The Notebooks of Leonardo Da Vinci

Page 76

The inversion of the images.

All the images of objects which pass through a window [glass pane]
from the free outer air to the air confined within walls, are seen
on the opposite side; and an object which moves in the outer air
from east to west will seem in its shadow, on the wall which is
lighted by this confined air, to have an opposite motion.

Page 75

If the judgment of the eye is situated within it, the straight lines
of the images are refracted on its surface because they pass through
the rarer to the denser medium. If, when you are under water, you
look at objects in the air you will see them out of their true
place; and the same with objects under water seen from the air.

The intersection of the rays (76-82).

Page 74

The lines sent forth by the image of an object to the eye do not
reach the point within the eye in straight lines.

Page 73

The object which is opposite to the pupil of the eye is seen by that
pupil and that which is opposite to the eye is seen by the pupil.

Refraction of the rays falling upon the eye (74. 75)

Page 72

In the practice of perspective the same rules apply to light and to
the eye.

Page 71

HOW THE IMAGES OF OBJECTS RECEIVED BY THE EYE INTERSECT WITHIN THE
CRYSTALLINE HUMOUR OF THE EYE.

An experiment, showing how objects transmit their images or
pictures, intersecting within the eye in the crystalline humour, is
seen when by some small round hole penetrate the images of
illuminated objects into a very dark chamber. Then, receive these
images on a white paper placed within this dark room and rather near
to the hole and you will see all the objects on the paper in their
proper forms and colours, but much smaller; and they will be upside
down by reason of that very intersection. These images being
transmitted from a place illuminated by the sun will seem actually
painted on this paper which must be extremely thin and looked at
from behind. And let the little perforation be made in a very thin
plate of iron. Let _a b e d e_ be the object illuminated by the sun
and _o r_ the front of the dark chamber in which is the said hole at
_n m_. Let _s t_ be the sheet of paper intercepting the rays of the
images of these objects upside down, because the rays being
straight, _a_ on the right hand becomes _k_ on the left, and _e_ on
the left becomes _f_ on the right; and the same takes place inside
the pupil.

[Footnote: This chapter is already known through a translation into
French by VENTURI. Compare his '_Essai sur les ouvrages
physico-mathematiques de L. da Vinci avec des fragments tires de ses
Manuscrits, apportes de l'Italie. Lu a la premiere classe de
l'Institut national des Sciences et Arts.' Paris, An V_ (1797).]

The practice of perspective (72. 73).

Page 70

If the object in front of the eye sends its image to the eye, the
eye, on the other hand, sends its image to the object, and no
portion whatever of the object is lost in the images it throws off,
for any reason either in the eye or the object. Therefore we may
rather believe it to be the nature and potency of our luminous
atmosphere which absorbs the images of the objects existing in it,
than the nature of the objects, to send their images through the
air. If the object opposite to the eye were to send its image to the
eye, the eye would have to do the same to the object, whence it
might seem that these images were an emanation. But, if so, it would
be necessary [to admit] that every object became rapidly smaller;
because each object appears by its images in the surrounding
atmosphere. That is: the whole object in the whole atmosphere, and
in each part; and all the objects in the whole atmosphere and all of
them in each part; speaking of that atmosphere which is able to
contain in itself the straight and radiating lines of the images
projected by the objects. From this it seems necessary to admit that
it is in the nature of the atmosphere, which subsists between the
objects, and which attracts the images of things to itself like a
loadstone, being placed between them.

PROVE HOW ALL OBJECTS, PLACED IN ONE POSITION, ARE ALL EVERYWHERE
AND ALL IN EACH PART.

I say that if the front of a building--or any open piazza or
field--which is illuminated by the sun has a dwelling opposite to
it, and if, in the front which does not face the sun, you make a
small round hole, all the illuminated objects will project their
images through that hole and be visible inside the dwelling on the
opposite wall which may be made white; and there, in fact, they will
be upside down, and if you make similar openings in several places
in the same wall you will have the same result from each. Hence the
images of the illuminated objects are all everywhere on this wall
and all in each minutest part of it. The reason, as we clearly know,
is that this hole must admit some light to the said dwelling, and
the light admitted by it is derived from one or many luminous
bodies. If these bodies are of various colours and shapes the rays
forming the images are of various colours and shapes, and so will
the representations be on the wall.

[Footnote: 70. 15--23. This section has already been published in the
"_Saggio delle Opere di Leonardo da Vinci_" Milan 1872, pp. 13, 14.
G. Govi observes upon it, that Leonardo is not to be regarded as the
inventor of the Camera obscura, but that he was the first to explain
by it the structure of the eye. An account of the Camera obscura
first occurs in CESARE CESARINI's Italian version of Vitruvius, pub.
1523, four years after Leonardo's death. Cesarini expressly names
Benedettino Don Papnutio as the inventor of the Camera obscura. In
his explanation of the function of the eye by a comparison with the
Camera obscura Leonardo was the precursor of G. CARDANO, Professor
of Medicine at Bologna (died 1576) and it appears highly probable
that this is, in fact, the very discovery which Leonardo ascribes to
himself in section 21 without giving any further details.]

Page 69

A parallel case.

Just as a stone flung into the water becomes the centre and cause of
many circles, and as sound diffuses itself in circles in the air: so
any object, placed in the luminous atmosphere, diffuses itself in
circles, and fills the surrounding air with infinite images of
itself. And is repeated, the whole every-where, and the whole in
every smallest part. This can be proved by experiment, since if you
shut a window that faces west and make a hole [Footnote: 6. Here the
text breaks off.] . .

[Footnote: Compare LIBRI, _Histoire des sciences mathematiques en
Italie_. Tome III, p. 43.]

The function of the eye as explained by the camera obscura (70. 71).

Page 68

That the contrary is impossible.

It is impossible that the eye should project from itself, by visual
rays, the visual virtue, since, as soon as it opens, that front
portion [of the eye] which would give rise to this emanation would
have to go forth to the object and this it could not do without
time. And this being so, it could not travel so high as the sun in a
month's time when the eye wanted to see it. And if it could reach
the sun it would necessarily follow that it should perpetually
remain in a continuous line from the eye to the sun and should
always diverge in such a way as to form between the sun and the eye
the base and the apex of a pyramid. This being the case, if the eye
consisted of a million worlds, it would not prevent its being
consumed in the projection of its virtue; and if this virtue would
have to travel through the air as perfumes do, the winds would bent
it and carry it into another place. But we do [in fact] see the mass
of the sun with the same rapidity as [an object] at the distance of
a braccio, and the power of sight is not disturbed by the blowing of
the winds nor by any other accident.

[Footnote: The view here refuted by Leonardo was maintained among
others by Bramantino, Leonardo's Milanese contemporary. LOMAZZO
writes as follows in his Trattato dell' Arte della pittura &c.
(Milano 1584. Libr. V cp. XXI): Sovviemmi di aver gia letto in certi
scritti alcune cose di Bramantino milanese, celebratissimo pittore,
attenente alla prospettiva, le quali ho voluto riferire, e quasi
intessere in questo luogo, affinche sappiamo qual fosse l'opinione
di cosi chiaro e famoso pittore intorno alla prospettiva . . Scrive
Bramantino che la prospettiva e una cosa che contrafa il naturale, e
che cio si fa in tre modi

Circa il primo modo che si fa con ragione, per essere la cosa in
poche parole conclusa da Bramantino in maniera che giudico non
potersi dir meglio, contenendovi si tutta Parte del principio al
fine, io riferiro per appunto le proprie parole sue (cp. XXII, Prima
prospettiva di Bramantino). La prima prospettiva fa le cose di
punto, e l'altra non mai, e la terza piu appresso. Adunque la prima
si dimanda prospettiva, cioe ragione, la quale fa l'effetto dell'
occhio, facendo crescere e calare secondo gli effetti degli occhi.
Questo crescere e calare non procede della cosa propria, che in se
per esser lontana, ovvero vicina, per quello effetto non puo
crescere e sminuire, ma procede dagli effetti degli occhi, i quali
sono piccioli, e percio volendo vedere tanto gran cosa_, bisogna che
mandino fuora la virtu visiva, _la quale si dilata in tanta
larghezza, che piglia tutto quello che vuoi vedere, ed_ arrivando a
quella cosa la vede dove e: _e da lei agli occhi per quello circuito
fino all' occhio, e tutto quello termine e pieno di quella cosa_.

It is worthy of note that Leonardo had made his memorandum refuting
this view, at Milan in 1492]

Page 67

General conclusions.

All objects project their whole image and likeness, diffused and
mingled in the whole of the atmosphere, opposite to themselves. The
image of every point of the bodily surface, exists in every part of
the atmosphere. All the images of the objects are in every part of
the atmosphere. The whole, and each part of the image of the
atmosphere is [reflected] in each point of the surface of the bodies
presented to it. Therefore both the part and the whole of the images
of the objects exist, both in the whole and in the parts of the
surface of these visible bodies. Whence we may evidently say that
the image of each object exists, as a whole and in every part, in
each part and in the whole interchangeably in every existing body.
As is seen in two mirrors placed opposite to each other.

Page 66

The images of objects are all diffused through the atmosphere which
receives them; and all on every side in it. To prove this, let _a c
e_ be objects of which the images are admitted to a dark chamber by
the small holes _n p_ and thrown upon the plane _f i_ opposite to
these holes. As many images will be produced in the chamber on the
plane as the number of the said holes.

Page 65

PERSPECTIVE.

The air is filled with endless images of the objects distributed in
it; and all are represented in all, and all in one, and all in each,
whence it happens that if two mirrors are placed in such a manner as
to face each other exactly, the first will be reflected in the
second and the second in the first. The first being reflected in the
second takes to it the image of itself with all the images
represented in it, among which is the image of the second mirror,
and so, image within image, they go on to infinity in such a manner
as that each mirror has within it a mirror, each smaller than the
last and one inside the other. Thus, by this example, it is clearly
proved that every object sends its image to every spot whence the
object itself can be seen; and the converse: That the same object
may receive in itself all the images of the objects that are in
front of it. Hence the eye transmits through the atmosphere its own
image to all the objects that are in front of it and receives them
into itself, that is to say on its surface, whence they are taken in
by the common sense, which considers them and if they are pleasing
commits them to the memory. Whence I am of opinion: That the
invisible images in the eyes are produced towards the object, as the
image of the object to the eye. That the images of the objects must
be disseminated through the air. An instance may be seen in several
mirrors placed in a circle, which will reflect each other endlessly.
When one has reached the other it is returned to the object that
produced it, and thence--being diminished--it is returned again to
the object and then comes back once more, and this happens
endlessly. If you put a light between two flat mirrors with a
distance of 1 braccio between them you will see in each of them an
infinite number of lights, one smaller than another, to the last. If
at night you put a light between the walls of a room, all the parts
of that wall will be tinted with the image of that light. And they
will receive the light and the light will fall on them, mutually,
that is to say, when there is no obstacle to interrupt the
transmission of the images. This same example is seen in a greater
degree in the distribution of the solar rays which all together, and
each by itself, convey to the object the image of the body which
causes it. That each body by itself alone fills with its images the
atmosphere around it, and that the same air is able, at the same
time, to receive the images of the endless other objects which are
in it, this is clearly proved by these examples. And every object is
everywhere visible in the whole of the atmosphere, and the whole in
every smallest part of it; and all the objects in the whole, and all
in each smallest part; each in all and all in every part.

Page 64

The body of the atmosphere is full of infinite radiating pyramids
produced by the objects existing in it. These intersect and cross
each other with independent convergence without interfering with
each other and pass through all the surrounding atmosphere; and are
of equal force and value--all being equal to each, each to all. And
by means of these, images of the body are transmitted everywhere and
on all sides, and each receives in itself every minutest portion of
the object that produces it.

Proof by experiment (65-66).

Page 63

Every body in light and shade fills the surrounding air with
infinite images of itself; and these, by infinite pyramids diffused
in the air, represent this body throughout space and on every side.
Each pyramid that is composed of a long assemblage of rays includes
within itself an infinite number of pyramids and each has the same
power as all, and all as each. A circle of equidistant pyramids of
vision will give to their object angles of equal size; and an eye at
each point will see the object of the same size. The body of the
atmosphere is full of infinite pyramids composed of radiating
straight lines, which are produced from the surface of the bodies in
light and shade, existing in the air; and the farther they are from
the object which produces them the more acute they become and
although in their distribution they intersect and cross they never
mingle together, but pass through all the surrounding air,
independently converging, spreading, and diffused. And they are all
of equal power [and value]; all equal to each, and each equal to
all. By these the images of objects are transmitted through all
space and in every direction, and each pyramid, in itself, includes,
in each minutest part, the whole form of the body causing it.

Page 62

Every point is the termination of an infinite number of lines, which
diverge to form a base, and immediately, from the base the same
lines converge to a pyramid [imaging] both the colour and form. No
sooner is a form created or compounded than suddenly infinite lines
and angles are produced from it; and these lines, distributing
themselves and intersecting each other in the air, give rise to an
infinite number of angles opposite to each other. Given a base, each
opposite angle, will form a triangle having a form and proportion
equal to the larger angle; and if the base goes twice into each of
the 2 lines of the pyramid the smaller triangle will do the same.

Page 61

All bodies together, and each by itself, give off to the surrounding
air an infinite number of images which are all-pervading and each
complete, each conveying the nature, colour and form of the body
which produces it.

It can clearly be shown that all bodies are, by their images,
all-pervading in the surrounding atmosphere, and each complete in
itself as to substance form and colour; this is seen by the images
of the various bodies which are reproduced in one single perforation
through which they transmit the objects by lines which intersect and
cause reversed pyramids, from the objects, so that they are upside
down on the dark plane where they are first reflected. The reason of
this is--

[Footnote: The diagram intended to illustrate the statement (Pl. II
No. i) occurs in the original between lines 3 and 4. The three
circles must be understood to represent three luminous bodies which
transmit their images through perforations in a wall into a dark
chamber, according to a law which is more fully explained in 75?81.
So far as concerns the present passage the diagram is only intended
to explain that the images of the three bodies may be made to
coalesce at any given spot. In the circles are written,
giallo--yellow, biacho--white, rosso--red.

The text breaks off at line 8. The paragraph No.40 follows here in
the original MS.]