there will ariſe RGC - RFF + TFF to as -FF to &c. And taking the laſt ratio's that ariſe when the orbits come to a circular form, there will come forth GG to as FF to and again GG to FF as to . This proportion. by expreſſing the greateſt altitude *CV* or T arithmetically by unity, becomes, GG to FF as *b* + *c* to *mb* + *nc*, and therefore as 1 to . Whence G becomes to F, that is the angle *VCp* to the angle *VCP* as 1 to . And therefore ſince the angle *VCP* between the upper and the lower apſis, in an immovable ellipſis, is of 180 deg. the angle *VCp* between the ſame apſides in an orbit which a body deſcribes with a centripetal force. that is as will be equal to an angle of deg. And by the ſame reaſoning if the centripetal force be as the angle between the apſides will be found equal to deg. After the ſame manner the problem is ſolved in more difficult caſes. The quantity to which the centripetal force is proportional. muſt always be reſolved into a converging

# Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/268

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