Let A B C d be the given square. Draw the two diagonal lines A c, and b d, crossing each other in O. Then, with the radius a o, that is, half the diagonal, and with a as a centre, describe the arc E F, cutting the sides of the square in E and F; then, from b as a centre, describe the arc G H ; and in like manner from c and D describe the arcs I k and l m. Draw the lines l g, f i, h m, and K E, and these, with the parts of the given square G f, i h, m k, and x L, form the octagon required.

Fig. 34.