Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/342

 at ret are not attracted, or were much more or much les attracted or much lire or much les agitated.

This may be demotrated after the ame mamner as prop. 66. but by a more prolix reaoning, which I therefore pas over. It will be ufficient to conider it after this manner. From the demontration of the lat propoition it is plain, that the centre, towards which the body S is urged by the two forces conjunctly, is very near to the common centre of gravity of thoe two other bodies. If this centre were to coincide with that common centre, and moreover the common centre of gravity of all the three bodies were at ret; the body S on one ide, and the common centre of gravity of the other two bodies on the other ide. would decribe true ellipes about that quiecent common centre. This appears from cor. 2. prop. 58. compared with what was demontrated in prop. 64 and 65. Now this accurate elliptical motion will be ditributed a little by the ditance of the centre of the two bodies from the centre towards which the third body S is attracted. Let there be added moreover a motion to the common centre of the three, and the perturbation will be increaed yet more. Therefore the perturbation is leat when the common centre of the three bodies is at ret; that is, when the innermot and greatet body T is attracted according to the ame law as the ret are; and is always greatet, when the common centre of the three, by the diminution of the motion of the body T; begins to be moved, and is more and more agitated.