Gravesande, Willem Jacob 's - An essay on perspective

Gravesande, Willem Jacob 's, An essay on perspective

Table of contents

[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.

4821on PERSPECTIVE.

Method. IV.

31. Draw the Line F O G through the Eye O,
parallel to the Baſe Line, then aſſume F O in
11Fig. 10. this Line, equal to the Height of the Eye, and
O G equal to the Length of the principal Ray.
A is the given Point.

Operation,
Without Compaſſes.

From the given Point A, draw the Lines AO,
A F, to the Points O and F, and from the
Point E, wherein A F cuts the Baſe Line, draw
the Line E G to the Point G; then the Point a,
the Interſection of A O, and E G, is the Repre-
ſentation ſought.

Demonstration.

Let fall the perpendicular G M from the Point
G, upon the Baſe Line, and through the Eye O,
draw the Line O D to the Point D, the Inter-
ſection of the Horizontal Line, and the Line G E.

Then becauſe the Triangles G D L, G E M are
fimilar,
G D: G E: : G L: G M.
But G O is equal to G L, and G F to L M.
whence
G D: G E: : G O: G F.

And conſequenely the Triangles G O D: and
G F E, are ſimilar, and the Lines O D, and
A E F, are parallel between themſelves; and
therefore the Appearance of A E, is a 2213 of the Line E D G. It has alſo been 3327. that the Repreſentation of the Point A, is in the
Line A O; therefore i@ is in a the

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