Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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LIBER
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PRIMUS.</
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PROPOSITIO LXXXVI. THEOREMA XLIII.
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Si particularum, ex quibus corpus attractivum componitur, vires
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in receſſu corporis attracti decreſcunt in triplicata vel pluſquam
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triplicata ratione diſtantiarum a particulis: attractio longe for
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tior erit in contactu, quam cum attrahens & attractum inter
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vallo vel minimo ſeparantur ab invicem.
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>Nam attractionem in acceſſu attracti corpuſculi ad hujuſmodi
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Sphæram trahentem augeri in infinitum, conſtat per ſolutionem Pro
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blematis XLI, in Exemplo ſecundo ac tertio exhibitam. </
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>Idem, per
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Exempla illa & Theorema XLI inter ſe collata, facile colligitur
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de attractionibus corporum verſus Orbes concavo-convexos, ſive
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corpora attracta collocentur extra Orbes, ſive intra in eorum cavi
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tatibus. </
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>Sed & addendo vel auferendo his Sphæris & Orbibus ubi
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vis extra locum contactus materiam quamlibet attractivam, eo ut
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corpora attractiva induant figuram quamvis aſſignatam, conſtabit
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Propoſitio de corporibus univerſis.
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E. D.
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PROPOSITIO LXXXVII. THEOREMA XLIV.
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Si corpora duo ſibi invicem ſimilia, & ex materia æqualiter attra
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ctiva conſtantia, ſeorſim attrahant corpuſcula ſibi ipſis proporti
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onalia & ad ſe ſimiliter poſita: attractiones acceleratrices cor
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puſculorum in corpora tota erunt ut attractiones acceleratrices
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corpuſculorum in eorum particulas totis proportionales & in to
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tis ſimiliter poſitas.
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>Nam ſi corpora diſtinguantur in particulas, quæ ſint totis pro
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portionales & in totis ſimiliter ſitæ; erit, ut attractio in particulam
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quamlibet unius corporis ad attractionem in particulam correſpon
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dentem in corpore altero, ita attractiones in particulas ſingulas
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primi corporis ad attractiones in alterius particulas ſingulas correſ
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pondentes; & componendo, ita attractio in totum primum corpus
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ad attractionem in totum ſecundum.
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E. D.
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Corol.
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1. Ergo ſi vires attractivæ particularum, augendo diſtan
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tias corpuſculorum attractorum, decreſcant in ratione dignitatis </
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