Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/73

whoſe centres they are; and therefore while thoſe two centres retain their ſtate of motion or reſt, the common centre of all does alſo retain its ſtate: it is manifeſt that the common centre of all never ſuffers any change in the ſtate of its motion or reſt from the actions of any two bodies between themſelves. But in ſuch a ſyſtem all the actions of the bodies among themſelves either happen between two bodies, or are compoſed of actions interchanged between ſome two bodies; and therefore they do never produce any alteration in the common centre of all as to its ſtate of motion or reſt. Wherefore ſince that centre, when the bodies do not act mutually one upon another, either is at reſt or moves uniformly forward in ſome right line, it will, notwithſtanding the mutual actions of the bodies among themſelves, always perſevere in its ſtate, either of reſt, or of proceeding uniformly in a right line, unleſs it is forced out of this ſtate by the action of ſome power impreſſed from without upon the whole ſyſtem. And therefore the ſame law takes place in a ſyſtem conſiſting of many bodies as in one ſingle body, with regard to their perſevering in their ſtate of motion or of reſt. For the progreſſive motion, whether of one ſingle body, or of a whole ſyſtem of bodies, is always to be eſtimated from the motion of the centre of gravity.