Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/316

 error, be either at ret or move uniformly forward in a right line; and the leer will revolve about that great one in ellipes, and by radii drawn thereto will decribe 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 leer bodies upon each other. But the leer bodies may be o far diminihed, as that this reces and the mutual actions of the bodies on each other may become les than any aignable and therefore o as that the orbits may come ellipes, and the areas anwer to the times, without any error that is not les than any aignable. Q. E. O.

Let us imagine a ytemp of leer bodies revolving about a very great one in the manner decribed, or any other ytem of two bodies revolving about each other to be moving uniformly forward in a right line, and in the mean time to impelled ide-aways by the force of another vatly greater body ituate at a great ditance. And becaue the equal accelerative forces with which the bodies are impelled in parallel directions do not change the ituation of the bodies with repect to each other, but only oblige the whole ytem to change its place while the parts till retain their motions among themelves; it is manifet, that no change in thoe motions of the attracted bodies can arie from their attractions towards the greater, unles by the inequality of the accelerative attractions, or by the inclinations of the lines towards each other, in whoe directions the attractions are made. Suppoe therefore all the accelerative attractions made towards the great body to be among themelves