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

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          <p>
            <s xml:id="echoid-s5901" xml:space="preserve">
              <pb o="240" file="0260" n="260" rhead="GEOMETRIÆ"/>
            circulo ſunt ſexcupla rectangulorum ſub portione, RFV, & </s>
            <s xml:id="echoid-s5902" xml:space="preserve">qua-
              <lb/>
            drilineo, RTHYV, .</s>
            <s xml:id="echoid-s5903" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5904" xml:space="preserve">ſunt adilla, vt cubus, RV, ad ſui ipſius
              <lb/>
            ſextam partem. </s>
            <s xml:id="echoid-s5905" xml:space="preserve">In ellipſi verò omnia quadrata, RZ, ad rectangu-
              <lb/>
            la ſub portione, RFV, & </s>
            <s xml:id="echoid-s5906" xml:space="preserve">quadrilineo, RTHYV, ſunt vt cubus,
              <lb/>
            RV, vel parallelepipedum ſub altitudine, RV, baſi rhombo, RZ,
              <lb/>
            ad ſui ipſius eam partem, ad quam ſexta pars eiuſdem cubi, vel pa-
              <lb/>
            rallelepipedi ſit, vt quadratum, CE, primæ diametri, ad quadra-
              <lb/>
            tum, FH, ſecundæ; </s>
            <s xml:id="echoid-s5907" xml:space="preserve">ergo ex æqualiin circulo omnia quadrata, K
              <lb/>
            G, adrectangula ſub portione, RFV, & </s>
            <s xml:id="echoid-s5908" xml:space="preserve">ſub quadrilineo, RTH
              <lb/>
            YV, erunt vt parallelepipedum ſub altitudine, BK, baſi quadra-
              <lb/>
            to, KL, vel (quodidem eſt) vt parallelepipedum ſub, LK, & </s>
            <s xml:id="echoid-s5909" xml:space="preserve">re-
              <lb/>
            ctangulo, KG, ad, {1/6}, cubi, RV. </s>
            <s xml:id="echoid-s5910" xml:space="preserve">In ellipſi verò eadem erunt, vt
              <lb/>
            parallelepipedum ſub altitudine, LK, baſi parallelogrammo, KG,
              <lb/>
            ad eam partem cubi, RV, vel dicti parallelepipedi ſub, RV, & </s>
            <s xml:id="echoid-s5911" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0260-01" xlink:href="fig-0260-01a" number="161">
                <image file="0260-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0260-01"/>
              </figure>
            rhombo, RZ, ad quam eiuſdem cubi,
              <lb/>
            vel parallelepipedi ſexta pars ſit, vt
              <lb/>
            quad. </s>
            <s xml:id="echoid-s5912" xml:space="preserve">CE, ad quadratum, FH.</s>
            <s xml:id="echoid-s5913" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5914" xml:space="preserve">Sunt autem omnia quadrata, KG, ad
              <lb/>
            omnia quadrata figurarum, RCLT,
              <lb/>
            VEGY, demptis, omnibus quadratis
              <lb/>
            trilineorum, CLT, EGY, vna cum
              <lb/>
            omnibus quadratis, RY, & </s>
            <s xml:id="echoid-s5915" xml:space="preserve">cum re
              <lb/>
            δtangulis ſub portione, RFV, & </s>
            <s xml:id="echoid-s5916" xml:space="preserve">ſub,
              <lb/>
            RY, ſemel, vt, KG, ad portionem,
              <lb/>
            TCFEY, vt oſtendimus .</s>
            <s xml:id="echoid-s5917" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5918" xml:space="preserve">ſumpta, K
              <lb/>
            L, communi altitudine, vt parallelepi-
              <lb/>
            pedum ſub altitudine, KL, baſi paral
              <lb/>
              <note position="left" xlink:label="note-0260-01" xlink:href="note-0260-01a" xml:space="preserve">G. B. Cor.
                <lb/>
              4. Gen.
                <lb/>
              34. l. 2.</note>
            lelogrammo, KG, ad cylindricum ſub
              <lb/>
            eadem altitudine, KL, & </s>
            <s xml:id="echoid-s5919" xml:space="preserve">ſub baſi por
              <lb/>
            tione, TCFEY, ergo, colligendo,
              <lb/>
            omnia quadrata, KG, ad omnia qua
              <lb/>
            drata portionum, RCT, VEY, cum
              <lb/>
            rectangulis bis ſub ijſdem, & </s>
            <s xml:id="echoid-s5920" xml:space="preserve">ſub trili
              <lb/>
            neis, CLT, EGY, inſuper ad omnia
              <lb/>
            quadrata, RY, cum rectangulis ſub, R
              <lb/>
            Y, & </s>
            <s xml:id="echoid-s5921" xml:space="preserve">portione, RFV, ſemel, & </s>
            <s xml:id="echoid-s5922" xml:space="preserve">ad rectangula ſub eadem portio-
              <lb/>
            ne, RFV, & </s>
            <s xml:id="echoid-s5923" xml:space="preserve">quadrilineo, RTHYV, ideſt ad omnia quadrata
              <lb/>
            portionis, RFV, cum rectangulis iterum ſub eadem, & </s>
            <s xml:id="echoid-s5924" xml:space="preserve">ſub, RY,
              <lb/>
            quia rectangula ſub portione, RFV, & </s>
            <s xml:id="echoid-s5925" xml:space="preserve">quadrilineo, RTHYV,
              <lb/>
            ſeparantur per lineam, TY, inrectangula ſub, RY, & </s>
            <s xml:id="echoid-s5926" xml:space="preserve">portione,
              <lb/>
            RFV, & </s>
            <s xml:id="echoid-s5927" xml:space="preserve">ſub portione, THY, & </s>
            <s xml:id="echoid-s5928" xml:space="preserve">portione, RFV, quæ ſunt om-
              <lb/>
              <note position="left" xlink:label="note-0260-02" xlink:href="note-0260-02a" xml:space="preserve">A. 23. l. 2.</note>
            nia quadrata portionis, RFV, .</s>
            <s xml:id="echoid-s5929" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5930" xml:space="preserve">(his omnibus in vnam </s>
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