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
zoom in
zoom out
zoom area
full page
page width
set mark
remove mark
get reference
digilib