Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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porum velocitates in
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E
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&
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K
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& eodem argumento ſemper reperi
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entur æquales in ſubſequentibus æqualibus diſtantiis.
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E. D.
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LIBER
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PRIMUS.</
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DE MOTU
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CORPORUM</
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>Sed & eodem argumento corpora æquivelocia & æqualiter a cen
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tro diſtantia, in aſcenſu ad æquales diſtantias æqualiter retarda
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buntur.
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Q.E.D.
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Corol.
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1. Hinc ſi corpus vel funipendulum oſcilletur, vel im
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pedimento quovis politiſſimo & perfecte lubrico cogatur in li
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nea curva moveri, & corpus aliud recta aſcendat vel deſcendat,
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ſintque velocitates eorum in eadem quacunque altitudine æquales:
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erunt velocitates eorum in aliis quibuſcunque æqualibus altitudi
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nibus æquales. </
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>NamQ.E.I.pedimento vaſis abſolute lubrici idem
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præſtatur quod vi tranſverſa
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NT.
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Corpus eo non retardatur,
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non acceleratur, ſed tantum cogitur de curſu rectilineo diſcedere. </
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Corol.
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2. Hinc etiam ſi quantitas P ſit maxima a centro diſtan
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tia, ad quam corpus vel oſcillans vel in Trajectoria quacunque re
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volvens, deque quovis Trajectoriæ puncto, ea quam ibi habet
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velocitate ſurſum projectum aſcendere poſſit; ſitque quantitas A
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diſtantia corporis a centro in alio quovis Orbitæ puncto, & vis
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centripeta ſemper ſit ut ipſius A dignitas quælibet A
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-1
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, cujus
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Index
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-1 eſt numerus quilibet
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unitate diminutus; velocitas
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corporis in omni altitudine A erit ut √P
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-A
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, atque adeo da
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tur. </
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>Namque velocitas recta aſcendentis ac deſcendentis (per Prop. </
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XXXIX) eſt in hac ipſa ratione. </
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