deſcribed, and the attracted bodies are ſpheres of the ſame kind.
Scholium.
I have now explained the two principal caſe of attractions; to wit, when the centripetal forces decreaſe in a duplicate ratio of the diſtances, or increaſe in a ſimple ratio of the diſtances; cauſing the bodies in both caſes to revolve in conic ſections, and compoſing ſphærical bodies whoſe centripetal forces obſerve the ſame law of increaſe or decreaſe in the receſs from the centre as the forces of the particles themſelves do; which is very remarkable. It would be tedious to run over the other caſes, whoſe concluſions are leſs elegant and important, ſo particularly as I have done theſe. I chuſe rather to comprehend and determine them all by one general method as follows.
Lemma XXIX.
If about the centre S (Pl. 22. Fig. 4.) theſe le deſcribed arty circle at AEB, and about the centre P there be alſo deſcribed two circles EF, ef, cutting the firſt 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 ſay, that, if the diſŧance of the arcs EF, ef, be ſupposed to be infinitely, the laſt ratio of the evaneſcent
