Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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PROPOSITIO XX. PROBLEMA IV.
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DE MUNDI
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SYSTEMATE</
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Invenire & inter ſe comparare Pondera corporum in Terræ hujus
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regionibus diverſis.
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>Quoniam pondera inæqualium crurum canalis aqueæ
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ACQqca
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æqualia ſunt; & pondera partium, cruribus totis proportionalium
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& ſimiliter in totis ſitarum, ſunt ad invicem ut pondera totorum,
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adeoque etiam æquantur inter ſe; erunt pondera æqualium & in
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cruribus ſimiliter ſitarum partium reciproce ut crura, id eſt, reci
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proce ut 230 ad 229. Et par eſt ratio homogeneorum & æqua
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lium quorumvis & in canalis cruribus ſimiliter ſitorum corporum.
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Horum pondera ſunt reciproce ut crura, id eſt, reciproce ut di
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ſtantiæ corporum a centro Terræ. Proinde ſi corpora in ſupre
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mis canalium partibus, ſive in ſuperficie Terræ conſiſtant; erunt
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pondera eorum ad invicem reciproce ut diſtantiæ eorum a centro.
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Et eodem argumento pondera, in aliis quibuſcunque per totam
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Terræ ſuperficiem regionibus, ſunt reciproce ut diſtantiæ loeorum
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a centro; & propterea, ex Hypotheſi quod Terra Sphærois ſit,
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dantur proportione.
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>Unde tale confit Theorema, quod incrementum ponderis per
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gendo ab Æquatore ad Polos, ſit quam proxime ut ſinus verſus
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Latitudinis duplicatæ, vel, quod perinde eſt, ut quadratum ſinus
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recti Latitudinis. </
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>Et in eadem circiter ratione augentur arcus
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graduum Latitudinis in Meridiano. </
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<
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>Ideoque cum Latitudo
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Lu
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tetiæ Pariſiorum
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ſit 48
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gr.
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50′, ea loeorum ſub Æquatore 00
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gr.
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00′,
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& ea loeorum ad Polos 90
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gr.
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& duplorum ſinus verſi ſint 11334,
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00000 & 20000, exiſtente Radio 10000, & gravitas ad Polum ſit
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ad gravitatem ſub Æquatore ut 230 ad 229, & exceſſus gravi
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tatis ad Polum ad gravitatem ſub Æquatore ut 1 ad 229: erit ex
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ceſſus gravitatis in Latitudine
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Lutetiæ
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ad gravitatem ſub Æquatore,
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ut 1X(11334/20000) ad 229, ſeu 5667 ad 2290000. Et propterea gravitates
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totæ in his locis erunt ad invicem ut 2295667 ad 2290000. Quare
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cum longitudines pendulorum æqualibus temporibus oſcillantium
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ſint ut gravitates, & in Latitudine
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Lutetiæ Pariſiorum
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longitudo
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penduli ſingulis minutis ſecundis oſcillantis ſit pedum trium Pa
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riſienſium & linearum 8 1/9: longitudo penduli ſub Æquatore ſu
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perabitur a longitudine ſynchroni penduli
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Pariſienſis,
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exceſſu li
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neæ unius & 87 partium milleſimarum lineæ. Et ſimili computo
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confit Tabula ſequens.
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