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

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            <s xml:id="echoid-s6251" xml:space="preserve">
              <pb o="251" file="0271" n="271" rhead="LIBER III."/>
            ta figuræ, BDMO, cum rectangulis bis ſub eadem ſigura, & </s>
            <s xml:id="echoid-s6252" xml:space="preserve">ſub
              <lb/>
            trilineis, BCO, ONM, erunt vt, AN, ad figuram, BDMO,
              <lb/>
            quod oſtendere opus erat.</s>
            <s xml:id="echoid-s6253" xml:space="preserve"/>
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        <div xml:id="echoid-div602" type="section" level="1" n="350">
          <head xml:id="echoid-head367" xml:space="preserve">THEOREMA XXIX. PROPOS. XXX.</head>
          <p>
            <s xml:id="echoid-s6254" xml:space="preserve">EXponatur figura Theor. </s>
            <s xml:id="echoid-s6255" xml:space="preserve">antecedentis, dimiſſis tamen re-
              <lb/>
            ctis lineis, DO, VR, & </s>
            <s xml:id="echoid-s6256" xml:space="preserve">ſit adhuc regula, EN, produ-
              <lb/>
            cantur autem ad eaſdem partes, AC, EN, in, HF, ita vt, C
              <lb/>
            H, ſit æqualis, NF, iuncta igitur, HF, erit, HF, parallela
              <lb/>
            ipſi, CN, quoniam, CH, NF, ſunt æquales, & </s>
            <s xml:id="echoid-s6257" xml:space="preserve">parallelæ,
              <lb/>
            & </s>
            <s xml:id="echoid-s6258" xml:space="preserve">erit parallelogrammum, AF, &</s>
            <s xml:id="echoid-s6259" xml:space="preserve">, CF. </s>
            <s xml:id="echoid-s6260" xml:space="preserve">Dico ergo omnia
              <lb/>
            quadrata, AN, cumrectangulis bis ſub, AN, NH, ad om-
              <lb/>
            nia quadrata figuræ, BDMO, cum rectangulis bis ſub ea-
              <lb/>
            dem, & </s>
            <s xml:id="echoid-s6261" xml:space="preserve">ſub quadrilineo, BOMFH, eſſe vt, AN, adfigu-
              <lb/>
            ram, BDMO.</s>
            <s xml:id="echoid-s6262" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6263" xml:space="preserve">Omnia quadrata. </s>
            <s xml:id="echoid-s6264" xml:space="preserve">n. </s>
            <s xml:id="echoid-s6265" xml:space="preserve">parallelogrammi, AN, ad omnia quadrata fi-
              <lb/>
            gurę, BDMO, cum rectangulis bis ſub eadem, & </s>
            <s xml:id="echoid-s6266" xml:space="preserve">ſub trilineis, BC
              <lb/>
              <note position="right" xlink:label="note-0271-01" xlink:href="note-0271-01a" xml:space="preserve">Ex antec.</note>
            O, ONM, ſunt vt, AN, ad figuram, BDMO. </s>
            <s xml:id="echoid-s6267" xml:space="preserve">Item rectangula
              <lb/>
              <note position="right" xlink:label="note-0271-02" xlink:href="note-0271-02a" xml:space="preserve">Coroll. 1.
                <lb/>
              26. lib. 2
                <unsure/>
              .</note>
            ſub, AN, NH, ad rectangula ſub figura, BDMO, & </s>
            <s xml:id="echoid-s6268" xml:space="preserve">ſub, NH,
              <lb/>
            ſunt vt, AN, ad f
              <unsure/>
            iguram, BDMO, & </s>
            <s xml:id="echoid-s6269" xml:space="preserve">eadem rectangula ſub, AN,
              <lb/>
            NH, bis ſumpta ad rectangula ſub figura, BDMO, & </s>
            <s xml:id="echoid-s6270" xml:space="preserve">ſub, NH,
              <lb/>
            bis ſumpta erunt pariter, vt, AN, ad figuram, BDMO, . </s>
            <s xml:id="echoid-s6271" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6272" xml:space="preserve">vt omnia
              <lb/>
            quadrata, AN, ad rectangula bis ſub figura, BDMO, & </s>
            <s xml:id="echoid-s6273" xml:space="preserve">ſub trili-
              <lb/>
            neis, BCO, ONM, cum omnibus quadratis eiuſdem figurę, BDM
              <lb/>
            O, ergo vt vnum ad vnum, ita omnia ad omnia. </s>
            <s xml:id="echoid-s6274" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s6275" xml:space="preserve">vt omnia quadra-
              <lb/>
              <figure xlink:label="fig-0271-01" xlink:href="fig-0271-01a" number="167">
                <image file="0271-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0271-01"/>
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            ta, AN, ad omnia quadrata figuræ, BD
              <lb/>
              <figure xlink:label="fig-0271-02" xlink:href="fig-0271-02a" number="168">
                <image file="0271-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0271-02"/>
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            MO, cum rectangulis bis ſub eadem figu-
              <lb/>
            ra, & </s>
            <s xml:id="echoid-s6276" xml:space="preserve">ſub trilineis, BCO, ONM, ita om-
              <lb/>
            nia quadrata, AN, cum rectangulis bis ſub,
              <lb/>
            AN, NH, ad omnia quadrata figuræ, B
              <lb/>
            DMO, cum rectangulis bis ſub eadem, & </s>
            <s xml:id="echoid-s6277" xml:space="preserve">
              <lb/>
            ſub trilineis, BCO, ONM, & </s>
            <s xml:id="echoid-s6278" xml:space="preserve">bis ſub ea-
              <lb/>
            dem, & </s>
            <s xml:id="echoid-s6279" xml:space="preserve">ſub, NH, .</s>
            <s xml:id="echoid-s6280" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6281" xml:space="preserve">ad rectangula bis ſub
              <lb/>
            eadem, & </s>
            <s xml:id="echoid-s6282" xml:space="preserve">ſub quadrilineo, BOMFH;
              <lb/>
            </s>
            <s xml:id="echoid-s6283" xml:space="preserve">ſunt autem omnia quadrata, AN, ad om-
              <lb/>
            nia quadrata figurę, BDMO, cum rectangulis bis ſub eadem, & </s>
            <s xml:id="echoid-s6284" xml:space="preserve">ſub
              <lb/>
            trilineis, BCO, ONM, vt, AN, ad, BDMO; </s>
            <s xml:id="echoid-s6285" xml:space="preserve">ergo omnia qua-
              <lb/>
            drata, AN, cum rectangulis bis ſub, AN, NH, ad omnia quadrata
              <lb/>
            figurę, BDMO, cum rectangulis bis ſub, eadem, & </s>
            <s xml:id="echoid-s6286" xml:space="preserve">ſub </s>
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