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

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          <p>
            <s xml:id="echoid-s8062" xml:space="preserve">
              <pb o="332" file="0352" n="352" rhead="GEOMETRIÆ"/>
            ctangulo ſub ſexquitertia, ME, & </s>
            <s xml:id="echoid-s8063" xml:space="preserve">ſub, ED, quia baſes eorum
              <lb/>
            ſunt altitudinibus reciprocę, & </s>
            <s xml:id="echoid-s8064" xml:space="preserve">eadem ratione rectangulum ſub ſex-
              <lb/>
            quitertia, EF, & </s>
            <s xml:id="echoid-s8065" xml:space="preserve">ſub, FM, æquatur rectãgulo ſub EF, & </s>
            <s xml:id="echoid-s8066" xml:space="preserve">ſexquitertia,
              <lb/>
            FM, ideò ſupradicta ratio erit eadem ei, quam habet rectangulũ ſub,
              <lb/>
            DE, vel, EF, & </s>
            <s xml:id="echoid-s8067" xml:space="preserve">ſub ſexquitertia, EM, cum {1/2}. </s>
            <s xml:id="echoid-s8068" xml:space="preserve">quadrati, DE, ideſt
              <lb/>
            cum rectangulo ſub, EF, & </s>
            <s xml:id="echoid-s8069" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s8070" xml:space="preserve">EF, ad rectangulum ſub, EF, & </s>
            <s xml:id="echoid-s8071" xml:space="preserve">ſub
              <lb/>
            ſexquitertia, FM, cum {5/6}. </s>
            <s xml:id="echoid-s8072" xml:space="preserve">quadrati, EF, ideſt cum rectangulo ſub,
              <lb/>
            EF, & </s>
            <s xml:id="echoid-s8073" xml:space="preserve">{5/6}. </s>
            <s xml:id="echoid-s8074" xml:space="preserve">EF, duo autem rectangula ſub, EF, & </s>
            <s xml:id="echoid-s8075" xml:space="preserve">ſub ſexquitertia,
              <lb/>
            EM, & </s>
            <s xml:id="echoid-s8076" xml:space="preserve">ſub, EF, & </s>
            <s xml:id="echoid-s8077" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s8078" xml:space="preserve">EF, conficiunt rectangulum ſub, EF, & </s>
            <s xml:id="echoid-s8079" xml:space="preserve">ſub
              <lb/>
            compoſita ex {1/2}. </s>
            <s xml:id="echoid-s8080" xml:space="preserve">EF, & </s>
            <s xml:id="echoid-s8081" xml:space="preserve">ſexquitertia, EM; </s>
            <s xml:id="echoid-s8082" xml:space="preserve">pariter alia duo rectan-
              <lb/>
            gula ſub, EF, & </s>
            <s xml:id="echoid-s8083" xml:space="preserve">{5/6}. </s>
            <s xml:id="echoid-s8084" xml:space="preserve">EF, & </s>
            <s xml:id="echoid-s8085" xml:space="preserve">ſub, EF, & </s>
            <s xml:id="echoid-s8086" xml:space="preserve">ſexquitertia, FM, conficiunt
              <lb/>
            rectangulum ſub, EF, & </s>
            <s xml:id="echoid-s8087" xml:space="preserve">compoſita ex {5/6}. </s>
            <s xml:id="echoid-s8088" xml:space="preserve">EF, & </s>
            <s xml:id="echoid-s8089" xml:space="preserve">ſexquitertia, FM,
              <lb/>
            ergo omnia quadrata figuræ, BDMH, demptis omnibus quadra-
              <lb/>
            tis, BM, ad omnia quadrata, BM, demptis omnibus quadratis figu-
              <lb/>
              <note position="left" xlink:label="note-0352-01" xlink:href="note-0352-01a" xml:space="preserve">1.2,elem.</note>
            ræ, BFMH; </s>
            <s xml:id="echoid-s8090" xml:space="preserve">erunt vt rectangulum ſub, EF, & </s>
            <s xml:id="echoid-s8091" xml:space="preserve">compoſita ex {1/2}. </s>
            <s xml:id="echoid-s8092" xml:space="preserve">E
              <lb/>
            F, & </s>
            <s xml:id="echoid-s8093" xml:space="preserve">ſexquitertia, EM, ad rectangulum ſub eadem altitudine, EF,
              <lb/>
            & </s>
            <s xml:id="echoid-s8094" xml:space="preserve">ſub compoſita ex {5/6}. </s>
            <s xml:id="echoid-s8095" xml:space="preserve">EF, & </s>
            <s xml:id="echoid-s8096" xml:space="preserve">ſexquitertia, FM, .</s>
            <s xml:id="echoid-s8097" xml:space="preserve">i. </s>
            <s xml:id="echoid-s8098" xml:space="preserve">vt compoſita
              <lb/>
            ex {1/2}. </s>
            <s xml:id="echoid-s8099" xml:space="preserve">EF, vel {1/2}. </s>
            <s xml:id="echoid-s8100" xml:space="preserve">ED, & </s>
            <s xml:id="echoid-s8101" xml:space="preserve">ſexquitertia, EM, ad compoſitam ex {5/6}. </s>
            <s xml:id="echoid-s8102" xml:space="preserve">E
              <lb/>
            F, & </s>
            <s xml:id="echoid-s8103" xml:space="preserve">ſexquitertia, FM, ideſt vt, EM, cum {1/3}. </s>
            <s xml:id="echoid-s8104" xml:space="preserve">ME, & </s>
            <s xml:id="echoid-s8105" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s8106" xml:space="preserve">ED, ad, M
              <lb/>
            F, cum {1/2}. </s>
            <s xml:id="echoid-s8107" xml:space="preserve">MF, & </s>
            <s xml:id="echoid-s8108" xml:space="preserve">{5/6}. </s>
            <s xml:id="echoid-s8109" xml:space="preserve">FE, quod oſtendere oportebat.</s>
            <s xml:id="echoid-s8110" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div801" type="section" level="1" n="474">
          <head xml:id="echoid-head494" xml:space="preserve">THEOREMA XXXV. PROPOS. XXXVII.</head>
          <p>
            <s xml:id="echoid-s8111" xml:space="preserve">IN figura Prop. </s>
            <s xml:id="echoid-s8112" xml:space="preserve">32. </s>
            <s xml:id="echoid-s8113" xml:space="preserve">oſtendemus, regula, DF, omnia qua-
              <lb/>
            drata ſemiparabolæ, DBE, ad omnia quadrata ſiguræ,
              <lb/>
            CBDF, demptis omnibus quadratis trilinei, BCF, eſſe vt
              <lb/>
            octaua pars, DF, ad duas tertias eiuſdem, DF, .</s>
            <s xml:id="echoid-s8114" xml:space="preserve">i. </s>
            <s xml:id="echoid-s8115" xml:space="preserve">vt 3. </s>
            <s xml:id="echoid-s8116" xml:space="preserve">ad 16.</s>
            <s xml:id="echoid-s8117" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8118" xml:space="preserve">Nam omnia quadrata ſemiparabolæ, BDE, ſunt dimidium om.
              <lb/>
            </s>
            <s xml:id="echoid-s8119" xml:space="preserve">
              <figure xlink:label="fig-0352-01" xlink:href="fig-0352-01a" number="238">
                <image file="0352-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0352-01"/>
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            nium quadratorum, AE, ideſt
              <lb/>
            ſunt ad illa, vt {1/2}. </s>
            <s xml:id="echoid-s8120" xml:space="preserve">quadrati, D
              <lb/>
              <note position="left" xlink:label="note-0352-02" xlink:href="note-0352-02a" xml:space="preserve">20. huius.</note>
            E, ad quadratum, DE, item
              <lb/>
            omnia quadrata, AE, ad om-
              <lb/>
            nia quadrata, AF, ſunt vt qua-
              <lb/>
            dratum, DE, ad quadratum,
              <lb/>
            DF; </s>
            <s xml:id="echoid-s8121" xml:space="preserve">tandem omnia quadrata,
              <lb/>
            DF, ad omnia quadrata figurę,
              <lb/>
              <note position="left" xlink:label="note-0352-03" xlink:href="note-0352-03a" xml:space="preserve">Corol. 32.
                <lb/>
              huius.</note>
            CBDF, demptis omnibus
              <lb/>
            quadratis trilinei, BCF, ſunt ſexquialtera, ideſt ſunt vt quadratũ,
              <lb/>
            DF, ad rectangulum ſub, DF, & </s>
            <s xml:id="echoid-s8122" xml:space="preserve">{2/3}. </s>
            <s xml:id="echoid-s8123" xml:space="preserve">DF, ergo, exæquali, </s>
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