Therefore, the images of the illuminated objects are all everywhere on this wall and all in each minutest part of it. The reason is this—we know clearly that this hole must admit some light to the said dwelling and the light admitted by it is derived from one or many luminous bodies. If these bodies are of various shapes and colours the rays forming the images are of various colours and shapes and the representation on the wall will be of various colours and shapes.9
The circle of light which is in the centre of the white of the eye is by nature adapted to apprehend objects. This same circle contains a point which seems black. This is a nerve bored through, which penetrates to the seat of the powers within where impressions are received and judgement formed by the ‘sensus communis’.
Now the objects which are over against the eyes send the rays of their images after the manner of many archers who aim to shoot through the bore of a carbine. The one among them who finds himself in a straight line with the direction of the bore of the carbine will be more likely to hit its bottom with his arrow. Likewise of the objects opposite to the eye those will be more directly transferred to the sense which are more in line with the perforated nerve.
That liquid which is in the light that surrounds the black centre of the eye acts like hounds in the chase, which start the quarry for the hunters to capture. Likewise the humour that is derived from the power of the imprensiva and sees many things without seizing hold of them, suddenly turns thither the central beam which proceeds along the line to the sense and this seizes on the images and confines such as please it within the prison of its memory.10
All bodies together, and each by itself, give off to the surrounding air an infinite number of images which are all in all and all in each part, each conveying the nature, colour, and form of the body which produces it. It can clearly be shown that all bodies pervade all the surrounding atmosphere with their images all in each part as to substance, form, and colour; this is shown by the images of many and various bodies which are reproduced by transmittance through one single perforation, where the lines are made to intersect causing the reversal of the pyramids emanating from the objects, so that their images are reflected upside down on the dark plane (opposite the perforation).11
An experiment, showing how objects transmit their images or pictures, intersecting within the eye in the crystalline humour.
This is shown when the images of illuminated objects penetrate into a very dark chamber by some small round hole. Then you will receive these images on a white paper placed within this dark room rather near to the hole; and you will see all the objects on the paper in their proper forms and colours, but much smaller; and they will be upside down by reason of that very intersection. These images, being transmitted from a place illuminated by the sun, will seem as if actually painted on this paper, which must be extremely thin and looked at from behind. And let the little perforation be made in a very thin plate of iron.
Let abcde be the objects illuminated by the sun and or the front of the dark chamber in which is the hole nm. Let st be the sheet of paper intercepting the rays of the images of these objects and turning them upside down because since the rays are straight a on the right becomes k on the left, and e on the left becomes f on the right; and the same takes place inside the pupil.12
Necessity has provided that all the images of objects in front of the eye shall intersect in two planes. One of these intersections is in the pupil, the other in the crystalline lens; and if this were not the case the eye could not see so great a number of objects as it does. . . . No image, even of the smaller object, enters the eye without being turned upside down; but as it penetrates into the crystalline lens it is once more reversed and thus the image is restored to the same position within the eye as that of the object outside the eye.*13
It is impossible that the eye should project from itself, by visual rays, the visual power,* since as soon as it opens, the front portion (of the eye) which would give rise to this emanation would have to go forth to the object, and it could not do this without time. And this being so, it could not travel so high as the sun in a month’s time when the eye wanted to see it. And if it could reach the sun it would necessarily follow that it should perpetually remain in a continuous line from the eye to the sun and should always diverge in such a way as to form between the sun and the eye the base and the apex of a pyramid. This being the case, if the eye consisted of a million worlds, it would not prevent its being consumed in the projection of its power; and if this power would have to travel through the air as perfumes do, the winds would bend it and carry it into another place. But we do (in fact) see the mass of the sun with the same rapidity as (an object) at the distance of a braccio, and the power of sight is not disturbed by the blowing of the winds nor by any other accident.14
I say that the power of vision extends through the visual rays to the surface of non-transparent bodies, while the power possessed by these bodies extends to the power of vision. Likewise each body pervades the surrounding air with its image; each separately and all together do the same; and not only do they pervade it with the semblance of the shape, but also with that of their power.
Example
You will see when the sun is over the centre of our hemisphere that wherever it reveals itself there are semblances of form; and you will also perceive the reflections of its radiance as well as the glow of its heat; and all these powers proceed from the same source by means of radiant lines that issue from its body and they end in the opaque objects without entailing any diminution at the source.
Confutation
Those mathematicians then who argue that no spiritual power can emanate from the eye, because this could not be without greatly impairing the power of vision, and therefore maintain that the eye takes in but does not send forth anything from itself.
Example
What will they say of the musk which always keeps a great quantity of its surrounding atmosphere charged with odour, and which when carried miles will permeate a thousand miles with that perfume without diminution of itself?
Or will they say that the ringing of the bell by its clapper, which daily fills the whole countryside with its sound, must of necessity consume this bell?
Certainly it seems, there are such men as these—but enough! Is not that snake called lamia seen daily by the rustics attracting to itself with fixed gaze as the magnet attracts iron, the nightingale which hastens to her death with mournful song? . . . Maidens are said to have power in their eyes to attract to themselves the love of men. . . .15
(c) Perspective
Perspective is the bridle and rudder of painting.16
Painting is based upon perspective which is nothing else than a thorough knowledge of the function of the eye. And this function simply consists in receiving in a pyramid the forms and colours of all objects placed before it. I say in a pyramid, because there is no object so small that it will not be larger than the spot where these pyramids are received into the eye. Therefore if you extend the lines from the edges of each body as they converge you will bring them to a single point, and necessarily the said lines must form a pyramid.17
There are three branches of perspective; the first deals with the reasons of the (apparent) diminution of objects as they recede from the eye, and is known as Perspective of Diminution; the second contains the way in which colours vary as they recede from the eye; the third and last explains how objects should appear less distinct in proportion as they are more remote. And the names are as follows: Linear perspective, the perspective of colour, the perspective of disappearance.*18
The science of painting deals with all the colours of the surfaces of bodies and with the shapes of the bodies thus enclosed; with their relative nearness and distance; with the degrees of diminution required as distances gradually increase; and this science is the mother of perspective, that is the science of visual rays. Perspective is divided into three parts, of which the first deals only with the line-drawing of bodies; the second with the to
ning down of colours as they recede into the distance; the third with the loss of distinctness of bodies at various distances. Now the first part which deals only with lines and boundaries of bodies is called drawing, that is to say the figuration of any body. From it springs another science that deals with shade and light, also called chiaroscuro which requires much explanation.19
Perspective is nothing else than the seeing a place behind a sheet of glass, smooth and quite transparent, on the surface of which all the things may be marked that are behind this glass. The things approach the point of the eye in pyramids, and these pyramids are intersected on the glass plane.20
A method of drawing an object in relief at night
Place a sheet of not too transparent paper between the object and the light and you can draw it very well.20
Every bodily form, so far as it affects the eye, includes three attributes; namely mass, shape, and colour; and the mass is recognizable at a greater distance from its source than either colour or shape. Again colour is discernible at a greater distance than shape, but this law does not apply to luminous bodies.21
Perspective
Among objects of equal size that which is most remote from the eye will look smallest.22
Of several bodies of equal size and tone, that which is furthest will appear lightest and smallest.23
Of several bodies, all equally large and equally distant, that which is most brightly illuminated will appear to the eye nearest and largest.24
Among shadows of equal depth those nearest to the eye will look least deep.25
A dark object will appear bluer in proportion as it has more luminous atmosphere between it and the eye, as may be seen in the colour of the sky.26
I ask to have this much granted me (as axiom)—to assert that every ray passing through air of equal density travels in a straight line from its cause to the object or place where it strikes.*27
The air is full of infinite straight and radiating lines intersected and interwoven with one another, without one occupying the place of another. They represent to whatever object the true form of their cause.28
The body of the atmosphere is full of infinite radiating pyramids produced by the objects existing in it. These intersect and cross each other with independent convergence without interference with each other and pass through all the surrounding atmosphere.29
The vertical plane is represented by a perpendicular line and it is imagined as being placed in front of the common point where the concourse of the pyramid converges. And this plane bears the same relation to this point as a plane of glass would, upon which you drew the various objects that you saw through it. And the objects thus drawn would be so much smaller than the originals as the space between the glass and the eye was smaller than that between the glass and the objects.30
If the eye be in the middle of a course with two horses running to their goal along parallel tracks, it will seem to it as if they were running to meet one another. This, as has been stated, occurs because the images of the horses which impress themselves upon the eye are moving towards the centre of the surface of the pupil of the eye.31
As regards the point in the eye it may be comprehended with greater ease if you look into the eye of anyone you will see your image there. Now imagine two lines starting from your ears and going to the ears of that image which you see of yourself in the eye of the other person. You will clearly recognize that these lines converge in such a way that they would meet in a point a little way beyond your own image mirrored in the eye.32
And if you want to measure the diminution of the pyramid in the air which occupies the space between the object seen and the eye, you must do it according to the diagram figured above. Let mn be a tower, and ef a rod which you must move backwards and forwards till its ends correspond with those of the tower; then bring it nearer to the eye, at cd and you will see that the image of the tower seems smaller as at to. Then bring it still closer to the eye, and you will see the rod project far beyond the image of the tower, . . . and so you will discern that, a little further within the lines must converge in a point.32
Only one line of all those that reach the visual power has no intersection and this has no sensible dimensions because it is a mathematical line which originates from a mathematical point which has no dimension.33
Let ab be the vertical [picture] plane and r the point of the pyramids terminating in the eye and n the point of diminution which is always in a straight line opposite the eye and always moves as the eye moves—just as when a rod is moved its shadow moves, precisely as the shadow moves with a body. And each of the two points is the apex of pyramids having common bases at the intervening vertical planes. But, although their bases are equal, their angles are not equal because the point of diminution is the termination of a smaller angle than that of the eye. If you ask me: ‘By what practical experience can you show me these points?’ I reply—so far as concerns the point of diminution which moves with you—when you walk by a ploughed field look at the straight furrows which come down with their ends to the path where you are walking, and you will see that each pair of furrows will look as though they tried to get nearer and meet at the [further] end. . . .34
2. THE SURFACE OF THINGS AND LIGHT
In so far as the art of painting is concerned with the representation of the surfaces of objects it is allied to spatial geometry. The surfaces are conceived as without substance like geometric planes; and the axioms of Euclid’s Elements defining the point, the line, the plane apply to them.
Moreover, the places and colours of objects are revealed by rays of light which radiate from their source in pyramidal formation. At the bases of these pyramids are the objects which the rays strike at different angles as they drive away the surrounding darkness; and through this interplay of light and shadow the objects emerge into view.
Leonardo excelled in modelling by gradations of light and dark, and was a developer of chiaroscuro (the modelling of forms from white to black) and sfumato (the ‘smoked’ effect of blurring edges).
His treatise on painting was imbued with the conception which he had formed of nature. The four simple colours, red, blue, green, and yellow were related to the four elements, fire, air, water, and earth, the way in which objects were enveloped in space was similar to the way in which the elements came in contact with one another.
(a) The Geometric Foundation
Let no man who is not a mathematician read the Elements of my work.35
The science of painting begins with the point, then comes the line, the plane comes third, and the fourth the body in its vesture of planes. This is as far as the representation of objects goes. For painting does not, as a matter of fact, extend beyond the surface; and it is by its surface that the body of any visible thing is represented.36
A point is that which has no centre. It has neither breadth, length, nor depth. A line is a length produced by the movement of a point, and its extremities are points. It has neither breadth nor depth. A surface is an extension made by the transversal movement of a line, and its extremities are lines. (A surface has no depth.) A body is a quantity formed by the lateral movement of a surface and its boundaries are surfaces. A body is a length, and it has breadth with depth formed by the lateral movement of its surface.37
1. The surface is a limitation of the body. 2. The limitation of the body is no part of that body. 3. That which is not part of any body is a thing of naught. 4. A thing of naught is that which fills no space. The limitation of one body is that which begins another.38
The limiting surface is the beginning of another. The limits of two coterminous bodies are interchangeably the surface of the one and of the other, as water with air. None of the surfaces of bodies are parts of these bodies.39
The boundaries of bodies are the boundaries of their planes, and the boundaries of the planes are lines. Which lines do not form part of the size of the planes, nor of the atmosphere which surrounds these planes; therefore that which is not part of anything is invi
sible as is proved in geometry.40
The boundary of one thing with another is of the nature of a mathematical line, but not of a drawn line, because the end of one colour is the beginning of another colour—the boundary is a thing invisible.41
Empty space begins where the object ends. Where empty space ends the object begins and where the object ends emptiness begins.42
The point has no centre, but is itself a centre and nothing can be smaller. The point is the minimum. The point is indivisible by the mind. The point has no parts. The point is the end which nothingness and the line have in common. It is neither nothingness nor line, nor does it occupy a space between them. Therefore the end of nothingness and the beginning of the line are in contact with one another, but they are not joined together, for between them, dividing them, is the point. . . .
And from this it follows that many points imagined in continuous contact do not constitute the line and therefore many lines in continuous contact along their sides do not make a surface, nor do many surfaces in continuous contact make a body, because among us bodies are not formed of incorporeal things. . . .
The contact of the liquid with the solid is a surface common to the liquid and the solid. Similarly the contact between a heavier and a lighter liquid is a surface common to them both. The surface does not form part of either—it is merely the common boundary.
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