Gravesande, Willem Jacob 's
,
Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1
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MATHEMATICA. LIB. I. CAP XVIII.
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tur, ſi eodem tempore cadere incipiant, ſunt ſemper in ea-
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dem ratione quam in principio caſus ; </
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<
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tempore percurrunt, quæ ſunt in ratione longitudinis plani
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ad illius altitudinem.
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<
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B ſpatium a corpore percurſum, dum aliud li-
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bere cadit per altitudinem plani
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C, determinatur, du-
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fig. 9.</
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cendo ad
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B perpendicularem CG: </
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<
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plani
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B eſt ad illius altitudinem
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C, ut
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C ad
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G. </
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circulus deſcribatur diametro
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C, punctum G erit in pe-
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ripheria circuli; </
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">quia angulus in ſemicirculo, ut
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GC,
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ſemper eſt rectus ; </
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">ideo punctum ut G, pro plano
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cunque inclinato, ſemper eſt in eadem illa peripheria: </
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de ſequitur, chordas omnes, ut
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G eſſe inter ſe ut vires,
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quibus corpora ſuper his deſcendere conantur; </
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curri a corporibus devolventibus, in tempore in quo cor-
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pus, libere cadendo, poteſt percurrere diametrum
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C;
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</
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">ita tempora devolutionum per illas chordasſunt æqualia.</
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<
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">Per punctum C nulla poteſt duci chorda ut HC, quin de-
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tur per
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chorda ut
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G ei parallela, id eſt, æqualiter in-
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clinata, & </
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<
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">igitur in ſemicirculo, ut
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HC, Vires
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quibus corpora juxta chordas, in puncto infimo terminatas
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deſcendere conantur, ſunt inter ſe ut hæ chordæ & </
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<
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corpus ſibi permittitur eodem tempore, ad punctum infimum
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ſemicirculi perveniet, ſive libere cadat juxta diametrum,
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ſive deſcendat ſuper chorda HC quacunque.</
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<
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B poteſt confer-
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ri cum tempore deſcenſus per plani altitudinem
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C; </
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hocce tempus eſt æquale tempori devolutionis per
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G; </
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quadrata temporum ſunt inter ſe ut
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B ad
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G ; </
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B eſt ad
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C ut
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C ad
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G: </
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B & </
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C ſunt inter ſe, ut
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B ad
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G; </
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B
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& </
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C ſunt inter ſe, ut tempora deſcenſus per
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B, & </
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G, aut
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C, id eſt, tempora, in eo caſu, ſunt ut ſpa-
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tia percurſa.</
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nam poſt tempora æqualia, quando corpora ſunt in G & </
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