Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/188



To decribe a trajectory that hall pas through a given point, and touch four right lines given by poition. Pl. 11. Fig. 1

From the common interections of any two of the tangents to the common interection of the other two draw an indefinite right line; and taking this line for the firt ordinate radius tranform the figure (by lem. 22.) into a new figure, and the two pairs of tangents each of which are concurred in the firt ordinate radius will now become parallel. Let hi and kl, ik and hl, be thoe points of parallels compleat, the parallelogram hikm. And let p be the point in this new figure correponding to the given point in the firt figure. Through O the centre of the figure draw pq; and Oq being equal to Op, q will be the other point through which the conic ection mull pas in this new figure. Let this point be tranferred by the invere operation of lem. 22. into the firt figure. and there we hall have the two points, through which the trajectory is to be decribed. But through thoe points that trajectory may be decribed by prob. 17. Q. E. F.