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

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        <div xml:id="echoid-div78" type="section" level="1" n="60">
          <p>
            <s xml:id="echoid-s635" xml:space="preserve">
              <pb o="20" file="0040" n="40" rhead="GEOMETRIÆ"/>
            datur planum, quod baſimiſecet in recta, DV, figuram planam, M
              <lb/>
              <note position="left" xlink:label="note-0040-01" xlink:href="note-0040-01a" xml:space="preserve">16. Vnde.
                <lb/>
              cimi Ele.</note>
            BOF, in recta, OM, & </s>
            <s xml:id="echoid-s636" xml:space="preserve">iungantur, MN, puncta, quia ergo plana
              <lb/>
            parallela, BF, CE, ſecantur plano quodam, communes eorum ſe-
              <lb/>
            ctiones, nempè, OM, DV, erunt inuicem parallelæ, ſed etiam, O
              <lb/>
            D, MV, ſunt parallelæ, ergo, OV, erit parallelogrammum, &</s>
            <s xml:id="echoid-s637" xml:space="preserve">, O
              <lb/>
            D, æqualis ipſi, MV, eſt autem, MV, æqualis ipſi, ND, quia am-
              <lb/>
            bo ſunt latera eiuſdem cylindrici, ergo, DO, æqualis erit ipſi, DN,
              <lb/>
            pars toti, quod eſt abſurdum, non igitur aliquod punctum circuitus
              <lb/>
            deſcripti a puncto, M, eſt extra planum æquidiſtans baſi, CE, igi-
              <lb/>
            tur omnia ſunt in tali plano, iuncta igitur, NM, ipſa erit in eodem
              <lb/>
            cum illis plano, in quo pariter iacebunt duo quæuis puncta iungen-
              <lb/>
            tes eiuſdem circuitus, & </s>
            <s xml:id="echoid-s638" xml:space="preserve">ideò figura tali ambitu contenta eſt ſuper-
              <lb/>
            ficies plana ipſi baſi, CE, æquidiſtans, quod erat oſtendendum: </s>
            <s xml:id="echoid-s639" xml:space="preserve">iſte
              <lb/>
            autem vocantur cylindrici oppoſitæ baſes.</s>
            <s xml:id="echoid-s640" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div80" type="section" level="1" n="61">
          <head xml:id="echoid-head72" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s641" xml:space="preserve">_Q_Voniam vero ſuppoſito ipſam, MBOF, eſſe ſuperficiem planam
              <lb/>
            baſi æquidictantem, & </s>
            <s xml:id="echoid-s642" xml:space="preserve">ducto per latera, OD, MV, plano oſten-
              <lb/>
            dimus, OV, eſſe parallelogrammum, ideò cum ſciamus, MANH,
              <lb/>
            eſſe ſuperficiem planam baſi, CE, æquidiſtantem, ducto per latera vtcum-
              <lb/>
            que plano cylindricum ſecante, oſtendemus eodem pacto, ducti plani ſe-
              <lb/>
            cantis in cylindrico conceptam figuram eſſe parallelogrammum, cum ſci-
              <lb/>
            licet planum ducitur tantum per duo latera, vel parallelogramma, cum
              <lb/>
              <note position="left" xlink:label="note-0040-02" xlink:href="note-0040-02a" xml:space="preserve">_Defin. 3._</note>
            per plura duobus, ipſum in eorum aliquo non tangens.</s>
            <s xml:id="echoid-s643" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div82" type="section" level="1" n="62">
          <head xml:id="echoid-head73" xml:space="preserve">THEOREMA IV. PROPOS. VII.</head>
          <p>
            <s xml:id="echoid-s644" xml:space="preserve">SI cylindricus ſecetur, vel tangatur à duobus planis per
              <lb/>
            eiuſdem latera ductis, quę non fint inter ſe parallela, ſint
              <lb/>
            autem illa producta donec ſibi occurrant, communis eorum
              <lb/>
            ſectio erit eiuſdem cylindrici lateribus parallela.</s>
            <s xml:id="echoid-s645" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s646" xml:space="preserve">Sit quilibet cylindricus, FG, per cuius latera ſint ducta duo pla-
              <lb/>
            na non parallela, quæ ita ſint producta, donec ſibi occurrant, ſint
              <lb/>
            autem illa plana, AM, DN, quorum, & </s>
            <s xml:id="echoid-s647" xml:space="preserve">oppoſitarum baſium cy-
              <lb/>
            lyndrici, FG, communes ſectiones, AC, HM, DE, SN, erunt
              <lb/>
              <note position="left" xlink:label="note-0040-03" xlink:href="note-0040-03a" xml:space="preserve">Corol. n
                <lb/>
              teced.</note>
            igitur, AM, DN, parallelogramma, intelligantur oppoſitarum
              <lb/>
            baſium, FL, GK, indefinitè productarum plana ſecarià planis di-
              <lb/>
            ctorum parallelogrammorum pariter indefinitè productis, in rectis,
              <lb/>
            AR, DR, HO, SO, & </s>
            <s xml:id="echoid-s648" xml:space="preserve">eadem ſe inuicem ſecare in recta, RO.</s>
            <s xml:id="echoid-s649" xml:space="preserve"/>
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