Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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DE MOTU
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CORPORUM</
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Cas.
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2. Si Figura illa
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RPB
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Hyperbola eſt, deſcribatur ad ean
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dem diametrum principalem
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AB
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Hyperbola rectangula
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BED:
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& quoniam areæ
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CSP, CBfP, SPfB
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ſunt ad areas
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CSD,
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CBED, SDEB,
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ſingulæ ad ſingulas, in data ratione altitudi
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num
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CP, CD
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; & area
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SPfB
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<
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proportionalis eſt tempori quo
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corpus
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P
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movebitur per arcum
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PfB
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; erit etiam area
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SDEB
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ei
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dem tempori proportionalis. </
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Minuatur latus rectum Hyper
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bolæ
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RPB
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in infinitum ma
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nente latere tranſverſo, & coibit
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arcus
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PB
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cum recta
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CB
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& um
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bilicus
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S
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cum vertice
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B
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& recta
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SD
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cum recta
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BD.
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Proinde a
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rea
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BDEB
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proportionalis erit
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tempori quo corpus
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C
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recto
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deſcenſu deſcribit lineam
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CB.
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E. I.
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Cas.
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3. Et ſimili argumento ſi
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Figura
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RPB
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Parabola eſt, &
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eodem vertice principali
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B
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de
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ſcribatur alia Parabola
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BED,
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quæ ſemper maneat data interea
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dum Parabola prior in cujus perimetro corpus
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P
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movetur, dimi
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nuto & in nihilum redacto ejus latere recto, conveniat cum linea
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CB
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; fiet ſegmentum Parabolicum
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BDEB
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proportionale tempori
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quo corpus illud
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P
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vel
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C
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deſcendet ad centrum
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S
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vel
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B.
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E. I.
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PROPOSITIO XXXIII. THEOREMA IX.
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Poſitis jam inventis, dico quod corporis cadentis Velocitas in loco quo
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vis
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C
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est ad velocitatem corporis centro
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B
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intervallo
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BC
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Circu
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lum deſcribentis, in ſubduplicata ratione quam
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AC,
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diſtantia cor
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poris a Circuli vel Hyperbolæ rect angulæ vertice ulteriore
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A,
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habet
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ad Figuræ ſemidiametrum principalem
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1/2 AB. </
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<
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AB,
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communis utriuſque Figuræ
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RPB, DEB
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dia
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meter, in
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O
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; & agatur recta
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PT
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quæ tangat Figuram
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RPB
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in
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P,
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atque </
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