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.
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.
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.
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).
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.
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].
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.
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 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.
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.
That portion of a body of uniform breadth which is against a lighter background will look narrower [than the rest].
 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.
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.]
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.
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.
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.
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).
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.
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.
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.]
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.]
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.]
If several luminous bodies are seen from a great distance although they are really separate they will appear united as one body.
If several objects in shadow, standing very close together, are seen against a bright background they will appear separated by wide intervals.
Of several bodies of equal size and tone, that which is farthest will appear the lightest and smallest.
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.
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.
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].
Among shadows of equal depth those which are nearest to the eye will look least deep.
The more brilliant the light given by a luminous body, the deeper will the shadows be cast by the objects it illuminates.
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.
The reciprocal effects of colours on objects placed opposite each other (263-272).
The hue of an illuminated object is affected by that of the luminous body.
The surface of any opaque body is affected by the colour of surrounding objects.
A shadow is always affected by the colour of the surface on which it is cast.
An image produced in a mirror is affected by the colour of the mirror.
OF LIGHT AND SHADE.
Every portion of the surface of a body is varied [in hue] by the [reflected] colour of the object that may be opposite to it.
If you place a spherical body between various objects that is to say with [direct] sunlight on one side of it, and on the other a wall illuminated by the sun, which wall may be green or of any other colour, while the surface on which it is placed may be red, and the two lateral sides are in shadow, you will see that the natural colour of that body will assume something of the hue reflected from those objects. The strongest will be [given by] the luminous body; the second by the illuminated wall, the third by the shadows. There will still be a portion which will take a tint from the colour of the edges.
The surface of every opaque body is affected by the colour of the objects surrounding it. But this effect will be strong or weak in proportion as those objects are more or less remote and more or less strongly [coloured].
The surface of every opaque body assumes the hues reflected from surrounding objects.
The surface of an opaque body assumes the hues of surrounding objects more strongly in proportion as the rays that form the images of those objects strike the surface at more equal angles.
And the surface of an opaque body assumes a stronger hue from the surrounding objects in proportion as that surface is whiter and the colour of the object brighter or more highly illuminated.
OF THE RAYS WHICH CONVEY THROUGH THE AIR THE IMAGES OF OBJECTS.
All the minutest parts of the image intersect each other without interfering with each other. To prove this let r be one of the sides of the hole, opposite to which let s be the eye which sees the lower end o of the line n o. The other extremity cannot transmit its image to the eye s as it has to strike the end r and it is the same with regard to m at the middle of the line. The case is the same with the upper extremity n and the eye u. And if the end n is red the eye u on that side of the holes will not see the green colour of o, but only the red of n according to the 7th of this where it is said: Every form projects images from itself by the shortest line, which necessarily is a straight line, &c.
[Footnote: 13. This probably refers to the diagram given under No. 66.]
The surface of a body assumes in some degree the hue of those around it. The colours of illuminated objects are reflected from the surfaces of one to the other in various spots, according to the various positions of those objects. Let o be a blue object in full light, facing all by itself the space b c on the white sphere a b e d e f, and it will give it a blue tinge, m is a yellow body reflected onto the space a b at the same time as o the blue body, and they give it a green colour (by the 2nd [proposition] of this which shows that blue and yellow make a beautiful green &c.) And the rest will be set forth in the Book on Painting. In that Book it will be shown, that, by transmitting the images of objects and the colours of bodies illuminated by sunlight through a small round perforation and into a dark chamber onto a plane surface, which itself is quite white, &c.
But every thing will be upside down.
Combination of different colours in cast shadows.
That which casts the shadow does not face it, because the shadows are produced by the light which causes and surrounds the shadows. The shadow caused by the light e, which is yellow, has a blue tinge, because the shadow of the body a is cast upon the pavement at b, where the blue light falls; and the shadow produced by the light d, which is blue, will be yellow at c, because the yellow light falls there and the surrounding background to these shadows b c will, besides its natural colour, assume a hue compounded of yellow and blue, because it is lighted by the yellow light and by the blue light both at once.
Shadows of various colours, as affected by the lights falling on them. That light which causes the shadow does not face it.
[Footnote: In the original diagram we find in the circle e "giallo" (yellow) and the cirle d "azurro" (blue) and also under the circle of shadow to the left "giallo" is written and under that to the right "azurro".
In the second diagram where four circles are placed in a row we find written, beginning at the left hand, "giallo" (yellow), "azurro" (blue), "verde" (green), "rosso" (red).]
The effect of colours in the camera obscura (273-274).
The edges of a colour(ed object) transmitted through a small hole are more conspicuous than the central portions.
The edges of the images, of whatever colour, which are transmitted through a small aperture into a dark chamber will always be stronger than the middle portions.
OF THE INTERSECTIONS OF THE IMAGES IN THE PUPIL OF THE EYE.
The intersections of the images as they enter the pupil do not mingle in confusion in the space where that intersection unites them; as is evident, since, if the rays of the sun pass through two panes of glass in close contact, of which one is blue and the other yellow, the rays, in penetrating them, do not become blue or yellow but a beautiful green. And the same thing would happen in the eye, if the images which were yellow or green should mingle where they [meet and] intersect as they enter the pupil. As this does not happen such a mingling does not exist.
OF THE NATURE OF THE RAYS COMPOSED OF THE IMAGES OF OBJECTS, AND OF THEIR INTERSECTIONS.
The directness of the rays which transmit the forms and colours of the bodies whence they proceed does not tinge the air nor can they affect each other by contact where they intersect. They affect only the spot where they vanish and cease to exist, because that spot faces and is faced by the original source of these rays, and no other object, which surrounds that original source can be seen by the eye where these rays are cut off and destroyed, leaving there the spoil they have conveyed to it. And this is proved by the 4th [proposition], on the colour of bodies, which says: The surface of every opaque body is affected by the colour of surrounding objects; hence we may conclude that the spot which, by means of the rays which convey the image, faces--and is faced by the cause of the image, assumes the colour of that object.
On the colours of derived shadows (275. 276).
ANY SHADOW CAST BY AN OPAQUE BODY SMALLER THAN THE LIGHT CAUSING THE SHADOW WILL THROW A DERIVED SHADOW WHICH IS TINGED BY THE COLOUR OF THE LIGHT.
Let n be the source of the shadow e f; it will assume its hue. Let o be the source of h e which will in the same way be tinged by its hue and so also the colour of v h will be affected by p which causes it; and the shadow of the triangle z k y will be affected by the colour of q, because it is produced by it.  In proportion as c d goes into a d, will n r s be darker than m; and the rest of the space will be shadowless . f g is the highest light, because here the whole light of the window a d falls; and thus on the opaque body m e is in equally high light; z k y is a triangle which includes the deepest shadow, because the light a d cannot reach any part of it. x h is the 2nd grade of shadow, because it receives only 1/3 of the light from the window, that is c d. The third grade of shadow is h e, where two thirds of the light from the window is visible. The last grade of shadow is b d e f, because the highest grade of light from the window falls at f.
[Footnote: The diagram Pl. III, No. 1 belongs to this chapter as well as the text given in No. 148. Lines 7-11 (compare lines 8-12 of No. 148) which are written within the diagram, evidently apply to both sections and have therefore been inserted in both.]
OF THE COLOURS OF SIMPLE DERIVED SHADOWS.
The colour of derived shadows is always affected by that of the body towards which they are cast. To prove this: let an opaque body be placed between the plane s c t d and the blue light d e and the red light a b, then I say that d e, the blue light, will fall on the whole surface s c t d excepting at o p which is covered by the shadow of the body q r, as is shown by the straight lines d q o e r p. And the same occurs with the light a b which falls on the whole surface s c t d excepting at the spot obscured by the shadow q r; as is shown by the lines d q o, and e r p. Hence we may conclude that the shadow n m is exposed to the blue light d e; but, as the red light a b cannot fall there, n m will appear as a blue shadow on a red background tinted with blue, because on the surface s c t d both lights can fall. But in the shadows only one single light falls; for this reason these shadows are of medium depth, since, if no light whatever mingled with the shadow, it would be of the first degree of darkness &c. But in the shadow at o p the blue light does not fall, because the body q r interposes and intercepts it there. Only the red light a b falls there and tinges the shadow of a red hue and so a ruddy shadow appears on the background of mingled red and blue.
The shadow of q r at o p is red, being caused by the blue light d e; and the shadow of q r at o' p' is blue being caused by the red light a b. Hence we say that the blue light in this instance causes a red derived shadow from the opaque body q' r', while the red light causes the same body to cast a blue derived shadow; but the primary shadow [on the dark side of the body itself] is not of either of those hues, but a mixture of red and blue.
The derived shadows will be equal in depth if they are produced by lights of equal strength and at an equal distance; this is proved. [Footnote 53: The text is unfinished in the original.]
[Footnote: In the original diagram Leonardo has written within the circle q r corpo obroso (body in shadow); at the spot marked A, luminoso azzurro (blue luminous body); at B, luminoso rosso (red luminous body). At E we read ombra azzurra (blue tinted shadow) and at D ombra rossa (red tinted shadow).]
On the nature of colours (277. 278).
No white or black is transparent.
[Footnote 2: See Footnote 3] Since white is not a colour but the neutral recipient of every colour [Footnote 3: il bianco non e colore ma e inpotentia ricettiva d'ogni colore (white is not a colour, but the neutral recipient of every colour). LEON BATT. ALBERTI "Della pittura" libro I, asserts on the contrary: "Il bianco e'l nero non sono veri colori, ma sono alteratione delli altri colori" (ed. JANITSCHEK, p. 67; Vienna 1877).], when it is seen in the open air and high up, all its shadows are bluish; and this is caused, according to the 4th [prop.], which says: the surface of every opaque body assumes the hue of the surrounding objects. Now this white [body] being deprived of the light of the sun by the interposition of some body between the sun and itself, all that portion of it which is exposed to the sun and atmosphere assumes the colour of the sun and atmosphere; the side on which the sun does not fall remains in shadow and assumes the hue of the atmosphere. And if this white object did not reflect the green of the fields all the way to the horizon nor get the brightness of the horizon itself, it would certainly appear simply of the same hue as the atmosphere.
On gradations in the depth of colours (279. 280).
Since black, when painted next to white, looks no blacker than when next to black; and white when next to black looks no whiter than white, as is seen by the images transmitted through a small hole or by the edges of any opaque screen ...
Of several colours, all equally white, that will look whitest which is against the darkest background. And black will look intensest against the whitest background.
And red will look most vivid against the yellowest background; and the same is the case with all colours when surrounded by their strongest contrasts.
On the reflection of colours (281-283).
Every object devoid of colour in itself is more or less tinged by the colour [of the object] placed opposite. This may be seen by experience, inasmuch as any object which mirrors another assumes the colour of the object mirrored in it. And if the surface thus partially coloured is white the portion which has a red reflection will appear red, or any other colour, whether bright or dark.
Every opaque and colourless body assumes the hue of the colour reflected on it; as happens with a white wall.
That side of an object in light and shade which is towards the light transmits the images of its details more distinctly and immediately to the eye than the side which is in shadow.
The solar rays reflected on a square mirror will be thrown back to distant objects in a circular form.
Any white and opaque surface will be partially coloured by reflections from surrounding objects.
[Footnote 281. 282: The title line of these chapters is in the original simply "pro", which may be an abbreviation for either Propositione or Prospettiva--taking Prospettiva of course in its widest sense, as we often find it used in Leonardo's writings. The title "pro" has here been understood to mean Prospettiva, in accordance with the suggestion afforded by page 10b of this same MS., where the first section is headed Prospettiva in full (see No. 94), while the four following sections are headed merely "pro" (see No. 85).]
WHAT PORTION OF A COLOURED SURFACE OUGHT IN REASON TO BE THE MOST INTENSE.
If a is the light, and b illuminated by it in a direct line, c, on which the light cannot fall, is lighted only by reflection from b which, let us say, is red. Hence the light reflected from it, will be affected by the hue of the surface causing it and will tinge the surface c with red. And if c is also red you will see it much more intense than b; and if it were yellow you would see there a colour between yellow and red.
On the use of dark and light colours in painting (284--286).
WHY BEAUTIFUL COLOURS MUST BE IN THE [HIGHEST] LIGHT.
Since we see that the quality of colour is known [only] by means of light, it is to be supposed that where there is most light the true character of a colour in light will be best seen; and where there is most shadow the colour will be affected by the tone of that. Hence, O Painter! remember to show the true quality of colours in bright lights.
An object represented in white and black will display stronger relief than in any other way; hence I would remind you O Painter! to dress your figures in the lightest colours you can, since, if you put them in dark colours, they will be in too slight relief and inconspicuous from a distance. And the reason is that the shadows of all objects are dark. And if you make a dress dark there is little variety in the lights and shadows, while in light colours there are many grades.
Colours seen in shadow will display more or less of their natural brilliancy in proportion as they are in fainter or deeper shadow.
But if these same colours are situated in a well-lighted place, they will appear brighter in proportion as the light is more brilliant.
The variety of colours in shadow must be as great as that of the colours in the objects in that shadow.
Colours seen in shadow will display less variety in proportion as the shadows in which they lie are deeper. And evidence of this is to be had by looking from an open space into the doorways of dark and shadowy churches, where the pictures which are painted in various colours all look of uniform darkness.
Hence at a considerable distance all the shadows of different colours will appear of the same darkness.
It is the light side of an object in light and shade which shows the true colour.
On the colours of the rainbow (287. 288).
Treat of the rainbow in the last book on Painting, but first write the book on colours produced by the mixture of other colours, so as to be able to prove by those painters' colours how the colours of the rainbow are produced.
WHETHER THE COLOURS OF THE RAINBOW ARE PRODUCED BY THE SUN.
The colours of the rainbow are not produced by the sun, for they occur in many ways without the sunshine; as may be seen by holding a glass of water up to the eye; when, in the glass--where there are those minute bubbles always seen in coarse glass--each bubble, even though the sun does not fall on it, will produce on one side all the colours of the rainbow; as you may see by placing the glass between the day light and your eye in such a way as that it is close to the eye, while on one side the glass admits the [diffused] light of the atmosphere, and on the other side the shadow of the wall on one side of the window; either left or right, it matters not which. Then, by turning the glass round you will see these colours all round the bubbles in the glass &c. And the rest shall be said in its place.
THAT THE EYE HAS NO PART IN PRODUCING THE COLOURS OF THE RAINBOW.
In the experiment just described, the eye would seem to have some share in the colours of the rainbow, since these bubbles in the glass do not display the colours except through the medium of the eye. But, if you place the glass full of water on the window sill, in such a position as that the outer side is exposed to the sun's rays, you will see the same colours produced in the spot of light thrown through the glass and upon the floor, in a dark place, below the window; and as the eye is not here concerned in it, we may evidently, and with certainty pronounce that the eye has no share in producing them.
OF THE COLOURS IN THE FEATHERS OF CERTAIN BIRDS.
There are many birds in various regions of the world on whose feathers we see the most splendid colours produced as they move, as we see in our own country in the feathers of peacocks or on the necks of ducks or pigeons, &c.