Full text: Gravesande, Willem Jacob: An essay on perspective

An ESSAY Sides a d and d c of the Figure a b c d. The
ſame may be demonſtrated of the other Sides; and therefore the Figures are ſimilar.

Now to prove the other Part of the Theorem: If a perpendicular be ſuppoſed to be let fall from
the Eye upon the Plane of the Figure, and con-
tinued as is neceſſary; it is evident, that O D,
will be to O d, as this Perpendicular, which
meaſures the Diſtance from the Eye to the Plane
of the Figure, is to the Diſtance of the Eye
from the Perſpective Plane, which is meaſur’d
by the Part of the perpendicular, contain’d be-
tween the Eye and the perſpective Plane. Now
this before was manifeſt; viz. that
O D : O d : : A D : a d :

Whence there is the ſame Proportion between
A d one of the Sides of the Figure, and A D its
Appearance, as the Theorem expreſſes. The
ſame may be demonſtrated of the other Sides of
the Figure. Which was to be demonſtrated.

15. Corollary I.

10. If from a Point in the Geometrical Plane, three
right Lines proceed, which are equal between them-
ſelves, and parallel to the perſpective Plane; the firſt
of which is in the Geometrical Plane, the ſecond ele-
vated Perpendicular to the firſt, and the third in-
clined to it; the Appearances of theſe three right
Lines are equal.

This will appear clear enough in conſidering
the Lines as a Figure parallel to the perſpective
Plane; and ſo conſequently they will have the
ſame Proportion as their Appearances.

Note, The firſt of the aforeſaid Lines is always
parallel to the baſe Line; and the ſecond, when
the perſpective Plane is perpendicular or up-

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