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

Rh the accelerative attractions of the corpucule towards particles of the bodies proportional to the wholes, and alike ituated in them.

For if the bodies are divided into particles proportional to the wholes and alike ituated in them, it will be, as the attraction towards any particle of one of the bodies to the attraction towards the correpondent particle in the other body, o are the attractions towards the everal particles of the firt body to the attractions towards the everal correpondent particles of the other body; and by compoition, o is the attraction towards the firt whole body to the attraction towards the econd whole body. Q. E. D.

Therefore, if as the ditances of the corpucles attracted increae, the attractive forces of the particles decreae in the ratio of any power of the ditances; the accelerative attractions towards the whole bodies will be as the bodies directly and thoe powers of the ditances inverely. As if the forces of the particles decreae in a duplicate ratio of the ditances from the corpucles attracted, and the bodies are as $$\scriptstyle A^3$$ and $$\scriptstyle B^3$$, and therefore both the cubic ides of the bodies, and the ditance of the attracted corpucles from the bodies are as A and B; the accelerative attractions towards the bodies will be as $$\scriptstyle \frac {A^3}{A^2}$$ and $$\scriptstyle \frac {B^3}{B^2}$$, that is, as A and B the cubic ides of thoe bodies. If the forces of the particles decreae in a triplicate ratio of the ditances from the attracted corpucles; the accelerative