An ESSAY Plane; and at the Points R and S, raiſe the in-
definite perpendiculars R G and S M; and aſſume
the Point M at Pleaſure on S M; from which
raiſe the Perpendicular M N, equal to the given
Line, and draw the Lines M O and N O, cutting
the Line R G in the Points E and G. Then
having drawn a Line at Pleaſure in the per-
ſpective Plane through the Point T, which is
that wherein a Perpendicular falling from the
Eye on the perſpective Plane meets it, aſſume
T H in the ſaid Line, equal to R E, and T I e-
qual to R G; draw the Lines Ta, Ha, through
the Point a, the Perſpective of the Foot of the
given Perpendicular, and through the Point I,
the Line I X, parallel to Ha, and cutting Ta
in X, then a X will be the Appearance ſought.

Fig. 50.
Fig. 41.

## 146. Demonstration .

It is manifeſt , that the Point T, is the acci- dental Point of Lines perpendicular to the Geo-
metrical Plane; and conſequently the Per-
ſpective ſought is a Part of T a. Moreover, it
is manifeſt , that if the Feet and Extremities of two equal right Lines, perpendicular to the
Geometrical Plane be joyn’d by Lines, theſe
Lines of Junction will have parallel Repreſen-
tations; becauſe they are parallel to each other,
as likewiſe to the perſpective Plane. And con-
ſequently, ſince H I, by Conſtruction, is the
Perſpective of a Line perpendicular to the
Geometrical Plane, and equal to the given Line,
and H a paſſes through the Appearances of the
Foot of the ſaid Perpendicular, and the given
Perpendicular; I ſay, that X I, which is paral-
lel to Ha, and paſſes through the Extremity of
the Appeaarance H I, likewiſe paſſes through
the Extremity of the given Line; and there-