Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  DE MOTU
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                  CORPORUM</s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  3. Et concurſus tangentis cujuſvis
                    <emph type="italics"/>
                  PM
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                  cum recta
                    <emph type="italics"/>
                  SN,
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                  quæ ab umbilico in ipſam perpendicularis eſt, incidit in rectam
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                  AN,
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                  quæ Parabolam tangit in vertice principali. </s>
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                  <s>
                    <emph type="center"/>
                  PROPOSITIO. XIII. PROBLEMA VIII.
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                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Moveatur corpus in perimetro Parabolæ: requiritur Lex vis centri­
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                  petæ tendentis ad umbilicum hujus figuræ.
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                    <emph.end type="center"/>
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                <p type="main">
                  <s>Maneat conſtructio Lemmatis, ſitque
                    <emph type="italics"/>
                  P
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                  corpus in perimetro Pa­
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                  rabolæ, & a loco
                    <emph type="italics"/>
                  Q
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                  in quem corpus proxime movetur, age ipſi
                    <emph type="italics"/>
                  SP
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                    <lb/>
                  parallelam
                    <emph type="italics"/>
                  QR
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                  & perpendicularem
                    <emph type="italics"/>
                  QT,
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                  necnon
                    <emph type="italics"/>
                  Qv
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                  tangenti pa­
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                  rallelam & occurrentem tum diametro
                    <emph type="italics"/>
                  YPG
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                  in
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                  v,
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                  tum diſtantiæ
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                    <emph type="italics"/>
                  SP
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                  in
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                  x.
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                  Jam ob ſimilia triangula
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                  Pxv, SPM
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                  & æqualia unius
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                  latera
                    <emph type="italics"/>
                  SM, SP,
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                  æqualia ſunt alterius latera
                    <emph type="italics"/>
                  Px
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                  ſeu
                    <emph type="italics"/>
                  QR
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                  &
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                  Pv.
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                    <lb/>
                  Sed, ex Conicis, quadratum ordinatæ
                    <emph type="italics"/>
                  Qv
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                  æquale eſt rectangulo ſub
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                  latere recto & ſegmento diametri
                    <emph type="italics"/>
                  Pv,
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                  id eſt (per Lem. </s>
                  <s>XIII.) rectangu­
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                  lo 4
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                  PSXPv,
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                  ſeu 4
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                  PSXQR
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                  ; & punctis
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Q
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                  coeuntibus, ra­
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                  tio
                    <emph type="italics"/>
                  Qv
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  Qx
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                  per (per Corol. </s>
                  <s>2 Lem. </s>
                  <s>VII.) fit ratio æqualitatis. </s>
                  <s>Er­
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                  go
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                  Qxquad.
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                  eo
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                    <figure id="id.039.01.080.1.jpg" xlink:href="039/01/080/1.jpg" number="24"/>
                    <lb/>
                  in caſu, æquale
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                  eſt rectangu­
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                  lo 4
                    <emph type="italics"/>
                  PSXQR.
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                    <lb/>
                  Eſt autem (ob
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                  ſimilia trian­
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                  gula
                    <emph type="italics"/>
                  QxT,
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                  SPN)
                    <expan abbr="Qxq.">Qxque</expan>
                    <emph.end type="italics"/>
                    <lb/>
                  ad
                    <emph type="italics"/>
                    <expan abbr="QTq.">QTque</expan>
                    <emph.end type="italics"/>
                  ut
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                    <emph type="italics"/>
                    <expan abbr="PSq.">PSque</expan>
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                    <expan abbr="SNq.">SNque</expan>
                    <emph.end type="italics"/>
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                  hoc eſt (per
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                  Corol. </s>
                  <s>1. Lem. </s>
                  <s>XIV.) ut
                    <emph type="italics"/>
                  PS
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SA,
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                  id eſt ut 4
                    <emph type="italics"/>
                  PSXQR
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                    <lb/>
                  ad 4
                    <emph type="italics"/>
                  SAXQR,
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                  & inde (per Prop. </s>
                  <s>IX. Lib. </s>
                  <s>v. </s>
                  <s>Elem.)
                    <emph type="italics"/>
                    <expan abbr="QTq.">QTque</expan>
                    <emph.end type="italics"/>
                  &
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                  4
                    <emph type="italics"/>
                  SAXQR
                    <emph.end type="italics"/>
                  æquantur. </s>
                  <s>Ducantur hæc æqualia in (
                    <emph type="italics"/>
                  SPq./QR
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                  ), & fiet
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                  (
                    <emph type="italics"/>
                  SPq.XQTq./QR
                    <emph.end type="italics"/>
                  ) æquale
                    <emph type="italics"/>
                  SPq.X4SA:
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                  & propterea (per Corol. </s>
                  <s>1 & 5
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                  Prop. </s>
                  <s>VI.) vis centripeta eſt reciproce ut
                    <emph type="italics"/>
                  SPq.X4SA,
                    <emph.end type="italics"/>
                  id eſt, ob da­
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                  tam 4
                    <emph type="italics"/>
                  SA,
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                  reciproce in duplicata ratione diſtantiæ
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                  SP. Q.E.I.
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                  </s>
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