The Notebooks of Leonardo Da Vinci — Complete
parts: that is with short and thick arms, wide thick hands, with
short fingers with their joints of the same character, and so on
with the rest. I would have the same thing understood as applying to
all animals and plants; in diminishing, [the various parts] do so in
due proportion to the size, as also in enlarging.
367.
OF THE AGREEMENT OF THE PROPORTION OF THE LIMBS.
And again, remember to be very careful in giving your figures limbs,
that they must appear to agree with the size of the body and
likewise to the age. Thus a youth has limbs that are not very
muscular not strongly veined, and the surface is delicate and round,
and tender in colour. In man the limbs are sinewy and muscular,
while in old men the surface is wrinkled, rugged and knotty, and the
sinews very prominent.
HOW YOUNG BOYS HAVE THEIR JOINTS JUST THE REVERSE OF THOSE OF MEN,
AS TO SIZE.
Little children have all the joints slender and the portions between
them are thick; and this happens because nothing but the skin covers
the joints without any other flesh and has the character of sinew,
connecting the bones like a ligature. And the fat fleshiness is laid
on between one joint and the next, and between the skin and the
bones. But, since the bones are thicker at the joints than between
them, as a mass grows up the flesh ceases to have that superfluity
which it had, between the skin and the bones; whence the skin clings
more closely to the bone and the limbs grow more slender. But since
there is nothing over the joints but the cartilaginous and sinewy
skin this cannot dry up, and, not drying up, cannot shrink. Thus,
and for this reason, children are slender at the joints and fat
between the joints; as may be seen in the joints of the fingers,
arms, and shoulders, which are slender and dimpled, while in man on
the contrary all the joints of the fingers, arms, and legs are
thick; and wherever children have hollows men have prominences.
The movement of the human figure (368-375).
368.
Of the manner of representing the 18 actions of man. Repose,
movement, running, standing, supported, sitting, leaning, kneeling,
lying down, suspended. Carrying or being carried, thrusting,
pulling, striking, being struck, pressing down and lifting up.
[As to how a figure should stand with a weight in its hand [Footnote
8: The original text ends here.] Remember].
369.
A sitting man cannot raise himself if that part of his body which is
front of his axis [centre of gravity] does not weigh more than that
which is behind that axis [or centre] without using his arms.
A man who is mounting any slope finds that he must involuntarily
throw the most weight forward, on the higher foot, rather than
behind--that is in front of the axis and not behind it. Hence a man
will always, involuntarily, throw the greater weight towards the
point whither he desires to move than in any other direction.
The faster a man runs, the more he leans forward towards the point
he runs to and throws more weight in front of his axis than behind.
A man who runs down hill throws the axis onto his heels, and one who
runs up hill throws it into the points of his feet; and a man
running on level ground throws it first on his heels and then on the
points of his feet.
This man cannot carry his own weight unless, by drawing his body
back he balances the weight in front, in such a way as that the foot
on which he stands is the centre of gravity.
[Footnote: See Pl. XXII, No. 4.]
370.
How a man proceeds to raise himself to his feet, when he is sitting
on level ground.
371.
A man when walking has his head in advance of his feet.
A man when walking across a long level plain first leans [rather]
backwards and then as much forwards.
[Footnote 3-6: He strides forward with the air of a man going down
hill; when weary, on the contrary he walks like a man going up
hill.]
372.
A man when running throws less weight on his legs than when standing
still. And in the same way a horse which is running feels less the
weight of the man he carries. Hence many persons think it wonderful
that, in running, the horse can rest on one single foot. From this
it may be stated that when a weight is in progressive motion the
more rapid it is the less is the perpendicular weight towards the
centre.
373.
If a man, in taking a jump from firm ground, can leap 3 braccia, and
when he was taking his leap it were to recede 1/3 of a braccio, that
would be taken off his former leap; and so if it were thrust forward
1/3 of a braccio, by how much would his leap be increased?
374.
OF DRAWING.
When a man who is running wants to neutralise the impetus that
carries him on he prepares a contrary impetus which is generated by
his hanging backwards. This can be proved, since, if the impetus
carries a moving body with a momentum equal to 4 and the moving body
wants to turn and fall back with a momentum of 4, then one momentum
neutralises the other contrary one, and the impetus is neutralised.
Of walking up and down (375-379)
375.
When a man wants to stop running and check the impetus he is forced
to hang back and take short quick steps. [Footnote: Lines 5-31 refer
to the two upper figures, and the lower figure to the right is
explained by the last part of the chapter.] The centre of gravity of
a man who lifts one of his feet from the ground always rests on the
centre of the sole of the foot [he stands on].
A man, in going up stairs involuntarily throws so much weight
forward and on the side of the upper foot as to be a counterpoise to
the lower leg, so that the labour of this lower leg is limited to
moving itself.
The first thing a man does in mounting steps is to relieve the leg
he is about to lift of the weight of the body which was resting on
that leg; and besides this, he gives to the opposite leg all the
rest of the bulk of the whole man, including [the weight of] the
other leg; he then raises the other leg and sets the foot upon the
step to which he wishes to raise himself. Having done this he
restores to the upper foot all the weight of the body and of the leg
itself, and places his hand on his thigh and throws his head forward
and repeats the movement towards the point of the upper foot,
quickly lifting the heel of the lower one; and with this impetus he
lifts himself up and at the same time extends the arm which rested
on his knee; and this extension of the arm carries up the body and
the head, and so straightens the spine which was curved.
[32] The higher the step is which a man has to mount, the farther
forward will he place his head in advance of his upper foot, so as
to weigh more on _a_ than on _b_; this man will not be on the step
_m_. As is shown by the line _g f_.
[Footnote: See Pl. XXIII, No. 1. The lower sketch to the left
belongs to the four first lines.]
376.
I ask the weight [pressure] of this man at every degree of motion on
these steps, what weight he gives to _b_ and to _c_.
[Footnote 8: These lines are, in the original, written in ink]
Observe the perpendicular line below the centre of gravity of the
man.
[Footnote: See Pl. XXIII, No. 2.]
377.
In going up stairs if you place your hands on your knees all the
labour taken by the arms is removed from the sinews at the back of
the knees.
[Footnote: See Pl. XXIII, No. 3.]
378.
The sinew which guides the leg, and which is connected with the
patella of the knee, feels it a greater labour to carry the man
upwards, in proportion as the leg is more bent; and the muscle which
acts upon the angle made by the thigh where it joins the body has
less difficulty and has a less weight to lift, because it has not
the [additional] weight of the thigh itself. And besides this it has
stronger muscles, being those which form the buttock.
379.
A man coming down hill takes little steps, because the weight rests
upon the hinder foot, while a man mounting takes wide steps, because
his weight rests on the foremost foot.
[Footnote: See Pl. XXIII, No. 4.]
On the human body in action (380-388).
380.
OF THE HUMAN BODY IN ACTION.
When you want to represent a man as moving some weight consider what
the movements are that are to be represented by different lines;
that is to say either from below upwards, with a simple movement, as
a man does who stoops forward to take up a weight which he will lift
as he straightens himself. Or as a man does who wants to squash
something backwards, or to force it forwards or to pull it downwards
with ropes passed through pullies [Footnote 10: Compare the sketch
on page 198 and on 201 (S. K. M. II.1 86b).]. And here remember that
the weight of a man pulls in proportion as his centre of gravity is
distant from his fulcrum, and to this is added the force given by
his legs and bent back as he raises himself.
381.
Again, a man has even a greater store of strength in his legs than
he needs for his own weight; and to see if this is true, make a man
stand on the shore-sand and then put another man on his back, and
you will see how much he will sink in. Then take the man from off
his back and make him jump straight up as high as he can, and you
will find that the print of his feet will be made deeper by the jump
than from having the man on his back. Hence, here, by 2 methods it
is proved that a man has double the strength he requires to support
his own body.
382.
OF PAINTING.
If you have to draw a man who is in motion, or lifting or pulling,
or carrying a weight equal to his own, in what way must you set on
his legs below his body?
[Footnote: In the MS. this question remains unanswered.]
383.
OF THE STRENGTH OF MAN.
A man pulling a [dead] weight balanced against himself cannot pull
more than his own weight. And if he has to raise it he will [be able
to] raise as much more than his weight as his strength may be more
than that of other men. [Footnote 7: The stroke at the end of this
line finishes in the original in a sort of loop or flourish, and a
similar flourish occurs at the end of the previous passage written
on the same page. M. RAVAISSON regards these as numbers (compare the
photograph of page 30b in his edition of MS. A). He remarks: "_Ce
chiffre_ 8 _et, a la fin de l'alinea precedent, le chiffre_ 7 _sont,
dans le manuscrit, des renvois_."] The greatest force a man can
apply, with equal velocity and impetus, will be when he sets his
feet on one end of the balance [or lever] and then presses his
shoulders against some stable body. This will raise a weight at the
other end of the balance [lever], equal to his own weight and [added
to that] as much weight as he can carry on his shoulders.
384.
No animal can simply move [by its dead weight] a greater weight than
the sum of its own weight outside the centre of his fulcrum.
385.
A man who wants to send an arrow very far from the bow must be
standing entirely on one foot and raising the other so far from the
foot he stands on as to afford the requisite counterpoise to his
body which is thrown on the front foot. And he must not hold his arm
fully extended, and in order that he may be more able to bear the
strain he must hold a piece of wood which there is in all crossbows,
extending from the hand to the breast, and when he wishes to shoot
he suddenly leaps forward at the same instant and extends his arm
with the bow and releases the string. And if he dexterously does
every thing at once it will go a very long way.
386.
When two men are at the opposite ends of a plank that is balanced,
and if they are of equal weight, and if one of them wants to make a
leap into the air, then his leap will be made down from his end of
the plank and the man will never go up again but must remain in his
place till the man at the other end dashes up the board.