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

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            <s xml:id="echoid-s6388" xml:space="preserve">
              <pb o="255" file="0275" n="275" rhead="LIBER III."/>
            ergo omnia quadrata, AR, ad omnia quadrata ellipſis, BDMG,
              <lb/>
            cum rectangulis bis ſub eadem, & </s>
            <s xml:id="echoid-s6389" xml:space="preserve">ſub trilineis, BCG, GRM, erunt
              <lb/>
            vt, AR, ad ellipſim, BDMG. </s>
            <s xml:id="echoid-s6390" xml:space="preserve">Eodem modo, ſumpta pro regula,
              <lb/>
            CR, oſtendemus omnia quadrata, AR, ad omnia quadrata ellipſis,
              <lb/>
            BDMG, vna cum rectangulis bis ſub eadem, & </s>
            <s xml:id="echoid-s6391" xml:space="preserve">ſub trilineis, DAB,
              <lb/>
            CG, eſſe vt, AR, ad ellipſim, BDMG, quod oſtendere oportebat.</s>
            <s xml:id="echoid-s6392" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div610" type="section" level="1" n="354">
          <head xml:id="echoid-head371" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s6393" xml:space="preserve">_H_Inc babetur omnia quadrata, AR, regula, FR, ad omnia quadra@
              <lb/>
            ta ellipſis, BDGM, vna cum rectangulis bis ſub eadem, & </s>
            <s xml:id="echoid-s6394" xml:space="preserve">ſub
              <lb/>
            trilineis, BCG, GRM, eſſe vt omnia quadrata, AR, regula, CR, ad
              <lb/>
            omnia quadrata ellipſis, BDMG, vna cum rectangulis bis ſub eadem,
              <lb/>
            & </s>
            <s xml:id="echoid-s6395" xml:space="preserve">ſub trilineis, DAB, BCG; </s>
            <s xml:id="echoid-s6396" xml:space="preserve">vtraq; </s>
            <s xml:id="echoid-s6397" xml:space="preserve">enim oſtenſa ſunt eſſe, vt, AR,
              <lb/>
            ad ellipſim, BDMG.</s>
            <s xml:id="echoid-s6398" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div611" type="section" level="1" n="355">
          <head xml:id="echoid-head372" xml:space="preserve">THEOREMA XXXII. PROPOS. XXXIII.</head>
          <p>
            <s xml:id="echoid-s6399" xml:space="preserve">ASſumpta antecedentis figura, dimiſſis lineis, EG, DV,
              <lb/>
            producantur ad eandem partem, AC, FR, in, TX,
              <lb/>
            ita vt, AT, ſit æqualis, FX, & </s>
            <s xml:id="echoid-s6400" xml:space="preserve">iungatur, TX, ergo ipſa, A
              <lb/>
            X, CX, erunt parallelogramma. </s>
            <s xml:id="echoid-s6401" xml:space="preserve">Dico igitur, omnia qua-
              <lb/>
            drata, AR, cum
              <unsure/>
            rectanguli
              <unsure/>
            s bis ſub, AR, RT, ad omnia
              <lb/>
            quadrata ellipſis, BDMG, cum rectangulis bis ſub eadem,
              <lb/>
            & </s>
            <s xml:id="echoid-s6402" xml:space="preserve">quadrilineo, BGMXT, eſſe vt, AR, ad ellipſim, BDM
              <lb/>
            G, regula, FX.</s>
            <s xml:id="echoid-s6403" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6404" xml:space="preserve">Omnia. </s>
            <s xml:id="echoid-s6405" xml:space="preserve">n. </s>
            <s xml:id="echoid-s6406" xml:space="preserve">quadrata, AR, ad rectangula bis ſub ellipſi, BDMG,
              <lb/>
              <figure xlink:label="fig-0275-01" xlink:href="fig-0275-01a" number="171">
                <image file="0275-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0275-01"/>
              </figure>
            & </s>
            <s xml:id="echoid-s6407" xml:space="preserve">ſub trilineis, BCG, GRM, vna cum
              <lb/>
              <note position="right" xlink:label="note-0275-01" xlink:href="note-0275-01a" xml:space="preserve">Ex antec.</note>
            omnibus quadrati
              <unsure/>
            s eiuldem ellipſis, BD
              <lb/>
            MG, ſunt vt, AR, ad ellipſim, BDM
              <lb/>
              <note position="right" xlink:label="note-0275-02" xlink:href="note-0275-02a" xml:space="preserve">Coroll. 1.
                <lb/>
              26. lib. @.</note>
            G, item rectangula ſub, AR, RT, ad re-
              <lb/>
            ctangula ſub ellipſi, BDMG, & </s>
            <s xml:id="echoid-s6408" xml:space="preserve">ſub, R
              <lb/>
            T, ſunt vt, AR, ad ellipſim, BDMG,
              <lb/>
            & </s>
            <s xml:id="echoid-s6409" xml:space="preserve">eadem bis ſumpta ſunt pariter, vt, AR,
              <lb/>
            ad ellipſim, BDMG, ergo omnia qua-
              <lb/>
            drata, AR, cum rectangulis bis ſub, A
              <lb/>
            R, RT, ad omnia quadrata ellipſis, B
              <lb/>
            DMG, cum rectangulis bis ſub eadem, & </s>
            <s xml:id="echoid-s6410" xml:space="preserve">ſub trilineis, BCG,
              <lb/>
            GRM, & </s>
            <s xml:id="echoid-s6411" xml:space="preserve">cum rectangulis bis ſub eadem, & </s>
            <s xml:id="echoid-s6412" xml:space="preserve">ſub, RT, ideſt </s>
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