16177on PERSPECTIVE.
fore the Point X is the Repreſentation of the
ſaid Extremity.
ſaid Extremity.
Corollary.
94.
It is manifeſt from hence, that when the
Perſpective of a Line, perpendicular to the
Geometrical Plane is once found, it is eaſy af-
terwards to find the Repreſentations of any Per-
pendiculars of the ſame Length as that.
Perſpective of a Line, perpendicular to the
Geometrical Plane is once found, it is eaſy af-
terwards to find the Repreſentations of any Per-
pendiculars of the ſame Length as that.
Method II.
The Perſpective Plane being conſider’d as the Geo-
metrical Plane.
metrical Plane.
95.
Let T (as in Fig.
51.)
be the accidental
11Fig. 53. Point of perpendicular Lines to the Geometri-
cal Plane; H I the Arc of a Circle, whoſe Cen-
ter is T, and ſemidiameter the Eye’s Diſtance
from the perſpective Plane: Alſo let a be the
Point where the Perpendicular, whoſe Appear-
ance is ſought, meets the perſpective Plane, and
B C the Length of this Perpendicular.
11Fig. 53. Point of perpendicular Lines to the Geometri-
cal Plane; H I the Arc of a Circle, whoſe Cen-
ter is T, and ſemidiameter the Eye’s Diſtance
from the perſpective Plane: Alſo let a be the
Point where the Perpendicular, whoſe Appear-
ance is ſought, meets the perſpective Plane, and
B C the Length of this Perpendicular.
Operation,
About the Point a, as a Center, and with the
Semidiameter B C, deſcribe the Circle L F, and
draw the Line I L, or H F, touching each of the
Circles H I, and F L; and then a X or a x, is
the Appearance ſought, viz. a X, when the Per-
pendicular is above that Surface of the per-
ſpective Plane next to the Eye, and a x, when
the Perpendicular is on the oppoſite Side.
Semidiameter B C, deſcribe the Circle L F, and
draw the Line I L, or H F, touching each of the
Circles H I, and F L; and then a X or a x, is
the Appearance ſought, viz. a X, when the Per-
pendicular is above that Surface of the per-
ſpective Plane next to the Eye, and a x, when
the Perpendicular is on the oppoſite Side.
Demonstration.
Draw the Radii a F, a L, T I, T H, to the
Points of Contact F, L, I, and H. Then
Points of Contact F, L, I, and H. Then