Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/098.jpg" pagenum="70"/>
                    <arrow.to.target n="note46"/>
                  ad
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                  PS,
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                  adeoque ratio
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                  PQ
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                  ad
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                    <figure id="id.039.01.098.1.jpg" xlink:href="039/01/098/1.jpg" number="43"/>
                    <lb/>
                    <emph type="italics"/>
                  PS.
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                  Auferendo hanca data ra­
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                  tione
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                  PQXPR
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                  ad
                    <emph type="italics"/>
                  PSXPT,
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                    <lb/>
                  dabitur ratio
                    <emph type="italics"/>
                  PR
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                  ad
                    <emph type="italics"/>
                  PT,
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                  &
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                  addendo datas rationes
                    <emph type="italics"/>
                  PI
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                  ad
                    <lb/>
                    <emph type="italics"/>
                  PR,
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                  &
                    <emph type="italics"/>
                  PT
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                  ad
                    <emph type="italics"/>
                  PH
                    <emph.end type="italics"/>
                  dabitur
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                  ratio
                    <emph type="italics"/>
                  PI
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PH
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                  atque adeo
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                  punctum
                    <emph type="italics"/>
                  P. Q.E.I.
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                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note46"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  1. Hinc etiam ad Loci
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                  punctorum infinitorum
                    <emph type="italics"/>
                  P
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                  pun­
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                  ctum quodvis
                    <emph type="italics"/>
                  D
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                  tangens duci
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                  poteſt. </s>
                  <s>Nam chorda
                    <emph type="italics"/>
                  PD
                    <emph.end type="italics"/>
                  ubi
                    <lb/>
                  puncta
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  ac
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  conveniunt, hoc
                    <lb/>
                  eſt, ubi
                    <emph type="italics"/>
                  AH
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                  ducitur per punctum
                    <emph type="italics"/>
                  D,
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                  tangens evadit. </s>
                  <s>Quo in caſu,
                    <lb/>
                  ultima ratio evaneſcentium
                    <emph type="italics"/>
                  IP
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  PH
                    <emph.end type="italics"/>
                  invenietur ut ſupra. </s>
                  <s>Ipſi
                    <lb/>
                  igitur
                    <emph type="italics"/>
                  AD
                    <emph.end type="italics"/>
                  due parallelam
                    <emph type="italics"/>
                  CF,
                    <emph.end type="italics"/>
                  occurrentem
                    <emph type="italics"/>
                  BD
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  F,
                    <emph.end type="italics"/>
                  & in ea ul­
                    <lb/>
                  tima ratione ſectam in
                    <emph type="italics"/>
                  E,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  DE
                    <emph.end type="italics"/>
                  tangens erit, propterea quod
                    <emph type="italics"/>
                  CF
                    <emph.end type="italics"/>
                    <lb/>
                  & evaneſcens
                    <emph type="italics"/>
                  IH
                    <emph.end type="italics"/>
                  parallelæ ſunt, & in
                    <emph type="italics"/>
                  E
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  fimiliter ſectæ. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Hinc etiam Locus punctorum omnium
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  definiri poteſt. </s>
                  <s>
                    <lb/>
                  Per quodvis punctorum
                    <emph type="italics"/>
                  A, B, C, D,
                    <emph.end type="italics"/>
                  puta
                    <emph type="italics"/>
                  A,
                    <emph.end type="italics"/>
                  duc Loci tangentem
                    <lb/>
                    <emph type="italics"/>
                  AE
                    <emph.end type="italics"/>
                  & per aliud quodvis punctum
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  duc tangenti parallelam
                    <emph type="italics"/>
                  BF
                    <emph.end type="italics"/>
                    <lb/>
                  occurrentem Loco in
                    <emph type="italics"/>
                  F.
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                  Invenie­
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                    <figure id="id.039.01.098.2.jpg" xlink:href="039/01/098/2.jpg" number="44"/>
                    <lb/>
                  tur autem punctum
                    <emph type="italics"/>
                  F
                    <emph.end type="italics"/>
                  per Lem. </s>
                  <s>XIX. </s>
                  <s>
                    <lb/>
                  Biſeca
                    <emph type="italics"/>
                  BF
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  G,
                    <emph.end type="italics"/>
                  & acta indefinita
                    <lb/>
                    <emph type="italics"/>
                  AG
                    <emph.end type="italics"/>
                  erit poſitio diametri ad quam
                    <lb/>
                    <emph type="italics"/>
                  BG
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  FG
                    <emph.end type="italics"/>
                  ordinatim applicantur. </s>
                  <s>
                    <lb/>
                  Hæc
                    <emph type="italics"/>
                  AG
                    <emph.end type="italics"/>
                  occurrat Loco in
                    <emph type="italics"/>
                  H,
                    <emph.end type="italics"/>
                  &
                    <lb/>
                  erit
                    <emph type="italics"/>
                  AH
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                  diameter ſive latus tranſ­
                    <lb/>
                  verſum, ad quod latus rectum erit
                    <lb/>
                  ut
                    <emph type="italics"/>
                    <expan abbr="BGq.">BGque</expan>
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AGH.
                    <emph.end type="italics"/>
                  Si
                    <emph type="italics"/>
                  AG
                    <emph.end type="italics"/>
                  nullibi
                    <lb/>
                  occurrit Loco, linea
                    <emph type="italics"/>
                  AH
                    <emph.end type="italics"/>
                  exiſtente
                    <lb/>
                  infinita, Locus erit Parabola & la­
                    <lb/>
                  rum rectum ejus ad diametrum
                    <emph type="italics"/>
                  AG
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                    <lb/>
                  pertinens erit (
                    <emph type="italics"/>
                  BGq./AG
                    <emph.end type="italics"/>
                  ) Sin ea alicubi occurrit, Locus Hyperbola erit
                    <lb/>
                  ubi puncta
                    <emph type="italics"/>
                  A
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                  &
                    <emph type="italics"/>
                  H
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                  ſita ſunt ad eaſdem partes ipſius
                    <emph type="italics"/>
                  G:
                    <emph.end type="italics"/>
                  & Ellipſis,
                    <lb/>
                  ubi
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  intermedium eſt, niſi forte angulus
                    <emph type="italics"/>
                  AGB
                    <emph.end type="italics"/>
                  rectus ſit & inſuper
                    <lb/>
                    <emph type="italics"/>
                  BG quad.
                    <emph.end type="italics"/>
                  æquale rectangulo
                    <emph type="italics"/>
                  AGH,
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                  quo in caſu Circulus habebitur. </s>
                </p>
                <p type="main">
                  <s>AtQ.E.I.a Problematis Veterum de quatuor lineis ab
                    <emph type="italics"/>
                  Euclide
                    <emph.end type="italics"/>
                  incæp­
                    <lb/>
                  ti & ab
                    <emph type="italics"/>
                  Apollonio
                    <emph.end type="italics"/>
                  continuati non calculus, ſed compoſitio Geometri­
                    <lb/>
                  ca, qualem Veteres quærebant, in hoc Corollario exhibetur. </s>
                </p>
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