The Notebooks of Leonardo Da Vinci (17 page)

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.

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.

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.

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.

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.

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).

263.

The hue of an illuminated object is affected by that of the luminous
body.

264.

The surface of any opaque body is affected by the colour of
surrounding objects.

265.

A shadow is always affected by the colour of the surface on which it
is cast.

266.

An image produced in a mirror is affected by the colour of the
mirror.

267.

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.

268.

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].

269.

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.

270.

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.]

271.

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.

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.

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.

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.