will deſcribe an ellipſis round the ſame centre C; and the point D, becauſe the lines CS and CD are proportional, will deſcribe a like ellipſis over-againſt: it. But the bodies T and L, attracted by the motive forces SD x T and SD x L, the firſt by the firſt, and the laſt by the laſt equally and in the direction of the parallel lines TI and LK as was ſaid before. will (by cor. 5. and 6. of the laws of motion) continue to deſcribe their ellipſes round the moveable centre D as before. Q. E. I.
Let there be added a fourth body V, and by the like reaſoning it will be demonſtrated that this body and the point C will deſcribe ellipſes about the common centre of gravity B; the motions of the bodies T, L and S round the centres D and C remaining the ſame as before; but accelerated. And by the ſame method one may add yet more bodies at pleaſure. Q. E. I.
This would be the caſe, though the bodies T and L artract each other mutually with accelerative forces either greater or leſs than thoſe with which they attract the other bodies in proportion to their diſtance. Let all the mutual accelerative attractions be to each other as the diſtances multiplyed into the attracting bodies; and from what has gone before it will eaſily be concluded that all the bodies will deſcribe different ellipſes with equal periodical times about their common centre of gravity B, in an immoveable plane. Q. E. I.
