16480An ESSAY
to the Length of the ſaid Perpendiculars:
And
therefore
therefore
H I: T H:: a X: a T.
But in the Conſtruction of this Problem, be-
cauſe the Triangles T C D and T H G, are
ſimilar;
cauſe the Triangles T C D and T H G, are
ſimilar;
H G = H I:
T H:
: C D = a X:
T D = a T;
and conſequently H I and a X, repreſent Perpen-
diculars of the ſame Length. Which was to be
demonſtrated.
and conſequently H I and a X, repreſent Perpen-
diculars of the ſame Length. Which was to be
demonſtrated.
Prob. III.
98.
To find the accidental Point of any Number
of parallel Lines inclined to the Geometrical Plane.
of parallel Lines inclined to the Geometrical Plane.
Let a b be the Perſpective of the Direction
11Fig. 55. of one of the given Lines.
11Fig. 55. of one of the given Lines.
Operation.
Draw the Line F T L, parallel to a b, through
the accidental Point T of the Lines perpendicu-
lar to the Geometrical Plane; and at the Point
T, raiſe the Perpendicular T G, which make e-
qual to the Diſtance of the Eye from the per-
ſpective Plane; then draw the Line G L, or
G F, ſo that the Angle T L G, or T F G, be e-
qual to the Angle of the Inclination of the given
Lines; and the Point L, will be the Accidental
Point ſought, if the given Lines incline to-
wards b; but if they incline towards a, F will
be the Accidental Point.
the accidental Point T of the Lines perpendicu-
lar to the Geometrical Plane; and at the Point
T, raiſe the Perpendicular T G, which make e-
qual to the Diſtance of the Eye from the per-
ſpective Plane; then draw the Line G L, or
G F, ſo that the Angle T L G, or T F G, be e-
qual to the Angle of the Inclination of the given
Lines; and the Point L, will be the Accidental
Point ſought, if the given Lines incline to-
wards b; but if they incline towards a, F will
be the Accidental Point.
Demonstration.
It is manifeſt by Conſtruction, that if T G be
ſuppoſed to be raiſed perpendicularly to the Geo-
metrical Plane, G L or G F, will be parallel
ſuppoſed to be raiſed perpendicularly to the Geo-
metrical Plane, G L or G F, will be parallel