The Notebooks of Leonardo Da Vinci, Complete
by
Leonardo Da Vinci
Part 3 out of 16
The greater the difference between a light and the body lighted by
it, the light being the larger, the more vague will be the outlines
of the shadow of that object.
The derived shadow will be most confused towards the edges of its
interception by a plane, where it is remotest from the body casting
it.
195.
What is the cause which makes the outlines of the shadow vague and
confused?
Whether it is possible to give clear and definite outlines to the
edges of shadows.
On the relative size of shadows (196. 197).
196.
THE BODY WHICH IS NEAREST TO THE LIGHT CASTS THE LARGEST SHADOW, AND
WHY?
If an object placed in front of a single light is very close to it
you will see that it casts a very large shadow on the opposite wall,
and the farther you remove the object from the light the smaller
will the image of the shadow become.
WHY A SHADOW LARGER THAN THE BODY THAT PRODUCES IT BECOMES OUT OF
PROPORTION.
The disproportion of a shadow which is larger than the body
producing it, results from the light being smaller than the body, so
that it cannot be at an equal distance from the edges of the body
[Footnote 11: H. LUDWIG in his edition of the old copies, in the
Vatican library--in which this chapter is included under Nos. 612,
613 and 614 alters this passage as follows: _quella parte ch'e piu
propinqua piu cresce che le distanti_, although the Vatican copy
agrees with the original MS. in having _distante_ in the former and
_propinque_ in the latter place. This supposed amendment seems to me
to invert the facts. Supposing for instance, that on Pl. XXXI No. 3.
_f_ is the spot where the light is that illuminates the figure there
represented, and that the line behind the figure represents a wall
on which the shadow of the figure is thrown. It is evident, that in
that case the nearest portion, in this case the under part of the
thigh, is very little magnified in the shadow, and the remoter
parts, for instance the head, are more magnified.]; and the portions
which are most remote are made larger than the nearer portions for
this reason [Footnote 12: See Footnote 11].
WHY A SHADOW WHICH IS LARGER THAN THE BODY CAUSING IT HAS
ILL-DEFINED OUTLINES.
The atmosphere which surrounds a light is almost like light itself
for brightness and colour; but the farther off it is the more it
loses this resemblance. An object which casts a large shadow and is
near to the light, is illuminated both by that light by the luminous
atmosphere; hence this diffused light gives the shadow ill-defined
edges.
197.
A luminous body which is long and narrow in shape gives more
confused outlines to the derived shadow than a spherical light, and
this contradicts the proposition next following: A shadow will have
its outlines more clearly defined in proportion as it is nearer to
the primary shadow or, I should say, the body casting the shadow;
[Footnote 14: The lettering refers to the lower diagram, Pl. XLI,
No. 5.] the cause of this is the elongated form of the luminous body
_a c_, &c. [Footnote 16: See Footnote 14].
Effects on cast shadows by the tone of the back ground.
198.
OF MODIFIED SHADOWS.
Modified shadows are those which are cast on light walls or other
illuminated objects.
A shadow looks darkest against a light background. The outlines of a
derived shadow will be clearer as they are nearer to the primary
shadow. A derived shadow will be most defined in shape where it is
intercepted, where the plane intercepts it at the most equal angle.
Those parts of a shadow will appear darkest which have darker
objects opposite to them. And they will appear less dark when they
face lighter objects. And the larger the light object opposite, the
more the shadow will be lightened.
And the larger the surface of the dark object the more it will
darken the derived shadow where it is intercepted.
A disputed proposition.
199.
OF THE OPINION OF SOME THAT A TRIANGLE CASTS NO SHADOW ON A PLANE
SURFACE.
Certain mathematicians have maintained that a triangle, of which the
base is turned to the light, casts no shadow on a plane; and this
they prove by saying [5] that no spherical body smaller than the
light can reach the middle with the shadow. The lines of radiant
light are straight lines [6]; therefore, suppose the light to be _g
h_ and the triangle _l m n_, and let the plane be _i k_; they say
the light _g_ falls on the side of the triangle _l n_, and the
portion of the plane _i q_. Thus again _h_ like _g_ falls on the
side _l m_, and then on _m n_ and the plane _p k_; and if the whole
plane thus faces the lights _g h_, it is evident that the triangle
has no shadow; and that which has no shadow can cast none. This, in
this case appears credible. But if the triangle _n p g_ were not
illuminated by the two lights _g_ and _h_, but by _i p_ and _g_ and
_k_ neither side is lighted by more than one single light: that is
_i p_ is invisible to _h g_ and _k_ will never be lighted by _g_;
hence _p q_ will be twice as light as the two visible portions that
are in shadow.
[Footnote: 5--6. This passage is so obscure that it would be rash to
offer an explanation. Several words seem to have been omitted.]
On the relative depth of cast shadows (200-202).
200.
A spot is most in the shade when a large number of darkened rays
fall upon it. The spot which receives the rays at the widest angle
and by darkened rays will be most in the dark; a will be twice as
dark as b, because it originates from twice as large a base at an
equal distance. A spot is most illuminated when a large number of
luminous rays fall upon it. d is the beginning of the shadow _d f_,
and tinges _c_ but _a_ little; _d e_ is half of the shadow _d f_ and
gives a deeper tone where it is cast at _b_ than at _f_. And the
whole shaded space _e_ gives its tone to the spot _a_. [Footnote:
The diagram here referred to is on Pl. XLI, No. 2.]
201.
_A n_ will be darker than _c r_ in proportion to the number of times
that _a b_ goes into _c d_.
202.
The shadow cast by an object on a plane will be smaller in
proportion as that object is lighted by feebler rays. Let _d e_ be
the object and _d c_ the plane surface; the number of times that _d
e_ will go into _f g_ gives the proportion of light at _f h_ to _d
c_. The ray of light will be weaker in proportion to its distance
from the hole through which it falls.
FIFTH BOOK ON LIGHT AND SHADE.
Principles of reflection (203. 204).
203.
OF THE WAY IN WHICH THE SHADOWS CAST BY OBJECTS OUGHT TO BE DEFINED.
If the object is the mountain here figured, and the light is at the
point _a_, I say that from _b d_ and also from _c f_ there will be
no light but from reflected rays. And this results from the fact
that rays of light can only act in straight lines; and the same is
the case with the secondary or reflected rays.
204.
The edges of the derived shadow are defined by the hues of the
illuminated objects surrounding the luminous body which produces the
shadow.
On reverberation.
205.
OF REVERBERATION.
Reverberation is caused by bodies of a bright nature with a flat and
semi opaque surface which, when the light strikes upon them, throw
it back again, like the rebound of a ball, to the former object.
WHERE THERE CAN BE NO REFLECTED LIGHTS.
All dense bodies have their surfaces occupied by various degrees of
light and shade. The lights are of two kinds, one called original,
the other borrowed. Original light is that which is inherent in the
flame of fire or the light of the sun or of the atmosphere. Borrowed
light will be reflected light; but to return to the promised
definition: I say that this luminous reverberation is not produced
by those portions of a body which are turned towards darkened
objects, such as shaded spots, fields with grass of various height,
woods whether green or bare; in which, though that side of each
branch which is turned towards the original light has a share of
that light, nevertheless the shadows cast by each branch separately
are so numerous, as well as those cast by one branch on the others,
that finally so much shadow is the result that the light counts for
nothing. Hence objects of this kind cannot throw any reflected light
on opposite objects.
Reflection on water (206. 207).
206.
PERSPECTIVE.
The shadow or object mirrored in water in motion, that is to say in
small wavelets, will always be larger than the external object
producing it.
207.
It is impossible that an object mirrored on water should correspond
in form to the object mirrored, since the centre of the eye is above
the surface of the water.
This is made plain in the figure here given, which demonstrates that
the eye sees the surface _a b_, and cannot see it at _l f_, and at
_r t_; it sees the surface of the image at _r t_, and does not see
it in the real object _c d_. Hence it is impossible to see it, as
has been said above unless the eye itself is situated on the surface
of the water as is shown below [13].
[Footnote: _A_ stands for _ochio_ [eye], _B_ for _aria_ [air], _C_
for _acqua_ [water], _D_ for _cateto_ [cathetus].--In the original
MS. the second diagram is placed below line 13.]
Experiments with the mirror (208-210).
208.
THE MIRROR.
If the illuminated object is of the same size as the luminous body
and as that in which the light is reflected, the amount of the
reflected light will bear the same proportion to the intermediate
light as this second light will bear to the first, if both bodies
are smooth and white.
209.
Describe how it is that no object has its limitation in the mirror
but in the eye which sees it in the mirror. For if you look at your
face in the mirror, the part resembles the whole in as much as the
part is everywhere in the mirror, and the whole is in every part of
the same mirror; and the same is true of the whole image of any
object placed opposite to this mirror, &c.
210.
No man can see the image of another man in a mirror in its proper
place with regard to the objects; because every object falls on [the
surface of] the mirror at equal angles. And if the one man, who sees
the other in the mirror, is not in a direct line with the image he
will not see it in the place where it really falls; and if he gets
into the line, he covers the other man and puts himself in the place
occupied by his image. Let _n o_ be the mirror, _b_ the eye of your
friend and _d_ your own eye. Your friend's eye will appear to you at
_a_, and to him it will seem that yours is at _c_, and the
intersection of the visual rays will occur at _m_, so that either of
you touching _m_ will touch the eye of the other man which shall be
open. And if you touch the eye of the other man in the mirror it
will seem to him that you are touching your own.
Appendix:--On shadows in movement (211. 212).
211.
OF THE SHADOW AND ITS MOTION.
When two bodies casting shadows, and one in front of the other, are
between a window and the wall with some space between them, the
shadow of the body which is nearest to the plane of the wall will
move if the body nearest to the window is put in transverse motion
across the window. To prove this let _a_ and _b_ be two bodies
placed between the window _n m_ and the plane surface _o p_ with
sufficient space between them as shown by the space _a b_. I say
that if the body _a_ is moved towards _s_ the shadow of the body _b_
which is at _c_ will move towards _d_.
212.
OF THE MOTION OF SHADOWS.
The motion of a shadow is always more rapid than that of the body
which produces it if the light is stationary. To prove this let _a_
be the luminous body, and _b_ the body casting the shadow, and _d_
the shadow. Then I say that in the time while the solid body moves
from _b_ to _c_, the shadow _d_ will move to _e_; and this
proportion in the rapidity of the movements made in the same space
of time, is equal to that in the length of the space moved over.
Thus, given the proportion of the space moved over by the body _b_
to _c_, to that moved over by the shadow _d_ to _e_, the proportion
in the rapidity of their movements will be the same.
But if the luminous body is also in movement with a velocity equal
to that of the solid body, then the shadow and the body that casts
it will move with equal speed. And if the luminous body moves more
rapidly than the solid body, the motion of the shadow will be slower
than that of the body casting it.
But if the luminous body moves more slowly than the solid body, then
the shadow will move more rapidly than that body.
SIXTH BOOK ON LIGHT AND SHADE.
The effect of rays passing through holes (213. 214).
213.
PERSPECTIVE.
If you transmit the rays of the sun through a hole in the shape of a
star you will see a beautiful effect of perspective in the spot
where the sun's rays fall.
[Footnote: In this and the following chapters of MS. C the order of
the original paging has been adhered to, and is shown in
parenthesis. Leonardo himself has but rarely worked out the subject
of these propositions. The space left for the purpose has
occasionally been made use of for quite different matter. Even the
numerous diagrams, most of them very delicately sketched, lettered
and numbered, which occur on these pages, are hardly ever explained,
with the exception of those few which are here given.]
214.
No small hole can so modify the convergence of rays of light as to
prevent, at a long distance, the transmission of the true form of
the luminous body causing them. It is impossible that rays of light
passing through a parallel [slit], should not display the form of
the body causing them, since all the effects produced by a luminous
body are [in fact] the reflection of that body: The moon, shaped
like a boat, if transmitted through a hole is figured in the surface
[it falls on] as a boatshaped object. [Footnote 8: In the MS. a
blank space is left after this question.] Why the eye sees bodies at
a distance, larger than they measure on the vertical plane?.
[Footnote: This chapter, taken from another MS. may, as an
exception, be placed here, as it refers to the same subject as the
preceding section.]
On gradation of shadows (215. 216).
215.
Although the breadth and length of lights and shadow will be
narrower and shorter in foreshortening, the quality and quantity of
the light and shade is not increased nor diminished.
[3]The function of shade and light when diminished by
foreshortening, will be to give shadow and to illuminate an object
opposite, according to the quality and quantity in which they fall
on the body.
[5]In proportion as a derived shadow is nearer to its penultimate
extremities the deeper it will appear, _g z_ beyond the intersection
faces only the part of the shadow [marked] _y z_; this by
intersection takes the shadow from _m n_ but by direct line it takes
the shadow _a m_ hence it is twice as deep as _g z_. _Y x_, by
intersection takes the shadow _n o_, but by direct line the shadow
_n m a_, therefore _x y_ is three times as dark as _z g_; _x f_, by
intersection faces _o b_ and by direct line _o n m a_, therefore we
must say that the shadow between _f x_ will be four times as dark as
the shadow _z g_, because it faces four times as much shadow.
Let _a b_ be the side where the primary shadow is, and _b c_ the
primary light, _d_ will be the spot where it is intercepted,_f g_
the derived shadow and _f e_ the derived light.
And this must be at the beginning of the explanation.
[Footnote: In the original MS. the text of No. 252 precedes the one
given here. In the text of No. 215 there is a blank space of about
four lines between the lines 2 and 3. The diagram given on Pl. VI,
No. 2 is placed between lines 4 and 5. Between lines 5 and 6 there
is another space of about three lines and one line left blank
between lines 8 and 9. The reader will find the meaning of the whole
passage much clearer if he first reads the final lines 11--13.
Compare also line 4 of No. 270.]
On relative proportion of light and shadows (216--221).
216.
That part of the surface of a body on which the images [reflection]
from other bodies placed opposite fall at the largest angle will
assume their hue most strongly. In the diagram below, 8 is a larger
angle than 4, since its base _a n_ is larger than _e n_ the base of
4. This diagram below should end at _a n_ 4 8. [4]That portion of
the illuminated surface on which a shadow is cast will be brightest
which lies contiguous to the cast shadow. Just as an object which is
lighted up by a greater quantity of luminous rays becomes brighter,
so one on which a greater quantity of shadow falls, will be darker.
Let 4 be the side of an illuminated surface 4 8, surrounding the
cast shadow _g e_ 4. And this spot 4 will be lighter than 8, because
less shadow falls on it than on 8. Since 4 faces only the shadow _i
n_; and 8 faces and receives the shadow _a e_ as well as _i n_ which
makes it twice as dark. And the same thing happens when you put the
atmosphere and the sun in the place of shade and light.
[12] The distribution of shadow, originating in, and limited by,
plane surfaces placed near to each other, equal in tone and directly
opposite, will be darker at the ends than at the beginning, which
will be determined by the incidence of the luminous rays. You will
find the same proportion in the depth of the derived shadows _a n_
as in the nearness of the luminous bodies _m b_, which cause them;
and if the luminous bodies were of equal size you would still
farther find the same proportion in the light cast by the luminous
circles and their shadows as in the distance of the said luminous
bodies.
[Footnote: The diagram originally placed between lines 3 and 4 is on
Pl. VI, No. 3. In the diagram given above line 14 of the original,
and here printed in the text, the words _corpo luminoso_ [luminous
body] are written in the circle _m_, _luminoso_ in the circle _b_
and _ombroso_ [body in shadow] in the circle _o_.]
217.
THAT PART OF THE REFLECTION WILL BE BRIGHTEST WHERE THE REFLECTED
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.
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
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.
_V._
_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.
OF PAINTING.
The hue of an illuminated object is affected by that of the luminous
body.
264.
OF SHADOW.
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.
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.
EXAMPLE.
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.
OF PAINTING.
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.
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.]
271.
OF PAINTING.
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.
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.
[Footnote 7: _reta_ here has the sense of _malanno_.]
301.
Experience shows us that the air must have darkness beyond it and
yet it appears blue. If you produce a small quantity of smoke from
dry wood and the rays of the sun fall on this smoke, and if you then
place behind the smoke a piece of black velvet on which the sun does
not shine, you will see that all the smoke which is between the eye
and the black stuff will appear of a beautiful blue colour. And if
instead of the velvet you place a white cloth smoke, that is too
thick smoke, hinders, and too thin smoke does not produce, the
perfection of this blue colour. Hence a moderate amount of smoke
produces the finest blue. Water violently ejected in a fine spray
and in a dark chamber where the sun beams are admitted produces
these blue rays and the more vividly if it is distilled water, and
thin smoke looks blue. This I mention in order to show that the
blueness of the atmosphere is caused by the darkness beyond it, and
these instances are given for those who cannot confirm my experience
on Monboso.
302.
When the smoke from dry wood is seen between the eye of the
spectator and some dark space [or object], it will look blue. Thus
the sky looks blue by reason of the darkness beyond it. And if you
look towards the horizon of the sky, you will see the atmosphere is
not blue, and this is caused by its density. And thus at each
degree, as you raise your eyes above the horizon up to the sky over
your head, you will see the atmosphere look darker [blue] and this
is because a smaller density of air lies between your eye and the
[outer] darkness. And if you go to the top of a high mountain the
sky will look proportionately darker above you as the atmosphere
becomes rarer between you and the [outer] darkness; and this will be
more visible at each degree of increasing height till at last we
should find darkness.
That smoke will look bluest which rises from the driest wood and
which is nearest to the fire and is seen against the darkest
background, and with the sunlight upon it.
303.
A dark object will appear bluest in proportion as it has a greater
mass of luminous atmosphere between it and the eye. As may be seen
in the colour of the sky.
304.
The atmosphere is blue by reason of the darkness above it because
black and white make blue.
305.
In the morning the mist is denser above than below, because the sun
draws it upwards; hence tall buildings, even if the summit is at the
same distance as the base have the summit invisible. Therefore,
also, the sky looks darkest [in colour] overhead, and towards the
horizon it is not blue but rather between smoke and dust colour.
The atmosphere, when full of mist, is quite devoid of blueness, and
only appears of the colour of clouds, which shine white when the
weather is fine. And the more you turn to the west the darker it
will be, and the brighter as you look to the east. And the verdure
of the fields is bluish in a thin mist, but grows grey in a dense
one.
The buildings in the west will only show their illuminated side,
where the sun shines, and the mist hides the rest. When the sun
rises and chases away the haze, the hills on the side where it lifts
begin to grow clearer, and look blue, and seem to smoke with the
vanishing mists; and the buildings reveal their lights and shadows;
through the thinner vapour they show only their lights and through
the thicker air nothing at all. This is when the movement of the
mist makes it part horizontally, and then the edges of the mist will
be indistinct against the blue of the sky, and towards the earth it
will look almost like dust blown up. In proportion as the atmosphere
is dense the buildings of a city and the trees in a landscape will
look fewer, because only the tallest and largest will be seen.
Darkness affects every thing with its hue, and the more an object
differs from darkness, the more we see its real and natural colour.
The mountains will look few, because only those will be seen which
are farthest apart; since, at such a distance, the density increases
to such a degree that it causes a brightness by which the darkness
of the hills becomes divided and vanishes indeed towards the top.
There is less [mist] between lower and nearer hills and yet little
is to be distinguished, and least towards the bottom.
306.
The surface of an object partakes of the colour of the light which
illuminates it; and of the colour of the atmosphere which lies
between the eye and that object, that is of the colour of the
transparent medium lying between the object and the eye; and among
colours of a similar character the second will be of the same tone
as the first, and this is caused by the increased thickness of the
colour of the medium lying between the object and the eye.
307. OF PAINTING.
Of various colours which are none of them blue that which at a great
distance will look bluest is the nearest to black; and so,
conversely, the colour which is least like black will at a great
distance best preserve its own colour.
Hence the green of fields will assume a bluer hue than yellow or
white will, and conversely yellow or white will change less than
green, and red still less.
_VII._
_On the Proportions and on the Movements of the Human Figure._
_Leonardo's researches on the proportions and movements of the human
figure must have been for the most part completed and written before
the year_ 1498; _for LUCA PACIOLO writes, in the dedication to
Ludovico il Moro, of his book_ Divina Proportione, _which was
published in that year:_ "Leonardo da venci ... hauedo gia co tutta
diligetia al degno libro de pictura e movimenti humani posto fine".
_The selection of Leonardo's axioms contained in the Vatican copy
attributes these words to the author:_ "e il resto si dira nella
universale misura del huomo". (_MANZI, p. 147; LUDWIG, No. 264_).
_LOMAZZO, again, in his_ Idea del Tempio della Pittura Milano 1590,
cap. IV, _says:_ "Lionardo Vinci ... dimostro anco in figura tutte
le proporzioni dei membri del corpo umano".
_The Vatican copy includes but very few sections of the_ "Universale
misura del huomo" _and until now nothing has been made known of the
original MSS. on the subject which have supplied the very extensive
materials for this portion of the work. The collection at Windsor,
belonging to her Majesty the Queen, includes by far the most
important part of Leonardo's investigations on this subject,
constituting about half of the whole of the materials here
published; and the large number of original drawings adds greatly to
the interest which the subject itself must command. Luca Paciolo
would seem to have had these MSS. (which I have distinguished by the
initials W. P.) in his mind when he wrote the passage quoted above.
Still, certain notes of a later date--such as Nos. 360, 362 and 363,
from MS. E, written in 1513--14, sufficiently prove that Leonardo did
not consider his earlier studies on the Proportions and Movements of
the Human Figure final and complete, as we might suppose from Luca
Paciolo's statement. Or else he took the subject up again at a
subsequent period, since his former researches had been carried on
at Milan between 1490 and 1500. Indeed it is highly probable that
the anatomical studies which he was pursuing zvith so much zeal
between 1510--16 should have led him to reconsider the subject of
Proportion.
Preliminary observations (308. 309).
308.
Every man, at three years old is half the full height he will grow
to at last.
309.
If a man 2 braccia high is too small, one of four is too tall, the
medium being what is admirable. Between 2 and 4 comes 3; therefore
take a man of 3 braccia in height and measure him by the rule I will
give you. If you tell me that I may be mistaken, and judge a man to
be well proportioned who does not conform to this division, I answer
that you must look at many men of 3 braccia, and out of the larger
number who are alike in their limbs choose one of those who are most
graceful and take your measurements. The length of the hand is 1/3
of a braccio [8 inches] and this is found 9 times in man. And the
face [Footnote 7: The account here given of the _braccio_ is of
importance in understanding some of the succeeding chapters. _Testa_
must here be understood to mean the face. The statements in this
section are illustrated in part on Pl. XI.] is the same, and from
the pit of the throat to the shoulder, and from the shoulder to the
nipple, and from one nipple to the other, and from each nipple to
the pit of the throat.
Proportions of the head and face (310-318).
310.
The space between the parting of the lips [the mouth] and the base
of the nose is one-seventh of the face.
The space from the mouth to the bottom of the chin _c d_ is the
fourth part of the face and equal to the width of the mouth.
The space from the chin to the base of the nose _e f_ is the third
part of the face and equal to the length of the nose and to the
forehead.
The distance from the middle of the nose to the bottom of the chin
_g h_, is half the length of the face.
The distance from the top of the nose, where the eyebrows begin, to
the bottom of the chin, _i k_, is two thirds of the face.
The space from the parting of the lips to the top of the chin _l m_,
that is where the chin ends and passes into the lower lip of the
mouth, is the third of the distance from the parting of the lips to
the bottom of the chin and is the twelfth part of the face. From the
top to the bottom of the chin _m n_ is the sixth part of the face
and is the fifty fourth part of a man's height.
From the farthest projection of the chin to the throat _o p_ is
equal to the space between the mouth and the bottom of the chin, and
a fourth of the face.
The distance from the top of the throat to the pit of the throat
below _q r_ is half the length of the face and the eighteenth part
of a man's height.
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