Newton, Isaac, Philosophia naturalis principia mathematica, 1713
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                  DE MOTU
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                  CORPORUM</s>
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                  PROPOSITIO X. PROBLEMA. V.
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                  <s>
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                  Gyretur corpus in Ellipſi: requiritur lex vis centripetæ tendentis ad
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                  centrum Ellipſeos.
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                  <s>Sunto
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                  CA, CB
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                  ſemiaxes Ellipſeos;
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                  GP, DK
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                  diametri conju­
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                  gatæ;
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                  PF, Qt
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                  perpendicula ad diametros;
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                  Qv
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                  ordinatim appli­
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                  cata ad diametrum
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                    <emph type="italics"/>
                  GP
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                  ; & ſi compleatur
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                  parallelogrammum
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                    <emph type="italics"/>
                  QvPR,
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                  erit (ex CoNI­
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                  cis)
                    <emph type="italics"/>
                  PvG
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                  ad
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                  Qv quad.
                    <emph.end type="italics"/>
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                  ut
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                  PC quad.
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                  ad
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                  CD
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                  quad.
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                  & (ob ſimilia
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                  triangula
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                  Qvt, PCF
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                  )
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                    <emph type="italics"/>
                  Qv quad.
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                  eſt ad
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                  Qt
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                  quad.
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  PC quad.
                    <emph.end type="italics"/>
                  ad
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                    <emph type="italics"/>
                  PF quad.
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                  & conjun­
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                  ctis rationibus,
                    <emph type="italics"/>
                  PvG
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                    <lb/>
                  ad
                    <emph type="italics"/>
                  Qt quad.
                    <emph.end type="italics"/>
                  ut
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                  PC
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                  quad.
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                  ad
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                  CD quad.
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                  &
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                  PC quad.
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                  ad
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                  PF
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                  quad.
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                  id eſt,
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                  vG
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                  ad
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                  (
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                  Qt quad./Pv
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                  ) ut
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                  PC quad.
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                  ad (
                    <emph type="italics"/>
                  CDqXPFq/PCq
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                  ). Scribe
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                  QR
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                  pro
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                  Pv,
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                  & (per Lemma XII.)
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                  BCXCA
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                  pro
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                  CDXPF,
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                  nec non, punctis
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                  P
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                  &
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                  Q
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                  coeuntibus, 2
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                  PC
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                  pro
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                  vG,
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                  & ductis extremis & mediis in ſe mutuo, fiet (
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                  Qt quad.XPCq/QR
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                  )
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                  æquale (2
                    <emph type="italics"/>
                  BCqXCAq/PC
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                  ). Eſt ergo (per Corol. </s>
                  <s>5 Prop. </s>
                  <s>VI.) vis centri­
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                  peta reciproce ut (2
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                  BCqXGAq;/PC
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                  ) id eſt (ob datum 2
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                  BCqXCAq
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                  )
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                  reciproce ut (1/
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                  PC
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                  ); hoc eſt, directe ut diſtantia
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                  PC.
                    <expan abbr="q.">que</expan>
                  E. I.
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                  Idem aliter.
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                <p type="main">
                  <s>In
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                  PG
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                  ab altera parte puncti
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                  t
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                  poſita intelligatur
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                  tu
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                  æqualis ipſi
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                    <emph type="italics"/>
                  tv
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                  ; deinde cape
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                  uV
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                  quæ ſit ad
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                  vG
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                  ut eſt
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                  DC quad.
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                  ad
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                  PC quad.
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                  Et quoniam ex Conicis est
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                  Qv quad.
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                  ad
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                  PvG,
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                  ut
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                  DC quad.
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                  ad
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                  PC quad:
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                  erit
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                  Qv quad.
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                  æquale
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                  PvXuV.
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                  Unde quadratum chor-</s>
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