Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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DE MOTU
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CORPORUM</
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Corol.
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2. In Syſtemate vero trium corporum
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T, P, S,
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ſi attracti
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ones acceleratrices binorum quorumcunQ.E.I. tertium ſint ad invi
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cem reciproce ut quadrata diſtantiarum; corpus
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P,
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radio
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PT,
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are
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am circa corpus
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T
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velocius deſcribet prope Conjunctionem
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A
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& Op
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poſitionem
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B,
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quam prope Quadraturas
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C, D.
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Namque vis omnis
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qua corpus
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P
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urgetur & corpus
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T
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non urgetur, quæque non agit
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ſecundum lineam
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PT
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accelerat vel retardat deſcriptionem areæ,
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perinde ut ipſa in conſequentia vel in antecedentia dirigitur. </
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eſt vis
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NM.
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Hæc in tranſitu corporis
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P
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a
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C
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ad
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A
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tendit in con
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ſequentia, motumque accelerat; dein uſque ad
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D
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in antecedentia,
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& motum retardat; tum in conſequentia uſque ad
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B,
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& ultimo in
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antecedentia tranſeundo a
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B
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ad
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C.
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Corol.
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3. Et eodem argumento patet quod corpus
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P,
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cæteris pa
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ribus, velocius movetur in Conjunctione & Oppoſitione quam in
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Quadraturis. </
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Corol.
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4. Orbita corporis
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P,
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cæteris paribus, curvior eſt in Qua
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draturis quam in Conjunctione & Oppoſitione. </
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lociora minus deflec
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tunt a recto tramite. </
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<
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præterea vis
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KL
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vel
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NM,
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in Conjunctione
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& Oppoſitione, con
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traria eſt vi qua cor
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pus
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T
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trahit corpus
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P,
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adeoque vim illam mi
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nuit; corpus autem
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P
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minus deflectet a recto
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tramite, ubi minus urgetur in corpus
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T.
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Corol.
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5. Unde corpus
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P,
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cæteris paribus, longius recedet a cor
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pore
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T
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in Quadraturis, quam in Conjunctione & Oppoſitione. </
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>Hæc
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ita ſe habent excluſo motu Excentricitatis. </
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>Nam ſi Orbita corpo
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ris
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P
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excentrica ſit: Excentricitas ejus (ut mox in hujus Corol. </
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oſtendetur) evadet maxima ubi Apſides ſunt in Syzygiis; indeque
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fieri poteſt ut corpus
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P,
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ad Apſidem ſummam appellans, abſit lon
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gius a corpore
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T
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in Syzygiis quam in Quadraturis. </
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Corol.
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6. Quoniam vis centripeta corporis centralis
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T,
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qua cor
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pus
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P
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retinetur in Orbe ſuo, augetur in Quadraturis per additio
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nem vis
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LM,
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ac diminuitur in Syzygiis per ablationem vis
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KL,
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&
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ob magnitudinem vis
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KL,
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magis diminuitur quam augetur; eſt au
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tem vis illa centripeta (per Corol. </
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>2, Prop. </
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>IV.) in ratione compo
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ſita ex ratione ſimplici radii
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TP
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directe & ratione duplicata tempo-</
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