Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/074.jpg" pagenum="46"/>
                    <arrow.to.target n="note22"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note22"/>
                  DE MOTU
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                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO X. PROBLEMA. V.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Gyretur corpus in Ellipſi: requiritur lex vis centripetæ tendentis ad
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                  centrum Ellipſeos.
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                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Sunto
                    <emph type="italics"/>
                  CA, CB
                    <emph.end type="italics"/>
                  ſemiaxes Ellipſeos;
                    <emph type="italics"/>
                  GP, DK
                    <emph.end type="italics"/>
                  diametri conju­
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                  gatæ;
                    <emph type="italics"/>
                  PF, Qt
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                  perpendicula ad diametros;
                    <emph type="italics"/>
                  Qv
                    <emph.end type="italics"/>
                  ordinatim appli­
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                  cata ad diametrum
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                    <figure id="id.039.01.074.1.jpg" xlink:href="039/01/074/1.jpg" number="20"/>
                    <lb/>
                    <emph type="italics"/>
                  GP
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                  ; & ſi compleatur
                    <lb/>
                  parallelogrammum
                    <lb/>
                    <emph type="italics"/>
                  QvPR,
                    <emph.end type="italics"/>
                  erit (ex CoNI­
                    <lb/>
                  cis)
                    <emph type="italics"/>
                  PvG
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  Qv quad.
                    <emph.end type="italics"/>
                    <lb/>
                  ut
                    <emph type="italics"/>
                  PC quad.
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  CD
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                  quad.
                    <emph.end type="italics"/>
                  & (ob ſimilia
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                  triangula
                    <emph type="italics"/>
                  Qvt, PCF
                    <emph.end type="italics"/>
                  )
                    <lb/>
                    <emph type="italics"/>
                  Qv quad.
                    <emph.end type="italics"/>
                  eſt ad
                    <emph type="italics"/>
                  Qt
                    <lb/>
                  quad.
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  PC quad.
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  PF quad.
                    <emph.end type="italics"/>
                  & conjun­
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                  ctis rationibus,
                    <emph type="italics"/>
                  PvG
                    <emph.end type="italics"/>
                    <lb/>
                  ad
                    <emph type="italics"/>
                  Qt quad.
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  PC
                    <lb/>
                  quad.
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  CD quad.
                    <emph.end type="italics"/>
                    <lb/>
                  &
                    <emph type="italics"/>
                  PC quad.
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PF
                    <lb/>
                  quad.
                    <emph.end type="italics"/>
                  id eſt,
                    <emph type="italics"/>
                  vG
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                  (
                    <emph type="italics"/>
                  Qt quad./Pv
                    <emph.end type="italics"/>
                  ) ut
                    <emph type="italics"/>
                  PC quad.
                    <emph.end type="italics"/>
                    <lb/>
                  ad (
                    <emph type="italics"/>
                  CDqXPFq/PCq
                    <emph.end type="italics"/>
                  ). Scribe
                    <emph type="italics"/>
                  QR
                    <emph.end type="italics"/>
                  pro
                    <emph type="italics"/>
                  Pv,
                    <emph.end type="italics"/>
                  & (per Lemma XII.)
                    <emph type="italics"/>
                  BCXCA
                    <emph.end type="italics"/>
                    <lb/>
                  pro
                    <emph type="italics"/>
                  CDXPF,
                    <emph.end type="italics"/>
                  nec non, punctis
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Q
                    <emph.end type="italics"/>
                  coeuntibus, 2
                    <emph type="italics"/>
                  PC
                    <emph.end type="italics"/>
                  pro
                    <lb/>
                    <emph type="italics"/>
                  vG,
                    <emph.end type="italics"/>
                  & ductis extremis & mediis in ſe mutuo, fiet (
                    <emph type="italics"/>
                  Qt quad.XPCq/QR
                    <emph.end type="italics"/>
                  )
                    <lb/>
                  æquale (2
                    <emph type="italics"/>
                  BCqXCAq/PC
                    <emph.end type="italics"/>
                  ). Eſt ergo (per Corol. </s>
                  <s>5 Prop. </s>
                  <s>VI.) vis centri­
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                  peta reciproce ut (2
                    <emph type="italics"/>
                  BCqXGAq;/PC
                    <emph.end type="italics"/>
                  ) id eſt (ob datum 2
                    <emph type="italics"/>
                  BCqXCAq
                    <emph.end type="italics"/>
                  )
                    <lb/>
                  reciproce ut (1/
                    <emph type="italics"/>
                  PC
                    <emph.end type="italics"/>
                  ); hoc eſt, directe ut diſtantia
                    <emph type="italics"/>
                  PC.
                    <expan abbr="q.">que</expan>
                  E. I.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Idem aliter.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>In
                    <emph type="italics"/>
                  PG
                    <emph.end type="italics"/>
                  ab altera parte puncti
                    <emph type="italics"/>
                  t
                    <emph.end type="italics"/>
                  poſita intelligatur
                    <emph type="italics"/>
                  tu
                    <emph.end type="italics"/>
                  æqualis ipſi
                    <lb/>
                    <emph type="italics"/>
                  tv
                    <emph.end type="italics"/>
                  ; deinde cape
                    <emph type="italics"/>
                  uV
                    <emph.end type="italics"/>
                  quæ ſit ad
                    <emph type="italics"/>
                  vG
                    <emph.end type="italics"/>
                  ut eſt
                    <emph type="italics"/>
                  DC quad.
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PC quad.
                    <emph.end type="italics"/>
                    <lb/>
                  Et quoniam ex Conicis est
                    <emph type="italics"/>
                  Qv quad.
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PvG,
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  DC quad.
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  PC quad:
                    <emph.end type="italics"/>
                  erit
                    <emph type="italics"/>
                  Qv quad.
                    <emph.end type="italics"/>
                  æquale
                    <emph type="italics"/>
                  PvXuV.
                    <emph.end type="italics"/>
                  Unde quadratum chor-</s>
                </p>
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