Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
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                    <arrow.to.target n="note162"/>
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                <p type="margin">
                  <s>
                    <margin.target id="note162"/>
                  DE MOTU
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                  CORPORUM</s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO LXXXI. PROBLEMA XLI.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Stantibus jam poſitis, menſuranda est Area
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                  ABNA.
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                  </s>
                </p>
                <p type="main">
                  <s>A puncto
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  ducatur recta
                    <emph type="italics"/>
                  PH
                    <emph.end type="italics"/>
                  Sphæram tangens in
                    <emph type="italics"/>
                  H,
                    <emph.end type="italics"/>
                  & ad
                    <lb/>
                  axem
                    <emph type="italics"/>
                  PAB
                    <emph.end type="italics"/>
                  demiſſa normali
                    <emph type="italics"/>
                  HI,
                    <emph.end type="italics"/>
                  biſecetur
                    <emph type="italics"/>
                  PI
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  L;
                    <emph.end type="italics"/>
                  & erit
                    <lb/>
                  (per Prop. </s>
                  <s>12, Lib. </s>
                  <s>2. Elem.)
                    <emph type="italics"/>
                  PEq
                    <emph.end type="italics"/>
                  æquale
                    <emph type="italics"/>
                  PSq + SEq
                    <emph.end type="italics"/>
                  +
                    <lb/>
                  2
                    <emph type="italics"/>
                  PSD.
                    <emph.end type="italics"/>
                  Eſt autem
                    <emph type="italics"/>
                  SEq
                    <emph.end type="italics"/>
                  ſeu
                    <emph type="italics"/>
                  SHq
                    <emph.end type="italics"/>
                  (ob ſimilitudinem triangu­
                    <lb/>
                  lorum
                    <emph type="italics"/>
                  SPH, SHI
                    <emph.end type="italics"/>
                  ) æquale rectangulo
                    <emph type="italics"/>
                  PSI.
                    <emph.end type="italics"/>
                  Ergo
                    <emph type="italics"/>
                  PEq
                    <emph.end type="italics"/>
                  æquale
                    <lb/>
                  eſt contento ſub
                    <emph type="italics"/>
                  PS
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  PS+SI
                    <emph.end type="italics"/>
                  +2
                    <emph type="italics"/>
                  SD,
                    <emph.end type="italics"/>
                  hoc eſt, ſub
                    <emph type="italics"/>
                  PS
                    <emph.end type="italics"/>
                  &
                    <lb/>
                  2
                    <emph type="italics"/>
                  LS
                    <emph.end type="italics"/>
                  +2
                    <emph type="italics"/>
                  SD,
                    <emph.end type="italics"/>
                  id eſt, ſub
                    <emph type="italics"/>
                  PS
                    <emph.end type="italics"/>
                  & 2
                    <emph type="italics"/>
                  LD.
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                  Porro
                    <emph type="italics"/>
                  DE quad
                    <emph.end type="italics"/>
                  æquale
                    <lb/>
                  eſt
                    <emph type="italics"/>
                  SEq-SDq,
                    <emph.end type="italics"/>
                  ſeu
                    <emph type="italics"/>
                  SEq -LSq
                    <emph.end type="italics"/>
                  +2
                    <emph type="italics"/>
                  SLD-LDq,
                    <emph.end type="italics"/>
                  id eſt,
                    <lb/>
                  2
                    <emph type="italics"/>
                  SLD-LDq-ALB.
                    <emph.end type="italics"/>
                  Nam
                    <emph type="italics"/>
                  LSq-SEq
                    <emph.end type="italics"/>
                  ſeu
                    <emph type="italics"/>
                  LSq-SAq
                    <emph.end type="italics"/>
                    <lb/>
                    <figure id="id.039.01.214.1.jpg" xlink:href="039/01/214/1.jpg" number="121"/>
                    <lb/>
                  (per Prop. </s>
                  <s>6, Lib. </s>
                  <s>2. Elem.) æquatur rectangulo
                    <emph type="italics"/>
                  ALB.
                    <emph.end type="italics"/>
                  Scriba­
                    <lb/>
                  tur itaque 2
                    <emph type="italics"/>
                  SLD -LDq -ALB
                    <emph.end type="italics"/>
                  pro
                    <emph type="italics"/>
                  DEq
                    <emph.end type="italics"/>
                  ; & quantitas
                    <lb/>
                  (
                    <emph type="italics"/>
                  DEqXPS/PEXV
                    <emph.end type="italics"/>
                  ), quæ ſecundum Corollarium quartum Propoſitionis
                    <lb/>
                  præcedentis eſt ut longitudo ordinatim applicatæ
                    <emph type="italics"/>
                  DN,
                    <emph.end type="italics"/>
                  reſolvet
                    <lb/>
                  ſeſe in tres partes (2
                    <emph type="italics"/>
                  SLDXPS/PE
                    <emph.end type="italics"/>
                  XV)-(
                    <emph type="italics"/>
                  LDqXPS/PE
                    <emph.end type="italics"/>
                  XV)-(
                    <emph type="italics"/>
                  ALBXPS/PE
                    <emph.end type="italics"/>
                  XV):
                    <lb/>
                  ubi ſi pro V ſcribatur ratio inverſa vis centripetæ, & pro
                    <emph type="italics"/>
                  PE
                    <emph.end type="italics"/>
                  me­
                    <lb/>
                  dium proportionale inter
                    <emph type="italics"/>
                  PS
                    <emph.end type="italics"/>
                  & 2
                    <emph type="italics"/>
                  LD
                    <emph.end type="italics"/>
                  ; tres illæ partes evadent
                    <lb/>
                  ordinatim applicatæ linearum totidem curvarum, quarum areæ per
                    <lb/>
                  Methodos vulgatas innoteſcunt.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. F.
                    <emph.end type="italics"/>
                  </s>
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