Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/235



To determine the times of the decent of a body falling from a given place A. Pl. 16. Fig. 3.

Upon the diameter AS, the ditance of the body from the centre at the beginning. decribe the emi-circle ADS, as likewie the emi-circle OKH equal thereto, about the centre S. From any place C of the body, erect the ordinate CD, join SD, and make the ector OSI equal to the area ASD. It is evident by prop. 35. that the body in falling will decribe the pace AC in the ame time in which another body, uniformly revolving about the centre S, may decribe the arc OK. Q. E. F.

To decribe the times of the acent or decent of a body projected upwards or downwards from a given place. Pl. 16. Fig. 4.



Suppoe the body to go off from the given place G, in the direction of the line GS, with any velocity. In the duplicate ratio of this velocity to the uniform velocity in a circle, with which the body may revolve about the centre