error, be either at reſt or move uniformly forward in a right line; and the leſſer will revolve about that great one in ellipſes, and by radii drawn thereto will deſcribe areas proportional to the times; if we except the errors that may be introduced by the receding of the great body from the common centre of gravity, or by the mutual actions of the leſſer bodies upon each other. But the leſſer bodies may be ſo far diminiſhed, as that this receſs and the mutual actions of the bodies on each other may become leſs than any aſſignable and therefore ſo as that the orbits may come ellipſes, and the areas anſwer to the times, without any error that is not leſs than any aſſignable. Q. E. O.
Case 2. Let us imagine a ſyſtemp of leſſer bodies revolving about a very great one in the manner deſcribed, or any other ſyſtem of two bodies revolving about each other to be moving uniformly forward in a right line, and in the mean time to impelled ſide-aways by the force of another vaſtly greater body ſituate at a great diſtance. And becauſe the equal accelerative forces with which the bodies are impelled in parallel directions do not change the ſituation of the bodies with reſpect to each other, but only oblige the whole ſyſtem to change its place while the parts ſtill retain their motions among themſelves; it is manifeſt, that no change in thoſe motions of the attracted bodies can ariſe from their attractions towards the greater, unleſs by the inequality of the accelerative attractions, or by the inclinations of the lines towards each other, in whoſe directions the attractions are made. Suppoſe therefore all the accelerative attractions made towards the great body to be among themſelves
