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

on PERSPECTIVE. Line T B X; which interſect in the Point X,
by a Perpendicular to the Baſe Line, in the
Point G; and then the Point X is the Appear-
ance ſought.

124. Demonstration .

In Fig. 44. where V, S, T, and H, repreſent
the ſame Points as thoſe that are denoted with
the ſame Letters in this Figure; we have,

T H: H S: : T V: V O.

Compon. and altern.

T H: T V: : T H + H S: T V + V O.

This being apply’d to Fig. 45. and it will be,
T H: T V: : T S: T V + V O.

If now T X be continued, till it cuts the Ho-
rizontal Line in F; we ſhall have,

T H: T V: : T B: T F.

And conſequently,

T B: T F: : T S: T V + V O.

Whence it follows, that if a Line be drawn
ſrom the Eye, to the Point F, it will be paral-
lel to S B A. Therefore the Perſpective of B A, is a Part of B X; and ſo the Repreſenta-
tion of A is in the ſaid Line. The Perſpective
of a Line perpendicular to the Geometrical
Plane, in the Point A, paſſes thro’ the Perſpe-
ctive of the Point A, and thro’ the Point T ; therefore it is a Part of T X. But the given Point
is in the aſoreſaid Perpendicular: And ſo its Per-
ſpective is in T X.


13, 14.

Again; it is otherwiſe manifeſt, that the Per-
ſpective of C L, is a Part of C X; and conſe- quently, the Appearance of L is in this Line. Now, if a Line be ſuppos’d to be drawn from
the Point L, thro’ the propos’d Point, it will be
parallel to the Vertical Line; and ſo its Per- ſpective is parallel to the Baſe Line. And ſince


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