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

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        <div xml:id="echoid-div1194" type="section" level="1" n="715">
          <p>
            <s xml:id="echoid-s13434" xml:space="preserve">
              <pb o="520" file="0540" n="540" rhead="GEOMETRIÆ"/>
            limus etiam caſum intelligere cum tantum figura planaeſt in illius
              <lb/>
            ambitu; </s>
            <s xml:id="echoid-s13435" xml:space="preserve">hoc in ſchemate ant. </s>
            <s xml:id="echoid-s13436" xml:space="preserve">prop. </s>
            <s xml:id="echoid-s13437" xml:space="preserve">facilè percipiemus, in qua
              <lb/>
            ſint regulæ, SI, IH, continentes verò figuræ, QI, ΔΜ, quarum,
              <lb/>
            QI, ſupponatur eſſe parallelogrammum, ſed non in ambitu con-
              <lb/>
            tenti eiſdem ſolidi, quod ſit, CM, ΔΜ, verò ſit figura plana, quæ
              <lb/>
            debet in ambitu ſolidi reperiri, igitur conſimili methodo oſtende-
              <lb/>
            mus etiam, CM, eſſe cylindricum, in baſi, ΔΜ, conſtitutum. </s>
            <s xml:id="echoid-s13438" xml:space="preserve">Quod
              <lb/>
            ſicontinentes figuræ, QI, IO, fuerint ambo parallelogramma, ac
              <lb/>
            in ambitu contenti ſolidi, quod ſit, PI, manifeſtum eſt nedum, PI,
              <lb/>
            eſſe cylindricum, ſed etiam eſſe parallelepipedum, ſunt enim pla-
              <lb/>
            na, RI, PB, parallela, necnon, PH, eſt ſuperficies plana ipſi, QI,
              <lb/>
            parallela, ac, PS, eſt plana, necnon ipſi, HB, ſimiliter parallela,
              <lb/>
            quod oſtendere oportebat.</s>
            <s xml:id="echoid-s13439" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1196" type="section" level="1" n="716">
          <head xml:id="echoid-head749" xml:space="preserve">COROLLARIVM I.</head>
          <p style="it">
            <s xml:id="echoid-s13440" xml:space="preserve">_E_X hoc colligitur, ſi, ducta, EH, per, H, parallela, DC, in paral-
              <lb/>
            lelis, EH, DC, ind finitè productis, reperiatur alia quæcunq;
              <lb/>
            </s>
            <s xml:id="echoid-s13441" xml:space="preserve">plana figura, vt, EHC, ſolidum rectangulum ſub parallelogrammo
              <lb/>
            propoſito, AC, ſeu illi analoga ſuperficie ſecundum regulam planum,
              <lb/>
            GC, & </s>
            <s xml:id="echoid-s13442" xml:space="preserve">ſub figura, FHC, in ambitu contenti ſolidi exi lente, quod ſit,
              <lb/>
            AFCH, ad contentum ſub eodem parallelogrammo, AC, ſeu illi ana-
              <lb/>
            loga ſuperficie ſecundum dictam regulam, & </s>
            <s xml:id="echoid-s13443" xml:space="preserve">ſub figura, HDC, dummo-
              <lb/>
            do ea ſit in ambitu pariter contenti ſolidii, eſſe vt figura, EHC, ad figu-
              <lb/>
            ram, HDC, ſunt cnim hæc ſolida, ABFHC, ABGHC, cylindrici in ea-
              <lb/>
              <note position="left" xlink:label="note-0540-01" xlink:href="note-0540-01a" xml:space="preserve">5. huius.</note>
            dem altitudine ſumpta reſpectu baſium, EHC, DHC, & </s>
            <s xml:id="echoid-s13444" xml:space="preserve">ideò ſunt inter
              <lb/>
            ſe vt ipſæ baſes, vnde cum ipſæ fuerint æquales etiam dicta ſolida re-
              <lb/>
            ctangula æqualia erunt.</s>
            <s xml:id="echoid-s13445" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1198" type="section" level="1" n="717">
          <head xml:id="echoid-head750" xml:space="preserve">COROLLARIVM II.</head>
          <p style="it">
            <s xml:id="echoid-s13446" xml:space="preserve">_H_Abetur inſuper ſi in eodem ſchemate ducatur in parallelogram-
              <lb/>
            mo, AC, quacumq; </s>
            <s xml:id="echoid-s13447" xml:space="preserve">parallela, HC, vt, RS, conſtituens paralle-
              <lb/>
            logrammum, RG, rectangulum ſolidu n ſub, AC, & </s>
            <s xml:id="echoid-s13448" xml:space="preserve">figura plana ex. </s>
            <s xml:id="echoid-s13449" xml:space="preserve">g.
              <lb/>
            </s>
            <s xml:id="echoid-s13450" xml:space="preserve">HDC, contentum, dummodo hæc ſit in ipſius ambitu, ad rectangulum
              <lb/>
            ſolidum ſub, RC, & </s>
            <s xml:id="echoid-s13451" xml:space="preserve">eadem figura, HDC, in huius etiam ambitu exi-
              <lb/>
            ſtente, ſeu ſub quacumq; </s>
            <s xml:id="echoid-s13452" xml:space="preserve">alia plana figura in eiſdem parallelis cum, H
              <lb/>
            DC, exiſtent, dummodo ſit in ipſius ambitu, regulis ijſdem, BC, CD, eſſe
              <lb/>
            vt parallelogrammum, AC, ad par allelogrammum, CR, ſeu vt, BC, ad,
              <lb/>
            CS; </s>
            <s xml:id="echoid-s13453" xml:space="preserve">Et ſi ſint etiam parallelogramma, HV, HD, habetur etiam rectaã-
              <lb/>
            gulum ſolidum ſub, AC, CE, ad rectangulum ſolidum ſub, RC, CT, </s>
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