Philosophiae naturalis principia mathematica . fumantur cpntinue pro-portionaleSj denfitates fluidi iii iifdem difkantlUeriinf etiinn continueproportionales. Defignet A T V fundum Sphaericum cui fluidum incumbit, Scentrum, SA^SB, SC,SD^SEr &c. diftantias continue propor-tionales. Erigantur perpendicula AH^BI, CK^DL^EM^& fint ut denfitates Medii in locis A^ Z>, C, T>, E; & fperificae sravitates in iifdem locis erunt ut , , , &c. vehquod . , a AH BI CK. Jwh •pennde eft, ut —•> — ?> — &c. Fmge pn- mum has gravitatesuniformiter continuariabA ad B, a B ad C, aCadD &c. fa£Hs pergra
Philosophiae naturalis principia mathematica . fumantur cpntinue pro-portionaleSj denfitates fluidi iii iifdem difkantlUeriinf etiinn continueproportionales. Defignet A T V fundum Sphaericum cui fluidum incumbit, Scentrum, SA^SB, SC,SD^SEr &c. diftantias continue propor-tionales. Erigantur perpendicula AH^BI, CK^DL^EM^& fint ut denfitates Medii in locis A^ Z>, C, T>, E; & fperificae sravitates in iifdem locis erunt ut , , , &c. vehquod . , a AH BI CK. Jwh •pennde eft, ut —•> — ?> — &c. Fmge pn- mum has gravitatesuniformiter continuariabA ad B, a B ad C, aCadD &c. fa£Hs pergradus decrementis in: pun£tis I>, C, D &c. Ethae gravitates duclae in altitudines AB, BC^CD &c. conficient preffiones AH^BI, CK, qui-bus fundum AT Vf juxta Theorema XIV.)urgetur. iSuftinet ergo particula A preffionesomnes AI% B I, CK^ DL, pergendo in in-finirum:, & particula B prcfiiones omnes praeter primam AH; &particula C onines praeter duas primas A H, BI; & fic deinceps: adeoque. [ w 3 adeoque particula? primae A denfitas AH eft ad particula* fecun-dx B deniltatein BI ut fumma omnium AH^-BIi-CK^-D L,in infinitum, ad fummam omnium B I -f C K -\-D L, &c. Et BIdeniltas fecundse £, eft ad C K denfitatem terriae C,ut fummaom-nium Bl-\-CK-\-DL, &c. adfummam omnium CK-\-DL,& fummae illa; difterentiis fuis AH, B I, CK, &c. pro-portionales, atque adeo continue proportionales per difterentiae AHy £/, Cl£,&c. fummis proportionales, funtetiam continue proportionales. Quare cum denfitates in locis AyB,C fint ut A H, B J, C K, &c. erunt etiam hx continue propor-tionales. Pergatur per faltum, & ( ex aequo J) in diftantiis SA, «SC,SE continue proportionalibus,erunt denfitates AHy CK, E Mcontinue proportionales. Et eodem argumento in diftantiis qui-bufviscontinueproportionalibus«S,y^, ££>, Si^denfitates AH,DL,Q 0 erunt continue proportionales. Coeant jam pun&a^, f>, C,Dy E, &c. eo ut progreffio g
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