Sunday, October 22, 2006

From the Notebooks of Leonardo da Vinci

Mona Lisa

Florentine artist Leonardo da Vinci painted Mona Lisa (1503-1506, Louvre, Paris) in oil on a wood background. Originally, he portrayed the subject in a loggia with columns on either side, but in the end the artist decided to simplify the content. This painting is remarkable for many things, among them the way that the images are created with tones rather than lines and the impeccable use of chiaroscuro (light and dark).Bridgeman Art Library, London/New York
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The life and structure of things

Although the painter's eye sees but the surface of things it must in rendering the surface discern and interpret the organic structure that lies beneath. The representation of the human figure entails a knowledge of its anatomy and its proportions. Landscapes entail a study of the morphology of plants, of the formation of the earth, of the movements of water and wind.

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

Then I will describe which are the members which after the boy is born, grow more than the others, and determine the proportions of a boy of one year. Then describe the fully grown man and woman, with their proportions, and the nature of their complexions, colour, and physiognomy.

Then how they are composed of veins, tendons, muscles, and bones. Then in four drawings represent four universal conditions of men. That is, mirth with various acts of laughter; and describe the cause of laughter. Weeping in various aspects with its causes. Strife with various acts of killing: flight, fear, ferocity, boldness, murder, and everything pertaining to such conditions. Then represent Labour with pulling, thrusting, carrying, stopping, supporting, and such-like things.

Further, I would describe attitudes and movements. Then perspective concerning the function of the eye; and of hearing—here I will speak of music—and treat of the other senses—and describe the nature of the five senses. This mechanism of man we will demonstrate with [drawings of] figures.

(a) Proportion

The theory of proportions had a great fascination for Renaissance artists. Their canons were not only intended as a means of artistic workmanship, they were meant to achieve harmony. Proportions in painting, sculpture, and architecture were like harmony in music and gave intense delight.

Proportion is not only found in numbers and measurements but also in sounds, weights, time, and position, and whatever power there may be.

The Roman architect Vitruvius had transmitted some data of a Greek canon for the proportions of the human figure and these were revived in Renaissance time. A drawing by Leonardo, now in the Academy at Venice, was reproduced in an edition of Vitruvius' book, published in 1511, in order to illustrate the statement that a well-made human body with arms outstretched and feet together can be inscribed in a square; while the same body spread-eagled occupies a circle described around the navel. The proportions of the human body are here related to the most perfect geometric figures and may be said to be integrated into the spherical cosmos. Leonardo endeavoured to verify and elaborate Vitruvius' mathematical formulae in order to put them on a scientific basis by empirical observations, and for this purpose he collected data from living models.

Geometry is infinite because every continuous quantity is divisible to infinity in one direction or the other. But the discontinuous quantity commences in unity and increases to infinity, and as it has been said the continuous quantity increases to infinity and decreases to infinity. And if you give me a line of twenty braccia I will tell you how to make one of twenty-one.

Every part of the whole must be in proportion to the whole … I would have the same thing understood as applying to all animals and plants.

From painting which serves the eye, the noblest sense, arises harmony of proportions; just as many different voices joined together and singing simultaneously produce a harmonious proportion which gives such satisfaction to the sense of hearing that listeners remain spellbound with admiration as if half alive. But the effect of the beautiful proportion of an angelic face in painting is much greater, for these proportions produce a harmonious concord which reaches the eye simultaneously, just as a chord in music affects the ear; and if this beautiful harmony be shown to the lover of her whose beauty is portrayed, he will without doubt remain spellbound in admiration and in a joy without parallel and superior to all other sensations.

The painter in his harmonious proportions makes the component parts react simultaneously so that they can be seen at one and the same time both together and separately; together, by viewing the design of the composition as a whole; and separately by viewing the design of its component parts.

Vitruvius, the architect, says in his work on architecture that the measurements of the human body are distributed by nature as follows: 4 fingers make 1 palm; 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 buildings.

If you open your legs so much as to decrease your height by 1/14 and spread and raise your arms so that your middle fingers are on a level with the top of your head, you must know that the navel will be the centre of a circle of which the outspread limbs touch the circumference; and the space between the legs will form an equilateral triangle.

The span 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 part of a man's height; from the bottom of the chin to the crown of the head is the eighth of the man's height; from the top of the breast to the crown of the head is the sixth of the man; from the top of the breast to the roots of the hair is the seventh part of the whole height; from the nipples to the crown of the head is a fourth part of the man. The maximum width of the shoulders is the fourth part of the height; from the elbow to the tip of the middle finger is the fifth part; from the elbow to the end of the shoulder is the eighth part. The complete hand is the tenth part. The penis begins at the centre of the man. The foot is the seventh part of the man. From the sole of the foot to just below the knee is the fourth part of the man. From below the knee to where the penis begins is the fourth part of the man.

The distance between the chin and the nose and that between the eyebrows and the beginning of the hair is equal to the height of the ear and is a third of the face.

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 joins the thigh bone. The hand to the wrist goes four times into the distance from the tip of the longest finger to the shoulder-joint.

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 he 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 armpits and the bottom of the buttock.

Every man at three years is half the full height he will grow to at last.

There is a great difference in the length between the joints in men and boys. In man the distance from the shoulder joint 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 only one head; because Nature forms for us the size which is the home of the intellect before forming what contains the vital elements.

Remember to be very careful in giving your figures limbs that they should appear to be in proportion to the size of the body and agree with the age. Thus a youth has limbs that are not very muscular nor 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 veins very prominent.

(b) The Anatomy and Movement of the Body

The human body is a complex unity within the larger field of nature, a microcosm wherein the Elements and Powers of the universe were incorporated. In order to study its structure Leonardo dissected corpses and examined bones, joints, and muscles separately and in relation to one another, making drawings from many points of view and taking recourse to visual demonstration since an adequate description could not be given in words. According to him such visual demonstrations gave 'complete and accurate conceptions of the various shapes such as neither ancient nor modern writers have ever been able to give without an infinitely tedious and confused prolixity of writing and of time.' Moreover, there are not only the various points of view, the infinity of aspects to be considered, there are also the continuous successions of phases in movements. The circular movements of shoulder, arm, and hand, for instance, is suggestive of a pictorial continuity such as we may see on a strip of film.

The study of structure included that of function, of the manner in which actions and gestures were performed, how the various muscles work together in bending and straightening the joints; how the weight of a body is supported and balanced. Leonardo looked upon anatomy with the eye of a mechanician. Each limb, each organ was believed to be designed and perfectly adapted to perform its special function. Thus the muscles of the tongue were made to produce innumerable sounds within the mouth enabling man to pronounce many languages. In his time divisions between the various branches of anatomy did not exist. He investigated problems of physiology and embryology, the systems of nerves and arteries. He anticipated the principle of blood circulation and prepared the ground for further analyses on many subjects.

You who say that it is better to watch an anatomical demonstration than to see these drawings, you would be right if it were possible to observe all the details shown in such drawings in a single figure, in which with all your cleverness you will not see or acquire knowledge of more than some few veins, while in order to obtain a true and complete knowledge of these, I have dissected more than ten human bodies, destroying all the various members and removing the minutest particles of the flesh which surrounded these veins, without causing any effusion of blood other than the imperceptible bleeding of the capillary veins. And as one single body did not suffice for so long a time, it was necessary to proceed by stages with so many bodies as would render my knowledge complete; this I repeated twice in order to discover the differences. And though you should have a love for such things you may perhaps be deterred by natural repugnance, and if this does not prevent you, you may perhaps be deterred by fear of passing the night hours in the company of these corpses, quartered and flayed and horrible to behold; and if this does not deter you, then perhaps you may lack the skill in drawing, essential for such representation; and if you had the skill in drawing, it may not be combined with a knowledge of perspective; and if it is so combined you may not understand the methods of geometrical demonstration and the method of estimating the forces and strength of muscles; or perhaps you may be wanting in patience so that you will not be diligent.

Concerning which things, whether or no they have all been found in me, the hundred and twenty books which I have composed will give verdict 'yes' or 'no.' In these I have not been hindered either by avarice or negligence, but only by want of time. Farewell.

How it is necessary for the painter to know the inner structure of man

The painter who has a knowledge of the nature of the sinews, muscles, and tendons will know very well in the movement of a limb how many and which of the sinews are the cause of it, and which muscle by swelling is the cause of the contraction of that sinew; and which sinews expanded into most delicate cartilage surround and support the said muscle.

Thus he will in divers ways and universally indicate the various muscles by means of the different attitudes of his figures; and will not do like many who, in a variety of movements, still display the same things in the arms, the backs, the breasts, and legs. And these things are not to be regarded as minor faults.

In fifteen entire figures there shall be revealed to you the microcosm on the same plan as before me was adopted by Ptolemy in his cosmography; and I shall divide them into limbs as he divided the macrocosm into provinces; and I shall then define the functions of the parts in every direction, placing before your eyes the representation of the whole figure of man and his capacity of movements by means of his parts. And would that it might please our Creator that I were able to reveal the nature of man and his customs even as I describe his figure.

Remember, in order to make sure of the origin of each muscle to pull the tendon produced by this muscle in such a way as to see this muscle move, and its attachment to the ligaments of the bones. You will make nothing but confusion in demonstrating the muscles and their positions, origins and ends, unless you first make a demonstration of thin muscles after the manner of threads; and in this way you will be able to represent them one over the other as nature has placed them; and thus you can name them according to the limb they serve, for instance the mover of the tip of the big toe, and of its middle bone or of the first bone, etc. And when you have given this information you will draw by the side of it the true form and size and position of each muscle; but remember to make the threads which denote the muscles in the same positions as the central line of each muscle; and so these threads will demonstrate the shape of the leg and their distance in a plain and clear manner.

Of the hand from within

When you begin the hand from within first separate all the bones a little from each other so that you may be able quickly to recognize the true shape of each bone from the palm side of the hand and also the real number and position in each finger; and have some sawn through lengthwise, so as to show which is hollow and which is full. And having done this replace the bones together at their true contacts and represent the whole hand from within wide open. The next demonstration should be of the muscles around the wrist and the rest of the hand. The fifth shall represent the tendons which move the first joints of the fingers. The sixth the tendons which move the second joints of the fingers. The seventh those which move the third joints of these fingers. The eighth shall represent the nerves which give them the sense of touch. The ninth the veins and the arteries. The tenth shall show the whole hand complete with its skin and its measurements; and measurements should also be taken of the bones. And whatever you do for this side of the hand you should also do for the other three sides—that is for the palmar side, for the dorsal side, and for the sides of the extensor and flexor muscles. And thus in the chapter on the hand you will give forty demonstrations; and you should do the same with each limb. And in this way you will attain thorough knowledge. You should afterwards make a discourse concerning the hands of each of the animals, in order to show in what way they vary. In the bear for instance the ligaments of the tendons of the toes are attached above the ankle of the foot.

Weight, force, and the motion of bodies and percussion are the four elemental powers in which all the visible actions of mortals have their being and their end.

After the demonstration of all the parts of the limbs or men and of the other animals you will represent the proper way of action of these limbs, that is in rising from lying down, in moving, running, and jumping in various attitudes, in lifting and carrying heavy weights, in throwing things to a distance, and in swimming; and in every action you will show which limbs and which muscles perform it, and deal especially with the play of the arms.

As regards the disposition of the limbs in movement you will have to consider that when you wish to represent a man who for some reason has to turn backwards or to one side you must not make him move his feet and all his limbs towards the side to which he turns his head. Rather must you make the action proceed by degrees and through the different joints, that is those of the foot, the knee, the hips, and the neck. If you set him on the right leg, you must make his left knee bend inwards and his left foot slightly raised on the outside; and let the left shoulder be somewhat lower than the right; and the nape of the neck is in a line directly over the outer ankle of the left foot. And the left shoulder will be in a perpendicular line above the toes of the right foot. And always set your figures so that the side to which the head turns is not the side to which the breast faces, since nature for our convenience has made us with a neck which bends with ease in many directions as the eye turns to various points and the other joints are partly obedient to it.

On the grace of the limbs

The limbs should be adapted to the body with grace and with reference to the effect that you wish the figure to produce. If you wish to produce a figure that shall look light and graceful in itself you must make the limbs elegant and extended, and without too much display of the muscles; and the few that are needed you must indicate softly, that is, not very prominently and without strong shadows; the limbs and particularly the arms easy, so that they should not be in a straight line with the adjoining parts. If the hips, which are the pole of a man, are placed so that the right is higher than the left, then let the right shoulder be lower than the left and make the joint of the higher shoulder in a perpendicular line above the highest prominence of the hip. Let the pit of the throat always be over the centre of the ankle of that foot on which the man is leaning. The leg which is free should have the knee lower than the other, and near the other leg. The positions of head and arms are infinitely varied and I shall therefore not enlarge on any rules for them. Let them, however, be easy and pleasing, with various turns and twists and the joints gracefully bent, that they may not look like pieces of wood.

That is called simple movement in a man when he simply bends forward, or backwards, or to the side.

That is called a compound movement in a man when some purpose required bending down and to the side at the same time.…

Of human movement

When you wish to represent a man in the act of moving some weight reflect that these movements are to be represented in different directions. A man may stoop to lift a weight with the intention of lifting it as he straightens himself; this is a simple movement from below upwards; or he may wish to pull something backward, or push it forward or draw it down with a rope that passes over a pulley. Here you should remember that a man's weight drags in proportion as the centre of his gravity is distant from that of his support, and you must add to this the force exerted by his legs and bent spine as he straightens himself.

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; the muscle which acts upon the angle made by the thigh where it joins the body has less difficulty and less weight to lift, because it has not the weight of the thigh itself. And besides this its muscles are stronger being those which form the buttock.

The first thing that the man does when he ascends by steps is to free the leg which he wishes to raise from the weight of the trunk which is resting upon this leg, and at the same time he loads the other leg with his entire weight including that of the raised leg. Then he raises the leg and places the foot on the step where he wishes to mount; having done this he conveys to the higher foot all the weight of the trunk and of the leg and leaning his hand upon his thigh, thrusts the head forward and moves towards the point of the higher foot, while raising swiftly the heel of the lower foot; and with the impetus thus acquired he raises himself up; and at the same time by extending the arm which was resting upon his knee he pushes the trunk and head upwards and thus straightens the curve of his back.

Man and every animal undergoes more fatigue in going upwards than downwards, for as he ascends he bears his weight with him and as he descends he simply lets it go.

A man, in running, throws less of his weight on his legs than when he is standing still. In like manner the horse, when running, is less conscious of the weight of the man whom it is carrying; consequently many consider it marvellous that a horse in a race can support itself on one foot only. Therefore we may say regarding weight in transverse movement that the swifter the movement, the less the weight towards the centre of the earth.…

It is impossible that any memory can hold all the aspects and mutations of any limb of any animal. We shall demonstrate this by taking the hand for an example. Since every continuous quantity is divisible in infinitum the movement of the eye, which observes the hand, travels through a space, which is also a continuous quantity and there divisible in infinitum. And in every stage of the movement the aspect and shape of the hand varies when it is seen, and will continue to vary as the eye moves in a complete circle. And the hand in turn will act in a similar way as it is raised in its movement, that is to say it will travel through space which is a continuous quantity.

There are [four] principal simple movements in the flexion performed by the joint of the shoulder, namely when the arm attached to the same moves upward or downwards or forward or backward. One might say, though, that such movements are infinite. For if we turn our shoulder towards a wall and describe a circular figure with our arm we shall have performed all the movements contained in the said shoulder. And, since [every circle is] a continuous quantity, the movement of the arm [has produced] a continuous quantity. This movement would not produce a continuous quantity were it not guided by the principle of continuation. Therefore, the movement of that arm has been through all the parts of the circle. And as the circle is divisible in infinitum the variations of the shoulder have been infinite.

One and the same action seen from various places

One and the same attitude is shown in an infinite number of variations, because it can be viewed from an infinite number of places and these places are of a continuous quantity, and a continuous quantity is divisible into an infinite number of parts. Consequently every human action shows itself in an infinite variety of situations.

The movements of man performed on one single occasion or for one single purpose are infinitely varied in themselves. This can be proved thus. Let us assume that a man strikes some object. Then I say that his stroke is made up of two states. Either he is lifting the thing which must descend in order to bring about the stroke, or this thing is already descending. Whichever may be the case, it is undeniable that the movement occurs in space and that space is a continuous quantity, and that every continuous quantity is divisible in infinitum. The conclusion is that every movement of the thing which descends is variable in infinitum.

Source: Da Vinci, Leonardo. The Notebooks of Leonardo da Vinci. Richter, Irma A., ed. © 1998. Reproduced by permission of Oxford University Press.

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