Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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