XL] OF NATURAL PHILOSOPHY. 2 In of the poles be corrected, unless by placing that mountain ei '. er in one ol the poles; in which case, by Cor. 21, the nodes of the equator will go for wards ; or in the equatorial regions, in which case, by Cor. 20, the nodes will go backwards: or, lastly, by adding on the other side of the axis anew quantity of matter, by which the mountain may be balanced in its motion; and then the nodes will either go forwards or backwards, as the mountain and this newly added matter happen to be nearer to the pole or to the equator. PROPOSITION LXV1I. THEOREM XXVII. The same laics of attraction being' supposed, I say, that the exterior body S does, by radii dra.cn to the point O, the common centre of gravity of the interior bodies P and T, describe round that centre areas more proportional to the times, and an orbit more approaching to the form of an ellipsis having its focus in that cen > •.-. than, it can describe round the innermost and greatest body T by ra Hi drawn to that body. For the attractions of the body S towards T and P compose its absolute attraction, which is more directed towards O, the common centre of gravity S(i of the bodies T and P, than it is to the «. reatest body T ; and which is more in a reciprocal propor tion to the square of the distance SO, than it is to the square of the distance ST : as will easily appear by a little consideration. PROPOSITION LXVIII. THEOREM XXVIII. The same laws of attraction supposed, I say, that the exterior body S will, by radii drawn to O, the common centre of gravity of the interior bodies P and T, describe round that centre areas more propor tional to the times, and an orbit more approaching to the form of an ellipsis having its focus in that centre, if the innermost and greatest body be agitated by these attractions as well as the rest, than it would do if that body were either at rest as not attracted, or were much tnore or much less attracted, or much more or much less agitated. This may be demonstrated after the same manner as Prop. LXVI, but by a more prolix reasoning, which I therefore pass over. It will be suf ficient to consider it after this manner. From the demonstration of the last Proposition 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 those 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 rest, the body S on one side, and the common centre of gravity of the other two bodies on the other side, would describe true ellip*