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

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.]
    56.
    there are only bases without pyramids which constantly diminish up
to this point. And from the first base where the vertical plane is
placed towards the point in the eye there will be only pyramids
without bases; as shown in the example given above. Now, let a b be the said vertical plane and r the point of the pyramid
terminating in the eye, and n the point of diminution which is
always in a straight line opposite the eye and always moves as the
eye moves—just as when a rod is moved its shadow moves, and moves
with it, precisely as the shadow moves with a body. And each point
is the apex of a pyramid, all having a common base with the
intervening vertical plane. But although their bases are equal their
angles are not equal, because the diminishing point is the
termination of a smaller angle than that of the eye. If you ask me:
"By what practical experience can you show me these points?" I
reply—so far as concerns the diminishing point which moves with you
—when you walk by a ploughed field look at the straight furrows
which come down with their ends to the path where you are walking,
and you will see that each pair of furrows will look as though they
tried to get nearer and meet at the [farther] end.
    [Footnote: For the easier understanding of the diagram and of its
connection with the preceding I may here remark that the square
plane shown above in profile by the line c s is here indicated by e d o p . According to lines 1, 3 a b must be imagined as a plane
of glass placed perpendicularly at o p .]
    57.
    How to measure the pyramid of vision.
    As regards the point in the eye; it is made more intelligible by
this: If you look into the eye of another person you will see your
own image. Now imagine 2 lines starting from your ears and going to
the ears of that image which you see in the other man's eye; you
will understand that these lines converge in such a way that they
would meet in a point a little way beyond your own image mirrored in
the eye. And if you want to measure the diminution of the pyramid in
the air which occupies the space between the object seen and the
eye, you must do it according to the diagram figured below. Let m
n be a tower, and e f a, rod, which you must move backwards and
forwards till its ends correspond with those of the tower [Footnote
9: I sua stremi .. della storre (its ends … of the tower) this
is the case at e f .]; then bring it nearer to the eye, at c d and you will see that the image of the tower seems smaller, as at r
o . Then [again] bring