13162An ESSAY
Proe. III.
79.
To find the Repreſentation of a Figure in the
Geometrical Plane, when the Perſpective Plane is
placed above the Eye.
Geometrical Plane, when the Perſpective Plane is
placed above the Eye.
When the perſpective Plane is ſituated above
the Eye, we ſuppoſe the Geometrical Plane to
paſs through the Top of the Perſpective Plane;
upon which Geometrical Plane are drawn the
Figures of Objects meeting it; as alſo the Seats
of thoſe Objects that are underneath it, by
Means of Perpendiculars; and the Height of the
Eye is here meaſur’d by a Perpendicular drawn
from the Eye to the Geometrical Plane; whence
the perſpective Plane, elevated in reſpect to the
Eye, is the ſame thing, as an Eye elevated in
regard to the perſpective Plane.
the Eye, we ſuppoſe the Geometrical Plane to
paſs through the Top of the Perſpective Plane;
upon which Geometrical Plane are drawn the
Figures of Objects meeting it; as alſo the Seats
of thoſe Objects that are underneath it, by
Means of Perpendiculars; and the Height of the
Eye is here meaſur’d by a Perpendicular drawn
from the Eye to the Geometrical Plane; whence
the perſpective Plane, elevated in reſpect to the
Eye, is the ſame thing, as an Eye elevated in
regard to the perſpective Plane.
Let I L be the Baſe Line, and H the Foot of
11Fig. 42. the vertical Line; then in the Baſe Line aſ-
ſume the Points I and L at Pleaſure, towards
the Sides of the perſpective Plane. Make I S
equal to {1/3} or {1/4} Part of I H, and raiſe the Per-
pendicular S X, in the Point S, to the Baſe Line,
equal to a correſpondent Part of the Height and
Diſtance of the Eye taken together; draw the
Line X I G, and moreover Y L Q, in aſſuming
L T equal to {1/3} or {1/4} & c. of L H. Again draw
the Line G Q in the Geometrical Plane, pa-
rallel to the Baſe Line, and diſtant therefrom
(for Example) a third Part of the Height of
the Eye; draw alſo F P in the perſpective Plane,
parallel to the Baſe Line, and diſtant therefrom,
a fourth Part of the Eye’s Diſtance; theſe two
Lines will cut X I in G and F, and Y L in Q
and P. Note, if the Diſtance of G Q from the
Baſe Line, had been aſſumed equal to a fourth
Part of the Eye’s Diſtance; then F P muſt
11Fig. 42. the vertical Line; then in the Baſe Line aſ-
ſume the Points I and L at Pleaſure, towards
the Sides of the perſpective Plane. Make I S
equal to {1/3} or {1/4} Part of I H, and raiſe the Per-
pendicular S X, in the Point S, to the Baſe Line,
equal to a correſpondent Part of the Height and
Diſtance of the Eye taken together; draw the
Line X I G, and moreover Y L Q, in aſſuming
L T equal to {1/3} or {1/4} & c. of L H. Again draw
the Line G Q in the Geometrical Plane, pa-
rallel to the Baſe Line, and diſtant therefrom
(for Example) a third Part of the Height of
the Eye; draw alſo F P in the perſpective Plane,
parallel to the Baſe Line, and diſtant therefrom,
a fourth Part of the Eye’s Diſtance; theſe two
Lines will cut X I in G and F, and Y L in Q
and P. Note, if the Diſtance of G Q from the
Baſe Line, had been aſſumed equal to a fourth
Part of the Eye’s Diſtance; then F P muſt