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

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          <p>
            <s xml:id="echoid-s10085" xml:space="preserve">
              <pb o="391" file="0411" n="411" rhead="LIBER V."/>
            bis, cum {2/3}. </s>
            <s xml:id="echoid-s10086" xml:space="preserve">quadrati, EM. </s>
            <s xml:id="echoid-s10087" xml:space="preserve">Ducanturper, M, O, puncta paralie
              <lb/>
              <note position="right" xlink:label="note-0411-01" xlink:href="note-0411-01a" xml:space="preserve">17. P
                <unsure/>
              imi
                <lb/>
              Con.</note>
            lę, AC, ipſę, VS, TR, igitur, TR, tanget ſectionem, AMC, & </s>
            <s xml:id="echoid-s10088" xml:space="preserve">
              <lb/>
            ſunt parallelogramma, TC, VC, VD: </s>
            <s xml:id="echoid-s10089" xml:space="preserve">Omnia ergo quadrata pa.
              <lb/>
            </s>
            <s xml:id="echoid-s10090" xml:space="preserve">rallelogrammi, VC, ad omnia quadrata hyperbolæ, AMC, ha
              <lb/>
            bent ratiíonem compoſtionem ex ea, quam habent omnia quadrata,
              <lb/>
              <note position="right" xlink:label="note-0411-02" xlink:href="note-0411-02a" xml:space="preserve">Defin. 12
                <lb/>
              l. 1.
                <lb/>
              10. l.2.</note>
            VC, ad omnia quadrata, TC, .</s>
            <s xml:id="echoid-s10091" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10092" xml:space="preserve">exratione, OE, ad, EM, & </s>
            <s xml:id="echoid-s10093" xml:space="preserve">ex
              <lb/>
              <figure xlink:label="fig-0411-01" xlink:href="fig-0411-01a" number="280">
                <image file="0411-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0411-01"/>
              </figure>
            ratione omnium quadratorum, TC,
              <lb/>
            ad omnia quadrata hyperbolę, AMC,
              <lb/>
            ideſt ex ea, quam habet, NE, ad cõ-
              <lb/>
            poſitam ex, OM, & </s>
            <s xml:id="echoid-s10094" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s10095" xml:space="preserve">ME, iſtę duę
              <lb/>
              <note position="right" xlink:label="note-0411-03" xlink:href="note-0411-03a" xml:space="preserve">.huius.</note>
            rationes autem .</s>
            <s xml:id="echoid-s10096" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10097" xml:space="preserve">quam habet, OE,
              <lb/>
            ad, EM, &</s>
            <s xml:id="echoid-s10098" xml:space="preserve">, NE, ad compoſitam ex,
              <lb/>
            OM, & </s>
            <s xml:id="echoid-s10099" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s10100" xml:space="preserve">ME, componuntrationem
              <lb/>
            rectanguli ſub, NE, EO, ad rectangu-
              <lb/>
            lum ſub, EM, & </s>
            <s xml:id="echoid-s10101" xml:space="preserve">ſub compoſita ex, O
              <lb/>
            M, & </s>
            <s xml:id="echoid-s10102" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s10103" xml:space="preserve">ME, ergo omnia quadrata,
              <lb/>
            VC, ad omnia quadrata hyperbolę,
              <lb/>
            AMC, ſunt vt rectangulum, NEO, ad
              <lb/>
              <note position="right" xlink:label="note-0411-04" xlink:href="note-0411-04a" xml:space="preserve">6.‘.2.</note>
            rectangulum ſub, EM, & </s>
            <s xml:id="echoid-s10104" xml:space="preserve">ſub compo-
              <lb/>
            ſita ex, OM, & </s>
            <s xml:id="echoid-s10105" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s10106" xml:space="preserve">ME, quod eſt ęqua
              <lb/>
            le rectangulis ſub, OM, &</s>
            <s xml:id="echoid-s10107" xml:space="preserve">, ME, & </s>
            <s xml:id="echoid-s10108" xml:space="preserve">ſub
              <lb/>
            {1/3}. </s>
            <s xml:id="echoid-s10109" xml:space="preserve">ME, & </s>
            <s xml:id="echoid-s10110" xml:space="preserve">ſub, ME, .</s>
            <s xml:id="echoid-s10111" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10112" xml:space="preserve">rectangulo, OME, cum {1/3}. </s>
            <s xml:id="echoid-s10113" xml:space="preserve">quadrati, ME;
              <lb/>
            </s>
            <s xml:id="echoid-s10114" xml:space="preserve">qu
              <unsure/>
            a verò rectangulum, NEO, ęquatur rectangulo, NEO, cum
              <lb/>
              <note position="right" xlink:label="note-0411-05" xlink:href="note-0411-05a" xml:space="preserve">4. Sec. E.
                <lb/>
              lem.</note>
            quadrato, OE, quadratum verò, OE, ęquatur quadratis, EM, M
              <lb/>
            O, cum rectangulis bis ſub, EMO, ideò ſi ab his dempſeris ſemel
              <lb/>
            rectangulum, EMO, remanebit de quadrato, OE, rectangulum,
              <lb/>
            EMO, cum quadratis, EM, MO, rurſus ſi dempſeris {1/3}. </s>
            <s xml:id="echoid-s10115" xml:space="preserve">quadrati,
              <lb/>
            EM, à quadrato, EM, remanebunt {2/3}. </s>
            <s xml:id="echoid-s10116" xml:space="preserve">quadrati, EM, rectangulũ,
              <lb/>
            EMO, cum quadrato, MO, rectangulum verò, EMO, cum qua-
              <lb/>
            drato, OM, ęquatur rectangulo, EOM, vel, EON, quod collectũ
              <lb/>
            ſimul cum {2/3}. </s>
            <s xml:id="echoid-s10117" xml:space="preserve">quadrati, EM, eſt reſiduum, quod remanet detracto
              <lb/>
            rectangulo, EMO, cum {1/3}. </s>
            <s xml:id="echoid-s10118" xml:space="preserve">quadrati, EM, a quadrato, EO, ergo
              <lb/>
            detracto rectangulo, EMO, cum {1/3}. </s>
            <s xml:id="echoid-s10119" xml:space="preserve">quadrati, EM, à quadrato, E
              <lb/>
            O, iuncto rectangulo, EON, .</s>
            <s xml:id="echoid-s10120" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10121" xml:space="preserve">à rectangulo, NEO, remanent
              <lb/>
            duo rectangula, NOE, cum {2/3}. </s>
            <s xml:id="echoid-s10122" xml:space="preserve">quadrati, ME; </s>
            <s xml:id="echoid-s10123" xml:space="preserve">quia ergo oſtenſum
              <lb/>
            eſt omnia quadrata, VC, ad omnia quadrata hyperbolę, AMC,
              <lb/>
            eiſe vt rectangulum, NEO, ad rectangulum, OME, cum {1/3} qua-
              <lb/>
            drati, ME, ideò, per conuerſionem rationis, omnia quadrata, V
              <lb/>
            O, ad reliquum, demptis ab ijſdem omnibus, quadratis hyperbo-
              <lb/>
            lę, AMC, erunt vt rectangulum, NEO, ad rectangulum bisſub,
              <lb/>
            NOE, cum {2/3}. </s>
            <s xml:id="echoid-s10124" xml:space="preserve">quadrati, EM. </s>
            <s xml:id="echoid-s10125" xml:space="preserve">Eodem pacto, ſi ducamus per, </s>
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