Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/396

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306
Mathematical Principles
Book I.


Proposition XCIII. Theorem XLVIII.

If a ſolid be plane one one ſide, and infinitely extended on all other ſides, and conſiſt of equal particles equally attractive, whoſe forces decreaſe, in the receſs from the ſolid, in the ratio of any power greater than the ſquare of the diſŧances; and a corpuſcle placed towards either part of the plane is attracted by the force of the whole ſolid; I ſay that the attractive force of the whole ſolid, in the attractive force of the whole ſolid, in the receſs from its plane ſuperficies, will decreaſe in the ratio of a power whoſe ſide is the diſtance of the corpuſcle from the plane, and its index leſs by 3 than the index of the power of the diſtance.

Plate 24, Figure 6
Plate 24, Figure 6

Case. 1. Let LGI (Pl. 24. Fig. 6.) be the plane by which the ſolid is terminated. Let the ſolid lie on that hand of the plane that is towards I, and let it be reſolved into innumerable planes mHM, nIN, oKO, &c. parallel to GL. And firſt let the attracted body C be placed without the ſolid. Let there be drawn CGHI perpendicular to thoſe innumerable planes, and let the attractive forces of the points of the ſolid decreaſe in the ratio of a power of the diſtances whoſe index is the number as not leſs than 3. Therefore