Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/31

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Mr. Cotes's Preface.

as alſo from that very ſlow motion of the apſides, above taken notice of, and which ariſes from a like cauſe.

We have now proceeded ſo far as to ſhew that it muſt be acknowledged, that the Sun, and the Earth, and all the heavenly bodies attending the Sun, attract each other mutually. Therefore all the leaſt particles of matter in every one muſt have their ſeveral attractive forces, whoſe effect is as their quantity of matter; as was ſhewn above of the terreſtrial particles. At different diſtances theſe forces will be alſo in the duplicate ratio of the diſtances reciprocally; for it is mathematically demonſtrated that particles attracting according to this law will compoſe globes attracting according to the ſame law.

The foregoing concluſions are grounded on this axiom, which is received by all philoſophers; namely that effects of the ſame kind; that is, whoſe known properties are the ſame, take their riſe from the ſame cauſes and have the ſame unknown properties alſo. For who doubts, if gravity be the cauſe of the deſcent of a ſtone in Europe, but that it is alſo the cauſe of the ſame deſcent in America? If there is a mutual gravitation between a ſtone and the Earth in Europe, who will deny the ſame to be mutual in America? If in Europe, the attractive force of a ſtone and the Earth is compounded of the attractive forces of the parts; who will deny the like compoſition in America? If in Europe, the attraction of the Earth be propagated to all kinds of bodies and to all diſtances; why may it not as well be propagated in like manner in America? All philoſophy is founded on this rule;

for if that be taken away we can affirm nothing

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