7233on PERSPECTIVE.
firſt found ;
and then if Lines be drawn 1147.
the Repreſentation of the Vertex touching the
Repreſentation of the Baſe, the Repreſentation
of the Cone will be had.
Repreſentation of the Baſe, the Repreſentation
of the Cone will be had.
But ſince, according to this Manner, we are
obliged to find the Perſpective of all the Baſe;
whereas it often cannot be all ſeen; we may de-
termine, by the following Method, what Part
of the Baſe is viſible, and ſo only find the Re-
preſentation thereof. And then, to compleat
the Cone, we draw Lines from the Extremities
of the viſible Part of the Baſe, to the Repreſen-
tation of the Vertex.
obliged to find the Perſpective of all the Baſe;
whereas it often cannot be all ſeen; we may de-
termine, by the following Method, what Part
of the Baſe is viſible, and ſo only find the Re-
preſentation thereof. And then, to compleat
the Cone, we draw Lines from the Extremities
of the viſible Part of the Baſe, to the Repreſen-
tation of the Vertex.
53. To determine the viſible Part of the Baſe of
a Cone.
a Cone.
Let the Circle L I F be the Baſe of a Cone
22Fig. 21. in the Geometrical Plane, and A the Center
thereof.
22Fig. 21. in the Geometrical Plane, and A the Center
thereof.
Operation.
Aſſume P Q ſomewhere in the Baſe Line,
equal to the Semidiameter of the Circle L F;
and from the Point P, raiſe P D G perpendicu-
lar to the Baſe Line, meeting the Horizontal
Line in G; and in this Perpendicular, make
P D equal to the Height of the Cone; and draw
the Line Q D H, meeting the Horizontal Line
in H. Then, about the Point A as a Center,
and with the Radius G H, draw the Circle B C E;
and from the ſaid Point A, draw a Line to the
Station Point S: Biſect A S in R; and about
R, as a Center, with the Radius R A, deſcribe
the Circular Arc B A C, cutting the Circle BEC
in the Points B and C. Draw the Lines B A F,
and C A L; and the viſible Portion, (L I F)
equal to the Semidiameter of the Circle L F;
and from the Point P, raiſe P D G perpendicu-
lar to the Baſe Line, meeting the Horizontal
Line in G; and in this Perpendicular, make
P D equal to the Height of the Cone; and draw
the Line Q D H, meeting the Horizontal Line
in H. Then, about the Point A as a Center,
and with the Radius G H, draw the Circle B C E;
and from the ſaid Point A, draw a Line to the
Station Point S: Biſect A S in R; and about
R, as a Center, with the Radius R A, deſcribe
the Circular Arc B A C, cutting the Circle BEC
in the Points B and C. Draw the Lines B A F,
and C A L; and the viſible Portion, (L I F)