Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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PROPOSITIO LX. THEOREMA XXIII.
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LIBER
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PRIMUS.</
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St corpora duo
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&
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P,
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Viribus quadrato diſtantiæ ſuæ reciproee
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proportionalibus ſe mutuo trahentia, revalvuntur circa gravi
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tatis centrum commune: dico quod Ellipſeos, quam corpus al
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terutrum
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P
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hoc motu circa alterum
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S
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deſcribit, Axis principa
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lis erit ad Axem principalem Ellipſeos, quam corpus idem
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P
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circa alterum quieſcens
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S
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eodem tempore periodico deſcribere
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poſſet, ut ſumma corporum duorum
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S+P
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ad primam duarum
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medie proportionalium inter hanc ſummam & corpus illud al
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terum
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S. </
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>Nam ſi deſcriptæ Ellipſes eſſent ſibi invicem æquales, tempora
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periodica (per Theorema ſuperius) forent in ſubduplicata ratione
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corporis
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S
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ad ſummam corporum
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S+P.
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Minuatur in hac ratione
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tempus periodicum in Ellipſi poſteriore, & tempora periodica eva
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dent æqualia; Ellipſeos autem axis principalis (per Prop. </
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>XV.) minu
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etur in ratione cujus hæc eſt ſeſquiplicata, id eſt in ratione, cujus
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ratio
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S
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ad
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S+P
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eſt triplicata; adeoque erit ad axem principalem
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Ellipſeos alterius, ut prima duarum medie proportionalium inter
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S+P
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&
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S
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ad
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S+P.
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Et inverſe, axis principalis Ellipſeos circa
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corpus mobile deſcriptæ erit ad axem principalem deſcriptæ circa
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immobile, ut
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S+P
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ad primam duarum medie proportionalium in
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ter
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S+P
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&
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S. Q.E.D.
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PROPOSITIO LXI. THEOREMA XXIV.
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Si corpora duo Viribus quibuſvis ſe mutuo trahentia, neque alias
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agitata vel impedita, quomodocunque moveantur; motus eo
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rum perinde ſe habebunt ac ſi non traherent ſe mutuo, ſed u
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trumque a corpore tertio in communi gravitatis centro conſtituto
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Viribus iiſdem traberetur: Et Virium trahentium eadem erit Lex
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reſpectu diſtantiæ corporum a centro illo communi atque reſpe
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ctu diſtantiæ totius inter corpora.
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>Nam vires illæ, quibus corpora ſe mutuo trahunt, tendendo
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ad corpora, tendunt ad commune gravitatis centrum interme-</
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