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.

6128An ESSAY ſinding the reſt. But yet the Work may be
ſhorten’d by the two precedent Problems, as we
ſhall ſhew in the following Examples.

Example I.

To throw a Pentagon having one Side parallel to
the Baſe Line, into Perſpective.

Let A B C D E, be the propoſed Pentagon,
11Fig. 15. wherein draw the Line B D which will be paral-
lel to A E, becauſe the Pentagon is a regular
one.

Now find the Repreſentation of the ſaid 2242. Lines A E and B D, and you will have the Re-
preſentation of four of the Corners of the Pen-
tagon; and to determine the Repreſentation of
the fifth Corner, find the Appearance of 3343. Line drawn from C to E, which in this Example
is parallel to A B, which is ſuppoſed parallel
to the Baſe Line.

Example II.

To throw a Parallelogram, divided into ſeveral
other Parallelograms into Perſpective.

Let A B C D be a Parallelogram, divided
44Fig. 17. into ſeveral other Parallelograms.

Draw the Line O G thro’ the Eye O parallel to
the Side A D, cutting the Horizontal Line in G;
likewiſe draw O F parallel to the Side A B cutting
the Horizontal Line in F, and produce the Sides
of the Parallelogram, and the Lines dividing it,
to the Baſe Line; then from the Points wherein
A D and C B, and the Lines parallel thereto
cut the Baſe Line, draw Lines to the Point G.
Alſo from the Points wherein A B and C D and
their parallels cut the ſaid Line, draw Lines to
the Point F, whoſe Interſections with

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