Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/299

 AOP be the ellipis pQ And becaue the magnitude of that little circle Tt, and TN or PO its ditance from the axis CO is alo given, the ellipis pQ will be given both in kind and magnitude, as alo its poition to the right line PO. And ince the area POp is proportional to the time, and therefore given becaue the time is given the angle POp will be given. And thence will be given p the common interection of the ellipis and the right line Op, together with the angle OPp in which the projection APp of the trajectory cuts the line OP. But from thence (by conferring prop. 41. with its 2d cor.) the manner of determining the curve APp eaily appears. Then from the everal points P of that projection erecting to the plane AOP the perpendicular PT meeting the curve uperficies in T, there will be given the everal points T of the trajectory. Q. E. I.