Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/128.jpg" pagenum="100"/>
                    <arrow.to.target n="note76"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note76"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Corollarium.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Hinc area Ellipſeos, quæ radio ab umbilico ad corpus mobile
                    <lb/>
                  ducto deſcribitur, non prodit ex dato tempore, per æquationem
                    <lb/>
                  finitam; & propterea per deſcriptionem Curvarum Geometrice ra­
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                  tionalium determinari nequit. </s>
                  <s>Curvas Geometrice rationales ap­
                    <lb/>
                  pello quarum puncta omnia per longitudines æquationibus defiNI­
                    <lb/>
                  tas, id eſt, per longitudinum rationes complicatas, determinari
                    <lb/>
                  poſſunt; cæteraſque (ut Spirales, Quadratrices, Trochoides) Geo­
                    <lb/>
                  metrice irrationales. </s>
                  <s>Nam longitudines quæ ſunt vel non ſunt ut
                    <lb/>
                  numerus ad numerum (quemadmodum in decimo Elementorum)
                    <lb/>
                  ſunt Arithmetice rationales vel irrationales. </s>
                  <s>Aream igitur Ellipſeos
                    <lb/>
                  tempori proportionalem abſcindo per Curvam Geometrice irratio­
                    <lb/>
                  nalem ut ſequitur. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XXXI. PROBLEMA XXIII.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Corporis in data Trajectoria Elliptica moti invenire locum ad
                    <lb/>
                  tempus aſſignatum.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Ellipſeos
                    <emph type="italics"/>
                  APB
                    <emph.end type="italics"/>
                  ſit
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  vertex principalis,
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  umbilicus, &
                    <emph type="italics"/>
                  O
                    <emph.end type="italics"/>
                    <lb/>
                  centrum, ſitque
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  corporis locus inveniendus. </s>
                  <s>Produc
                    <emph type="italics"/>
                  OA
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  G,
                    <emph.end type="italics"/>
                    <lb/>
                  ut ſit
                    <emph type="italics"/>
                  OG
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  OA
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  OA
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  OS.
                    <emph.end type="italics"/>
                  Erige perpendiculum
                    <emph type="italics"/>
                  GH,
                    <emph.end type="italics"/>
                  centroque
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                    <figure id="id.039.01.128.1.jpg" xlink:href="039/01/128/1.jpg" number="74"/>
                    <lb/>
                    <emph type="italics"/>
                  O
                    <emph.end type="italics"/>
                  & intervallo
                    <emph type="italics"/>
                  OG
                    <emph.end type="italics"/>
                  deſcribe circulum
                    <emph type="italics"/>
                  EFG,
                    <emph.end type="italics"/>
                  & ſuper regula
                    <emph type="italics"/>
                  GH,
                    <emph.end type="italics"/>
                    <lb/>
                  ceu fundo, progrediatur Rota
                    <emph type="italics"/>
                  GEF
                    <emph.end type="italics"/>
                  revolvendo circa axem
                    <lb/>
                  ſuum, & interea puncto ſuo
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  deſcribendo Trochoidem
                    <emph type="italics"/>
                  ALI.
                    <emph.end type="italics"/>
                  </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
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