[Footnote: The diagram belonging to this passage is placed between lines 5 and 6; it is No. 4 on Pl. VI. ]
A guiding rule.
225
OF THE ATMOSPHERE THAT INTERPOSES BETWEEN THE EYE AND VISIBLE OBJECTS.
An object will appear more or less distinct at the same distance, in proportion as the atmosphere existing between the eye and that object is more or less clear. Hence, as I know that the greater or less quantity of the air that lies between the eye and the object makes the outlines of that object more or less indistinct, you must diminish the definiteness of outline of those objects in proportion to their increasing distance from the eye of the spectator.
An experiment.
226
When I was once in a place on the sea, at an equal distance from the shore and the mountains, the distance from the shore looked much greater than that from the mountains.
On indistinctness at short distances (227-231).
227
If you place an opaque object in front of your eye at a distance of four fingers' breadth, if it is smaller than the space between the two eyes it will not interfere with your seeing any thing that may be beyond it. No object situated beyond another object seen by the eye can be concealed by this [nearer] object if it is smaller than the space from eye to eye.
228
The eye cannot take in a luminous angle which is too close to it.
229
That part of a surface will be better lighted on which the light falls at the greater angle. And that part, on which the shadow falls at the greatest angle, will receive from those rays least of the benefit of the light.
230
OF THE EYE.
The edges of an object placed in front of the pupil of the eye will be less distinct in proportion as they are closer to the eye. This is shown by the edge of the object n placed in front of the pupil d; in looking at this edge the pupil also sees all the space a c which is beyond the edge; and the images the eye receives from that space are mingled with the images of the edge, so that one image confuses the other, and this confusion hinders the pupil from distinguishing the edge.
231
The outlines of objects will be least clear when they are nearest to the eye, and therefore remoter outlines will be clearer. Among objects which are smaller than the pupil of the eye those will be less distinct which are nearer to the eye.
On indistinctness at great distances (232-234).
232
Objects near to the eye will appear larger than those at a distance.
Objects seen with two eyes will appear rounder than if they are seen with only one.
Objects seen between light and shadow will show the most relief.
233
OF PAINTING.
Our true perception of an object diminishes in proportion as its size is diminished by distance.
234
PERSPECTIVE.
Why objects seen at a distance appear large to the eye and in the image on the vertical plane they appear small.
PERSPECTIVE.
I ask how far away the eye can discern a non-luminous body, as, for instance, a mountain. It will be very plainly visible if the sun is behind it; and could be seen at a greater or less distance according to the sun's place in the sky.
[Footnote: The clue to the solution of this problem (lines 1-3) is given in lines 4-6, No. 232. Objects seen with both eyes appear solid since they are seen from two distinct points of sight separated by the distance between the eyes, but this solidity cannot be represented in a flat drawing. Compare No. 535.]
The importance of light and shade in the perspective of disappearance (235-239).
235
An opaque body seen in a line in which the light falls will reveal no prominences to the eye. For instance, let a be the solid body and c the light; c m and c n will be the lines of incidence of the light, that is to say the lines which transmit the light to the object a. The eye being at the point b, I say that since the light c falls on the whole part m n the portions in relief on that side will all be illuminated. Hence the eye placed at c cannot see any light and shade and, not seeing it, every portion will appear of the same tone, therefore the relief in the prominent or rounded parts will not be visible.
236
OF PAINTING.
When you represent in your work shadows which you can only discern with difficulty, and of which you cannot distinguish the edges so that you apprehend them confusedly, you must not make them sharp or definite lest your work should have a wooden effect.
237
OF PAINTING.
You will observe in drawing that among the shadows some are of undistinguishable gradation and form, as is shown in the 3rd [proposition] which says: Rounded surfaces display as many degrees of light and shade as there are varieties of brightness and darkness reflected from the surrounding objects.
238
OF LIGHT AND SHADE.
You who draw from nature, look (carefully) at the extent, the degree, and the form of the lights and shadows on each muscle; and in their position lengthwise observe towards which muscle the axis of the central line is directed.
239
An object which is [so brilliantly illuminated as to be] almost as bright as light will be visible at a greater distance, and of larger apparent size than is natural to objects so remote.
The effect of light or dark backgrounds on the apparent size of objects (240-250).
240
A shadow will appear dark in proportion to the brilliancy of the light surrounding it and conversely it will be less conspicuous where it is seen against a darker background.
241
OF ORDINARY PERSPECTIVE.
An object of equal breadth and colour throughout, seen against a background of various colours will appear unequal in breadth.
And if an object of equal breadth throughout, but of various colours, is seen against a background of uniform colour, that object will appear of various breadth. And the more the colours of the background or of the object seen against the ground vary, the greater will the apparent variations in the breadth be though the objects seen against the ground be of equal breadth [throughout].
242
A dark object seen against a bright background will appear smaller than it is.
A light object will look larger when it is seen against a background darker than itself.
243
OF LIGHT.
A luminous body when obscured by a dense atmosphere will appear smaller; as may be seen by the moon or sun veiled by mists.
OF LIGHT.
Of several luminous bodies of equal size and brilliancy and at an equal distance, that will look the largest which is surrounded by the darkest background.
OF LIGHT.
I find that any luminous body when seen through a dense and thick mist diminishes in proportion to its distance from the eye. Thus it is with the sun by day, as well as the moon and the other eternal lights by night. And when the air is clear, these luminaries appear larger in proportion as they are farther from the eye.
244
That portion of a body of uniform breadth which is against a lighter background will look narrower [than the rest].
[4] e is a given object, itself dark and of uniform breadth; a b and c d are two backgrounds one darker than the other; b c is a bright background, as it might be a spot lighted by the sun through an aperture in a dark room. Then I say that the object e g will appear larger at e f than at g h; because e f has a darker background than g h; and again at f g it will look narrower from being seen by the eye o, on the light background b c. [Footnote 12: The diagram to which the text, lines 1-11, refers, is placed in the original between lines 3 and 4, and is given on Pl. XLI, No. 3. Lines 12 to 14 are explained by the lower of the two diagrams on Pl. XLI, No. 4. In the original these are placed after line 14.] That part of a luminous body, of equal breadth and brilliancy throughout, will look largest which is seen against the darkest background; and the luminous body will seem on fire.
245
WHY BODIES IN LIGHT AND SHADE HAVE THEIR OUTLINES ALTERED BY THE COLOUR AND BRIGHTNESS OF THE OBJECTS SERVING AS A BACKGROUND TO THEM.
If you look at a body of which the illuminated portion lies and ends against a dark background, that part of the light which will look brightest will be that which lies against the dark [background] at d. But if this brighter part lies against a light background, the edge of the object, which is itself light, will be less distinct than before, and the highest light will appear to be between the limit of the background m f and the shadow. The same thing is seen with regard to the dark [side], inasmuch as that edge of the shaded portion of the object which lies against a light background, as at l, it looks much darker than the rest. But if this shadow lies against a dark background, the edge of the shaded part will appear lighter than before, and the deepest shade will appear between the edge and the light at the point o.
[Footnote: In the original diagram o is inside the shaded surface at the level of d.]
246
An opaque body will appear smaller when it is surrounded by a highly luminous background, and a light body will appear larger when it is seen against a darker background. This may be seen in the height of buildings at night, when lightning flashes behind them; it suddenly seems, when it lightens, as though the height of the building were diminished. For the same reason such buildings look larger in a mist, or by night than when the atmosphere is clear and light.
247
ON LIGHT BETWEEN SHADOWS
When you are drawing any object, remember, in comparing the grades of light in the illuminated portions, that the eye is often deceived by seeing things lighter than they are. And the reason lies in our comparing those parts with the contiguous parts. Since if two [separate] parts are in different grades of light and if the less bright is conterminous with a dark portion and the brighter is conterminous with a light background—as the sky or something equally bright—, then that which is less light, or I should say less radiant, will look the brighter and the brighter will seem the darker.
248
Of objects equally dark in themselves and situated at a considerable and equal distance, that will look the darkest which is farthest above the earth.
249
TO PROVE HOW IT IS THAT LUMINOUS BODIES APPEAR LARGER, AT A DISTANCE, THAN THEY ARE.
If you place two lighted candles side by side half a braccio apart, and go from them to a distance 200 braccia you will see that by the increased size of each they will appear as a single luminous body with the light of the two flames, one braccio wide.
TO PROVE HOW YOU MAY SEE THE REAL SIZE OF LUMINOUS BODIES.
If you wish to see the real size of these luminous bodies, take a very thin board and make in it a hole no bigger than the tag of a lace and place it as close to your eye as possible, so that when you look through this hole, at the said light, you can see a large space of air round it. Then by rapidly moving this board backwards and forwards before your eye you will see the light increase [and diminish].
Propositions on perspective of disappearance from MS. C. (250-262).
250
Of several bodies of equal size and equally distant from the eye, those will look the smallest which are against the lightest background.
Every visible object must be surrounded by light and shade. A perfectly spherical body surrounded by light and shade will appear to have one side larger than the other in proportion as one is more highly lighted than the other.
251
PERSPECTIVE.
No visible object can be well understood and comprehended by the human eye excepting from the difference of the background against which the edges of the object terminate and by which they are bounded, and no object will appear [to stand out] separate from that background so far as the outlines of its borders are concerned. The moon, though it is at a great distance from the sun, when, in an eclipse, it comes between our eyes and the sun, appears to the eyes of men to be close to the sun and affixed to it, because the sun is then the background to the moon.
252
A luminous body will appear more brilliant in proportion as it is surrounded by deeper shadow. [Footnote: The diagram which, in the original, is placed after this text, has no connection with it.]
253
The straight edges of a body will appear broken when they are conterminous with a dark space streaked with rays of light. [Footnote: Here again the diagrams in the original have no connection with the text.]
254
Of several bodies, all equally large and equally distant, that which is most brightly illuminated will appear to the eye nearest and largest. [Footnote: Here again the diagrams in the original have no connection with the text.]
255
If several luminous bodies are seen from a great distance although they are really separate they will appear united as one body.
256
If several objects in shadow, standing very close together, are seen against a bright background they will appear separated by wide intervals.
257
Of several bodies of equal size and tone, that which is farthest will appear the lightest and smallest.
258
Of several objects equal in size, brightness of background and length that which has the flattest surface will look the largest. A bar of iron equally thick throughout and of which half is red hot, affords an example, for the red hot part looks thicker than the rest.
259
Of several bodies of equal size and length, and alike in form and in depth of shade, that will appear smallest which is surrounded by the most luminous background.
260
DIFFERENT PORTIONS OF A WALL SURFACE WILL BE DARKER OR BRIGHTER IN PROPORTION AS THE LIGHT OR SHADOW FALLS ON THEM AT A LARGER ANGLE.
The foregoing proposition can be clearly proved in this way. Let us say that m q is the luminous body, then f g will be the opaque body; and let a e be the above-mentioned plane on which the said angles fall, showing [plainly] the nature and character of their bases. Then: a will be more luminous than b; the base of the angle a is larger than that of b and it therefore makes a greater angle which will be a m q; and the pyramid b p m will be narrower and m o c will be still finer, and so on by degrees, in proportion as they are nearer to e, the pyramids will become narrower and darker. That portion of the wall will be the darkest where the breadth of the pyramid of shadow is greater than the breadth of the pyramid of light.
At the point a the pyramid of light is equal in strength to the pyramid of shadow, because the base f g is equal to the base r f. At the point d the pyramid of light is narrower than the pyramid of shadow by so much as the base s f is less than the base f g.
Divide the foregoing proposition into two diagrams, one with the pyramids of light and shadow, the other with the pyramids of light [only].
261
Among shadows of equal depth those which are nearest to the eye will look least deep.
262
The more brilliant the light given by a luminous body, the deeper will the shadows be cast by the objects it illuminates.
V.
Theory of colours
Leonardo's theory of colours is even more intimately connected with his principles of light and shade than his Perspective of Disappearance and is in fact merely an appendix or supplement to those principles, as we gather from the titles to sections 264, 267_, and 276, while others again_ (Nos. 281, 282_) are headed_ Prospettiva.
A very few of these chapters are to be found in the oldest copies and editions of the Treatise on Painting, and although the material they afford is but meager and the connection between them but slight, we must still attribute to them a special theoretical value as well as practical utility—all the more so because our knowledge of the theory and use of colours at the time of the Renaissance is still extremely limited.