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

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              <pb o="331" file="0351" n="351" rhead="LIBER IV."/>
            E, ideſt rectangulum bis ſub, MF, & </s>
            <s xml:id="echoid-s8023" xml:space="preserve">ſub {1/3}. </s>
            <s xml:id="echoid-s8024" xml:space="preserve">FE, remanebitrectangu-
              <lb/>
            lum bis ſub, MF, & </s>
            <s xml:id="echoid-s8025" xml:space="preserve">{2/3}. </s>
            <s xml:id="echoid-s8026" xml:space="preserve">FE, idtſt ſemel ſub, MF, & </s>
            <s xml:id="echoid-s8027" xml:space="preserve">ſexquitertia, FE:
              <lb/>
            </s>
            <s xml:id="echoid-s8028" xml:space="preserve">Tandem ablato {1/6}. </s>
            <s xml:id="echoid-s8029" xml:space="preserve">aquadrato, FE, remanent {5/6}. </s>
            <s xml:id="echoid-s8030" xml:space="preserve">eiuſdem quadrati, vnde
              <lb/>
            omnia quadrata, BM, ad reſiduum, demptis omnibus quadratis figuræ,
              <lb/>
            BFMH, erunt vt quadratum, EM, ad rectangulum ſub, MF, & </s>
            <s xml:id="echoid-s8031" xml:space="preserve">ſex-
              <lb/>
            quitertia, FE, cum {5/6}. </s>
            <s xml:id="echoid-s8032" xml:space="preserve">quadrati, FE.</s>
            <s xml:id="echoid-s8033" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div799" type="section" level="1" n="473">
          <head xml:id="echoid-head493" xml:space="preserve">THEOREMA XXXIV. PROPOS. XXXVI.</head>
          <p>
            <s xml:id="echoid-s8034" xml:space="preserve">INeodem Schemate Theor. </s>
            <s xml:id="echoid-s8035" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s8036" xml:space="preserve">34. </s>
            <s xml:id="echoid-s8037" xml:space="preserve">oſtendemus omnia
              <lb/>
            quadrata figuræ, BDMH, demptis omnibus quadra-
              <lb/>
            tis, BM, ad omnia quadrata, BM, demptis omnibus qua-
              <lb/>
            dratis figuræ, BFMH, eſſe vt, EM, cum {1/2}. </s>
            <s xml:id="echoid-s8038" xml:space="preserve">EM, & </s>
            <s xml:id="echoid-s8039" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s8040" xml:space="preserve">ED,
              <lb/>
            ad, MF, cum {1/3}. </s>
            <s xml:id="echoid-s8041" xml:space="preserve">MF, & </s>
            <s xml:id="echoid-s8042" xml:space="preserve">{5/6}. </s>
            <s xml:id="echoid-s8043" xml:space="preserve">FE.</s>
            <s xml:id="echoid-s8044" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8045" xml:space="preserve">Omnia enim quadrata, AM, ad omnia quadrata figuræ, DBH
              <lb/>
              <figure xlink:label="fig-0351-01" xlink:href="fig-0351-01a" number="237">
                <image file="0351-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0351-01"/>
              </figure>
            M, oſtendimus eſſe,
              <lb/>
              <note position="right" xlink:label="note-0351-01" xlink:href="note-0351-01a" xml:space="preserve">34. huius.</note>
            vt quadratum, D
              <lb/>
            M, ad quadratum,
              <lb/>
            ME, rectangulum
              <lb/>
            ſub, ME, & </s>
            <s xml:id="echoid-s8046" xml:space="preserve">ſexqui-
              <lb/>
            tertia, ED, cum {1/2}.
              <lb/>
            </s>
            <s xml:id="echoid-s8047" xml:space="preserve">quadrati, ED, ea-
              <lb/>
            dem verò ad omnia
              <lb/>
            quadrata, BM, ſunt
              <lb/>
            vt quadratum, DM, ad quadratum, ME, ergo omnia quadrata, A
              <lb/>
            M, ad omnia quadrata figuræ, HBDM, demptis omnibus qua-
              <lb/>
            Matis, BM, erunt vt quadratum, DM, ad rectangulum ſub, ME,
              <lb/>
            & </s>
            <s xml:id="echoid-s8048" xml:space="preserve">ſexquitertia, ED, cum {1/2}. </s>
            <s xml:id="echoid-s8049" xml:space="preserve">quadrati, ED, &</s>
            <s xml:id="echoid-s8050" xml:space="preserve">, conuertendo, hæc
              <lb/>
            ad illa erunt, vt rectangulum ſub ſexquitertia, ED, cum {1/2}. </s>
            <s xml:id="echoid-s8051" xml:space="preserve">quadra-
              <lb/>
            ti, ED, ad quadratum, DM: </s>
            <s xml:id="echoid-s8052" xml:space="preserve">Omnia verò quadrata, AM, ad om-
              <lb/>
            nia quadrata. </s>
            <s xml:id="echoid-s8053" xml:space="preserve">BM, ſunt vt quadratum, DM, ad quadratum, ME,
              <lb/>
            & </s>
            <s xml:id="echoid-s8054" xml:space="preserve">tandem omnia quadrata, BM, adeorum reſiduum, demptis
              <lb/>
            omnibus quadratis figuræ, BHMF, ſunt vt quadratum, EM,
              <lb/>
              <note position="right" xlink:label="note-0351-02" xlink:href="note-0351-02a" xml:space="preserve">Ex corol.
                <lb/>
              autec.</note>
            ad rectangulum ſub, MF, & </s>
            <s xml:id="echoid-s8055" xml:space="preserve">ſexquitertia, FE, cum {5/6}. </s>
            <s xml:id="echoid-s8056" xml:space="preserve">quadrati,
              <lb/>
            FE, ergo, ex æquali, omnia quadrata figuræ, BDMH,
              <lb/>
            demptis omnibus quadratis, BM, ad omnia quadrata, BM,
              <lb/>
            demptis omnibus quadratis figuræ, BFMH, erunt vt rectangu-
              <lb/>
            lum ſub, ME, & </s>
            <s xml:id="echoid-s8057" xml:space="preserve">ſexquitertia, ED, cum {1/2}. </s>
            <s xml:id="echoid-s8058" xml:space="preserve">quadrati, ED, ad re-
              <lb/>
            ctangulum ſub, MF, & </s>
            <s xml:id="echoid-s8059" xml:space="preserve">ſexquitertia, FE, cum {5/6}. </s>
            <s xml:id="echoid-s8060" xml:space="preserve">quadrati, FE;
              <lb/>
            </s>
            <s xml:id="echoid-s8061" xml:space="preserve">quia verò rectangulum ſub, ME, & </s>
            <s xml:id="echoid-s8062" xml:space="preserve">ſexquitertia, ED, </s>
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