Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <pb xlink:href="039/01/303.jpg" pagenum="275"/>
                <p type="margin">
                  <s>
                    <margin.target id="note250"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  Igitur motus velociſſimus in Medio reſiſtente non incidit
                    <lb/>
                    <arrow.to.target n="note251"/>
                  in punctum infimum
                    <emph type="italics"/>
                  C,
                    <emph.end type="italics"/>
                  ſed reperitur in puncto illo
                    <emph type="italics"/>
                  O,
                    <emph.end type="italics"/>
                  quo arcus
                    <lb/>
                  totus deſcriptus
                    <emph type="italics"/>
                  aB
                    <emph.end type="italics"/>
                  biſecatur. </s>
                  <s>Et corpus ſubinde pergendo ad
                    <emph type="italics"/>
                  a,
                    <emph.end type="italics"/>
                    <lb/>
                  iiſdem gradibus retardatur quibus antea accelerabatur in deſcenſu
                    <lb/>
                  ſuo a
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  O.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note251"/>
                  LIBER
                    <lb/>
                  SECUNDUS.</s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XXVI. THEOREMA XXI.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corporum Funependulorum, quibus reſiſtitur in ratione velocitatum,
                    <lb/>
                  oſcillationes in Cycloide ſunt Iſochronæ.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Nam ſi corpora duo, a centris ſuſpenſionum æqualiter diſtantia,
                    <lb/>
                  oſcillando deſcribant arcus inæquales, & velocitates in arcuum par­
                    <lb/>
                  tibus correſpondentibus ſint ad invicem ut arcus toti: reſiſtentiæ
                    <lb/>
                  velocitatibus proportionales, erunt etiam ad invicem ut iidem ar­
                    <lb/>
                  cus. </s>
                  <s>Proinde ſi viribus motricibus a gravitate oriundis, quæ ſint
                    <lb/>
                  ut iidem arcus, auferantur vel addantur hæ reſiſtentiæ, erunt dif­
                    <lb/>
                  ferentiæ vel ſummæ ad invicem in eadem arcuum ratione: cumque
                    <lb/>
                  velocitatum incrementa vel decrementa ſint ut hæ differentiæ vel
                    <lb/>
                  ſummæ, velocitates ſemper erunt ut arcus toti: Igitur velocitates,
                    <lb/>
                  ſi ſint in aliquo caſu ut arcus toti, manebunt ſemper in eadem ra­
                    <lb/>
                  tione. </s>
                  <s>Sed in principio motus, ubi corpora incipiunt deſcendere
                    <lb/>
                  & arcus illos deſcribere, vires, cum ſint arcubus proportionales, ge­
                    <lb/>
                  nerabunt velocitates arcubus proportionales. </s>
                  <s>Ergo velocitates ſem­
                    <lb/>
                  per erunt ut arcus toti deſcribendi, & propterea arcus illi ſimul de­
                    <lb/>
                  ſcribentur.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XXVII. THEOREMA XXII.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si Corporibus Funependulis reſiſtitur in duplicata ratione veloci­
                    <lb/>
                  tatum, differentiæ inter tempora oſcillationum in Medio reſi­
                    <lb/>
                  ſtente ac tempora oſcillationum in ejuſdem gravitatis ſpecificæ
                    <lb/>
                  Medio non reſiſtente, erunt arcubus oſcillando deſcriptis pro­
                    <lb/>
                  portionales, quam proxime.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Nam pendulis æqualibus in Medio reſiſtente deſcribantur arcus
                    <lb/>
                  inæquales A, B; & reſiſtentia corporis in arcu A, erit ad reſiſten­
                    <lb/>
                  tiam corporis in parte correſpondente arcus B, in duplicata ratio­
                    <lb/>
                  ne velocitatum, id eſt, ut AA ad BB, quam proxime. </s>
                  <s>Si reſi-</s>
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