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

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              <pb o="225" file="0245" n="245" rhead="LIBER III."/>
            M,B, E, G. </s>
            <s xml:id="echoid-s5490" xml:space="preserve">Dico igitur omnia quadrata parallelogrammi, HF,
              <lb/>
            ſimul cum rectangulis bis ſub, HF, & </s>
            <s xml:id="echoid-s5491" xml:space="preserve">parallelogrammo, FC, ad
              <lb/>
            omnia quadrata circuli, vel ellipſis, MBEG, ſimul cum rectangu-
              <lb/>
            lis bis ſub eodem circulo, vel ellipſi, MBEG, & </s>
            <s xml:id="echoid-s5492" xml:space="preserve">ſub quadrilineo, M
              <lb/>
            GEOC, eſſe vt parallelogrammum, HF, ad circulum, vel ellipſim,
              <lb/>
            MBEG : </s>
            <s xml:id="echoid-s5493" xml:space="preserve">Omnia .</s>
            <s xml:id="echoid-s5494" xml:space="preserve">n. </s>
            <s xml:id="echoid-s5495" xml:space="preserve">quadrata parallelogrammi, HO, ad omnia
              <lb/>
              <note position="right" xlink:label="note-0245-01" xlink:href="note-0245-01a" xml:space="preserve">9. Lib. 2.</note>
            quadrata parallelogrammi, MO, ſunt vt quadratum, DO, ad qua-
              <lb/>
            dratum, OE, omnia item quadrata parallelogrammi, MO, ad re-
              <lb/>
              <note position="right" xlink:label="note-0245-02" xlink:href="note-0245-02a" xml:space="preserve">Coroll. 1.
                <lb/>
              26.lib.2.</note>
            ctangula ſub parallelogrammo, MO, & </s>
            <s xml:id="echoid-s5496" xml:space="preserve">portione, MGE, ſunt vt,
              <lb/>
            MO, ad portionem, MGE, fiat vt, MF, ad portionem, MGE,
              <lb/>
            ita, FE, ad, EI, erit ergo vt, MO, ad portionem, MGE, ita, O
              <lb/>
            E, ad, EI, ergo omnia quadrata, MO, ad rectangula ſub, MO, & </s>
            <s xml:id="echoid-s5497" xml:space="preserve">
              <lb/>
            portione, MGE, erunt vt, OE, ad, EI, .</s>
            <s xml:id="echoid-s5498" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5499" xml:space="preserve">vt quadratum, OE,
              <lb/>
              <note position="right" xlink:label="note-0245-03" xlink:href="note-0245-03a" xml:space="preserve">5.Lib.2.</note>
            ad rectangulum ſub, OE, EI, erant autem omnia quadrata, HO,
              <lb/>
            ad omnia quadrata, OM, vt quadratum, DO, ad quadratum, O
              <lb/>
            E, ergo ex æquali omnia quadrata, HO, ad rectangula ſub, MO,
              <lb/>
            & </s>
            <s xml:id="echoid-s5500" xml:space="preserve">ſub portione, MGE, erunt vt quadratum, DO, ad rectangu-
              <lb/>
            lum ſub, OE, EI, ad eadem verò quater ſumpta, vt quadratum, D
              <lb/>
            O, ad rectangulum ſub, OE, & </s>
            <s xml:id="echoid-s5501" xml:space="preserve">quadrupla, EI; </s>
            <s xml:id="echoid-s5502" xml:space="preserve">rectangula autem
              <lb/>
              <figure xlink:label="fig-0245-01" xlink:href="fig-0245-01a" number="152">
                <image file="0245-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0245-01"/>
              </figure>
            ſub, MO, & </s>
            <s xml:id="echoid-s5503" xml:space="preserve">por-
              <lb/>
              <note position="right" xlink:label="note-0245-04" xlink:href="note-0245-04a" xml:space="preserve">Per C, 23.
                <lb/>
              lib.2.</note>
            tione, MGE, æ-
              <lb/>
            quantur rectangulis
              <lb/>
            ſub quadrilineo, M
              <lb/>
            GEOC, & </s>
            <s xml:id="echoid-s5504" xml:space="preserve">por
              <lb/>
            tione, MGE, vna
              <lb/>
            cum omnibus qua
              <lb/>
            dratis portionis, M
              <lb/>
            GE, ilia ig tur qua-
              <lb/>
            ter ſumpta reddunt
              <lb/>
            quater rectangula ſub portione, MGE, & </s>
            <s xml:id="echoid-s5505" xml:space="preserve">quadrilineo, MGEO
              <lb/>
            C, vna cum omnibus quadratis portionis, MGE, quater ſumptis,
              <lb/>
            quia verò omnia quadrata circuli, vel ellipſis, MBEG, æquantur
              <lb/>
              <note position="right" xlink:label="note-0245-05" xlink:href="note-0245-05a" xml:space="preserve">Per D.23.
                <lb/>
              lib,2.</note>
            omnibus quadratis portionis, MBE, & </s>
            <s xml:id="echoid-s5506" xml:space="preserve">portionis, MGE, vna cum
              <lb/>
            rectangulis bis ſub vtriſq; </s>
            <s xml:id="echoid-s5507" xml:space="preserve">portionibus .</s>
            <s xml:id="echoid-s5508" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5509" xml:space="preserve">vna cum omnibus quadratis
              <lb/>
            portionis, MGE, bis ſumptis, & </s>
            <s xml:id="echoid-s5510" xml:space="preserve">omnia quadrata portionis, MBE,
              <lb/>
            æquantur omnibus quadratis portionis, MGE, ideò omnia quadra-
              <lb/>
            ta portionis, MGE, quater ſumpta æquantur omnib. </s>
            <s xml:id="echoid-s5511" xml:space="preserve">quadratis cir-
              <lb/>
            culi, vel ellipſis, MBEG, item rectangula ſub portione, MGE, & </s>
            <s xml:id="echoid-s5512" xml:space="preserve">
              <lb/>
            quadrilineo, MGEOC, quater æquantur rectangulis ſub toto circu-
              <lb/>
            lo, vel ellipſi, MBEG, & </s>
            <s xml:id="echoid-s5513" xml:space="preserve">ſub quadrilineo, MGEOC, bis ſumptis, itaut
              <lb/>
            hucuſq; </s>
            <s xml:id="echoid-s5514" xml:space="preserve">probauerimus rectangula ſub portione, MGE, & </s>
            <s xml:id="echoid-s5515" xml:space="preserve">paralle-
              <lb/>
            logrammo, MO, quater ſumpta æquari omnibus quadratis </s>
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