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

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          <pb o="27" file="0047" n="47" rhead="LIBER I."/>
        </div>
        <div xml:id="echoid-div97" type="section" level="1" n="70">
          <head xml:id="echoid-head81" xml:space="preserve">LEMMA PRO ANTECED. PROP.</head>
          <p>
            <s xml:id="echoid-s775" xml:space="preserve">DEſiderari tantum videtur huius euidentia, quod ſcilicet planum
              <lb/>
            inter oppoſita tangentia plana eiſdem a quidiſtanter ductum
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            tranſeat perlatera cylindrici, quod aſſumpra eiuſdem figura nunc
              <lb/>
              <figure xlink:label="fig-0047-01" xlink:href="fig-0047-01a" number="20">
                <image file="0047-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0047-01"/>
              </figure>
            fiet manifeſtum; </s>
            <s xml:id="echoid-s776" xml:space="preserve">intelliga-
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            tur ergo in ambitu vtriuſuis
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            oppoſitarum baſium cylin-
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            drici, PN, ſumptum pun-
              <lb/>
            ctum, vt, O, in ambitu fi-
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            guræ, ZON. </s>
            <s xml:id="echoid-s777" xml:space="preserve">Dico pla-
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            num, quod tranſit per, O,
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            æquidiſtans planis tangen-
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            tibus, AG, VL, tranſire
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            per latera cylindrici, PN.
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            </s>
            <s xml:id="echoid-s778" xml:space="preserve">Ducatur ergo à puncto, O,
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            latus cylindrici, PO, & </s>
            <s xml:id="echoid-s779" xml:space="preserve">ab
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            eodem pundo, O, in baſi,
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            ZON, recta, ON, paral-
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            lela ipſi, XL, igitur pla-
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            num, quod tranſit per, P
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            O, ON, æquidiſtat plano,
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              <note position="right" xlink:label="note-0047-01" xlink:href="note-0047-01a" xml:space="preserve">15. Vnde-
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              cimi Ele.</note>
            VL, nam, PO, ipſi, VX,
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            lateri cylindrici, &</s>
            <s xml:id="echoid-s780" xml:space="preserve">, ON,
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            ipſi, XL, ęquidiſtat, quod
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            ergo ducitur per, O, eidem plano tangenti æquidiſtans tranſit per
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            ipſas, PO, ON, ſi. </s>
            <s xml:id="echoid-s781" xml:space="preserve">n. </s>
            <s xml:id="echoid-s782" xml:space="preserve">non, erunt duo plana eidem plano, VL,
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            æquidiſtantia, & </s>
            <s xml:id="echoid-s783" xml:space="preserve">ideò inter ſe æquidiſtantia, quibus communis erit
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            punctus, O, igitur in eo concurrent, quod eſt abſurdum, non ergo
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            illa ſunt duo plana, ſed vnum tantum, illud nempè, quod ducitur
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            per punctum, O, ipſi plano, VL, æquidiſtans, tranſitque per, P
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            O, ON, neceſſariò: </s>
            <s xml:id="echoid-s784" xml:space="preserve">Siverò à punctis, I, M, N, erigantur latera
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            cylindrici, CI, ME, NK, erunt cuncta in plano per, PO, ON,
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            tranſeunte, ergo planum, quod ducitur per punctum, O, æquidi-
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            ſtans plano, VL, cylindricum tangenti tranſit per latera, PO, CI,
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            EM, KN, quod oſtendendum erat.</s>
            <s xml:id="echoid-s785" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div99" type="section" level="1" n="71">
          <head xml:id="echoid-head82" xml:space="preserve">THEOREMA IX. PROPOS. XII.</head>
          <p>
            <s xml:id="echoid-s786" xml:space="preserve">SI cylindricus planis ſecetur quomodocumque pet latera
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            ductis, eiuſdem oppoſitę baſes in figuras ſimiles, ęqua-
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            les, & </s>
            <s xml:id="echoid-s787" xml:space="preserve">ſimiliter poſitas diuiduntur, tales autem erunt, </s>
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