Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/71

Rh uch manner that the um of the conpiring and the difference of the contrary motions may remain the ame as before. From uch kind of reflexions alo ometimes arie the circular motions of bodies about their own centres. But thee are caes which I do not conider in what follows; and it would be too tedious to demontrate every particular that relates to this ubject.

For if two points proceed with an uniform motion in right lines, and their ditance be divided in a given ratio, the dividing point will be either at ret, or proceed uniformly in a right line. This is demontrated hereafter in Lem. 23 and its Corol., when the points are moved in the ame plane; and by a like way of arguing, it may be demontrated when the points are not moved in the ame 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 ret, or proceeds uniformly in a right line; becaue the line which connects the centres of thoe two bodies o moving is divided at that common centre in a given ratio. In like manner the common centre of thoe Rh