Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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A
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(11/9)
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vel A
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1/4
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, aut directe ut A
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6
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vel A
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13
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. </
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>Denique ſi corpus pergendo
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ab Apſide ſumma ad Apſidem ſummam confecerit revolutionem in
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tegram, & præterea gradus tres, adeoque Apſis illa ſingulis corporis
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revolutionibus confecerit in conſequentia gradus tres; erit
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m
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ad
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n
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ut
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363
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gr.
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ad 360
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gr.
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ſive ut 121 ad 120, adeoque A
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(
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nn/mm
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)-3
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erit æquale
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A
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-(29523/14641)
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; & propterea vis centripeta reciproce ut A
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(29523/14641)
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ſeu re
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ciproce ut A
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2 (4/2+3)
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proxime. </
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>Decreſcit igitur vis centripeta in ratio
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ne paulo majore quam duplicata, ſed quæ vicibus 59 3/4 propius ad
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duplicatam quam ad triplicatam accedit. </
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DE MOTU
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CORPORUM</
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LIBER
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PRIMUS.</
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Corol.
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2. Hinc etiam ſi corpus, vi centripeta quæ ſit reciproce
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ut quadratum altitudinis, revolvatur in Ellipſi umbilicum haben
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te in centro virium, & huic vi centripetæ addatur vel auferatur
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vis alia quævis extranea; cognoſci poteſt (per Exempla tertia)
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motus Apſidum qui ex vi illa extranea orietur: & contra. </
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<
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vis qua corpus revolvitur in Ellipſi ſit ut (1/AA), & vis extranea ab
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lata ut
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c
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A, adeoque vis reliqua ut (A-
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c
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A
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4
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/A
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cub.
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); erit (in Exemplis ter
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tiis)
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b
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æqualis 1,
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m
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æqualis 1,
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n
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æqualis 4, adeoque angulus revo
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lutionis inter Apſides æqualis angulo graduum 180 √(1-
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c
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/1-4
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c
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). Po
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natur vim illam extraneam eſſe 357,
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45
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partibus minorem quam vis
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altera qua corpus revolvitur in Ellipſi, id eſt
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c
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eſſe (100/35745), exiſtente A
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vel T æquali 1; & 180 √(1-
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c
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/1-4
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c
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) evadet 180 √(35645/35345), ſeu 180, 7623,
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id eſt, 180
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gr.
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45
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m.
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44
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ſ.
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Igitur corpus de Apſide ſumma diſce
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dens, motu angulari 180
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gr.
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45
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m.
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44.
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ſ.
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perveniet ad Apſidem
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imam, & hoc motu duplicato ad Apſidem ſummam redibit: adeo
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que Apſis ſumma ſingulis revolutionibus progrediendo conficiet
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1
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gr.
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31
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m.
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28
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ſec.
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<
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>Hactenus de Motu corporum in Orbibus quorum plana per
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centrum Virium tranſeunt. </
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<
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mus in planis excentricis. </
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<
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tractant, conſiderare ſolent aſcenſus & deſcenſus ponderum,
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tam obliquos in planis quibuſcunQ.E.D.tis, quam perpendicu
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lares: & pari jure Motus corporum Viribus quibuſcunque cen-</
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