Gravesande, Willem Jacob 's, An essay on perspective

Table of contents

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[41.] Demonstration.
[42.] Remarks.
[43.] Method V.
[44.] Operation, Without Compaſſes.
[45.] Demonstration.
[46.] Remark.
[47.] Corollary.
[48.] Method VI.
[49.] Operation.
[50.] Demonstration.
[51.] Remarks.
[52.] Corollary.
[53.] Problem II.
[54.] Remark.
[55.] Problem III.
[56.] Method. II.
[57.] Problem IV.
[58.] Example I.
[59.] Example II.
[60.] Remarks.
[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.
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4319on PERSPECTIVE. Sight to the Horizontal Line, equal in Length
to the principal Ray;
and the Extremity of this
Perpendicular will be the Point ſought.
If nothing is determin’d, the Place of the Eye
may be taken at pleaſure in the Horizontal
Plane.
Method III.
29. The ſame Things being given as in the
precedent Method, about the Eye O, as a Cen-
ter;
deſcribe the Arc of a Circle I H, touching
11Fig. 9. the Horizontal Line.
Operation.
About the given Point A, as a Center, de-
ſcribe the Arc of a Circle L C, touching the Baſe
Line:
Then draw two Lines, C H and L I,
touching the two Circles L C and H I;
and the
Point a, the Interſection of the ſaid two Lines,
will be the Appearance ſought.
Demonstration.
30. To demonſtrate this, draw the Line A B
perpendicular to the Baſe Line;
O V perpendi-
cular to the Horizontal Line;
and A C, O H
perpendicular to the Tangent H C.
All theſe
Perpendiculars will cut the Lines to which they
are perpendicular, in the Points wherein theſe
laſt touch the Circle L B C, or H V I.
Like-
wiſe draw the Line A E from the given Point
A, to the Point E, wherein the Line H C cuts
the Baſe Line.
Finally, draw O D, from the
Eye O to the Point D, wherein the ſaid Line
HC cuts the Horizontal Line.

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