Philosophiae naturalis principia mathematica . m fiunt zSIqXJL^ Sj^^ LL ^SIq. ? S Icttb. 3LI H^. vero fub« dudiis pofterioribus de priore , evadunt 4JL^ _• . Igitur vis tota^, 3 ^/ qqa corpufcdum-!P in Sphaeras , eft m efl, reciproce wtTS cub. X ? /. ^ ^. /. Eadem Methodo determinari poteft Attradlio corpufculi Sphaeram, fed £ Theorema fequens. FRO^ PRINCIPIA LXXXII. THEOREMA XLI. 189. L I B 1». In Sphara centro S tntervallo S A defcripta , fi capianturSl, SA, SP contmue proportionaks. dico quod corpuf-culi intra Spharam in loco q
Philosophiae naturalis principia mathematica . m fiunt zSIqXJL^ Sj^^ LL ^SIq. ? S Icttb. 3LI H^. vero fub« dudiis pofterioribus de priore , evadunt 4JL^ _• . Igitur vis tota^, 3 ^/ qqa corpufcdum-!P in Sphaeras , eft m efl, reciproce wtTS cub. X ? /. ^ ^. /. Eadem Methodo determinari poteft Attradlio corpufculi Sphaeram, fed £ Theorema fequens. FRO^ PRINCIPIA LXXXII. THEOREMA XLI. 189. L I B 1». In Sphara centro S tntervallo S A defcripta , fi capianturSl, SA, SP contmue proportionaks. dico quod corpuf-culi intra Spharam in loco quovis I attraBio eji ad attrdc^fionem ipfius extra Spharam in loco P , in ratione com^poftta ex fuhduplicata ratione difiantiarum a centro IS, VS^ fuhduplicata ratione virium centripeiarum ^ in locisit-lisV&\, ad centrmn tendentium. Ut fi vires centripetas particularum Sphserae fint reciproce ut di-ftantias corpufculi a fe attradi; vis, qua corpufculum fituro in /trahitur a-Sphaera tota, erit ad vim qua trahitur in ? , in ratione. compofita ex fubduplicata rStione diflantiffi J*/ ai difiantiam S^p& ration^ fubduplicata vis centripetse in loco /, a particula aliquain centro oriundas, ad vim centripetam in loco T ab eadem in cen-tro particula oriundam , id efl, ratione fubduplicata diilantiaTumJ*/, ly?* ad invicem reciproce. Hae duffi rationes fubduplicatJEcomponunt rationem-ffiqualitatis, &propterea attradiones in /& ^a Sphsera tota faftae aequantur. SimiU computo , fi vires particu-larum Sphagrae funt reciproce in duplicata ratione diftantiarum , coi-ligetur quod attradio in / fit ad attraftionem in ^, ut diftantia S^Rad Sph^rcE femidiametrum S A: Si vires illae funt reciproce in tri-pHcata ratione diltantiarum^., attradiones in / & ^ erunt ad invi- Aa 3 ceni:. I90 PHILOSOPHIiE NATURALrs DeMotu cem ut ST ^uad. ^d-SApiad. Si in quadruplicata , vM ST cub. adCoRPORUM, SA cub. Unde cum attra6tio in *P , in hoc ultimo cafu , inventafuit reciproce ut TS cub. , attraftio in /
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