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

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            <s xml:id="echoid-s687" xml:space="preserve">
              <pb o="23" file="0043" n="43" rhead="LIBER I."/>
            vel, DC, planum per, EM, XR, ductum æquidiſtabit plauo, AC,
              <lb/>
            eſt autem planum, quod tangit cylindricum in, O, æquidiſtans pla-
              <lb/>
            no, AC, & </s>
            <s xml:id="echoid-s688" xml:space="preserve">tranſit per idem punctum, O, per quod tranſit planum
              <lb/>
            per, EM, XR, ductum, ergo illa duo plana fiunt vnum planum,
              <lb/>
            iacet autem, EM, in plano per, EM, XR, ducto, ergo iacet etiam
              <lb/>
            in plano ęquidiſtante ipſi, AC, & </s>
            <s xml:id="echoid-s689" xml:space="preserve">cylindricum, AC, tangente, igi-
              <lb/>
            tur tangit cylindricum in recta, EM. </s>
            <s xml:id="echoid-s690" xml:space="preserve">Eodem pacto ſi in alio pun-
              <lb/>
            cto extra, EM, in ſuperficie cylindracea ſumpto tangeret cylindri-
              <lb/>
            cum, AC, oſtenderemus tangere ipſum in latere, quod per tale pun-
              <lb/>
            ctum tranſiret; </s>
            <s xml:id="echoid-s691" xml:space="preserve">in quo caſu tangeret cylindricum in lateribus vno
              <lb/>
            pluribus, vt contingere poteſt. </s>
            <s xml:id="echoid-s692" xml:space="preserve">Tangat autem ſecundò ipſum in
              <lb/>
            plano, igitur in eo plano ſnmpto vtcumque puncto, tanget cylindri-
              <lb/>
            cum in latere tranſeunte per tale punctum, igitur planum contactus
              <lb/>
            tale eſt, vt in eo omnes ductæ rectæ lineæ æquidiſtantes ipſi, EM,
              <lb/>
            ſint latera cylindrici, AC, & </s>
            <s xml:id="echoid-s693" xml:space="preserve">ſubinde eidem, EM, æqualia, vnde
              <lb/>
            ſuperſicies, in qua iacent erit parallelogrammum, igitur planum
              <lb/>
            contactus in hoc caſu erit parallelogrammum, & </s>
            <s xml:id="echoid-s694" xml:space="preserve">erit æquiangulum
              <lb/>
            parallelogrammo, AC, nam eius latera ſunt parallela lateribus pa-
              <lb/>
            rallelogrammi, AC, & </s>
            <s xml:id="echoid-s695" xml:space="preserve">ideò continent angulos æquales contentis
              <lb/>
            à lateribus parallelogrammi, AC, vnde talia parallelogramma ſunt
              <lb/>
            æquiangula, igitur contactus plani æquidiſtantis plano per latera
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            cylindrici ducto, vel fit in latere, aut lateribus contacti cylindrici,
              <lb/>
            vel in parallelogrammo, ſiue parallelogrammis, in eiuſdem ſuper-
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            ficie iacentibus, & </s>
            <s xml:id="echoid-s696" xml:space="preserve">æquiangulis ei, quod fit a plano per latera ducto,
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            quod oſtendendum erat.</s>
            <s xml:id="echoid-s697" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div89" type="section" level="1" n="66">
          <head xml:id="echoid-head77" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s698" xml:space="preserve">_H_Inc babetur communes ſectiones plani tangentis, & </s>
            <s xml:id="echoid-s699" xml:space="preserve">cylindrici op-
              <lb/>
            poſitarum baſium productorum planorum, quæ ſint, VF, XR,
              <lb/>
            eſſe inter ſe parallelas, & </s>
            <s xml:id="echoid-s700" xml:space="preserve">tangere eaſdem baſes; </s>
            <s xml:id="echoid-s701" xml:space="preserve">ſcilicet, VF, ipſam
              <lb/>
            baſim, EAD, &</s>
            <s xml:id="echoid-s702" xml:space="preserve">, XR, ipſam, MBC.</s>
            <s xml:id="echoid-s703" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div90" type="section" level="1" n="67">
          <head xml:id="echoid-head78" xml:space="preserve">THEOREMA VII. PROPOS. X.</head>
          <p>
            <s xml:id="echoid-s704" xml:space="preserve">SI cylindricus quomodocumque ſecetur per latera, diui-
              <lb/>
            ditur in cylindricos à ſecantibus planis, ſi autem ſecetur
              <lb/>
            planis omnibus eiuſdem lateribus coincidentibus inter ſe
              <lb/>
            parallelis; </s>
            <s xml:id="echoid-s705" xml:space="preserve">ſolidum compræhenſum conceptis in cylindrico
              <lb/>
            figuris, & </s>
            <s xml:id="echoid-s706" xml:space="preserve">incluſa ſuperficie cylindracea, erit cylindricus.</s>
            <s xml:id="echoid-s707" xml:space="preserve"/>
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