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.