The Notebooks of Leonardo Da Vinci

→ See the front page for how to read the Notebooks by RSS.

Page 55 of 1565.
Previous / Next

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 will be one and the same thing. If the eye
_f_ could see a perfect square of which all the sides were equal to
the distance between _s_ and _c_, and if at the nearest end of the
side towards the eye a pole were placed, or some other straight
object, set up by a perpendicular line as shown at _r s_--then, I
say, that if you were to look at the side of the square that is
nearest to you it will appear at the bottom of the vertical plane _r
s_, and then look at the farther side and it would appear to you at
the height of the point _n_ on the vertical plane. Thus, by this
example, you can understand that if the eye is above a number of
objects all placed on the same level, one beyond another, the more
remote they are the higher they will seem, up to the level of the
eye, but no higher; because objects placed upon the level on which
your feet stand, so long as it is flat--even if it be extended into
infinity--would never be seen above the eye; since the eye has in
itself the point towards which all the cones tend and converge which
convey the images of the objects to the eye. And this point always
coincides with the point of diminution which is the extreme of all
we can see. And from the base line of the first pyramid as far as
the diminishing point

[Footnote: The two diagrams above the chapter are explained by the
first five lines. They have, however, more letters than are referred
to in the text, a circumstance we frequently find occasion to
remark.]

Previous / Next