Let ab and c d (Fig. 411) be given axes. From c draw ce parallel to a b; from a draw ae parallel to cd; join e and d; bisect ea in f; join f and c, intersecting e d in i; bisect ic in o from o draw og at right, angles to ic, meeting cd extended to g; join i and g, cutting the transverse axis in r; make hj equal to hg, and h k equal to hr; from j, through r and k, draw jm and jn; also, from g, through k, draw gl; upon g and j, with gc: for radius, describe the arcs il and mn; upon r and k, with ra for radius, describe the arcs mi and ln; this will complete the figure.

Fig. 412.

When the axes are proportioned to one another, as at 2 to 3, the extremities, c and d, of the shortest axis, will be the centres for describing the arcs il and m n; and the intersection of e d with the transverse axis will be the centre for describing the arc m, i, etc. As the elliptic curve is continually changing its course from that of a circle, a true ellipsis cannot be described with a pair of compasses. The above, therefore, is only an approximation.