Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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<
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>Ex iis quæ hactenus dicta ſunt, conſtat Planetas in Orbitis ſuis
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retineri per Vim aliquam in ipſos perpetuo agentem: conſtat
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Vim illam dirigi ſemper verſus Orbitarum centra: conſtat hujus
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efficaciam augeri in acceſſu ad centrum, diminui in receſſu ab eo
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dem: & augeri quidem in eadem proportione qua diminuitur qua
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dratum diſtantiæ, diminui in eadem proportione qua diſtantiæ
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quadratum augetur. </
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<
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>Videamus jam, comparatione inſtituta inter
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Planetarum Vires centripetas & Vim Gravitatis, annon ejuſdem
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forte ſint generis. </
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<
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>Ejuſdem vero generis erunt, ſi deprehendan
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tur hinc & inde leges eædem eædemque affectiones. </
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<
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>Primo ita
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que Lunæ, quæ nobis proxima eſt, Vim centripetam expendamus. </
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<
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>Spatia rectilinea, quæ a corporibus e quiete demiſſis dato tem
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pore ſub ipſo motus initio deſeribuntur, ubi a viribus quibuſcun
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que urgentur, proportionalia ſunt ipſis viribus: Hoc utique con
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ſequitur ex ratiociniis Mathematicis. </
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<
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>Erit igitur Vis centripeta
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Lunæ in Orbita ſua revolventis, ad Vim Gravitatis in ſuperficie
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Terræ, ut ſpatium quod tempore quam minimo deſcriberet Luna
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deſcendendo per Vim centripetam verſus Terram, ſi circulari om
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ni motu privari fingeretur, ad ſpatium quod eodem tempore quam
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minimo deſcribit grave corpus in vicinia Terræ, per Vim gravita
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tis ſuæ cadendo. </
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<
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>Horum ſpatiorum prius æquale eſt arcus a Luna
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per idem tempus deſcripti ſinui verſo, quippe qui Lunæ tranſla
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tionem de Tangente, factam a Vi centripeta, metitur; atque adeo
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computari poteſt ex datis tum Lunæ tempore periodico tum di
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ſtantia ejus a centro Terræ. </
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<
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>Spatium poſterius invenitur per Ex
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perimenta Pendulorum, quemadmodum docuit
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Hugenius.
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Inito
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itaque calculo, ſpatium prius ad ſpatium pofterius, ſeu vis cen
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tripeta Lunæ in Orbita ſua revolventis ad vim Gravitatis in ſu
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perficie Terræ, erit ut quadratum ſemidiametri Terræ ad Orbitæ
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ſemidiametri quadratum. </
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<
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>Eandem habet rationem, per ea quæ
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ſuperius oſtenduntur, vis centripeta Lunæ in Orbita ſua revol
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ventis ad vim Lunæ centripetam prope Terræ ſuperficiem. </
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<
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>Vis
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itaque centripeta prope Terræ ſuperficiem æqualis eſt vi Gravita
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tis. </
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<
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>Non ergo diverſæ ſunt vires, ſed una atque eadem: ſi enim
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diverſæ eſſent, corpora viribus conjunctis duplo celerius in Ter
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ram caderent quam ex vi ſola Gravitatis. </
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<
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>Conſtat igitur Vim
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illam centripetam, qua Luna perpetuo de Tangente vel trahitur
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vel impellitur & in Orbita retinetur, ipſam eſſe vim Gravitatis
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terreſtris ad Lunam uſque pertingentem. </
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<
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>Et rationi quidem con
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ſentaneum eſt ut ad ingentes diſtantias illa ſeſe Virtus extendat, </
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