between themſelves, are as the diſtances AZ, BZ; but if they are ſuppoſed unequal, are as thoſe particles and their diſtances AZ, BZ conjunctly, or (if I may ſo ſpeak) as thoſe particles drawn into their diſtances AZ, BZ reſpectively. And let thoſe forces be expreſſed by the contents under A x AR, and B x BZ. Join AB, and let it be cut in G, ſo that AG may be to BG as the particle B to the particle A; and G will be the common centre of gravity of the particles A and B. The force A x AZ will (by cor. 2. of the laws) be reſolved into the forces A x GZ and A x AG; and the force B x BZ into the forces B x GZ and B x BG. Now the forces A x AG and B x BG, becauſe A is proportional to B, and BG to AG, are equal; and therefore having contrary directions deſtroy one other. There remain then the forces A x GZ and B x GZ. Theſe tend from Z towards the centre G, and compoſe the force ; that is the ſame force as if the attractive particles A and B were placed in their common centre of gravity G, compoſing there a little globe.
By the ſame reaſoning if there be added a third particle C, and the force of it be compounded with the force tending to the centre G; the force thence ariſing will tend to the common centre of gravity of that globe in G and of the particle C; that is, to the common centre of gravity of the three particles A, B, C; and will be the ſame as if that globe and the particle C were placed in that common centre compoſing a greater globe there. And ſo we may go on in infinitum. Therefore the whole force of all the
