The Notebooks of Leonardo Da Vinci, Complete by Leonardo Da Vinci

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But every thing will be upside down.

Combination of different colours in cast shadows.

272.

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).

273.

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.

274.

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).

275.

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. [7] 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 [11]. _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.]

276.

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).

277.

No white or black is transparent.

278.

OF PAINTING.

[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).

279.

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 ...

280.

OF COLOURS.

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).

281.

PERSPECTIVE.

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.

PERSPECTIVE.

Every opaque and colourless body assumes the hue of the colour
reflected on it; as happens with a white wall.

282.

PERSPECTIVE.

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.

PERSPECTIVE.

The solar rays reflected on a square mirror will be thrown back to
distant objects in a circular form.

PERSPECTIVE.

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).]

283.

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).

284.

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.

285.

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.

286.

OF PAINTING.

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 ADVERSARY.

The variety of colours in shadow must be as great as that of the
colours in the objects in that shadow.

THE ANSWER.

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).

287.

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.

288.

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.

Again, on the surface of antique glass found underground and on the
roots of turnips kept for some time at the bottom of wells or other
stagnant waters [we see] that each root displays colours similar to
those of the real rainbow. They may also be seen when oil has been
placed on the top of water and in the solar rays reflected from the
surface of a diamond or beryl; again, through the angular facet of a
beryl every dark object against a background of the atmosphere or
any thing else equally pale-coloured is surrounded by these rainbow
colours between the atmosphere and the dark body; and in many other
circumstances which I will not mention, as these suffice for my
purpose.

_VI._

_'Prospettiva de' colri' (Perspective of Colour)_

_and_

_'Prospettiva aerea' (Aerial Perspective)._

_Leonardo distinctly separates these branches of his subject, as may
be seen in the beginning of No._ 295. _Attempts have been made to
cast doubts on the results which Leonardo arrived at by experiment
on the perspective of colour, but not with justice, as may be seen
from the original text of section_ 294.

_The question as to the composition of the atmosphere, which is
inseparable from a discussion on Aerial Perspective, forms a
separate theory which is treated at considerable length. Indeed the
author enters into it so fully that we cannot escape the conviction
that he must have dwelt with particular pleasure on this part of his
subject, and that he attached great importance to giving it a
character of general applicability._

General rules (289--291).

289.

The variety of colour in objects cannot be discerned at a great
distance, excepting in those parts which are directly lighted up by
the solar rays.

290.

As to the colours of objects: at long distances no difference is
perceptible in the parts in shadow.

291.

OF THE VISIBILITY OF COLOURS.

Which colour strikes most? An object at a distance is most
conspicuous, when it is lightest, and the darkest is least visible.

An exceptional case.

292.

Of the edges [outlines] of shadows. Some have misty and ill defined
edges, others distinct ones.

No opaque body can be devoid of light and shade, except it is in a
mist, on ground covered with snow, or when snow is falling on the
open country which has no light on it and is surrounded with
darkness.

And this occurs [only] in spherical bodies, because in other bodies
which have limbs and parts, those sides of limbs which face each
other reflect on each other the accidental [hue and tone] of their
surface.

An experiment.

293.

ALL COLOURS ARE AT A DISTANCE UNDISTINGUISHABLE AND UNDISCERNIBLE.

All colours at a distance are undistinguishable in shadow, because
an object which is not in the highest light is incapable of
transmitting its image to the eye through an atmosphere more
luminous than itself; since the lesser brightness must be absorbed
by the greater. For instance: We, in a house, can see that all the
colours on the surface of the walls are clearly and instantly
visible when the windows of the house are open; but if we were to go
out of the house and look in at the windows from a little distance
to see the paintings on those walls, instead of the paintings we
should see an uniform deep and colourless shadow.

The practice of the prospettiva de colori.

294.

HOW A PAINTER SHOULD CARRY OUT THE PERSPECTIVE OF COLOUR IN
PRACTICE.

In order to put into practice this perspective of the variation and
loss or diminution of the essential character of colours, observe at
every hundred braccia some objects standing in the landscape, such
as trees, houses, men and particular places. Then in front of the
first tree have a very steady plate of glass and keep your eye very
steady, and then, on this plate of glass, draw a tree, tracing it
over the form of that tree. Then move it on one side so far as that
the real tree is close by the side of the tree you have drawn; then
colour your drawing in such a way as that in colour and form the two
may be alike, and that both, if you close one eye, seem to be
painted on the glass and at the same distance. Then, by the same
method, represent a second tree, and a third, with a distance of a
hundred braccia between each. And these will serve as a standard and
guide whenever you work on your own pictures, wherever they may
apply, and will enable you to give due distance in those works. [14]
But I have found that as a rule the second is 4/5 of the first when
it is 20 braccia beyond it.

[Footnote: This chapter is one of those copied in the Manuscript of
the Vatican library Urbinas 1270, and the original text is rendered
here with no other alterations, but in the orthography. H. LUDWIG,
in his edition of this copy translates lines 14 and 15 thus: "_Ich
finde aber als Regel, dass der zweite um vier Funftel des ersten
abnimmt, wenn er namlich zwanzig Ellen vom ersten entfernt ist
(?)"_. He adds in his commentary: "_Das Ende der Nummer ist wohl
jedenfalls verstummelt_". However the translation given above shows
that it admits of a different rendering.]

The rules of aerial perspective (295--297).

295.

OF AERIAL PERSPECTIVE.

There is another kind of perspective which I call Aerial
Perspective, because by the atmosphere we are able to distinguish
the variations in distance of different buildings, which appear
placed on a single line; as, for instance, when we see several
buildings beyond a wall, all of which, as they appear above the top
of the wall, look of the same size, while you wish to represent them
in a picture as more remote one than another and to give the effect
of a somewhat dense atmosphere. You know that in an atmosphere of
equal density the remotest objects seen through it, as mountains, in
consequence of the great quantity of atmosphere between your eye and
them--appear blue and almost of the same hue as the atmosphere
itself [Footnote 10: _quado il sole e per leuante_ (when the sun is
in the East). Apparently the author refers here to morning light in
general. H. LUDWIG however translates this passage from the Vatican
copy "_wenn namlich die Sonne (dahinter) im Osten steht_".] when the
sun is in the East [Footnote 11: See Footnote 10]. Hence you must
make the nearest building above the wall of its real colour, but the
more distant ones make less defined and bluer. Those you wish should
look farthest away you must make proportionately bluer; thus, if one
is to be five times as distant, make it five times bluer. And by
this rule the buildings which above a [given] line appear of the
same size, will plainly be distinguished as to which are the more
remote and which larger than the others.

296.

The medium lying between the eye and the object seen, tinges that
object with its colour, as the blueness of the atmosphere makes the
distant mountains appear blue and red glass makes objects seen
beyond it, look red. The light shed round them by the stars is
obscured by the darkness of the night which lies between the eye and
the radiant light of the stars.

297.

Take care that the perspective of colour does not disagree with the
size of your objects, hat is to say: that the colours diminish from
their natural [vividness] in proportion as the objects at various
distances dimmish from their natural size.

On the relative density of the atmosphere (298--290).

298.

WHY THE ATMOSPHERE MUST BE REPRESENTED AS PALER TOWARDS THE LOWER
PORTION.

Because the atmosphere is dense near the earth, and the higher it is
the rarer it becomes. When the sun is in the East if you look
towards the West and a little way to the South and North, you will
see that this dense atmosphere receives more light from the sun than
the rarer; because the rays meet with greater resistance. And if the
sky, as you see it, ends on a low plain, that lowest portion of the
sky will be seen through a denser and whiter atmosphere, which will
weaken its true colour as seen through that medium, and there the
sky will look whiter than it is above you, where the line of sight
travels through a smaller space of air charged with heavy vapour.
And if you turn to the East, the atmosphere will appear darker as
you look lower down because the luminous rays pass less freely
through the lower atmosphere.

299.

OF THE MODE OF TREATING REMOTE OBJECTS IN PAINTING.

It is easy to perceive that the atmosphere which lies closest to the
level ground is denser than the rest, and that where it is higher
up, it is rarer and more transparent. The lower portions of large
and lofty objects which are at a distance are not much seen, because
you see them along a line which passes through a denser and thicker
section of the atmosphere. The summits of such heights are seen
along a line which, though it starts from your eye in a dense
atmosphere, still, as it ends at the top of those lofty objects,
ceases in a much rarer atmosphere than exists at their base; for
this reason the farther this line extends from your eye, from point
to point the atmosphere becomes more and more rare. Hence, O
Painter! when you represent mountains, see that from hill to hill
the bases are paler than the summits, and in proportion as they
recede beyond each other make the bases paler than the summits;
while, the higher they are the more you must show of their true form
and colour.

On the colour of the atmosphere (300-307).

300.

OF THE COLOUR OF THE ATMOSPHERE.

I say that the blueness we see in the atmosphere is not intrinsic
colour, but is caused by warm vapour evaporated in minute and
insensible atoms on which the solar rays fall, rendering them
luminous against the infinite darkness of the fiery sphere which
lies beyond and includes it. And this may be seen, as I saw it by
any one going up [Footnote 5: With regard to the place spoken of as
_M'oboso_ (compare No. 301 line 20) its identity will be discussed
under Leonardo's Topographical notes in Vol. II.] Monboso, a peak of
the Alps which divide France from Italy. The base of this mountain
gives birth to the four rivers which flow in four different
directions through the whole of Europe. And no mountain has its base
at so great a height as this, which lifts itself almost above the
clouds; and snow seldom falls there, but only hail in the summer,
when the clouds are highest. And this hail lies [unmelted] there, so
that if it were not for the absorption of the rising and falling
clouds, which does not happen twice in an age, an enormous mass of
ice would be piled up there by the hail, and in the middle of July I
found it very considerable. There I saw above me the dark sky, and
the sun as it fell on the mountain was far brighter here than in the
plains below, because a smaller extent of atmosphere lay between the
summit of the mountain and the sun. Again as an illustration of the
colour of the atmosphere I will mention the smoke of old and dry
wood, which, as it comes out of a chimney, appears to turn very
blue, when seen between the eye and the dark distance. But as it
rises, and comes between the eye and the bright atmosphere, it at
once shows of an ashy grey colour; and this happens because it no
longer has darkness beyond it, but this bright and luminous space.
If the smoke is from young, green wood, it will not appear blue,
because, not being transparent and being full of superabundant
moisture, it has the effect of condensed clouds which take distinct
lights and shadows like a solid body. The same occurs with the
atmosphere, which, when overcharged with moisture appears white, and
the small amount of heated moisture makes it dark, of a dark blue
colour; and this will suffice us so far as concerns the colour of
the atmosphere; though it might be added that, if this transparent
blue were the natural colour of the atmosphere, it would follow that
wherever a larger mass air intervened between the eye and the
element of fire, the azure colour would be more intense; as we see
in blue glass and in sapphires, which are darker in proportion as
they are larger. But the atmosphere in such circumstances behaves in
an opposite manner, inasmuch as where a greater quantity of it lies
between the eye and the sphere of fire, it is seen much whiter. This
occurs towards the horizon. And the less the extent of atmosphere
between the eye and the sphere of fire, the deeper is the blue
colour, as may be seen even on low plains. Hence it follows, as I
say, that the atmosphere assumes this azure hue by reason of the
particles of moisture which catch the rays of the sun. Again, we may
note the difference in particles of dust, or particles of smoke, in
the sun beams admitted through holes into a dark chamber, when the
former will look ash grey and the thin smoke will appear of a most
beautiful blue; and it may be seen again in in the dark shadows of
distant mountains when the air between the eye and those shadows
will look very blue, though the brightest parts of those mountains
will not differ much from their true colour. But if any one wishes
for a final proof let him paint a board with various colours, among
them an intense black; and over all let him lay a very thin and
transparent [coating of] white. He will then see that this
transparent white will nowhere show a more beautiful blue than over
the black--but it must be very thin and finely ground.