Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/384

attractions towards the whole bodies will be as $\scriptstyle {\frac {A^{3}}{A^{3}}}$ and $\scriptstyle {\frac {B^{3}}{B^{3}}}$, that is, equal. If the forces decreaſe in a quadruplicate ratio; the attractions towards the bodies will be as $\scriptstyle {\frac {A^{3}}{A^{4}}}$ and $\scriptstyle {\frac {B^{3}}{B^{4}}}$; that is, reciprocally as the cubic ſides A and B. And ſo in other caſes.

Cor. 2. Hence on the other hand, from the forces with which like bodies attract corpuſcles ſimilarly ſituated, may be collected the ratio of the decreaſe of the attractive forces of the particles as the attracted corpuſcle recedes from them; if ſo be that decreaſe is directly or inverſely in any ratio of the diſtances.

Proposition LXXXVIII. Theorem XLV.

If the attractive forces of the equal particles of any body be at the diſtance of the places from the particles, the force of the whole body will tend to its centre of gravity; and will be the ſame with the force of a globe, conſiſting of ſimilar and equal matter; and having its centre in the centre of gravity.

Plate 23, Figure 7

Let the particles A, B, (Pl. 23. Fig. 7.) of the body RSTV attract any corpuſcle Z with forces which, ſuppoſing the particles to be equal