Lot a b c d be an ellipse, it is required to find its centre. Draw any two lines, as E F and G h, parallel and equal to each other.

Fig. 38.

Bisect these lines as in the points I and k, and bisect I k as in l. From l, as a centre, draw a circle cutting the ellipse in four points, 1, 2, 8, 4. Now l is the centre of the ellipse. But join the points 1, 3, and 2, 4; and bisect these lines as in m and ■. Draw the line m n, and produce it to a and B, and it will be the transverse axis. Draw c d through l, and perpendicular to a b, and it will be the conjugate or shorter axis.