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

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            <s xml:id="echoid-s9998" xml:space="preserve">Omnia .</s>
            <s xml:id="echoid-s9999" xml:space="preserve">n. </s>
            <s xml:id="echoid-s10000" xml:space="preserve">quadrata figuræ, RBCS, ſecantur per, BE, in omnia
              <lb/>
              <note position="left" xlink:label="note-0408-01" xlink:href="note-0408-01a" xml:space="preserve">D.Co.23.
                <lb/>
              l. 2.</note>
            quadrata, BS, in omnia quadrata ſemihyperbolæ, BCE, & </s>
            <s xml:id="echoid-s10001" xml:space="preserve">inre-
              <lb/>
            ctangula bis ſub, BCE, & </s>
            <s xml:id="echoid-s10002" xml:space="preserve">ſub, BS, ad horum ergo ſingula compa-
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            remus omnia quadrata, FS; </s>
            <s xml:id="echoid-s10003" xml:space="preserve">hæcigitur ad omnia quadrata, BS,
              <lb/>
            ſunt vt quadratum, CS, ad quadratum, SE, pariter omnia qua-
              <lb/>
            drata, FS, ad omnia quadrata, FE, ſunt vt quadratum, SC, ad
              <lb/>
            quadratum, CE, omnia verò quadrata, FE, ad omnia quadrata,
              <lb/>
              <figure xlink:label="fig-0408-01" xlink:href="fig-0408-01a" number="278">
                <image file="0408-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0408-01"/>
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            BCE, ſunt vt quadratum, CE, ad
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              <figure xlink:label="fig-0408-02" xlink:href="fig-0408-02a" number="279">
                <image file="0408-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0408-02"/>
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            quadratum, EI, ergo, ex æquali, om-
              <lb/>
            nia quadrata, FS, ad omnia quadra-
              <lb/>
            ta, BCE, erunt vt quadratum, CS, ad
              <lb/>
            quadratum, EI; </s>
            <s xml:id="echoid-s10004" xml:space="preserve">quodſerua. </s>
            <s xml:id="echoid-s10005" xml:space="preserve">Item
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            omnia quadrata, FS, ad rectangula
              <lb/>
            ſub, FE, ER, ſunt vt quadratum, C
              <lb/>
            S, ad rectangulum, CES, rectangula
              <lb/>
              <note position="left" xlink:label="note-0408-02" xlink:href="note-0408-02a" xml:space="preserve">14. @ 2.</note>
            verò ſub, FE, ER, adrectang. </s>
            <s xml:id="echoid-s10006" xml:space="preserve">ſub, BC
              <lb/>
            E, ER, ſunt vt, FE, ad, BCE, .</s>
            <s xml:id="echoid-s10007" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10008" xml:space="preserve">vt, C
              <lb/>
            E, ad, VE, .</s>
            <s xml:id="echoid-s10009" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10010" xml:space="preserve">ſumpta, ES, communi altitudine, vt rectangulum,
              <lb/>
            CES, ad rectangulum, VES, ergo, ex æquo, omnia quadrata, FS,
              <lb/>
              <note position="left" xlink:label="note-0408-03" xlink:href="note-0408-03a" xml:space="preserve">Coroll 1.
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              26. l. 2.</note>
            ad rectangula ſub, BCE, ER, erunt vt quadratum, CS, ad rectan-
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            gulum, VES, ad eadem verò bis ſumpta, vt quadratum, CS, ad
              <lb/>
            rectangulum bis ſub, VES; </s>
            <s xml:id="echoid-s10011" xml:space="preserve">ergo, conſequentibus ſimul collectis,
              <lb/>
            omnia quadrata, FS, ad omnia quadrata, BS, ad omnia quadra-
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            ta, BCE, & </s>
            <s xml:id="echoid-s10012" xml:space="preserve">ad rectangula bis ſub, BCE, ER, ideſt ad omnia qua-
              <lb/>
              <note position="left" xlink:label="note-0408-04" xlink:href="note-0408-04a" xml:space="preserve">D. Co 3. 2.
                <lb/>
              l. 2.</note>
            dratà figuræ, RBCS, erunt vt quadratum, CS, ad quadra-
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            SE, quadratum, EI, & </s>
            <s xml:id="echoid-s10013" xml:space="preserve">rectangulum bis ſub, VE, ES; </s>
            <s xml:id="echoid-s10014" xml:space="preserve">qua me-
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            thodo ſimiliter oſtendemus omnia quadrata, FD, ad omnia
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            quadrata figurę, GBCD, eſſe vt quadratum, CD, ad quadra-
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            tum, DE, quadratum, EI, & </s>
            <s xml:id="echoid-s10015" xml:space="preserve">rectangulum bis ſub, VE, ED;
              <lb/>
            </s>
            <s xml:id="echoid-s10016" xml:space="preserve">& </s>
            <s xml:id="echoid-s10017" xml:space="preserve">ſimiliter omnia quadrata, FM, ad omnia quadrata figuræ, HB
              <lb/>
            CM, eſſe vt quadratum, CM, ad quadratum, ME, quadratum,
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            EI, & </s>
            <s xml:id="echoid-s10018" xml:space="preserve">rectangulum bis ſub, VE, EM, quod oſtendere opus erat.</s>
            <s xml:id="echoid-s10019" xml:space="preserve"/>
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        <div xml:id="echoid-div927" type="section" level="1" n="553">
          <head xml:id="echoid-head577" xml:space="preserve">THE OREMA XVII. PROPOS. XVIII.</head>
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            <s xml:id="echoid-s10020" xml:space="preserve">IN eadem Prop. </s>
            <s xml:id="echoid-s10021" xml:space="preserve">15. </s>
            <s xml:id="echoid-s10022" xml:space="preserve">figura oſtendemus omnia quadrata
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            figuræ, HBCM, dempti omnibus quadratis figuræ, H
              <lb/>
            BDM regula eadem retenta, ad omnia quadrata figuræ,
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            GBCD, demptis omnibus quadratis trilinei, BGD, eſſe
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            vt compoſita ex, CM, MD, ad, DC.</s>
            <s xml:id="echoid-s10023" xml:space="preserve"/>
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