Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/81

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Laws.
of Natural Philopoſophy.
37


In attractions, I briefly demonſtrate the thing after this manner. Suppoſe an obſtacle is interpoſed to hinder the progreſs of any two bodies A, B, mutually attracting one the other: then if either body as A, is more attracted towards the other body B, than that other body B is towards the firſt body A, the obſtacle will be more ſtrongly urged by the preſſure of the body A than by the preſſure of the body B, and therefore will not remain in æquilibrio: but the ſtronger preſſure will prevail, and will make the ſyſtem of the two bodies, together with the obſtacle, to move directly towards the parts of which B lies; and in free ſpaces, to go forward in infinitum with a motion perpetually accelerated; which is abſurd and contrary to the firſt Law. For, by the firſt Law, the ſyſtem ought to perſevere in its ſtate of reſt, or of moving uniformly forward in a right line; and therefore the bodies muſt equally preſs the obſtacle, and be equally attracted one by the other. I made the experiment on the loadſtone and iron. If theſe plac'd apart in proper veſſels, are made to float by one another in ſtanding water, neither of them will propel the other; but, by being equally attracted, they will ſuſtain each other's preſſure, and reſt at laſt in an equilibrium.

Figure 5.

So the gravitation betwixt the earth and its parts is mutual. Let the earth FI (Fig. 5) be cut by any plane EG into two parts EGF and EGI, and their weights one towards the other will be mutually equal. For if by another plane HK, parallel to the former EG, the greater part EGI is cut into two parts EGKH and HKI, whereof HKI is equal to the part EFG, firſt cut off: it is evident that the middle part EGKH, will have no propenſion by its proper weight towards either ſide, but will hang as it were, and reſt in an equilibrium betwixt both. But the one extreme part HKI

will