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

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        <div xml:id="echoid-div274" type="section" level="1" n="175">
          <p>
            <s xml:id="echoid-s2673" xml:space="preserve">
              <pb o="113" file="0133" n="133" rhead="LIBER II."/>
            ræ, ADC, ſumptis, regula, AC, quod in figuris planis oſtenden
              <lb/>
            dum erat.</s>
            <s xml:id="echoid-s2674" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2675" xml:space="preserve">Ita ſuperpoſitis æqualibus figuris ſolidis, ita vt duæ in ipſis aſſum-
              <lb/>
            ptæ vtcunq; </s>
            <s xml:id="echoid-s2676" xml:space="preserve">regulæ ſint ad inuicem ſuperpoſitæ, vel æquidiſtantes,
              <lb/>
            & </s>
            <s xml:id="echoid-s2677" xml:space="preserve">reſiduorum facta ſemper ſuperpoſitione ita, vt omnia eorum pla-
              <lb/>
            na regulis iam iuperpoſitis ęquidiſtent, tandem, quia figurę ſunt æ-
              <lb/>
            quales, dictæ partes erunt ad inuicem congruentes, & </s>
            <s xml:id="echoid-s2678" xml:space="preserve">conſequen-
              <lb/>
            ter integrę quoq; </s>
            <s xml:id="echoid-s2679" xml:space="preserve">figuræ erunt congruentes, ergo earum omnia pla-
              <lb/>
            na ſumpta cum dictis regulis erunt ad inuicem congruentia, ergo & </s>
            <s xml:id="echoid-s2680" xml:space="preserve">
              <lb/>
            æqualia, quod in figuris ſolidis oſtendere quoque opus erat.</s>
            <s xml:id="echoid-s2681" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div276" type="section" level="1" n="176">
          <head xml:id="echoid-head191" xml:space="preserve">COROLLARIV M.</head>
          <p style="it">
            <s xml:id="echoid-s2682" xml:space="preserve">_H_Inc patet in eadem figura plana, omnes lineas ſumptas cum qua-
              <lb/>
            damregula æquart omnibus lineis ſumptis cum alia quauis regu-
              <lb/>
            la; </s>
            <s xml:id="echoid-s2683" xml:space="preserve">& </s>
            <s xml:id="echoid-s2684" xml:space="preserve">in figuris ſolidis omnia plana vnius ſumpta cum quadam regula
              <lb/>
            æquari omnibus planis eiuſdem, regula quauis aſſumpta; </s>
            <s xml:id="echoid-s2685" xml:space="preserve">vnde ex. </s>
            <s xml:id="echoid-s2686" xml:space="preserve">gr.
              <lb/>
            </s>
            <s xml:id="echoid-s2687" xml:space="preserve">ſecto planis cylindro æquidiſtanter axi, qua ſectione in ipſo creantur pa-
              <lb/>
              <note position="right" xlink:label="note-0133-01" xlink:href="note-0133-01a" xml:space="preserve">_Coroll. 6._
                <lb/>
              _lib. 1._</note>
            rallelogramma, & </s>
            <s xml:id="echoid-s2688" xml:space="preserve">ſecto eodem planis æquidistanter baſi ductis, qua ſe-
              <lb/>
            ctione creantur in eodem circuli, patet ex hoc, omnia parallelogramma
              <lb/>
              <note position="right" xlink:label="note-0133-02" xlink:href="note-0133-02a" xml:space="preserve">_Corol. 12._
                <lb/>
              _lib. 1._</note>
            dicti cylindri, regula eorundem vno, eſſe æqualia omnibus circulis eiu-
              <lb/>
            ſdem, regula baſi.</s>
            <s xml:id="echoid-s2689" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div278" type="section" level="1" n="177">
          <head xml:id="echoid-head192" xml:space="preserve">THEOREMA III. PROPOS. III.</head>
          <p>
            <s xml:id="echoid-s2690" xml:space="preserve">FIguræ planæ habent inter ſe eandem rationem, quam
              <lb/>
            eorum omnes lineæ iuxta quaniuis regulam aſſumptæ;
              <lb/>
            </s>
            <s xml:id="echoid-s2691" xml:space="preserve">Et figuræ ſolidæ, quam eorum omnia plana iuxta quamuis
              <lb/>
            regulam aſſumpta.</s>
            <s xml:id="echoid-s2692" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2693" xml:space="preserve">Sint figuræ planæ vtcunque, A, D. </s>
            <s xml:id="echoid-s2694" xml:space="preserve">Dico,
              <lb/>
              <figure xlink:label="fig-0133-01" xlink:href="fig-0133-01a" number="73">
                <image file="0133-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0133-01"/>
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            A, figuram ad nguram, D, eſſe vt omnes lineę
              <lb/>
            figuræ, A, iuxta quamuis regulam aſſumptæ
              <lb/>
            ad omnes lineas figuræ, D, iuxta quamuis re-
              <lb/>
            gulam aſſumptas. </s>
            <s xml:id="echoid-s2695" xml:space="preserve">Intelligantur ergo omnes
              <lb/>
            lineæ figuræ, A, &</s>
            <s xml:id="echoid-s2696" xml:space="preserve">, D, aſlumptæ iuxta qua-
              <lb/>
            ſdam regulas, deinde capiantur quotcunque fi-
              <lb/>
            guræ, BC, ſingulæ æquales figuræ, A, & </s>
            <s xml:id="echoid-s2697" xml:space="preserve">fi
              <lb/>
            guræ, D, quotcunque ęquales figurę, vt, E; </s>
            <s xml:id="echoid-s2698" xml:space="preserve">nunc, ſi continuum
              <lb/>
            componitur ex indiuiſibilibus, patet abſque alia demonſtratione fi-
              <lb/>
            guram, A, ad figuram, D, eſſe vt omnes lineæ figurę, A, ad </s>
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