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

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            <s xml:id="echoid-s4206" xml:space="preserve">
              <pb o="172" file="0192" n="192" rhead="GEOMETRIÆ"/>
            BEC, CEF, .</s>
            <s xml:id="echoid-s4207" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4208" xml:space="preserve">ſunt ad illa, vt, EF, ad, {1/6}, eiuſdem, EF, ergo ex
              <lb/>
              <note position="left" xlink:label="note-0192-01" xlink:href="note-0192-01a" xml:space="preserve">Elicitur
                <lb/>
              ex.</note>
            æquali, rectingula ſub, AE, EC, ad rectangula ſub triangulis, BE
              <lb/>
              <note position="left" xlink:label="note-0192-02" xlink:href="note-0192-02a" xml:space="preserve">24. huius.</note>
            C, CEF, erunt vt, DE, ad, {1/6}, EF, eadem verò ad rectangula ſub,
              <lb/>
            AE, & </s>
            <s xml:id="echoid-s4209" xml:space="preserve">triangulo, BEC, ſiue, CEF, oſtenſa ſunt eſſe, vt, DE,
              <lb/>
            ad, {1/2}, DE, ergo, colligendo, rectangula ſub, AE, EC, ad rectan-
              <lb/>
            gula ſub, AE, & </s>
            <s xml:id="echoid-s4210" xml:space="preserve">triangulo, CEF, & </s>
            <s xml:id="echoid-s4211" xml:space="preserve">ſub triangulo, BEC, & </s>
            <s xml:id="echoid-s4212" xml:space="preserve">eo-
              <lb/>
            dem, CEF, .</s>
            <s xml:id="echoid-s4213" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4214" xml:space="preserve">ad rectangula ſub trapezio, ADEC, & </s>
            <s xml:id="echoid-s4215" xml:space="preserve">triangulo,
              <lb/>
              <note position="left" xlink:label="note-0192-03" xlink:href="note-0192-03a" xml:space="preserve">Per A. Co
                <lb/>
              roll. 23.
                <lb/>
              huius.</note>
            CEF, erunt vt, DE, ad compoſitam ex, {1/2}, DE, &</s>
            <s xml:id="echoid-s4216" xml:space="preserve">, {1/6}, EF, quę
              <lb/>
            eſt Theorematis prima pars.</s>
            <s xml:id="echoid-s4217" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4218" xml:space="preserve">Dico vlterius rectangula ſub, AF, FB, ad rectangula ſub trape-
              <lb/>
            zio, ADEC, & </s>
            <s xml:id="echoid-s4219" xml:space="preserve">triangulo, BEC, eſſe vt, DF, ad compoſitam ex,
              <lb/>
            {1/6}, DE, &</s>
            <s xml:id="echoid-s4220" xml:space="preserve">, {1/3}, EF; </s>
            <s xml:id="echoid-s4221" xml:space="preserve">rectangula .</s>
            <s xml:id="echoid-s4222" xml:space="preserve">n. </s>
            <s xml:id="echoid-s4223" xml:space="preserve">ſub, AF, FB, ad rectangula ſub,
              <lb/>
            AE, EC, ſunt vt rectangulum, DFE, ad rectangulum, DEF, .</s>
            <s xml:id="echoid-s4224" xml:space="preserve">i.
              <lb/>
            </s>
            <s xml:id="echoid-s4225" xml:space="preserve">
              <note position="left" xlink:label="note-0192-04" xlink:href="note-0192-04a" xml:space="preserve">14. huius.</note>
            vt, FD, ad, DE, rectangula vero ſub, AE, EC, ad rectangula ſub,
              <lb/>
              <note position="left" xlink:label="note-0192-05" xlink:href="note-0192-05a" xml:space="preserve">3. huius.</note>
              <figure xlink:label="fig-0192-01" xlink:href="fig-0192-01a" number="112">
                <image file="0192-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0192-01"/>
              </figure>
            AE, & </s>
            <s xml:id="echoid-s4226" xml:space="preserve">triangulo, BEC, ſunt vt, B
              <lb/>
              <note position="left" xlink:label="note-0192-06" xlink:href="note-0192-06a" xml:space="preserve">Coroll. 1.
                <lb/>
              26. huius.</note>
            F, ad triangulum, BEC, .</s>
            <s xml:id="echoid-s4227" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4228" xml:space="preserve">dupla .</s>
            <s xml:id="echoid-s4229" xml:space="preserve">i.
              <lb/>
            </s>
            <s xml:id="echoid-s4230" xml:space="preserve">vt, DE, ad, {1/2}, ipſius, DE, ergo, ex
              <lb/>
            æquali rectangula ſub, AF, FB, ad
              <lb/>
            rectangula ſub, AE, & </s>
            <s xml:id="echoid-s4231" xml:space="preserve">triangulo, B
              <lb/>
            EC, erunt vt, FD, ad, {1/2}, DE, quod
              <lb/>
            ſerua. </s>
            <s xml:id="echoid-s4232" xml:space="preserve">Item rectangula ſub, AF, FB,
              <lb/>
              <note position="left" xlink:label="note-0192-07" xlink:href="note-0192-07a" xml:space="preserve">14. huius.
                <lb/>
              3. huius.
                <lb/>
              24. huius.</note>
            ad omnia quadrata, BF, ſunt vt re-
              <lb/>
            ctangulum, DFE, ad quadratum, F
              <lb/>
            E, .</s>
            <s xml:id="echoid-s4233" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4234" xml:space="preserve">vt, DF, ad, FE: </s>
            <s xml:id="echoid-s4235" xml:space="preserve">Omnia verò
              <lb/>
            quadrata, BF, ſunt tripla omnium
              <lb/>
            quadratorum trianguli, BEC, .</s>
            <s xml:id="echoid-s4236" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4237" xml:space="preserve">ſunt vt, FE, ad, {1/3}, FE, ergo ex
              <lb/>
            æquali rectangula ſub, AF, FB, ad omnia quadrata trianguli, BE
              <lb/>
            C, ſunt vt, DF, ad, {1/3}, FE, erant autem eadem ad rectangula ſub,
              <lb/>
            AE, & </s>
            <s xml:id="echoid-s4238" xml:space="preserve">triangulo, BEC, vt, DF, ad, {1/2}, DE, ergo, colligendo,
              <lb/>
            rectangula ſub, AF, FB, ad rectangula ſub, AE, & </s>
            <s xml:id="echoid-s4239" xml:space="preserve">triangulo, BE
              <lb/>
            C, vna cum omnibus quadratis trianguli, BEC, .</s>
            <s xml:id="echoid-s4240" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4241" xml:space="preserve">ad rectangula
              <lb/>
            ſub trapezio, ADEC, & </s>
            <s xml:id="echoid-s4242" xml:space="preserve">triangulo, BEC, erunt vt, DF, ad com-
              <lb/>
              <note position="left" xlink:label="note-0192-08" xlink:href="note-0192-08a" xml:space="preserve">Per C.
                <lb/>
              Coroll.
                <lb/>
              23. huius.</note>
            poſitam ex, {1/2}, DE, &</s>
            <s xml:id="echoid-s4243" xml:space="preserve">, {1/3}, EF, quę eſt Theorematis ſecunda pars;
              <lb/>
            </s>
            <s xml:id="echoid-s4244" xml:space="preserve">hæc autem erant demonſtranda.</s>
            <s xml:id="echoid-s4245" xml:space="preserve"/>
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        <div xml:id="echoid-div429" type="section" level="1" n="259">
          <head xml:id="echoid-head274" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s4246" xml:space="preserve">_C_Olligimus autem ex hoc Theoremate rectangula ſub maximis ab-
              <lb/>
            ſciſſarum propoſitæ lineæ, adiunctis eiſdem tot vni cuidam æquali-
              <lb/>
            bus, ad rectangula ſub omnibus abſciſſis eiuſdem adiunctaiam dicta li-
              <lb/>
            nea, & </s>
            <s xml:id="echoid-s4247" xml:space="preserve">ſub reſiduis abſciſſarum eiuſdem, eſſe vt adiuncta ad compoſitam
              <lb/>
            ex, {1/2}, adiunctæ, & </s>
            <s xml:id="echoid-s4248" xml:space="preserve">{1/2}, propoſitæ lineæ, & </s>
            <s xml:id="echoid-s4249" xml:space="preserve">hoc ex prima parte </s>
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