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

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          <pb o="529" file="0549" n="549" rhead="LIBER VII."/>
          <p>
            <s xml:id="echoid-s13673" xml:space="preserve">Hoc oſtendetur eodem modo, ac inſupradicta prop. </s>
            <s xml:id="echoid-s13674" xml:space="preserve">30. </s>
            <s xml:id="echoid-s13675" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s13676" xml:space="preserve">3.
              <lb/>
            </s>
            <s xml:id="echoid-s13677" xml:space="preserve">mutatis tantum ſupradictis nominibus, nempe ſi vbi dicimus re-
              <lb/>
            ctangula ſub duabus quibuſdam figuris, hic dicamus rectangulum
              <lb/>
            ſolidum ſub eiſdem figuris, ſicuti etiam cumdicuntur omnia qua-
              <lb/>
              <figure xlink:label="fig-0549-01" xlink:href="fig-0549-01a" number="360">
                <image file="0549-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0549-01"/>
              </figure>
            drata cuiuſdam figuræ, nos illius vice
              <lb/>
            nunc ſubſtituemus nomen quadrati ſo-
              <lb/>
            lidi eiuſdem figuræ, vt ſupra dicebatur.
              <lb/>
            </s>
            <s xml:id="echoid-s13678" xml:space="preserve">Igitur cum rectangulum ſolidum ſub
              <lb/>
            trapezio, ADEC, diuiſo per lineam, B
              <lb/>
              <note position="right" xlink:label="note-0549-01" xlink:href="note-0549-01a" xml:space="preserve">SI.huius@</note>
            E, & </s>
            <s xml:id="echoid-s13679" xml:space="preserve">ſub triangulo, CEF, indiuiſo, æ-
              <lb/>
            quetur rectangulo ſolido ſub, AE, & </s>
            <s xml:id="echoid-s13680" xml:space="preserve">
              <lb/>
            triangulo, CEF, vel triangulo, BEC, & </s>
            <s xml:id="echoid-s13681" xml:space="preserve">
              <lb/>
            rectangulo ſolido ſub triangulo, BEC,
              <lb/>
            & </s>
            <s xml:id="echoid-s13682" xml:space="preserve">triangulo, CEF, primò patet rectan-
              <lb/>
            gulum ſolidum ſub, AE, EC, adrectang. </s>
            <s xml:id="echoid-s13683" xml:space="preserve">ſolidum ſub, AE, & </s>
            <s xml:id="echoid-s13684" xml:space="preserve">triã-
              <lb/>
            gulo, BEC, eſſe vt, BF, ad, BEC, ideſt vt, DE, ad {1/2}. </s>
            <s xml:id="echoid-s13685" xml:space="preserve">DE, eſt enim,
              <lb/>
            BF, duplum trianguli, BEC. </s>
            <s xml:id="echoid-s13686" xml:space="preserve">Similiter rectangulum ſolidum ſub,
              <lb/>
              <note position="right" xlink:label="note-0549-02" xlink:href="note-0549-02a" xml:space="preserve">Coroll.1.
                <lb/>
              13. huius.
                <lb/>
              Coroll.2.
                <lb/>
              13. huius.
                <lb/>
              Coroll.2,
                <lb/>
              14.huius.</note>
            AE, EC, ad quadratum ſolidum, BF, eſt vt rectangulum, DEF, ad
              <lb/>
            quadratum, EF, ideſt vt, DE, ad, EF, quadratum verò ſolidum, B
              <lb/>
            F, cum ſit triplum quadrati ſolidi, CEF, & </s>
            <s xml:id="echoid-s13687" xml:space="preserve">quadrati ſolidi, BEC,
              <lb/>
            erit etiam triplum duorum rectangulorum ſolidorum ſub, BEC, CE
              <lb/>
            F, (quadratum ſolidum enim, BF, oſtenſum eſt æquari quadratis
              <lb/>
            ſolidis, BEC, CEF, cum duobus rectang. </s>
            <s xml:id="echoid-s13688" xml:space="preserve">ſolidis ſub, BEC, CEF,)
              <lb/>
              <note position="right" xlink:label="note-0549-03" xlink:href="note-0549-03a" xml:space="preserve">Coro. 15.
                <lb/>
              huius.</note>
            & </s>
            <s xml:id="echoid-s13689" xml:space="preserve">ideò erit ſexcuplum rectanguli ſolidi, ſub, BEC, CEF, ideſt erit
              <lb/>
            ad illud vt, EF, ad ſui {1/6}. </s>
            <s xml:id="echoid-s13690" xml:space="preserve">ergo ex æquali rectangulum ſolidum ſub,
              <lb/>
            AE, EC, ad rectangulum ſolidum ſub, BEC, CEF, erit vt, DE, ad
              <lb/>
            {1/6}. </s>
            <s xml:id="echoid-s13691" xml:space="preserve">EF, & </s>
            <s xml:id="echoid-s13692" xml:space="preserve">ad rectangulum ſolidum ſub, AE, & </s>
            <s xml:id="echoid-s13693" xml:space="preserve">triangulo, BEC, ſeu,
              <lb/>
            CEF, oſtenſum eſt eſſe vt, DE, ad {1/2}. </s>
            <s xml:id="echoid-s13694" xml:space="preserve">DE, ergo colligendo rectan-
              <lb/>
            gulum ſolidum ſub, AE, EC, ad rectangulum ſolidum ſub, AE, CE
              <lb/>
            F, & </s>
            <s xml:id="echoid-s13695" xml:space="preserve">ſub, CBE, CEF, ideſt ſub trapezio, CADE, & </s>
            <s xml:id="echoid-s13696" xml:space="preserve">triangulo, CE
              <lb/>
            F, erit vt, DE, ad compoſitam ex {1/2}. </s>
            <s xml:id="echoid-s13697" xml:space="preserve">DE, & </s>
            <s xml:id="echoid-s13698" xml:space="preserve">{1/6}. </s>
            <s xml:id="echoid-s13699" xml:space="preserve">EF, quod oſtendere
              <lb/>
            opuserat.</s>
            <s xml:id="echoid-s13700" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1224" type="section" level="1" n="737">
          <head xml:id="echoid-head770" xml:space="preserve">ANNOTATIO.</head>
          <p>
            <s xml:id="echoid-s13701" xml:space="preserve">Præſentem propoſitionem denuò ſecun
              <gap/>
              <lb/>
            thodum oſtendere volui, vt
              <gap/>
            um hanc nouam me-
              <lb/>
              <gap/>
            nuius imitationem, reliquæ
              <lb/>
            ſuppleri po
              <gap/>
            , non alia, quam ſupradictorum nomi-
              <lb/>
            num mutatione facta, demonſtratio ſimillima fit, cum ea pariter
              <lb/>
            fuerint ſtabilita principia, vt in antecedentibus potuit ſtudioſus
              <lb/>
            animaduertere, quæ principijs methodi indiuiſibilium ſimilia ap-
              <lb/>
            parebant, ſufficiet ergo tales propoſitiones, tantum innuere, </s>
          </p>
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