Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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curvam
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Vpk.
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Eſt autem hæc Curva
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Vpk
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eadem cum Curva illa
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VPQ
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in Corol. </
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<
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>3. Prop. </
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<
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>XLI inventa, in qua ibi diximus corpora
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hujuſmodi viribus attracta oblique aſcendere. </
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DE MOTU
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CORPORUM</
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PROPOSITIO XLV. PROBLEMA XXXI.
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Orbium qui ſunt Circulis maxime finitimi requiruntur motus Ap
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ſidum.
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<
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>Problema ſolvitur Arithmetice faciendo ut Orbis, quem corpus
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in Ellipſi mobili (ut in Propoſitionis ſuperioris Corol. </
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<
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revolvens deſcribit in plano immobili, accedat ad formam Orbis
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cujus Apſides requiruatur, & quærendo Apſides Orbis quem cor
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pus illud in plano immobili deſcribit. </
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<
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quirent formam, ſi vires centripetæ quibus deſcribuntur, inter ſe
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collatæ, in æqualibus altitudinibus reddantur proportionales. </
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<
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punctum
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V
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Apſis ſumma, & ſcribantur T pro altitudine maxima
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CV,
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A pro altitudine quavis alia
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CP
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vel
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Cp,
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& X pro alti
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titudinum differentia
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CV-CP
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; & vis qua corpus in Ellipſi
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circa umbilicum ſuum
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C
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(ut in Corollario 2.) revolvente move
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tur, quæQ.E.I. Corollario 2. erat ut (FF/AA)+(RGG-RFF/A
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cub.
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), id eſt
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ut (FFA+RGG-RFF/A
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cub.
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), ſubſtituendo T-X pro A, erit ut
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(RGG-RFF+TFF-FFX/A
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cub.
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). Reducenda ſimiliter eſt vis alia
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quævis centripeta ad fractionem cujus denominator ſit A
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cub.,
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&
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numeratores, facta homologorum terminorum collatione, ſtatuendi
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ſunt analogi. </
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<
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Exempl.
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1. Ponamus vim centripetam uniformem eſſe, adeoque
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ut (A
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cub.
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/A
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cub.
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), ſive (ſcribendo T-X pro A in Numeratore) ut
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(T
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cub.
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-3TTX+3TXX-X
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cub.
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/A
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cub.
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); & collatis Numeratorum ter
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minis correſpondentibus, nimirum datis cum datis & non datis
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cum non datis, fiet RGG-RFF+TFF ad T
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cub.
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ut-FFX ad
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-3TTX+3TXX-X
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cub.
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ſive ut-FF ad-3TT+3TX
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-XX. </
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<
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>Jam cum Orbis ponatur Circulo quam maxime finitimus,
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coeat Orbis cum Circulo; & ob factas R, T æquales, atque X in infi-</
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