giocondo the Veronese Architect left France
not before the year 1505. The greater part of the magnificent
Chateau of Blois has now disappeared. Whether this note was made for
a special purpose is uncertain. The original form and extent of the
Chateau is shown in Androvet, _Les plus excellents Bastiments de
France, Paris MDCVII,_ and it may be observed that there is in the
middle of the garden a Pavilion somewhat similar to that shown on
Pl. LXXXVIII No. 7.

See S. DE LA SAUSSAYE, _Histoire du Chateau de Blois 4eme edition
Blois et Paris_ p. 175: _En mariant sa fille ainee a Francois, comte
d'Angouleme, Louis XII lui avait constitue en dot les comtes de
Blois, d'Asti, de Coucy, de Montfort, d'Etampes et de Vertus. Une
ordonnance de Francois I. lui laissa en_ 1516 _l'administration du
comte de Blois.

Le roi fit commencer, dans la meme annee, les travaux de celle belle
partie du chateau, connue sous le nom d'aile de Francois I, et dont
nous avons donne la description au commencement de ce livre. Nous
trouvons en effet, dans les archives du Baron de Foursanvault, une
piece qui en fixe parfaitement la date. On y lit: "Je, Baymon
Philippeaux, commis par le Roy a tenir le compte et fair le payement
des bastiments, ediffices et reparacions que le dit seigneur fait
faire en son chastu de Blois, confesse avoir eu et receu ... la
somme de trois mille livres tournois ... le cinquieme jour de
juillet, l'an mil cinq cent et seize._ P. 24: _Les jardins avaient
ete decores avec beaucoup de luxe par les differents possesseurs du
chateau. Il ne reste de tous les batiments qu'ils y eleverent que
ceux des officiers charges de l'ad_ministration et de la culture des
jardins, et un pavilion carre en pierre et en brique flanque de
terrasses a chacun de ses angles. Quoique defigure par des mesures
elevees sur les terrasses, cet edifice est tris-digne d'interet par
l'originalite du plan, la decoration architecturale et le souvenir
d'Anne de Bretagne qui le fit construire._ Felibien describes the
garden as follows: _Le jardin haut etait fort bien dresse par grands
compartimens de toutes sortes de figures, avec des allees de
meuriers blancs et des palissades de coudriers. Deux grands berceaux
de charpenterie separoient toute la longueur et la largeur du
jardin, et dans les quatres angles des allees, ou ces berceaux se
croissent, il y auoit 4 cabinets, de mesme charpenterie ... Il y a
pas longtemps qu'il y auoit dans ce mesme jardin, a l'endroit ou se
croissent les allees du milieu, un edifice de figure octogone, de
plus de 7 thoises de diametre et de plus de neuf thoises de haut;
avec 4 enfoncements en forme de niches dans les 4 angles des allies.
Ce bastiment.... esloit de charpente mais d'un extraordinairement
bien travaille. On y voyait particulierement la cordiliere qui
regnati tout autour en forme de cordon. Car la Reyne affectait de la
mettre nonseulement a ses armes et a ses chiffres mais de la faire
representer en divers manieres dans tous les ouvrages qu'on lui
faisait pour elle ... le bastiment estati couvert en forme de dome
qui dans son milieu avait encore un plus petit dome, ou lanterne
vitree au-dessus de laquelle estait une figure doree representant
Saint Michel. Les deux domes estoient proprement couvert d'ardoise
et de plomb dore par dehors; par dedans ils esloient lambrissez
d'une menuiserie tres delicate. Au milieu de ce Salon il y avait un
grand bassin octogone de marbre blanc, dont toutes les faces
estoient enrichies de differentes sculptures, avec les armes et les
chiffres du Roy Louis XII et de la Reine Anne, Dans ce bassin il y
en avait un autre pose sur un piedestal lequel auoit sept piedz de
diametre. Il estait de figure ronde a godrons, avec des masques et
d'autres ornements tres scauamment taillez. Du milieu de ce
deuxiesme bassin s'y levoit un autre petit piedestal qui portait un
troisiesme bassin de trois pieds de diametre, aussy parfaitement
bien taille; c'estoit de ce dernier bassin que jallissoit l'eau qui
se rependoit en suitte dans les deux autres bassins. Les beaux
ouvrages faits d'un marbre esgalement blanc et poli, furent brisez
par la pesanteur de tout l'edifice, que les injures de l'air
renverserent de fond en comble.]

1074.

The river Loire at Amboise.

The river is higher within the bank _b d_ than outside that bank.

The island where there is a part of Amboise.

This is the river that passes through Amboise; it passes at _a b c
d_, and when it has passed the bridge it turns back, against the
original current, by the channel _d e_, _b f_ in contact with the
bank which lies between the two contrary currents of the said river,
_a b_, _c d_, and _d e_, _b f_. It then turns down again by the
channel _f l_, _g h_, _n m_, and reunites with the river from which
it was at first separated, which passes by _k n_, which makes _k m_,
_r t_. But when the river is very full it flows all in one channel
passing over the bank _b d_. [Footnote: See Pl. CXV. Lines 1-7 are
above, lines 8-10 in the middle of the large island and the word
_Isola_ is written above _d_ in the smaller island; _a_ is written
on the margin on the bank of the river above 1. I; in the
reproduction it is not visible. As may be seen from the last
sentence, the observation was made after long study of the river's
course, when Leonardo had resided for some time at, or near,
Amboise.]

1075.

The water may be dammed up above the level of Romorantin to such a
height, that in its fall it may be used for numerous mills.

1075.

The river at Villefranche may be conducted to Romorantin which may
be done by the inhabitants; and the timber of which their houses are
built may be carried in boats to Romorantin [Footnote: Compare No.
744.]. The river may be dammed up at such a height that the waters
may be brought back to Romorantin with a convenient fall.

1076.

As to whether it is better that the water should all be raised in a
single turn or in two?

The answer is that in one single turn the wheel could not support
all the water that it can raise in two turns, because at the half
turn of the wheel it would be raising 100 pounds and no more; and if
it had to raise the whole, 200 pounds in one turn, it could not
raise them unless the wheel were of double the diameter and if the
diameter were doubled, the time of its revolution would be doubled;
therefore it is better and a greater advantage in expense to make
such a wheel of half the size (?) the land which it would water and
would render the country fertile to supply food to the inhabitants,
and would make navigable canals for mercantile purposes.

The way in which the river in its flow should scour its own channel.

By the ninth of the third; the more rapid it is, the more it wears
away its channel; and, by the converse proposition, the slower the
water the more it deposits that which renders it turbid.

And let the sluice be movable like the one I arranged in Friuli
[Footnote 19: This passage reveals to us the fact that Leonardo had
visited the country of Friuli and that he had stayed there for some
time. Nothing whatever was known of this previously.], where when
one sluice was opened the water which passed through it dug out the
bottom. Therefore when the rivers are flooded, the sluices of the
mills ought to be opened in order that the whole course of the river
may pass through falls to each mill; there should be many in order
to give a greater impetus, and so all the river will be scoured. And
below the site of each of the two mills there may be one of the said
sluice falls; one of them may be placed below each mill.

1078.

A trabocco is four braccia, and one mile is three thousand of the
said braccia. Each braccio is divided into 12 inches; and the water
in the canals has a fall in every hundred trabocchi of two of these
inches; therefore 14 inches of fall are necessary in two thousand
eight hundred braccia of flow in these canals; it follows that 15
inches of fall give the required momentum to the currents of the
waters in the said canals, that is one braccio and a half in the
mile. And from this it may be concluded that the water taken from
the river of Ville-franche and lent to the river of Romorantin
will..... Where one river by reason of its low level cannot flow
into the other, it will be necessary to dam it up, so that it may
acquire a fall into the other, which was previously the higher.

The eve of Saint Antony I returned from Romorantin to Amboise, and
the King went away two days before from Romorantin.

>From Romorantin as far as the bridge at Saudre it is called the
Saudre, and from that bridge as far as Tours it is called the Cher.

I would test the level of that channel which is to lead from the
Loire to Romorantin, with a channel one braccio wide and one braccio
deep.

[Footnote: Lines 6-18 are partly reproduced in the facsimile on p.
254, and the whole of lines 19-25.

The following names are written along the rivers on the larger
sketch, _era f_ (the Loire) _scier f_ (the Cher) three times. _Pote
Sodro_ (bridge of the Soudre). _Villa francha_ (Villefranche)
_banco_ (sandbank) _Sodro_ (Soudre). The circle below shows the
position of Romorantin. The words '_orologio del sole_' written
below do not belong to the map of the rivers. The following names
are written by the side of the smaller sketch-map:--_tors_ (Tours),
_Abosa_ (Amboise) _bres_--for Bles (Blois) _mo rica_ (Montrichard).
_Lione_ (Lyons). This map was also published in the 'Saggio'
(Milano, 1872) Pl. XXII, and the editors remark: _Forse la linia
retta che va da Amboise a Romorantin segna l'andamento proposto d'un
Canale, che poi rembra prolungarsi in giu fin dove sta scritto
Lione._

M. Ravaisson has enlarged on this idea in the Gazette des Beaux Arts
(1881 p. 530): _Les traces de Leonard permettent d'entrevoir que le
canal commencant soit aupres de Tours, soit aupres de Blois et
passant par Romorantin, avec port d'embarquement a Villefranche,
devait, au dela de Bourges, traverser l'Allier au-dessous des
affluents de la Dore et de la Sioule, aller par Moulins jusqu' a
Digoin; enfin, sur l'autre rive de la Loire, depasser les monts du
Charolais et rejoindre la Saone aupres de Macon._ It seems to me
rash, however, to found so elaborate an hypothesis on these sketches
of rivers. The slight stroke going to _Lione_ is perhaps only an
indication of the direction.--With regard to the Loire compare also
No. 988. l. 38.]

1079.

THE ROAD TO ORLEANS

At 1/4 from the South to the South East. At 1/3 from the South to
the South East. At 1/4 from the South to the South East. At 1/5 from
the South to the South East. Between the South West and South, to
the East bearing to the South; from the South towards the East 1/8;
thence to the West, between the South and South West; at the South.

[Footnote: The meaning is obscure; a more important passage
referring to France is to be found under No. 744]

On the Germans (1080. 1081).

1080.

The way in which the Germans closing up together cross and
interweave their broad leather shields against the enemy, stooping
down and putting one of the ends on the ground while they hold the
rest in their hand. [Footnote: Above the text is a sketch of a few
lines crossing each other and the words _de ponderibus_. The meaning
of the passage is obscure.]

1081.

The Germans are wont to annoy a garrison with the smoke of feathers,
sulphur and realgar, and they make this smoke last 7 or 8 hours.
Likewise the husks of wheat make a great and lasting smoke; and also
dry dung; but this must be mixed with olive husks, that is olives
pressed for oil and from which the oil has been extracted.
[Footnote: There is with this passage a sketch of a round tower
shrouded in smoke.]

The Danube.

1082.

That the valleys were formerly in great part covered by lakes the
soil of which always forms the banks of rivers,--and by seas, which
afterwards, by the persistent wearing of the rivers, cut through the
mountains and the wandering courses of the rivers carried away the
other plains enclosed by the mountains; and the cutting away of the
mountains is evident from the strata in the rocks, which correspond
in their sections as made by the courses of the rivers [Footnote 4:
_Emus_, the Balkan; _Dardania_, now Servia.], The Haemus mountains
which go along Thrace and Dardania and join the Sardonius mountains
which, going on to the westward change their name from Sardus to
Rebi, as they come near Dalmatia; then turning to the West cross
Illyria, now called Sclavonia, changing the name of Rebi to Albanus,
and going on still to the West, they change to Mount Ocra in the
North; and to the South above Istria they are named Caruancas; and
to the West above Italy they join the Adula, where the Danube rises
[8], which stretches to the East and has a course of 1500 miles; its
shortest line is about l000 miles, and the same or about the same is
that branch of the Adula mountains changed as to their name, as
before mentioned. To the North are the Carpathians, closing in the
breadth of the valley of the Danube, which, as I have said extends
eastward, a length of about 1000 miles, and is sometimes 200 and in
some places 300 miles wide; and in the midst flows the Danube, the
principal river of Europe as to size. The said Danube runs through
the middle of Austria and Albania and northwards through Bavaria,
Poland, Hungary, Wallachia and Bosnia and then the Danube or Donau
flows into the Black Sea, which formerly extended almost to Austria
and occupied the plains through which the Danube now courses; and
the evidence of this is in the oysters and cockle shells and
scollops and bones of great fishes which are still to be found in
many places on the sides of those mountains; and this sea was formed
by the filling up of the spurs of the Adula mountains which then
extended to the East joining the spurs of the Taurus which extend to
the West. And near Bithynia the waters of this Black Sea poured into
the Propontis [Marmora] falling into the Aegean Sea, that is the
Mediterranean, where, after a long course, the spurs of the Adula
mountains became separated from those of the Taurus. The Black Sea
sank lower and laid bare the valley of the Danube with the above
named countries, and the whole of Asia Minor beyond the Taurus range
to the North, and the plains from mount Caucasus to the Black Sea to
the West, and the plains of the Don this side--that is to say, at
the foot of the Ural mountains. And thus the Black Sea must have
sunk about 1000 braccia to uncover such vast plains.

[Footnote 8: _Danubio_, in the original _Reno_; evidently a mistake
as we may infer from _come dissi_ l. 10 &c.]

III.

THE COUNTRIES OF THE WESTERN END OF THE MEDITERRANEAN.

The straits of Gibraltar (1083-1085).

1083.

WHY THE SEA MAKES A STRONGER CURRENT IN THE STRAITS OF SPAIN THAN
ELSEWHERE.

A river of equal depth runs with greater speed in a narrow space
than in a wide one, in proportion to the difference between the
wider and the narrower one.

This proposition is clearly proved by reason confirmed by
experiment. Supposing that through a channel one mile wide there
flows one mile in length of water; where the river is five miles
wide each of the 5 square miles will require 1/5 of itself to be
equal to the square mile of water required in the sea, and where the
river is 3 miles wide each of these square miles will require the
third of its volume to make up the amount of the square mile of the
narrow part; as is demonstrated in _f g h_ at the mile marked _n_.

[Footnote: In the place marked A in the diagram _Mare Mediterano_
(Mediterranean Sea) is written in the original. And at B, _stretto
di Spugna_ (straits of Spain, _i.e._ Gibraltar). Compare No. 960.]

1084.

WHY THE CURRENT OF GIBRALTAR IS ALWAYS GREATER TO THE WEST THAN TO
THE EAST.

The reason is that if you put together the mouths of the rivers
which discharge into the Mediterranean sea, you would find the sum
of water to be larger than that which this sea pours through the
straits into the ocean. You see Africa discharging its rivers that
run northwards into this sea, and among them the Nile which runs
through 3000 miles of Africa; there is also the Bagrada river and
the Schelif and others. [Footnote 5: _Bagrada_ (Leonardo writes
Bragada) in Tunis, now Medscherda; _Mavretano_, now Schelif.]
Likewise Europe pours into it the Don and the Danube, the Po, the
Rhone, the Arno, and the Tiber, so that evidently these rivers, with
an infinite number of others of less fame, make its great breadth
and depth and current; and the sea is not wider than 18 miles at the
most westerly point of land where it divides Europe from Africa.

1085.

The gulf of the Mediterranean, as an inland sea, received the
principal waters of Africa, Asia and Europe that flowed towards it;
and its waters came up to the foot of the mountains that surrounded
it and made its shores. And the summits of the Apennines stood up
out of this sea like islands, surrounded by salt water. Africa
again, behind its Atlas mountains did not expose uncovered to the
sky the surface of its vast plains about 3000 miles in length, and
Memphis [Footnote 6: _Mefi._ Leonardo can only mean here the citadel
of Cairo on the Mokattam hills.] was on the shores of this sea, and
above the plains of Italy, where now birds fly in flocks, fish were
wont to wander in large shoals.

1086.

Tunis.

The greatest ebb made anywhere by the Mediterranean is above Tunis,
being about two and a half braccia and at Venice it falls two
braccia. In all the rest of the Mediterranean sea the fall is little
or none.

1087.

Libya.

Describe the mountains of shifting deserts; that is to say the
formation of waves of sand borne by the wind, and of its mountains
and hills, such as occur in Libya. Examples may be seen on the wide
sands of the Po and the Ticino, and other large rivers.

1088.

Majorca.

Circumfulgore is a naval machine. It was an invention of the men of
Majorca. [Footnote: The machine is fully described in the MS. and
shown in a sketch.]

1089.

The Tyrrhene Sea.

Some at the Tyrrhene sea employ this method; that is to say they
fastened an anchor to one end of the yard, and to the other a cord,
of which the lower end was fastened to an anchor; and in battle they
flung this anchor on to the oars of the opponent's boat and by the
use of a capstan drew it to the side; and threw soft soap and tow,
daubed with pitch and set ablaze, on to that side where the anchor
hung; so that in order to escape that fire, the defenders of that
ship had to fly to the opposite side; and in doing this they aided
to the attack, because the galley was more easily drawn to the side
by reason of the counterpoise. [Footnote: This text is illustrated
in the original by a pen and ink sketch.]

IV.

THE LEVANT.

The Levantine Sea.

1090.

On the shores of the Mediterranean 300 rivers flow, and 40, 200
ports. And this sea is 3000 miles long. Many times has the increase
of its waters, heaped up by their backward flow and the blowing of
the West winds, caused the overflow of the Nile and of the rivers
which flow out through the Black Sea, and have so much raised the
seas that they have spread with vast floods over many countries. And
these floods take place at the time when the sun melts the snows on
the high mountains of Ethiopia that rise up into the cold regions of
the air; and in the same way the approach of the sun acts on the
mountains of Sarmatia in Asia and on those in Europe; so that the
gathering together of these three things are, and always have been,
the cause of tremendous floods: that is, the return flow of the sea
with the West wind and the melting of the snows. So every river will
overflow in Syria, in Samaria, in Judea between Sinai and the
Lebanon, and in the rest of Syria between the Lebanon and the Taurus
mountains, and in Cilicia, in the Armenian mountains, and in
Pamphilia and in Lycia within the hills, and in Egypt as far as the
Atlas mountains. The gulf of Persia which was formerly a vast lake
of the Tigris and discharged into the Indian Sea, has now worn away
the mountains which formed its banks and laid them even with the
level of the Indian ocean. And if the Mediterranean had continued
its flow through the gulf of Arabia, it would have done the same,
that is to say, would have reduced the level of the Mediterranean to
that of the Indian Sea.

The Red Sea. (1091. 1092).

1091.

For a long time the water of the Mediterranean flowed out through
the Red Sea, which is 100 miles wide and 1500 long, and full of
reefs; and it has worn away the sides of Mount Sinai, a fact which
testifies, not to an inundation from the Indian sea beating on these
coasts, but to a deluge of water which carried with it all the
rivers which abound round the Mediterranean, and besides this there
is the reflux of the sea; and then, a cutting being made to the West
3000 miles away from this place, Gibraltar was separated from Ceuta,
which had been joined to it. And this passage was cut very low down,
in the plains between Gibraltar and the ocean at the foot of the
mountain, in the low part, aided by the hollowing out of some
valleys made by certain rivers, which might have flowed here.
Hercules [Footnote 9: Leonardo seems here to mention Hercules half
jestingly and only in order to suggest to the reader an allusion to
the legend of the pillars of Hercules.] came to open the sea to the
westward and then the sea waters began to pour into the Western
Ocean; and in consequence of this great fall, the Red Sea remained
the higher; whence the water, abandoning its course here, ever after
poured away through the Straits of Spain.

1092.

The surface of the Red Sea is on a level with the ocean.

A mountain may have fallen and closed the mouth of the Red Sea and
prevented the outlet of the Mediterranean, and the Mediterranean Sea
thus overfilled had for outlet the passage below the mountains of
Gades; for, in our own times a similar thing has been seen [Footnote
6: Compare also No. 1336, ll. 30, 35 and 36.-- Paolo Giovio, the
celebrated historian (born at Como in 1483) reports that in 1513 at
the foot of the Alps, above Bellinzona, on the road to Switzerland,
a mountain fell with a very great noise, in consequence of an
earthquake, and that the mass of rocks, which fell on the left
(Western) side blocked the river Breno (T. I p. 218 and 345 of D.
Sauvage's French edition, quoted in ALEXIS PERCY, _Memoire des
tremblements de terre de la peninsule italique; Academie Royale de
Belgique._ T. XXII).--]; a mountain fell seven miles across a valley
and closed it up and made a lake. And thus most lakes have been made
by mountains, as the lake of Garda, the lakes of Como and Lugano,
and the Lago Maggiore. The Mediterranean fell but little on the
confines of Syria, in consequence of the Gaditanean passage, but a
great deal in this passage, because before this cutting was made the
Mediterranean sea flowed to the South East, and then the fall had to
be made by its run through the Straits of Gades.

At _a_ the water of the Mediterranean fell into the ocean.

All the plains which lie between the sea and mountains were formerly
covered with salt water.

Every valley has been made by its own river; and the proportion
between valleys is the same as that between river and river.

The greatest river in our world is the Mediterranean river, which
moves from the sources of the Nile to the Western ocean.

And its greatest height is in Outer Mauritania and it has a course
of ten thousand miles before it reunites with its ocean, the father
of the waters.

That is 3000 miles for the Mediterranean, 3000 for the Nile, as far
as discovered and 3000 for the Nile which flows to the East, &c.

[Footnote: See Pl. CXI 2, a sketch of the shores of the
Mediterranean Sea, where lines 11 to 16 may be seen. The large
figures 158 are not in Leonardo's writing. The character of the
writing leads us to conclude that this text was written later than
the foregoing. A slight sketch of the Mediterranean is also to be
found in MS. I', 47a.]

The Nile (1093-1098).

1093.

Therefore we must conclude those mountains to be of the greatest
height, above which the clouds falling in snow give rise to the
Nile.

1094.

The Egyptians, the Ethiopians, and the Arabs, in crossing the Nile
with camels, are accustomed to attach two bags on the sides of the
camel's bodies that is skins in the form shown underneath.

In these four meshes of the net the camels for baggage place their
feet.

[Footnote: Unfortunately both the sketches which accompany this
passage are too much effaced to be reproduced. The upper represents
the two sacks joined by ropes, as here described, the other shows
four camels with riders swimming through a river.]

1095.

The Tigris passes through Asia Minor and brings with it the water of
three lakes, one after the other of various elevations; the first
being Munace and the middle Pallas and the lowest Triton. And the
Nile again springs from three very high lakes in Ethiopia, and runs
northwards towards the sea of Egypt with a course of 4000 miles, and
by the shortest and straightest line it is 3000 miles. It is said
that it issues from the Mountains of the Moon, and has various
unknown sources. The said lakes are about 4000 braccia above the
surface of the sphere of water, that is 1 mile and 1/3, giving to
the Nile a fall of 1 braccia in every mile.

[Footnote 5: _Incogniti principio._ The affluents of the lakes are
probably here intended. Compare, as to the Nile, Nos. 970, 1063 and
1084.]

1096.

Very many times the Nile and other very large rivers have poured out
their whole element of water and restored it to the sea.

1097.

Why does the inundation of the Nile occur in the summer, coming from
torrid countries?

1098.

It is not denied that the Nile is constantly muddy in entering the
Egyptian sea and that its turbidity is caused by soil that this
river is continually bringing from the places it passes; which soil
never returns in the sea which receives it, unless it throws it on
its shores. You see the sandy desert beyond Mount Atlas where
formerly it was covered with salt water.

Customs of Asiatic Nations (1099. 1100).

1099.

The Assyrians and the people of Euboea accustom their horses to
carry sacks which they can at pleasure fill with air, and which in
case of need they carry instead of the girth of the saddle above and
at the side, and they are well covered with plates of cuir bouilli,
in order that they may not be perforated by flights of arrows. Thus
they have not on their minds their security in flight, when the
victory is uncertain; a horse thus equipped enables four or five men
to cross over at need.

1100.

SMALL BOATS.

The small boats used by the Assyrians were made of thin laths of
willow plaited over rods also of willow, and bent into the form of a
boat. They were daubed with fine mud soaked with oil or with
turpentine, and reduced to a kind of mud which resisted the water
and because pine would split; and always remained fresh; and they
covered this sort of boats with the skins of oxen in safely crossing
the river Sicuris of Spain, as is reported by Lucant; [Footnote 7:
See Lucan's Pharsalia IV, 130: _Utque habuit ripas Sicoris camposque
reliquit, Primum cana salix madefacto vimine parvam Texitur in
puppim, calsoque inducto juvenco Vectoris patiens tumidum supernatat
amnem. Sic Venetus stagnante Pado, fusoque Britannus Navigat oceano,
sic cum tenet omnia Nilus, Conseritur bibula Memphitis cymbo papyro.
His ratibus transjecta manus festinat utrimque Succisam cavare nemus
]

The Spaniards, the Scythians and the Arabs, when they want to make a
bridge in haste, fix hurdlework made of willows on bags of ox-hide,
and so cross in safety.

Rhodes (1101. 1102).

1101.

In [fourteen hundred and] eighty nine there was an earthquake in the
sea of Atalia near Rhodes, which opened the sea--that is its
bottom--and into this opening such a torrent of water poured that
for more than three hours the bottom of the sea was uncovered by
reason of the water which was lost in it, and then it closed to the
former level.

[Footnote: _Nello ottanto_ 9. It is scarcely likely that Leonardo
should here mean 89 AD. Dr. H. MULLER- STRUBING writes to me as
follows on this subject: "With reference to Rhodes Ross says (_Reise
auf den Griechischen Inseln, III_ 70 _ff_. 1840), that ancient
history affords instances of severe earthquakes at Rhodes, among
others one in the second year of the 138th Olympiad=270 B. C.; a
remarkably violent one under Antoninus Pius (A. D. 138-161) and
again under Constantine and later. But Leonardo expressly speaks of
an earthquake "_nel mar di Atalia presso a Rodi_", which is
singular. The town of Attalia, founded by Attalus, which is what he
no doubt means, was in Pamphylia and more than 150 English miles
East of Rhodes in a straight line. Leake and most other geographers
identify it with the present town of Adalia. Attalia is rarely
mentioned by the ancients, indeed only by Strabo and Pliny and no
earthquake is spoken of. I think therefore you are justified in
assuming that Leonardo means 1489". In the elaborate catalogue of
earthquakes in the East by Sciale Dshelal eddin Sayouthy (an
unpublished Arabic MS. in the possession of Prof. SCHEFER, (Membre
de l'Institut, Paris) mention is made of a terrible earthquake in
the year 867 of the Mohamedan Era corresponding to the year 1489,
and it is there stated that a hundred persons were killed by it in
the fortress of Kerak. There are three places of this name. Kerak on
the sea of Tiberias, Kerak near Tahle on the Libanon, which I
visited in the summer of l876--but neither of these is the place
alluded to. Possibly it may be the strongly fortified town of
Kerak=Kir Moab, to the West of the Dead Sea. There is no notice
about this in ALEXIS PERCY, _Memoire sur les tremblements de terres
ressentis dans la peninsule turco- hellenique et en Syrie (Memoires
couronnes et memoires des savants etrangers, Academie Royale de
Belgique, Tome XXIII)._]

1102.

Rhodes has in it 5000 houses.

Cyprus (1103. 1104).

1103.

SITE FOR [A TEMPLE OF] VENUS.

You must make steps on four sides, by which to mount to a meadow
formed by nature at the top of a rock which may be hollowed out and
supported in front by pilasters and open underneath in a large
portico,

[Footnote: See Pl. LXXXIII. Compare also p. 33 of this Vol. The
standing male figure at the side is evidently suggested by Michael
Angelo's David. On the same place a slight sketch of horses seems to
have been drawn first; there is no reason for assuming that the text
and this sketch, which have no connection with each other, are of
the same date.

_Sito di Venere._ By this heading Leonardo appears to mean Cyprus,
which was always considered by the ancients to be the home and birth
place of Aphrodite (Kirpic in Homer).]

in which the water may fall into various vases of granite,
porphyryand serpentine, within semi-circular recesses; and the water
may overflow from these. And round this portico towards the North
there should be a lake with a little island in the midst of which
should be a thick and shady wood; the waters at the top of the
pilasters should pour into vases at their base, from whence they
should flow in little channels.

Starting from the shore of Cilicia towards the South you discover
the beauties of the island of Cyprus.

The Caspian Sea (1105. 1106).

1104.

>From the shore of the Southern coast of Cilicia may be seen to the
South the beautiful island of Cyprus, which was the realm of the
goddess Venus, and many navigators being attracted by her beauty,
had their ships and rigging broken amidst the reefs, surrounded by
the whirling waters. Here the beauty of delightful hills tempts
wandering mariners to refresh themselves amidst their flowery
verdure, where the winds are tempered and fill the island and the
surrounding seas with fragrant odours. Ah! how many a ship has here
been sunk. Ah! how many a vessel broken on these rocks. Here might
be seen barks without number, some wrecked and half covered by the
sand; others showing the poop and another the prow, here a keel and
there the ribs; and it seems like a day of judgment when there
should be a resurrection of dead ships, so great is the number of
them covering all the Northern shore; and while the North gale makes
various and fearful noises there.

1105.

Write to Bartolomeo the Turk as to the flow and ebb of the Black
sea, and whether he is aware if there be such a flow and ebb in the
Hyrcanean or Caspian sea. [Footnote: The handwriting of this note
points to a late date.]

1106.

WHY WATER IS FOUND AT THE TOP OF MOUNTAINS.

>From the straits of Gibraltar to the Don is 3500 miles, that is one
mile and 1/6, giving a fall of one braccio in a mile to any water
that moves gently. The Caspian sea is a great deal higher; and none
of the mountains of Europe rise a mile above the surface of our
seas; therefore it might be said that the water which is on the
summits of our mountains might come from the height of those seas,
and of the rivers which flow into them, and which are still higher.

The sea of Azov.

1107.

Hence it follows that the sea of Azov is the highest part of the
Mediterranean sea, being at a distance of 3500 miles from the
Straits of Gibraltar, as is shown by the map for navigation; and it
has 3500 braccia of descent, that is, one mile and 1/6; therefore it
is higher than any mountains which exist in the West.

[Footnote: The passage before this, in the original, treats of the
exit of the waters from Lakes in general.]

The Dardanelles.

1108.

In the Bosphorus the Black Sea flows always into the Egean sea, and
the Egean sea never flows into it. And this is because the Caspian,
which is 400 miles to the East, with the rivers which pour into it,
always flows through subterranean caves into this sea of Pontus; and
the Don does the same as well as the Danube, so that the waters of
Pontus are always higher than those of the Egean; for the higher
always fall towards the lower, and never the lower towards the
higher.

Constantinople.

1109.

The bridge of Pera at Constantinople, 40 braccia wide, 70 braccia
high above the water, 600 braccia long; that is 400 over the sea and
200 on the land, thus making its own abutments.

[Footnote: See Pl. CX No. 1. In 1453 by order of Sultan Mohamed II.
the Golden Horn was crossed by a pontoon bridge laid on barrels (see
Joh. Dukas' History of the Byzantine Empire XXXVIII p. 279). --The
biographers of Michelangelo, Vasari as well as Condivi, relate that
at the time when Michelangelo suddenly left Rome, in 1506, he
entertained some intention of going to Constantinople, there to
serve the Sultan, who sought to engage him, by means of certain
Franciscan Monks, for the purpose of constructing a bridge to
connect Constantinople with Pera. See VASARI, _Vite_ (ed. Sansoni
VII, 168): _Michelangelo, veduto questa furia del papa, dubitando di
lui, ebbe, secondo che si dice, voglia di andarsene in
Gostantinopoli a servire il Turco, per mezzo di certi frati di San
Francesco, che desiderava averlo per fare un ponte che passassi da
Gostantinopoli a Pera._ And CONDIVI, _Vita di M. Buonaroti chap._
30_; Michelangelo allora vedendosi condotto a questo, temendo
dell'ira del papa, penso d'andarsene in Levante; massimamente
essendo stato dal Turco ricercato con grandissime promesse per mezzo
di certi frati di San Francesco, per volersene servire in fare un
ponte da Costantinopoli a Pera ed in altri affari._ Leonardo's plan
for this bridge was made in 1502. We may therefore conclude that at
about that time the Sultan Bajazet II. had either announced a
competition in this matter, or that through his agents Leonardo had
first been called upon to carry out the scheme.]

The Euphrates.

1110.

If the river will turn to the rift farther on it will never return
to its bed, as the Euphrates does, and this may do at Bologna the
one who is disappointed for his rivers.

Centrae Asia.

1111.

Mounts Caucasus, Comedorum, and Paropemisidae are joined together
between Bactria and India, and give birth to the river Oxus which
takes its rise in these mountains and flows 500 miles towards the
North and as many towards the West, and discharges its waters into
the Caspian sea; and is accompanied by the Oxus, Dargados, Arthamis,
Xariaspes, Dargamaim, Ocus and Margus, all very large rivers. From
the opposite side towards the South rises the great river Indus
which sends its waters for 600 miles Southwards and receives as
tributaries in this course the rivers Xaradrus, Hyphasis, Vadris,
Vandabal Bislaspus to the East, Suastes and Coe to the West, uniting
with these rivers, and with their waters it flows 800 miles to the
West; then, turning back by the Arbiti mountains makes an elbow and
turns Southwards, where after a course of about 100 miles it finds
the Indian Sea, in which it pours itself by seven branches. On the
side of the same mountains rises the great Ganges, which river flows
Southwards for 500 miles and to the Southwest a thousand ... and
Sarabas, Diarnuna, Soas and Scilo, Condranunda are its tributaries.
It flows into the Indian sea by many mouths.

On the natives of hot countries.

1112.

Men born in hot countries love the night because it refreshes them
and have a horror of light because it burns them; and therefore they
are of the colour of night, that is black. And in cold countries it
is just the contrary.

[Footnote: The sketch here inserted is in MS. H3 55b.]

_XVIII._

_Naval Warfare.--Mechanical Appliances.--Music._

_Such theoretical questions, as have been laid before the reader in
Sections XVI and XVII, though they were the chief subjects of
Leonardo's studies of the sea, did not exclusively claim his
attention. A few passages have been collected at the beginning of
this section, which prove that he had turned his mind to the
practical problems of navigation, and more especially of naval
warfare. What we know for certain of his life gives us no data, it
is true, as to when or where these matters came under his
consideration; but the fact remains certain both from these notes in
his manuscripts, and from the well known letter to Ludovico il Moro
(No._ 1340_), in which he expressly states that he is as capable as
any man, in this very department._

_The numerous notes as to the laws and rationale of the flight of
birds, are scattered through several note-books. An account of these
is given in the Bibliography of the manuscripts at the end of this
work. It seems probable that the idea which led him to these
investigations was his desire to construct a flying or aerial
machine for man. At the same time it must be admitted that the notes
on the two subjects are quite unconnected in the manuscripts, and
that those on the flight of birds are by far the most numerous and
extensive. The two most important passages that treat of the
construction of a flying machine are those already published as Tav.
XVI, No._ 1 _and Tav. XVIII in the_ "Saggio delle opere di Leonardo
da Vinci" _(Milan_ 1872_). The passages--Nos._ 1120-1125--_here
printed for the first time and hitherto unknown--refer to the same
subject and, with the exception of one already published in the
Saggio-- No._ 1126--_they are, so far as I know, the only notes,
among the numerous observations on the flight of birds, in which the
phenomena are incidentally and expressly connected with the idea of
a flying machine._

_The notes on machines of war, the construction of fortifications,
and similar matters which fall within the department of the
Engineer, have not been included in this work, for the reasons given
on page_ 26 _of this Vol. An exception has been made in favour of
the passages Nos._ 1127 _and_ 1128, _because they have a more
general interest, as bearing on the important question: whence the
Master derived his knowledge of these matters. Though it would be
rash to assert that Leonardo was the first to introduce the science
of mining into Italy, it may be confidently said that he is one of
the earliest writers who can be proved to have known and understood
it; while, on the other hand, it is almost beyond doubt that in the
East at that time, the whole science of besieging towns and mining
in particular, was far more advanced than in Europe. This gives a
peculiar value to the expressions used in No._ 1127.

_I have been unable to find in the manuscripts any passage whatever
which throws any light on Leonardo's great reputation as a musician.
Nothing therein illustrates VASARPS well-known statement:_ Avvenne
che morto Giovan Galeazze duca di Milano, e creato Lodovico Sforza
nel grado medesimo anno 1494, fu condotto a Milano con gran
riputazione Lionardo al duca, il quale molto si dilettava del suono
della lira, perche sonasse; e Lionardo porto quello strumento
ch'egli aveva di sua mano fabbricato d'argento gran parte, in forma
d'un teschio di cavallo, cosa bizzarra e nuova, acciocche l'armonia
fosse con maggior tuba e piu sonora di voce; laonde supero tutti i
musici che quivi erano concorsi a sonare.

_The only notes on musical matters are those given as Nos._ 1129
_and_ 1130, _which explain certain arrangements in instruments._

The ship's logs of Vitruvius, of Alberti and of Leonardo

1113.

ON MOVEMENTS;--TO KNOW HOW MUCH A SHIP ADVANCES IN AN HOUR.

The ancients used various devices to ascertain the distance gone by
a ship each hour, among which Vitruvius [Footnote 6: See VITRUVIUS,
_De Architectura lib. X._ C. 14 (p. 264 in the edition of Rose and
Muller- Strubing). The German edition published at Bale in 1543 has,
on fol. 596, an illustration of the contrivance, as described by
Vitruvius.] gives one in his work on Architecture which is just as
fallacious as all the others; and this is a mill wheel which touches
the waves of the sea at one end and in each complete revolution
describes a straight line which represents the circumference of the
wheel extended to a straightness. But this invention is of no worth
excepting on the smooth and motionless surface of lakes. But if the
water moves together with the ship at an equal rate, then the wheel
remains motionless; and if the motion of the water is more or less
rapid than that of the ship, then neither has the wheel the same
motion as the ship so that this invention is of but little use.
There is another method tried by experiment with a known distance
between one island and another; and this is done by a board or under
the pressure of wind which strikes on it with more or less
swiftness. This is in Battista Alberti [Footnote 25: LEON BATTISTA
ALBERTI, _De Architectura lib. V._, c. 12 treats '_de le navi e
parti loro_', but there is no reference to the machine, mentioned by
Leonardo. Alberti says here: _Noi abbiamo trattato lungamente in
altro luogo de' modi de le navi, ma in questo luogo ne abbiamo detto
quel tanto che si bisogna_. To this the following note is added in
the most recent Italian edition: _Questo libro e tuttora inedito e
porta il titolo, secondo Gesnero di_ '_Liber navis_'.].

Battista Alberti's method which is made by experiment on a known
distance between one island and another. But such an invention does
not succeed excepting on a ship like the one on which the experiment
was made, and it must be of the same burden and have the same sails,
and the sails in the same places, and the size of the waves must be
the same. But my method will serve for any ship, whether with oars
or sails; and whether it be small or large, broad or long, or high
or low, it always serves [Footnote 52: Leonardo does not reveal the
method invented by him.].

Methods of staying and moving in water

1114.

How an army ought to cross rivers by swimming with air-bags ... How
fishes swim [Footnote 2: Compare No. 821.]; of the way in which they
jump out of the water, as may be seen with dolphins; and it seems a
wonderful thing to make a leap from a thing which does not resist
but slips away. Of the swimming of animals of a long form, such as
eels and the like. Of the mode of swimming against currents and in
the rapid falls of rivers. Of the mode of swimming of fishes of a
round form. How it is that animals which have not long hind quartres
cannot swim. How it is that all other animals which have feet with
toes, know by nature how to swim, excepting man. In what way man
ought to learn to swim. Of the way in which man may rest on the
water. How man may protect himself against whirlpools or eddies in
the water, which drag him down. How a man dragged to the bottom must
seek the reflux which will throw him up from the depths. How he
ought to move his arms. How to swim on his back. How he can and how
he cannot stay under water unless he can hold his breath [13]. How
by means of a certain machine many people may stay some time under
water. How and why I do not describe my method of remaining under
water, or how long I can stay without eating; and I do not publish
nor divulge these by reason of the evil nature of men who would use
them as means of destruction at the bottom of the sea, by sending
ships to the bottom, and sinking them together with the men in them.
And although I will impart others, there is no danger in them;
because the mouth of the tube, by which you breathe, is above the
water supported on bags or corks [19].

[Footnote: L. 13-19 will also be found in Vol. I No. 1.]

On naval warfare (1115. 1116).

1115.

Supposing in a battle between ships and galleys that the ships are
victorious by reason of the high of heir tops, you must haul the
yard up almost to the top of the mast, and at the extremity of the
yard, that is the end which is turned towards the enemy, have a
small cage fastened, wrapped up below and all round in a great
mattress full of cotton so that it may not be injured by the bombs;
then, with the capstan, haul down the opposite end of this yard and
the top on the opposite side will go up so high, that it will be far
above the round-top of the ship, and you will easily drive out the
men that are in it. But it is necessary that the men who are in the
galley should go to the opposite side of it so as to afford a
counterpoise to the weight of the men placed inside the cage on the
yard.

1116.

If you want to build an armada for the sea employ these ships to ram
in the enemy's ships. That is, make ships 100 feet long and 8 feet
wide, but arranged so that the left hand rowers may have their oars
to the right side of the ship, and the right hand ones to the left
side, as is shown at M, so that the leverage of the oars may be
longer. And the said ship may be one foot and a half thick, that is
made with cross beams within and without, with planks in contrary
directions. And this ship must have attached to it, a foot below the
water, an iron-shod spike of about the weight and size of an anvil;
and this, by force of oars may, after it has given the first blow,
be drawn back, and driven forward again with fury give a second
blow, and then a third, and so many as to destroy the other ship.

The use of swimming belts.

1117.

A METHOD OF ESCAPING IN A TEMPEST AND SHIPWRECK AT SEA.

Have a coat made of leather, which must be double across the breast,
that is having a hem on each side of about a finger breadth. Thus it
will be double from the waist to the knee; and the leather must be
quite air-tight. When you want to leap into the sea, blow out the
skirt of your coat through the double hems of the breast; and jump
into the sea, and allow yourself to be carried by the waves; when
you see no shore near, give your attention to the sea you are in,
and always keep in your mouth the air-tube which leads down into the
coat; and if now and again you require to take a breath of fresh
air, and the foam prevents you, you may draw a breath of the air
within the coat.

[Footnote: AMORETTI, _Memorie Storiche_, Tav. II. B. Fig. 5, gives
the same figure, somewhat altered. 6. _La canna dell' aria_. Compare
Vol. I. No. I. Note]

On the gravity of water.

1118.

If the weight of the sea bears on its bottom, a man, lying on that
bottom and having l000 braccia of water on his back, would have
enough to crush him.

Diving apparatus and Skating (1119-1121).

1119.

Of walking under water. Method of walking on water.

[Footnote: The two sketches belonging to this passage are given by
AMORETTI, _Memorie Storiche_. Tav. II, Fig. 3 and 4.]

1120.

Just as on a frozen river a man may run without moving his feet, so
a car might be made that would slide by itself.

[Footnote: The drawings of carts by the side of this text have no
direct connection with the problem as stated in words.--Compare No.
1448, l. 17.]

1121.

A definition as to why a man who slides on ice does not fall.
[Footnote: An indistinct sketch accompanies the passage, in the
original.]

On Flying machines (1122-1126).

1122.

Man when flying must stand free from the waist upwards so as to be
able to balance himself as he does in a boat so that the centre of
gravity in himself and in the machine may counterbalance each other,
and be shifted as necessity demands for the changes of its centre of
resistance.

1123.

Remember that your flying machine must imitate no other than the
bat, because the web is what by its union gives the armour, or
strength to the wings.

If you imitate the wings of feathered birds, you will find a much
stronger structure, because they are pervious; that is, their
feathers are separate and the air passes through them. But the bat
is aided by the web that connects the whole and is not pervious.

1124.

TO ESCAPE THE PERIL OF DESTRUCTION.

Destruction to such a machine may occur in two ways; of which the
first is the breaking of the machine. The second would be when the
machine should turn on its edge or nearly on its edge, because it
ought always to descend in a highly oblique direction, and almost
exactly balanced on its centre. As regards the first--the breaking
of the machine--, that may be prevented by making it as strong as
possible; and in whichever direction it may tend to turn over, one
centre must be very far from the other; that is, in a machine 30
braccia long the centres must be 4 braccia one from the other.

[Footnote: Compare No. 1428.]

1125.

Bags by which a man falling from a height of 6 braccia may avoid
hurting himself, by a fall whether into water or on the ground; and
these bags, strung together like a rosary, are to be fixed on one's
back.

1126.

An object offers as much resistance to the air as the air does to
the object. You may see that the beating of its wings against the
air supports a heavy eagle in the highest and rarest atmosphere,
close to the sphere of elemental fire. Again you may see the air in
motion over the sea, fill the swelling sails and drive heavily laden
ships. From these instances, and the reasons given, a man with wings
large enough and duly connected might learn to overcome the
resistance of the air, and by conquering it, succeed in subjugating
it and rising above it. [Footnote: A parachute is here sketched,
with an explanatory remark. It is reproduced on Tav. XVI in the
Saggio, and in: _Leonardo da Vinci als Ingenieur etc., Ein Beitrag
zur Geschichte der Technik und der induktiven Wissenschaften, von
Dr. Hermann Grothe, Berlin_ 1874, p. 50.]

Of mining.

1127.

If you want to know where a mine runs, place a drum over all the
places where you suspect that it is being made, and upon this drum
put a couple of dice, and when you are over the spot where they are
mining, the dice will jump a little on the drum at every blow which
is given underground in the mining.

There are persons who, having the convenience of a river or a lake
in their lands, have made, close to the place where they suspect
that a mine is being made, a great reservoir of water, and have
countermined the enemy, and having found them, have turned the water
upon them and destroyed a great number in the mine.

Of Greek fire.

1128.

GREEK FIRE.

Take charcoal of willow, and saltpetre, and sulphuric acid, and
sulphur, and pitch, with frankincense and camphor, and Ethiopian
wool, and boil them all together. This fire is so ready to burn that
it clings to the timbers even under water. And add to this
composition liquid varnish, and bituminous oil, and turpentine and
strong vinegar, and mix all together and dry it in the sun, or in an
oven when the bread is taken out; and then stick it round hempen or
other tow, moulding it into a round form, and studding it all over
with very sharp nails. You must leave in this ball an opening to
serve as a fusee, and cover it with rosin and sulphur.

Again, this fire, stuck at the top of a long plank which has one
braccio length of the end pointed with iron that it may not be burnt
by the said fire, is good for avoiding and keeping off the ships, so
as not to be overwhelmed by their onset.

Again throw vessels of glass full of pitch on to the enemy's ships
when the men in them are intent on the battle; and then by throwing
similar burning balls upon them you have it in your power to burn
all their ships.

[Footnote: Venturi has given another short text about the Greek fire
in a French translation (Essai Section XIV). He adds that the
original text is to be found in MS. B. 30 (?). Libri speaks of it in
a note as follows (_Histoire des sciences mathematiques en Italie
Vol. II_ p. 129): _La composition du feu gregeois est une des chases
qui ont ete les plus cherchees et qui sont encore les plus
douteuses. On dit qu'il fut invente au septieme siecle de l'ere
chretienne par l'architecte Callinique (Constantini Porphyrogenetae
opera, Lugd. Batav._ 1617,-- _in-_8vo; p. 172, _de admin, imper.
exp._ 48_), et il se trouve souvent mentionne par les Historiens
Byzantins. Tantot on le langait avec des machines, comme on
lancerait une banche, tantot on le soufflait avec de longs tubes,
comme on soufflerait un gaz ou un liquide enflamme (Annae Comnenae
Alexias_, p. 335, _lib. XI.--Aeliani et Leonis, imperatoris tactica,
Lugd.-Bat._ 1613, _in_-4. part. 2 a, p. 322, _Leonis tact. cap._
l9.--_Joinville, histoire du Saint Louis collect. Petitot tom. II,_
p. 235). _Les ecrivains contemporains disent que l'eau ne pouvait
pas eteindre ce feu, mais qu'avec du vinaigre et du sable on y
parvenait. Suivant quelques historiens le feu gregeois etait compose
de soufre et de resine. Marcus Graecus (Liber ignium, Paris,_ 1804,
_in_-40_) donne plusieurs manieres de le faire qui ne sont pas tres
intelligibles, mais parmi lesquelles on trouve la composition de la
poudre a canon. Leonard de Vinci (MSS. de Leonard de Vinci, vol. B.
f. 30,) dit qu'on le faisait avec du charbon de saule, du salpetre,
de l'eau de vie, de la resine, du soufre, de la poix et du camphre.
Mais il est probable que nous ne savons pas qu'elle etait sa
composition, surtout a cause du secret qu'en faisaient les Grecs. En
effet, l'empereur Constantin Porphyrogenete recommende a son fils de
ne jamais en donner aux Barbares, et de leur repondre, s'ils en
demandaient, qu'il avait ete apporti du ciel par un ange et que le
secret en avait ete confie aux Chretiens (Constantini
Porphyrogennetae opera,_ p. 26-27, _de admin. imper., cap. _12_)._]

Of Music (1129. 1130).

1129.

A drum with cogs working by wheels with springs [2].

[Footnote: This chapter consists of explanations of the sketches
shown on Pl. CXXI. Lines 1 and 2 of the text are to be seen at the
top at the left hand side of the first sketch of a drum. Lines 3-5
refer to the sketch immediately below this. Line 6 is written as the
side of the seventh sketch, and lines 7 and 8 at the side of the
eighth. Lines 9-16 are at the bottom in the middle. The remainder of
the text is at the side of the drawing at the bottom.]

A square drum of which the parchment may be drawn tight or slackened
by the lever _a b_ [5].

A drum for harmony [6].

[7] A clapper for harmony; that is, three clappers together.

[9] Just as one and the same drum makes a deep or acute sound
according as the parchments are more or less tightened, so these
parchments variously tightened on one and the same drum will make
various sounds [16].

Keys narrow and close together; (bicchi) far apart; these will be
right for the trumpet shown above.

_a_ must enter in the place of the ordinary keys which have the ...
in the openings of a flute.

1130.

Tymbals to be played like the monochord, or the soft flute.

[6] Here there is to be a cylinder of cane after the manner of
clappers with a musical round called a Canon, which is sung in four
parts; each singer singing the whole round. Therefore I here make a
wheel with 4 teeth so that each tooth takes by itself the part of a
singer.

[Footnote: In the original there are some more sketches, to which
the text, from line 6, refers. They are studies for a contrivance
exactly like the cylinder in our musical boxes.]

1131.

Of decorations.

White and sky-blue cloths, woven in checks to make a decoration.

Cloths with the threads drawn at _a b c d e f g h i k_, to go round
the decoration.

_XIX._

_Philosophical Maxims. Morals. Polemics and Speculations_.

_Vasari indulges in severe strictures on Leonardo's religious views.
He speaks, among other things, of his_ "capricci nel filosofar delle
cose naturali" _and says on this point:_ "Per il che fece nell'animo
un concetto si eretico che e' non si accostava a qualsi voglia
religione, stimando per avventura assai piu lo esser filosofo che
cristiano" _(see the first edition of_ 'Le Vite'_). But this
accusation on the part of a writer in the days of the Inquisition is
not a very serious one--and the less so, since, throughout the
manuscripts, we find nothing to support it._

_Under the heading of "Philosophical Maxims" I have collected all
the passages which can give us a clear comprehension of Leonardo's
ideas of the world at large. It is scarcely necessary to observe
that there is absolutely nothing in them to lead to the inference
that he was an atheist. His views of nature and its laws are no
doubt very unlike those of his contemporaries, and have a much
closer affinity to those which find general acceptance at the
present day. On the other hand, it is obvious from Leonardo's will
(see No._ 1566_) that, in the year before his death, he had
professed to adhere to the fundamental doctrines of the Roman
Catholic faith, and this evidently from his own personal desire and
impulse._

_The incredible and demonstrably fictitious legend of Leonardo's
death in the arms of Francis the First, is given, with others, by
Vasari and further embellished by this odious comment:_ "Mostrava
tuttavia quanto avea offeso Dio e gli uomini del mondo, non avendo
operato nell'arte come si conveniva." _This last accusation, it may
be remarked, is above all evidence of the superficial character of
the information which Vasari was in a position to give about
Leonardo. It seems to imply that Leonardo was disdainful of diligent
labour. With regard to the second, referring to Leonardo's morality
and dealings with his fellow men, Vasari himself nullifies it by
asserting the very contrary in several passages. A further
refutation may be found in the following sentence from the letter in
which Melsi, the young Milanese nobleman, announces the Master's
death to Leonardo's brothers:_ Credo siate certificati della morte
di Maestro Lionardo fratello vostro, e mio quanto optimo padre, per
la cui morte sarebbe impossibile che io potesse esprimere il dolore
che io ho preso; e in mentre che queste mia membra si sosterranno
insieme, io possedero una perpetua infelicita, e meritamente perche
sviscerato et ardentissimo amore mi portava giornalmente. E dolto ad
ognuno la perdita di tal uomo, quale non e piu in podesta della
natura, ecc.

_It is true that, in April_ 1476, _we find the names of Leonardo and
Verrocchio entered in the_ "Libro degli Uffiziali di notte e de'
Monasteri" _as breaking the laws; but we immediately after find the
note_ "Absoluti cum condizione ut retamburentur" (Tamburini _was the
name given to the warrant cases of the night police). The acquittal
therefore did not exclude the possibility of a repetition of the
charge. It was in fact repeated, two months later, and on this
occasion the Master and his pupil were again fully acquitted.
Verrocchio was at this time forty and Leonardo four-and-twenty. The
documents referring to this affair are in the State Archives of
Florence; they have been withheld from publication, but it seemed to
me desirable to give the reader this brief account of the leading
facts of the story, as the vague hints of it, which have recently
been made public, may have given to the incident an aspect which it
had not in reality, and which it does not deserve._

_The passages here classed under the head "Morals" reveal Leonardo
to us as a man whose life and conduct were unfailingly governed by
lofty principles and aims. He could scarcely have recorded his stern
reprobation and unmeasured contempt for men who do nothing useful
and strive only for riches, if his own life and ambitions had been
such as they have so often been misrepresented._

_At a period like that, when superstition still exercised unlimited
dominion over the minds not merely of the illiterate crowd, but of
the cultivated and learned classes, it was very natural that
Leonardo's views as to Alchemy, Ghosts, Magicians, and the like
should be met with stern reprobation whenever and wherever he may
have expressed them; this accounts for the argumentative tone of all
his utterances on such subjects which I have collected in
Subdivision III of this section. To these I have added some passages
which throw light on Leonardo's personal views on the Universe. They
are, without exception, characterised by a broad spirit of
naturalism of which the principles are more strictly applied in his
essays on Astronomy, and still more on Physical Geography._

_To avoid repetition, only such notes on Philosophy, Morals and
Polemics, have been included in this section as occur as independent
texts in the original MSS. Several moral reflections have already
been given in Vol. I, in section "Allegorical representations,
Mottoes and Emblems". Others will be found in the following section.
Nos._ 9 _to_ 12, _Vol. I, are also passages of an argumentative
character. It did not seem requisite to repeat here these and
similar passages, since their direct connection with the context is
far closer in places where they have appeared already, than it would
be here._

I.

PHILOSOPHICAL MAXIMS.

Prayers to God (1132. 1133).

1132.

I obey Thee Lord, first for the love I ought, in all reason to bear
Thee; secondly for that Thou canst shorten or prolong the lives of
men.

1133.

A PRAYER.

Thou, O God, dost sell us all good things at the price of labour.

The powers of Nature (1134-1139).

1134.

O admirable impartiality of Thine, Thou first Mover; Thou hast not
permitted that any force should fail of the order or quality of its
necessary results.

1135.

Necessity is the mistress and guide of nature.

Necessity is the theme and the inventress, the eternal curb and law
of nature.

1136.

In many cases one and the same thing is attracted by two strong
forces, namely Necessity and Potency. Water falls in rain; the earth
absorbs it from the necessity for moisture; and the sun evaporates
it, not from necessity, but by its power.

1137.

Weight, force and casual impulse, together with resistance, are the
four external powers in which all the visible actions of mortals
have their being and their end.

1138.

Our body is dependant on heaven and heaven on the Spirit.

1139.

The motive power is the cause of all life.

Psychology (1140-1147).

1140.

And you, O Man, who will discern in this work of mine the wonderful
works of Nature, if you think it would be a criminal thing to
destroy it, reflect how much more criminal it is to take the life of
a man; and if this, his external form, appears to thee marvellously
constructed, remember that it is nothing as compared with the soul
that dwells in that structure; for that indeed, be it what it may,
is a thing divine. Leave it then to dwell in His work at His good
will and pleasure, and let not your rage or malice destroy a
life--for indeed, he who does not value it, does not himself deserve
it [Footnote 19: In MS. II 15a is the note: _chi no stima la vita,
non la merita._].

[Footnote: This text is on the back of the drawings reproduced on
Pl. CVII. Compare No. 798, 35 note on p. 111: Compare also No. 837
and 838.]

1141.

The soul can never be corrupted with the corruption of the body,,
but is in the body as it were the air which causes the sound of the
organ, where when a pipe bursts, the wind would cease to have any
good effect. [Footnote: Compare No. 845.]

1142.

The part always has a tendency to reunite with its whole in order to
escape from its imperfection.

The spirit desires to remain with its body, because, without the
organic instruments of that body, it can neither act, nor feel
anything.

1143.

If any one wishes to see how the soul dwells in its body, let him
observe how this body uses its daily habitation; that is to say, if
this is devoid of order and confused, the body will be kept in
disorder and confusion by its soul.

1144.

Why does the eye see a thing more clearly in dreams than with the
imagination being awake?

1145.

The senses are of the earth; Reason, stands apart in contemplation.

[Footnote: Compare No. 842.]

1146.

Every action needs to be prompted by a motive.

To know and to will are two operations of the human mind.

Discerning, judging, deliberating are acts of the human mind.

1147.

All our knowledge has its origin in our preceptions.

Science, its principles and rules (1148--1161)

1148.

Science is the observation of things possible, whether present or
past; prescience is the knowledge of things which may come to pass,
though but slowly.

1149.

Experience, the interpreter between formative nature and the human
race, teaches how that nature acts among mortals; and being
constrained by necessity cannot act otherwise than as reason, which
is its helm, requires her to act.

1150.

Wisdom is the daughter of experience.

1151.

Nature is full of infinite causes that have never occured in
experience.

1152.

Truth was the only daughter of Time.

1153.

Experience never errs; it is only your judgments that err by
promising themselves effects such as are not caused by your
experiments.

Experience does not err; only your judgments err by expecting from
her what is not in her power. Men wrongly complain of Experience;
with great abuse they accuse her of leading them astray but they set
Experience aside, turning from it with complaints as to our
ignorance causing us to be carried away by vain and foolish desires
to promise ourselves, in her name, things that are not in her power;
saying that she is fallacious. Men are unjust in complaining of
innocent Experience, constantly accusing her of error and of false
evidence.

1154.

Instrumental or mechanical science is of all the noblest and the
most useful, seeing that by means of this all animated bodies that
have movement perform all their actions; and these movements are
based on the centre of gravity which is placed in the middle
dividing unequal weights, and it has dearth and wealth of muscles
and also lever and counterlever.

1155.

OF MECHANICS.

Mechanics are the Paradise of mathematical science, because here we
come to the fruits of mathematics. [Footnote: Compare No. 660, 11.
19--22 (Vol. I., p. 332). 1156.

Every instrument requires to be made by experience.

1157.

The man who blames the supreme certainty of mathematics feeds on
confusion, and can never silence the contradictions of sophistical
sciences which lead to an eternal quackery.

1158.

There is no certainty in sciences where one of the mathematical
sciences cannot be applied, or which are not in relation with these
mathematics.

1159.

Any one who in discussion relies upon authority uses, not his
understanding, but rather his memory. Good culture is born of a good
disposition; and since the cause is more to be praised than the
effect, I will rather praise a good disposition without culture,
than good culture without the disposition.

1160.

Science is the captain, and practice the soldiers.

1161.

OF THE ERRORS OF THOSE WHO DEPEND ON PRACTICE WITHOUT SCIENCE.

Those who fall in love with practice without science are like a
sailor who enters a ship without a helm or a compass, and who never
can be certain whither he is going.

II.

MORALS.

What is life? (1162. 1163).

1162.

Now you see that the hope and the desire of returning home and to
one's former state is like the moth to the light, and that the man
who with constant longing awaits with joy each new spring time, each
new summer, each new month and new year--deeming that the things he
longs for are ever too late in coming--does not perceive that he is
longing for his own destruction. But this desire is the very
quintessence, the spirit of the elements, which finding itself
imprisoned with the soul is ever longing to return from the human
body to its giver. And you must know that this same longing is that
quintessence, inseparable from nature, and that man is the image of
the world.

1163.

O Time! consumer of all things; O envious age! thou dost destroy all
things and devour all things with the relentless teeth of years,
little by little in a slow death. Helen, when she looked in her
mirror, seeing the withered wrinkles made in her face by old age,
wept and wondered why she had twice been carried away.

O Time! consumer of all things, and O envious age! by which all
things are all devoured.

Death.

1164.

Every evil leaves behind a grief in our memory, except the supreme
evil, that is death, which destroys this memory together with life.

How to spend life (1165-1170).

1165.

0 sleepers! what a thing is slumber! Sleep resembles death. Ah, why
then dost thou not work in such wise as that after death thou mayst
retain a resemblance to perfect life, when, during life, thou art in
sleep so like to the hapless dead? [Footnote: Compare No. 676, Vol.
I. p. 353.]

1166.

One pushes down the other.

By these square-blocks are meant the life and the studies of men.

1167.

The knowledge of past times and of the places on the earth is both
an ornament and nutriment to the human mind.

1168.

To lie is so vile, that even if it were in speaking well of godly
things it would take off something from God's grace; and Truth is so
excellent, that if it praises but small things they become noble.

Beyond a doubt truth bears the same relation to falsehood as light
to darkness; and this truth is in itself so excellent that, even
when it dwells on humble and lowly matters, it is still infinitely
above uncertainty and lies, disguised in high and lofty discourses;
because in our minds, even if lying should be their fifth element,
this does not prevent that the truth of things is the chief
nutriment of superior intellects, though not of wandering wits.

But you who live in dreams are better pleased by the sophistical
reasons and frauds of wits in great and uncertain things, than by
those reasons which are certain and natural and not so far above us.

1169.

Avoid studies of which the result dies with the worker.

1170.

Men are in error when they lament the flight of time, accusing it of
being too swift, and not perceiving that it is sufficient as it
passes; but good memory, with which nature has endowed us, causes
things long past to seem present.

1171.

Learning acquired in youth arrests the evil of old age; and if you
understand that old age has wisdom for its food, you will so conduct
yourself in youth that your old age will not lack for nourishment.

1172.

The acquisition of any knowledge is always of use to the intellect,
because it may thus drive out useless things and retain the good.

For nothing can be loved or hated unless it is first known.

1173.

As a day well spent procures a happy sleep, so a life well employed
procures a happy death.

1174.

The water you touch in a river is the last of that which has passed,
and the first of that which is coming. Thus it is with time present.

Life if well spent, is long.

1175.

Just as food eaten without caring for it is turned into loathsome
nourishment, so study without a taste for it spoils memory, by
retaining nothing which it has taken in.

1176.

Just as eating against one's will is injurious to health, so study
without a liking for it spoils the memory, and it retains nothing it
takes in.

1177.

On Mount Etna the words freeze in your mouth and you may make ice of
them.[Footnote 2: There is no clue to explain this strange
sentence.]

Just as iron rusts unless it is used, and water putrifies or, in
cold, turns to ice, so our intellect spoils unless it is kept in
use.

You do ill if you praise, and still worse if you reprove in a matter
you do not understand.

When Fortune comes, seize her in front with a sure hand, because
behind she is bald.

1178.

It seems to me that men of coarse and clumsy habits and of small
knowledge do not deserve such fine instruments nor so great a
variety of natural mechanism as men of speculation and of great
knowledge; but merely a sack in which their food may be stowed and
whence it may issue, since they cannot be judged to be any thing
else than vehicles for food; for it seems to me they have nothing
about them of the human species but the voice and the figure, and
for all the rest are much below beasts.

1179.

Some there are who are nothing else than a passage for food and
augmentors of excrement and fillers of privies, because through them
no other things in the world, nor any good effects are produced,
since nothing but full privies results from them.

On foolishness and ignorance (1180--1182).

1180.

The greatest deception men suffer is from their own opinions.

1181.

Folly is the shield of shame, as unreadiness is that of poverty
glorified.

1182.

Blind ignorance misleads us thus and delights with the results of
lascivious joys.

Because it does not know the true light. Because it does not know
what is the true light.

Vain splendour takes from us the power of being .... behold! for its
vain splendour we go into the fire, thus blind ignorance does
mislead us. That is, blind ignorance so misleads us that ...

O! wretched mortals, open your eyes.

On riches (1183--1187).

1183.

That is not riches, which may be lost; virtue is our true good and
the true reward of its possessor. That cannot be lost; that never
deserts us, but when life leaves us. As to property and external
riches, hold them with trembling; they often leave their possessor
in contempt, and mocked at for having lost them.

1184.

Every man wishes to make money to give it to the doctors, destroyers
of life; they then ought to be rich. [Footnote 2: Compare No. 856.]

Man has much power of discourse which for the most part is vain and
false; animals have but little, but it is useful and true, and a
small truth is better than a great lie.

1185.

He who possesses most must be most afraid of loss.

1186.

He who wishes to be rich in a day will be hanged in a year.

1187.

That man is of supreme folly who always wants for fear of wanting;
and his life flies away while he is still hoping to enjoy the good
things which he has with extreme labour acquired.

Rules of Life (1188-1202).

1188.

If you governed your body by the rules of virtue you would not walk
on all fours in this world.

You grow in reputation like bread in the hands of a child.
[Footnote: The first sentence is obscure. Compare Nos. 825, 826.]

1189.

Savage he is who saves himself.

1190.