Fig. 130.
Ex. 25.—To describe an octagon on a given straight line, [Fig. 130]. Produce the given line A B both ways and draw perpendiculars A E, B F; bisect the external angles A and B by the lines A H, B C, which make equal to A B. Draw C D and H G parallel to A E and equal to A B; from the center G D, with the radius A B, cut the perpendiculars at E F, and draw E F to complete the hexagon.
Fig. 131.
Ex. 26.—To convert a square into an octagon, [Fig. 131].—Draw the diagonals of the square cutting at E; from the corners A, B, C, D, with A E as radius, describe arcs cutting the sides at G, H, etc., and join the points so found to complete the octagon.
Fig. 132.
Ex. 27.—To inscribe an octagon in a circle, [Fig. 132]. Draw two diameters A C, B D, at right angles; bisect the arcs A B, B C, at E, F, etc., to form the octagon.
Fig. 133.