The Notebooks of Leonardo Da Vinci — Complete
RAYS ARE SHORTEST.
[2] The darkness occasioned by the casting of combined shadows will
be in conformity with its cause, which will originate and terminate
between two plane surfaces near together, alike in tone and directly
opposite each other.
[4] In proportion as the source of light is larger, the luminous and
shadow rays will be more mixed together. This result is produced
because wherever there is a larger quantity of luminous rays, there
is most light, but where there are fewer there is least light,
consequently the shadow rays come in and mingle with them.
[Footnote: Diagrams are inserted before lines 2 and 4.]
218.
In all the proportions I lay down it must be understood that the
medium between the bodies is always the same. [2] The smaller the
luminous body the more distinct will the transmission of the shadows
be.
[3] When of two opposite shadows, produced by the same body, one is
twice as dark as the other though similar in form, one of the two
lights causing them must have twice the diameter that the other has
and be at twice the distance from the opaque body. If the object is
lowly moved across the luminous body, and the shadow is intercepted
at some distance from the object, there will be the same relative
proportion between the motion of the derived shadow and the motion
of the primary shadow, as between the distance from the object to
the light, and that from the object to the spot where the shadow is
intercepted; so that though the object is moved slowly the shadow
moves fast.
[Footnote: There are diagrams inserted before lines 2 and 3 but they
are not reproduced here. The diagram above line 6 is written upon as
follows: at _A lume_ (light), at _B obbietto_ (body), at _C ombra
d'obbietto_ (shadow of the object).]
219.
A luminous body will appear less brilliant when surrounded by a
bright background.
[2] I have found that the stars which are nearest to the horizon
look larger than the others because light falls upon them from a
larger proportion of the solar body than when they are above us; and
having more light from the sun they give more light, and the bodies
which are most luminous appear the largest. As may be seen by the
sun through a mist, and overhead; it appears larger where there is
no mist and diminished through mist. No portion of the luminous body
is ever visible from any spot within the pyramid of pure derived
shadow.
[Footnote: Between lines 1 and 2 there is in the original a large
diagram which does not refer to this text. ]
220.
A body on which the solar rays fall between the thin branches of
trees far apart will cast but a single shadow.
[2] If an opaque body and a luminous one are (both) spherical the
base of the pyramid of rays will bear the same proportion to the
luminous body as the base of the pyramid of shade to the opaque
body.
[4] When the transmitted shadow is intercepted by a plane surface
placed opposite to it and farther away from the luminous body than
from the object [which casts it] it will appear proportionately
darker and the edges more distinct.
[Footnote: The diagram which, in the original, is placed above line
2, is similar to the one, here given on page 73 (section 120).--The
diagram here given in the margin stands, in the original, between
lines 3 and 4.]
221.
A body illuminated by the solar rays passing between the thick
branches of trees will produce as many shadows as there are branches
between the sun and itself.
Where the shadow-rays from an opaque pyramidal body are intercepted
they will cast a shadow of bifurcate outline and various depth at
the points. A light which is broader than the apex but narrower than
the base of an opaque pyramidal body placed in front of it, will
cause that pyramid to cast a shadow of bifurcate form and various
degrees of depth.
If an opaque body, smaller than the light, casts two shadows and if
it is the same size or larger, casts but one, it follows that a
pyramidal body, of which part is smaller, part equal to, and part
larger than, the luminous body, will cast a bifurcate shadow.
[Footnote: Between lines 2 and 3 there are in the original two large
diagrams.]
_IV._
_Perspective of Disappearance._
_The theory of the_ "Prospettiva de' perdimenti" _would, in many
important details, be quite unintelligible if it had not been led up
by the principles of light and shade on which it is based. The word_
"Prospettiva" _in the language of the time included the principles
of optics; what Leonardo understood by_ "Perdimenti" _will be
clearly seen in the early chapters, Nos._ 222--224. _It is in the
very nature of the case that the farther explanations given in the
subsequent chapters must be limited to general rules. The sections
given as_ 227--231 _"On indistinctness at short distances" have, it
is true, only an indirect bearing on the subject; but on the other
hand, the following chapters,_ 232--234, _"On indistinctness at
great distances," go fully into the matter, and in chapters_
235--239, _which treat "Of the importance of light and shade in the
Perspective of Disappearance", the practical issues are distinctly
insisted on in their relation to the theory. This is naturally
followed by the statements as to "the effect of light or dark
backgrounds on the apparent size of bodies"_ (_Nos._ 240--250). _At
the end I have placed, in the order of the original, those sections
from the MS._ C _which treat of the "Perspective of Disappearance"
and serve to some extent to complete the treatment of the subject_
(251--262).
Definition (222. 223).
222.
OF THE DIMINISHED DISTINCTNESS OF THE OUTLINES OF OPAQUE BODIES.
If the real outlines of opaque bodies are indistinguishable at even
a very short distance, they will be more so at long distances; and,
since it is by its outlines that we are able to know the real form
of any opaque body, when by its remoteness we fail to discern it as
a whole, much more must we fail to discern its parts and outlines.
223.
OF THE DIMINUTION IN PERSPECTIVE OF OPAQUE OBJECTS.
Among opaque objects of equal size the apparent diminution of size
will be in proportion to their distance from the eye of the
spectator; but it is an inverse proportion, since, where the
distance is greater, the opaque body will appear smaller, and the
less the distance the larger will the object appear. And this is the
fundamental principle of linear perspective and it
follows:--[11]every object as it becomes more remote loses first
those parts which are smallest. Thus of a horse, we should lose the
legs before the head, because the legs are thinner than the head;
and the neck before the body for the same reason. Hence it follows
that the last part of the horse which would be discernible by the
eye would be the mass of the body in an oval form, or rather in a
cylindrical form and this would lose its apparent thickness before
its length--according to the 2nd rule given above, &c. [Footnote 23:
Compare line 11.].
If the eye remains stationary the perspective terminates in the
distance in a point. But if the eye moves in a straight [horizontal]
line the perspective terminates in a line and the reason is that
this line is generated by the motion of the point and our sight;
therefore it follows that as we move our sight [eye], the point
moves, and as we move the point, the line is generated, &c.
An illustration by experiment.
224.
Every visible body, in so far as it affects the eye, includes three
attributes; that is to say: mass, form and colour; and the mass is
recognisable at a greater distance from the place of its actual
existence than either colour or form. Again, colour is discernible
at a greater distance than form, but this law does not apply to
luminous bodies.
The above proposition is plainly shown and proved by experiment;
because: if you see a man close to you, you discern the exact
appearance of the mass and of the form and also of the colouring; if
he goes to some distance you will not recognise who he is, because
the character of the details will disappear, if he goes still
farther you will not be able to distinguish his colouring, but he
will appear as a dark object, and still farther he will appear as a
very small dark rounded object. It appears rounded because distance
so greatly diminishes the various details that nothing remains
visible but the larger mass. And the reason is this: We know very
well that all the images of objects reach the senses by a small
aperture in the eye; hence, if the whole horizon _a d_ is admitted
through such an aperture, the object _b c_ being but a very small
fraction of this horizon what space can it fill in that minute image
of so vast a hemisphere? And because luminous bodies have more power
in darkness than any others, it is evident that, as the chamber of
the eye is very dark, as is the nature of all colored cavities, the
images of distant objects are confused and lost in the great light
of the sky; and if they are visible at all, appear dark and black,
as every small body must when seen in the diffused light of the
atmosphere.
[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.