Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
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                    <arrow.to.target n="note28"/>
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                  <s>
                    <margin.target id="note28"/>
                  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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                    <lb/>
                  quæ ab umbilico in ipſam perpendicularis eſt, incidit in rectam
                    <emph type="italics"/>
                  AN,
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                  quæ Parabolam tangit in vertice principali. </s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO. XIII. PROBLEMA VIII.
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                  </s>
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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"/>
                  </s>
                </p>
                <p type="main">
                  <s>Maneat conſtructio Lemmatis, ſitque
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  corpus in perimetro Pa­
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                  rabolæ, & a loco
                    <emph type="italics"/>
                  Q
                    <emph.end type="italics"/>
                  in quem corpus proxime movetur, age ipſi
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                    <lb/>
                  parallelam
                    <emph type="italics"/>
                  QR
                    <emph.end type="italics"/>
                  & perpendicularem
                    <emph type="italics"/>
                  QT,
                    <emph.end type="italics"/>
                  necnon
                    <emph type="italics"/>
                  Qv
                    <emph.end type="italics"/>
                  tangenti pa­
                    <lb/>
                  rallelam & occurrentem tum diametro
                    <emph type="italics"/>
                  YPG
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  v,
                    <emph.end type="italics"/>
                  tum diſtantiæ
                    <lb/>
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  x.
                    <emph.end type="italics"/>
                  Jam ob ſimilia triangula
                    <emph type="italics"/>
                  Pxv, SPM
                    <emph.end type="italics"/>
                  & æqualia unius
                    <lb/>
                  latera
                    <emph type="italics"/>
                  SM, SP,
                    <emph.end type="italics"/>
                  æqualia ſunt alterius latera
                    <emph type="italics"/>
                  Px
                    <emph.end type="italics"/>
                  ſeu
                    <emph type="italics"/>
                  QR
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Pv.
                    <emph.end type="italics"/>
                    <lb/>
                  Sed, ex Conicis, quadratum ordinatæ
                    <emph type="italics"/>
                  Qv
                    <emph.end type="italics"/>
                  æquale eſt rectangulo ſub
                    <lb/>
                  latere recto & ſegmento diametri
                    <emph type="italics"/>
                  Pv,
                    <emph.end type="italics"/>
                  id eſt (per Lem. </s>
                  <s>XIII.) rectangu­
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                  lo 4
                    <emph type="italics"/>
                  PSXPv,
                    <emph.end type="italics"/>
                  ſeu 4
                    <emph type="italics"/>
                  PSXQR
                    <emph.end type="italics"/>
                  ; & punctis
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Q
                    <emph.end type="italics"/>
                  coeuntibus, ra­
                    <lb/>
                  tio
                    <emph type="italics"/>
                  Qv
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  Qx
                    <emph.end type="italics"/>
                  per (per Corol. </s>
                  <s>2 Lem. </s>
                  <s>VII.) fit ratio æqualitatis. </s>
                  <s>Er­
                    <lb/>
                  go
                    <emph type="italics"/>
                  Qxquad.
                    <emph.end type="italics"/>
                  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.
                    <emph.end type="italics"/>
                    <lb/>
                  Eſt autem (ob
                    <lb/>
                  ſimilia trian­
                    <lb/>
                  gula
                    <emph type="italics"/>
                  QxT,
                    <lb/>
                  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
                    <lb/>
                    <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"/>
                    <lb/>
                  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,
                    <emph.end type="italics"/>
                  id eſt ut 4
                    <emph type="italics"/>
                  PSXQR
                    <emph.end type="italics"/>
                    <lb/>
                  ad 4
                    <emph type="italics"/>
                  SAXQR,
                    <emph.end type="italics"/>
                  & 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"/>
                  &
                    <lb/>
                  4
                    <emph type="italics"/>
                  SAXQR
                    <emph.end type="italics"/>
                  æquantur. </s>
                  <s>Ducantur hæc æqualia in (
                    <emph type="italics"/>
                  SPq./QR
                    <emph.end type="italics"/>
                  ), & fiet
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                  (
                    <emph type="italics"/>
                  SPq.XQTq./QR
                    <emph.end type="italics"/>
                  ) æquale
                    <emph type="italics"/>
                  SPq.X4SA:
                    <emph.end type="italics"/>
                  & 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,
                    <emph.end type="italics"/>
                  reciproce in duplicata ratione diſtantiæ
                    <emph type="italics"/>
                  SP. Q.E.I.
                    <emph.end type="italics"/>
                  </s>
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