Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/364

278 decribed, and the attracted bodies are pheres of the ame kind.

I have now explained the two principal cae of attractions; to wit, when the centripetal forces decreae in a duplicate ratio of the ditances, or increae in a imple ratio of the ditances; cauing the bodies in both caes to revolve in conic ections, and compoing phærical bodies whoe centripetal forces oberve the ame law of increae or decreae in the reces from the centre as the forces of the particles themelves do; which is very remarkable. It would be tedious to run over the other caes, whoe concluions are les elegant and important, o particularly as I have done thee. I chue rather to comprehend and determine them all by one general method as follows.

If about the centre S (Pl. 22. Fig. 4.) thee le decribed arty circle at AEB, and about the centre P there be alo decribed two circles EF, ef, cutting the firt in R and e, and the line PS in F and f; and the line PS in F and f; and there be let fall to PS the perpendiculars ED, ed; I ay, that, if the diŧance of the arcs EF, ef, be upposed to be infinitely, the lat ratio of the evanecent