Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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        <body>
          <chap>
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              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/093.jpg" pagenum="65"/>
                  tes
                    <emph type="italics"/>
                  TR,
                    <emph.end type="italics"/>
                  vel plura puncta
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  devenietur ſemper ad lineas totidem
                    <lb/>
                    <arrow.to.target n="note41"/>
                    <emph type="italics"/>
                  YH,
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  PH,
                    <emph.end type="italics"/>
                  a dictis punctis
                    <emph type="italics"/>
                  Y
                    <emph.end type="italics"/>
                  vel
                    <lb/>
                    <figure id="id.039.01.093.1.jpg" xlink:href="039/01/093/1.jpg" number="36"/>
                    <lb/>
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  ad umbilicum
                    <emph type="italics"/>
                  H
                    <emph.end type="italics"/>
                  ductas, quæ vel
                    <lb/>
                  æquantur axibus, vel datis longitu­
                    <lb/>
                  dinibus
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                  differunt ab iiſdem, at­
                    <lb/>
                  que adeo quæ vel æquantur ſibi invi­
                    <lb/>
                  cem, vel datas habent differentias; &
                    <lb/>
                  inde, per Lemma ſuperius, datur umbi­
                    <lb/>
                  licus ille alter
                    <emph type="italics"/>
                  H.
                    <emph.end type="italics"/>
                  Habitis autem um­
                    <lb/>
                  bilicis una cum axis longitudine (quæ
                    <lb/>
                  vel eſt
                    <emph type="italics"/>
                  YH
                    <emph.end type="italics"/>
                  ; vel, ſi Trajectoria Ellipſis eſt,
                    <emph type="italics"/>
                  PH+SP
                    <emph.end type="italics"/>
                  ; ſin Hy­
                    <lb/>
                  perbola,
                    <emph type="italics"/>
                  PH-SP
                    <emph.end type="italics"/>
                  ) habetur Trajectoria.
                    <emph type="italics"/>
                  Q.E.I.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note41"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Scholium.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Caſus ubi dantur tria puncta ſic ſolvitur expeditius. </s>
                  <s>Dentur
                    <lb/>
                  puncta
                    <emph type="italics"/>
                  B, C, D.
                    <emph.end type="italics"/>
                  Junctas
                    <emph type="italics"/>
                  BC, CD
                    <emph.end type="italics"/>
                  produc ad
                    <emph type="italics"/>
                  E, F,
                    <emph.end type="italics"/>
                  ut ſit
                    <emph type="italics"/>
                  EB
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  EC
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  SB
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SC,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  FC
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  FD
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  SC
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SD.
                    <emph.end type="italics"/>
                  Ad
                    <emph type="italics"/>
                  EF
                    <emph.end type="italics"/>
                  ductam
                    <lb/>
                  & productam demitte normales
                    <emph type="italics"/>
                  SG, BH,
                    <emph.end type="italics"/>
                  inque
                    <emph type="italics"/>
                  GS
                    <emph.end type="italics"/>
                  infinite
                    <lb/>
                  producta cape
                    <emph type="italics"/>
                  GA
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AS
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Ga
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  aS
                    <emph.end type="italics"/>
                  ut eſt
                    <emph type="italics"/>
                  HB
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  BS
                    <emph.end type="italics"/>
                  ; & erit
                    <lb/>
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  vertex, &
                    <emph type="italics"/>
                  Aa
                    <emph.end type="italics"/>
                  axis principalis Trajectoriæ: quæ, perinde ut
                    <emph type="italics"/>
                  GA
                    <emph.end type="italics"/>
                    <lb/>
                  major, æqualis, vel minor fuerit quam
                    <emph type="italics"/>
                  AS,
                    <emph.end type="italics"/>
                  erit Ellipſis, Parabola
                    <lb/>
                  vel Hyperbola; pun­
                    <lb/>
                    <figure id="id.039.01.093.2.jpg" xlink:href="039/01/093/2.jpg" number="37"/>
                    <lb/>
                  cto
                    <emph type="italics"/>
                  a
                    <emph.end type="italics"/>
                  in primo caſu
                    <lb/>
                  cadente ad eandem
                    <lb/>
                  partem lineæ
                    <emph type="italics"/>
                  GF
                    <emph.end type="italics"/>
                    <lb/>
                  cum puncto
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  ; in
                    <lb/>
                  ſecundo caſu abeunte
                    <lb/>
                  in infinitum; in tertio
                    <lb/>
                  cadente ad contrari­
                    <lb/>
                  am partem lineæ
                    <emph type="italics"/>
                  GF.
                    <emph.end type="italics"/>
                    <lb/>
                  Nam ſi demittantur
                    <lb/>
                  ad
                    <emph type="italics"/>
                  GF
                    <emph.end type="italics"/>
                  perpendicula
                    <lb/>
                    <emph type="italics"/>
                  CI, DK
                    <emph.end type="italics"/>
                  ; erit
                    <emph type="italics"/>
                  IC
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  HB
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  EC
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  EB,
                    <emph.end type="italics"/>
                  hoc eſt, ut
                    <emph type="italics"/>
                  SC
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SB
                    <emph.end type="italics"/>
                  ; & vi­
                    <lb/>
                  ciſſim
                    <emph type="italics"/>
                  IC
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SC
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  HB
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SB
                    <emph.end type="italics"/>
                  ſive ut
                    <emph type="italics"/>
                  GA
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SA.
                    <emph.end type="italics"/>
                  Et ſimili argumento
                    <lb/>
                  probabitur eſſe
                    <emph type="italics"/>
                  KD
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SD
                    <emph.end type="italics"/>
                  in eadem ratione. </s>
                  <s>Jacent ergo puncta
                    <emph type="italics"/>
                  B,
                    <lb/>
                  C, D
                    <emph.end type="italics"/>
                  in Coniſectione circa umbilicum
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  ita deſcripta, ut rectæ omnes
                    <lb/>
                  ab umbilico
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  ad ſingula Sectionis puncta ductæ, ſint ad perpendicula
                    <lb/>
                  a punctis iiſdem ad rectam
                    <emph type="italics"/>
                  GF
                    <emph.end type="italics"/>
                  demiſſa in data illa ratione. </s>
                </p>
                <p type="main">
                  <s>Methodo haud multum diſſimili hujus problematis ſolutionem
                    <lb/>
                  tradit Clariſſimus Geometra
                    <emph type="italics"/>
                  de la Hire,
                    <emph.end type="italics"/>
                  Conieorum ſuorum Lib. </s>
                  <s>
                    <lb/>
                  VIII. Prop. XXV. </s>
                </p>
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            </subchap1>
          </chap>
        </body>
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    </archimedes>
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