Light and Shade 

'No substance can be comprehended without light and shade; light and shade are caused by light! 

That place is most shaded on which the greatest number of shaded rays converge. 

That place which is smitten by the shaded rays at the greatest angle is darkest. 

That place will be most luminous from which the greatest number of luminous rays are reflected. c.a. 31 v. b 


Light is the expeller of darkness. Shadow is the suppression of light. 

Primary light is that which is the cause of the lighting of shaded bodies. 

And the derived lights are those parts of bodies which are illumined by the primary light. 

Primary shadow is that side of a body on which the light does not fall. 

Derived shadow is simply the striking of shaded rays. 

Each body which creates a concourse of rays fills the surrounding air with an infinite number of its images. 

A shaded and luminous concourse is that mass of rays which emanate from a shaded and luminous body running through the air without 

Shaded or luminous percussion is that which impedes and cuts above itself the concourse of shaded and luminous rays. c.a. 116 r. b 

The shadow in diaphanous and spherical bodies is darker at the top than in the hollow, and darker amid the darkness of the derived shadow of the body of the ball. Every object seen is surrounded by second objects, and from this it is known: and in proportion as the second object is farther away than the first so much the more does the first cover it from the eye. c.a. 125 r. b 


Among the things of equal obscurity which are situated at a considerable and equal distance, that will appear more obscure which has 
its station higher up from the earth. The edges of a derived shadow will be most distinct where it is cast nearest to the original shadow. 

A shaded body will appear of less size when it is surrounded by a very luminous background, and a luminous body will show itself greater when it is set against a darker background: as is shown* in the heights of buildings at night when there are flashes of lightning behind them. For it instantly appears, as the lightning flashes, that the building loses a part of its height. 

And from this it comes to pass that these buildings appear larger when there is mist, or by night, than when the air is clear and illumined. c.a. 126 r. b 

The breadth and length of shadow and of light, although through foreshortening it may appear less in quantity, will not therefore appear diminished as to quality either in respect of brightness or darkness. c.a. 144 v. a 


All the illuminated parts of a body which see the whole circle of the luminous body will be the more dissimilar in brightness, one from another, as they are nearer to the source of the light, c.a. 150 r. a 

The atmosphere is of itself adapted to gather up instantaneously and to leave behind it every image and likeness of whatever body it sees. 

When the sun appears in the eastern horizon it permeates at once the whole of our hemisphere and fills it with its luminous semblance. 

All the surfaces of solid bodies turned towards the sun or towards the atmosphere illumined by the sun, become clothed and dyed by the light of the atmosphere or of the sun. 

Every solid body is surrounded and clothed with light and darkness. 

You will get only a poor perception of the detail of a body when the part visible is all the part in shadow, or only the part that is illumined. 

The length of the space which exists between the eye and the solid bodies determines how much the part that is illumined increases, and 
that in shadow diminishes. 

The shape of a body cannot be accurately perceived when its extremities are bounded by something of the same colour as itself, and the eye is between the part in shadow and that in light. c.a. 179 r. b 


No separated shadow can reproduce upon a wall the true form of the body of which it is the shadow, unless the centre of the light is equidistant from the extremities of this body. c.a. 187 v. a 


I Camera Obscura] 

The boundaries of the images of any colour which penetrate through a narrow hole into a dark place will be always of a more powerful colour than its centre. c.a. 190 r. b 

Why black painted in juxtaposition with white never seems to show itself more black than where it borders upon black, and white does not show itself more white in juxtaposition with black than with white; as is seen with the images passed through a hole or at the edge of any dark obstacle. 

This comes about because the images tinge with their colour the spot on which they fall, and when the different images approach the same spot they make a blend of their colours, and this blend participates more in one colour than in another as the one colour is present in greater quantity than the other. 

And the colours are more intense and more sharply defined at their edges than in any other part. c.a. 195 v. 



Those who have experience use in all intricate things such as trees, meadows, hair, beards and fur, four stages of clearness in order to reproduce the same colour; that is, first a dark foundation, second a blur which has something of the shape of the part, third a clearer and more defined part, fourth the lights more in high parts for movements of the figure [ ? ] ; x it seems however to me that these varieties are 1 MS., ilumi piii che alte parte moti di figura infinite in the case of a continuous quantity, which is in itself divisible to infinity, and thus I prove it: 

| Two diagrams} 

Let a g be a continuous quantity and d the light that illumines it. 
I refer now to the fourth which says that that part of the illuminated 
body will be more luminous which is nearer to the source of its illumi- 
nation; g therefore is darker than c in proportion as the line d g is 
longer than the line d c. And from the conclusion that such grades of 
brightness, or if you so prefer of darkness, are not four only, but may 
be conceived of as infinite, because c d is a continuous quantity, and 
every continuous quantity is divisible to infinity, therefore the variety 
in the length of the lines that extend from the luminous to the illumi- 
nated body is infinite; and the proportion of the lights corresponds 
to the lengths of the lines between them, which extend from the centre 
of the luminous body to the part of the object which is illuminated by it. 

c.a. 199 v. a 


If the whole light were what caused the shadows behind the bodies 
placed against it, it would be necessary that that body, which is much 
less than the light, should have a pyramidal shadow behind itself, and 
as experience does not confirm this, it must be that it is the centre of 
the light which performs this function. 



The cannon-ball from the mortar, if it be of uniform substance, and 
its surface be equidistant from its centre, and the fire strikes it in the 
middle, as reason would suggest, must needs take its course without 
any revolution. Seeing that the fire that expels it is of uniform nature, 
it drives equally the air which withstands its course, and as this also is 
equal it offers equal resistance. 


Thus for example, one sees the moon, which is also a spherical body 
and meets with equal resistance, to be much swifter as compared with 



the cannon-ball, but nevertheless the dark spots that are on it never 
change their position, and the fact of this change not appearing, clearly 
confirms the fact that it does not revolve. 


If you look at the sun or other luminous object and then shut your 
eyes, you will see it again in the same form within your eye for a long 
space of time: this is a sign that the images enter within it. 

c.a. 204 r. a 

When the intersection of two columns of shadow produces their 
derived shadows by means of the two luminous ones, it must follow 
that four derived shadows are produced, and these shadows are com- 
posite, and they intersect at four places; and of these intersections there 
are two that form simple shadow, and two are of composite shadow, 
and these two simple shadows are produced where the two lights 
cannot be seen, and the composite shadows are produced where one of 
the two lights cannot illumine. But the intersections of the composite 
shadows are produced always by a single luminous body, and of the 
simple ones by two luminous bodies, and the right intersection of the 
composite shadow is produced by the left light, and the left intersection 
is produced by the right light; but the two intersections of the simple 
shadows, both the upper and the lower, are produced by the two lumi- 
nous bodies, that is the light on the right and the light on the left. 

c.a. 241 r. c 

Many minute lustres continue in the far distance and make them- 
selves perceptible. 




With reference to the light that penetrates the vent holes, it may be. 
doubted whether it reconstitutes with the dilatation of its rays as much 
breadth of impression beyond the vent hole as the width of the body 
which is the cause of the rays. 



And in addition to this, whether this dilatation has a power equal to 
that of the luminous body. As regards the first doubt the reply is that 
the dilatation made by the rays after their intersection recreates as much 
breadth beyond the vent hole as in front of the vent hole, there being 
as much space from the luminous body to the vent hole as from the 
vent hole to the impress of its rays; this is proved by the straightness 
of the luminous rays, from which it follows that there is the same 
proportion between their breadth and between the distances at which 
they intersect. 

But power does not proceed in the same proportion; as is proved 
where it is stated: just such proportion exists between the heat and the 
radiance in the different luminous rays as between their distances from 
their source. It is proved therefore that the luminous ray loses in heat 
and radiance in proportion as it is more remote from its luminous 
body. It is true however that the composite shadows, being derived, 
and starting from the edges of these vent holes, break this rule by 
means of their intersections; and this is treated of fully in the second 
book concerning shadow. c.a. 241 r. d 

The rays of the shaded and luminous images intersect after they have 
penetrated within the vent holes, turning in opposite directions every 
part of their thickness. c.a. 241 v. c 

The shadow will never show itself of uniform density in the place of 
its incidence, unless this place be equidistant from the luminous body. 
This is proved by the seventh which says : that shadow will show itself 
lighter or darker which is against a darker or lighter background; by 
the eighth of this : that background will have its parts so much darker 
or lighter as it is more remote from or nearer to the luminous body; 
and among the positions at an equal distance from the luminous body 
that will show itself more illuminated which receives the luminous 
rays at more equal angles. No matter with what inequality of position a 
shadow is defined, it will always show itself with its true boundaries 
equal to the shaded body if the eye rests upon the centre of the lumi- 
nous body. 

That shadow will show itself darker that is more remote from its 
shaded body. c.a. 241 v. d 



The image of the sun is all in all the parts of the objects upon which 
its rays fall, and all in each particular part. 

Why in the far distance a radiance which is long will appear round 
to us, and the horns of the moon do not follow this rule, and yet the 
light near by follows as its point indicates. c.a. 243 r. a 



Having, as I think, sufficiently treated of the natures and different 
characteristics of primary and derived shadows, and the manner of 
their incidence, it seems to me that the time has now come to explain 
the different results upon the various surfaces which are touched by 
these shadows. 



It seems to me that the shadows are of supreme importance in 
perspective, seeing that without them opaque and solid bodies will be 
indistinct, both as to what lies within their boundaries and also as to 
their boundaries themselves, unless these are seen against a background 
differing in colour from that of the substance; and consequently in the 
first proposition I treat of shadows, and say in this connection that 
every opaque body is surrounded and has its surface clothed with 
shadows and lights, and to this I devote the first book. Moreover these 
shadows are in themselves of varying degrees of darkness, because they 
have been abandoned by a varying quantity of luminous rays; and 
these I call primary shadows, because they are the first shadows and so 
form a covering to the bodies to which they attach themselves, and to 
this I shall devote the second book. From these primary shadows there 
issue certain dark rays, which are diffused throughout the air and vary 
in intensity according to the varieties of the primary shadows from 
which they are derived; and consequently I call these shadows derived 
shadows, because they have their origin in other shadows; and of this 
I will make the third book. Moreover these derived shadows in striking 
upon anything create as many different effects as are the different 
places where they strike; and of this I will make the fourth book. And 
since where the derived shadow strikes, it is always surrounded by the 



striking of the luminous rays, it leaps back with these in a reflex stream 
towards its source and meets the primary shadow, and mingles with 
and becomes changed into it, altering thereby somewhat of its nature; 
and to this I will devote the fifth book. In addition to this I will make 
the sixth book to contain an investigation of the many different varieties 
of the rebound of the reflected rays, which will modify the primary 
shadow by as many different colours as there are different points from 
whence these luminous reflected rays proceed. Further I will make the 
seventh division treat of the various distances that may exist between 
the point of striking of each reflected ray and the point from whence 
it proceeds, and of the various different shades of colour which it 
acquires in striking against opaque bodies. c.a. 250 r. a 

In proportion as the luminous body is nearer to the shaded body, it 
throws out more light if the luminous body is greater than the dark 

In proportion as the luminous body is more distant from the shaded 
body and is less than it, it will give more light. 

But in proportion as the luminous body being less than the shaded 
body is more distant from this shaded body it will give more light. 

And if the luminous body being greater than the shaded body is 
moved farther away from the shaded body, the total amount that is 
illuminated will continue to diminish until it is approximately half. 

c.a. 250 v. a 


The actions of compound shadows are always made up of contrary 
movements. That is, that if the concourse of luminous rays before 
arriving at their point of intersection be touched by an opaque body, 
all the shadows of that body which break in upon the upper ray will 
show themselves beyond this point of intersection in the percussion of 
the lower ray, and as the upper ray becomes the lower after the inter- 
section, so the movements which the shaded body makes within this 
upper ray will show themselves of contrary movement after this inter- 
section; and this will reveal itself in the incidence of the compound 
shadow upon the pavement, or on a wall that is struck by the sun or 
other luminous body. 



But if the Luminous ray is interrupted by the opaque body some 
distance from its intersection, the percussion of the derived shadow of 
the opaque body will make a movement similar to that of the opaque 

And if these rays are interrupted at the actual point of their inter- 
section, then the shadows of the opaque body will be twofold, and they 
will move with contrary movements one to another before they reach 
the point of union. 

The derived compound shadow is the cause why the percussion of 
the solar ray when passing through any kind of angle does not leave its 
impression on this angle; but portions of ... so much greater or less 
... in proportion as these impressions are more remote from or nearer 
to these angles. c.a. 277 v. a 

The site that is most luminous will vary according to the different 
positions of the eye and the light; and the shadow will always be im- 
movable, for whatever the change it makes, the eye sees it. 

c.a. 322 v. b 

No opaque body can be visible unless it is clothed with a shaded and 
illuminated surface. 

The air and every transparent body becomes a passage from the 
objects to the eye for the images of those bodies which find themselves 
either within or beyond them. 

Derived light should be surrounded by primitive shadow. 

Derived shadow will be surrounded by derived light. 

Derived light should be surrounded, in whole or in part, by primitive 
or derived shadows. 

Every opaque body has its image all in all and all in every part of 
the transparence that surrounds it. c.a. 349 v. d 


Of the shadows — where they ought to be dark; where the shadows 
ought to be of a middle degree, and the lights where they ought to be 

Where they are darker. Where there ought to be glimmers and 



reflections, that is lights thrown back in one place, and leaping up again 
in another. 

How lights ought to be so rendered that they draw natural things. 

How natural figures when they have intense light on one side seem 
to be in the deepest shadow on the opposite side. 

How men show a small variation from light to shadow when the 
atmosphere is overcast or the sun is on the point of setting. 

For what reason objects as they recede from the eye are perceived 
poorly and seem to lose clearness of outline, and in the far distance 
appear blue. 

Why things when painted seem greater than they are. 

c.a. 360 r. c 

That light is brightest which has the greatest angle. 
That shadow is darkest which is produced at a most acute angle. 

c.a. 385 v. c 

Primary and derived shadow are deeper when they are caused by 
the light of the candle than by that of the atmosphere. 

The more the derived shadow which is greater enters in the less, the 
more the cause of the less is more luminous than the greater. 

Tr. 24 a 

The edges of the window which are illuminated by two different 
lights of equal radiance will not throw light of equal quality into the 
room. Tr. 25 a 

[With sketch] 

At the window a h the sun enters into the house; this sun will 
increase the size of the window and lessen the shadow of a man, with 
the result that when the said man shall approach this shadow of him- 
self, lost in that which carries the true shape of the window, he will see 
the contact of the shadows lost and confused by the power of the light, 
close themselves up and not suffer the solar rays to pass . . . 

And the shadow made by the man upon the said contact has pre- 
cisely the efTect that is represented above. a i r. 

[With diagram] 
If you wish to measure a height by the shadow of the sun, take a 



stick which may be one braccio, set it up and wait until the sun makes 
it cast a shadow of two braccia. Then measure immediately the shadow 
of the tower, and it this is one hundred braccia the tower will be fifty; 
and this is a good rule. a 6 r. 

That part of a shaded body which is illuminated will transmit to the 
eye the image of its details more distinctly and more rapidly than that 
which finds itself in shadow. a 20 r. 



Among bodies equal in size and distance that which shines the more 
brightly seems to the eye nearer and larger. c 1 r. 

The straight edges of bodies will appear broken when they serve as 
boundary of a dark space streaked by the percussion of luminous rays. 

c 1 v. 

The body illuminated by the solar rays which have passed through 
the thick branches of the trees, will cast as many shadows as is the 
number of the branches interposed between the sun and itself. 

The shaded rays which proceed from a pyramidal shaded body will 
bifurcate when they intersect, and the shadow will be of varying de- 
grees of depth at its points. 

A light which is greater than the point and less than the base of the 
shaded pyramidal body placed in front of it, will cause the shaded body 
to produce at its percussion a bifurcated shadow of varying degrees of 

If a shaded body being smaller than a luminous body casts two 
shadows, and a shaded body the same size as a luminous body or greater 
than it casts one, it follows that the pyramidal body of which part is 
smaller than, part equal to, and part larger than the luminous body, 
will cast a bifurcated shadow. c 2 r. 

The body that receives the solar rays which have passed between the 
minute ramifications of trees at a great distance will have but a single 

If the body, part in shadow and part in light, be of the shape of a per- 
fect sphere, the base of the luminous pyramid will bear the same pro- 



portion to its body as that which the base of the shaded pyramid bears 
to the shaded body. 

In proportion as the percussion made by the convergence of the 
shadow on the opposite wall is more distant from the luminous body 
and nearer the source from which it is derived, so much the darker and 
of more defined contours will it appear. c 2 v. 

That luminous body will appear of less radiance which is surrounded 
by a more luminous background: 

I have found that those stars that are nearest the horizon appear 
larger in form than the others, because they see and are seen by a 
greater amount of the solar body than when they are above us; and 
since they see more of the sun they have a greater light. And the body 
that is most luminous shows itself of greater form, as the sun shows 
itself in the mist above us, for it seems larger when it is without mist 
and with the mist it diminishes. 

No part of the luminous body is ever visible from the pyramid of 
pure derived shadow. c 3 r. 

[Movement of shadows] 

If the object is moved slowly before the luminous body and the per- 
cussion of the shadow of this object is remote from its object, the move- 
ment of the derived shadow will have the same proportion with the 
movement of the primary, as the space between the object and the light 
has with that between the object and the percussion of the shadow, — so 
that when the object moves slowly the shadow is rapid. c 3 v. 

That part of the reflection will be brightest in which the reflected 
rays are shortest. 

The darkness caused by a number of shadows intersecting will be in 
conformity with their cause, which has its beginning and end between 
smooth surfaces near to each other, of the same quality and directly 
opposite to each other. 

In proportion as the luminous body is greater the course of the 
luminous and shadow rays will be more mingled together. 

This comes about because where the larger number of luminous rays 
are found, there is most light, and where a lesser number, less light, 
from which it comes about that the shadow rays enter and mingle with 
them. c 4 r. 



That part of the surface of bodies on which the images of the bodies 
placed opposite, fall at the largest angle will be tinged most with their 

The most luminous part of the illuminated body which encompasses 
the percussion of the shadow will be that which' is nearest to this per- 

Just as a thing touched by a greater mass of luminous rays becomes 
brighter, so that will become darker which is struck by a greater mass 
of shadow rays. c 4 v. 

A luminous body will seem more brilliant when it is surrounded by 
deeper shadow. 

The breadth and length of shadow and light, although through fore- 
shortening they become straighter and shorter, will neither diminish nor 
increase the quality or quantity of their brightness or darkness. 

The function of shadow and of light diminished by foreshortening, 
will be to shade and illumine an object opposite to it, according to the 
quality and quantity that appear in this object. 

The more a derived shadow approaches its penultimate extremities 
the deeper it will appear. c 5 r. 


If you cause the rays of the sun to pass through a small hole of the 
shape of a star you will see beautiful effects of perspective in the per- 
cussion caused by the passage of the sun. c 7 r. 


The forms of shadows are three : for if the substance which casts the 
shadow is equal in size to the light, the shadow is like a column which 
has no end; if the substance is greater than the light, its shadow is like 
a pyramid which grows larger as it recedes and of which the length has 
no end; but if the substance is smaller than the light the shadow 
resembles a pyramid and comes to an end, as is seen in the eclipses of 
the moon. 07 V. 




The shape of a luminous body although it has length will at a great 
distance seem round. 

This is shown by the flame of the candle, which although it is long 
seems round at a great distance; and the same thing may happen with 
the stars, for even if they were horned like the moon they would seem 
round by reason of their great distance. c 8 r. 

Among bodies equal in size and length and equal also in form and 
depth of shade, that will appear the smaller which is surrounded by a 
more luminous background. 

A shaded body placed between equal lights will cast as many shadows 
as there are lights, shadows of which one will be darker than the others 
as the light situated on the opposite side is nearer this body than the 

A shaded body equidistant between two lights will cast two shadows, 
one darker than the other in proportion as one of the lights which cause 
them is greater than the other. c 8 v. 

The places occupied by the shadows caused by a small luminous body 
are, as regards size, similar and corresponding to those of which the 
visual rays are cut ofT. 

And when the luminous ray has passed through a small hole and 
been broken upon some opposing object near at hand, the impress of its 
percussion resembles more the hole through which it has passed than 
the luminous body from which it proceeds. c 9 r. 

The greater the radiance of the luminous body the deeper will be 
the shadows cast by the bodies it illuminates. 

All the shaded bodies that are larger than the pupil, which interpose 
between the eye and the luminous body, will show themselves dark. 

If the eye be placed between the luminous body and the bodies 
illuminated by this light, it will see these bodies without any shadow. 

c 10 r. 

When a luminous ray has passed through a hole of some unusual 
shape after a long course, the impression it makes where it strikes 
resembles the luminous body from which it springs. 



It is Impossible for the ray horn of a luminous spherical body to be 
able, alter a long course, to convey to where it strikes the image ot any 
description of angle that exists in the angular hole through which it 
passes. c 10 v. 

The shape of the derived shadow will always conform to the shape of 
the original shadow. 

A light in the form of a cross thrown on to a shaded body of spherical 
roundness will produce its shadow in the figure of a cross, c 1 1 r. 

That boundary of the derived shadow is darker which is surrounded 
by a brighter derived light. c n v. 

Of things equal in respect of size, brightness, background and length, 
that which has the smoothest surface will seem largest. 

Iron of uniform thickness half of which is heated serves as a proof, 
for the part that is heated appears larger than the remainder, c 12 r. 

[Of broken shadow] 

The derived shadow which has as its origin and cause a spherical 
shaded and luminous body, and is broken by the percussion made by 
it upon different bodies situated at varying degrees of distance, will 
appear round to the eye that is in front of it situated near to the centre 
of the original shadow. 

A shaded body of spherical rotundity will cast a circular shadow 
blended [of light and shade] when it has a shaded body of its own 
substance interposed between it and the sun. c 12 v. 

Among shadows of equal quality that nearest the eye will appear 
least dark. 

That shadow will be darker which is derived from a greater number 
of different shaded and luminous bodies. 

It is impossible that simple derived shadows, which spring from dif- 
ferent bodies and are caused by a single light, can ever join or touch 
each other. c 13 v. 

[When adjacent bodies will appear separated] 

If many shaded bodies, so near to each other as to be almost touch- 
ing, are seen against a luminous background at a great distance, they 
wUl seem separated by a great space. c 14 r. 



[When separated bodies will appear adjacent] 

If many luminous bodies are seen in a distant landscape, although 
they may be separated one from another, they will appear united and 
joined together. 

That part of the air will participate most in its natural darkness 
which is smitten by the sharpest luminous angle. It is clearly to be 
understood that where there is a smaller luminous angle there is less 
light, because the pyramid of this angle has a smaller base, and there- 
fore from this smaller base a lesser number of luminous rays con- 
verge at its point. 


Darkness is the absence of light. 

Shadow is the diminution of light. 

Primitive shadow is that which is attached to shaded bodies. 

Derived shadow is that which separates itself from shaded bodies 
and travels through the air. 

Repercussed shadow is that which is surrounded by an illuminated 

The simple shadow is that which does not see any part of the light 
which causes it. 

The simple shadow commences in the line which parts it from the 
boundaries of the luminous bodies. c 14 v. 

Rays doubled by intersection in lights and shadows are also of dou- 
ble clearness or obscurity: 

Primitive light and derived reflected light, when they surround thick 
and spherical bodies, become the cause of the boundaries of the primi- 
tive shadows of these bodies, being so much more distinct and de- 
fined in the part near to the lights as the derived light is clearer than 
the primitive. 

That is said to be primitive light which first lights up shaded bodies, 
and that is called derived which leaps back from these bodies in those 
parts which are remote from this primitive light. 

That part of the primitive shadow will be more luminous which can 
see more equally the centres of the derived lights. 

One may clearly know that that part of the shaded bodies which is 



seen by a greater quantity is the more luminous, and especially if it is 
illumined by two lights; as is seen with reflected Lights which put in 
their midst the derived shadow made between them by the dense 
bodies opposite. 

Every luminous body illumines with its whole and with its part the 
part and the whole of the object turned to face it. 

This proposition is very evident, for one cannot deny that where 
the whole pupil of the eye is looking, there every part of it is looking, 
and the place seen by this pupil acts in the same way towards it. 

c 16 v. 

The middle of the length of each derived shadow is in a straight 
line with the middle of the primitive shadow and of the derived light, 
and the centres of the shaded and luminous bodies. 

This necessarily happens, since as the luminous lines are straight, 
those which pass by the extremities of the shaded bodies enclose within 
their concourse all that air which through the intervention of this 
shaded body cannot see the luminous body, and for this reason it be- 
comes dark. As the body is equally enclosed the parts of the shadow 
become equal in respect to its centre, because all the parts of shaded 
bodies are also equidistant from their centre, and so every body has a 
centre in itself. 

As the above-named luminous lines are in contact with each ex- 
tremity of the thing enclosed within them, they are equidistant from 
the middle of the length of any object that they enclose. 

That part of the primitive and derived shadow will be so much less 
dark as it is more distant from its centre. 

This comes about because the more the shadow separates from its 
centre the more it is seen by a greater quantity of luminous rays, and 
every man knows that where there is more light there is less shadow. 

c 17 r. 


If the sun is seen by all the seas which have the day, all these seas 
are seen by the sun. Therefore all the illumined water makes itself the 
mirror of the sun; and by its image all in the whole of this water and 
-all in a part it appears to the eye. I ask therefore why when a ship is 



travelling and the sun sees itself, the eye does not see the sea all 
illumined, and why it does not always seem that the sun is travelling 
along the pathway of the boat. 


The sun makes as many pyramids as there are holes and crevices by 
which it can penetrate with its rays, and as many as the eyes of the 
animated beings that look upon it. Therefore as the sun finds itself 
always the base of each pyramid, the sun mirrored in the water seems 
to the eye to be as much beneath the water as it is outside it, and this 
sun thus reflected forms the base of the pyramid which ends in the 
eye. And this reflected sun will appear as great as the section of the 
pyramid cut by the surface of the water at a n [figure]. c 17 v. 

Although the shaded and luminous body be of spherical rotundity 
and equal size, nevertheless its derived shadow will not resemble the 
rotundity of the body from which it proceeds, but will be of elongated 
shape if it falls within unequal angles. c 18 r. 

[Of the shapes of shadows] 

The shapes of shadows often resemble the shaded body which is 
their origin, and often the luminous body which is their cause. 

If the shape and size of the luminous body are like that of the 
shaded body, the primitive and derived shadows will have the shape 
and size of these bodies, falling within equal angles. 

The derived shadow at a certain distance will never resemble the 
shape of the shaded body from which it proceeds, unless the shape of 
the light from this illuminating body resembles the shape of the body 
illuminated by the said light. 

Light that is long in shape will cause the derived shadow born from 
a round body to be wide and low, although it makes its percussion 
between equal angles. 

It is impossible that the shape of the derived shadow should resemble 
that of the shaded body from which it was born, unless the light that 
causes it is similar in shape and size to this shaded body. c 18 v. 

There will be as much difference in the darkness of two partially 
shaded rays as between the shadow that results from their blending 
and its first condition. 



It is impossible that from the blending of two complete shadows 
there should ensue a shadow darker in degree. 

It is possible that from the blending of two incomplete shadows may 
result a perfect shadow darker in degree than any of the former? 

c 19 r. 

Universally all the points that form the extreme points of the pyra- 
midal images of things are continually all in all the air, united and 
joined together without any intermission. 

Necessity causes that nature ordains or has ordained that in all 
points of the air all the images of the things opposite to them con- 
verge, by the pyramidal concourse of the rays that have emanated from 
these things; and if it were not so the eye would not discern in every 
point of the air that is between it and the thing seen, the shape and 
quality of the thing facing it. 

That pyramid which proceeds from its base with more unequal 
angles will be narrower, and will give a less accurate impression of 
the true width of the base. 

Among the many pyramids that are founded upon a single base that 
will be more powerful which is larger, and that will be larger which 
has the angles of its base more equal one to the other. c 20 r. 

The less the brightness of the derived as compared with that of the 
original light, the less will its pyramids illumine the spot on which 
they strike. 

The pyramids will illumine the spot on which they strike the less 
as their angles are finer. c 20 v. 

The farther the derived shadow extends from the primitive the 
brighter it becomes. 

Such proportion as the diameter of the derived shadow has to that 
of the primitive, you will find between the darkness of the primitive 
shadow and that of the derived. 

If the size of the illuminating body should surpass that of the body 
which is illumined, it will form an intersection of shadow, beyond 
which the divided shadows will pass off in two different directions, as 
though they derived from two different lights. 

3 Words crossed out in MS 



That part of the derived shadow will be darker which is nearer to its 

The above proposition holds good because, where the larger lumi- 
nous angle is united to the narrower shaded angle, this luminous angle 
subdues it and almost changes it to its luminous nature. And so it is 
presumed that, where the larger shaded angle is united with the nar- 
rower luminous angle, the shaded will almost transform to its own 
nature the luminous that is joined to it. c 21 r. 

Of things which are the same in size and colour that which is farther 
away will seem lighter and less in bulk. 

The percussion of the derived shadow is always surrounded by 
shadow that melts into the luminous background. 

That part of the shaded body which is struck by the largest luminous 
angle will be more illuminated than any other. c 21 v. 

When there are several bodies of equal size which are equally dis- 
tant from the eye, that will appear the smaller which is against a more 
luminous background. 

Every visible body is surrounded by light and shade. 

Every perfectly round body when surrounded by light and shade 
will seem to have one of its sides greater than the other, in proportion 
as the one is more lighted than the other. c 24 r. 

If the visual line that sees the shadow made by the light of the 
candle has an angle equal to that of the shadow, the shadow will 
almost seem to function beneath the body that causes it, as does the 
image of the bodies reflected by the water, for they are as much visi- 
ble beneath it as above. Even so this shadow will so function that its 
extremity will appear to be as far below the surface on which it is 
produced, as the summit of the body which causes it is above this 
surface, as is seen on a wall. c 25 r. 


The eye that finds itself between the light and shade which surround 
opaque bodies, will see there the shadow separated from the luminous 
part pass transversely through the centre of this body. 



When two objects arc seen within the above-mentioned visual pyra- 
mids, in such a way as not to fall short of or protrude beyond these 
lines, although there be a great intervening space between them, this 
distance, nevertheless, will never be capable of being seen or recognised 
by the eye. 

The greater the distance between the above-named bodies enclosed 
within visual pyramidal lines, the more necessary is it that there be a 
proportionate lack of conformity between them. c 27 r. 


The first of the lights with which opaque bodies are illumined is 
called particular, and it is the sun or other light from a window or 
flame. The second is universal, as is seen in cloudy weather or in mist 
or the like. The third is the composite, that is when the sun in the 
evening or the morning is entirely below the horizon. e 3 v. 

Among bodies in varying degrees of darkness deprived of the same 
light, there will be the same proportion between their shadows as there 
is between their natural degrees of darkness, and you have to under- 
stand the same of their lights. e 15 r. 


You will note in drawing how among shadows some are indistin- 
guishable in gradation and form; and this is proved by the fifch which 
says: — spherical surfaces have as many different degrees of light and 
shadow as there are varieties of brightness and darkness reflected from 
the objects round them. 

That part of an opaque body will be more in shadow or more in 
light which is nearer to the dark body which shades it, or to the 
luminous body which gives it light. 

The surface of every opaque body partakes of the colour of its ob- 
ject, but the impression is greater or less in proportion as this object 
is nearer or more remote, and of greater or less power. 

Objects seen between light and shadow will appear in greater relief 
than those which are in the light or in the shadow. e 17 r. 



In the position of the eye which sees illuminated such part of plants 
as behold the light, one plant will never appear illuminated like the 
other. This is proved as follows: — let c be the eye that beholds the 
two plants b d which are illuminated by the sun a; I affirm that this 
eye c will not perceive the lights in the same proportion to their 
shadows in the one tree as in the other; for the tree that is nearer to 
the sun will show itself more in shadow than that farther away, in 
proportion as the one tree is nearer than the other to the concourse of 
the solar rays which come to the eye. 

When a tree is seen from below, the eye sees the top of it set within 
the circle formed by its branches. 

Remember, O painter, that the degrees of depth of shade in one 
particular species of tree vary as much as the sparseness or density of 
its ramifications. e 18 v. 


As regards the equal diffusion of light, there will be the same pro- 
portion between the degrees of obscurity of the shadows produced, as 
there is between the degrees of obscurity of the colours to which these 
shadows are joined. 



The movement of the shadow is always more rapid than the move- 
ment of the body which produces it, if the luminous body be station- 
ary. This may be proved: — let a be the luminous, b the shaded body, d 
the shadow. I say that the shaded body b moves to c in the same time 
as the shadow d moves to e, and there is the same proportion of speed 
to speed over the same time as there is of length of movement to 
length of movement. Therefore the proportion of the length of the 
movement made by the shaded body b as far as c, to the length of the 
movement made by the shadow d as far as e, is such as the above- 
mentioned speeds of movement have to each other. 

But if the luminous body be equal in speed to the movement of the 
shaded body, then the shadow and the shaded body will be of equal 
movements one to another. And if the luminous be swifter than the 



shaded body, then the movement of the shadow will be slower than the 
movement of the shaded body. 

But if the luminous is slower than the shaded body then the shadow 
will be swifter than the shaded body. e 30 v. 



The pyramidal shadow produced by the parallel body will be nar- 
rower than the shaded body, in proportion as the simple derived 
shadow is intersected at a greater distance from its shaded body. 



The simple derived shadows are of two kinds, that is to say one 
finite in length and two infinite. The finite is pyramidal, and of those 
that are infinite one is columnar and the other expanding. And all 
three have straight sides, but the convergent, that is the pyramidal 
shadow, proceeds from a shaded body that is less than the luminous 
body, the columnar proceeds from a shaded body equal to the lumi- 
nous body, and the expanding from a shaded body greater than the 
luminous body. 


Compound derived shadows are of two kinds, that is, columnar and 
expanding. e 31 r. 


The difference that exists between light and lustre that reveals itself 
on the smooth surface of opaque bodies: — The lights that are pro- 
duced on the smooth surfaces of opaque bodies will be stationary in 
stationary bodies, although the eye which sees them moves; but there 
will be lustres upon the same bodies in as many points of its surface 
as are the positions upon which the eye rests. 

Which bodies are those that have light without lustre? 

Opaque bodies which have a thick rough surface will never produce 
lustre in any portion of their illuminated part. 



Which bodies are those that have lustre and have no illuminated 
part ? 

Thick, opaque bodies, with smooth surface, are those which have all 
the lustre in as many places, in the illuminated part, as there are posi- 
tions that can receive the angle of the incidence of the light and of the 
eye, but, because such surface reflects all the things that surround 
the light, the illuminated body is not distinguishable in this part of 
the illuminated background. 

A luminous body of long shape will make the contours of its derived 
shadow more indistinct than light that is spherical, and this it is that 
controverts the following proposition: — that shadow will have its con- 
tours more distinct which is nearer the primitive shadow, or if you 
prefer, the shaded body, but of this the long shape of the luminous body 
is the cause. e 31 v. 


Derived shadows are of three kinds, of which one is expanding, 
another in the form of a column, the third converging at the point of 
the intersection of its sides which continue beyond in infinite length 
and straightness. And if you should say that this shadow is terminated 
in the angle formed by the meeting of its sides and does not pass be- 
yond, this is controverted by the fact that, in the first concerning 
shadows, it was proved that a thing is entirely ended when no part of 
it exceeds its terminating lines; and, in the case of this shadow, one sees 
the contrary, inasmuch as where this derived shadow originates, there 
there are manifestly created the figures of two shaded pyramids which 
meet at their angles. If however as the adversary says, the first shaded 
pyramid terminates the derived shadow with its angle, from whence 
does the second shaded pyramid proceed? The adversary says that it is 
caused by the angle and not by the shaded body, but this is denied by 
the help of the second of this, which says: — the shadow is an accident 
created by the shaded bodies interposed between the position of this 
shadow and the luminous body. 

Thus it has become clear that the shadow is not produced by the 
angle of the derived shadow but only by the shaded body. 

If a spherical shaded body is illumined by an elongated luminous 
body, the shadow that is produced by the longest part of this luminous 



body will have its contours less defined than that produced by the 
breadth of the same light. And this is proved by what was said before, 
namely that that shadow is of less defined contours which is created by 
a greater luminous body, and conversely that shadow is of more defined 
contours 1 which is lit by a smaller luminous body. 

Broken shadows is the term given to those which are seen on a 
bright wall or other luminous object. 

That shadow will seem the darker which is against a lighter ground. 

The contours of the derived shadows will be more distinct when 
they are nearer to the primitive shadow. 

The derived shadow will have the contours of its impress more 
distinct when they cut against the wall within more equal angles. 

That part of the same shadow will seem darker which has over 
against it darker objects; and that will seem less dark which is facing a 
brighter object. And the bright object when it is larger will shine more 

And that dark object which is of greater bulk will darken the derived 
shadow most in the place of its percussion. e 32 r. 

The surface of every opaque body shares in the colour of surround- 
ing objects. 

Shadow is the diminution of light. Darkness is the exclusion of light. 

Shadow is divided into two parts, of which the first is called primary 
shadow and the second derived shadow. 

Primary shadow always serves as a basis for derived shadow. 

The boundaries of derived shadows are straight lines. 

The darkness of the derived shadow diminishes in proportion as it is 
farther removed from primary shadow. 

That shadow will show itself darker which is surrounded by more 
dazzling brightness, and it will be less evident when it is produced on 
a darker ground. 

Particular light has as a result that it gives better relief to shaded 
bodies than does universal light; as may be shown by the comparison 
of the part of a landscape lit by the sun and that shaded by a cloud 
which is lit merely by the universal light of the air. e 32 v. 

The surface of every opaque body partakes of the colour of its object* 

1 MS., di termini men noti. 



That part of the surface of the opaque bodies partakes most of the 
colour of its object which is nearest to it. f i v. 

That part of a dark object of uniform thickness will show itself 
thinner which is seen against a more luminous background. 

That part of a luminous body of uniform thickness and radiance 
will seem thicker which is seen against a darker background. 


The ray of the sun after having passed through the bubbles of the 
surface of the water, sends to the bottom of the water an image of this 
bubble which bears the form of a cross. I have not yet investigated the 
cause, but I judge it to be a result of other small bubbles which are 
clustered together round the larger bubble. f 28 v. 

A luminous hole seen from a dark place, though it be of uniform 
size, will seem to contract considerably when near to any object what- 
ever that is interposed between the eye and this hole. 

This statement is proved by the seventh of this, which shows that 
the contours of any object interposed between the eye and the light will 
never be seen distinctly, but confused through the air becoming darker 
near these contours, this darkness becoming more intense the nearer it 
is to these contours. f 31 r. 

Two separated lights will at a certain distance appear joined and 

In this case it has been held by many who have made a study of 
perspective, that the air that surrounds these lights at a great distance is 
so illuminated that it seems of the nature of these lights, and therefore 
the light and air that surround them appear to be the same body. 

What they say is not true, for if it were the case that the air that 
surrounds these lights at a great distance was so illuminated as to 
appear all uniformly luminous, this would be more readily discerned 
near at hand where the exact shape of the light is known than it would 
be at a distance, and if, in becoming separated, the perception of the 
exact shape of this light is lost because it suffers a slight decrease in its 
radiance, how much more would be the diminution and loss of that 
radiance of the air, which is much less effulgent than the light! 



We shall prove therefore that this increase is caused by two images 
in the eye. 

The excessive brilliance of the light when near to the eye diminishes 
the visual faculty, seeing that the pupil being hurt contracts and so 
makes itself less, and as the light becomes more separated the injury 
to the eye ceases to exist, because the light has less brilliance, and so 
the pupil increases and sees a greater light. f 35 v. 

If there are two luminous bodies somewhat near to each other at a 
great distance they will seem united: 

This can happen for two reasons, of which the first is that in being 
near to these lights one knows instantly the distance or space that 
separates them, and the images of them that imprint themselves in our 
eye are still very distinct, and on the other hand their rays do not touch, 
whilst at a long distance these images look so near that not only their 
rays but the luminous bodies seem to touch. 

Further, at this distance the pupil which at first was contracted 
becomes enlarged, because the brilliance of the light is not as powerful 
as when it was near the eye, and so the eye increasing the size of its 
pupil sees a thing appearing enlarged. 

If all the images were to meet in an angle they would meet in a 
mathematical point, and this being indivisible all the different kinds 
would seem to you united; being united the sense would not be able 
to discern any difference. f 36 r. 

If some luminous body can be seen through a very small hole made 
in a piece of paper, approach the luminous body as nearly as possible 
with the eye; even though it still may be seen in its entirety it will 
seem so much less than before as this hole is of less size. f 36 v. 

If the shape of the waves were in the figure of a half-circle, as are 
the bubbles of the water, the converging lines of the images of the sun, 
which emanate from these waves and come to the eye, would be of a 
very great angle, if this eye were upon the edge of the sea that comes 
between it and the sun. f 62 v. 

Why does every luminous object that is of long shape appear round 
in the far distance? 

It is never a perfect round, but it happens with it as with the leaden 



die when beaten and much crushed that it appears round in shape. 
So this light at a great distance acquires such breadth in every direction, 
for as that which had been added is equal, and the first stock of light 
goes for nothing in comparison to what is added, the acquisition makes 
it appear uniformly round. 

And this serves to prove that the horns of every star are imperceptible 
at a great distance. f 64 r. 


The lights which illumine opaque bodies are of four kinds, that is 
to say, universal, as that of the atmosphere within our horizon, and 
particular, like that of the sun or of a window or door or other space; 
and the third is reflected light; and there is also a fourth which passes 
through substances of the degree of transparency of linen or paper or 
suchlike things, but not those transparent like glass or crystal or other 
diaphanous bodies, with which the effect is the same as if there was 
nothing interposed between the body in shadow and the light that 
illumines it; and of these we shall treat separately in our discourse. 

[Transparency of leaves] 

The shadows in transparent leaves seen from the underside are the 
same shadows as those on the right side of this leaf, and the shadow is 
seen in transparency on the reverse at the same time as the luminous 
part; but the lustre can never show itself in transparency. g 3 v. 

Of trees seen from below and against the light, one behind the other 
at a short distance, the topmost part of the first will be transparent and 
clear in great part, and it will stand out against the dark part of the 
second tree; and so it will be with all in succession which are situated 
under the same conditions. g 6 r. 

The shadows of plants are never black, for where the atmosphere 
penetrates there cannot be utter darkness. g 8 r. 

[Foliage in light] 

If the light comes from m and the eye is at n, this eye will see the 
colour of the leaves a b all affected by the colour of m, that is of the 
atmosphere, and that of b c will be seen on the underside in transpar- 
ency, with a very beautiful green colour that verges on yellow. 



If m is the luminous body which lights up the leaf s, all the eyes that 
see the underside of the leaf will see it of a very beautiful light green 
because it is transparent. 

There will be many occasions when the positions of the leaves will 
be without shadows, and they will have the underside transparent and 
the right side shining. g 8 v. 

The willow and other similar trees which are pollarded every third 
or fourth year put out very straight branches. Their shadow is towards 
the centre where these branches grow, and near their extremities they 
cast but little shade because of their small leaves and few and slender 

Therefore the branches which rise towards the sky will have but 
little shadow and little relief, and the branches which point downwards 
towards the horizon spring from the dark part of the shadow. And they 
become clearer by degrees down to their extremities, and show them- 
selves in strong relief being in varying stages of brightness against a 
background of shadow. 

That plant will have least shadow which has fewest branches and 
fewest leaves. g 9 r. 

The leaf of concave surface seen on the underside from below up- 
ward, will sometimes show itself half in shadow and half transparent. 
Thus let o p be the leaf, m the light and n the eye which will see in 
shadow, because the light does not strike there between equal angles 
either on the right side or on the reverse; p is lit up on the right side, 
and its light is seen in transparency on its reverse. g 10 v. 



When you represent the dark shadows in shaded bodies, represent 
always the cause of the darkness, and you should do the same for 
reflections; this is because the dark shadows proceed from dark objects 
and the reflections from objects of but little brightness, that is from 
diminished lights. And there is the same proportion between the illumi- 
nated part of bodies and the part lit by reflection as there is between 
the cause of the light on the bodies and the cause of the reflection. 





That part of the tree will be seen to be clothed in shadows of least 
obscurity which is farthest away from the earth. 

This may be proved : — let a p be the tree, n b c the illuminated hemi- 
sphere. The under part of the tree faces the earth p c, that is on the side 
o, and it faces a small part of the hemisphere at c d. But the highest 
part of the convexity a is visible to the greatest mass of the hemisphere, 
that is b c\ and for this reason, and because it does not face the darkness 
of the earth, it remains more illuminated. But if the tree is one thick 
with leaves, as the laurel, the arbutus, the box or the ilex, then it is 
different, for though a does not see the earth it sees the darkness of the 
leaves divided by many shadows, and this darkness is reflected upwards 
on to the undersides of the leaves above; and these trees have the 
shadows so much darker as they are nearer to the centre of the tree. 

g 12 r. 


When drawing any object, remember in comparing the potency of 
the lights of its illuminated portions, that the eye is often deceived into 
thinking one brighter than it really is. The reason springs from our 
comparing them with the parts which border on them, for if there are 
two parts of unequal degrees of brightness, and the less bright borders 
on a dark part while the brighter is set against a light background, such 
as the sky or some similar bright surface, then that which is less bright, 
or I should say less radiant, will appear more radiant and what was 
more radiant will seem darker. g 12 v. 



The painter deceives himself many times in representing the prin- 
cipal lights. c 13 r. 

Of representing an arrangement of bodies which receives the par- 
ticular light of the sun or of another luminous body for its illumina- 
tion. g 15 r. 




When the sun is in the east and the eye is above the centre of a city, 
the eye will see the southern part of this city with its roofs half in 
shadow and half in light, and the same towards the north; but those 
in the east will be entirely in shadow and those in the west entirely in 
light. g 19 v. 


The oudines and forms of each part of bodies in shadow are poorly 
distinguished in their shadows and lights, but in such parts as are 
between the lights and shadows parts of these bodies are of the first 
degree of distinctness. c 3: 


[2 r. 



Take careful note of the situation of your figures, for you will have 
the light and shade different if the object is in a dark place with a 
particular light, and if it is in a bright place with the direct light of the 
sun, and different also if it is in a dark place with the diffused light of 
evening or in dull weather, and if it is in the diffused light of the 
atmosphere lit by the sun. g 33 v. 

That part of the primary shadow will be least dark which is at the 
farthest distance from its extremities. 

The derived shadow which borders on the primary shadow will be 
darker than this primary shadow. h 66 [18] r. 

That place will be most luminous which is farthest away from moun- 
tains, h 68 [20] r. 

The derived shadow is never like the body from which it proceeds, 
unless the light is of the shape and size of the body in shadow. 

The derived shadow cannot be like the primitive in shape unless it 
strikes within equal angles. h 76 [28] v. 





Because the luminous ray is of pyramidal power, and especially 
when the atmosphere is uniform, it will come about that when two 
rays emanating from equal lights meet in a straight line, the ray will 
be everywhere doubled and of uniform power; for where one has the 
apex of the pyramid the other has its base, as n m shows. i 33 r. 

The imprint of the shadow of any body of uniform thickness will 
never resemble the body from whence it proceeds. 

Although a shaded body be pyramidal and equally distant in each 
of its parts from the luminous object, nevertheless that part of the 
pyramid which is smaller than the light that illumines it will not throw 
its shadow any distance from its cause. 1 37 v. 


Shadows and lights are observed by the eye under three aspects. One 
of these is when the eye and the light are both on the same side of the 
body which is seen; the second is when the eye is in front of the object 
and the light behind it; and the third is that in which the eye is in 
front of the object and the light at the side, in such a way that when 
the line which extends from the object to the eye meets that which 
extends from the object to the light, they will at their junction * form 
a right angle. k 105 [25] v. 

There is another division, namely that of the nature of the reflected 
object when placed between the eye and the light in different aspects. 

k 106 [26] r. 


{Derived shadow] 

The derived shadow is stronger in proportion as it is nearer to its 

1 MS., cogfitio, and so Dr. Richter. M. Ravaisson-Mollien has cognition. 



The same quality of shadow seems stronger in proportion as it is 
nearer to the eye. 

The percussion and section of the derived shadow is darker in pro- 
portion as it is shorter. k. hi [31 J v. 

[Luminous rays] 

That part of the body will be illuminated which is struck by the 
luminous rays at more equal angles. m 77 v. 

The image of the sun will show itself brighter in the small waves 
than in the large ones. This happens because the reflections or images 
of the sun occur more frequently in the small waves than in the large 
ones, and the more numerous brightnesses give a greater light than the 
lesser number. 

The waves which intersect after the manner of the scales of a fir-cone 
reflect the image of the sun with the greatest splendour; and this occurs 
because there are as many images as there are ridges of the waves seen 
by the sun, and the shadows which intervene between these waves are 
small and not very dark; and the radiance of so many reflections is 
blended together in the image which proceeds from them to the eye, 
in such a way that these shadows are imperceptible. b.m. 25 r. 

There are two different kinds of light; the one is called free, the 
other restricted. The free is that which freely illuminates bodies; 
restricted is that which illuminates bodies in the same manner, through 
some hole or window. b.m. 170 v. 

Lights are of two different natures, the one separated and the other 
united to bodies. 

Separated is that which illuminates the body, united is the part of 
the body illuminated by this light; the one light is called primary, the 
other derived. 

And so also there are shadows of two kinds; the one primary the 
other derived. Primary is that which is fastened to bodies, derived is 
that which is separated from bodies, bearing in itself to the surface of 
walls the resemblance of its cause. b.m. 171 r. 

A simple shadow is one which does not see any light. 
A compound shadow is one which is illuminated by one or more 
lights. b.m. 248 v. 



A sieve through which penetrates the luminous air, at a great dis 
tance will seem without holes and entirely luminous. 

Forster in 35 v. 

Between walls at an equal distance and quality which are seen 
behind the extremities of an opaque body set over against them, that 
part of the wall will appear more illuminated which is seen by a greater 
amount of the pupil. Forster in 36 r. 

Among things of equal distance and size that which has the greater 
light will seem of greater body. Forster m 42 v. 

If the illuminated object is the size of the thing that illuminates, 
and of that where this light is reflected, the quality of the reflex light 
will have the same proportion to the intermediate light as this second 
light has to the first, if these bodies are smooth and white. 

Forster in 54 r. 

The luminous or illuminated object contiguous to the shadow cuts 
as much as it touches. 

There will be as much lacking in the extremities of the shadows of 
bodies as is touched by the illuminated or luminous field. 

Forster in 87 v. 
[Of shadow] 

Shadow is the diminution of light and of darkness, and it is inter- 
posed between darkness and light. 

Shadow is of infinite obscurity, and this obscurity may be infinitely 

The beginnings and the ends of shadow extend between light and 
darkness, and they may be infinitely diminished and increased. 

Shadow is the expression of bodies and of their shapes. 

The shapes of bodies will convey no perception of their quality 
without shadow. 

Shadow partakes always of the colour of its object. 

Of the boundaries of shadows: some are like smoke, with boundaries 
that cannot be perceived, in others they are distinct. 

Keep the drawings for the end of the [book on] shadows. They may 



be seen in the workshop of Gherardo the miniaturist in San Marco at 

No opaque body is without shadow or light, except when there is a 
mist lying over the ground when it is covered with snow, or it is the 
same when it snows in the country; this will be without light and it 
will be surrounded by darkness. 

And this occurs in spherical bodies, because in the case of other 
bodies which have members, the parts of the members which face each 
other steep each other in the tone of their surface. 

The surface of every body is infused into all the illuminated air 
which serves as its object. 

The surface of opaque bodies has its whole image in all the illu- 
minated air which surrounds it from every quarter. 

Make the rainbow in the last book 'On Painting'. But first make the 
book of the colours produced by the mixture of the other colours, so 
that by means of these colours used by painters you may be able to 
prove the genesis of the colours of the rainbow. 

Describe how no body is in itself defined in the mirror; but the eye 
on seeing it in this mirror puts boundaries to it; for if you cause your 
face to be represented in the mirror the part is like the whole, seeing 
that the part is all in the whole of the mirror and it is complete in 
every part of the same mirror; and the same happens with every image 
of every object set in front of this mirror. 

The boundaries of the derived shadow are surrounded by the colours 
of the illuminated objects which are round the luminous body, the 
cause of this shadow. 

Derived shadow does not exist without primary light: this is proved 
by the First of this, which states that darkness is the entire privation of 
light, and shadow is the gradual diminution of darkness and of light; 
and it partakes so much the more or the less of darkness than of light 
in proportion as the darkness has been broken up by this light. 

What is the cause which makes the boundaries of the shadow con- 
fused and indistinct. 

Whether it is possible to give the contours of the shadows clear-cut 
and precise boundaries. Quaderni 11 6 r. 



[ Of luminous bodies] 


Of bodies equal in size and distance that which is most luminous 
tinges most with its essence the opposite object. 

Of bodies of equal luminosity that which is largest in outline tinges 
most of the surface of its object, the distance of all being equal. 

Of bodies which are equal in luminosity and size that which is 
nearest tinges its object most. Quaderni n 16 r. 

The reason why we know that light has in itself a single centre is as 
follows: — we recognise clearly that a large light often outspans a small 
object, which nevertheless, although it surrounds it much more than 
twice with its rays, always has its shadow appearing on the first sur- 
face and it is always visible. 

Let c f be the large light and n the object in front of it which pro- 
duces the shadow on the wall, and a b the wall; it clearly appears that 
it is not the large light that will cast the shadow of n upon the wall; 
but since the light has a centre in itself I prove by experiment the 
shadow is cast upon the wall as is shown ax. m o t r. [Diagram] 

Why to two or in front of two eyes do three things when represented 
appear as two. 

Why in surveying a direction with two sights the first appears 

I say the eye projects an infinite number of lines, and these attach 
themselves to or mingle with those that come towards it which emanate 
from the things seen, and only the centre line of this perceptive faculty 
is that which knows and judges bodies and colours; all the others are 
false and deceitful. 

And when you place two things at a distance of a cubit one from the 
other, the nearer being close to the eye, the surface of this nearer one 
will remain far more confused than that of the second, the reason being 
that the nearer is overrun by a greater number of false lines than the 
second and so is more uncertain. 

Light acts like this because in the effects of its lines and especially 
in the working of its perspective it is very similar to the eye; and its 



centre ray carries truth in its testing of shadows. When the object 
placed in front of it is too rapidly subdued by dim rays, it will cast a 
shadow broad and disproportionately large and ill defined; but when 
the object that has to produce the shadow cuts the rays of the light and 
is near the place of percussion, then the shadow becomes distinct; and 
this especially when the light is at a distance, because the centre ray at 
a long distance is less interfered with by false rays, seeing that the lines 
of the eye and the solar and other luminous rays proceeding through 
the air are obliged to keep a straight course. Otherwise if they were 
impeded by the atmosphere being denser or more rarefied they would 
remain bent at some point, but if the air is free from heaviness or 
humidity they will observe their straight nature, always carrying back 
to their point of origin the image of the intercepting object, and if it 
is the eye the intercepting object will be estimated by its colour as well 
as by its shape and size. But if the surface of the said interposing object 
shall have within it some small hole that enters into a room dark not 
on account of its colour but through absence of light, you will see the 
rays entering through this small hole transmitting there, to the wall 
beyond, all the traits of their original both as to colour and form, except 
that everything will be inverted. Windsor: Drawings 19148 v. 

The way in which the images of bodies intersect at the edges of the 
small holes by which they penetrate : 

What difference is there between the manner of penetration of the 
images which pass through narrow apertures and those which pass 
through wide ones or those which pass at the sides of shaded bodies. 



The images of the immovable objects move by the moving of the 
edges of that aperture through which the rays of the images penetrate, 
and this comes about by the ninth [section] which says: — the images of 
any body are all in all and all in every part of the area that is round 
about them. It follows that the moving of one of the edges of the 
aperture by which these images penetrate to a dark place releases the 



rays of the images that were in contact with it, and they unite with 
other rays of those images which were remote from it. 



If you move the right side of the opening the impression on the left 
will move, being that of the object on the right which entered by this 
opening, and the same will happen with all the other sides of this open- 
ing, and this is proved with the help of the second [section] of this 
[treatise] which says: — all the rays which carry the images of bodies 
through the air are straight lines. Therefore as the images of the great- 
est bodies have to pass through the smallest openings, and beyond this 
opening to re-form in their utmost expansion, it is necessary that this 
intersection be uninterrupted. Windsor: Drawings 19 149 r. 

The images of bodies are all diffused through the air which sees 
them and all in every part of it. 

This is proved: — let a c and e be objects, of which the images pene- 
trate to a dark place by the small holes n p, and imprint themselves on 
the wall / i opposite to these holes; as many impressions will be made 
at as many different places on this wall as is the number of the said 
small holes. 



All the smallest parts of the images penetrate one another without 
occupation the one of the other. . . . 

. . . the seventh of this where it is said: — every simulacrum sends 
forth from itself its images by the shortest line, which of necessity is 
straight. Windsor: Drawings 19150 v. 

Demonstration how every part of light converges in a point. 

Although the balls a b c have their light from one window, never- 
theless if you follow the lines of their shadows you will see that they 
make intersection and point in the angle n. Windsor ms. r 137 



Shadow is light diminished by means of the intervention of an 
opaque body. Shadow is the counterpart of the luminous ray cut off by 
an opaque body. 

This is proved because the shaded ray is of the same shape and size 
as was the luminous ray in which this shadow projects itself. 

Windsor: Drawings 19152 v. 

Demonstration and argument why of parts in light some portions 
are in higher light than others. 
[Diagram | 

Since it is proved that every light with fixed boundaries emanates 
or appears to emanate from a single point, that part illuminated by it 
will have those portions in highest light upon which the line of radi- 
ance falls, between two equal angles, as is shown above in the lines 
a g, also in a h, and similarly in a I; and that portion of the illuminated 
part will be less luminous upon which the line of incidence strikes at 
two more unequal angles, as may be seen in b c and d; and in this 
way you will also be able to discern the parts deprived of light, as may 
be seen at m and \. 

When the angles made by the lines of incidence are more equal the 
place will have more light, and where they are more unequal it will be 

I will treat further of the cause of the reflection. 

Windsor ms. r 575