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

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        <div xml:id="echoid-div449" type="section" level="1" n="270">
          <pb o="183" file="0203" n="203" rhead="LIBER II."/>
        </div>
        <div xml:id="echoid-div451" type="section" level="1" n="271">
          <head xml:id="echoid-head286" xml:space="preserve">A. COROLLARII IV. GENERALIS.</head>
          <head xml:id="echoid-head287" xml:space="preserve">SECTIO I.</head>
          <p style="it">
            <s xml:id="echoid-s4488" xml:space="preserve">_E_T quoniam, vt oſtenſum eſt Prop. </s>
            <s xml:id="echoid-s4489" xml:space="preserve">33. </s>
            <s xml:id="echoid-s4490" xml:space="preserve">huius Libri, vt omnia qua-
              <lb/>
            drata duarum figurarum inter ſe ſumpta cum datis regulis, ita
              <lb/>
            ſunt ſolida ſimilaria genita ex ijſdem figuris iuxta eaſdem regulas, ideò
              <lb/>
            cumin Propoſitionibus huius Libri inuenta eſt ratio omnium quadrato-
              <lb/>
            rum par allelogrammorum, vel triangulorum, vel trapeziorum, regu-
              <lb/>
            lis eorum lateribus, eandem rationem comperiemus habere ſolida ſimi-
              <lb/>
            laria genita ex parallelogrammis, ideſt cylindricos, vel ex triangulis,
              <lb/>
            ideſt conicos, vel ex trapezijs, ideſt fruſta conica, genitainquam iuxta
              <lb/>
            eaſdem regulas, quæ amplius dilucidabimus ſingula, quæ opportuna
              <lb/>
            fuerint, Theoremata denuò aſſumentes.</s>
            <s xml:id="echoid-s4491" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div452" type="section" level="1" n="272">
          <head xml:id="echoid-head288" xml:space="preserve">B. SECTIO II.</head>
          <p style="it">
            <s xml:id="echoid-s4492" xml:space="preserve">_I_N Propoſ. </s>
            <s xml:id="echoid-s4493" xml:space="preserve">9. </s>
            <s xml:id="echoid-s4494" xml:space="preserve">igitur expoſita denuò eius figura, intelligantur baſes,
              <lb/>
            GM, MH, deſcribere ſimiles figuras planas, quæ ſint, GIMR, M
              <lb/>
            THS, vt eorum lineæ, vel latera homologa, æquè erectas planis, AM,
              <lb/>
              <figure xlink:label="fig-0203-01" xlink:href="fig-0203-01a" number="121">
                <image file="0203-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0203-01"/>
              </figure>
            MC, & </s>
            <s xml:id="echoid-s4495" xml:space="preserve">in ijs, tanquam in baſibus conſiſte-
              <lb/>
            re cylindricos, AM, BH, quorum latera
              <lb/>
            ſint, AG, CH, erunt igitur hi cylindrici
              <lb/>
            ſolida ſimilaria genita ex parallelogram-
              <lb/>
              <note position="right" xlink:label="note-0203-01" xlink:href="note-0203-01a" xml:space="preserve">_Coroll. 3._
                <lb/>
              _ant._</note>
            mis, AM, MC, iuxta regulas, GM, M
              <lb/>
            H, igitur erunt, vt omnia quadrata eorun-
              <lb/>
            dem regulis eiſdem, GM, MH, ſunt au-
              <lb/>
              <note position="right" xlink:label="note-0203-02" xlink:href="note-0203-02a" xml:space="preserve">_9. huius._</note>
            tem omnia eorum quadrata, vt quadrata baſium, GM, MH, .</s>
            <s xml:id="echoid-s4496" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4497" xml:space="preserve">ergo cy-
              <lb/>
            lindrici, AM, MC, erunt vt quadrata baſium, GM, MH, .</s>
            <s xml:id="echoid-s4498" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4499" xml:space="preserve">vt figu-
              <lb/>
            ræ ſimiles, GIMR, MSHT, igitur cylindrici in eadem altitudine, & </s>
            <s xml:id="echoid-s4500" xml:space="preserve">
              <lb/>
            ſimilibus baſibus inſiſtentes ſunt, vt ipſæ baſes.</s>
            <s xml:id="echoid-s4501" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div454" type="section" level="1" n="273">
          <head xml:id="echoid-head289" xml:space="preserve">C. SECTIO III.</head>
          <p style="it">
            <s xml:id="echoid-s4502" xml:space="preserve">_I_N Propoſ. </s>
            <s xml:id="echoid-s4503" xml:space="preserve">10. </s>
            <s xml:id="echoid-s4504" xml:space="preserve">conſimiliter procedentes collige@@us, cylindricos in
              <lb/>
            eadem, vel æqualibus, ac ſimilibus baſibus conſiſtentes eſſe, vt alti-
              <lb/>
            tudines, vel vt latera ęqualiter eorundem baſibus inclinata.</s>
            <s xml:id="echoid-s4505" xml:space="preserve"/>
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