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

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            <s xml:id="echoid-s787" xml:space="preserve">
              <pb o="28" file="0048" n="48" rhead="GEOMETRIÆ"/>
            ad eandem partem ſecantium planorum exiſtent: </s>
            <s xml:id="echoid-s788" xml:space="preserve">Et ſi idem
              <lb/>
            ſecetur planis parallelis quomodocumq; </s>
            <s xml:id="echoid-s789" xml:space="preserve">omnibus eiuſdem
              <lb/>
            lateribus coincidentibus, conceptæ in cylindrico figuræ e-
              <lb/>
            runt ſimiles, æquales, & </s>
            <s xml:id="echoid-s790" xml:space="preserve">ſimiliter poſitæ.</s>
            <s xml:id="echoid-s791" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s792" xml:space="preserve">Conſpiciatur figura Propoſit. </s>
            <s xml:id="echoid-s793" xml:space="preserve">10. </s>
            <s xml:id="echoid-s794" xml:space="preserve">in qua iam propoſitas ſectiones
              <lb/>
            habemus, plana enim, AE, ME, tranſeuntia per cylindrici latera
              <lb/>
              <figure xlink:label="fig-0048-01" xlink:href="fig-0048-01a" number="21">
                <image file="0048-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0048-01"/>
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            ipſum ſecant, & </s>
            <s xml:id="echoid-s795" xml:space="preserve">plana, BNG, COF, omni-
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            bus eiuſdem lateribus coincidunt, & </s>
            <s xml:id="echoid-s796" xml:space="preserve">ſunt paral-
              <lb/>
            lela. </s>
            <s xml:id="echoid-s797" xml:space="preserve">Dico ergo figuras, MZH, EIV, eſſe ſi-
              <lb/>
            miles, & </s>
            <s xml:id="echoid-s798" xml:space="preserve">æquales, & </s>
            <s xml:id="echoid-s799" xml:space="preserve">ſimiliter poſitas, quod pa-
              <lb/>
            tet, nam illæ ſunt cylindrici, MHZI, oppoſi-
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            tæ baſes; </s>
            <s xml:id="echoid-s800" xml:space="preserve">idem eodem modo probabitur de figu-
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            ris, AMH, DVE, & </s>
            <s xml:id="echoid-s801" xml:space="preserve">de, ARH, DXE, & </s>
            <s xml:id="echoid-s802" xml:space="preserve">
              <lb/>
            tandem oſtendemus pariter figuras, BNGK, C
              <lb/>
            OFL, eſſe ſimiles, æquales, & </s>
            <s xml:id="echoid-s803" xml:space="preserve">ſimiliter poſitas,
              <lb/>
              <note position="left" xlink:label="note-0048-01" xlink:href="note-0048-01a" xml:space="preserve">11. Huius.</note>
            quia ſunt cylindrici, BF, oppoſitæ baſes, quod
              <lb/>
            demonſtrandum erat.</s>
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          <head xml:id="echoid-head83" xml:space="preserve">COROLLARIV M.</head>
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            <s xml:id="echoid-s805" xml:space="preserve">_H_Inc apparet, quamuis figuram planam ex ſectione plani, oppofi-
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            tis baſibus cylindrici æquidiſtantis, in eo productam, eiſdem op-
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            poſitis baſibus eſſe ſimilem, æqualem, & </s>
            <s xml:id="echoid-s806" xml:space="preserve">ſimiliter poſitam.</s>
            <s xml:id="echoid-s807" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div102" type="section" level="1" n="73">
          <head xml:id="echoid-head84" xml:space="preserve">THEOREMA X. PROPOS. XIII.</head>
          <p>
            <s xml:id="echoid-s808" xml:space="preserve">SI quis cylindricus ſecetur plano per latera, deinde ſece-
              <lb/>
            tur planis oppoſitis eiuſdem baſibus æquidiſtantibus:
              <lb/>
            </s>
            <s xml:id="echoid-s809" xml:space="preserve">Communes ſectiones plani per latera ducti, & </s>
            <s xml:id="echoid-s810" xml:space="preserve">planorum ba-
              <lb/>
            ſibus æquidiſtantium, erunt lineæ, vellatera homologa fi-
              <lb/>
            gurarum ſimilium, quæ ex ſectione æquidiſtantium plano-
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            rum in cylindrico effecta in eodem producuntur.</s>
            <s xml:id="echoid-s811" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s812" xml:space="preserve">Sit cylindricus, ADM, cuius oppoſitæ baſes, ABC, TDF, ſe-
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            cetur autem plano vtcumque per latera ducto, quod in eo producat
              <lb/>
            parallelogrammum, BF, & </s>
            <s xml:id="echoid-s813" xml:space="preserve">alio vtcumque plano oppoſitis baſibus
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            æquidiſtante, quodin eo producat figuram, YNXO, & </s>
            <s xml:id="echoid-s814" xml:space="preserve">in paral-
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            lelogrammo, BF, rectam, NO. </s>
            <s xml:id="echoid-s815" xml:space="preserve">Dicorectas, DF, NO, BC, eſſe
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            lineas, vellatera homologa figurarum, TDF, YNO, ABC, </s>
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