Free The Notebooks of Leonardo Da Vinci by Leonardo Da Vinci Page A

f is from the object a b ; and yet c d , which is
the base made by the painter's point, is smaller than a b which
is the base of the lines from the objects converging in the eye and
refracted at s t , the surface of the eye. This may be proved by
experiment, by the lines of vision and then by the lines of the
painter's plumbline by cutting the real lines of vision on one and
the same plane and measuring on it one and the same object.
    85.
PERSPECTIVE.
    The vertical plane is a perpendicular line, imagined as in front of
the central point where the apex of the pyramids converge. And this
plane bears the same relation to this point as a plane of glass
would, through which you might see the various objects and draw them
on it. And the objects thus drawn would be smaller than the
originals, in proportion as the distance between the glass and the
eye was smaller than that between the glass and the objects.
PERSPECTIVE.
    The different converging pyramids produced by the objects, will
show, on the plane, the various sizes and remoteness of the objects
causing them.
PERSPECTIVE.
    All those horizontal planes of which the extremes are met by
perpendicular lines forming right angles, if they are of equal width
the more they rise to the level of eye the less this is seen, and
the more the eye is above them the more will their real width be
seen.
PERSPECTIVE.
    The farther a spherical body is from the eye the more you will see
of it.
    The angle of sight varies with the distance (86-88)
    86.
    A simple and natural method; showing how objects appear to the eye
without any other medium.
    The object that is nearest to the eye always seems larger than
another of the same size at greater distance. The eye m , seeing
the spaces o v x , hardly detects the difference between them, and
the. reason of this is that it is close to them [Footnote 6: It is
quite inconceivable to me why M. RAVAISSON, in a note to his French
translation of this simple passage should have remarked: Il est
clair que c'est par erreur que Leonard a �crit per esser visino au
lieu de per non esser visino. (See his printed ed. of MS. A. p.
38.)]; but if these spaces are marked on the vertical plane n o the space o v will be seen at o r , and in the same way the space v x will appear at r q . And if you carry this out in any place
where you can walk round, it will look out of proportion by reason
of the great difference in the spaces o r and r q . And this
proceeds from the eye being so much below [near] the plane that the
plane is foreshortened. Hence, if you wanted to carry it out, you
would have [to arrange] to see the perspective through a single hole
which must be at the point m , or else you must go to a distance of
at least 3 times the height of the object you see. The plane o p being always equally remote from the eye will reproduce the objects
in a satisfactory way, so that they may be seen from place to place.
    87.
    How every large mass sends forth its images, which may diminish
through infinity.
    The images of any large mass being infinitely divisible may be
infinitely diminished.
    88.
    Objects of equal size, situated in various places, will be seen by
different pyramids which will each be smaller in proportion as the
object is farther off.
    89.
    Perspective, in dealing with distances, makes use of two opposite
pyramids, one of which has its apex in the eye and the base as
distant as the horizon. The other has the base towards the eye and
the apex on the horizon. Now, the first includes the [visible]
universe, embracing all the mass of the objects that lie in front of
the eye; as it might be a vast landscape seen through a very small
opening; for the more remote the objects are from the eye, the
greater number can be seen through the opening, and thus the pyramid
is constructed with the base on the horizon and the apex in the eye,
as has been said. The second pyramid is extended to a spot which is
smaller in proportion as it is farther from the eye; and this