Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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Corol.
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1. Ex tribus noviſſimis Propoſitionibus conſequens eſt, quod </
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ſi corpus quodvis
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P,
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ſecundum lineam quamvis rectam
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PR,
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qua
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cunque cum velocitate exeat de loco
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P,
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& vi centripeta quæ ſit re
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ciproce proportionalis quadrato diſtantiæ loeorum a centro, ſimul
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agitetur; movebitur hoc corpus in aliqua ſectionum Conicarum
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umbilicum habente in centro virium; & contra. </
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<
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>Nam datis umbi
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lico & puncto contactus & poſitione tangentis, deſcribi poteſt ſectio
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Conica quæ curvaturam datam ad punctum illud habebit. </
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<
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>Datur
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autem curvatura ex data vi centripeta: & Orbes duo ſe mutuo tan
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gentes, eadem vi centripeta deſcribi non poſſunt. </
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LIBER
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PRIMUS.</
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Corol.
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2. Si velocitas, quacum corpus exit de loco ſuo
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P,
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ea
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ſit, qua lineola
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PR
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in minima aliqua temporis particula deſcribi
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poſſit, & vis centripeta potis ſit eodem tempore corpus idem mo
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vere per ſpatium
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QR:
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movebitur hoc corpus in Conica aliqua ſe
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ctione, cujus latus rectum principale eſt quantitas illa (
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QTq./QR
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) quæ
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ultimo fit ubi lineolæ
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PR, QR
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in infinitum diminuuntur. </
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lum in his Corollariis refero ad Ellipſin, & caſum excipio ubi cor
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pus recta deſcendit ad centrum. </
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PROPOSITIO XIV. THEOREMA VI.
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Si corpora plura revolvantur circa centrum commune, & vis centri
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peta ſit reciproce in duplicata ratione diſtantiæ loeorum a centro;
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dico quod Orbium Latera recta principalia ſunt in duplicata ratio
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one arearum quas corpora, radiis ad centrum ductis, eodem tempore
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deſcribunt.
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<
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>Nam, per Corol. </
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<
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>2. Prop. </
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>XIII, Latus rectum
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L
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æquale eſt quan
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titati (
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QTq./QR
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) quæ ultimo fit ubi coeunt puncta
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P
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&
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Sed linea
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minima
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QR,
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dato tempore, eſt ut vis centripeta generans, hoc
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eſt (per Hypotheſin) reciproce ut
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Ergo (
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QTq./QR
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) eſt ut
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QTq.XSPq.
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hoc eſt, latus rectum
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L
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in duplicata ratione areæ
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QTXSP. Q.E.D.
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