Page:The Elements of Euclid for the Use of Schools and Colleges - 1872.djvu/424

 parts, which, when properly arranged, shall form a parallelogram whose angles are of given magnitude.

624. ABCD is a parallelogram, and P is any point: shew that the triangle PAC is equal to the difference of the triangles PAB and PAD, if P is within the angle BAD or that which is vertically opposite to it; and that the triangle PAC is equal to the sum of the triangles PAB and PAD, if P has any other position.

625. Two circles cut each other, and a straight line ABCDE is drawn, which meets one circle at A and D, the other at B and E, and their common chord at C: shew that the square on BD is to the square on AE as the rectangle BC,CD is to the rectangle AC, CE.