Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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LIBER
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SECUNDUS.</
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DE
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MOTU CORPORUM
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LIBER SECUNDUS.
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SECTIO I.
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De Motu Corporum quibus reſiſtitur in ratione
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Velocitatis.
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PROPOSITIO I. THEOREMA I.
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Corporis, cui reſiſtitur in ratione velocitatis, motus ex reſiſtentia
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amiſſus eſt ut ſpatium movendo confectum.
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>NAm cum motus ſingulis temporis particulis æqualibus amiſſus
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ſit ut velocitas, hoc eſt, ut itineris confecti particula: erit,
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componendo, motus toto tempore amiſſus ut iter totum.
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Q.E.D.
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Corol.
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Igitur ſi corpus, gravitate omni deſtitutum, in ſpatiis libe
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ris ſola vi inſita moveatur; ac detur tum motus totus ſub initio, tum
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etiam motus reliquus poſt ſpatium aliquod confectum: dabitur ſpa
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tium totum quod corpus infinito tempore deſcribere poteſt. </
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enim ſpatium illud ad ſpatium jam deſcriptum, ut motus totus ſub
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initio ad motus illius partem amiſſam. </
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LEMMA I.
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Quantitates differentiis ſuis proportionales, ſunt continue propor
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tionales.
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<
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>Sit A ad A-B ut B ad B-C & C ad C-D, &c. </
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>& dividendo
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fiet A ad B ut B ad C & C ad D, &c.
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Q.E.D.
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