The Notebooks of Leonardo Da Vinci by Leonardo Da Vinci Read Free Book Online Page A

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 t must always be kept on the same level. For example if you raise
or lower the eye from the distance point f you must do the same
with the direction point t . And if the point f shows how far the
eye is distant from the square plane but does not show on which side
it is placed—and, if in the same way, the point t show s the
direction and not the distance, in order to ascertain both you must
use both points and they