Whence PR and Pq are equal one to the other, againſt the ſuppoſſition.
Lemma XXI.
if two moveable and indefinite right lines BM, CM drawn through given paints B, C, at poles, do by their point of courſe M deſcrihe a third right line MN given by poſition; and other two indefinite right lines BD, CD are drawn, making with the former two at thoſe given points B, C, given angler, MBD, MCD: I ſay that thoſe two right lines BD, CD will lines their point of concourſe D deſcrihe a conic ſection paſſing through the points B, C. And vice verſa, if the right lines BD, CD do by their point of concourſe D deſcribe a conic ſection paſſing through the given points B, C, A, and the angle DBM is always equal to the given angle ABC, as well as the angle DCM always equal to the given angle ACB: the point M will lie in a right line given by poſition, at its locus. Pl. 9. Fig. 3.
For in the right line MN let a point N be given, and when the moveable point M falls on the immoveable point N, let the moveable point D fall on an immoveable point P. Join CN, BN, CP
