on PERSPECTIVE.
the Geometrical Plane, make Angles with the baſe

Line, equal to thoſe Angles that the Lines whereof

they are the Appearances, make with the Parallels

to the baſe Line, which cut them; and conſequently

the ſaid Appearances are parallel between them-

ſelves.

This is evident, becauſe the Appearances of

Lines parallel to the baſe Line, are parallel to

the ſaid Line; and the Appearances of the in-

clined Lines are parallel to theſe Lines.

##
14.
Theorem
II.

8, 9. The Repreſentation of a Figure, parallel to

the perſpective Plane, is ſimilar to the ſaid Figure; and

the Sides of the ſaid Figure are to their Repreſen-

tations, as the Diſtance of the Eye from the Plane

of the Figure, to the Diſtance of the Eye from the

perſpective Plane.

The given Figure is A B C D. We are firſt to

prove, that its Repreſentation a b c d, is ſimilar

thereto; that is, that the correſponding Angles

of theſe two Figures A B C D, a b c d, are equal,

and their Sides proportional.

I. The Angles are equal, becauſe the Lines
of which the two Figures conſiſt, are parallel be-

tween themſelves.

II. In the ſimilar Triangles A D O, and a d o,

we have

A D: a d : : O D : O d.

And in the ſimilar Triangles O D C, and O d c,

we have

D C : d c : : O D : O d. then

A D: a d : : D c : d c. altern. A D : D C : : a d : d c.

And conſequently the Sides A D, and D C of

the Figure A B C D, are Proportional to the