Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  PROPOSITIO LX. THEOREMA XXIII.
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                    <arrow.to.target n="note127"/>
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                <p type="margin">
                  <s>
                    <margin.target id="note127"/>
                  LIBER
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                  PRIMUS.</s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  St corpora duo
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                  S
                    <emph type="italics"/>
                  &
                    <emph.end type="italics"/>
                  P,
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                  Viribus quadrato diſtantiæ ſuæ reciproee
                    <lb/>
                  proportionalibus ſe mutuo trahentia, revalvuntur circa gravi­
                    <lb/>
                  tatis centrum commune: dico quod Ellipſeos, quam corpus al­
                    <lb/>
                  terutrum
                    <emph.end type="italics"/>
                  P
                    <emph type="italics"/>
                  hoc motu circa alterum
                    <emph.end type="italics"/>
                  S
                    <emph type="italics"/>
                  deſcribit, Axis principa­
                    <lb/>
                  lis erit ad Axem principalem Ellipſeos, quam corpus idem
                    <emph.end type="italics"/>
                  P
                    <lb/>
                    <emph type="italics"/>
                  circa alterum quieſcens
                    <emph.end type="italics"/>
                  S
                    <emph type="italics"/>
                  eodem tempore periodico deſcribere
                    <lb/>
                  poſſet, ut ſumma corporum duorum
                    <emph.end type="italics"/>
                  S+P
                    <emph type="italics"/>
                  ad primam duarum
                    <lb/>
                  medie proportionalium inter hanc ſummam & corpus illud al­
                    <lb/>
                  terum
                    <emph.end type="italics"/>
                  S. </s>
                </p>
                <p type="main">
                  <s>Nam ſi deſcriptæ Ellipſes eſſent ſibi invicem æquales, tempora
                    <lb/>
                  periodica (per Theorema ſuperius) forent in ſubduplicata ratione
                    <lb/>
                  corporis
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  ad ſummam corporum
                    <emph type="italics"/>
                  S+P.
                    <emph.end type="italics"/>
                  Minuatur in hac ratione
                    <lb/>
                  tempus periodicum in Ellipſi poſteriore, & tempora periodica eva­
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                  dent æqualia; Ellipſeos autem axis principalis (per Prop. </s>
                  <s>XV.) minu­
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                  etur in ratione cujus hæc eſt ſeſquiplicata, id eſt in ratione, cujus
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                  ratio
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  S+P
                    <emph.end type="italics"/>
                  eſt triplicata; adeoque erit ad axem principalem
                    <lb/>
                  Ellipſeos alterius, ut prima duarum medie proportionalium inter
                    <lb/>
                    <emph type="italics"/>
                  S+P
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  S+P.
                    <emph.end type="italics"/>
                  Et inverſe, axis principalis Ellipſeos circa
                    <lb/>
                  corpus mobile deſcriptæ erit ad axem principalem deſcriptæ circa
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                  immobile, ut
                    <emph type="italics"/>
                  S+P
                    <emph.end type="italics"/>
                  ad primam duarum medie proportionalium in­
                    <lb/>
                  ter
                    <emph type="italics"/>
                  S+P
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  S. Q.E.D.
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                  </s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO LXI. THEOREMA XXIV.
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                  </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si corpora duo Viribus quibuſvis ſe mutuo trahentia, neque alias
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                  agitata vel impedita, quomodocunque moveantur; motus eo­
                    <lb/>
                  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
                    <lb/>
                  Viribus iiſdem traberetur: Et Virium trahentium eadem erit Lex
                    <lb/>
                  reſpectu diſtantiæ corporum a centro illo communi atque reſpe­
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                  ctu diſtantiæ totius inter corpora.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Nam vires illæ, quibus corpora ſe mutuo trahunt, tendendo
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                  ad corpora, tendunt ad commune gravitatis centrum interme-</s>
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