Page:The Elements of Euclid for the Use of Schools and Colleges - 1872.djvu/232

208 Therefore the sides of the parallelograms ABCD and AEFG about their equal angles are proportional, and the parallelograms are therefore similar to one another. [VI. Definition 1.

For the same reason the parallelogram ABCD is similar to the parallelogram FHCK. Therefore each of the parallelograms EG and HK is similar to BD; therefore the parallelogram EG is similar to the parallelogram HK.

Wherefore, parallelograms &c.

PROPOSITION 25. PROBLEM.

To describe a rectilineal figure which shall he similar to one given rectilineal figure and equal to another given rectilineal figure.

Let ABC be the given rectilineal figure to which the figure to be described is to be similar, and D that to which it is to be equal: it is required to describe a rectilineal figure similar to ABC and equal to D.

On the straight line BC describe the parallelogram BE equal to the figure ABC. On the straight line CE describe the parallelogram CM equal to D, and having the angle FCE equal to the angle CBL; [I. 45, Corollary.