Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                    <margin.target id="note266"/>
                  DE MOTU
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                  CORPORUM</s>
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                <p type="main">
                  <s>In experimento columnæ quartæ, motus æquales oſcillationibus
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                  535 in aere, & 1 1/5 in aqua amiſſi ſunt. </s>
                  <s>Erant quidem oſcillationes
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                  in aere paulo celeriores quam in aqua. </s>
                  <s>At ſi oſcillationes in aqua
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                  in ea ratione accelerarentur ut motus pendulorum in Medio utro­
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                  que fierent æquiveloces, maneret numerus idem oſcillationum 1 1/5
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                  in aqua, quibus motus idem ac prius amitteretur; ob reſiſtentiam
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                  auctam & ſimul quadratum temporis diminutum in eadem ratione
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                  illa duplicata. </s>
                  <s>Paribus igitur pendulorum velocitatibus motus æ­
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                  quales in aere oſcillationibus 535 & in aqua oſcillationibus 1 1/5 amiſſi
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                  ſunt; ideoque reſiſtentia penduli in aqua eſt ad ejus reſiſtentiam in
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                  aere ut 535 ad 1 1/5. Hæc eſt proportio reſiſtentiarum totarum in
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                  caſu columnæ quartæ.
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                  </s>
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                  <s>Deſignet jam AV+CV differentiam arcuum in deſcenſu & ſub­
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                  ſequente aſcenſu deſcriptorum a Globo, in Aere cum velocitate maxi­
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                  ma V moto; & cum velocitas maxima, in caſu columnæ quartæ, ſit
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                  ad velocitatem maximam in caſu columnæ primæ, ut 1 ad 8; & diffe­
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                  rentia illa arcuum, in caſu columnæ quartæ, ad differentiam in caſu
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                  columnæ primæ ut (2/535) ad (16/85 1/2), ſeu ut 85 1/2 ad 4280: ſeribamus in
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                  his caſibus 1 & 8 pro velocitatibus, atque 85 1/2 & 4280 pro dif­
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                  ferentiis arcuum, & fiet A+C=85 1/2 & 8A+64C=4280 ſeu
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                  A+8C=535; indeque per reductionem æquationum proveniet
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                  7C=449 1/2 & C=(64 1/14) & A=21 1/7: atque adeo reſiſtentia, cum
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                  ſit ut (7/11) AV+1/4 CV
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                  2
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                  , erit ut (13 6/11)V+(48 1/56)V
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                  2
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                  . Quare in caſu co­
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                  lumnæ quartæ, ubi velocitas erat 1, reſiſtentia tota eſt ad partem
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                  ſuam quadrato velocitatis proportionalem, ut (13 6/11)+(48 2/56) ſeu
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                  (61 12/17) ad (48 9/56); & idcirco reſiſtentia penduli in aqua eſt ad reſiſten­
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                  tiæ partem illam in aere quæ quadrato velocitatis proportionalis
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                  eſt, quæque ſola in motibus velocioribus conſideranda venit, ut (61 12/17)
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                  ad (48 9/56) & 535 ad 1 1/5 conjunctim, id eſt, ut 571 ad 1. Si penduli
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                  in aqua oſcillantis filum totum fuiſſet immerſum, reſiſtentia ejus
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                  fuiſſet adhuc major; adeo ut penduli in aere oſcillantis reſiſtentia
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                  illa quæ velocitatis quadrato proportionalis eſt, quæque ſola in
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                  corporibus velocioribus conſideranda venit, ſit ad reſiſtentiam e­
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                  juſdem penduli totius, eadem cum velocitate, in aqua oſcillantis,
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                  ut 800 vel 900 ad 1 circiter, hoc eſt, ut denſitas aquæ ad denſita­
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                  tatem aeris quamproxime.
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                  </s>
                </p>
                <p type="main">
                  <s>In hoc calculo ſumi quoQ.E.D.beret pars illa reſiſtentiæ penduli
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                  in aqua, quæ eſſet ut quadratum velocitatis, ſed (quod mirum for­
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                  te videatur) reſiſtentia in aqua augebatur in ratione velocitatis </s>
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