Draw a square pillar, A B G E, [Fig. 26.], on the square base of the pyramid, and make the height of the pillar A F equal [p36] ]to the vertical height of the pyramid C D ([Problem IX.]). Draw the diagonals G F, H I, on the top of the square pillar, cutting each other in C. Therefore C is the center of the square F G H I. (Prob. VIII. [Cor. II.])
Fig. 27.
Join C E, C A, C B.
Then A B C E is the pyramid required. If the base of the pyramid is above the eye, as when a square spire is seen on the top of a church-tower, the construction will be as in [Fig. 27].
[Footnote 19: ] If, instead of the vertical height, the length of A D is given, the vertical must be deduced from it. See the Exercises on this Problem in the Appendix, [p. 79].] [Return to text]
[p38]
][PROBLEM XI.]
TO DRAW ANY CURVE IN A HORIZONTAL OR VERTICAL PLANE.
Fig. 28.