Perspective 

'Perspective is a rational demonstration whereby experience confirms how all things transmit their images to the eye by pyramidal lines! 

Saxdro! you do not say why these second things seem lower than the third. 1 

[Diagram ] 

The eye between two parallel lines will never see them at so great a distance that they meet in a point. c.a. 120 r. d 

All the cases of perspective are expressed by means of the five mathematical terms, to wit: point, line, angle, surface and body. Of these the point is unique of its kind, and this point has neither height nor breadth, nor length nor depth, wherefore we conclude that it is indivisible and does not occupy space. A line is of three kinds, namely straight, curved and bent, and it has neither breadth, height nor depth, consequently it is indivisible except in its length; its ends are two points. 

An angle is the ending of two lines in a point, and they are of three kinds, namely right angles, acute angles and obtuse angles. 

Surface is the name given to that which is the boundary of bodies, and it is without depth, and in such depth as it has it is indivisible as is the line or point, being divided only in respect of length or breadth. There are as many different kinds of surfaces as there are bodies that create them. 

Body is that which has height, breadth, length and depth, and in all these attributes it is divisible. These bodies are of infinite and varied forms. The visible bodies are of two kinds only, of which the first is 1 Fragment probably of a discussion with Botticelli concerning the law of diminishing 
perspective. References to Sandro [Botticelli] are also to be found in c.a. 313 r. b. p. 555, and Trattato (Ludwig) 60. without shape or any distinct or definite extremities, and these though present are imperceptible and consequently their colour is difficult to determine. The second kind of visible bodies is that of which the surface defines and distinguishes the shape. 

The first kind, which is without surface, is that of those bodies which are thin or rather liquid, and which readily melt into and mingle with other thin bodies, as mud with water, mist or smoke with air, or the element of air with fire, and other similar things, the extremities of which are mingled with the bodies near to them, whence by this intermingling their boundaries become confused and imperceptible, for which reason they find themselves without surface, because they enter into each other's bodies, and consequently such bodies are said to be without surface. 

The second kind is divided into two other kinds, namely transparent and opaque. The transparent is that which shows its whole self along the whole of its side, and nothing is hidden behind it, as is the case with glass, crystal, water and the like. The second division of bodies of which the surface reveals and defines the shape is called opaque. 

This it behoves us to treat of at some length, seeing that out of it are derived an infinite number of cases. c.a. 132 r. b 

Perspective 

The air is full of an infinite number of images of the things which 
are distributed through it, and all of these are represented in all, all in 
one, and all in each. Consequently it so happens that if two mirrors be 
placed so as to be exactly facing each other, the first will be reflected 
in the second and the second in the first. Now the first being reflected 
in the second carries to it its own image together with all the images 
which are represented in it, among these being the image of the second 
mirror; and so they continue from image to image on to infinity, in 
such a way that each mirror has an infinite number of mirrors within 
it, each smaller than the last, and one inside another. 

By this example, therefore, it is clearly proved that each thing trans- 
mits the image of [itself] to all those places where the thing itself is 
visible, and so conversely this object is able to receive into itself all the 
images of the things which are in front of it. 

Consequently the eye transmits its own image through the air to all 
the objects which are in front of it, and receives them into itself, that is 
on its surface, whence the understanding takes them and considers 
them, and such as it finds pleasing, these it commits to the memory. 

So I hold that the invisible powers of the images in the eyes may 
project themselves forth to the object as do the images of the object to 
the eye. 

An instance of how the images of all things are spread through the 
air may be seen in a number of mirrors placed in a circle, and they will 
then reflect each other for an infinite number of times, for as the image 
of one reaches another it rebounds back to its source, and then becom- 
ing less rebounds yet again to the object, and then returns, and so con- 
tinues for an infinite number of times. 

If at night you place a light between two flat mirrors which are 
a cubit's space apart, you will see in each of these mirrors an infinite 
number of lights, one smaller than another, in succession. 

If at night you place a light between the walls of a [room], every 
part of these walls will become tinged by the images of this light, and 
all those parts which are exposed to the light will likewise be directly 
lit by it; that is when there is no obstacle between them to interrupt 
the transmission of the images. 

This same example is even more apparent in the transmission of 
solar rays, which all [pass] through all objects, and consequently into 
each minutest part of each object, and each ray of itself conveys to its 
object the image of its source. 

That each body alone of itself fills the whole surrounding air with 
its images, and that this same air is [able] at the same time to receive 
into itself the images of the countless other bodies which are within it, 
is clearly shown by these instances; and each body is seen in its entirety 
throughout the whole of the said atmosphere, and each in each 
minutest part of the same, and all throughout the whole of it and all in 
each minutest part; each in all, and all in every part. ca. 138 r. b 

OF PAINTING 

The true knowledge of the form of an object becomes gradually lost 
in proportion as distance decreases its size. ca. 176 v. b 

PERSPECTIVE 989 

[ With drawing \ 

Body formed irom the perspective by Leonardo Vinci, disciple of 
experience. 

This body may be made without the example of any other body but 
merely with plain lines. c.a. 191 r. a 

Among the various studies of natural processes, that of light gives 
most pleasure to those who contemplate it; and among the noteworthy 
characteristics of mathematical science, the certainty of its demonstra- 
tions is what operates most powerfully to elevate the minds of its 
investigators. 

Perspective therefore is to be preferred to all the formularies and 
systems of the schoolmen, for in its province the complex beam of light 
is made to show the stages of its development, wherein is found the 
glory not only of mathematical but also of physical science, adorned as 
it is with the flowers of both. And whereas its propositions have been 
expanded with much circumlocution I will epitomise them with con- 
clusive brevity, introducing however illustrations drawn either from 
nature or from mathematical science according to the nature of the 
subject, and sometimes deducing the results from the causes and at 
other times the causes from the results; adding also to my conclusions 
some which are not contained in these, but which nevertheless are to be 
inferred from them; even as the Lord who is the Light of all things 
shall vouchsafe to reveal to me, who seek to interpret this light — and 
consequently I will divide the present work into three parts. 

Light, when in the course of its incidence it sees things which have 
been turned against itself, retains their images in part. This conclusion 
is proved by results, because the vision as it looks upon the light has a 
measure of fear. Even so after the glance there remain in the eye the 
images of vivid objects, and they make the place of lesser light appear 
in shadow until the eye has lost the trace of the impression of the 
greater light. c.a. 203 r. a 

METHODS OF PERSPECTIVE 

If you wish to represent a figure in the corner of a dwelling which 
shall appear to have been made in a level place, get someone to strip 
naked, and with the light of a candle make their shadow fall as vou 

990 PERSPECTIVE 

wish in the said corner, and draw the outline of it with charcoal; but 
your sight will wish to be in the spot exactly through a hole placed 
where the light passed, and again the light of the window after its work 
will wish to come by the said line, so that the walls joined together in 
the corner will not be any darker on account of the shadow, the one 
than the other. 

THE LIGHT IN THE OPERATION OF THE LAW OF 
PERSPECTIVE DOES NOT DIFFER FROM THE EYE 

That the light has not any difference from the eye as regards losing 
the thing which is behind the first object is due to this reason: you 
know that in swiftness of movement and in concourse of straight lines 
the visual ray and the ray of light resemble each other. As an example: 
suppose you hold a coin near to the eye, that space which exists between 
the coin and the boundary of the position, will be more capable of 
expansion, in proportion as the part of the boundary of the position 
which is not visible to the eye is the greater, and the nearer the coin 
is brought to the eye the more the boundary of the position will be 
filled up. 

OF LIGHT 

Of the eye. The same process may be seen with light, for as you 
bring the said coin nearer or remove it farther from this light you will 
see the shadow on the opposite wall growing larger or failing, and if 
you wish an example let it be in this form : have many bodies of differ- 
ent things placed in a large room, then take in your hand a long pole 
with a piece of charcoal at the point and mark with that on the ground 
and along the walls all the outlines of the things 1 as they appear 
against the boundaries of the wall. 

Of the light. Then at the same distance and height place a light, and 
you will see the shadows of the said bodies covering as much of the 
wall as the part that found itself enclosed within the marks made by 
the charcoal placed at the point of the pole. 

1 Reading cose. MS. has deUe pariete. 

PERSPECTIVE 99 1 

Experiment 

If you wish to sec a similar experiment place a light upon a table, 
and then retire a certain distance away, and you will see that all the 
shadows of the objects which are between the wall and the light remain 
stamped with the shadow of the form of the objects, and all the lines of 
their length converge in the point where the light is. 

Afterwards bring your eye nearer to this light, using the blade of a 
knife for a screen so that the light may not hurt your eye, and you will 
see all the bodies opposite without their shadows, and the shadows 
which were in the partitions of the walls will be covered as regards the 
eye by the bodies which are set before them. c.a. 204 v. b 

Of things of equal size situated at an equal distance from the eye, 
that will appear the larger which is whiter in colour. 

Equal things equally distant from the eye will be judged by the eye 
to be 'of equal size. 

Equal things through being at different distances from the eye come 
to appear of unequal size. 

Unequal things by reason of their different distances from the eye 
may appear equal. c.a. 221 v. c 

Many things of great bulk lose their visibility in the far distance by 
reason of their colour, and many small things in the far distance retain 
their visibility by reason of the said colour. 

An object of a colour similar to that of the air retains its visibility 
at a moderate distance, and an object that is paler than the air retains it 
in the far distance, and an object which is darker than the air ceases to 
be visible at a short distance. 

But of these three kinds of objects that will be visible at the greatest 
distance of which the colour presents the strongest contrast to itself. 

c.a. 249 r. c 

PERSPECTIVE 

That dimness (il mezzo confuso) which occurs by reason of distance, 
or at night, or when mist comes between the eye and the object, causes 
the boundaries of this object to become almost indistinguishable from 
the atmosphere. c.a. 316 v. b 

992 PERSPECTIVE 

An object placed between the eye and an object of dazzling white- 
ness loses half its size. c.a. 320 v. b 

MIRRORS 

If you place a candle between two tall mirrors shaped like curved 
roofing tiles in the manner here shown [drawing], you will see every- 
thing that offers resistance melted in this candle with the help of these 
mirrors. c.a. 338 r. a 

If you wish to furnish a proof of how things seen by the eye diminish, 
it is necessary to fix the eye on the centre of the wall, and the curve of 
the wall will then give you the true clearness of the things seen. 

When the cause of the shadow is near the place where it strikes and 
distant from the light, you will see the shape of the cause of the severed 
rays clearly upon the wall. c.a. 353 r. b 

Among things of equal size, that will show itself less in form .which 
is farther away from the eye. c.a. 353 v. b 

PERSPECTIVE 

It is asked of you, O painter, why the figures which you draw on a 
minute scale as a demonstration of perspective do not appear — not- 
withstanding the demonstration of distance — as large as real ones, 
which are of the same height as those painted upon the wall. 

And why [representations of] things, seen a short distance away, 
notwithstanding the distance, seem larger than the reality. Tr. 66 a 

WALL OF GLASS 

Perspective is nothing else than the seeing of an object behind a sheet 
of glass, smooth and quite transparent, on the surface of which all the 
things may be marked that are behind this glass; these things approach 
the point of the eye in pyramids, and these pyramids are cut by the said 
glass. a 1 v. 

Citation of the things that I ask to have admitted in the proofs of this 
my perspective: — I ask that it may be permitted me to affirm that 

STUDIES FOR HEAD OF LEDA 
Royal Library, Windsor 

PERSPECTIVE 993 

every ray which passes through air of uniform density proceeds in a 
direct line from its cause to its object or the place at which it strikes. 

OF THE DIMINUTION OF OBJECTS AT VARIOUS DISTANCES 

A second object as far removed from the first as the first is from the 
eye will appear half the size of the first, although they are of the same 
size. 

A small object near at hand and a large one at a distance, when seen 
between equal angles will appear the same size. 

I ask how far away the eye can see a non-luminous body, as for 
instance a mountain. It will see it to advantage if the sun is behind it, 
and it will seem at a greater or less distance away according to the sun's 
place in the sky. a 8 v. 

Perspective is a rational demonstration whereby experience confirms 
how all things transmit their images to the eye by pyramidal lines. By 
pyramidal lines I mean those which start from the extremities of the 
surface of bodies, and by gradually converging from a distance arrive 
at the same point; the said point being, as I shall show, in this par- 
ticular case located in the eye, which is the universal judge of all 
objects. I call a point that which cannot be divided up into any parts; 
and as this point which is situated in the eye is indivisible, no body can 
be seen by the eye which is not greater than this point, and this being 
the case it is necessary that the lines which extend from the object to 
the point should be pyramidal. And if anyone should wish to prove 
that the faculty of sight does not belong to this point, but rather to that 
black spot which is seen in the centre of the pupil, one might reply to 
him that a small object never could diminish at any distance, as for 
example a grain of millet or panic-seed or other similar thing, and that 
this thing which was greater than the said point could never be entirely 
seen. a io r. 

No object can be of so great a size as not to appear less to the eye at a 
great distance than a smaller object which is nearer. 

A wall surface is a perpendicular plane represented in front of the 
common point at which the concourse of the pyramids converges. And 

994 PERSPECTIVE 

this wall surface performs the same function for the said point as a flat 
piece of glass upon which you drew the various objects that you saw 
through it, and the things drawn would be so much less than the orig- 
inals, as the space that existed between the glass and the eye was less 
than that between the glass and the object. 

The concourse of the pyramids created by the bodies will show upon 
the wall surface the variety of the size and distance of their causes. 

All these planes which have their extremities joined by perpendicular 
lines forming right angles must necessarily, if of equal size, be less 
visible the nearer they rise to the level of the eye, and the farther they 
pass beyond it the more will their real size be seen. 

The farther distant from the eye is the spherical body, the more it is 
seen. a 10 v. 

As soon as ever the air is illuminated it is filled with an infinite num- 
ber of images, caused by the various substances and colours collected 
together within it, and of these images the eye is the target and the 
magnet. a 27 r. 

PRINCIPLE OF PERSPECTIVE 

All things transmit their image to the eye by means of pyramids; 
the nearer to the eye these are intersected the smaller the image of their 
cause will appear. a 36 v. 

If you should ask how you can demonstrate these points to me from 
experience, I should tell you, as regards the vanishing point which 
moves with you, to notice as you go along by lands ploughed in straight 
furrows, the ends of which start from the path where you are walking, 
you will see that continually each pair of furrows seem to approach 
each other and to join at their ends. 

As regards the point that comes to the eye, it may be comprehended 
with greater ease; for if you look in the eye of anyone you will see 
your own image there; consequently if you suppose two lines to start 
from your ears and proceed to the ears of the image which you see of 
yourself in the eye of the other person, you will clearly recognise that 
these lines contract so much that when they have continued only a little 
way beyond your image as mirrored in the said eye they will touch one 
another in a point. a y] r. and v. 

PERSPECTIVE 995 

The thing that is nearer to the eye always appears larger than another 
of the same size which is more remote. a 38 r. 

Perspective is of such a nature that it makes what is flat appear in 
relief, and what is in relief appear flat. a 38 v. 

The perspective by means of which a thing is represented will be 
better understood when it is seen from the view-point at which it was 
drawn. 

If you wish to represent a thing near, which should produce the effect 
of natural things, it is impossible for your perspective not to appear 
false, by reason of all the illusory appearances and errors in proportion 
of which the existence may be assumed in a mediocre work, unless 
whoever is looking at this perspective finds himself surveying it from 
the exact distance, elevation, angle of vision or point at which you were 
situated to make this perspective. Therefore it would be necessary to 
make a window of the size of your face or in truth a hole through 
which you would look at the said work. And if you should do this, 
then without any doubt your work will produce the effect of nature if 
the light and shade are correctly rendered, and you will hardly be able 
to convince yourself that these things are painted. Otherwise do not 
trouble yourself about representing anything, unless you take your 
view-point at a distance of at least twenty times the maximum width 
and height of the thing that you represent; and this will satisfy every 
beholder who places himself in front of the work at any angle what- 
ever. 

If you wish to see a proof of this quickly, take a piece of a staff like 
a small column eight times as high as its width without plinth or cap- 
ital, then measure off on a flat wall forty equal spaces which are in 
conformity with the spaces; they will make between them forty col- 
umns similar to your small column. Then let there be set up in front 
of the middle of these spaces, at a distance of four braccia from the 
wall, a thin band of iron, in the centre of which there is a small round 
hole of the size of a large pearl; place a light beside this hole so as to 
touch it, then go and place your column above each mark of the wall 
and draw the outline of the shadow, then shade it and observe it 
through the hole in the iron. a 40 v. 

996 PERSPECTIVE 

In Vitolone there are eight hundred and five conclusions about 
perspective. b 58 r. 

PERSPECTIVE 

No visible body can be comprehended and well judged by human 
eyes, except by the difference of the background where the extremities 
of this body terminate and are bounded, and so far as its contour lines 
are concerned no object will seem to be separated from this background. 
The moon, although far distant from the body of the sun, when by 
reason of eclipses it finds itself between our eyes and the sun, having 
the sun for its background will seem to human eyes to be joined and 
attached to it. c 23 r. 

Perspective comes to aid us where judgment fails in things that 
diminish. c 27 v. 

[Of perspective in nature and in art] 

It is possible to bring about that the eye does not see distant objects 
as much diminished as they are in natural perspective, where they are 
diminished by reason of the convexity of the eye, which is obliged to 
intersect upon its surface the pyramids of every kind of image that 
approach the eye at a right angle. But the method that I show here in 
the margin cuts these pyramids at right angles near the surface of the 
pupil. But whereas the convex pupil of the eye can take in the whole of 
our hemisphere, this will show only a single star; but where many 
small stars transmit their images to the surface of the pupil these stars 
are very small; here only one will be visible but it will be large; and so 
the moon will be greater in size and its spots more distinct. You should 
place close to the eye a glass filled with the water mentioned in [chap- 
ter] four of book 113 'Concerning Natural Things', water which 
causes things congealed in balls of crystalline glass to appear as though 
they were without glass. 

Of the eye. Of bodies less than the pupil of the eye that which is 
nearest to it will be least discerned by this pupil — and from this expe- 
rience it follows that the power of sight is not reduced to a point. 

But the images of objects which meet in the pupil of the eye are 
spread over this pupil in the same way as they are spread about in the 
air; and the proof of this is pointed out to us when we look at the 

PERSPECTIVE 997 

scarry heavens without fixing our gaze more upon one star than upon 
another, for then the sky shows itself to us strewn with stars, and they 
hear to the eye the same proportions as in the sky, and the spaces 
between them also are the same. b 15 v. 

Natural perspective acts in the opposite way, for the greater the 
distance the smaller does the thing seen appear, and the less the distance 
the larger it appears. But this invention constrains the beholder to stand 
with his eye at a small hole, and then with this small hole it will be 
seen well. But since many eyes come together to see at the same time 
one and the same work produced by this art, only one of them will 
have a good view of the function of this perspective and all the others 
will only see it confusedly. It is well therefore to shun this compound 
perspective, and to keep to the simple which does not purport to view 
planes foreshortened but as far as possible in exact form. 

And of this simple perspective in which the plane intersects the 
pyramid that conveys the images to the eye that are at an equal distance 
from the visual faculty, an example is afforded us by the curve of the 
pupil of the eye upon which these pyramids intersect at an equal dis- 
tance from the visual faculty. e 16 r. 

OF EQUAL THINGS THE MORE REMOTE APPEARS LESS 

The practice of perspective is divided into [two] parts, of which the 
first treats of all the things seen by the eye at whatsoever distance, and 
this in itself shows all these things diminished as the eye beholds them, 
without the man being obliged to stand in one place rather than in 
another, provided that the wall does not foreshorten it a second time. 

But the second practice is a combination of perspective made partly 
by art and partly by nature, and the work done according to its rules 
has no part that is not influenced by natural and accidental perspective. 
Natural perspective I understand has to do with the flat surface on 
which this perspective is represented; which surface, although it is 
parallel to it in length and height, is constrained to diminish the distant 
parts more than its near ones. And this is proved by the first of what 
has been said above, and its diminution is natural. 

Accidental perspective, that is that which is created by art, acts in 

998 PERSPECTIVE 

the contrary way; because it causes bodies equal in themselves to 
increase on the foreshortened plane, in proportion as the eye is more 
natural and nearer to the plane, and as the part of this plane where it 
is represented is more remote from the eye. e 16 v. 

THE PERSPECTIVE OF THE DISAPPEARANCE OF THE 
OUTLINES OF OPAQUE BODIES 

If the true outlines of opaque bodies become indistinguishable at any 
short distance they will be still more invisible at great distances; and 
since it is by the outlines that the true shape of each opaque body 
becomes known, whenever because of distance we lack the perception 
of the whole we shall lack yet more the perception of its parts and 
outlines. e 80 r. 

OF PAINTING AND PERSPECTIVE 

There are three divisions of perspective as employed in painting. Of 
these the first relates to the diminution in the volume of opaque bodies; 
the second treats of the diminution and disappearance of the outlines 
of these opaque bodies; the third is their diminution and loss of colour 
when at a great distance. 

OF THE PERSPECTIVE OF THE DIMINUTION OF OPAQUE 

BODIES 

Among opaque bodies of equal magnitude, the diminution apparent 
in their size will vary according to their distance from the eye which 
sees them; but it will be in inverse proportion, for at the greater dis- 
tance the opaque body appears less, and at a less distance this body will 
appear greater, and on this is founded linear perspective. And show 
secondly how every object at a great distance loses first that portion of 
itself which is the thinnest. Thus with a horse, it would lose the legs 
sooner than the head because the legs are thinner than the head, and it 
would lose the neck before the trunk for the same reason. It follows 
therefore that the part of the horse which the eye will be able last to 
discern will be the trunk, retaining still its oval form, but rather ap- 
proximating to the shape of a cylinder, and it will lose its thickness 

PERSPECTIVE 999 

sooner than its length from the second conclusion aforsaid. If the eye 
is immovable the perspective terminates its distance in a point; but if 
the eye moves in a straight line the perspective ends in a line, because 
it is proved that the line is produced by the movement of the point, and 
our sight is fixed upon the point, and consequently it follows that as the 
sight moves the point moves, and as the point moves the line is pro- 
duced, e 80 v. 

Of objects of equal size placed at equal distances from the eye the 
more luminous will appear the greater. 

Of equal objects equally distant from the eye the more obscure will 
appear the less. f 36 r. 

Of things removed an equal distance from the eye that will appear 
to be less diminished which was at first more. 

Of things removed from the eye at an equal distance from their first 
position, that is less diminished which at first was more distant from 
this eye. 

And the proportion of the diminution will be the same as that of the 
distances at which they were from the eye before their movement. 

f 60 v. 

SIMPLE PERSPECTIVE 

Simple perspective is that which is made by art upon a position 
equally distant from the eye in each of its parts. 

Complex perspective is that which is made upon a position in which 
no two of the parts are equally distant from the eye. g 13 v. 

PERSPECTIVE 

If two similar and equal things be placed one behind the other at a 
given distance, the difference in their size will appear greater in pro- 
portion as they are nearer to the eye which sees them. And conversely 
there will appear less difference in size between them as they are 
farther removed from the eye. 

This is proved by means of the proportions that they have between 
their distances, for if there are two bodies with as great a distance from 
the eye to the first as from the first to the second this proportion is 

iooo PERSPECTIVE 

called double; because if the first is one braccio distant from the eye 
and the second is at a distance of two braccia, the second space is double 
the first, and for this reason the first body will show itself double the 
second. And if you remove the first to a distance of a hundred braccia 
and the second to a hundred and one braccia, you will find that the 
first is greater than the second by the extent to which a hundred is 
less than a hundred and one, and this conversely. 

The same thing also is proved by the fourth of this, which says: in 
the case of equal things there is the same proportion of size to size as 
that of distance to distance from the eye that sees them. g 29 v. 

DISCOURSE ON PAINTING 

Perspective as it concerns Painting is divided into three chief parts, 
of which the first treats of the diminution in the size of bodies at dif- 
ferent distances. The second is that which treats of the diminution in 
the colour of these bodies. The third of the gradual loss of distinctness 
of the forms and outlines of these bodies at various distances. 

Perspective employs in distances two opposite pyramids, one of which 
has its apex in the eye and its base as far away as the horizon. The 
other has the base towards the eye and the apex on the horizon. But the 
first is concerned with the universe, embracing all the mass of the ob- 
jects that pass before the eye, as though a vast landscape was seen 
through a small hole, the number of the objects seen through such a 
hole being so much the greater in proportion as the objects are more 
remote from the eye; and thus the base is formed on the horizon and 
the apex in the eye, as I have said above. 

The second pyramid has to do with a peculiarity of landscape, in 
showing itself so much smaller in proportion as it recedes farther from 
the eye; and this second instance of perspective springs from the first. 

[Perspective of disappearance] 

In every figure placed at a great distance you lose first the knowledge 
of its most minute parts, and preserve to the last that of the larger 
parts, losing, however, the perception of all their extremities; and they 
become oval or spherical in shape, and their boundaries are indistinct. 

g 53 v. 

PERSPECTIVE iooi 

The eye cannot comprehend a luminous angle when close to itself. 

h 71 [23] r. 

PERSPECTIVE 

The shadows or reflections of things seen in moving water, that is to 
say with tiny waves, will always be greater than the object outside the 
water which causes them. 

The eye cannot judge where an object high up ought to descend. 

h y6 [28] v. 

No surface will reveal itself exactly if the eye which see it is not 
equally distant from its extremities. h 81 [33] r. 

OF ORDINARY PERSPECTIVE 

An object of uniform thickness and colour seen against a background 
of various colours will appear not to be of uniform thickness. 

And if an object of uniform thickness and of various colours is seen 
against a background of uniform colour, the object will seem of a 
varying thickness. 

And in proportion as the colours of the background, or of the object 
seen against the background, have more variety, the more will their 
thickness seem to vary, although the objects seen against the back- 
ground may be of equal thickness. 1 17 v. 

A dark object seen against a light background will seem smaller 
than it is. 

A light object will appear greater in size when it is seen against a 
background that is darker in colour. 1 18 r. 

If the eye be in the middle of a course with two horses running to 
their goal along parallel tracks, it will seem to it that they are running 
to meet one another. 

This that has been stated occurs because the images of the horses 
which impress themselves upon the eye are moving towards the centre 
of the surface of the pupil of the eye. k 120 [40] v. 

ioo2 PERSPECTIVE 

PAINTING 

Foreshorten, on the summits and sides of the hills, the outlines of 
the estates and their divisions; and, as regards the things turned to- 
wards you, make them in their true shape. l 21 r. 

Among things of equal velocity, that will appear of slower move- 
ment which is more remote from the eye. 

Therefore that will appear swifter which is nearer to the eye. 

b.m. 134 v. 
[Aerial perspective'] 

In the morning the mist is thicker up above than in the lower parts 
because the sun draws it upwards; so with high buildings the summit 
will be invisible although it is at the same distance as the base. And this 
is why the sky seems darker up above and towards the horizon, and 
does not approximate to blue but is all the colour of smoke and dust. 

The atmosphere when impregnated with mist is altogether devoid of 
blueness and merely seems to be the colour of the clouds, which turn 
white when it is fine weather. And the more you turn to the west the 
darker you will find it to be, and the brighter and clearer towards the 
east. And the verdure of the countryside will assume a bluish hue in 
the half-mist but will turn black when the mist is thicker. 

Buildings which face the west only show their illuminated side, the 
rest the mist hides. 

When the sun rises and drives away the mists, and the hills begin to 
grow distinct on the side from which the mists are departing, they 
become blue and seem to put forth smoke in the direction of the mists 
that are flying away, and the buildings reveal their lights and shadows; 
and where the mist is less dense they show only their lights, and where 
it is more dense nothing at all. Then it is that the movement of the 
mist causes it to pass horizontally and so its edges are scarcely percep- 
tible against the blue of the atmosphere, and against the ground it will 
seem almost like dust rising. 

In proportion as the atmosphere is more dense the buildings in a city 
and the trees in landscapes will seem more infrequent, for only the 
most prominent and the largest will be visible. 

And the mountains will seem few in number, for only those will be 

PERSPECTIVE 1003 

seen which are farthest apart from each other, since at such distances 
the increases in the density creates a brightness so pervading that the 
darkness of the hills is divided, and quite disappears towards their 
summits. In the small adjacent hills it cannot find such foothold, and 
therefore they are less visible and least of all at their bases. 

Darkness steeps everything with its hue, and the more an object is 
divided from darkness the more it shows its true and natural colour. 

b.m. 169 r. 

Equal things equally distant from the eye will be judged to be of 
equal size by this eye. 

OF PERSPECTIVE 

The shaded and the illuminated parts of opaque bodies will be in 
the same proportion of brightness and darkness as are those of their 
objects [that is of the body or bodies which project upon them]. 

Forster 11 5 r. 

OF PERSPECTIVE 

Of things of equal size that which is farther away from the eye will 
appear of less bulk. Forster 11 15 v. 

OF PERSPECTIVE 

When the eye turns away from a white object which is illuminated 
by the sun, and goes to a place where there is less light, everything 
there will seem dark. And this happens, because the eye that rests upon 
this white illuminated object proceeds to contract its pupil to such an 
extent that whatever the original surface that was visible they will have 
lost more than three quarters of it, and thus lacking in size they will 
also be lacking in power. 

Though you might say to me: — a small bird then would see in pro- 
portion very little, and because of the smallness of its pupils the white 
there would appear black. To this I should reply to you that we are 
here paying attention to the proportion of the mass of that part of the 
brain which is devoted to the sense of sight, and not to any other thing. 
Or — to return — this pupil of ours expands and contracts according to 
the brightness or darkness of its object, and since it needs an interval 

ioo 4 PERSPECTIVE 

of time thus to expand and contract, it cannot see all at once when 
emerging from the light and going to the shade, nor similarly from the 
shade to what is illuminated; and this circumstance has already de- 
ceived me when painting an eye, and from it I have learnt. 

Forster n 158 v. 

Among equal things the more remote will seem the smaller; and the 
proportion of the diminutions will be as that of the distances. 

Quaderni iv 10 r. 
[Perspective of colours] 

Make the perspective of the colours so that it is not at variance with 
the size of any object, that is that the colours lose part of their nature 
in proportion as the bodies at different distances suffer loss of their nat- 
ural quantity. Quaderni vi 18 r.