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

24. Theorem VI.

19. Let A C be a Line inclined to the Geometrical
Plane, and O D another Line drawn parallel to
A C, from the Eye to the perſpective Plane. Now
if B A be drawn in the Geometrical Plane, pa-
rallel to the baſe Line, and likewiſe D E, in the
perſpective Plane, parallel to the ſaid Line, ſo that
B A be to A C, as E d to D O. I ſay, the Ap-
pearance of the Line B C, paſſing through the Point
B, and the Extremity of the Line A C, being con-
tinued, will meet the Point E.

24.1.

Fig. 6.

Now to prove this; it is evident, that we need but demonſtrate, that O E is parallel to
B C: And this may be done in the following
Manner:

24.1.

13.

A B is parallel to E D, and A C to O D; whence the Angle (E D O) of the Triangle
O E D, is equal to the Angle (B A C) of the
Triangle A C B: And ſo theſe two Triangles
are ſimilar; becauſe they have alſo their Sides
Proportional. But ſince theſe two ſimilar Tri-
angles, have two of their Sides parallel, the
third B C is alſo parallel to O E; which was to be
demonſtrated.

25. Corollary .

20. If A B be made equal to A C, and E D to D O,
the Appearance of B C will paſs thro’ the Point E,

26. CHAP. III.

The Practice of Perſpective upon the Per-
ſpective Plane, ſuppoſed to be perpendicu-
lar, or upright.

IN order to give a diſtinct Idea of the Theory, I
have hitherto conſider’d the Geometrical Plane,
as it were the Ground upon which the Spectator

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