Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/152

 will either pas through the two points P, p, or touch the two right lines TR, tr. Q. E. F.

About a given focus, to decribe parabolic trajectory, which hall pas through given points, and touch right lines given by poition. Pl. 7. Fig. 3.

Let S the the focus, P a point, and TR a tangent of the trajectory to be decribed. About P as a centre, with the interval PS, decribe the circle FG; From the focus let fall ST perpendicular on the tangent, and produce the ame to V, o as TV may be equal to ST. After the ame manner another circle fg is to be decribed, if another point p is given; or another point v is to be found, if another tangent tr is given; then draw the right line IF, which hall touch the two circles FG, fg, if two points P, p are given, or pas through the two points V, v, if two tangents TR, tr are given, or touch the circle FG and pas through the point V, if the point P and the tangent TR are given. On FI let fall the perpendicular SL and bisect the ame in K; and with the axis SK, and principal vertex K decribe a parabola. I ay the thing is done. For this parabola (becaue SK is equal to IK, and SP to FP) will pas through the point P; and (by cor. 3. lem. 14.) becaue ST is equal to TV and STR; a right angle, it will touch the right line TR. Q. E. F.