Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/173

 Whence PR and Pq are equal one to the other, againt the uppoition.

if two moveable and indefinite right lines BM, CM drawn through given paints B, C, at poles, do by their point of coure M decrihe a third right line MN given by poition; and other two indefinite right lines BD, CD are drawn, making with the former two at thoe given points B, C, given angler, MBD, MCD: I ay that thoe two right lines BD, CD will lines their point of concoure D decrihe a conic ection paing through the points B, C''. And vice vera, if the right lines BD, CD do by their point of concoure D decribe a conic ection paing 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 poition, 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