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

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            <s xml:id="echoid-s7232" xml:space="preserve">
              <pb o="299" file="0319" n="319" rhead="LIBER IV."/>
            E, & </s>
            <s xml:id="echoid-s7233" xml:space="preserve">iungatur, AG. </s>
            <s xml:id="echoid-s7234" xml:space="preserve">Dico trilineum, ABH, ad trilineum, AM
              <lb/>
            H, eſſe vt, BH, cum, CE, ad ipſam, AM, cum, CE: </s>
            <s xml:id="echoid-s7235" xml:space="preserve">Prius au-
              <lb/>
            tem dico portionculam, ASB, eſſe æqualem portionculæ, MIH,
              <lb/>
            & </s>
            <s xml:id="echoid-s7236" xml:space="preserve">enim trapezium, ABOR, æquatur trapezio, ROHM, & </s>
            <s xml:id="echoid-s7237" xml:space="preserve">
              <lb/>
            quadrilineum, RASBO, ipſi quadrilineo, RMIHO, cum, A
              <lb/>
            O, axis, vel diameter bifariam diuidat omnes æquidiſtantes ipſi, B
              <lb/>
            H, & </s>
            <s xml:id="echoid-s7238" xml:space="preserve">ideò omnes lineæ quadrilinei, RASBO, æquentur omni-
              <lb/>
            bus lineis quadrilinei, RMHO, vnde dicta quadrilinea etiam ſunt
              <lb/>
            ęqualia, & </s>
            <s xml:id="echoid-s7239" xml:space="preserve">ideo portionculæ, ASB, MIH, inter ſe ſunt æquales:
              <lb/>
            </s>
            <s xml:id="echoid-s7240" xml:space="preserve">
              <note position="right" xlink:label="note-0319-01" xlink:href="note-0319-01a" xml:space="preserve">3.2.</note>
            Quoniam vero portio, ASBC, ad triangulum, ABC, eſt vt com-
              <lb/>
            poſita ex {1/3}, BC, & </s>
            <s xml:id="echoid-s7241" xml:space="preserve">ex, CH, ad, CH, ideò, diuidendo, portion-
              <lb/>
              <note position="right" xlink:label="note-0319-02" xlink:href="note-0319-02a" xml:space="preserve">8. huius.</note>
            cula, ASB, ad triangulum, ABC, erit vt {1/3}, BC, ad, CH, vel
              <lb/>
            vt, BC, ad triplam, CH, . </s>
            <s xml:id="echoid-s7242" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7243" xml:space="preserve">ſumpta, BC, communi altitudine, vt
              <lb/>
            quadratum, BC, ad rectangulum ſub, BC, & </s>
            <s xml:id="echoid-s7244" xml:space="preserve">tripla, CH; </s>
            <s xml:id="echoid-s7245" xml:space="preserve">eſt au-
              <lb/>
              <note position="right" xlink:label="note-0319-03" xlink:href="note-0319-03a" xml:space="preserve">5. l. 2.</note>
            tem triangulum, ABC, ad triangulum, ABH, vt, CB, ad, BH,
              <lb/>
            ideſt (ſumpta communi altitudine tripla, CH,) vt rectangulum
              <lb/>
            ſub, BC, & </s>
            <s xml:id="echoid-s7246" xml:space="preserve">tripla, CH, ad rectangulum ſub, BH, & </s>
            <s xml:id="echoid-s7247" xml:space="preserve">tripla, CH,
              <lb/>
              <figure xlink:label="fig-0319-01" xlink:href="fig-0319-01a" number="212">
                <image file="0319-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0319-01"/>
              </figure>
            ergo ex æquali portioncula, ASB,
              <lb/>
            ad triangulum, ABH, erit vt qua-
              <lb/>
            dratum, BC, ad rectangulum ſub,
              <lb/>
            BH, & </s>
            <s xml:id="echoid-s7248" xml:space="preserve">tripla, HC, quoniam vero,
              <lb/>
            BC, eſt media proportionalis inter
              <lb/>
            triplam, HC, & </s>
            <s xml:id="echoid-s7249" xml:space="preserve">ipſam, CE, ideò
              <lb/>
              <note position="right" xlink:label="note-0319-04" xlink:href="note-0319-04a" xml:space="preserve">Elicitur
                <lb/>
              ex 12. 1. 2.</note>
            quadiatum, BC, æquatur rectan-
              <lb/>
            gulo ſub tripla, HC, & </s>
            <s xml:id="echoid-s7250" xml:space="preserve">ſub, CE,
              <lb/>
            vnde portioncula, ASB, ad triangulum, ABH, erit vt rectangu-
              <lb/>
            lum ſub, CE, & </s>
            <s xml:id="echoid-s7251" xml:space="preserve">tripla, CH, ad rectangulum ſub, BH, & </s>
            <s xml:id="echoid-s7252" xml:space="preserve">tripla,
              <lb/>
            CH, ideſt erit, vt baſis, CE, ad baſim, BH, ergo, componendo,
              <lb/>
            trilineum, ASBH, ad triangulum, ABH, erit vt, CE, cum, B
              <lb/>
            H, ad ipſam, BH, triangulum verò, ABH, ad triangulum, AC
              <lb/>
            G, vel ad triangulum, AGM, eſt vt, BH, ad, CG, vel ad, AM,
              <lb/>
            eſt vero triangulum, AGM, æquale triangulo, AHM, ergo tri-
              <lb/>
            lineum, ASBH, ad triangulum, AMH, erit vt, CE, cum, BH,
              <lb/>
            ad, AM, eſt verò trilineum, ASBH, ad portionculam, ASB,
              <lb/>
            vel, MIH, illi æqualem, per conuerſionem rationis, vt, BH,
              <lb/>
            cum, CE, ad ipſam, CE, ergo, colligendo, trilineum, ASBH,
              <lb/>
            ad triangulum, AHM, & </s>
            <s xml:id="echoid-s7253" xml:space="preserve">portionculam, MIH, . </s>
            <s xml:id="echoid-s7254" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7255" xml:space="preserve">ad trilineum,
              <lb/>
            AMIH, erit vt, BH, cum, CE, ad ipſam, AM, cum, CE,
              <lb/>
            quod oſtendere oportebat.</s>
            <s xml:id="echoid-s7256" xml:space="preserve"/>
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