[p 36 ] PROBLEM X. TO DRAW A PYRAMID, GIVEN IN POSITION AND MAGNITUDE, ON A SQUARE BASE IN A HORIZONTAL PLANE .

[Geometric diagram]
Fig.25.

Let AB, Fig.25., be the four-sided pyramid. As it is given in position and magnitude, the square base on which it stands must be given in position and magnitude, and its vertical height, CD.[Footnote 19]

[Geometric diagram]
Fig.26.

Draw a square pillar, ABGE, Fig.26., on the square base of the pyramid, and make the height of the pillar AF equal [p36] to the vertical height of the pyramid CD (ProblemIX.). Draw the diagonals GF, HI, on the top of the square pillar, cutting each other in C. Therefore C is the center of the square FGHI. (Prob.VIII. Cor.II.)

[Geometric diagram]
Fig.27.

Join CE, CA, CB.

Then ABCE 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.