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

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            <s xml:id="echoid-s8245" xml:space="preserve">
              <pb o="336" file="0356" n="356" rhead="GEOMETRIÆ"/>
            quitertia, NX, & </s>
            <s xml:id="echoid-s8246" xml:space="preserve">ſub, XP, conficiunt rationem @ {7/4}. </s>
            <s xml:id="echoid-s8247" xml:space="preserve">quadrati, DF,
              <lb/>
            ad hæc ſpatia vltimo dicta, hæc vero ratio, cum ea, quam habet, E
              <lb/>
            B, ad BX, conficit rationem parallelepidi ſub, BE, & </s>
            <s xml:id="echoid-s8248" xml:space="preserve">{1/2} {7/4}. </s>
            <s xml:id="echoid-s8249" xml:space="preserve">quadra-
              <lb/>
            ti, DF, ad parallelepipedum ſub, BX, & </s>
            <s xml:id="echoid-s8250" xml:space="preserve">dictis ſpatijs vltimò dictis,
              <lb/>
            ſcilicet quadrato, PX, {1/2}, quadrati, NX, & </s>
            <s xml:id="echoid-s8251" xml:space="preserve">rectangulo ſub ſexquiter-
              <lb/>
            nia, NX, & </s>
            <s xml:id="echoid-s8252" xml:space="preserve">ſub, XP, ergo omnia quadrata figurę, CBDF, ad om-
              <lb/>
            nia quadrata figuræ, CBNP, erunt vt parallelepipedum ſub, BE, & </s>
            <s xml:id="echoid-s8253" xml:space="preserve">
              <lb/>
            {1/2} {7/8}. </s>
            <s xml:id="echoid-s8254" xml:space="preserve">quadrati, DF, ad parallelepipedum ſub, BX, & </s>
            <s xml:id="echoid-s8255" xml:space="preserve">dictis ſpatijs
              <lb/>
            vltimo dictis.</s>
            <s xml:id="echoid-s8256" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8257" xml:space="preserve">Eadem methodo compoſitionis proportionum, ſumptis medijs
              <lb/>
            omnibus quadratis, AM, AV, QV, inter omnia quadrata figura-
              <lb/>
            rum, HBDM, HBNV, oſtendemus parjter omnia quadrata fi-
              <lb/>
            guræ, HBDM, ad omnia quadrata figuræ, HBNV, eſſe vt pa-
              <lb/>
            rallelepipedum ſub, BE, & </s>
            <s xml:id="echoid-s8258" xml:space="preserve">his ſpatijs .</s>
            <s xml:id="echoid-s8259" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8260" xml:space="preserve">quadrato, ME, {1/2}, quadra-
              <lb/>
            ti, ED, & </s>
            <s xml:id="echoid-s8261" xml:space="preserve">rectangulo ſub ſexquitertia, DE, & </s>
            <s xml:id="echoid-s8262" xml:space="preserve">ſub, EM, ad paral-
              <lb/>
            lelepipedum ſub, BX, & </s>
            <s xml:id="echoid-s8263" xml:space="preserve">ſub his ſpatijs, .</s>
            <s xml:id="echoid-s8264" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8265" xml:space="preserve">quadrato, VX, {1/2}. </s>
            <s xml:id="echoid-s8266" xml:space="preserve">qua-
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            drati, XN, & </s>
            <s xml:id="echoid-s8267" xml:space="preserve">rectangulo ſub ſexquitertia, XN, & </s>
            <s xml:id="echoid-s8268" xml:space="preserve">ſub, XV, quæ
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            erant nobis oſtendenda.</s>
            <s xml:id="echoid-s8269" xml:space="preserve"/>
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        <div xml:id="echoid-div811" type="section" level="1" n="480">
          <head xml:id="echoid-head500" xml:space="preserve">THEOREMA XL. PROPOS. XLII.</head>
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            <s xml:id="echoid-s8270" xml:space="preserve">SI intra parabolam axi, vel diametro eiuſdem parallela
              <lb/>
            ducatur recta linea in curuam, & </s>
            <s xml:id="echoid-s8271" xml:space="preserve">baſim parabolæ ter-
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            minata, quæ baſis ſumatur pro regula, ducta verò tangente
              <lb/>
            parabolam intermino dicti axis, vel diametri, & </s>
            <s xml:id="echoid-s8272" xml:space="preserve">producta
              <lb/>
            dicta parallela vſque ad ipſam, compleatur parallelogram-
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            mum ſub ipſa, & </s>
            <s xml:id="echoid-s8273" xml:space="preserve">baſis maiori portione: </s>
            <s xml:id="echoid-s8274" xml:space="preserve">Omnia quadrata
              <lb/>
            conſtituti parallelogrammi ad omnia quadrata reſiduæ fi-
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            guræ eodem iincluſæ parallelogrammo, ab eodem dempto
              <lb/>
            trilineo extra ſemiparabolam facto, erunt vt quadratum ba-
              <lb/>
            ſis dicti fruſti ad quadratum reſidui eiuſdem baſi, dempta
              <lb/>
            ab eadem dimidia baſis totius parabolæ, ſimul cum {1/2}.
              <lb/>
            </s>
            <s xml:id="echoid-s8275" xml:space="preserve">quadrati huius dimidiæ, & </s>
            <s xml:id="echoid-s8276" xml:space="preserve">rectangulo ſub ſexquitertia ta-
              <lb/>
            lis dimidiæ, & </s>
            <s xml:id="echoid-s8277" xml:space="preserve">eodem baſis reſiduo iam dicto.</s>
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