Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/224

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Suppoing that the centripetal force is reciprocally proportional to the quare of the ditance of the places from the centre; it is required to define the paces which a body, falling directly, decribes in given times.

If the body does not fall perpendicularly it will (by cor. 1. prop. 13.) decribe ome conic ection whoe focus is placed in the centre of force. Suppoe that conic ection to be ARPB (Pl. 15. Fig. 1.) and its focus S. And firt, if the figure be an ellipsis; upon the greater axe thereof AB decribe the emi-circle ADB, and let the right line DPC pas through the falling body, making