Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/162



If from any point P of a given conic ection, to the four produced ides AB, CD, AC, DB of any trapezium ABDC incribde in that ection, as many right lines PQ, PR, PS, PT are drawn in given angles, each line to each ide; the rectangle PQ x PR of thoe on the oppoite ides AB, CD, will be to the rectangle PS x PT of thoe on the other two oppoite ides AC, BD, in a given ratio.

Let us uppose firt that the lines drawn to one pair of oppoite ides are parallel to either of the other ides; as PQ and PR (Pl. 8. Fig. 4) to the ide AC, and PS and PT to the ide AB. And farther, that one pair of the oppoite ides, as AC and BD, are parallel betwixt themelves; then