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

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            <s xml:id="echoid-s7937" xml:space="preserve">
              <pb o="329" file="0349" n="349" rhead="LIB ER IV."/>
            quadrata, AM, ad rectangula ſub, AE, EH, ſunt vt quadratum,
              <lb/>
            DM, ad rectangulum, DEM, rectangula verò ſub, AE, EH, ad
              <lb/>
            rectangula ſub ſemiparabola, BDE, & </s>
            <s xml:id="echoid-s7938" xml:space="preserve">ſub, EH, ſunt vt, AE, ad
              <lb/>
            ſemiparabolam, BDE, (quia, EH, eſt parallelogrammum) idelt
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            ſexquialtera .</s>
            <s xml:id="echoid-s7939" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7940" xml:space="preserve">vt, DE, ad {2/3}. </s>
            <s xml:id="echoid-s7941" xml:space="preserve">DE, .</s>
            <s xml:id="echoid-s7942" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7943" xml:space="preserve">vt rectangulum ſub, DEM,
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            (ſumpta, EM, communi altitudine) ad rectangulum ſub {2/3}, DE, & </s>
            <s xml:id="echoid-s7944" xml:space="preserve">
              <lb/>
            ſub, EM, ergo, ex æquali, omnia quadrata, AM, ad rectangula
              <lb/>
            ſub ſemiparabola, BDE, & </s>
            <s xml:id="echoid-s7945" xml:space="preserve">ſub, BM, erunt vt quadratum, DM,
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              <note position="right" xlink:label="note-0349-01" xlink:href="note-0349-01a" xml:space="preserve">Coroll. 1.
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              26. l. 2.</note>
            ad rectangulum ſub {2/3}. </s>
            <s xml:id="echoid-s7946" xml:space="preserve">DE, & </s>
            <s xml:id="echoid-s7947" xml:space="preserve">ſub, EM; </s>
            <s xml:id="echoid-s7948" xml:space="preserve">ad eadem verò bis ſumpta
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            erunt, vt idem quadratum, DM, ad rectangulum bis ſub {2/3}. </s>
            <s xml:id="echoid-s7949" xml:space="preserve">DE, .</s>
            <s xml:id="echoid-s7950" xml:space="preserve">i.
              <lb/>
            </s>
            <s xml:id="echoid-s7951" xml:space="preserve">ſub ſexquitertia, DE, ſemel, & </s>
            <s xml:id="echoid-s7952" xml:space="preserve">ſub, EM, ergó, colligendo, omnia
              <lb/>
            quadrata, AM, ad omnia quadrata, BM, & </s>
            <s xml:id="echoid-s7953" xml:space="preserve">ad omnia quadrata ſe-
              <lb/>
            miparabolæ, BDE, cum rectangulis bis ſub, HE, & </s>
            <s xml:id="echoid-s7954" xml:space="preserve">ſemiparabo-
              <lb/>
            la, BDE, ideſt ad omnia quadrata figuræ, HBDM, erunt vt qua-
              <lb/>
            dratum, DM, ad quadratum, ME, & </s>
            <s xml:id="echoid-s7955" xml:space="preserve">dimidium quadrati, ED,
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            cum rectangulo ſub ſexquitertia, DE, & </s>
            <s xml:id="echoid-s7956" xml:space="preserve">ſub, EM, ſimul iuncta quæ
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            nobis erant demonſtranda.</s>
            <s xml:id="echoid-s7957" xml:space="preserve"/>
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        <div xml:id="echoid-div795" type="section" level="1" n="470">
          <head xml:id="echoid-head490" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s7958" xml:space="preserve">_H_Inc apparet, quod methodo huius in Propoſ. </s>
            <s xml:id="echoid-s7959" xml:space="preserve">32. </s>
            <s xml:id="echoid-s7960" xml:space="preserve">oſtendi poterat
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            omnia quadrata, AF, ad omnia quadrata figuræ, CBDF, eſſe
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            vt 24. </s>
            <s xml:id="echoid-s7961" xml:space="preserve">ad 17. </s>
            <s xml:id="echoid-s7962" xml:space="preserve">prius demonſtrando omnia quadrata, AF, ad omnia qua-
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            drata figuræ, CBDF, eſſe vt quadratum, DF, ad quadratum, FE, {1/2}. </s>
            <s xml:id="echoid-s7963" xml:space="preserve">qua-
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            drati, ED, & </s>
            <s xml:id="echoid-s7964" xml:space="preserve">rectangulum ſub ſexquitertia, DE, & </s>
            <s xml:id="echoid-s7965" xml:space="preserve">ſub, EF, vt nem-
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            pè 24. </s>
            <s xml:id="echoid-s7966" xml:space="preserve">ad 17. </s>
            <s xml:id="echoid-s7967" xml:space="preserve">veluti calculanti patebit, quod bic appoſui, vt eam ratio-
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            nem etiam hoc pacto teneamus.</s>
            <s xml:id="echoid-s7968" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div796" type="section" level="1" n="471">
          <head xml:id="echoid-head491" xml:space="preserve">THEOREMA XXXIII. PROPOS. XXXV.</head>
          <p>
            <s xml:id="echoid-s7969" xml:space="preserve">IN eadem anteced. </s>
            <s xml:id="echoid-s7970" xml:space="preserve">Propoſ. </s>
            <s xml:id="echoid-s7971" xml:space="preserve">figura oſtendemus omnia
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            quadrata, BM, ad omnia quadrata figurę, BFMH, eſſe
              <lb/>
            vt quadratum, EM, ad quadratum, MF, cum rectangulo ſub
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            {2/3}. </s>
            <s xml:id="echoid-s7972" xml:space="preserve">EF, & </s>
            <s xml:id="echoid-s7973" xml:space="preserve">ſub, FM, vna cum {1/6}. </s>
            <s xml:id="echoid-s7974" xml:space="preserve">quadrati, EF, regula eadem
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            retenta.</s>
            <s xml:id="echoid-s7975" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7976" xml:space="preserve">Omnia .</s>
            <s xml:id="echoid-s7977" xml:space="preserve">n. </s>
            <s xml:id="echoid-s7978" xml:space="preserve">quadrata figuræ, BFMH, per rectam, CF, di
              <unsure/>
            uidun-
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            tur in omnia quadrata, CM, in omnia quadrata trilinei, BCF, & </s>
            <s xml:id="echoid-s7979" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0349-02" xlink:href="note-0349-02a" xml:space="preserve">D. Corol.
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              23. l. 2.</note>
            in rectangula bis ſub trilineo, BCF, & </s>
            <s xml:id="echoid-s7980" xml:space="preserve">ſub, CM; </s>
            <s xml:id="echoid-s7981" xml:space="preserve">ad horum ergo
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            fingula comparemus omnia quadrata, BM; </s>
            <s xml:id="echoid-s7982" xml:space="preserve">hæc igitur ad </s>
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