Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/054.jpg" pagenum="26"/>
                    <arrow.to.target n="note12"/>
                  centium arcuum
                    <emph type="italics"/>
                  ab, bc, cd, &c.
                    <emph.end type="italics"/>
                  comprehenditur, coincidit ultimo
                    <lb/>
                  cum Figura curvilinea. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note12"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Ut & Figura rectilinea circumſcripta quæ tangentibus
                    <lb/>
                  eorundem arcuum comprehenditur. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  4. Et propterea hæ Figuræ ultimæ (quoad perimetros
                    <emph type="italics"/>
                  acE,
                    <emph.end type="italics"/>
                  )
                    <lb/>
                  non ſunt rectilineæ, ſed rectilinearum limites curvilinei. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA IV.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si in duabus Figuris
                    <emph.end type="italics"/>
                  AacE, PprT,
                    <emph type="italics"/>
                  inſcribantur (ut ſupra) duæ
                    <lb/>
                  parallelogrammorum ſeries, ſitQ.E.I.em amborum numerus, & ubi
                    <lb/>
                  latitudines in infinitum diminuuntur, rationes ultimæ parallelo­
                    <lb/>
                  grammorum in una Figura ad parallelogramma in altera, ſingulorum
                    <lb/>
                  ad fingula, ſint eædem; dico quod Figuræ duæ
                    <emph.end type="italics"/>
                  AacE, PprT,
                    <lb/>
                    <emph type="italics"/>
                  ſunt ad invicem in eadem illa ratione.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <figure id="id.039.01.054.1.jpg" xlink:href="039/01/054/1.jpg" number="7"/>
                <p type="main">
                  <s>Etenim ut ſunt parallelogramma ſingula ad ſingula, ita (compo­
                    <lb/>
                  nendo) fit ſumma omnium ad ſummam omnium, & ita Figura ad
                    <lb/>
                  Figuram; exiſtente nimirum Figura priore (per Lemma 111) ad ſum­
                    <lb/>
                  mam priorem, & Figura poſteriore ad ſummam poſteriorem in ra­
                    <lb/>
                  tione æqualitatis.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  Hinc ſi duæ cujuſcunque generis quantitates in eundem
                    <lb/>
                  partium numerum utcunQ.E.D.vidantur; & partes illæ, ubi numerus
                    <lb/>
                  earum augetur & magnitudo diminuitur in infinitum, datam obti­
                    <lb/>
                  neant rationem ad invicem, prima ad primam, ſecunda ad ſecundam,
                    <lb/>
                  cæteræque ſuo ordine ad cæteras: erunt tota ad invicem in eadem
                    <lb/>
                  illa data ratione. </s>
                  <s>Nam ſi in Lemmatis hujus Figuris ſumantur pa-</s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
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