Problem VI. On a given right line, A, B, to construct a pentagon, or five-sided figure.
Fig. 6
Draw B, F, perpendicular and equal to the half of A, B. Produce A, F, to G, making F, G, equal to F, B. From the points A and B, with the radius B, G, describe arcs cutting each other at I. From I, with the radius I, B, describe a circle. Inscribe the successive chords A, E; E, D; D, C; C, B, which with the base A, B, completes the pentagon.
If the circle be given, and a pentagon to be inscribed in it, the following is as simple as it is practical. From the centre erect a perpendicular, which shall meet the circumference at D. At each side of this point divide the circumference into five equal parts, and connect every two of them from D to E, from E to A, and from D to C, C to B. Now connect A and B and the pentagon is formed.
Problem VII. On a given line A, B, to construct a hexagon, or six-sided figure.
Take the length of the radius I, G, and lay it off from F to A, A to B, B to C, C to D, D to E, and E to F.
Fig. 7