Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/296

 aymptote be the right line SQ landing upon the line CS at right angles, the area SQPND will be proportional to the time in which the body in its decent hath decribed the line ST; and therefore that area being found the time is alo given. Q. E. I.

If a body move in any curve uperficies whoe axis paes trough the centre of force, and from the body a perpendicular be let fall upon the axis; and a line parallel and equal thereto be drawn from any given point of the axis; I ay, that this parallel line will decribe an area proportional to the time.

Let BKL (Pl. 20. Fig. 5.) be a curve uperficies, T a body revolving in it, STR a trajectory which the body decribes in the ame, S the beginning of the trajectory, OMK the axis of the curve uperficies, TN a right line let fall perpendicularly from the body to the axis; OP a line parallel and equal thereto drawn from the given point O in the axis; AP the orthographic projection of the trajectory decribed by the point P in the plane AOP in which the revolving line OP is found; A the beginning of that projection anwering to the point S; TC a right line drawn from the body to the centre; TG a part