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

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            <s xml:id="echoid-s2949" xml:space="preserve">
              <pb o="126" file="0146" n="146" rhead="GEOMETRIÆ"/>
            omnia quadrata, EG, regula, FG, ſunt in ratione compoſita ex
              <lb/>
            ratione quadrati, BC, ad quadratum, FG, & </s>
            <s xml:id="echoid-s2950" xml:space="preserve">ex ratione, DC, ad,
              <lb/>
              <note position="left" xlink:label="note-0146-01" xlink:href="note-0146-01a" xml:space="preserve">11. huius.</note>
            HG, ſiue, BC, ad, FG, .</s>
            <s xml:id="echoid-s2951" xml:space="preserve">i. </s>
            <s xml:id="echoid-s2952" xml:space="preserve">in ratione compoſita ex tribus rationi-
              <lb/>
            bus, BC, ad, FG, ideſt habent eandem rationem, quam, BC, ad
              <lb/>
              <note position="left" xlink:label="note-0146-02" xlink:href="note-0146-02a" xml:space="preserve">Defin. 11.
                <lb/>
              Quin. El.</note>
            quartam propo tionalem duarum, quarum prima, BC, ſecunda eſt,
              <lb/>
            FG, .</s>
            <s xml:id="echoid-s2953" xml:space="preserve">. ſunt in tripla ratione eius, quam habet, BC, ad, FG, quod
              <lb/>
              <note position="left" xlink:label="note-0146-03" xlink:href="note-0146-03a" xml:space="preserve">Defin. 11.
                <lb/>
              Quin. El.</note>
            erat oſtendendum.</s>
            <s xml:id="echoid-s2954" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div316" type="section" level="1" n="195">
          <head xml:id="echoid-head210" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s2955" xml:space="preserve">_H_Inc patet, quod eodem modo idem oſtendemus de omnibus quibuſ-
              <lb/>
            uis alijs figuris ſimilibus parallelogrammorum, AC, EG vice
              <lb/>
            quadratorum ſumptis, regulis eiſdem, ex ſuperioribus Corollarijs id de-
              <lb/>
            ducentes.</s>
            <s xml:id="echoid-s2956" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div317" type="section" level="1" n="196">
          <head xml:id="echoid-head211" xml:space="preserve">THEOREMA XIV. PROPOS. XIV.</head>
          <p>
            <s xml:id="echoid-s2957" xml:space="preserve">SI duo parallelogramma fuerint in eadem altitudine con-
              <lb/>
            ſtituta, omnes figuræ ſimiles vnius ad omnes figuras ſi-
              <lb/>
              <note position="left" xlink:label="note-0146-04" xlink:href="note-0146-04a" xml:space="preserve">A. Def. 8.
                <lb/>
              huius.</note>
            miles alterius, etiamſi ſint diffimiles primò dictis, regulis ba-
              <lb/>
            ſibus, iuxta quas altitudo ſumitur, erunt, vt figura deſcripta
              <lb/>
            à baſi parallelogrammi primò dicti ad figuram deſcriptam à
              <lb/>
            baſi parallelogrammi ſecundò dicti.</s>
            <s xml:id="echoid-s2958" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2959" xml:space="preserve">Sint parallelogramma in eadem altitudine conſtituta, AE, EC.
              <lb/>
            </s>
            <s xml:id="echoid-s2960" xml:space="preserve">Dico omnes figuras ſimiles parallelogrammi, AE, ad omnes figu-
              <lb/>
              <note position="left" xlink:label="note-0146-05" xlink:href="note-0146-05a" xml:space="preserve">A. Def. 8.
                <lb/>
              huius.</note>
            ras ſimiles parallelogrammi, EC, etiamſi ſint diſſimiles prædictis,
              <lb/>
            eſſe vt figura deſcripta à, DE, ad figuram deſcriptam ab, EF, quæ
              <lb/>
              <figure xlink:label="fig-0146-01" xlink:href="fig-0146-01a" number="86">
                <image file="0146-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0146-01"/>
              </figure>
            ſunt baſes, iuxta quas ſumitur dictorum paral-
              <lb/>
            lelogrammorum altitudo .</s>
            <s xml:id="echoid-s2961" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s2962" xml:space="preserve">ex. </s>
            <s xml:id="echoid-s2963" xml:space="preserve">g. </s>
            <s xml:id="echoid-s2964" xml:space="preserve">omnia qua-
              <lb/>
            drata, AE, ad omnes circulos, EC, eſſe vt
              <lb/>
            quadratum, DE, ad circulum deſcriptum ab,
              <lb/>
            EF. </s>
            <s xml:id="echoid-s2965" xml:space="preserve">Ducta enim ipſa, HN, vtcunque paral-
              <lb/>
            lela, DF, reperiemus, vt figura, DE, ad fi-
              <lb/>
            guram, EF, ita eſſe figuram, HM, ad figu-
              <lb/>
            ram, MN, quia quæ deſcribuntur lateribus,
              <lb/>
            HM, DE, equalibus ſunt ęquales, veluti de
              <lb/>
              <note position="left" xlink:label="note-0146-06" xlink:href="note-0146-06a" xml:space="preserve">25. lib. 1.</note>
            ſcriptę à lateribus, MN, EF, pariter ſunt æquales, & </s>
            <s xml:id="echoid-s2966" xml:space="preserve">ideò, vt vnum
              <lb/>
            ad vnum, ſic omnia ad omnia .</s>
            <s xml:id="echoid-s2967" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s2968" xml:space="preserve">vt figura deſcripta à, DE, ad figu-
              <lb/>
              <note position="left" xlink:label="note-0146-07" xlink:href="note-0146-07a" xml:space="preserve">Coroll. 4
                <lb/>
              huius.</note>
            rain deſcriptam ab, EF, ſic erunt omnes figuræ ſimiles </s>
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