## 95. Demonstration .

If a Plane be conceiv’d to paſs thro’ the Eye,
perpendicular to the Geometrical Plane, and paral-
lel to the given Lines; it is evident, that the ſaid
Plane will cut the Horizontal Plane in the Line
O D, and the perſpective Plane in D F. It is,
moreover, manifeſt, that a Line drawn thro’ the
Eye, parallel to the given Line, is in the ſaid
Plane, and (with the Line O D) makes an An-
gle, equal to the Angle E C P, below the Hori-
zontal Plane, if the Lines be inclin’d towards
the perſpective Plane, and above it, if they in-
cline to the oppoſite ſide; whence this laſt Line
makes a right-angled Triangle with O D and
D F, whoſe Angle at the Point O, is equal to
the Angle C E P. But D G F is likewiſe a
right-angled Triangle, as having the Angle at the
Point G, equal to ECP; therefore theſe two
Triangles are ſimilar. And ſince the Side D G
is equal to the Side D O, the Triangles are alſo
equal: Therefore the Line D F, being common
to theſe two Triangles; the Point F, is the
Point wherein the Line, paſſing thro’ the Eye
parallel to the given Line, meets the Per-
ſpective Plane: And this Point is the acciden- tal one ſought.

Note, This Demonſtration as well regards
inclin’d Lines entirely ſeparate from the Geo-
metrical Plane, as thoſe that meet it in one of
their Extremes only.

13, 14.

## 96. Problem X.

69. To find the Repreſentation of one or more
Lines, inclin’d to the Geometrical Plane.

### 96.1.

Fig. 36.

Let A be a Point given in the Geometrical
Plane; whereon ſtands a Line, whoſe Length,
Direction, and Angle of Inclination is known.

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