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

63. Prob . V.
50. To find the Repreſentation of a Point, elevated
above the Geometrical Planc.

Let G S be the Geometrical Line, and S the
Station Point: Make S F, in the Geometrical
Line, equal to the Height of the Eye; and let
A be the Seat of the given Line.

63.1.

Fig. 18.

64. Operation .

Aſſume F C in the Geometrical Line, equal to
the Height of the Eye, above the Geometrical
Plane: Then draw Lines from the Point A to
the Points S and C, and on the Point B, the In-
terſection of the Line AS and the Baſe Line,
raiſe the Perpendicular BI to the Baſe Line,
equal to E B, plus FC; and the Point I will be
the Perſpective ſought.

65. Demonstration .

51. Let us ſuppoſe a Plane to paſs thro’ the
given Point, and the Eye perpendicular to the
Geometrical Plane; then it is manifeſt, that the
Interſection of theſe two Planes is the Line
A B S, and the Interſection of the ſaid ſuppos’d
Plane and the perſpective Plane, is B I. Now,
let X be this ſuppos’d Plane; a, b, s, the Point
mark’d with the ſame Letters in the precedent
Figure, bi the Interſection of this Plane and
the perſpective Plane; O the Eye, and D the
propos’d Point: We are to prove, that if O D
be drawn, the Line B I of the precedent Figure
will be equal to b i in this Figure.

65.1.

Fig. 19.

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer