### Full text

## 24. Theorem VI.

19. Let A C be a Line inclined to the Geometrical

Plane, and O D another Line drawn parallel to

A C, from the Eye to the perſpective Plane. Now

if B A be drawn in the Geometrical Plane, pa-

rallel to the baſe Line, and likewiſe D E, in the

perſpective Plane, parallel to the ſaid Line, ſo that

B A be to A C, as E d to D O. I ſay, the Ap-

pearance of the Line B C, paſſing through the Point

B, and the Extremity of the Line A C, being con-

tinued, will meet the Point E.

### 24.1.

Now to prove this; it is evident, that we
need but demonſtrate, that O E is parallel to

B C: And this may be done in the following

Manner:

### 24.1.

A B is parallel to E D, and A C to O D; whence the Angle (E D O) of the Triangle

O E D, is equal to the Angle (B A C) of the

Triangle A C B: And ſo theſe two Triangles

are ſimilar; becauſe they have alſo their Sides

Proportional. But ſince theſe two ſimilar Tri-

angles, have two of their Sides parallel, the

third B C is alſo parallel to O E; which was to be

demonſtrated.

## 25. Corollary .

20. If A B be made equal to A C, and E D to D O,

the Appearance of B C will paſs thro’ the Point E,

## 26. CHAP. III.

The Practice of Perſpective upon the Per-

ſpective Plane, ſuppoſed to be perpendicu-

lar, or upright.

IN order to give a diſtinct Idea of the Theory, I

have hitherto conſider’d the Geometrical Plane,

as it were the Ground upon which the Spectator