Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/139.jpg" pagenum="111"/>
                  Dein junctis
                    <emph type="italics"/>
                  SI, SD,
                    <emph.end type="italics"/>
                  fiant ſegmentis
                    <emph type="italics"/>
                  SEIS, SEDS,
                    <emph.end type="italics"/>
                  ſec­
                    <lb/>
                    <arrow.to.target n="note87"/>
                  tores
                    <emph type="italics"/>
                  HSK, HSk
                    <emph.end type="italics"/>
                  æquales, & per Prop. </s>
                  <s>XXXV, corpus
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  deſcri­
                    <lb/>
                  bet ſpatium
                    <emph type="italics"/>
                  GC
                    <emph.end type="italics"/>
                  eodem Tempore quo corpus
                    <emph type="italics"/>
                  K
                    <emph.end type="italics"/>
                  deſcribere po­
                    <lb/>
                  teſt arcum
                    <emph type="italics"/>
                  Kk. </s>
                  <s>
                    <expan abbr="q.">que</expan>
                  E. F.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note87"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XXXVIII. THEOREMA XII.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Poſito quod Vis centripeta proportionalis ſit altitudini ſeu diſtantiæ lo­
                    <lb/>
                  eorum a centro, dico quod cadentium Tempora, Velocitates & Spa­
                    <lb/>
                  tia deſcripta ſunt arcubus, arcuumque finibus rectis & ſinibus
                    <lb/>
                  verſis reſpective proportionalia.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Cadat corpus de loco quovis
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  ſecun­
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                    <figure id="id.039.01.139.1.jpg" xlink:href="039/01/139/1.jpg" number="87"/>
                    <lb/>
                  dum rectam
                    <emph type="italics"/>
                  AS
                    <emph.end type="italics"/>
                  ; & centro virium
                    <emph type="italics"/>
                  S,
                    <emph.end type="italics"/>
                  in­
                    <lb/>
                  tervallo
                    <emph type="italics"/>
                  AS,
                    <emph.end type="italics"/>
                  deſcribatur Circuli quadrans
                    <lb/>
                    <emph type="italics"/>
                  AE,
                    <emph.end type="italics"/>
                  ſitque
                    <emph type="italics"/>
                  CD
                    <emph.end type="italics"/>
                  ſinus rectus arcus cujuſ­
                    <lb/>
                  vis
                    <emph type="italics"/>
                  AD
                    <emph.end type="italics"/>
                  ; & corpus
                    <emph type="italics"/>
                  A,
                    <emph.end type="italics"/>
                  Tempore
                    <emph type="italics"/>
                  AD,
                    <emph.end type="italics"/>
                  ca­
                    <lb/>
                  dendo deſcribet Spatium
                    <emph type="italics"/>
                  AC,
                    <emph.end type="italics"/>
                  inque loco
                    <lb/>
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  acquiret Velocitatem
                    <emph type="italics"/>
                  CD.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Demonſtratur eodem modo ex Propoſi­
                    <lb/>
                  tione X, quo Propoſitio XXXII, ex Propo­
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                  ſitione XI demonſtrata fuit. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Hinc æqualia ſunt Tempora quibus corpus unum de loco
                    <lb/>
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  cadendo pervenit ad centrum
                    <emph type="italics"/>
                  S,
                    <emph.end type="italics"/>
                  & corpus aliud revolvendo de­
                    <lb/>
                  ſcribit arcum quadrantalem
                    <emph type="italics"/>
                  ADE.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Proinde æqualia ſunt Tempora omnia quibus corpora de
                    <lb/>
                  locis quibuſvis ad uſque centrum cadunt. </s>
                  <s>Nam revolventium tem­
                    <lb/>
                  pora omnia periodica (per Corol. </s>
                  <s>3. Prop. </s>
                  <s>IV.) æquantur. </s>
                </p>
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