The Notebooks of Leonardo Da Vinci — Complete
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