19195on PERSPECTIVE.
lar drawn from the Eye to the Geometrical
Plane, meets the ſaid Plane; and T the Per-
ſpective of that Point, found by the aforegoing
Problem. Now make F L and C R, equal to the
Length of the given Lines; and about the
Points R and S, as Centers, with the Radius
M N or P Q, deſcribe two Arcs cutting the
Perpendiculars H D and G H, in the Points
X and S: Then fix the Extremities of the
Threads, which before were faſten’d to the
Points F and E, to the Points L and S; and alſo
the Extremities of thoſe two Threads, which
were before faſten’d to the Points C and D, in
the Points R and X: Then moving the two
Rulers, until the Threads S P and X M, croſs
each other in the Point T, mark the Point O,
wherein the two other Threads croſs one another,
through which, and the Point B, draw the
indefinite Line B O V: this being done, tranſ-
poſe the Lines of the Geometrical Plane, ſo that
the Point B, coincides with the Point O, and
the Line B O, with O V. And by the precedent
Problem, find the Appearances of the Feet of
the Perpendiculars, and you will have the Re-
preſentations of their Extremities.
Plane, meets the ſaid Plane; and T the Per-
ſpective of that Point, found by the aforegoing
Problem. Now make F L and C R, equal to the
Length of the given Lines; and about the
Points R and S, as Centers, with the Radius
M N or P Q, deſcribe two Arcs cutting the
Perpendiculars H D and G H, in the Points
X and S: Then fix the Extremities of the
Threads, which before were faſten’d to the
Points F and E, to the Points L and S; and alſo
the Extremities of thoſe two Threads, which
were before faſten’d to the Points C and D, in
the Points R and X: Then moving the two
Rulers, until the Threads S P and X M, croſs
each other in the Point T, mark the Point O,
wherein the two other Threads croſs one another,
through which, and the Point B, draw the
indefinite Line B O V: this being done, tranſ-
poſe the Lines of the Geometrical Plane, ſo that
the Point B, coincides with the Point O, and
the Line B O, with O V. And by the precedent
Problem, find the Appearances of the Feet of
the Perpendiculars, and you will have the Re-
preſentations of their Extremities.
Demonstration.
If a Plane be ſuppoſed to paſs through the
Extremities of the Perpendiculars, it will be
parallel to the Geometrical Plane, and conſe-
quently, likewiſe to the perſpective Plane, be-
cauſe all the Perpendiculars are ſuppoſed equal.
But the Figure formed by the Extremities of
the Perpendiculars in the ſaid Plane, is ſimilar
and equal to that form’d by their Feet in the
Geometrical Plane: and therefore, the
Extremities of the Perpendiculars, it will be
parallel to the Geometrical Plane, and conſe-
quently, likewiſe to the perſpective Plane, be-
cauſe all the Perpendiculars are ſuppoſed equal.
But the Figure formed by the Extremities of
the Perpendiculars in the ſaid Plane, is ſimilar
and equal to that form’d by their Feet in the
Geometrical Plane: and therefore, the