Let fall a perpendicular, I, E, from the centre to the circumference,
and with that as a radius and E as a centre, cut the circumference at
A, B, C, and D, and join the points. The four-sided figure called a
square is thus formed.
[Illustration: _Fig. 5_]
PROBLEM VI. _On a given right line_, A, B, _to construct a pentagon, or
five-sided figure_.
[Illustration: _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.
[Illustration: _Fig. 7_]