Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/383

From Wikisource
Jump to navigation Jump to search
This page has been proofread, but needs to be validated.
Sect. XIII.
of Natural Philopoſophy.
295

the accelerative attractions of the corpuſcule towards particles of the bodies proportional to the wholes, and alike ſituated in them.

For if the bodies are divided into particles proportional to the wholes and alike ſituated in them, it will be, as the attraction towards any particle of one of the bodies to the attraction towards the correſpondent particle in the other body, ſo are the attractions towards the ſeveral particles of the firſt body to the attractions towards the ſeveral correſpondent particles of the other body; and by compoſition, ſo is the attraction towards the firſt whole body to the attraction towards the ſecond whole body. Q. E. D.

Cor. 1. Therefore, if as the diſtances of the corpuſcles attracted increaſe, the attractive forces of the particles decreaſe in the ratio of any power of the diſtances; the accelerative attractions towards the whole bodies will be as the bodies directly and thoſe powers of the diſtances inverſely. As if the forces of the particles decreaſe in a duplicate ratio of the diſtances from the corpuſcles attracted, and the bodies are as and , and therefore both the cubic ſides of the bodies, and the diſtance of the attracted corpuſcles from the bodies are as A and B; the accelerative attractions towards the bodies will be as and , that is, as A and B the cubic ſides of thoſe bodies. If the forces of the particles decreaſe in a triplicate ratio of the diſtances from the attracted corpuſcles; the accelerative