Gravesande, Willem Jacob 's - An essay on perspective

Gravesande, Willem Jacob 's, An essay on perspective

Table of contents

[61.] Example III. 48. To throw a circle into Perſpective.

[62.] Remarks.

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

[64.] Operation.

[65.] Demonstration.

[66.] Prob. VI. 52. To throm a Pyramid, or Cone, into Perſpective.

[67.] 53. To determine the viſible Part of the Baſe of a Cone.

[68.] Operation.

[69.] Demonstration.

[70.] Remarks.

[71.] Problem VII. 55. To find the Perſpective of a Line, perpendicular to the Geometrical Plane.

[72.] Operation.

[73.] Demonstration.

[74.] Method II.

[75.] Demonstration.

[76.] Method III.

[77.] Operation, Without Compaſſes.

[78.] Demonstration.

[79.] Scholium.

[80.] Corollary.

[81.] Problem VIII.

[82.] To do this another Way.

[83.] Demonstration.

[84.] Problem IX.

[85.] Problem X.

[86.] Demonstration.

[87.] EG: EN:: GY: NM.

[88.] Definition.

[89.] Problem XI.

[90.] Lemma.

7031on PERSPECTIVE.

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
11Fig. 18. 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.

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.

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
22Fig. 19. 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.

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