Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/087.jpg" pagenum="59"/>
                    <arrow.to.target n="note35"/>
                  </s>
                </p>
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              <subchap2>
                <p type="margin">
                  <s>
                    <margin.target id="note35"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  SECTIO IV.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  De Inventione Orbium Elliptieorum, Parabolieorum & Hyperbolico­
                    <lb/>
                  rum ex umbilico dato.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA XV.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si ab Ellipſeos vel Hyperbolæ cujuſvis umbilicis duobus
                    <emph.end type="italics"/>
                  S, H,
                    <emph type="italics"/>
                  ad
                    <lb/>
                  punctum quodvis tertium
                    <emph.end type="italics"/>
                  V
                    <emph type="italics"/>
                  inflectantur rectæ duæ
                    <emph.end type="italics"/>
                  SV, HV,
                    <lb/>
                    <emph type="italics"/>
                  quarum una
                    <emph.end type="italics"/>
                  HV
                    <emph type="italics"/>
                  æqualis ſit axi principali figuræ, altera
                    <emph.end type="italics"/>
                  SV
                    <emph type="italics"/>
                  a
                    <lb/>
                  perpendiculo
                    <emph.end type="italics"/>
                  TR
                    <emph type="italics"/>
                  in ſe demiſſo bi-
                    <emph.end type="italics"/>
                    <lb/>
                    <figure id="id.039.01.087.1.jpg" xlink:href="039/01/087/1.jpg" number="28"/>
                    <lb/>
                    <emph type="italics"/>
                  ſecetur in
                    <emph.end type="italics"/>
                  T;
                    <emph type="italics"/>
                  perpendiculum illud
                    <emph.end type="italics"/>
                    <lb/>
                  TR
                    <emph type="italics"/>
                  ſectionem Conicam alicubi tan­
                    <lb/>
                  get: & contra, ſi tangit, erit
                    <emph.end type="italics"/>
                  HV
                    <lb/>
                    <emph type="italics"/>
                  æqualis axi principali figuræ.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Secet enim perpendiculum
                    <emph type="italics"/>
                  TR
                    <emph.end type="italics"/>
                  re­
                    <lb/>
                  ctam
                    <emph type="italics"/>
                  HV
                    <emph.end type="italics"/>
                  productam, ſi opus fuerit,
                    <lb/>
                  in
                    <emph type="italics"/>
                  R
                    <emph.end type="italics"/>
                  ; & jungatur
                    <emph type="italics"/>
                  SR.
                    <emph.end type="italics"/>
                  Ob æquales
                    <lb/>
                    <emph type="italics"/>
                  TS, TV,
                    <emph.end type="italics"/>
                  æquales erunt & rectæ
                    <emph type="italics"/>
                  SR, VR
                    <emph.end type="italics"/>
                  & anguli
                    <emph type="italics"/>
                  TRS, TRV.
                    <emph.end type="italics"/>
                    <lb/>
                  Unde punctum
                    <emph type="italics"/>
                  R
                    <emph.end type="italics"/>
                  erit ad Sectionem Conicam, & perpendiculum
                    <lb/>
                    <emph type="italics"/>
                  TR
                    <emph.end type="italics"/>
                  tanget eandem: & contra.
                    <emph type="italics"/>
                  Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XVIII. PROBLEMA X.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Datis umbilico & axibus principalibus deſcribere Trajectorias Ellipti­
                    <lb/>
                  cas & Hyperbolicas, quæ tranſibunt per puncta data, & rectas po­
                    <lb/>
                  ſitione datas contingent.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Sit
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  communis umbilicus figurarum;
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  longitudo axis prin­
                    <lb/>
                  cipalis Trajectoriæ cujuſvis;
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  punctum per quod Trajectoria de­
                    <lb/>
                  bet tranſire; &
                    <emph type="italics"/>
                  TR
                    <emph.end type="italics"/>
                  recta quam debet tangere. </s>
                  <s>Centro
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  inter­
                    <lb/>
                  vallo
                    <emph type="italics"/>
                  AB-SP,
                    <emph.end type="italics"/>
                  ſi orbita ſit Ellipſis, vel
                    <emph type="italics"/>
                  AB+SP,
                    <emph.end type="italics"/>
                  ſi ea ſit Hy­
                    <lb/>
                  perbola, deſcribatur circulus
                    <emph type="italics"/>
                  HG.
                    <emph.end type="italics"/>
                  Ad tangentem
                    <emph type="italics"/>
                  TR
                    <emph.end type="italics"/>
                  demittatur
                    <lb/>
                  perpendiculum
                    <emph type="italics"/>
                  ST,
                    <emph.end type="italics"/>
                  & producatur idem ad
                    <emph type="italics"/>
                  V,
                    <emph.end type="italics"/>
                  ut ſit
                    <emph type="italics"/>
                  TV
                    <emph.end type="italics"/>
                  æqualis
                    <lb/>
                    <emph type="italics"/>
                  ST
                    <emph.end type="italics"/>
                  ; centroque
                    <emph type="italics"/>
                  V
                    <emph.end type="italics"/>
                  & intervallo
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  deſcribatur circulus
                    <emph type="italics"/>
                  FH.
                    <emph.end type="italics"/>
                  Hac </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
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