Proposition XXXVI. Problem XXV.

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

Upon the diameter AS, the diſtance of the body from the centre at the beginning. deſcribe the ſemi-circle *ADS*, as likewiſe the ſemi-circle *OKH* equal thereto, about the centre *S*. From any place *C* of the body, erect the ordinate *CD*, join *SD*, and make the ſector *OSI* equal to the area *ASD*. It is evident by prop. 35. that the body in falling will deſcribe the ſpace *AC* in the ſame time in which another body, uniformly revolving about the centre *S*, may deſcribe the arc *OK*. *Q. E. F.*

Proposition XXXVII. Problem XXVI.

*To deſcribe the times of the aſcent or deſcent* of a body projected upwards or downwards from a given place. *Pl. 16. Fig. 4.*

Suppoſe 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