Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/079.jpg" pagenum="51"/>
                    <arrow.to.target n="note27"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note26"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note27"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Idem aliter.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Inveniatur vis quæ tendit ab Hyperbolæ centro
                    <emph type="italics"/>
                  C.
                    <emph.end type="italics"/>
                  Prodibit hæc
                    <lb/>
                  diſtantiæ
                    <emph type="italics"/>
                  CP
                    <emph.end type="italics"/>
                  proportionalis. </s>
                  <s>Inde vero (per Corol. </s>
                  <s>3 Prop. </s>
                  <s>VII.)
                    <lb/>
                  vis ad umbilicum
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  tendens erit ut (
                    <emph type="italics"/>
                  PEcub/SPq
                    <emph.end type="italics"/>
                  ), hoc eſt, ob datam
                    <emph type="italics"/>
                  PE,
                    <emph.end type="italics"/>
                    <lb/>
                  reciproce ut
                    <emph type="italics"/>
                    <expan abbr="SPq.">SPque</expan>
                  Q.E.I.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Eodem modo demonſtratur quod corpus, hac vi centripeta in
                    <lb/>
                  centrifugam verſa, movebitur in Hyperbola conjugata. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA XIII.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Latus rectum Parabolæ ad verticem quemvis pertinens, eſt quadru­
                    <lb/>
                  plum diſtantiæ verticis illius ab umbilico figuræ.
                    <emph.end type="italics"/>
                  Patet ex Conicis. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA XIV.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Perpendiculum quod ab umbilico Parabolæ ad tangentem ejus demitti­
                    <lb/>
                  tur, medium eſt proportionale inter diſtantias umbilici a puncto con­
                    <lb/>
                  tactus & a vertice principali figuræ.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Sit enim
                    <emph type="italics"/>
                  AQP
                    <emph.end type="italics"/>
                  Parabola,
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  umbilicus ejus,
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  vertex principa­
                    <lb/>
                  lis
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  punctum
                    <lb/>
                    <figure id="id.039.01.079.1.jpg" xlink:href="039/01/079/1.jpg" number="23"/>
                    <lb/>
                  contactus,
                    <emph type="italics"/>
                  PO
                    <emph.end type="italics"/>
                    <lb/>
                  ordinatim ap­
                    <lb/>
                  plicata ad dia­
                    <lb/>
                  metrum prin­
                    <lb/>
                  cipalem,
                    <emph type="italics"/>
                  PM
                    <emph.end type="italics"/>
                    <lb/>
                  tangens dia­
                    <lb/>
                  metro princi­
                    <lb/>
                  pali occurrens
                    <lb/>
                  in
                    <emph type="italics"/>
                  M,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  SN,
                    <emph.end type="italics"/>
                    <lb/>
                  linea perpen­
                    <lb/>
                  dicularis ab umbilico in tangentem. </s>
                  <s>Jungatur
                    <emph type="italics"/>
                  AN,
                    <emph.end type="italics"/>
                  & ob æquales
                    <lb/>
                    <emph type="italics"/>
                  MS
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  SP, MN
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  NP, MA
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  AO,
                    <emph.end type="italics"/>
                  parallelæ erunt rectæ
                    <lb/>
                    <emph type="italics"/>
                  AN
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  OP,
                    <emph.end type="italics"/>
                  & inde triangulum
                    <emph type="italics"/>
                  SAN
                    <emph.end type="italics"/>
                  rectangulum erit ad
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  &
                    <lb/>
                  ſimile triangulis æqualibus
                    <emph type="italics"/>
                  SNM, SNP:
                    <emph.end type="italics"/>
                  Ergo
                    <emph type="italics"/>
                  PS
                    <emph.end type="italics"/>
                  eſt ad
                    <emph type="italics"/>
                  SN,
                    <emph.end type="italics"/>
                    <lb/>
                  ut
                    <emph type="italics"/>
                  SN
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SA. Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1.
                    <emph type="italics"/>
                    <expan abbr="PSq.">PSque</expan>
                    <emph.end type="italics"/>
                  eſt ad
                    <emph type="italics"/>
                    <expan abbr="SNq.">SNque</expan>
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  PS
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SA.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Et ob datam
                    <emph type="italics"/>
                  SA,
                    <emph.end type="italics"/>
                  eſt
                    <emph type="italics"/>
                    <expan abbr="SNq.">SNque</expan>
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  PS.
                    <emph.end type="italics"/>
                  </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
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