The Notebooks of Leonardo Da Vinci (24 page)

[32] The higher the step is which a man has to mount, the farther
forward will he place his head in advance of his upper foot, so as
to weigh more on
a
than on
b
; this man will not be on the step
m
. As is shown by the line
g f
.

[Footnote: See Pl. XXIII, No. 1. The lower sketch to the left
belongs to the four first lines.]

376.

I ask the weight [pressure] of this man at every degree of motion on
these steps, what weight he gives to
b
and to
c
.

[Footnote 8: These lines are, in the original, written in ink]
Observe the perpendicular line below the centre of gravity of the
man.

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

377.

In going up stairs if you place your hands on your knees all the
labour taken by the arms is removed from the sinews at the back of
the knees.

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

378.

The sinew which guides the leg, and which is connected with the
patella of the knee, feels it a greater labour to carry the man
upwards, in proportion as the leg is more bent; and the muscle which
acts upon the angle made by the thigh where it joins the body has
less difficulty and has a less weight to lift, because it has not
the [additional] weight of the thigh itself. And besides this it has
stronger muscles, being those which form the buttock.

379.

A man coming down hill takes little steps, because the weight rests
upon the hinder foot, while a man mounting takes wide steps, because
his weight rests on the foremost foot.

[Footnote: See Pl. XXIII, No. 4.]

On the human body in action (380-388).

380.

When you want to represent a man as moving some weight consider what
the movements are that are to be represented by different lines;
that is to say either from below upwards, with a simple movement, as
a man does who stoops forward to take up a weight which he will lift
as he straightens himself. Or as a man does who wants to squash
something backwards, or to force it forwards or to pull it downwards
with ropes passed through pullies [Footnote 10: Compare the sketch
on page 198 and on 201 (S. K. M. II.1 86b).]. And here remember that
the weight of a man pulls in proportion as his centre of gravity is
distant from his fulcrum, and to this is added the force given by
his legs and bent back as he raises himself.

381.

Again, a man has even a greater store of strength in his legs than
he needs for his own weight; and to see if this is true, make a man
stand on the shore-sand and then put another man on his back, and
you will see how much he will sink in. Then take the man from off
his back and make him jump straight up as high as he can, and you
will find that the print of his feet will be made deeper by the jump
than from having the man on his back. Hence, here, by 2 methods it
is proved that a man has double the strength he requires to support
his own body.

382.

If you have to draw a man who is in motion, or lifting or pulling,
or carrying a weight equal to his own, in what way must you set on
his legs below his body?

[Footnote: In the MS. this question remains unanswered.]

383.

A man pulling a [dead] weight balanced against himself cannot pull
more than his own weight. And if he has to raise it he will [be able
to] raise as much more than his weight as his strength may be more
than that of other men. [Footnote 7: The stroke at the end of this
line finishes in the original in a sort of loop or flourish, and a
similar flourish occurs at the end of the previous passage written
on the same page. M. RAVAISSON regards these as numbers (compare the
photograph of page 30b in his edition of MS. A). He remarks: "
Ce
chiffre
8
et, a la fin de l'alinea precedent, le chiffre
7
sont,
dans le manuscrit, des renvois
."] The greatest force a man can
apply, with equal velocity and impetus, will be when he sets his
feet on one end of the balance [or lever] and then presses his
shoulders against some stable body. This will raise a weight at the
other end of the balance [lever], equal to his own weight and [added
to that] as much weight as he can carry on his shoulders.

384.

No animal can simply move [by its dead weight] a greater weight than
the sum of its own weight outside the centre of his fulcrum.

385.

A man who wants to send an arrow very far from the bow must be
standing entirely on one foot and raising the other so far from the
foot he stands on as to afford the requisite counterpoise to his
body which is thrown on the front foot. And he must not hold his arm
fully extended, and in order that he may be more able to bear the
strain he must hold a piece of wood which there is in all crossbows,
extending from the hand to the breast, and when he wishes to shoot
he suddenly leaps forward at the same instant and extends his arm
with the bow and releases the string. And if he dexterously does
every thing at once it will go a very long way.

386.

When two men are at the opposite ends of a plank that is balanced,
and if they are of equal weight, and if one of them wants to make a
leap into the air, then his leap will be made down from his end of
the plank and the man will never go up again but must remain in his
place till the man at the other end dashes up the board.

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

387.

Of delivering a blow to the right or left.

[Footnote: Four sketches on Pl. XXIV, No. 1 belong to this passage.
The rest of the sketches and notes on that page are of a
miscellaneous nature.]

388.

Why an impetus is not spent at once [but diminishes] gradually in
some one direction? [Footnote 1: The paper has been damaged at the
end of line 1.] The impetus acquired in the line
a b c d
is spent
in the line
d e
but not so completely but that some of its force
remains in it and to this force is added the momentum in the line
d
e
with the force of the motive power, and it must follow than the
impetus multiplied by the blow is greater that the simple impetus
produced by the momentum
d e
.

[Footnote 8: The sketch No. 2 on Pl. XXIV stands, in the original,
between lines 7 and 8. Compare also the sketches on Pl. LIV.] A man
who has to deal a great blow with his weapon prepares himself with
all his force on the opposite side to that where the spot is which
he is to hit; and this is because a body as it gains in velocity
gains in force against the object which impedes its motion.

On hair falling down in curls.

389.

Observe the motion of the surface of the water which resembles that
of hair, and has two motions, of which one goes on with the flow of
the surface, the other forms the lines of the eddies; thus the water
forms eddying whirlpools one part of which are due to the impetus of
the principal current and the other to the incidental motion and
return flow.

[Footnote: See Pl. XXV. Where also the text of this passage is given
in facsimile.]

On draperies (390—392).

390.

That part of a fold which is farthest from the ends where it is
confined will fall most nearly in its natural form.

Every thing by nature tends to remain at rest. Drapery, being of
equal density and thickness on its wrong side and on its right, has
a tendency to lie flat; therefore when you give it a fold or plait
forcing it out of its flatness note well the result of the
constraint in the part where it is most confined; and the part which
is farthest from this constraint you will see relapses most into the
natural state; that is to say lies free and flowing.

[Footnote 13:
a c sia
. In the original text
b
is written instead
of
c
—an evident slip of the pen.] Let
a b c
be the fold of the
drapery spoken of above,
a c
will be the places where this folded
drapery is held fast. I maintain that the part of the drapery which
is farthest from the plaited ends will revert most to its natural
form.

Therefore,
b
being farthest from
a
and
c
in the fold
a b c
it will be wider there than anywhere else.

[Footnote: See Pl. XXVIII, No. 6, and compare the drawing from
Windsor Pl. XXX for farther illustration of what is here stated.]

391.

How figures dressed in a cloak should not show the shape so much as
that the cloak looks as if it were next the flesh; since you surely
cannot wish the cloak to be next the flesh, for you must suppose
that between the flesh and the cloak there are other garments which
prevent the forms of the limbs appearing distinctly through the
cloak. And those limbs which you allow to be seen you must make
thicker so that the other garments may appear to be under the cloak.
But only give something of the true thickness of the limbs to a
nymph [Footnote 9:
Una nifa
. Compare the beautiful drawing of a
Nymph, in black chalk from the Windsor collection, Pl. XXVI.] or an
angel, which are represented in thin draperies, pressed and clinging
to the limbs of the figures by the action of the wind.

392.

You ought not to give to drapery a great confusion of many folds,
but rather only introduce them where they are held by the hands or
the arms; the rest you may let fall simply where it is its nature to
flow; and do not let the nude forms be broken by too many details
and interrupted folds. How draperies should be drawn from nature:
that is to say if youwant to represent woollen cloth draw the folds
from that; and if it is to be silk, or fine cloth or coarse, or of
linen or of crape, vary the folds in each and do not represent
dresses, as many do, from models covered with paper or thin leather
which will deceive you greatly.

[Footnote: The little pen and ink drawing from Windsor (W. 102),
given on Pl. XXVIII, No. 7, clearly illustrates the statement made
at the beginning of this passage; the writing of the cipher 19 on
the same page is in Leonardo's hand; the cipher 21 is certainly
not.]

Botany for Painters and Elements of Landscape Painting.

The chapters composing this portion of the work consist of
observations on Form, Light and Shade in Plants, and particularly in
Trees summed up in certain general rules by which the author intends
to guide the artist in the pictorial representation of landscape.

With these the first principles of a
Theory of Landscape painting
are laid down—a theory as profoundly thought out in its main
lines as it is lucidly worked out in its details. In reading these
chapters the conviction is irresistible that such a
Botany for
painters
is or ought to be of similar importance in the practice of
painting as the principles of the Proportions and Movements of the
human figure
i. e. Anatomy for painters.

There can be no doubt that Leonardo, in laying down these rules,
did not intend to write on Botany in the proper scientific
sense—his own researches on that subject have no place here; it
need only be observed that they are easily distinguished by their
character and contents from those which are here collected and
arranged under the title 'Botany for painters'. In some cases where
this division might appear doubtful,—as for instance in No.
402—
the Painter is directly addressed and enjoined to take the
rule to heart as of special importance in his art.

The original materials are principally derived from MS.
G,
in
which we often find this subject treated on several pages in
succession without any of that intermixture of other matters, which
is so frequent in Leonardo's writings. This MS., too, is one of the
latest; when it was written, the great painter was already more than
sixty years of age, so we can scarcely doubt that he regarded all he
wrote as his final views on the subject. And the same remark applies
to the chapters from MSS.
E
and
M
which were also written
between
1513—15.

For the sake of clearness, however, it has been desirable to
sacrifice—with few exceptions—the original order of the passages
as written, though it was with much reluctance and only after long
hesitation that I resigned myself to this necessity. Nor do I mean
to impugn the logical connection of the author's ideas in his MS.;
but it will be easily understood that the sequence of disconnected
notes, as they occurred to Leonardo and were written down from time
to time, might be hardly satisfactory as a systematic arrangement of
his principles. The reader will find in the Appendix an exact
account of the order of the chapters in the original MS. and from
the data there given can restore them at will. As the materials are
here arranged, the structure of the tree as regards the growth of
the branches comes first
(394-411)
and then the insertion of the
leaves on the stems
(412-419).
Then follow the laws of Light and
Shade as applied, first, to the leaves (420-434), and, secondly, to
the whole tree and to groups of trees
(435-457).
After the remarks
on the Light and Shade in landscapes generally
(458-464),
we find
special observations on that of views of towns and buildings
(465-469).
To the theory of Landscape Painting belong also the
passages on the effect of Wind on Trees
(470-473)
and on the Light
and Shade of Clouds
(474-477),
since we find in these certain
comparisons with the effect of Light and Shade on Trees
(e. g.:
in
No.
476, 4. 5;
and No.
477, 9. 12).
The chapters given in the
Appendix Nos.
478
and
481
have hardly any connection with the
subjects previously treated.