The Notebooks of Leonardo Da Vinci, Volume 1
by
Leonardo Da Vinci
Part 4 out of 7
From the chin to the back of the neck _s t_, is the same distance as
between the mouth and the roots of the hair, that is three quarters
of the head.
From the chin to the jaw bone _v x_ is half the head and equal to
the thickness of the neck in profile.
The thickness of the head from the brow to the nape is once and 3/4
that of the neck.
[Footnote: The drawings to this text, lines 1-10 are on Pl. VII, No.
I. The two upper sketches of heads, Pl. VII, No. 2, belong to lines
11-14, and in the original are placed immediately below the sketches
reproduced on Pl. VII, No. 1.]
311.
The distance from the attachment of one ear to the other is equal to
that from the meeting of the eyebrows to the chin, and in a fine
face the width of the mouth is equal to the length from the parting
of the lips to the bottom of the chin.
312.
The cut or depression below the lower lip of the mouth is half way
between the bottom of the nose and the bottom of the chin.
The face forms a square in itself; that is its width is from the
outer corner of one eye to the other, and its height is from the
very top of the nose to the bottom of the lower lip of the mouth;
then what remains above and below this square amounts to the height
of such another square, _a_ _b_ is equal to the space between _c_
_d_; _d_ _n_ in the same way to _n_ _c_, and likewise _s_ _r_, _q_
_p_, _h_ _k_ are equal to each other.
It is as far between _m_ and _s_ as from the bottom of the nose to
the chin. The ear is exactly as long as the nose. It is as far from
_x_ to _j_ as from the nose to the chin. The parting of the mouth
seen in profile slopes to the angle of the jaw. The ear should be as
high as from the bottom of the nose to the top of the eye-lid. The
space between the eyes is equal to the width of an eye. The ear is
over the middle of the neck, when seen in profile. The distance from
4 to 5 is equal to that from s_ to _r_.
[Footnote: See Pl. VIII, No. I, where the text of lines 3-13 is also
given in facsimile.]
313.
(_a_ _b_) is equal to (_c_ _d_).
[Footnote: See Pl. VII, No. 3. Reference may also be made here to
two pen and ink drawings of heads in profile with figured
measurements, of which there is no description in the MS. These are
given on Pl. XVII, No. 2.--A head, to the left, with part of the
torso [W. P. 5a], No. 1 on the same plate is from MS. A 2b and in
the original occurs on a page with wholly irrelevant text on matters
of natural history. M. RAVAISSON in his edition of the Paris MS. A
has reproduced this head and discussed it fully [note on page 12];
he has however somewhat altered the original measurements. The
complicated calculations which M. RAVAISSON has given appear to me
in no way justified. The sketch, as we see it, can hardly have been
intended for any thing more than an experimental attempt to
ascertain relative proportions. We do not find that Leonardo made
use of circular lines in any other study of the proportions of the
human head. At the same time we see that the proportions of this
sketch are not in accordance with the rules which he usually
observed (see for instance No. 310).]
The head _a_ _f_ 1/6 larger than _n_ _f_.
315.
From the eyebrow to the junction of the lip with the chin, and the
angle of the jaw and the upper angle where the ear joins the temple
will be a perfect square. And each side by itself is half the head.
The hollow of the cheek bone occurs half way between the tip of the
nose and the top of the jaw bone, which is the lower angle of the
setting on of the ear, in the frame here represented.
From the angle of the eye-socket to the ear is as far as the length
of the ear, or the third of the face.
[Footnote: See Pl. IX. The text, in the original is written behind
the head. The handwriting would seem to indicate a date earlier than
1480. On the same leaf there is a drawing in red chalk of two
horsemen of which only a portion of the upper figure is here
visible. The whole leaf measures 22 1/2 centimetres wide by 29 long,
and is numbered 127 in the top right-hand corner.]
316.
From _a_ to _b_--that is to say from the roots of the hair in front
to the top of the head--ought to be equal to _c_ _d_;--that is from
the bottom of the nose to the meeting of the lips in the middle of
the mouth. From the inner corner of the eye _m_ to the top of the
head _a_ is as far as from _m_ down to the chin _s_. _s_ _c_ _f_ _b_
are all at equal distances from each other.
[Footnote: The drawing in silver-point on bluish tinted paper--Pl.
X--which belongs to this chapter has been partly drawn over in ink
by Leonardo himself.]
317.
From the top of the head to the bottom of the chin is 1/9, and from
the roots of the hair to the chin is 1/9 of the distance from the
roots of the hair to the ground. The greatest width of the face is
equal to the space between the mouth and the roots of the hair and
is 1/12 of the whole height. From the top of the ear to the top of
the head is equal to the distance from the bottom of the chin to the
lachrymatory duct of the eye; and also equal to the distance from
the angle of the chin to that of the jaw; that is the 1/16 of the
whole. The small cartilage which projects over the opening of the
ear towards the nose is half-way between the nape and the eyebrow;
the thickness of the neck in profile is equal to the space between
the chin and the eyes, and to the space between the chin and the
jaw, and it is 1/18 of the height of the man.
318.
_a b_, _c d_, _e f_, _g h_, _i k_ are equal to each other in size
excepting that _d f_ is accidental.
[Footnote: See Pl. XI.]
Proportions of the head seen in front (319-321).
319.
_a n o f_ are equal to the mouth.
_a c_ and _a f_ are equal to the space between one eye and the
other.
_n m o f q r_ are equal to half the width of the eye lids, that is
from the inner [lachrymatory] corner of the eye to its outer corner;
and in like manner the division between the chin and the mouth; and
in the same way the narrowest part of the nose between the eyes. And
these spaces, each in itself, is the 19th part of the head, _n o_ is
equal to the length of the eye or of the space between the eyes.
_m c_ is 1/3 of _n m_ measuring from the outer corner of the eyelids
to the letter _c_. _b s_ will be equal to the width of the nostril.
[Footnote: See Pl. XII.]
320.
The distance between the centres of the pupils of the eyes is 1/3 of
the face. The space between the outer corners of the eyes, that is
where the eye ends in the eye socket which contains it, thus the
outer corners, is half the face.
The greatest width of the face at the line of the eyes is equal to
the distance from the roots of the hair in front to the parting of
the lips.
[Footnote: There are, with this section, two sketches of eyes, not
reproduced here.]
321.
The nose will make a double square; that is the width of the nose at
the nostrils goes twice into the length from the tip of the nose to
the eyebrows. And, in the same way, in profile the distance from the
extreme side of the nostril where it joins the cheek to the tip of
the nose is equal to the width of the nose in front from one nostril
to the other. If you divide the whole length of the nose--that is
from the tip to the insertion of the eyebrows, into 4 equal parts,
you will find that one of these parts extends from the tip of the
nostrils to the base of the nose, and the upper division lies
between the inner corner of the eye and the insertion of the
eyebrows; and the two middle parts [together] are equal to the
length of the eye from the inner to the outer corner.
[Footnote: The two bottom sketches on Pl. VII, No. 4 face the six
lines of this section,--With regard to the proportions of the head
in profile see No. 312.]
322.
The great toe is the sixth part of the foot, taking the measure in
profile, on the inside of the foot, from where this toe springs from
the ball of the sole of the foot to its tip _a b_; and it is equal
to the distance from the mouth to the bottom of the chin. If you
draw the foot in profile from the outside, make the little toe begin
at three quarters of the length of the foot, and you will find the
same distance from the insertion of this toe as to the farthest
prominence of the great toe.
323.
For each man respectively the distance between _a b_ is equal to _c
d_.
324.
Relative proportion of the hand and foot.
The foot is as much longer than the hand as the thickness of the arm
at the wrist where it is thinnest seen facing.
Again, you will find that the foot is as much longer than the hand
as the space between the inner angle of the little toe to the last
projection of the big toe, if you measure along the length of the
foot.
The palm of the hand without the fingers goes twice into the length
of the foot without the toes.
If you hold your hand with the fingers straight out and close
together you will find it to be of the same width as the widest part
of the foot, that is where it is joined onto the toes.
And if you measure from the prominence of the inner ancle to the end
of the great toe you will find this measure to be as long as the
whole hand.
From the top angle of the foot to the insertion of the toes is equal
to the hand from wrist joint to the tip of the thumb.
The smallest width of the hand is equal to the smallest width of the
foot between its joint into the leg and the insertion of the toes.
The width of the heel at the lower part is equal to that of the arm
where it joins the hand; and also to the leg where it is thinnest
when viewed in front.
The length of the longest toe, from its first division from the
great toe to its tip is the fourth of the foot from the centre of
the ancle bone to the tip, and it is equal to the width of the
mouth. The distance between the mouth and the chin is equal to that
of the knuckles and of the three middle fingers and to the length of
their first joints if the hand is spread, and equal to the distance
from the joint of the thumb to the outset of the nails, that is the
fourth part of the hand and of the face.
The space between the extreme poles inside and outside the foot
called the ancle or ancle bone _a b_ is equal to the space between
the mouth and the inner corner of the eye.
325.
The foot, from where it is attached to the leg, to the tip of the
great toe is as long as the space between the upper part of the chin
and the roots of the hair _a b_; and equal to five sixths of the
face.
326.
_a d_ is a head's length, _c b_ is a head's length. The four smaller
toes are all equally thick from the nail at the top to the bottom,
and are 1/13 of the foot.
[Footnote: See Pl. XIV, No. 1, a drawing of a foot with the text in
three lines below it.]
327.
The whole length of the foot will lie between the elbow and the
wrist and between the elbow and the inner angle of the arm towards
the breast when the arm is folded. The foot is as long as the whole
head of a man, that is from under the chin to the topmost part of
the head[Footnote 2: _nel modo che qui i figurato_. See Pl. VII, No.
4, the upper figure. The text breaks off at the end of line 2 and
the text given under No. 321 follows below. It may be here remarked
that the second sketch on W. P. 311 has in the original no
explanatory text.] in the way here figured.
Proportions of the leg (328-331).
328.
The greatest thickness of the calf of the leg is at a third of its
height _a b_, and is a twentieth part thicker than the greatest
thickness of the foot.
_a c_ is half of the head, and equal to _d b_ and to the insertion
of the five toes _e f_. _d k_ diminishes one sixth in the leg _g h_.
_g h_ is 1/3 of the head; _m n_ increases one sixth from _a e_ and
is 7/12 of the head, _o p_ is 1/10 less than _d k_ and is 6/17 of
the head. _a_ is at half the distance between _b q_, and is 1/4 of
the man. _r_ is half way between _s_ and _b_[Footnote 11: _b_ is
here and later on measured on the right side of the foot as seen by
the spectator.]. The concavity of the knee outside _r_ is higher
than that inside _a_. The half of the whole height of the leg from
the foot _r_, is half way between the prominence _s_ and the ground
_b_. _v_ is half way between _t_ and _b_. The thickness of the thigh
seen in front is equal to the greatest width of the face, that is
2/3 of the length from the chin to the top of the head; _z r_ is 5/6
of 7 to _v_; _m n_ is equal to 7 _v_ and is 1/4 of _r b_, _x y_ goes
3 times into _r b_, and into _r s_.
[Footnote 22-35: The sketch illustrating these lines is on Pl. XIII,
No. 2.]
[Footnote 22: a b _entra in_ c f 6 _e_ 6 _in_ c n. Accurate
measurement however obliges us to read 7 for 6.] _a b_ goes six
times into _c f_ and six times into _c n_ and is equal to _g h_; _i
k l m_ goes 4 times into _d f_, and 4 times into _d n_ and is 3/7 of
the foot; _p q r s_ goes 3 times into _d f, and 3 times into _b n_;
[Footnote: 25. _y_ is not to be found on the diagram and _x_ occurs
twice; this makes the passage very obscure.] _x y_ is 1/8 of _x f_
and is equal to _n q_. 3 7 is 1/9 of _n f_; 4 5 is 1/10 of _n f_
[Footnote: 22-27. Compare with this lines 18-24 of No. 331, and the
sketch of a leg in profile Pl. XV.].
I want to know how much a man increases in height by standing on
tip-toe and how much _p g_ diminishes by stooping; and how much it
increases at _n q_ likewise in bending the foot.
[Footnote 34: _e f_ 4 _dal cazo_. By reading _i_ for _e_ the sense
of this passage is made clear.] _e f_ is four times in the distance
between the genitals and the sole of the foot; [Footnote 35: 2 is
not to be found in the sketch which renders the passage obscure. The
two last lines are plainly legible in the facsimile.] 3 7 is six
times from 3 to 2 and is equal to _g h_ and _i k_.
[Footnote: The drawing of a leg seen in front Pl. XIII, No. 1
belongs to the text from lines 3-21. The measurements in this
section should be compared with the text No. 331, lines 1-13, and
the sketch of a leg seen in front on Pl. XV.]
329.
The length of the foot from the end of the toes to the heel goes
twice into that from the heel to the knee, that is where the leg
bone [fibula] joins the thigh bone [femur].
330.
_a n b_ are equal; _c n d_ are equal; _n c_ makes two feet; _n d_
makes 2 feet.
[Footnote: See the lower sketch, Pl. XIV, No. 1.]
331.
_m n o_ are equal. The narrowest width of the leg seen in front goes
8 times from the sole of the foot to the joint of the knee, and is
the same width as the arm, seen in front at the wrist, and as the
longest measure of the ear, and as the three chief divisions into
which we divide the face; and this measurement goes 4 times from the
wrist joint of the hand to the point of the elbow. [14] The foot is
as long as the space from the knee between _a_ and _b_; and the
patella of the knee is as long as the leg between _r_ and _s_.
[18] The least thickness of the leg in profile goes 6 times from the
sole of the foot to the knee joint and is the same width as the
space between the outer corner of the eye and the opening of the
ear, and as the thickest part of the arm seen in profile and between
the inner corner of the eye and the insertion of the hair.
_a b c_ [_d_] are all relatively of equal length, _c d_ goes twice
from the sole of the foot to the centre of the knee and the same
from the knee to the hip.
[28]_a b c_ are equal; _a_ to _b_ is 2 feet--that is to say
measuring from the heel to the tip of the great toe.
[Footnote: See Pl. XV. The text of lines 2-17 is to the left of the
front view of the leg, to which it refers. Lines 18-27 are in the
middle column and refer to the leg seen in profile and turned to the
left, on the right hand side of the writing. Lines 20-30 are above,
to the left and apply to the sketch below them.
Some farther remarks on the proportion of the leg will be found in
No. 336, lines 6, 7.]
On the central point of the whole body.
332.
In kneeling down a man will lose the fourth part of his height.
When a man kneels down with his hands folded on his breast the navel
will mark half his height and likewise the points of the elbows.
Half the height of a man who sits--that is from the seat to the top
of the head--will be where the arms fold below the breast, and
below the shoulders. The seated portion--that is from the seat to
the top of the head--will be more than half the man's [whole height]
by the length of the scrotum.
[Footnote: See Pl. VIII, No. 2.]
The relative proportions of the torso and of the whole figure.
333.
The cubit is one fourth of the height of a man and is equal to the
greatest width of the shoulders. From the joint of one shoulder to
the other is two faces and is equal to the distance from the top of
the breast to the navel. [Footnote 9: _dalla detta somita_. It would
seem more accurate to read here _dal detto ombilico_.] From this
point to the genitals is a face's length.
[Footnote: Compare with this the sketches on the other page of the
same leaf. Pl. VIII, No. 2.]
The relative proportions of the head and of the torso.
334.
From the roots of the hair to the top of the breast _a b_ is the
sixth part of the height of a man and this measure is equal.
From the outside part of one shoulder to the other is the same
distance as from the top of the breast to the navel and this measure
goes four times from the sole of the foot to the lower end of the
nose.
The [thickness of] the arm where it springs from the shoulder in
front goes 6 times into the space between the two outside edges of
the shoulders and 3 times into the face, and four times into the
length of the foot and three into the hand, inside or outside.
[Footnote: The three sketches Pl. XIV, No. 2 belong to this text.]
The relative proportions of the torso and of the leg (335. 336).
335.
_a b c_ are equal to each other and to the space from the armpit of
the shoulder to the genitals and to the distance from the tip of the
fingers of the hand to the joint of the arm, and to the half of the
breast; and you must know that _c b_ is the third part of the height
of a man from the shoulders to the ground; _d e f_ are equal to each
other and equal to the greatest width of the shoulders.
[Footnote: See Pl. XVI, No. 1.]
336.
--Top of the chin--hip--the insertion of the middle finger. The end
of the calf of the leg on the inside of the thigh.--The end of the
swelling of the shin bone of the leg. [6] The smallest thickness of
the leg goes 3 times into the thigh seen in front.
[Footnote: See Pl. XVII, No. 2, middle sketch.]
The relative proportions of the torso and of the foot.
337.
The torso _a b_ in its thinnest part measures a foot; and from _a_
to _b_ is 2 feet, which makes two squares to the seat--its thinnest
part goes 3 times into the length, thus making 3 squares.
[Footnote: See Pl, VII, No. 2, the lower sketch.]
The proportions of the whole figure (338-341).
338.
A man when he lies down is reduced to 1/9 of his height.
339.
The opening of the ear, the joint of the shoulder, that of the hip
and the ancle are in perpendicular lines; _a n_ is equal to _m o_.
[Footnote: See Pl. XVI, No. 2, the upper sketch.]
340.
From the chin to the roots of the hair is 1/10 of the whole figure.
From the joint of the palm of the hand to the tip of the longest
finger is 1/10. From the chin to the top of the head 1/8; and from
the pit of the stomach to the top of the breast is 1/6, and from the
pit below the breast bone to the top of the head 1/4. From the chin
to the nostrils 1/3 Part of the face, the same from the nostrils to
the brow and from the brow to the roots of the hair, and the foot is
1/6, the elbow 1/4, the width of the shoulders 1/4.
341.
The width of the shoulders is 1/4 of the whole. From the joint of
the shoulder to the hand is 1/3, from the parting of the lips to
below the shoulder-blade is one foot.
The greatest thickness of a man from the breast to the spine is one
8th of his height and is equal to the space between the bottom of
the chin and the top of the head.
The greatest width is at the shoulders and goes 4.
The torso from the front and back.
342.
The width of a man under the arms is the same as at the hips.
A man's width across the hips is equal to the distance from the top
of the hip to the bottom of the buttock, when a man stands equally
balanced on both feet; and there is the same distance from the top
of the hip to the armpit. The waist, or narrower part above the hips
will be half way between the arm pits and the bottom of the buttock.
[Footnote: The lower sketch Pl. XVI, No. 2, is drawn by the side of
line 1.]
Vitruvius' scheme of proportions.
343.
Vitruvius, the architect, says in his work on architecture that the
measurements of the human body are distributed by Nature as follows:
that is that 4 fingers make 1 palm, and 4 palms make 1 foot, 6 palms
make 1 cubit; 4 cubits make a man's height. And 4 cubits make one
pace and 24 palms make a man; and these measures he used in his
buildings. If you open your legs so much as to decrease your height
1/14 and spread and raise your arms till your middle fingers touch
the level of the top of your head you must know that the centre of
the outspread limbs will be in the navel and the space between the
legs will be an equilateral triangle.
The length of a man's outspread arms is equal to his height.
From the roots of the hair to the bottom of the chin is the tenth of
a man's height; from the bottom of the chin to the top of his head
is one eighth of his height; from the top of the breast to the top
of his head will be one sixth of a man. From the top of the breast
to the roots of the hair will be the seventh part of the whole man.
From the nipples to the top of the head will be the fourth part of a
man. The greatest width of the shoulders contains in itself the
fourth part of the man. From the elbow to the tip of the hand will
be the fifth part of a man; and from the elbow to the angle of the
armpit will be the eighth part of the man. The whole hand will be
the tenth part of the man; the beginning of the genitals marks the
middle of the man. The foot is the seventh part of the man. From the
sole of the foot to below the knee will be the fourth part of the
man. From below the knee to the beginning of the genitals will be
the fourth part of the man. The distance from the bottom of the chin
to the nose and from the roots of the hair to the eyebrows is, in
each case the same, and like the ear, a third of the face.
[Footnote: See Pl. XVIII. The original leaf is 21 centimetres wide
and 33 1/2 long. At the ends of the scale below the figure are
written the words _diti_ (fingers) and _palmi_ (palms). The passage
quoted from Vitruvius is Book III, Cap. 1, and Leonardo's drawing is
given in the editions of Vitruvius by FRA GIOCONDO (Venezia 1511,
fol., Firenze 1513, 8vo.) and by CESARIANO (Como 1521).]
The arm and head.
344.
From _b_ to _a_ is one head, as well as from _c_ to _a_ and this
happens when the elbow forms a right angle.
[Footnote: See Pl. XLI, No. 1.]
Proportions of the arm (345-349).
345.
From the tip of the longest finger of the hand to the shoulder joint
is four hands or, if you will, four faces.
_a b c_ are equal and each interval is 2 heads.
[Footnote: Lines 1-3 are given on Pl. XV below the front view of the
leg; lines 4 and 5 are below again, on the left side. The lettering
refers to the bent arm near the text.]
346.
The hand from the longest finger to the wrist joint goes 4 times
from the tip of the longest finger to the shoulder joint.
347.
_a b c_ are equal to each other and to the foot and to the space
between the nipple and the navel _d e_ will be the third part of the
whole man.
_f g_ is the fourth part of a man and is equal to _g h_ and measures
a cubit.
[Footnote: See Pl. XIX, No. 1. 1. _mamolino_ (=_bambino_, little
child) may mean here the navel.]
348.
_a b_ goes 4 times into _a c_ and 9 into _a m_. The greatest
thickness of the arm between the elbow and the hand goes 6 times
into _a m_ and is equal to _r f_. The greatest thickness of the arm
between the shoulder and the elbow goes 4 times into _c m_, and is
equal to _h n g_. The smallest thickness of the arm above the elbow
_x y_ is not the base of a square, but is equal to half the space
_h_ 3 which is found between the inner joint of the arm and the
wrist joint.
[11]The width of the wrist goes 12 times into the whole arm; that is
from the tip of the fingers to the shoulder joint; that is 3 times
into the hand and 9 into the arm.
The arm when bent is 4 heads.
The arm from the shoulder to the elbow in bending increases in
length, that is in the length from the shoulder to the elbow, and
this increase is equal to the thickness of the arm at the wrist when
seen in profile. And the space between the bottom of the chin and
the parting of the lips, is equal to the thickness of the 2 middle
fingers, and to the width of the mouth and to the space between the
roots of the hair on the forehead and the top of the head [Footnote:
_Queste cose_. This passage seems to have been written on purpose to
rectify the foregoing lines. The error is explained by the
accompanying sketch of the bones of the arm.]. All these distances
are equal to each other, but they are not equal to the
above-mentioned increase in the arm.
The arm between the elbow and wrist never increases by being bent or
extended.
The arm, from the shoulder to the inner joint when extended.
When the arm is extended, _p n_ is equal to _n a_. And when it is
bent _n a_ diminishes 1/6 of its length and _p n_ does the same. The
outer elbow joint increases 1/7 when bent; and thus by being bent it
increases to the length of 2 heads. And on the inner side, by
bending, it is found that whereas the arm from where it joins the
side to the wrist, was 2 heads and a half, in bending it loses the
half head and measures only two: one from the [shoulder] joint to
the end [by the elbow], and the other to the hand.
The arm when folded will measure 2 faces up to the shoulder from the
elbow and 2 from the elbow to the insertion of the four fingers on
the palm of the hand. The length from the base of the fingers to the
elbow never alters in any position of the arm.
If the arm is extended it decreases by 1/3 of the length between _b_
and _h_; and if--being extended--it is bent, it will increase the
half of _o e_. [Footnote 59-61: The figure sketched in the margin is
however drawn to different proportions.] The length from the
shoulder to the elbow is the same as from the base of the thumb,
inside, to the elbow _a b c_.
[Footnote 62-64: The arm sketch on the margin of the MS. is
identically the same as that given below on Pl. XX which may
therefore be referred to in this place. In line 62 we read therefore
_z c_ for _m n_.] The smallest thickness of the arm in profile _z c_
goes 6 times between the knuckles of the hand and the dimple of the
elbow when extended and 14 times in the whole arm and 42 in the
whole man [64]. The greatest thickness of the arm in profile is
equal to the greatest thickness of the arm in front; but the first
is placed at a third of the arm from the shoulder joint to the elbow
and the other at a third from the elbow towards the hand.
[Footnote: Compare Pl. XVII. Lines 1-10 and 11-15 are written in two
columns below the extended arm, and at the tips of the fingers we
find the words: _fine d'unghie_ (ends of the nails). Part of the
text--lines 22 to 25--is visible by the side of the sketches on Pl.
XXXV, No. 1.]
349.
From the top of the shoulder to the point of the elbow is as far as
from that point to the joints of the four fingers with the palm of
the hand, and each is 2 faces.
[5]_a e_ is equal to the palm of the hand, _r f_ and _o g_ are equal
to half a head and each goes 4 times into _a b_ and _b c_. From _c_
to _m_ is 1/2 a head; _m n_ is 1/3 of a head and goes 6 times into
_c b_ and into _b a_; _a b_ loses 1/7 of its length when the arm is
extended; _c b_ never alters; _o_ will always be the middle point
between _a_ and _s_.
_y l_ is the fleshy part of the arm and measures one head; and when
the arm is bent this shrinks 2/5 of its length; _o a_ in bending
loses 1/6 and so does _o r_.
_a b_ is 1/7 of _r c_. _f s_ will be 1/8 of _r c_, and each of those
2 measurements is the largest of the arm; _k h_ is the thinnest part
between the shoulder and the elbow and it is 1/8 of the whole arm _r
c_; _o p_ is 1/5 of _r l_; _c z_ goes 13 times into _r c_.
[Footnote: See Pl. XX where the text is also seen from lines 5-23.]
The movement of the arm (350-354).
350.
In the innermost bend of the joints of every limb the reliefs are
converted into a hollow, and likewise every hollow of the innermost
bends becomes a convexity when the limb is straightened to the
utmost. And in this very great mistakes are often made by those who
have insufficient knowledge and trust to their own invention and do
not have recourse to the imitation of nature; and these variations
occur more in the middle of the sides than in front, and more at the
back than at the sides.
351.
When the arm is bent at an angle at the elbow, it will produce some
angle; the more acute the angle is, the more will the muscles within
the bend be shortened; while the muscles outside will become of
greater length than before. As is shown in the example; _d c e_ will
shrink considerably; and _b n_ will be much extended.
[Footnote: See Pl. XIX, No. 2.]
352.
OF PAINTING.
The arm, as it turns, thrusts back its shoulder towards the middle
of the back.
353.
The principal movements of the hand are 10; that is forwards,
backwards, to right and to left, in a circular motion, up or down,
to close and to open, and to spread the fingers or to press them
together.
354.
OF THE MOTIONS OF THE FINGERS.
The movements of the fingers principally consist in extending and
bending them. This extension and bending vary in manner; that is,
sometimes they bend altogether at the first joint; sometimes they
bend, or extend, half way, at the 2nd joint; and sometimes they bend
in their whole length and in all the three joints at once. If the 2
first joints are hindered from bending, then the 3rd joint can be
bent with greater ease than before; it can never bend of itself, if
the other joints are free, unless all three joints are bent. Besides
all these movements there are 4 other principal motions of which 2
are up and down, the two others from side to side; and each of these
is effected by a single tendon. From these there follow an infinite
number of other movements always effected by two tendons; one tendon
ceasing to act, the other takes up the movement. The tendons are
made thick inside the fingers and thin outside; and the tendons
inside are attached to every joint but outside they are not.
[Footnote 26: This head line has, in the original, no text to
follow.] Of the strength [and effect] of the 3 tendons inside the
fingers at the 3 joints.
The movement of the torso (355-361).
355.
Observe the altered position of the shoulder in all the movements of
the arm, going up and down, inwards and outwards, to the back and to
the front, and also in circular movements and any others.
And do the same with reference to the neck, hands and feet and the
breast above the lips &c.
356.
Three are the principal muscles of the shoulder, that is _b c d_,
and two are the lateral muscles which move it forward and backward,
that is _a o_; _a_ moves it forward, and _o_ pulls it back; and bed
raises it; _a b c_ moves it upwards and forwards, and _c d o_
upwards and backwards. Its own weight almost suffices to move it
downwards.
The muscle _d_ acts with the muscle _c_ when the arm moves forward;
and in moving backward the muscle _b_ acts with the muscle _c_.
[Footnote: See Pl. XXI. In the original the lettering has been
written in ink upon the red chalk drawing and the outlines of the
figures have in most places been inked over.]
357.
OF THE LOINS, WHEN BENT.
The loins or backbone being bent. The breasts are are always lower
than the shoulderblades of the back.
If the breast bone is arched the breasts are higher than the
shoulderblades.
If the loins are upright the breast will always be found at the same
level as the shoulderblades.
[Footnote: See Pl. XXII, No. 1.]
358.
_a b_ the tendon and ankle in raising the heel approach each other
by a finger's breadth; in lowering it they separate by a finger's
breadth.
[Footnote: See Pl. XXII, No. 2. Compare this facsimile and text with
Pl. III, No. 2, and p. 152 of MANZI'S edition. Also with No. 274 of
LUDWIG'S edition of the Vatican Copy.]
359.
Just so much as the part _d a_ of the nude figure decreases in this
position so much does the opposite part increase; that is: in
proportion as the length of the part _d a_ diminishes the normal
size so does the opposite upper part increase beyond its [normal]
size. The navel does not change its position to the male organ; and
this shrinking arises because when a figure stands on one foot, that
foot becomes the centre [of gravity] of the superimposed weight.
This being so, the middle between the shoulders is thrust above it
out of it perpendicular line, and this line, which forms the central
line of the external parts of the body, becomes bent at its upper
extremity [so as to be] above the foot which supports the body; and
the transverse lines are forced into such angles that their ends are
lower on the side which is supported. As is shown at _a b c_.
[Footnote: See Pl. XXII, No. 3.]
360.
OF PAINTING.
Note in the motions and attitudes of figures how the limbs vary, and
their feeling, for the shoulderblades in the motions of the arms and
shoulders vary the [line of the] back bone very much. And you will
find all the causes of this in my book of Anatomy.
361.
OF [CHANGE OF] ATTITUDE.
The pit of the throat is over the feet, and by throwing one arm
forward the pit of the throat is thrown off that foot. And if the
leg is thrown forward the pit of the throat is thrown forward; and.
so it varies in every attitude.
362.
OF PAINTING.
Indicate which are the muscles, and which the tendons, which become
prominent or retreat in the different movements of each limb; or
which do neither [but are passive]. And remember that these
indications of action are of the first importance and necessity in
any painter or sculptor who professes to be a master &c.
And indicate the same in a child, and from birth to decrepitude at
every stage of its life; as infancy, childhood, boyhood, youth &c.
And in each express the alterations in the limbs and joints, which
swell and which grow thinner.
363.
O Anatomical Painter! beware lest the too strong indication of the
bones, sinews and muscles, be the cause of your becoming wooden in
your painting by your wish to make your nude figures display all
their feeling. Therefore, in endeavouring to remedy this, look in
what manner the muscles clothe or cover their bones in old or lean
persons; and besides this, observe the rule as to how these same
muscles fill up the spaces of the surface that extend between them,
which are the muscles which never lose their prominence in any
amount of fatness; and which too are the muscles of which the
attachments are lost to sight in the very least plumpness. And in
many cases several muscles look like one single muscle in the
increase of fat; and in many cases, in growing lean or old, one
single muscle divides into several muscles. And in this treatise,
each in its place, all their peculiarities will be explained--and
particularly as to the spaces between the joints of each limb &c.
Again, do not fail [to observe] the variations in the forms of the
above mentioned muscles, round and about the joints of the limbs of
any animal, as caused by the diversity of the motions of each limb;
for on some side of those joints the prominence of these muscles is
wholly lost in the increase or diminution of the flesh of which
these muscles are composed, &c.
[Footnote: DE ROSSI remarks on this chapter, in the Roman edition of
the Trattato, p. 504: "_Non in questo luogo solo, ma in altri ancora
osserverà il lettore, che Lionardo va fungendo quelli che fanno
abuso della loro dottrina anatomica, e sicuramente con ciò ha in
mira il suo rivale Bonarroti, che di anatomia facea tanta pompa_."
Note, that Leonardo wrote this passage in Rome, probably under the
immediate impression of MICHAELANGELO'S paintings in the Sistine
Chapel and of RAPHAEL'S Isaiah in Sant' Agostino.]
364.
OF THE DIFFERENT MEASUREMENTS OF BOYS AND MEN.
There is a great difference in the length between the joints in men
and boys for, in man, from the top of the shoulder [by the neck] to
the elbow, and from the elbow to the tip of the thumb and from one
shoulder to the other, is in each instance two heads, while in a boy
it is but one because Nature constructs in us the mass which is the
home of the intellect, before forming that which contains the vital
elements.
365.
OF PAINTING.
Which are the muscles which subdivide in old age or in youth, when
becoming lean? Which are the parts of the limbs of the human frame
where no amount of fat makes the flesh thicker, nor any degree of
leanness ever diminishes it?
The thing sought for in this question will be found in all the
external joints of the bones, as the shoulder, elbow, wrists,
finger-joints, hips, knees, ankle-bone and toes and the like; all of
which shall be told in its place. The greatest thickness acquired by
any limb is at the part of the muscles which is farthest from its
attachments.
Flesh never increases on those portions of the limb where the bones
are near to the surface.
At _b r d a c e f_ the increase or diminution of the flesh never
makes any considerable difference. Nature has placed in front of man
all those parts which feel most pain under a blow; and these are the
shin of the leg, the forehead, and the nose. And this was done for
the preservation of man, since, if such pain were not felt in these
parts, the number of blows to which they would be exposed must be
the cause of their destruction.
Describe why the bones of the arm and leg are double near the hand
and foot [respectively].
And where the flesh is thicker or thinner in the bending of the
limbs.
366.
OF PAINTING.
Every part of the whole must be in proportion to the whole. Thus, if
a man is of a stout short figure he will be the same in all his
parts: that is with short and thick arms, wide thick hands, with
short fingers with their joints of the same character, and so on
with the rest. I would have the same thing understood as applying to
all animals and plants; in diminishing, [the various parts] do so in
due proportion to the size, as also in enlarging.
367.
OF THE AGREEMENT OF THE PROPORTION OF THE LIMBS.
And again, remember to be very careful in giving your figures limbs,
that they must appear to agree with the size of the body and
likewise to the age. Thus a youth has limbs that are not very
muscular not strongly veined, and the surface is delicate and round,
and tender in colour. In man the limbs are sinewy and muscular,
while in old men the surface is wrinkled, rugged and knotty, and the
sinews very prominent.
HOW YOUNG BOYS HAVE THEIR JOINTS JUST THE REVERSE OF THOSE OF MEN,
AS TO SIZE.
Little children have all the joints slender and the portions between
them are thick; and this happens because nothing but the skin covers
the joints without any other flesh and has the character of sinew,
connecting the bones like a ligature. And the fat fleshiness is laid
on between one joint and the next, and between the skin and the
bones. But, since the bones are thicker at the joints than between
them, as a mass grows up the flesh ceases to have that superfluity
which it had, between the skin and the bones; whence the skin clings
more closely to the bone and the limbs grow more slender. But since
there is nothing over the joints but the cartilaginous and sinewy
skin this cannot dry up, and, not drying up, cannot shrink. Thus,
and for this reason, children are slender at the joints and fat
between the joints; as may be seen in the joints of the fingers,
arms, and shoulders, which are slender and dimpled, while in man on
the contrary all the joints of the fingers, arms, and legs are
thick; and wherever children have hollows men have prominences.
The movement of the human figure (368-375).
368.
Of the manner of representing the 18 actions of man. Repose,
movement, running, standing, supported, sitting, leaning, kneeling,
lying down, suspended. Carrying or being carried, thrusting,
pulling, striking, being struck, pressing down and lifting up.
[As to how a figure should stand with a weight in its hand [Footnote
8: The original text ends here.] Remember].
369.
A sitting man cannot raise himself if that part of his body which is
front of his axis [centre of gravity] does not weigh more than that
which is behind that axis [or centre] without using his arms.
A man who is mounting any slope finds that he must involuntarily
throw the most weight forward, on the higher foot, rather than
behind--that is in front of the axis and not behind it. Hence a man
will always, involuntarily, throw the greater weight towards the
point whither he desires to move than in any other direction.
The faster a man runs, the more he leans forward towards the point
he runs to and throws more weight in front of his axis than behind.
A man who runs down hill throws the axis onto his heels, and one who
runs up hill throws it into the points of his feet; and a man
running on level ground throws it first on his heels and then on the
points of his feet.
This man cannot carry his own weight unless, by drawing his body
back he balances the weight in front, in such a way as that the foot
on which he stands is the centre of gravity.
[Footnote: See Pl. XXII, No. 4.]
370.
How a man proceeds to raise himself to his feet, when he is sitting
on level ground.
371.
A man when walking has his head in advance of his feet.
A man when walking across a long level plain first leans [rather]
backwards and then as much forwards.
[Footnote 3-6: He strides forward with the air of a man going down
hill; when weary, on the contrary he walks like a man going up
hill.]
372.
A man when running throws less weight on his legs than when standing
still. And in the same way a horse which is running feels less the
weight of the man he carries. Hence many persons think it wonderful
that, in running, the horse can rest on one single foot. From this
it may be stated that when a weight is in progressive motion the
more rapid it is the less is the perpendicular weight towards the
centre.
373.
If a man, in taking a jump from firm ground, can leap 3 braccia, and
when he was taking his leap it were to recede 1/3 of a braccio, that
would be taken off his former leap; and so if it were thrust forward
1/3 of a braccio, by how much would his leap be increased?
374.
OF DRAWING.
When a man who is running wants to neutralise the impetus that
carries him on he prepares a contrary impetus which is generated by
his hanging backwards. This can be proved, since, if the impetus
carries a moving body with a momentum equal to 4 and the moving body
wants to turn and fall back with a momentum of 4, then one momentum
neutralises the other contrary one, and the impetus is neutralised.
Of walking up and down (375-379)
375.
When a man wants to stop running and check the impetus he is forced
to hang back and take short quick steps. [Footnote: Lines 5-31 refer
to the two upper figures, and the lower figure to the right is
explained by the last part of the chapter.] The centre of gravity of
a man who lifts one of his feet from the ground always rests on the
centre of the sole of the foot [he stands on].
A man, in going up stairs involuntarily throws so much weight
forward and on the side of the upper foot as to be a counterpoise to
the lower leg, so that the labour of this lower leg is limited to
moving itself.
The first thing a man does in mounting steps is to relieve the leg
he is about to lift of the weight of the body which was resting on
that leg; and besides this, he gives to the opposite leg all the
rest of the bulk of the whole man, including [the weight of] the
other leg; he then raises the other leg and sets the foot upon the
step to which he wishes to raise himself. Having done this he
restores to the upper foot all the weight of the body and of the leg
itself, and places his hand on his thigh and throws his head forward
and repeats the movement towards the point of the upper foot,
quickly lifting the heel of the lower one; and with this impetus he
lifts himself up and at the same time extends the arm which rested
on his knee; and this extension of the arm carries up the body and
the head, and so straightens the spine which was curved.
[32] The higher the step is which a man has to mount, the farther
forward will he place his head in advance of his upper foot, so as
to weigh more on _a_ than on _b_; this man will not be on the step
_m_. As is shown by the line _g f_.
[Footnote: See Pl. XXIII, No. 1. The lower sketch to the left
belongs to the four first lines.]
376.
I ask the weight [pressure] of this man at every degree of motion on
these steps, what weight he gives to _b_ and to _c_.
[Footnote 8: These lines are, in the original, written in ink]
Observe the perpendicular line below the centre of gravity of the
man.
[Footnote: See Pl. XXIII, No. 2.]
377.
In going up stairs if you place your hands on your knees all the
labour taken by the arms is removed from the sinews at the back of
the knees.
[Footnote: See Pl. XXIII, No. 3.]
378.
The sinew which guides the leg, and which is connected with the
patella of the knee, feels it a greater labour to carry the man
upwards, in proportion as the leg is more bent; and the muscle which
acts upon the angle made by the thigh where it joins the body has
less difficulty and has a less weight to lift, because it has not
the [additional] weight of the thigh itself. And besides this it has
stronger muscles, being those which form the buttock.
379.
A man coming down hill takes little steps, because the weight rests
upon the hinder foot, while a man mounting takes wide steps, because
his weight rests on the foremost foot.
[Footnote: See Pl. XXIII, No. 4.]
On the human body in action (380-388).
380.
OF THE HUMAN BODY IN ACTION.
When you want to represent a man as moving some weight consider what
the movements are that are to be represented by different lines;
that is to say either from below upwards, with a simple movement, as
a man does who stoops forward to take up a weight which he will lift
as he straightens himself. Or as a man does who wants to squash
something backwards, or to force it forwards or to pull it downwards
with ropes passed through pullies [Footnote 10: Compare the sketch
on page 198 and on 201 (S. K. M. II.1 86b).]. And here remember that
the weight of a man pulls in proportion as his centre of gravity is
distant from his fulcrum, and to this is added the force given by
his legs and bent back as he raises himself.
381.
Again, a man has even a greater store of strength in his legs than
he needs for his own weight; and to see if this is true, make a man
stand on the shore-sand and then put another man on his back, and
you will see how much he will sink in. Then take the man from off
his back and make him jump straight up as high as he can, and you
will find that the print of his feet will be made deeper by the jump
than from having the man on his back. Hence, here, by 2 methods it
is proved that a man has double the strength he requires to support
his own body.
382.
OF PAINTING.
If you have to draw a man who is in motion, or lifting or pulling,
or carrying a weight equal to his own, in what way must you set on
his legs below his body?
[Footnote: In the MS. this question remains unanswered.]
383.
OF THE STRENGTH OF MAN.
A man pulling a [dead] weight balanced against himself cannot pull
more than his own weight. And if he has to raise it he will [be able
to] raise as much more than his weight as his strength may be more
than that of other men. [Footnote 7: The stroke at the end of this
line finishes in the original in a sort of loop or flourish, and a
similar flourish occurs at the end of the previous passage written
on the same page. M. RAVAISSON regards these as numbers (compare the
photograph of page 30b in his edition of MS. A). He remarks: "_Ce
chiffre_ 8 _et, a la fin de l'alinea precedent, le chiffre_ 7 _sont,
dans le manuscrit, des renvois_."] The greatest force a man can
apply, with equal velocity and impetus, will be when he sets his
feet on one end of the balance [or lever] and then presses his
shoulders against some stable body. This will raise a weight at the
other end of the balance [lever], equal to his own weight and [added
to that] as much weight as he can carry on his shoulders.
384.
No animal can simply move [by its dead weight] a greater weight than
the sum of its own weight outside the centre of his fulcrum.
385.
A man who wants to send an arrow very far from the bow must be
standing entirely on one foot and raising the other so far from the
foot he stands on as to afford the requisite counterpoise to his
body which is thrown on the front foot. And he must not hold his arm
fully extended, and in order that he may be more able to bear the
strain he must hold a piece of wood which there is in all crossbows,
extending from the hand to the breast, and when he wishes to shoot
he suddenly leaps forward at the same instant and extends his arm
with the bow and releases the string. And if he dexterously does
every thing at once it will go a very long way.
386.
When two men are at the opposite ends of a plank that is balanced,
and if they are of equal weight, and if one of them wants to make a
leap into the air, then his leap will be made down from his end of
the plank and the man will never go up again but must remain in his
place till the man at the other end dashes up the board.
[Footnote: See Pl. XXIV, No. 3.]
387.
Of delivering a blow to the right or left.
[Footnote: Four sketches on Pl. XXIV, No. 1 belong to this passage.
The rest of the sketches and notes on that page are of a
miscellaneous nature.]
388.
Why an impetus is not spent at once [but diminishes] gradually in
some one direction? [Footnote 1: The paper has been damaged at the
end of line 1.] The impetus acquired in the line _a b c d_ is spent
in the line _d e_ but not so completely but that some of its force
remains in it and to this force is added the momentum in the line _d
e_ with the force of the motive power, and it must follow than the
impetus multiplied by the blow is greater that the simple impetus
produced by the momentum _d e_.
[Footnote 8: The sketch No. 2 on Pl. XXIV stands, in the original,
between lines 7 and 8. Compare also the sketches on Pl. LIV.] A man
who has to deal a great blow with his weapon prepares himself with
all his force on the opposite side to that where the spot is which
he is to hit; and this is because a body as it gains in velocity
gains in force against the object which impedes its motion.
On hair falling down in curls.
389.
Observe the motion of the surface of the water which resembles that
of hair, and has two motions, of which one goes on with the flow of
the surface, the other forms the lines of the eddies; thus the water
forms eddying whirlpools one part of which are due to the impetus of
the principal current and the other to the incidental motion and
return flow.
[Footnote: See Pl. XXV. Where also the text of this passage is given
in facsimile.]
On draperies (390--392).
390.
OF THE NATURE OF THE FOLDS IN DRAPERY.
That part of a fold which is farthest from the ends where it is
confined will fall most nearly in its natural form.
Every thing by nature tends to remain at rest. Drapery, being of
equal density and thickness on its wrong side and on its right, has
a tendency to lie flat; therefore when you give it a fold or plait
forcing it out of its flatness note well the result of the
constraint in the part where it is most confined; and the part which
is farthest from this constraint you will see relapses most into the
natural state; that is to say lies free and flowing.
EXAMPLE.
[Footnote 13: _a c sia_. In the original text _b_ is written instead
of _c_--an evident slip of the pen.] Let _a b c_ be the fold of the
drapery spoken of above, _a c_ will be the places where this folded
drapery is held fast. I maintain that the part of the drapery which
is farthest from the plaited ends will revert most to its natural
form.
Therefore, _b_ being farthest from _a_ and _c_ in the fold _a b c_
it will be wider there than anywhere else.
[Footnote: See Pl. XXVIII, No. 6, and compare the drawing from
Windsor Pl. XXX for farther illustration of what is here stated.]
391.
OF SMALL FOLDS IN DRAPERIES.
How figures dressed in a cloak should not show the shape so much as
that the cloak looks as if it were next the flesh; since you surely
cannot wish the cloak to be next the flesh, for you must suppose
that between the flesh and the cloak there are other garments which
prevent the forms of the limbs appearing distinctly through the
cloak. And those limbs which you allow to be seen you must make
thicker so that the other garments may appear to be under the cloak.
But only give something of the true thickness of the limbs to a
nymph [Footnote 9: _Una nifa_. Compare the beautiful drawing of a
Nymph, in black chalk from the Windsor collection, Pl. XXVI.] or an
angel, which are represented in thin draperies, pressed and clinging
to the limbs of the figures by the action of the wind.
392.
You ought not to give to drapery a great confusion of many folds,
but rather only introduce them where they are held by the hands or
the arms; the rest you may let fall simply where it is its nature to
flow; and do not let the nude forms be broken by too many details
and interrupted folds. How draperies should be drawn from nature:
that is to say if youwant to represent woollen cloth draw the folds
from that; and if it is to be silk, or fine cloth or coarse, or of
linen or of crape, vary the folds in each and do not represent
dresses, as many do, from models covered with paper or thin leather
which will deceive you greatly.
[Footnote: The little pen and ink drawing from Windsor (W. 102),
given on Pl. XXVIII, No. 7, clearly illustrates the statement made
at the beginning of this passage; the writing of the cipher 19 on
the same page is in Leonardo's hand; the cipher 21 is certainly
not.]
_VIII._
_Botany for Painters and Elements of Landscape Painting._
_The chapters composing this portion of the work consist of
observations on Form, Light and Shade in Plants, and particularly in
Trees summed up in certain general rules by which the author intends
to guide the artist in the pictorial representation of landscape._
_With these the first principles of a_ Theory of Landscape painting
_are laid down--a theory as profoundly thought out in its main
lines as it is lucidly worked out in its details. In reading these
chapters the conviction is irresistible that such a_ Botany for
painters _is or ought to be of similar importance in the practice of
painting as the principles of the Proportions and Movements of the
human figure_ i. e. Anatomy for painters.
_There can be no doubt that Leonardo, in laying down these rules,
did not intend to write on Botany in the proper scientific
sense--his own researches on that subject have no place here; it
need only be observed that they are easily distinguished by their
character and contents from those which are here collected and
arranged under the title 'Botany for painters'. In some cases where
this division might appear doubtful,--as for instance in No._
402--_the Painter is directly addressed and enjoined to take the
rule to heart as of special importance in his art._
_The original materials are principally derived from MS._ G, _in
which we often find this subject treated on several pages in
succession without any of that intermixture of other matters, which
is so frequent in Leonardo's writings. This MS., too, is one of the
latest; when it was written, the great painter was already more than
sixty years of age, so we can scarcely doubt that he regarded all he
wrote as his final views on the subject. And the same remark applies
to the chapters from MSS._ E _and_ M _which were also written
between_ 1513--15.
_For the sake of clearness, however, it has been desirable to
sacrifice--with few exceptions--the original order of the passages
as written, though it was with much reluctance and only after long
hesitation that I resigned myself to this necessity. Nor do I mean
to impugn the logical connection of the author's ideas in his MS.;
but it will be easily understood that the sequence of disconnected
notes, as they occurred to Leonardo and were written down from time
to time, might be hardly satisfactory as a systematic arrangement of
his principles. The reader will find in the Appendix an exact
account of the order of the chapters in the original MS. and from
the data there given can restore them at will. As the materials are
here arranged, the structure of the tree as regards the growth of
the branches comes first_ (394-411) _and then the insertion of the
leaves on the stems_ (412-419). _Then follow the laws of Light and
Shade as applied, first, to the leaves (420-434), and, secondly, to
the whole tree and to groups of trees_ (435-457). _After the remarks
on the Light and Shade in landscapes generally_ (458-464), _we find
special observations on that of views of towns and buildings_
(465-469). _To the theory of Landscape Painting belong also the
passages on the effect of Wind on Trees_ (470-473) _and on the Light
and Shade of Clouds_ (474-477), _since we find in these certain
comparisons with the effect of Light and Shade on Trees_ (e. g.: _in
No._ 476, 4. 5; _and No._ 477, 9. 12). _The chapters given in the
Appendix Nos._ 478 _and_ 481 _have hardly any connection with the
subjects previously treated._
Classification of trees.
393.
TREES.
Small, lofty, straggling, thick, that is as to foliage, dark, light,
russet, branched at the top; some directed towards the eye, some
downwards; with white stems; this transparent in the air, that not;
some standing close together, some scattered.
The relative thickness of the branches to the trunk (393--396).
394.
All the branches of a tree at every stage of its height when put
together are equal in thickness to the trunk [below them].
All the branches of a water [course] at every stage of its course,
if they are of equal rapidity, are equal to the body of the main
stream.
395.
Every year when the boughs of a plant [or tree] have made an end of
maturing their growth, they will have made, when put together, a
thickness equal to that of the main stem; and at every stage of its
ramification you will find the thickness of the said main stem; as:
_i k_, _g h_, _e f_, _c d_, _a b_, will always be equal to each
other; unless the tree is pollard--if so the rule does not hold
good.
All the branches have a direction which tends to the centre of the
tree _m_.
[Footnote: The two sketches of leafless trees one above another on
the left hand side of Pl. XXVII, No. 1, belong to this passage.]
396.
If the plant n grows to the thickness shown at m, its branches will
correspond [in thickness] to the junction a b in consequence of the
growth inside as well as outside.
The branches of trees or plants have a twist wherever a minor branch
is given off; and this giving off the branch forms a fork; this said
fork occurs between two angles of which the largest will be that
which is on the side of the larger branch, and in proportion, unless
accident has spoilt it.
[Footnote: The sketches illustrating this are on the right hand side
of PI. XXVII, No. I, and the text is also given there in facsimile.]
397.
There is no boss on branches which has not been produced by some
branch which has failed.
The lower shoots on the branches of trees grow more than the upper
ones and this occurs only because the sap that nourishes them, being
heavy, tends downwards more than upwards; and again, because those
[branches] which grow downwards turn away from the shade which
exists towards the centre of the plant. The older the branches are,
the greater is the difference between their upper and their lower
shoots and in those dating from the same year or epoch.
[Footnote: The sketch accompanying this in the MS. is so effaced
that an exact reproduction was impossible.]
398.
OF THE SCARS ON TREES.
The scars on trees grow to a greater thickness than is required by
the sap of the limb which nourishes them.
399.
The plant which gives out the smallest ramifications will preserve
the straightest line in the course of its growth.
[Footnote: This passage is illustrated by two partly effaced
sketches. One of these closely resembles the lower one given under
No. 408, the other also represents short closely set boughs on an
upright trunk.]
400.
OF THE RAMIFICATION.
The beginning of the ramification [the shoot] always has the central
line [axis] of its thickness directed to the central line [axis] of
the plant itself.
401.
In starting from the main stem the branches always form a base with
a prominence as is shown at _a b c d_.
402.
WHY, VERY FREQUENTLY, TIMBER HAS VEINS THAT ARE NOT STRAIGHT.
When the branches which grow the second year above the branch of the
preceding year, are not of equal thickness above the antecedent
branches, but are on one side, then the vigour of the lower branch
is diverted to nourish the one above it, although it may be somewhat
on one side.
But if the ramifications are equal in their growth, the veins of the
main stem will be straight [parallel] and equidistant at every
degree of the height of the plant.
Wherefore, O Painter! you, who do not know these laws! in order to
escape the blame of those who understand them, it will be well that
you should represent every thing from nature, and not despise such
study as those do who work [only] for money.
The direction of growth (403-407).
403.
OF THE RAMIFICATIONS OF PLANTS.
The plants which spread very much have the angles of the spaces
which divide their branches more obtuse in proportion as their point
of origin is lower down; that is nearer to the thickest and oldest
portion of the tree. Therefore in the youngest portions of the tree
the angles of ramification are more acute. [Footnote: Compare the
sketches on the lower portion of Pl. XXVII, No. 2.]
404.
The tips of the boughs of plants [and trees], unless they are borne
down by the weight of their fruits, turn towards the sky as much as
possible.
The upper side of their leaves is turned towards the sky that it may
receive the nourishment of the dew which falls at night.
The sun gives spirit and life to plants and the earth nourishes them
with moisture. [9] With regard to this I made the experiment of
leaving only one small root on a gourd and this I kept nourished
with water, and the gourd brought to perfection all the fruits it
could produce, which were about 60 gourds of the long kind, andi set
my mind diligently [to consider] this vitality and perceived that
the dews of night were what supplied it abundantly with moisture
through the insertion of its large leaves and gave nourishment to
the plant and its offspring--or the seeds which its offspring had
to produce--[21].
The rule of the leaves produced on the last shoot of the year will
be that they will grow in a contrary direction on the twin branches;
that is, that the insertion of the leaves turns round each branch in
such a way, as that the sixth leaf above is produced over the sixth
leaf below, and the way they turn is that if one turns towards its
companion to the right, the other turns to the left, the leaf
serving as the nourishing breast for the shoot or fruit which grows
the following year.
[Footnote: A French translation of lines 9-12 was given by M.
RAVAISSON in the _Gazette des Beaux Arts_, Oct. 1877; his paper also
contains some valuable information as to botanical science in the
ancient classical writers and at the time of the Renaissance.]
405.
The lowest branches of those trees which have large leaves and heavy
fruits, such as nut-trees, fig-trees and the like, always droop
towards the ground.
The branches always originate above [in the axis of] the leaves.
406.
The upper shoots of the lateral branches of plants lie closer to the
parent branch than the lower ones.
407.
The lowest branches, after they have formed the angle of their
separation from the parent stem, always bend downwards so as not to
crowd against the other branches which follow them on the same stem
and to be better able to take the air which nourishes them. As is
shown by the angle _b a c_; the branch _a c_ after it has made the
corner of the angle _a c_ bends downwards to _c d_ and the lesser
shoot _c_ dries up, being too thin.
The main branch always goes below, as is shown by the branch _f n
m_, which does not go to _f n o_.
The forms of trees (408--411).
408.
The elm always gives a greater length to the last branches of the
year's growth than to the lower ones; and Nature does this because
the highest branches are those which have to add to the size of the
tree; and those at the bottom must get dry because they grow in the
shade and their growth would be an impediment to the entrance of the
solar rays and the air among the main branches of the tree.
The main branches of the lower part bend down more than those above,
so as to be more oblique than those upper ones, and also because
they are larger and older.
409.
In general almost all the upright portions of trees curve somewhat
turning the convexity towards the South; and their branches are
longer and thicker and more abundant towards the South than towards
the North. And this occurs because the sun draws the sap towards
that surface of the tree which is nearest to it.
And this may be observed if the sun is not screened off by other
plants.
410.
The cherry-tree is of the character of the fir tree as regards its
ramification placed in stages round its main stem; and its branches
spring, 4 or five or 6 [together] opposite each other; and the tips
of the topmost shoots form a pyramid from the middle upwards; and
the walnut and oak form a hemisphere from the middle upwards.
411.
The bough of the walnut which is only hit and beaten when it has
brought to perfection...
[Footnote: The end of the text and the sketch in red chalk belonging
to it, are entirely effaced.]
The insertion of the leaves (412--419).
412.
OF THE INSERTION OF THE BRANCHES ON PLANTS.
Such as the growth of the ramification of plants is on their
principal branches, so is that of the leaves on the shoots of the
same plant. These leaves have [Footnote 6: _Quattro modi_ (four
modes). Only three are described in the text, the fourth is only
suggested by a sketch.
This passage occurs in MANZI'S edition of the Trattato, p. 399, but
without the sketches and the text is mutilated in an important part.
The whole passage has been commented on, from MANZI'S version, in
Part I of the _Nuovo Giornale Botanico Italiano_, by Prof. G.
UZIELLI (Florence 1869, Vol. I). He remarks as to the 'four modes':
"_Leonardo, come si vede nelle linie sententi da solo tre esempli.
Questa ed altre inessattezze fanno desiderare, sia esaminato di
nuovo il manoscritto Vaticano_". This has since been done by D.
KNAPP of Tubingen, and his accurate copy has been published by H.
LUDWIG, the painter. The passage in question occurs in his edition
as No. 833; and there also the drawings are wanting. The space for
them has been left vacant, but in the Vatican copy '_niente_' has
been written on the margin; and in it, as well as in LUDWIG'S and
MANZI'S edition, the text is mutilated.] four modes of growing one
above another. The first, which is the most general, is that the
sixth always originates over the sixth below [Footnote 8: _la sesta
di sotto. "Disposizione 2/5 o 1/5. Leonardo osservo probabilmente
soltanto la prima"_ (UZIELLl).]; the second is that two third ones
above are over the two third ones below [Footnote 10: _terze di
sotto: "Intende qui senza dubbio parlare di foglie decussate, in cui
il terzo verticello e nel piano del primo"_ (UZIELLI).]; and the
third way is that the third above is over the third below [Footnote
11: 3a _di sotto: "Disposizione 1/2"_ (UZIELLI).].
[Footnote: See the four sketches on the upper portion of the page
reproduced as fig. 2 on P1. XXVII.]
413.
A DESCRIPTION OF THE ELM.
The ramification of the elm has the largest branch at the top. The
first and the last but one are smaller, when the main trunk is
straight.
The space between the insertion of one leaf to the rest is half the
extreme length of the leaf or somewhat less, for the leaves are at
an interval which is about the 3rd of the width of the leaf.
The elm has more leaves near the top of the boughs than at the base;
and the broad [surface] of the leaves varies little as to [angle
and] aspect.
[Footnote: See Pl. XXVII, No. 3. Above the sketch and close under
the number of the page is the word '_olmo_' (elm).]
414.
In the walnut tree the leaves which are distributed on the shoots of
this year are further apart from each other and more numerous in
proportion as the branch from which this shoot springs is a young
one. And they are inserted more closely and less in number when the
shoot that bears them springs from an old branch. Its fruits are
borne at the ends of the shoots. And its largest boughs are the
lowest on the boughs they spring from. And this arises from the
weight of its sap which is more apt to descend than to rise, and
consequently the branches which spring from them and rise towards
the sky are small and slender [20]; and when the shoot turns towards
the sky its leaves spread out from it [at an angle] with an equal
distribution of their tips; and if the shoot turns to the horizon
the leaves lie flat; and this arises from the fact that leaves
without exception, turn their underside to the earth [29].
The shoots are smaller in proportion as they spring nearer to the
base of the bough they spring from.
[Footnote: See the two sketches on Pl XXVII, No. 4. The second
refers to the passage lines 20-30.]
415.
OF THE INSERTION OF THE LEAVES ON THE BRANCHES.
The thickness of a branch never diminishes within the space between
one leaf and the next excepting by so much as the thickness of the
bud which is above the leaf and this thickness is taken off from the
branch above [the node] as far as the next leaf.
Nature has so placed the leaves of the latest shoots of many plants
that the sixth leaf is always above the first, and so on in
succession, if the rule is not [accidentally] interfered with; and
this occurs for two useful ends in the plant: First that as the
shoot and the fruit of the following year spring from the bud or eye
which lies above and in close contact with the insertion of the leaf
[in the axil], the water which falls upon the shoot can run down to
nourish the bud, by the drop being caught in the hollow [axil] at
the insertion of the leaf. And the second advantage is, that as
these shoots develop in the following year one will not cover the
next below, since the 5 come forth on five different sides; and the
sixth which is above the first is at some distance.
416.
OF THE RAMIFICATIONS OF TREES AND THEIR FOLIAGE.
The ramifications of any tree, such as the elm, are wide and slender
after the manner of a hand with spread fingers, foreshortened. And
these are seen in the distribution [thus]: the lower portions are
seen from above; and those that are above are seen from below; and
those in the middle, some from below and some from above. The upper
part is the extreme [top] of this ramification and the middle
portion is more foreshortened than any other of those which are
turned with their tips towards you. And of those parts of the middle
of the height of the tree, the longest will be towards the top of
the tree and will produce a ramification like the foliage of the
common willow, which grows on the banks of rivers.
Other ramifications are spherical, as those of such trees as put
forth their shoots and leaves in the order of the sixth being placed
above the first. Others are thin and light like the willow and
others.
417.
You will see in the lower branches of the elder, which puts forth
leaves two and two placed crosswise [at right angles] one above
another, that if the stem rises straight up towards the sky this
order never fails; and its largest leaves are on the thickest part
of the stem and the smallest on the slenderest part, that is towards
the top. But, to return to the lower branches, I say that the leaves
on these are placed on them crosswise like [those on] the upper
branches; and as, by the law of all leaves, they are compelled to
turn their upper surface towards the sky to catch the dew at night,
it is necessary that those so placed should twist round and no
longer form a cross.
[Footnote: See Pl. XXVII, No. 5.]
418.
A leaf always turns its upper side towards the sky so that it may
the better receive, on all its surface, the dew which drops gently
from the atmosphere. And these leaves are so distributed on the
plant as that one shall cover the other as little as possible, but
shall lie alternately one above another as may be seen in the ivy
which covers the walls. And this alternation serves two ends; that
is, to leave intervals by which the air and sun may penetrate
between them. The 2nd reason is that the drops which fall from the
first leaf may fall onto the fourth or--in other trees--onto the
sixth.
419.
Every shoot and every fruit is produced above the insertion [in the
axil] of its leaf which serves it as a mother, giving it water from
the rain and moisture from the dew which falls at night from above,
and often it protects them against the too great heat of the rays of
the sun.
LIGHT ON BRANCHES AND LEAVES (420--422).
420.
That part of the body will be most illuminated which is hit by the
luminous ray coming between right angles.
[Footnote: See Pl. XXVIII, No. 1.]
421.
Young plants have more transparent leaves and a more lustrous bark
than old ones; and particularly the walnut is lighter coloured in
May than in September.
422.
OF THE ACCIDENTS OF COLOURING IN TREES.
The accidents of colour in the foliage of trees are 4. That is:
shadow, light, lustre [reflected light] and transparency.
OF THE VISIBILITY OF THESE ACCIDENTS.
These accidents of colour in the foliage of trees become confused at
a great distance and that which has most breadth [whether light or
shade, &c.] will be most conspicuous.
The proportions of light and shade in a leaf (423-426).
423.
OF THE SHADOWS OF A LEAF.
Sometimes a leaf has three accidents [of light] that is: shade,
lustre [reflected light] and transparency [transmitted light]. Thus,
if the light were at _n_ as regards the leaf _s_, and the eye at
_m_, it would see _a_ in full light, _b_ in shadow and _c_
transparent.
424.
A leaf with a concave surface seen from the under side and
up-side-down will sometimes show itself as half in shade, and half
transparent. Thus, if _o p_ is the leaf and the light _m_ and the
eye _n_, this will see _o_ in shadow because the light does not fall
upon it between equal angles, neither on the upper nor the under
side, and _p_ is lighted on the upper side and the light is
transmitted to its under side. [Footnote: See Pl. XXVIII, No. 2, the
upper sketch on the page. In the original they are drawn in red
chalk.]
425.
Although those leaves which have a polished surface are to a great
extent of the same colour on the right side and on the reverse, it
may happen that the side which is turned towards the atmosphere will
have something of the colour of the atmosphere; and it will seem to
have more of this colour of the atmosphere in proportion as the eye
is nearer to it and sees it more foreshortened. And, without
exception the shadows show as darker on the upper side than on the
lower, from the contrast offered by the high lights which limit the
shadows.
The under side of the leaf, although its colour may be in itself the
same as that of the upper side, shows a still finer colour--a colour
that is green verging on yellow--and this happens when the leaf is
placed between
426.
the eye and the light which falls upon it from the opposite side.
And its shadows are in the same positions as those were of the
opposite side. Therefore, O Painter! when you do trees close at
hand, remember that if the eye is almost under the tree you will see
its leaves [some] on the upper and [some] on the under side, and the
upper side will be bluer in proportion as they are seen more
foreshortened, and the same leaf sometimes shows part of the right
side and part of the under side, whence you must make it of two
colours.
Of the transparency of leaves (427-429).
427.
The shadows in transparent leaves seen from the under side are the
same shadows as there are on the right side of this leaf, they will
show through to the underside together with lights, but the lustre
[reflected light] can never show through.
428.
When one green has another [green] behind it, the lustre on the
leaves and their transparent [lights] show more strongly than in
those which are [seen] against the brightness of the atmosphere.
And if the sun illuminates the leaves without their coming between
it and the eye and without the eye facing the sun, then the
reflected lights and the transparent lights are very strong.
It is very effective to show some branches which are low down and
dark and so set off the illuminated greens which are at some
distance from the dark greens seen below. That part is darkest which
is nearest to the eye or which is farthest from the luminous
atmosphere.
429.
Never paint leaves transparent to the sun, because they are
confused; and this is because on the transparency of one leaf will
be seen the shadow of another leaf which is above it. This shadow
has a distinct outline and a certain depth of shade and sometimes is
[as much as] half or a third of the leaf which is shaded; and
consequently such an arrangement is very confused and the imitation
of it should be avoided.
The light shines least through a leaf when it falls upon it at an
acute angle.
The gradations of shade and colour in leaves (430-434).
430.
The shadows of plants are never black, for where the atmosphere
penetrates there can never be utter darkness.
431.
If the light comes from _m_ and the eye is at _n_ the eye will see
the colour of the leaves _a b_ all affected by the colour of _m_
--that is of the atmosphere; and _b c_ will be seen from the under
side as transparent, with a beautiful green colour verging on
yellow.
If _m_ is the luminous body lighting up the leaf _s_ all the eyes
that see the under side of this leaf will see it of a beautiful
light green, being transparent.
In very many cases the positions of the leaves will be without
shadow [or in full light], and their under side will be transparent
and the right side lustrous [reflecting light].
432.
The willow and other similar trees, which have their boughs lopped
every 3 or 4 years, put forth very straight branches, and their
shadow is about the middle where these boughs spring; and towards
the extreme ends they cast but little shade from having small leaves
and few and slender branches. Hence the boughs which rise towards
the sky will have but little shade and little relief; and the
branches which are at an angle from the horizon, downwards, spring
from the dark part of the shadow and grow thinner by degrees up to
their ends, and these will be in strong relief, being in gradations
of light against a background of shadow.
That tree will have the least shadow which has the fewest branches
and few leaves.
433.
OF DARK LEAVES IN FRONT OF TRANSPARENT ONES.
When the leaves are interposed between the light and the eye, then
that which is nearest to the eye will be the darkest, and the most
distant will be the lightest, not being seen against the atmosphere;
and this is seen in the leaves which are away from the centre of the
tree, that is towards the light.
[Footnote: See Pl. XXVIII, No. 2, the lower sketch.]
434.
OF THE LIGHTS ON DARK LEAVES.
The lights on such leaves which are darkest, will be most near to
the colour of the atmosphere that is reflected in them. And the
cause of this is that the light on the illuminated portion mingles
with the dark hue to compose a blue colour; and this light is
produced by the blueness of the atmosphere which is reflected in the
smooth surface of these leaves and adds to the blue hue which this
light usually produces when it falls on dark objects.
OF THE LIGHTS ON LEAVES OF A YELLOWISH GREEN.
But leaves of a green verging on yellow when they reflect the
atmosphere do not produce a reflection verging on blue, inasmuch as
every thing which appears in a mirror takes some colour from that
mirror, hence the blue of the atmosphere being reflected in the
yellow of the leaf appears green, because blue and yellow mixed
together make a very fine green colour, therefore the lustre of
light leaves verging on yellow will be greenish yellow.
A classification of trees according to their colours.
435.
The trees in a landscape are of various kinds of green, inasmuch as
some verge towards blackness, as firs, pines, cypresses, laurels,
box and the like. Some tend to yellow such as walnuts, and pears,
vines and verdure. Some are both yellowish and dark as chesnuts,
holm-oak. Some turn red in autumn as the service-tree, pomegranate,
vine, and cherry; and some are whitish as the willow, olive, reeds
and the like. Trees are of various forms ...
The proportions of light and shade in trees (436-440).
436.
OF A GENERALLY DISTRIBUTED LIGHT AS LIGHTING UP TREES.
That part of the trees will be seen to lie in the least dark shadow
which is farthest from the earth.
To prove it let _a p_ be the tree, _n b c_ the illuminated
hemisphere [the sky], the under portion of the tree faces the earth
_p c_, that is on the side _o_, and it faces a small part of the
hemisphere at _c d_. But the highest part of the convexity a faces
the greatest part of the hemisphere, that is _b c_. For this
reason--and because it does not face the darkness of the earth--it
is in fuller light. But if the tree has dense foliage, as the
laurel, arbutus, box or holm oak, it will be different; because,
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