([Coroll. Prob. XII.]), and the corresponding angles of the polygons joined by right lines, the resulting figure will be a portion of a polygonal pyramid. (The dotted lines in [Fig. 38.], connecting the extremities of two diameters and one diagonal in the respective circles, occupy the position of the three nearest angles of a regular octagonal pyramid, having its angles set on the diagonals and diameters of the square

a d

, inclosing its base.)

If the cone or polygonal pyramid is not truncated, its apex will be the center of the upper square, as in [Fig. 26.]

COROLLARY II.

If equal circles, or equal and similar polygons, be inscribed in the upper and lower squares in [Fig. 38.], the resulting figure will be a vertical cylinder, or a vertical polygonal pillar, of given height and diameter, drawn in position. [p49] ]

COROLLARY III.

If the circles in [Fig. 38.], instead of being inscribed in the squares

b c

and