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

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            <s xml:id="echoid-s5648" xml:space="preserve">
              <pb o="230" file="0250" n="250" rhead="GEOMETRIÆ"/>
            nia quadrata, MO, ſunt vt quadratum, DO, ad quadratum, OE,
              <lb/>
            omnia item quadrata, MO, ad rectangula ſub, MO, & </s>
            <s xml:id="echoid-s5649" xml:space="preserve">ſemicir-
              <lb/>
            culo, vel ſemiellipſi, MBE, ſunt vt, OM, ad ſemicirculum, vel ſe-
              <lb/>
            miellipſim, MBE, .</s>
            <s xml:id="echoid-s5650" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5651" xml:space="preserve">vt, OE, ad, EI, nam facta eſt, FE, ad, EI,
              <lb/>
            vt, MF, ad ſemicirculum, vel ſemiellipſim, MGE; </s>
            <s xml:id="echoid-s5652" xml:space="preserve">ad eadem verò
              <lb/>
              <note position="left" xlink:label="note-0250-01" xlink:href="note-0250-01a" xml:space="preserve">Coroll.1.
                <lb/>
              26.lib.2.</note>
            rectangula bis ſumpta, erunt vt, OE, ad duplam, EI; </s>
            <s xml:id="echoid-s5653" xml:space="preserve">igitur, colli-
              <lb/>
            gendo, omnia quadrata, HO, ad omnia quadrata ſemicirculi, vel
              <lb/>
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                <image file="0250-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0250-01"/>
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            ſemiellipſis, MBE,
              <lb/>
            ad omnia quadrata,
              <lb/>
            MO, & </s>
            <s xml:id="echoid-s5654" xml:space="preserve">ad rectan-
              <lb/>
            gula bis ſub ſemicir-
              <lb/>
            culo, vel ſemiellipſi,
              <lb/>
            MBE, & </s>
            <s xml:id="echoid-s5655" xml:space="preserve">ſub, MO,
              <lb/>
            ſimul ſumpta .</s>
            <s xml:id="echoid-s5656" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5657" xml:space="preserve">ad
              <lb/>
            omnia quadrata fi-
              <lb/>
            guræ, CMBEO,
              <lb/>
            erunt vt quadratum,
              <lb/>
            OD, ad quadratum, OE, ad, {2/3}, quadrati, DE, cum rectangu-
              <lb/>
            lo ſub, OE, & </s>
            <s xml:id="echoid-s5658" xml:space="preserve">dupla, EI, ſimul ſumpta; </s>
            <s xml:id="echoid-s5659" xml:space="preserve">quia verò ſemicircu-
              <lb/>
            lus, vel ſemiellipſis, MGE, eſt pluſquam dimidium parallelogram-
              <lb/>
            mi, MF, etiam, EI, erit pluſquam dimidia, EF; </s>
            <s xml:id="echoid-s5660" xml:space="preserve">& </s>
            <s xml:id="echoid-s5661" xml:space="preserve">ideò dupla,
              <lb/>
            EI, excedet ipſam, EF, vel ipſam, DE, rectangulum ergo ſub,
              <lb/>
            OE, & </s>
            <s xml:id="echoid-s5662" xml:space="preserve">dupla, EI, poterimus diuidere in rectangulum ſub, OE,
              <lb/>
            &</s>
            <s xml:id="echoid-s5663" xml:space="preserve">, ED, & </s>
            <s xml:id="echoid-s5664" xml:space="preserve">in rectangulum ſub, OE, & </s>
            <s xml:id="echoid-s5665" xml:space="preserve">exceſſu, quo dupla, EI,
              <lb/>
            ſuperat, ED, iungamus rectangulum ſub, DE, EO, cum qua-
              <lb/>
            drato, EO, fiet rectangulum ſub, DO, OE; </s>
            <s xml:id="echoid-s5666" xml:space="preserve">quadratum ergo,
              <lb/>
            OE, {2/3}, quadrati, ED, & </s>
            <s xml:id="echoid-s5667" xml:space="preserve">rectangulum ſub, OE, & </s>
            <s xml:id="echoid-s5668" xml:space="preserve">dupla, EI,
              <lb/>
            commutata ſunt vt in, {2/3}, quadrati, ED, in rectangulum ſub, D
              <lb/>
            O, OE, cum rectangulo ſub, OE, & </s>
            <s xml:id="echoid-s5669" xml:space="preserve">ſub exceſſu duplæ, EI,
              <lb/>
            ſuper, ED. </s>
            <s xml:id="echoid-s5670" xml:space="preserve">Omnia ergo quadrata, HO, ad omnia quadrata fi-
              <lb/>
            guræ, CMBEO, erunt vt quadratum, DO, ad rectangulum
              <lb/>
            ſub, DO, OE, cum rectangulo ſub, OE, & </s>
            <s xml:id="echoid-s5671" xml:space="preserve">ſub exceſſu duplæ,
              <lb/>
            EI, ſuper, ED, vel, EF, cum, {2/3}, quadrati, DE, quod erat oſten,
              <lb/>
            dendum.</s>
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          <figure number="156">
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