Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/331

 it is manifet that in its motion from the node C, the body recedes continually from the former plane CD of its orbit till it comes to the next node; and therefore at that node, being now at its greatet ditance from the firt plane CD, it will pa through the plane of the orbit EST not in D, the other node of that plane, but in a point that lies nearer to the body S, which therefore becomes a new place of the node in antecedentia to its former place. And by a like reaoning, the nodes will continue to recede in their paage from this node to the next. The nodes therefore when ituate in the quadratures recede perpetually, and at the yzygies, where no perturbation can be produced in the motion as to latitude, are quiecent; in the intermediate places they partake of both conditions, and recede more lowly; and therefore being always either retrograde or tationary, they will be carried backwards, or in antecedentia, each revolution.

All the errors decribed in thee corollaries are a little greater at the conjunction of the bodies P, S, than at their oppoition; becaue the generating forces NM and ML are greater.

And ince the caues and proportions of the errors and variations mentioned in thee corollaries do not depend upon the magnitude of the body S, it follows that all things before demontrated will happen, if the magnitude of the body S be imagined o great as that the ytem of the two bodies P and T may revolve about it. And from this increae of the body S, and the conequent increae of its centripetal force from which the errors of the body P arie, it will follow that all thes errors, at equal ditances, will be greater