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Book 1.

*Mathematical Priciples*

Section VII.

*Concerning the rectilinear aſcent and deſcent of bodies.*

Proposition XXXII. Problem XXIV.

*Suppoſing that the centripetal force is reciprocally proportional to the ſquare* of the diſtance of the places from the centre; it is required to define the ſpaces which a body, falling directly, deſcribes in given times.

Case 1. If the body does not fall perpendicularly it will (by cor. 1. prop. 13.) deſcribe ſome conic ſection whoſe focus is placed in the centre of force. Suppoſe that conic ſection to be *ARPB* (*Pl.* 15. *Fig.* 1.) and its focus S. And firſt, if the figure be an ellipsis; upon the greater axe thereof *AB* deſcribe the ſemi-circle *ADB*, and let the right line *DPC* paſs through the falling body,

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