Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/319

 about the greatet; I ay that the interior of the two revolving bodies will, by radii drawn to the innermot and greatet, decribe round that body, area's more proportional to the times, and a figure more approaching to that of an ellipis having its focus in the point of concoure of the radii, if that great body be agitated by thoe attraction, than it would do if that great body were not attracted at all by the leer, but remained at ret; or than it would if that great body were very much more much les attracted, or very much more or very much les agitated by the attractions.

This appears plainly enough from the demontration of the econd corollary of the foregoing propoition; but it may be made out after this manner by a way of reaoning more ditinct and more univerally convincing.



Let the leer bodies P and S (Pl. 21. Fig. 2.) revolve in the ame plane about the greatet body T, the body P decribing the interior orbit PAB, and S the exterior orbit ESE, Let SK be the mean ditance of the bodies P and S; and let the accelerative attraction of the body P towards S, at that mean ditance, be expreed by that line SK. Make SL to SK as the quare of SK to the quare of SP, and SL