11454An ESSAY
Operation.
In ſome ſeparate Place, draw the Lines C E
and C P, making an Angle with each other
equal to the Angle of Inclination of the given
Line; and in one of theſe Lines, aſſume C E
equal to the given Line, and let fall the Perpen-
dicular E P, from the Point E upon the other
Line. Then aſſume A B, in the Direction of
the propos’d Line, equal to C P; and after ha-
ving found a, the Perſpective of A, and the
Point T , the Perſpective of a Point 1150. above B, the Height of P E; join the Points a
and T by a right Line; and the ſought Appear-
ance will be had.
and C P, making an Angle with each other
equal to the Angle of Inclination of the given
Line; and in one of theſe Lines, aſſume C E
equal to the given Line, and let fall the Perpen-
dicular E P, from the Point E upon the other
Line. Then aſſume A B, in the Direction of
the propos’d Line, equal to C P; and after ha-
ving found a, the Perſpective of A, and the
Point T , the Perſpective of a Point 1150. above B, the Height of P E; join the Points a
and T by a right Line; and the ſought Appear-
ance will be had.
Demonstration.
If from the Extremity of the inclin’d Line, a
Perpendicular be let fall upon the Geometrical
Plane, the ſaid Perpendicular will meet this
Plane in the Point B, and will be equal to P E;
as is evident by the Conſtruction of the Figure
C P E. But the Point T is the Repreſentation
of the Extremity of this Perpendicular; and
therefore it is alſo the Extremity of the inclin’d
Line. Which was to be demonſtrated.
Perpendicular be let fall upon the Geometrical
Plane, the ſaid Perpendicular will meet this
Plane in the Point B, and will be equal to P E;
as is evident by the Conſtruction of the Figure
C P E. But the Point T is the Repreſentation
of the Extremity of this Perpendicular; and
therefore it is alſo the Extremity of the inclin’d
Line. Which was to be demonſtrated.
Remarks.
There are ſome Caſes of this Propoſition, that
may be ſhorten’d. As, 1. When there are ſeve-
ral Lines of this Kind parallel between them-
ſelves, and whoſe accidental Point can be
found : And, 2. When an inclin’d Line is 2268. rallel to the perſpective Plane. The Manner
may be ſhorten’d. As, 1. When there are ſeve-
ral Lines of this Kind parallel between them-
ſelves, and whoſe accidental Point can be
found : And, 2. When an inclin’d Line is 2268. rallel to the perſpective Plane. The Manner