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

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            <s xml:id="echoid-s5730" xml:space="preserve">
              <pb o="233" file="0253" n="253" rhead="LIBER III."/>
            ſub, MX, &</s>
            <s xml:id="echoid-s5731" xml:space="preserve">, MYT, in omnia quadrata, MYT, & </s>
            <s xml:id="echoid-s5732" xml:space="preserve">in rectangula
              <lb/>
            ſub, MYT, & </s>
            <s xml:id="echoid-s5733" xml:space="preserve">ſub, MTXC, omnia ergo quadrata, MX, ad om-
              <lb/>
            nia quadrata, MYT, cum rectangulis ſub, MYT, & </s>
            <s xml:id="echoid-s5734" xml:space="preserve">ſub quadri-
              <lb/>
            lineo, MTXC, erunt vt, MX, ad, MYT, .</s>
            <s xml:id="echoid-s5735" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5736" xml:space="preserve">vt, XY, ad, YZ,
              <lb/>
            .</s>
            <s xml:id="echoid-s5737" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5738" xml:space="preserve">vt quadratum, XY, ad rectangulum ſub, XY, &</s>
            <s xml:id="echoid-s5739" xml:space="preserve">, YZ, eadem
              <lb/>
            verò ad hæc quater ſumpta erunt, vt quadratum, XY, adrectangu-
              <lb/>
            lum ſub, XY, & </s>
            <s xml:id="echoid-s5740" xml:space="preserve">quadrupla, YZ, ſunt autem omnia quadrata ſe-
              <lb/>
            miportionis, MYT, quater ſumpta æqualia omnibus quadratis por-
              <lb/>
              <note position="right" xlink:label="note-0253-01" xlink:href="note-0253-01a" xml:space="preserve">D.23. hu-
                <lb/>
              ius.</note>
            tionis, MST, & </s>
            <s xml:id="echoid-s5741" xml:space="preserve">rectangula ſub, MYT, & </s>
            <s xml:id="echoid-s5742" xml:space="preserve">quadrilineo, MTXC,
              <lb/>
            quater ſumpta æqualia rectangulis ſub eodem quadrilineo, & </s>
            <s xml:id="echoid-s5743" xml:space="preserve">ſub
              <lb/>
            portione, SMT, bis ſumptis, nam portio, SMT, bis continet ſe-
              <lb/>
            miportionem, MYT, ergo conuertendo, omnia quadrata portio.
              <lb/>
            </s>
            <s xml:id="echoid-s5744" xml:space="preserve">nis, SMT, cum rectangulis bis ſub eadem, & </s>
            <s xml:id="echoid-s5745" xml:space="preserve">quadrilineo, MTX
              <lb/>
            C, ad omnia quadrata, MX, erunt vt rectangulum ſub quadrupla,
              <lb/>
            YZ, & </s>
            <s xml:id="echoid-s5746" xml:space="preserve">ſub, YX, ad quadratum, YX, omnia autem quadrata, M
              <lb/>
            X, ad omnia quadrata, HV, cum rectangulis bis ſub parallelogram-
              <lb/>
              <figure xlink:label="fig-0253-01" xlink:href="fig-0253-01a" number="158">
                <image file="0253-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0253-01"/>
              </figure>
            mis, HV, VC, ſunt
              <lb/>
            vt vnum ad vnum.
              <lb/>
            </s>
            <s xml:id="echoid-s5747" xml:space="preserve">vt quadratum, YX,
              <lb/>
            ad quadratum, RV,
              <lb/>
            cum rectangulis bis
              <lb/>
            ſub, RV, VX, ergo
              <lb/>
            exęquali omnia qua-
              <lb/>
            drata portionis, SM
              <lb/>
            T, cum rectangulis
              <lb/>
            bis ſub eadem, & </s>
            <s xml:id="echoid-s5748" xml:space="preserve">ſub
              <lb/>
            quadrilineo, MTX, adomnia quadrata, HV, cum rectangulis bis
              <lb/>
            ſub parallelogrammis, HV, VC, erunt vt rectangulum ſub, XY, & </s>
            <s xml:id="echoid-s5749" xml:space="preserve">
              <lb/>
            quadrupla, YZ, ad quadratum, RV, cum rectangulis bis ſub, RV
              <lb/>
            X, vel vt eorum dim dia .</s>
            <s xml:id="echoid-s5750" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5751" xml:space="preserve">vt rectangulum ſub, XY, & </s>
            <s xml:id="echoid-s5752" xml:space="preserve">dupla, YZ,
              <lb/>
            ad dimidium quadrati, RV, ſeil cet ad rectangulum ſub, RV, VY,
              <lb/>
            cum rectangulo ſub, RV, VX, vel adhuc, vt horum dimidia (com-
              <lb/>
            pone autem rectangulum ſub, RV, VY, cumrectangulo ſub, RV,
              <lb/>
            VX, ex quibus fit rectangulum ſub, RV, YX,). </s>
            <s xml:id="echoid-s5753" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5754" xml:space="preserve">vtrectangulum
              <lb/>
            ſub, ZY, YX, ad rectangulum ſub, RY, YX, .</s>
            <s xml:id="echoid-s5755" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5756" xml:space="preserve">vt, ZY, ad, YR,
              <lb/>
            .</s>
            <s xml:id="echoid-s5757" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5758" xml:space="preserve">vt ſemiportio, MYT, ad, MV, vel vt portio, SMT, ad, HV.</s>
            <s xml:id="echoid-s5759" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5760" xml:space="preserve">Inſuper omnia quadrata, HV, cum rectangulis bis ſub parallelo-
              <lb/>
            grammis, HV, VC, ad omnia quadrata, RF, cum rectangulis bis
              <lb/>
            ſub parallelogrammis, RF, FX, funt vt, HR, ad, RD, & </s>
            <s xml:id="echoid-s5761" xml:space="preserve">tan-
              <lb/>
            dem modo ſuperiori oſtendemus omnia quadrata, RF, cum rectan-
              <lb/>
            gulis bis ſub parallelogrammis, RF, FX, ad omnia quadrata
              <lb/>
            portionis, SET, cum rectangulis bis ſub eadem, & </s>
            <s xml:id="echoid-s5762" xml:space="preserve">ſub </s>
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