Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Scholium.
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                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Et ſimili argumento corpus movebitur in Ellipſi vel etiam in
                    <lb/>
                  Hyperbola vel Parabola, vi centripeta quæ ſit reciproce ut cu­
                    <lb/>
                  bus ordinatim applicatæ ad centrum virium maxime longinquum
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                  tendentis. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO IX. PROBLEMA IV.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Gyretur corpus in Spirali
                    <emph.end type="italics"/>
                  PQS
                    <emph type="italics"/>
                  ſecante radios omnes
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                  SP, SQ,
                    <emph type="italics"/>
                  &c.
                    <emph.end type="italics"/>
                    <lb/>
                    <figure id="id.039.01.073.1.jpg" xlink:href="039/01/073/1.jpg" number="19"/>
                    <lb/>
                    <emph type="italics"/>
                  in angulo dato: requiritur Lex
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                  vis centripetæ tendentis ad
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                  centrum Spiralis.
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                  </s>
                </p>
                <p type="main">
                  <s>Detur angulus indefinite par­
                    <lb/>
                  vus
                    <emph type="italics"/>
                  PSQ,
                    <emph.end type="italics"/>
                  & ob datos omnes
                    <lb/>
                  angulos dabitur ſpecie figura
                    <emph type="italics"/>
                  SPQRT.
                    <emph.end type="italics"/>
                  Ergo datur ratio (
                    <emph type="italics"/>
                  QT/QR
                    <emph.end type="italics"/>
                  ), eſtque
                    <lb/>
                  (
                    <emph type="italics"/>
                  QT quad./QR
                    <emph.end type="italics"/>
                  ) ut
                    <emph type="italics"/>
                  QT,
                    <emph.end type="italics"/>
                  hoc eſt ut
                    <emph type="italics"/>
                  SP.
                    <emph.end type="italics"/>
                  Mutetur jam uteunque angulus
                    <emph type="italics"/>
                  PSQ,
                    <emph.end type="italics"/>
                    <lb/>
                  & recta
                    <emph type="italics"/>
                  QR
                    <emph.end type="italics"/>
                  angulum contactus
                    <emph type="italics"/>
                  QPR
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                  ſubtendens mutabitur (per
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                  Lemma XI.) in duplicata ratione ipſius
                    <emph type="italics"/>
                  PR
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  QT.
                    <emph.end type="italics"/>
                  Ergo manebit
                    <lb/>
                  (
                    <emph type="italics"/>
                  QT quad./QR
                    <emph.end type="italics"/>
                  ) eadem quæ prius, hoc eſt ut
                    <emph type="italics"/>
                  SP.
                    <emph.end type="italics"/>
                  Quare (
                    <emph type="italics"/>
                  QTq.XSPq/QR
                    <emph.end type="italics"/>
                  )
                    <lb/>
                  eſt ut
                    <emph type="italics"/>
                  SP cub.
                    <emph.end type="italics"/>
                  adeoque (per Corol. </s>
                  <s>1 & 5 Prop. </s>
                  <s>VI.) vis centripeta eſt
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                  reciproce ut cubus diſtantiæ
                    <emph type="italics"/>
                  SP.
                    <expan abbr="q.">que</expan>
                  E. I.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Idem aliter.
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                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Perpendiculum
                    <emph type="italics"/>
                  SY
                    <emph.end type="italics"/>
                  in tangentem demiſſum, & circuli Spiralem
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                  tangentis chorda
                    <emph type="italics"/>
                  PV
                    <emph.end type="italics"/>
                  ſunt ad altitudinem
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                  in datis rationibus;
                    <lb/>
                  ideoque
                    <emph type="italics"/>
                  SP cub.
                    <emph.end type="italics"/>
                  eſt ut
                    <emph type="italics"/>
                  SYqXPV,
                    <emph.end type="italics"/>
                  hoc eſt (per Corol. </s>
                  <s>3 & 5 Prop.VI.)
                    <lb/>
                  reciproce ut vis centripeta. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA XII.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Parallelogramma omnia, circa datæ Ellipſeos vel Hyperbolæ diametros
                    <lb/>
                  quaſvis conjugatas deſcripta, eſſe inter ſe æqualia.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Conſtat ex Conicis. </s>
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