Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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        <div xml:id="echoid-div84" type="section" level="1" n="63">
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            angula, eodem pacto oſtendemus parallelogramma, QF, BH, eſſe
              <lb/>
            æquiangula, vnde concludetur etiam parallelogramma, AN, QF,
              <lb/>
            eſſeinter ſe æquiangula, quod oſtendere opus erat.</s>
            <s xml:id="echoid-s669" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div86" type="section" level="1" n="64">
          <head xml:id="echoid-head75" xml:space="preserve">COROLLARIV M.</head>
          <p style="it">
            <s xml:id="echoid-s670" xml:space="preserve">_S_I autem intelligamus oppoſitarum baſium cylindrici, AF, ita pra-
              <lb/>
            ducta plana, vt ſecentur à plano per latera, AD, PN, QM, RF,
              <lb/>
            ducto in rectis, AR, DF, quarum portiones extra cylindricum manen-
              <lb/>
            tes ſint, PQ, NM, manifeſtum eſt etiam parallelogrammum, PM,
              <lb/>
            quod extra cylindricum conſtituitur, & </s>
            <s xml:id="echoid-s671" xml:space="preserve">quod integratur ex parallelo-
              <lb/>
            grammis, AN, PM, QF, .</s>
            <s xml:id="echoid-s672" xml:space="preserve">i. </s>
            <s xml:id="echoid-s673" xml:space="preserve">AF, eſſe prædictis æquiangulum.</s>
            <s xml:id="echoid-s674" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div87" type="section" level="1" n="65">
          <head xml:id="echoid-head76" xml:space="preserve">THEOREMA VI. PROPOS. IX.</head>
          <p>
            <s xml:id="echoid-s675" xml:space="preserve">SI planum æquidiſtans plano perlatera cylindrici ducto
              <lb/>
            tangat cylindricum, contactus fiet in recta linea, velre-
              <lb/>
            ctis lineis, quæ erunt latera eiuſdem cylindrici: </s>
            <s xml:id="echoid-s676" xml:space="preserve">Vel ſi tan-
              <lb/>
            gat in plano, aut planis, plana contactus erunt parallelo-
              <lb/>
            gramma, æquiangula perlatera ducto.</s>
            <s xml:id="echoid-s677" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s678" xml:space="preserve">Sit cylindricus, AC, per cuius latera ducatur planum in eo pro-
              <lb/>
            ducens parallelogrammum, AC, ſit autem ductum aliud plannm
              <lb/>
              <figure xlink:label="fig-0042-01" xlink:href="fig-0042-01a" number="17">
                <image file="0042-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0042-01"/>
              </figure>
            huic æquidiſtans, quod tangat cy-
              <lb/>
            lindricum, AC. </s>
            <s xml:id="echoid-s679" xml:space="preserve">Dico eiuſdem con-
              <lb/>
            tactum fieri in recta linea, vel rectis
              <lb/>
            lineis, quę erunt latera cylindrici, A
              <lb/>
            C, vel ſi tangat in plano, aut planis,
              <lb/>
            plana contactus eſſe parallelogram-
              <lb/>
            ma, æquiangula ipſi, AC. </s>
            <s xml:id="echoid-s680" xml:space="preserve">Primò
              <lb/>
            igitur non tangat ipſum in plano,
              <lb/>
            quia ergo tangit cylindricum, ali-
              <lb/>
            quid ſuperficiei cylindrici commune
              <lb/>
            eſt ipſi, & </s>
            <s xml:id="echoid-s681" xml:space="preserve">plano tangenti, ſit is pun-
              <lb/>
            ctus, O, exiſtens, & </s>
            <s xml:id="echoid-s682" xml:space="preserve">in plano tangen-
              <lb/>
            te, & </s>
            <s xml:id="echoid-s683" xml:space="preserve">in ſuperficie cylindracea, & </s>
            <s xml:id="echoid-s684" xml:space="preserve">
              <lb/>
            per, O, ſit ductum latus cylindrici,
              <lb/>
            quod ſit, EM. </s>
            <s xml:id="echoid-s685" xml:space="preserve">Dico totum, EM,
              <lb/>
            reperiri in plano tangente cylindri-
              <lb/>
            cumin, O, ęquidiſtante ipſi, AC. </s>
            <s xml:id="echoid-s686" xml:space="preserve">Ducatur per, M, ipſi, BC, pa-
              <lb/>
            rallela, XR, quia ergo, XR, ęquidiſtatipſi, BC, & </s>
            <s xml:id="echoid-s687" xml:space="preserve">EM, ipſi, </s>
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