Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/72

28 two and that of a third body will be either at ret or moving uniformly in a right line becaue at that centre the ditance between the common centre of the two bodies, and the centre of this lat, is divided in a given ratio. In like manner the common centre of thee three, and of a fourth body, is either at ret, or moves uniformly in a right line; becaue the ditance between the common centre of the three bodies, and the centre of the fourth is there alo divided in a given ratio, and o on in infinitum. Therefore, in a ytem of bodies where there is neither any mutual action among themelves, nor any foreign force impreed upon them from without, and which conequently move uniformly in right lines, the common centre of gravity of them all is either at ret or moves uniformly forward in a right line.

Moreover, in a ytem of two bodies mutually acting upon each other, the ditances between their centres and the common centre of gravity of both are reciprocally as the bodies; the relative motions of thoe bodies, whether of approaching to or of receding from that centre, will be equal among themelves. Therefore ince the changes which happen to motions are equal and directed to contrary parts, the common centre of thoe bodies, by their mutual action between themelves, is neither promoted nor retarded, nor uffers any change as to its tate of motion or ret. But in a ytem of everal bodies, becaue the common centre of gravity of any two acting mutually upon each other uffers no change in its tate by that action; and much les the common centre of gravity of the others with which that action does not intervene; but the ditance between thoe two centres is divided by the common centre of gravity of all the bodies into parts reciprocally proportional to the total ums of thoe bodies Rh