13866An ESSAY
Problem II.
82.
To find the Appearance of a Point above the
Geometrical Plane.
Geometrical Plane.
Let H C be the Baſe Line:
And let T be the
11Fig. 45. accidental Point of the Lines perpendicular
to the Geometrical Plane. This Point will
be in that Place of the Vertical Line, 2213. it is cut by the Prolongation of the Line mea-
ſuring the Height of the Eye; for this laſt
Line is parallel to the ſaid Perpendiculars. And
ſo likewiſe the aforeſaid Point is the ſame as
the Point T of Fig. 44: Let V be the Point of
Sight, S the Station Point, and Q the Station
Point of the upright perſpective Plane, to which
the inclined perſpective Plane is reduced . 3381. laſtly, let A be the Seat of the given Point.
11Fig. 45. accidental Point of the Lines perpendicular
to the Geometrical Plane. This Point will
be in that Place of the Vertical Line, 2213. it is cut by the Prolongation of the Line mea-
ſuring the Height of the Eye; for this laſt
Line is parallel to the ſaid Perpendiculars. And
ſo likewiſe the aforeſaid Point is the ſame as
the Point T of Fig. 44: Let V be the Point of
Sight, S the Station Point, and Q the Station
Point of the upright perſpective Plane, to which
the inclined perſpective Plane is reduced . 3381. laſtly, let A be the Seat of the given Point.
Operation.
Draw two Lines M P and P E ſeparately,
making a right Angle with each other; in one
of which, aſſume P E, equal to the Height of
the given Point, whoſe Perſpective is ſought;
and draw the Line E M, making an Angle with
M P, equal to the Angle of Inclination of the
perſpective Plane. Again let fall the Perpen-
dicular A D from the Point A to the Baſe
Line, in which aſſume A L equal to P M, to-
wards the Baſe Line, when the perſpective
Plane is inclined towards the Objects (as we
have here ſuppoſed) but on the other Side of A,
when the perſpective Plane inclines towards the
Eye. Then from the Point A, draw a Line
to the Point S, cutting the Baſe Line in B, and
joyn the Points L and Q, by a Line cutting the
Baſe Line in C. This being done, draw
making a right Angle with each other; in one
of which, aſſume P E, equal to the Height of
the given Point, whoſe Perſpective is ſought;
and draw the Line E M, making an Angle with
M P, equal to the Angle of Inclination of the
perſpective Plane. Again let fall the Perpen-
dicular A D from the Point A to the Baſe
Line, in which aſſume A L equal to P M, to-
wards the Baſe Line, when the perſpective
Plane is inclined towards the Objects (as we
have here ſuppoſed) but on the other Side of A,
when the perſpective Plane inclines towards the
Eye. Then from the Point A, draw a Line
to the Point S, cutting the Baſe Line in B, and
joyn the Points L and Q, by a Line cutting the
Baſe Line in C. This being done, draw