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.
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.
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
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.
+ N R = G R.
Becauſe the Triangles G M I and G N C are
ſimilar, we have
ſimilar, we have
G M:
G N:
: G I:
G C.
The Triangles G Z F and G R O being alſo
ſimilar,
ſimilar,
G Z:
G R:
: G F:
G O.
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