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

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        <div xml:id="echoid-div90" type="section" level="1" n="67">
          <pb o="24" file="0044" n="44" rhead="GEOMETRIÆ"/>
          <p>
            <s xml:id="echoid-s708" xml:space="preserve">Sit cylindricus, AE, ſectus a planis quomodocumque per latera.
              <lb/>
            </s>
            <s xml:id="echoid-s709" xml:space="preserve">Dico per eadem diuidi in cylindricos; </s>
            <s xml:id="echoid-s710" xml:space="preserve">ſint autem ſecantia plana, quę
              <lb/>
            in cylindrico, AE, producant parallelogramma, AE, ME. </s>
            <s xml:id="echoid-s711" xml:space="preserve">Quia
              <lb/>
            igitur, AE, eſt parallelogrammum, ſi in ipſo ducantur rectæ lineæ
              <lb/>
            ipſi, AD, HE, parallelæ, & </s>
            <s xml:id="echoid-s712" xml:space="preserve">in, AH, DE, terminatæ, erunt ei-
              <lb/>
            ſdem, AD, HE, æquales, & </s>
            <s xml:id="echoid-s713" xml:space="preserve">ſubinde erunt æquales, & </s>
            <s xml:id="echoid-s714" xml:space="preserve">parallelæ
              <lb/>
              <note position="left" xlink:label="note-0044-01" xlink:href="note-0044-01a" xml:space="preserve">Ex def. 3.</note>
            regulælateris cylindrici, AE, vnde erit, AE, ſuperficies cylindra-
              <lb/>
            cea deſcripta latere, AD, ſiue latere cylindrici, AE, ergo ſolidum,
              <lb/>
            ARXE, erit cylindricus. </s>
            <s xml:id="echoid-s715" xml:space="preserve">Eodem pacto oſtendemus ſolida, AM
              <lb/>
            HDVE, MZHVIE, eſſe cylindricos, talibus igitur planis cy-
              <lb/>
            lindricus, AE, ſemper diuiditur in cylindricos, quæ eſt prior pars
              <lb/>
            huius Theorematis.</s>
            <s xml:id="echoid-s716" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s717" xml:space="preserve">Secetur nunc duobus planis vtcumque inter ſe parallelis coinci-
              <lb/>
            dentibus cum omnibus ciuſdem lateribus, quæ in cylindrico, AE,
              <lb/>
            producant figuras, BNGK, COFL. </s>
            <s xml:id="echoid-s718" xml:space="preserve">Dico ſolidum compræhen-
              <lb/>
              <figure xlink:label="fig-0044-01" xlink:href="fig-0044-01a" number="18">
                <image file="0044-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0044-01"/>
              </figure>
            ſum inter has figuras, & </s>
            <s xml:id="echoid-s719" xml:space="preserve">ijs incluſam ſuperficiem
              <lb/>
            cylindraceam, eſſe cylindricum. </s>
            <s xml:id="echoid-s720" xml:space="preserve">Sintadhuc pla-
              <lb/>
            na per latera cylindrici, AE, vtcumque ducta, A
              <lb/>
            E, ME, quæ ſecent figuras, BNGK, COFL,
              <lb/>
            in rectis, BG, CF, NG, OF, igitur eiuſdem pla
              <lb/>
            ni, & </s>
            <s xml:id="echoid-s721" xml:space="preserve">ipſarum, BNGK, COFL, communes ſe-
              <lb/>
            ctiones erunt parallelæ, quę ſint, BG, CF, ſicut
              <lb/>
            etiam ipſæ, NG, OF, ſunt autem parallelę etiam
              <lb/>
            ipſæ, BC, NO, GF, ergo, BF, NF, erunt pa-
              <lb/>
            rallelogramma, & </s>
            <s xml:id="echoid-s722" xml:space="preserve">latera eorumdem, BC, GF,
              <lb/>
            NO, inter ſe æqualia, & </s>
            <s xml:id="echoid-s723" xml:space="preserve">æquidiſtantia; </s>
            <s xml:id="echoid-s724" xml:space="preserve">ſi igitur
              <lb/>
            eorum quoduis, vt, GF, ſtatuatur pro regula lateris ylindrici, ſu-
              <lb/>
            perficies incluſa duabus figuris, BNGK, COFL, erit deſcripta
              <lb/>
            vno laterum, BC, vel, NO, properante per circuitum figuræ, C
              <lb/>
            OFL, ſemper ipſi, GF, æquidiſtante, donec redeat vnde diſceſſit,
              <lb/>
            igitur hæc erit ſuperſicies cylindracea, cuius oppoſitæ baſes ipſæ fi-
              <lb/>
            guræ, BNGK, COFL, & </s>
            <s xml:id="echoid-s725" xml:space="preserve">ſolidum eiſdem incluſum erit cylindri-
              <lb/>
            cus, quod erat poſterior pars huius Theorematis à nobis demon-
              <lb/>
              <note position="left" xlink:label="note-0044-02" xlink:href="note-0044-02a" xml:space="preserve">Def. 3.</note>
            ſtranda.</s>
            <s xml:id="echoid-s726" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div93" type="section" level="1" n="68">
          <head xml:id="echoid-head79" xml:space="preserve">THEOREMA VIII. PROPOS. XI.</head>
          <p>
            <s xml:id="echoid-s727" xml:space="preserve">CViuſuis cylindrici oppoſitæ baſes ſunt fimiles, æquales,
              <lb/>
            & </s>
            <s xml:id="echoid-s728" xml:space="preserve">ſimiliter poſitæ.</s>
            <s xml:id="echoid-s729" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s730" xml:space="preserve">Sit cylindricus, PN, cuius oppoſitæ baſes, APK, OZN. </s>
            <s xml:id="echoid-s731" xml:space="preserve">Dico
              <lb/>
            eas eſſe ſimiles, æquales, & </s>
            <s xml:id="echoid-s732" xml:space="preserve">ſimiliter poſitas. </s>
            <s xml:id="echoid-s733" xml:space="preserve">Ducantur </s>
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