Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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æqualibus, vel deſcribent Ellipſes in plano illo circa centrum
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C,
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vel periodos movendi ultro citroQ.E.I. lineis rectis per centrum
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C
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in plano illo ductis, complebunt.
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E. D.
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DE MOTU
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CORPORUM</
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Scholium.
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<
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>His affines ſunt aſcenſus ac deſcenſus corporum in ſuperficiebus
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curvis. </
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>Concipe lineas curvas in plano deſcribi, dein circa axes
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quoſvis datos per centrum Virium tranſeuntes revolvi, & ea revo
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lutione ſuperficies curvas deſcribere; tum corpora ita moveri ut
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eorum centra in his ſuperficiebus perpetuo reperiantur. </
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<
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>Si cor
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pora illa oblique aſcendendo & deſcendendo currant ultro citroque
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peragentur eorum motus in planis per axem tranſeuntibus, atque
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adeo in lineis curvis quarum revolutione curvæ illæ ſuperficies ge
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nitæ ſunt. </
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>Iſtis igitur in caſibus ſufficit motum in his lineis cur
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vis conſiderare. </
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PROPOSITIO XLVIII. THEOREMA XVI.
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Si Rota Globo extrinſecus ad angulos rectos inſiſtat, & more ro
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tarum revolvendo progrediatur in circulo maximo; longitudo
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Itineris curvilinei, quod punctum quodvis in Rotæ perimetro da
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tum, ex quo Globum tetigit, confecit, (quodque Cycloidem vel
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Epicycloidem nominare licet) erit ad duplicatum ſinum verſum
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arcus dimidii qui Globum ex eo tempore inter eundum tetigit,
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ut ſumma diametrorum Globi & Rotæ ad ſemidiametrum Globi.
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PROPOSITIO XLIX. THEOREMA XVII.
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Si Rota Globo concavo ad rectos angulos intrinſecus inſiſtat & re
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volvendo progrediatur in circulo maximo; longitudo Itineris
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curvilinei quod punctum quodvis in Rotæ perimetro datum, ex
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quo Globum tetigit, confecit, erit ad duplicatum ſinum verſum
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arcus dimidii qui Globum toto hoc tempore inter eundum teti
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git, ut differentia diametrorum Globi & Rotæ ad ſemidiame
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trum Globi.
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