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

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          <p>
            <s xml:id="echoid-s10467" xml:space="preserve">
              <pb o="403" file="0423" n="423" rhead="LIBER V."/>
            quadratum, DC, quadratum, DC, ad quadratum, YN, & </s>
            <s xml:id="echoid-s10468" xml:space="preserve">qua-
              <lb/>
              <note position="right" xlink:label="note-0423-01" xlink:href="note-0423-01a" xml:space="preserve">Defin. 13.
                <lb/>
              lib .1.</note>
            dratum, YN, ad quadratum, AV, componunt rationem quadra-
              <lb/>
            ti, AV, ad quadratum, AV, quę ſimul cum ratione ipſius, EC, ad
              <lb/>
            MN, componit rationem parallelepipedi lub, EC, & </s>
            <s xml:id="echoid-s10469" xml:space="preserve">quadrato,
              <lb/>
            AV, ad parallelepipedum ſub, MN, & </s>
            <s xml:id="echoid-s10470" xml:space="preserve">quadrato, AV, quæ tandẽ
              <lb/>
            eſt eadem ei, quam habet, EC, ad, MN, quia illa ſunt parallelepi-
              <lb/>
            peda in eadem baſi, & </s>
            <s xml:id="echoid-s10471" xml:space="preserve">ideò omnia quadrata figuræ, FADCVE,
              <lb/>
            demptis omnibus quadratis triangulorum, KOI, POQ, ad om-
              <lb/>
            nia quadrata figuræ, TAYNVM, demptis omnibus quadratis
              <lb/>
            triangulorum, & </s>
            <s xml:id="echoid-s10472" xml:space="preserve">O℟, ΩΟΠ, erum vt, EC, ad, MN, vel, XL, ad,
              <lb/>
            HG, quod demonſtrare opus erat.</s>
            <s xml:id="echoid-s10473" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div951" type="section" level="1" n="567">
          <head xml:id="echoid-head592" xml:space="preserve">THEOREMA XXV. PROPOS. XXVI.</head>
          <p>
            <s xml:id="echoid-s10474" xml:space="preserve">ASumpta iterum figura Propoſ. </s>
            <s xml:id="echoid-s10475" xml:space="preserve">23. </s>
            <s xml:id="echoid-s10476" xml:space="preserve">dimiſſo quouis pa-
              <lb/>
            rallelogrammorum, FC, TN, vt dimiſſo, TN, cæte-
              <lb/>
            ris ijſdem manentibus, oſtendemus omnia quadrata, FC,
              <lb/>
            demptis omnibus quadratis oppoſitarum hyperbolarum,
              <lb/>
            FAD, EVC, regula, EC, ad omnia quadrata figuræ, FAD
              <lb/>
            CVE, regula, DC, vel, AV, habere rationem compoſitam
              <lb/>
            ex ratione rectanguli, AOZ, bis cum @. </s>
            <s xml:id="echoid-s10477" xml:space="preserve">quadrati, VZ, ad
              <lb/>
            rectangulum, AZO, & </s>
            <s xml:id="echoid-s10478" xml:space="preserve">ex ratione rectanguli ſub, DC, vel,
              <lb/>
            RZ, & </s>
            <s xml:id="echoid-s10479" xml:space="preserve">ſub EC, ad quadratum, AV, cum. </s>
            <s xml:id="echoid-s10480" xml:space="preserve">quadrati, KI,
              <lb/>
            vel cum rectangulo ſub, AZ, & </s>
            <s xml:id="echoid-s10481" xml:space="preserve">ſexquitertia, ZV.</s>
            <s xml:id="echoid-s10482" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10483" xml:space="preserve">Omnia namq; </s>
            <s xml:id="echoid-s10484" xml:space="preserve">quadrata, FC, demptis omnibus quadratis oppo-
              <lb/>
            ſitarum hyperbolarum, FAD, EVC, regula, EC, ad omnia qua-
              <lb/>
            drata figuræ, FADCVE, regula, AV, habent rationem compoſi-
              <lb/>
            tam ex ratione omnium quadratorum, FC, demptis omnious qua-
              <lb/>
            dratis oppoſitarum hyperbolarum, FAD, EVC, ad omnia qua-
              <lb/>
            drata, FC, communiregula, EC, .</s>
            <s xml:id="echoid-s10485" xml:space="preserve">f. </s>
            <s xml:id="echoid-s10486" xml:space="preserve">ex ratione rectanguli, AOZ,
              <lb/>
              <note position="right" xlink:label="note-0423-02" xlink:href="note-0423-02a" xml:space="preserve">10. huius.</note>
            bis cum {2/3}. </s>
            <s xml:id="echoid-s10487" xml:space="preserve">quadrati, VZ, ad rectangulum, AZO, & </s>
            <s xml:id="echoid-s10488" xml:space="preserve">ex ratione
              <lb/>
            omnium quadratorum, FC, regula, EC, ad omnia quadrata, FC,
              <lb/>
            regula, CD, vel, AV, .</s>
            <s xml:id="echoid-s10489" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s10490" xml:space="preserve">ex ratione, EC, ad, CD, vel rectanguli
              <lb/>
              <note position="right" xlink:label="note-0423-03" xlink:href="note-0423-03a" xml:space="preserve">29. l. 2.</note>
            ſub, EC, CD, ad quadratum, CD, & </s>
            <s xml:id="echoid-s10491" xml:space="preserve">tandem componitur ex ra-
              <lb/>
            tione omnium quadratorum, FC, regula, DC, ad omnia quadra-
              <lb/>
            ta figuræ, FADCVE, regula eadem, DC, .</s>
            <s xml:id="echoid-s10492" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s10493" xml:space="preserve">ex ratione quadrati,
              <lb/>
              <note position="right" xlink:label="note-0423-04" xlink:href="note-0423-04a" xml:space="preserve">21. huius.</note>
            DC, ad quadratum, AV, cum {1/3}. </s>
            <s xml:id="echoid-s10494" xml:space="preserve">quadrati KI, duæ verò rationes,
              <lb/>
            ſcilicet rectanguli ſub, ED, CD, ad quadratum, CD, & </s>
            <s xml:id="echoid-s10495" xml:space="preserve">quadrati,
              <lb/>
            CD, ad quadratum, AV, cum {1/3}. </s>
            <s xml:id="echoid-s10496" xml:space="preserve">quadrati, KI, componunt </s>
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