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

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          <p>
            <s xml:id="echoid-s614" xml:space="preserve">
              <pb o="19" file="0039" n="39" rhead="LIBER I."/>
            lela ipſi, HM, quæ ſit regula lateris cylindrici. </s>
            <s xml:id="echoid-s615" xml:space="preserve">Dico eam eſſe la-
              <lb/>
            tus huius cylindrici: </s>
            <s xml:id="echoid-s616" xml:space="preserve">Intelligatur per punctum, F, ductum latus cy-
              <lb/>
              <figure xlink:label="fig-0039-01" xlink:href="fig-0039-01a" number="13">
                <image file="0039-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0039-01"/>
              </figure>
            lindrici, quod ſit, FE, veligitur du-
              <lb/>
            cta ab, F, parallela ipſi, HM, ca-
              <lb/>
            dit ſuper, FE, & </s>
            <s xml:id="echoid-s617" xml:space="preserve">ſic erit, & </s>
            <s xml:id="echoid-s618" xml:space="preserve">ipſa la-
              <lb/>
            tus cylindrici, vel non, nempè ſi ca-
              <lb/>
            deret, vt, FG, tunc quia, FE, eſt
              <lb/>
            parallela ipſi, HM, & </s>
            <s xml:id="echoid-s619" xml:space="preserve">etiam, FG,
              <lb/>
            eſt ipſi, HM, parallela ſequitur, F
              <lb/>
            E, ipſi, FG, eſſe parallelam, & </s>
            <s xml:id="echoid-s620" xml:space="preserve">ſunt
              <lb/>
            FE, FG, eductæ ab eodem pun-
              <lb/>
            cto, F, In quo ſunt concurrentes,
              <lb/>
            quod eſt abſurdum, igitur quæ du-
              <lb/>
            citur à puncto, F, parallela ipſi, H
              <lb/>
            M, cadet ſuper, FE, latus cylindri-
              <lb/>
            ci, igitur erit latus huius cylindrici, quod erat oſtendendum.</s>
            <s xml:id="echoid-s621" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div78" type="section" level="1" n="60">
          <head xml:id="echoid-head71" xml:space="preserve">THEOREMA III. PROPOS. VI.</head>
          <p>
            <s xml:id="echoid-s622" xml:space="preserve">SVperficies, quæ clauditur ambitu deſcripto ab extremo
              <lb/>
            puncto lateris cylindrici, quod per circuitum eiuſdem
              <lb/>
            baſis non properat, eſt ſuperficies plana, & </s>
            <s xml:id="echoid-s623" xml:space="preserve">æquidiſtans bafi;
              <lb/>
            </s>
            <s xml:id="echoid-s624" xml:space="preserve">ſi ea ſumatur, in qua iacent iungentes duo quæuis puncta de-
              <lb/>
            ſcripti ambitus.</s>
            <s xml:id="echoid-s625" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s626" xml:space="preserve">Sit quilibet cylindricus, AE, cuius baſis, CDEV, latus, MV,
              <lb/>
            cuius punctum extremum, M, quod non properat per ambitum ba-
              <lb/>
              <figure xlink:label="fig-0039-02" xlink:href="fig-0039-02a" number="14">
                <image file="0039-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0039-02"/>
              </figure>
            ſis, in reuolutione deſeribat circuitum, MANH.
              <lb/>
            </s>
            <s xml:id="echoid-s627" xml:space="preserve">Dico figuram hoc circuitu comprehenſam, in qua
              <lb/>
            iacent iungentes duo quęuis puncta deſcripti am-
              <lb/>
            bitus eſſe ſuperficiem planam, ęquidiſtantem baſi,
              <lb/>
            CDEV, & </s>
            <s xml:id="echoid-s628" xml:space="preserve">ideò ſingula puncta huius circuitusre-
              <lb/>
            periri in tali plano. </s>
            <s xml:id="echoid-s629" xml:space="preserve">Sumatur ergo in tali circuitu
              <lb/>
            vtcumq; </s>
            <s xml:id="echoid-s630" xml:space="preserve">punctum, M, & </s>
            <s xml:id="echoid-s631" xml:space="preserve">per, M, ducatur baſi,
              <lb/>
            CE, æquidiſtans planum, MBOF. </s>
            <s xml:id="echoid-s632" xml:space="preserve">Dico om-
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            nia puncta deſcripti circuitus eſſe in hoc, plano: </s>
            <s xml:id="echoid-s633" xml:space="preserve">ſi
              <lb/>
            enim non ſint, aliquod erit extra, ſit hoc pun-
              <lb/>
            ctum, N, & </s>
            <s xml:id="echoid-s634" xml:space="preserve">per, N, ſit ductum latus cylindrici,
              <lb/>
            quod ſit, ND, ſecans circuitum figuræ planæ, B
              <lb/>
            F, in, O, & </s>
            <s xml:id="echoid-s635" xml:space="preserve">circuitum baſis in, D, deinde per, N
              <lb/>
            D, MV, quæ ſunt æquidiſtantes, cum fint cylindrici latera, </s>
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