Full text: Gravesande, Willem Jacob: An essay on perspective

10. Theorem I.

4. The Repreſentation of a Line Parallel to the
perſpective Plane, is parallel to the Line whereof it is
the Repreſentation.


Fig. 3.

Let A B be a Line Parallel to the perſpective
Plane; we are to prove that a b its Repreſentati-
on is Parallel thereto.

Theſe two Lines A B and a b, will never
meet each other, becauſe a b is in the perſpective
Plane, and A B is ſuppoſed parallel to the ſaid
Plane. But they are alſo in one and the ſame
Plane, becauſe a b is the Interſection of the per-
ſpective Plane, and the Plane O A B, paſſing
through the Eye and the Line A B; and there-
fore they are parallel between themſelves: Which
was to be demonſtrated.

11. Corollary I.

5. The Appearance of a Line, parallel to the baſe
Line, is alſo parallel to the ſaid baſe Line.

For the baſe Line, and the Repreſentation
being parallel to the ſame Line, are parallel to
one another.

12. Corollary II.

6. The Repreſentation of a Line parallel to the
vertical Line, is parallel to the ſaid vertical Line, and
conſequently perpendicular to the baſe Line. This
is demonſtrated as in the laſt Corollary.

13. Corollary III.

7. The Appearances of Lines parallel to the per-
ſpective Plane, and equally inclin’d the ſame Way upon


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