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

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            <s xml:id="echoid-s7982" xml:space="preserve">
              <pb o="330" file="0350" n="350" rhead="GEOMETRIÆ"/>
            quadrata, CM, ſunt vt quadratum, EM, ad quadratum, MF, quod
              <lb/>
            ſerua. </s>
            <s xml:id="echoid-s7983" xml:space="preserve">Item omnia quadrata, BM, ad omnia quadrata, BF, ſunt
              <lb/>
              <figure xlink:label="fig-0350-01" xlink:href="fig-0350-01a" number="236">
                <image file="0350-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0350-01"/>
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            vt quadratum, ME,
              <lb/>
            ad quadratum, EF,
              <lb/>
              <note position="left" xlink:label="note-0350-01" xlink:href="note-0350-01a" xml:space="preserve">30. huius.</note>
            omnia verò quadra-
              <lb/>
            ta, BF, ſunt ſexcupla
              <lb/>
            omnium quadratorú
              <lb/>
            trilinei, BCF, .</s>
            <s xml:id="echoid-s7984" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7985" xml:space="preserve">ſunt
              <lb/>
            ad illa, vt quadratum,
              <lb/>
            EF, ad eiuſdem {1/6}. </s>
            <s xml:id="echoid-s7986" xml:space="preserve">er-
              <lb/>
            go, ex æquali, om-
              <lb/>
            nia quadrata, BM, ad
              <lb/>
            omnia quadrata trili-
              <lb/>
            nei, BCF, ſunt vt quadratum, EM, ad {1/6}. </s>
            <s xml:id="echoid-s7987" xml:space="preserve">quadrati, EF, quod etiá
              <lb/>
            ſerua. </s>
            <s xml:id="echoid-s7988" xml:space="preserve">Tandem omnia quadrata, BM, ad rectangula ſub, BF, FH,
              <lb/>
            ſunt vt quadratum, EM, ad rectangulum ſub, EF, FM, rectangu-
              <lb/>
              <note position="left" xlink:label="note-0350-02" xlink:href="note-0350-02a" xml:space="preserve">Coroll. 1.
                <lb/>
              26. l. 2.</note>
            la verò ſub, BF, FH, ad rectangula ſub trilineo, BFC, & </s>
            <s xml:id="echoid-s7989" xml:space="preserve">ſub, C
              <lb/>
            M, ſunt vt, BF, ad trilineum, BCF, (nam, CM, eſt parallelogram-
              <lb/>
            mum) ideſt ſunt eorum tripla .</s>
            <s xml:id="echoid-s7990" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7991" xml:space="preserve">ſunt vt, EF, ad {1/3}. </s>
            <s xml:id="echoid-s7992" xml:space="preserve">EF, .</s>
            <s xml:id="echoid-s7993" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7994" xml:space="preserve">vt rectan-
              <lb/>
            gulum, EF/M, ad rectangulum ſub {1/3}. </s>
            <s xml:id="echoid-s7995" xml:space="preserve">EF, & </s>
            <s xml:id="echoid-s7996" xml:space="preserve">ſub, FM, ergo, ex æ-
              <lb/>
            quali, omnia quadrata, BM, ad rectangula ſub trilineo, BCF, & </s>
            <s xml:id="echoid-s7997" xml:space="preserve">
              <lb/>
            ſub, FH, erunt vt quadratum, EM, ad rectangulum ſub {1/3}. </s>
            <s xml:id="echoid-s7998" xml:space="preserve">EF, & </s>
            <s xml:id="echoid-s7999" xml:space="preserve">
              <lb/>
            ſub, FM, ad eadem verò bis ſumpta, vt quadratum, EM, ad re-
              <lb/>
            ctangulum bis ſub {1/3}. </s>
            <s xml:id="echoid-s8000" xml:space="preserve">EF, & </s>
            <s xml:id="echoid-s8001" xml:space="preserve">ſub, FM, ideſt ſemel ſub {2/3}. </s>
            <s xml:id="echoid-s8002" xml:space="preserve">EF, ſub, F
              <lb/>
            M, ergo, colligendo, omnia quadrata, BM, ad omnia quadrata; </s>
            <s xml:id="echoid-s8003" xml:space="preserve">C
              <lb/>
            M, ad omnia quadrata trilinei, BCF, & </s>
            <s xml:id="echoid-s8004" xml:space="preserve">ad rectangula bis ſub tri-
              <lb/>
            lineo, BCF, & </s>
            <s xml:id="echoid-s8005" xml:space="preserve">ſub, FH, .</s>
            <s xml:id="echoid-s8006" xml:space="preserve">i. </s>
            <s xml:id="echoid-s8007" xml:space="preserve">ad omnia quadrata figuræ, BFMH,
              <lb/>
            erunt vt quadratum, EM, ad quadratum, MF, rectangulum ſub
              <lb/>
            {2/3}. </s>
            <s xml:id="echoid-s8008" xml:space="preserve">EF, & </s>
            <s xml:id="echoid-s8009" xml:space="preserve">ſub, FM, vna cum {1/6}. </s>
            <s xml:id="echoid-s8010" xml:space="preserve">quadrati, EF, quod oſtendere opus
              <lb/>
            erat.</s>
            <s xml:id="echoid-s8011" xml:space="preserve"/>
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          <head xml:id="echoid-head492" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s8012" xml:space="preserve">_H_Inc colligimus omnia quadrata, BM, ad reſiduum, demptis ab
              <lb/>
            eiſdem omnibus quadratis figuræ, BFMH, eſſe vt quadratum,
              <lb/>
            EM, ad reſiduum, demptis à quadrato, EM, his omnibus .</s>
            <s xml:id="echoid-s8013" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8014" xml:space="preserve">quadrato,
              <lb/>
            FM, rectangulo ſub, MF, & </s>
            <s xml:id="echoid-s8015" xml:space="preserve">{2/3}. </s>
            <s xml:id="echoid-s8016" xml:space="preserve">FE, cum {1/6}. </s>
            <s xml:id="echoid-s8017" xml:space="preserve">quadrati, EF, hoc autem
              <lb/>
            reſiduum eſt rectangulum ſub, MF, & </s>
            <s xml:id="echoid-s8018" xml:space="preserve">ſexquitertia, FE, cum {5/@}. </s>
            <s xml:id="echoid-s8019" xml:space="preserve">qua-
              <lb/>
            drati, EF; </s>
            <s xml:id="echoid-s8020" xml:space="preserve">nam ſi à quadrato, EM, dempſeris quadratum, FM, rema-
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            nebunt duo rectangula ſub, MF, FE, cum quadratum, FE, vlterius ſi à
              <lb/>
            rectangulo bis ſub, MF, FE, dempſeris rectangulum ſub, MF, & </s>
            <s xml:id="echoid-s8021" xml:space="preserve">{2/3}. </s>
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