aſymptote be the right line SQ ſlanding upon the line CS at right angles, the area SQPND will be proportional to the time in which the body in its deſcent hath deſcribed the line ST; and therefore that area being found the time is alſo given. Q. E. I.
Proposition LV. Theorem XIX.
If a body move in any curve ſuperficies whoſe axis paſſes 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 ſay, that this parallel line will deſcribe an area proportional to the time.
Let BKL (Pl. 20. Fig. 5.) be a curve ſuperficies, T a body revolving in it, STR a trajectory which the body deſcribes in the ſame, S the beginning of the trajectory, OMK the axis of the curve ſuperficies, 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 deſcribed by the point P in the plane AOP in which the revolving line OP is found; A the beginning of that projection anſwering to the point S; TC a right line drawn from the body to the centre; TG a part
