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

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            <s xml:id="echoid-s9529" xml:space="preserve">
              <pb o="372" file="0392" n="392" rhead="GEOMETRIE"/>
            G, ideò omnia quadrata, AF, demptis omnibus quadratis hyper-
              <lb/>
            bolæ, DNF, ad omnia quadrata, SF, demptis omnibus quadra-
              <lb/>
            tis fruſti, HDFG, habebunt rationem compoſitam ex ea, quam
              <lb/>
            habet rectangulum ſub compoſita ex {1/2}: </s>
            <s xml:id="echoid-s9530" xml:space="preserve">ON, & </s>
            <s xml:id="echoid-s9531" xml:space="preserve">{2/3}. </s>
            <s xml:id="echoid-s9532" xml:space="preserve">NE, & </s>
            <s xml:id="echoid-s9533" xml:space="preserve">ſub, N
              <lb/>
            E, ad rectangulum, NEO, & </s>
            <s xml:id="echoid-s9534" xml:space="preserve">ex ea, quam habet, NE, ad, EM,
              <lb/>
            & </s>
            <s xml:id="echoid-s9535" xml:space="preserve">ex ea, quam habent omnia quadrata, SF, ad omnia quadrata,
              <lb/>
              <figure xlink:label="fig-0392-01" xlink:href="fig-0392-01a" number="268">
                <image file="0392-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0392-01"/>
              </figure>
            SF, demptis omnibus quadratis fruſti, HD
              <lb/>
            FG. </s>
            <s xml:id="echoid-s9536" xml:space="preserve">Quoniam autem omnia quadrata,
              <lb/>
            SF, ad omnia quadrata fruſti, HDFG, sũt
              <lb/>
            vt rectã gulum, OEN, ad rect. </s>
            <s xml:id="echoid-s9537" xml:space="preserve">ſub OE, NM,
              <lb/>
            cum'rectãg. </s>
            <s xml:id="echoid-s9538" xml:space="preserve">ſub compoſita ex {1/2}. </s>
            <s xml:id="echoid-s9539" xml:space="preserve">ON, & </s>
            <s xml:id="echoid-s9540" xml:space="preserve">{1/3}.
              <lb/>
            </s>
            <s xml:id="echoid-s9541" xml:space="preserve">ME, & </s>
            <s xml:id="echoid-s9542" xml:space="preserve">ſub, ME, ideò oĩa quadrata, SF, ad
              <lb/>
            reſiduum, daptis omnibus quadratis fruſti,
              <lb/>
            HDFG, erunt vt rectangulum, OEN, ad
              <lb/>
            reſiduum, demptis à rectangulo, OEN, re-
              <lb/>
              <note position="left" xlink:label="note-0392-01" xlink:href="note-0392-01a" xml:space="preserve">3. huius.</note>
            ctangulo, ſub, OE, NM, vna eum rectan-
              <lb/>
            gulo ſub compoſita ex {1/2}. </s>
            <s xml:id="echoid-s9543" xml:space="preserve">ON, & </s>
            <s xml:id="echoid-s9544" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s9545" xml:space="preserve">ME,
              <lb/>
            & </s>
            <s xml:id="echoid-s9546" xml:space="preserve">ſub, ME; </s>
            <s xml:id="echoid-s9547" xml:space="preserve">ſi igitur à rectangulo, OEN,
              <lb/>
            dempſeris rectangulum ſub, OE, MN, re-
              <lb/>
            manebit rectangulum ſub, OE, EM, rur-
              <lb/>
            ſus ſi à rectangulo ſub, OE, EM, dempſeris rectangulum ſub com-
              <lb/>
            poſita ex {1/2}. </s>
            <s xml:id="echoid-s9548" xml:space="preserve">ON, & </s>
            <s xml:id="echoid-s9549" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s9550" xml:space="preserve">ME, & </s>
            <s xml:id="echoid-s9551" xml:space="preserve">ſub, ME, .</s>
            <s xml:id="echoid-s9552" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9553" xml:space="preserve">ſi dempſeris rectangu-
              <lb/>
            lum ſub, OB, &</s>
            <s xml:id="echoid-s9554" xml:space="preserve">, ME, remanebit rectangulum ſub, BE, EM, à quo
              <lb/>
            ſi adhuc auferas rectangulum ſub {1/3}. </s>
            <s xml:id="echoid-s9555" xml:space="preserve">ME, & </s>
            <s xml:id="echoid-s9556" xml:space="preserve">ſub, ME, .</s>
            <s xml:id="echoid-s9557" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9558" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s9559" xml:space="preserve">qua-
              <lb/>
            drati, ME, habebimus rectangulum, BEM, dempto {1/3}. </s>
            <s xml:id="echoid-s9560" xml:space="preserve">quadrati,
              <lb/>
            ME, ad quod rectangulum, OEN, erit vt omnia quadrata, SF, ad
              <lb/>
            ſui reliquum, demptis omnibus quadratis fruſti, HDFG, ergo om-
              <lb/>
            nia quadrata, AF, demptis omnibus quadratis hyperbolæ, DNF,
              <lb/>
            ad omnia quadrata, SF, demptis omnibus quadratis fruſti, HDF
              <lb/>
            G, habebunt rationem compoſitam ex his rationibus .</s>
            <s xml:id="echoid-s9561" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s9562" xml:space="preserve">ex ea, quã
              <lb/>
            habet rectangulum ſub compoſita ex {1/2}. </s>
            <s xml:id="echoid-s9563" xml:space="preserve">ON, & </s>
            <s xml:id="echoid-s9564" xml:space="preserve">{2/3}. </s>
            <s xml:id="echoid-s9565" xml:space="preserve">NE, & </s>
            <s xml:id="echoid-s9566" xml:space="preserve">ſub, NE,
              <lb/>
            ad rectangulum, OEN, & </s>
            <s xml:id="echoid-s9567" xml:space="preserve">ex ratione, NE, ad, EM, & </s>
            <s xml:id="echoid-s9568" xml:space="preserve">ex ea, quam
              <lb/>
            habet rectangulum, OEN, ad rectangulum, BEM, dempto {1/3}. </s>
            <s xml:id="echoid-s9569" xml:space="preserve">qua-
              <lb/>
            drati, ME; </s>
            <s xml:id="echoid-s9570" xml:space="preserve">harum autem iſtæ duæ, quam .</s>
            <s xml:id="echoid-s9571" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s9572" xml:space="preserve">habet rectangulum
              <lb/>
            ſub compoſita ex {1/2}. </s>
            <s xml:id="echoid-s9573" xml:space="preserve">ON, & </s>
            <s xml:id="echoid-s9574" xml:space="preserve">{2/3}. </s>
            <s xml:id="echoid-s9575" xml:space="preserve">NE, & </s>
            <s xml:id="echoid-s9576" xml:space="preserve">ſub, NE, ad rectangulum,
              <lb/>
            OEN, & </s>
            <s xml:id="echoid-s9577" xml:space="preserve">quam habet rectangulum, OEN, ad rectangulum, BEM,
              <lb/>
            dempto {1/3}. </s>
            <s xml:id="echoid-s9578" xml:space="preserve">quadrati, ME, conficiunt rationem rectanguli ſub com.
              <lb/>
            </s>
            <s xml:id="echoid-s9579" xml:space="preserve">poſita ex {1/2}. </s>
            <s xml:id="echoid-s9580" xml:space="preserve">ON, & </s>
            <s xml:id="echoid-s9581" xml:space="preserve">{2/3}. </s>
            <s xml:id="echoid-s9582" xml:space="preserve">NE, & </s>
            <s xml:id="echoid-s9583" xml:space="preserve">ſub, NE, ad rectangulum, BEM
              <lb/>
            dempto {1/3}. </s>
            <s xml:id="echoid-s9584" xml:space="preserve">quadrati, ME, vel, his triplicatis, conficiunt rationem'
              <lb/>
            rectanguli ſub compoſita ex tribus, BN, .</s>
            <s xml:id="echoid-s9585" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s9586" xml:space="preserve">ex, NX, & </s>
            <s xml:id="echoid-s9587" xml:space="preserve">ter {2/3}. </s>
            <s xml:id="echoid-s9588" xml:space="preserve">NE,
              <lb/>
            .</s>
            <s xml:id="echoid-s9589" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s9590" xml:space="preserve">dupla, NE, .</s>
            <s xml:id="echoid-s9591" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s9592" xml:space="preserve">ſub compoſita ex, NE, &</s>
            <s xml:id="echoid-s9593" xml:space="preserve">, EX, & </s>
            <s xml:id="echoid-s9594" xml:space="preserve">ſub, NE, ad
              <lb/>
            rectangulum ſub tripla, BE, & </s>
            <s xml:id="echoid-s9595" xml:space="preserve">ſub, EM, demptis {3/3}. </s>
            <s xml:id="echoid-s9596" xml:space="preserve">ideſt </s>
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