shown above, wants to count the letters placed in front, the eye
will be obliged to turn from letter to letter, because it cannot
discern them unless they lie in the line _a b;_ as, for instance, in
the line _a c_. All visible objects reach the eye by the lines of a
pyramid, and the point of the pyramid is the apex and centre of it,
in the centre of the pupil, as figured above.

[Footnote: 51. In this problem the eye is conceived of as fixed and
immovable; this is plain from line 11.]

Experimental proof of the existence of the pyramid of sight (52-55).

52.

Perspective is a rational demonstration, confirmed by experience,
that all objects transmit their image to the eye by a pyramid of
lines.

By a pyramid of lines I understand those lines which start from the
edges of the surface of bodies, and converging from a distance, meet
in a single point; and this point, in the present instance, I will
show to be situated in the eye which is the universal judge of all
objects. By a point I mean that which cannot be divided into parts;
therefore this point, which is situated in the eye, being
indivisible, no body is seen by the eye, that is not larger than
this point. This being the case it is inevitable that the lines
which come from the object to the point must form a pyramid. And if
any man seeks to prove that the sense of sight does not reside in
this point, but rather in the black spot which is visible in the
middle of the pupil, I might reply to him that a small object could
never diminish at any distance, as it might be a grain of millet or
of oats or of some similar thing, and that object, if it were larger
than the said [black] spot would never be seen as a whole; as may be
seen in the diagram below. Let _a_. be the seat of sight, _b e_ the
lines which reach the eye. Let _e d_ be the grains of millet within
these lines. You plainly see that these will never diminish by
distance, and that the body _m n_ could not be entirely covered by
it. Therefore you must confess that the eye contains within itself
one single indivisible point _a_, to which all the points converge
of the pyramid of lines starting from an object, as is shown below.
Let _a_. _b_. be the eye; in the centre of it is the point above
mentioned. If the line _e f_ is to enter as an image into so small
an opening in the eye, you must confess that the smaller object
cannot enter into what is smaller than itself unless it is
diminished, and by diminishing it must take the form of a pyramid.

53.

PERSPECTIVE.

Perspective comes in where judgment fails [as to the distance] in
objects which diminish. The eye can never be a true judge for
determining with exactitude how near one object is to another which
is equal to it [in size], if the top of that other is on the level
of the eye which sees them on that side, excepting by means of the
vertical plane which is the standard and guide of perspective. Let
_n_ be the eye, _e f_ the vertical plane above mentioned. Let _a b c
d_ be the three divisions, one below the other; if the lines _a n_
and _c n_ are of a given length and the eye _n_ is in the centre,
then _a b_ will look as large as _b c. c d_ is lower and farther off
from _n_, therefore it will look smaller. And the same effect will
appear in the three divisions of a face when the eye of the painter
who is drawing it is on a level with the eye of the person he is
painting.

54.

TO PROVE HOW OBJECTS REACH THE EYE.

If you look at the sun or some other luminous body and then shut
your eyes you will see it again inside your eye for a long time.
This is evidence that images enter into the eye.

The relations of the distance points to the vanishing point (55-56).

55.

ELEMENTS OF PERSPECTIVE.

All objects transmit their image to the eye in pyramids, and the
nearer to the eye these pyramids are intersected the smaller will
the image appear of the objects which cause them. Therefore, you may
intersect the pyramid with a vertical plane [Footnote 4: _Pariete_.
Compare the definitions in 85, 2-5, 6-27. These lines refer
exclusively to the third diagram. For the better understanding of
this it should be observed that _c s_ must be regarded as
representing the section or profile of a square plane, placed
horizontally (comp. lines 11, 14, 17) for which the word _pianura_
is subsequently employed (20, 22). Lines 6-13 contain certain
preliminary observations to guide the reader in understanding the
diagram; the last three seem to have been added as a supplement.
Leonardo's mistake in writing _t denota_ (line 6) for _f denota_ has
been rectified.] which reaches the base of the pyramid as is shown
in the plane _a n_.

The eye _f_ and the eye _t_ are one and the same thing; but the eye
_f_ marks the distance, that is to say how far you are standing from
the object; and the eye _t_ shows you the direction of it; that is
whether you are opposite, or on one side, or at an angle to the
object you are looking at. And remember that the eye _f_ and the eye


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