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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3. Tempus quoQ.E.I.noteſcet erigendo ordinatam
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em
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re
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ciproce proportionalem lateri quadrato ex
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PQRD
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+vel-
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DFge,
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& capiendo tempus quo corpus deſcripſit lineam
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De
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ad tempus
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quo corpus alterum vi uniformi cecidit a
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P
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& cadendo pervenit ad
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D,
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ut area curvilinea
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DLme
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ad rectangulum 2
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PDXDL.
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Nam
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que tempus quo corpus vi uniformi deſcendens deſcripſit lineam
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PD
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eſt ad tempus quo corpus idem deſcripſit lineam
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PE
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in ſub
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duplicata ratione
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PD
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ad
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PE,
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id eſt (lineola
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DE
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jamjam naſcen
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te) in ratione
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PD
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ad
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PD
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+1/2
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DE
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ſeu 2
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PD
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ad 2
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PD+DE,
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& diviſim, ad tempus quo corpus idem deſcripſit lineolam
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DE
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ut 2
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PD
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ad
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DE,
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adeoque ut rectangulum 2
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PDXDL
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ad aream
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DLME
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; eſtque tempus quo corpus utrumQ.E.D.ſcripſit lineo
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lam
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DE
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ad tempus quo corpus alterum inæquabili motu deſcrip
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ſit lineam
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De
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ut area
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DLME
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ad aream
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DLme,
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& ex æquo
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tempus primum ad tempus ultimum ut rectangulum 2
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PDXDL
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ad aream
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DLme.
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SECTIO VIII.
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De Inventione Orbium in quibus corpora Viribus quibuſcunque cen
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tripetis agitata revolvuntur.
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PROPOSITIO XL. THEOREMA XIII.
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Si corpus, cogente Vi quacunque centripeta, moveatur utcunque, &
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corpus aliud recta aſcendat vel deſcendat, ſintque eorum Velocita
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tes in aliquo æqualium altitudinum caſu æquales, Velocitates eorum
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in omnibus æqualibus altitudinibus erunt æquales.
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>Deſcendat corpus aliquod ab
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A
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per
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D, E,
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ad centrum
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C,
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&
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moveatur corpus aliud a
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V
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in linea curva
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VIKk,
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Centro
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C
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in
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tervallis quibuſvis deſcribantur circuli concentrici
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DI, EK
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rectæ
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AC
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in
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D
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&
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E,
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curvæque
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VIK
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in
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I
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&
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K
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occurrentes. </
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tur
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IC
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occurrens ipſi
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KE
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in
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N;
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& in
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IK
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demittatur perpendi
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culum
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NT
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; ſitque circumferentiarum circulorum intervallum
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DE
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vel
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IN
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quam minimum, & habeant corpora in
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D
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&
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I
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velocita-</
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