Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/385

Rh between themelves, are as the ditances AZ, BZ; but if they are uppoed unequal, are as thoe particles and their ditances AZ, BZ conjunctly, or (if I may o peak) as thoe particles drawn into their ditances AZ, BZ repectively. And let thoe forces be expreed by the contents under A x AR, and B x BZ. Join AB, and let it be cut in G, o 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 reolved 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, becaue A is proportional to B, and BG to AG, are equal; and therefore having contrary directions detroy one other. There remain then the forces A x GZ and B x GZ. Thee tend from Z towards the centre G, and compoe the force $$\scriptstyle \overline {A + B} \times GZ$$; that is the ame force as if the attractive particles A and B were placed in their common centre of gravity G, compoing there a little globe.

By the ame reaoning if there be added a third particle C, and the force of it be compounded with the force $$\scriptstyle \overline {A + B} \times GZ$$ tending to the centre G; the force thence ariing 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 ame as if that globe and the particle C were placed in that common centre compoing a greater globe there. And o we may go on in infinitum. Therefore the whole force of all the