Gravesande, Willem Jacob 's, An essay on perspective

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13263on PERSPECTIVE. been drawn from the Baſe Line, equal to a fifth
Part of the Eye’s Diſtance, and ſo on.
Now
A is a Point whoſe Repreſentation is requir’d.
Operation.
Draw the Lines A F and A P, from the Point
A to the Points F and P, cutting the Baſe Line
in the Points E and B;
then draw the Lines E G
and B Q, which continue till they interſect
each other in a, which is the Repreſentation
ſought.
Demonstration.
Let us ſuppoſe the perſpective Plane continu-
ed, C D the Horizontal Line, and O the Eye
denoted in the Horizontal Plane.
It is evi-
dent by Conſtruction, that the Line G F 1177. tinued, paſſes through the Eye O;
produce the
Line G S a, until it meets the Horizontal Line
in D, and draw the Line O D.
Let fall the
Perpendicular G N R, from the Point G upon
the Horizontal Line, which interſect in R, by
the Line O R, paſſing through the Eye parallel
to the Horizontal Line.
Now by Conſtruction,
G M is {1/3} of M N;
and conſequently it is {1/4} of
G N;
M Z is likewiſe {1/4} of N R: Therefore
G M: M Z: : G N: N R.
Compon. and Altern.
G M: G N: : G M + M Z = G Z: G N
+ N R = G R.
Becauſe the Triangles G M I and G N C are
ſimilar, we have
G M: G N: : G I: G C.
The Triangles G Z F and G R O being alſo
ſimilar,
G Z: G R: : G F: G O.

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