ſuch manner that the ſum of the conſpiring and the difference of the contrary motions may remain the ſame as before. From ſuch kind of reflexions alſo ſometimes ariſe the circular motions of bodies about their own centres. But theſe are caſes which I do not conſider in what follows; and it would be too tedious to demonſtrate every particular that relates to this ſubject.
For if two points proceed with an uniform motion in right lines, and their diſtance be divided in a given ratio, the dividing point will be either at reſt, or proceed uniformly in a right line. This is demonſtrated hereafter in Lem. 23 and its Corol., when the points are moved in the ſame plane; and by a like way of arguing, it may be demonſtrated when the points are not moved in the ſame plane. Therefore if any number of bodies move uniformly in right lines, the common centre of gravity of any two of them is either at reſt, or proceeds uniformly in a right line; becauſe the line which connects the centres of thoſe two bodies ſo moving is divided at that common centre in a given ratio. In like manner the common centre of thoſe
