Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/367

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If to the everal equal parts of a phere ABE, (Pl. 22. Fig. 6.) decribed about the centre S, there tend equal centripetal forces; and from the everal points D in the axis of the phere AB in which a corpucle, as, is placed, there be erected the perpendiculars DE meeting the phere in E, and if in thoe perpendiculars the lengths DN be taken as the quantity $$\textstyle \frac {DE^2 \times PS}{PE}$$ and as the force which a particle of the phere ituate in the axis exerts at the ditance PE upon the corpucle P, conjunctly; I ay that the whole force with which the corpucle P is attracted towards the phere is as the area ANB, comprehended under the axis of the phere AB, and the curve line ANB, the locus of the point N.

For uppoing the contruction in the lat lemma and theorem to tand. conceive the axis of the phere AB to be divided into innumerable equal particles Dd, and the whole phere to be divided into o many phærical concavo-convex laminæ 'EFfe;