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

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        <div xml:id="echoid-div1011" type="section" level="1" n="604">
          <p>
            <s xml:id="echoid-s11068" xml:space="preserve">
              <pb o="424" file="0444" n="444" rhead="GEOMETRIÆ"/>
            drum, FC, in figura Coroll. </s>
            <s xml:id="echoid-s11069" xml:space="preserve">23. </s>
            <s xml:id="echoid-s11070" xml:space="preserve">demptis oppoſitis conoidibus, F
              <lb/>
            AD, EVC, ad tympanum hyperbolicum genitum ex figura, EVC
              <lb/>
            DAF, in figura Coroll. </s>
            <s xml:id="echoid-s11071" xml:space="preserve">24. </s>
            <s xml:id="echoid-s11072" xml:space="preserve">ſcilicet ad tympanum hyperbolicum,
              <lb/>
            EVCDAF, habere rationem compoſitam ex ratione rectanguli,
              <lb/>
            AOZ, bis cum {2/3}. </s>
            <s xml:id="echoid-s11073" xml:space="preserve">quadrati, VZ, ad rectangulum, AZO, & </s>
            <s xml:id="echoid-s11074" xml:space="preserve">ex ra-
              <lb/>
            tione rectanguli ſub, DC, vel, RZ, & </s>
            <s xml:id="echoid-s11075" xml:space="preserve">ſub, EC, ad quadratum, A
              <lb/>
            V, cum {1/3}. </s>
            <s xml:id="echoid-s11076" xml:space="preserve">quadrati, KI, vel cum rectangulo ſub, AZ, & </s>
            <s xml:id="echoid-s11077" xml:space="preserve">ſexqui.
              <lb/>
            </s>
            <s xml:id="echoid-s11078" xml:space="preserve">tertia, ZV, & </s>
            <s xml:id="echoid-s11079" xml:space="preserve">ſic eſſe quodlibet ſolidum ſimilare genitum ex, FC,
              <lb/>
            de@nptis ſolidis ſimilaribus genitis ex oppoſitis hyperbolis, FAD,
              <lb/>
            EVC, iuxta communem regulam, EC, ad ſolidum ſimilare ſibi
              <lb/>
            genitum ex figura, EVCDAF, iuxta regulam, CD.</s>
            <s xml:id="echoid-s11080" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1012" type="section" level="1" n="605">
          <head xml:id="echoid-head630" xml:space="preserve">COROLLARIVM XXVII.</head>
          <p>
            <s xml:id="echoid-s11081" xml:space="preserve">IN Prop. </s>
            <s xml:id="echoid-s11082" xml:space="preserve">27. </s>
            <s xml:id="echoid-s11083" xml:space="preserve">conſpecta figura Coroll. </s>
            <s xml:id="echoid-s11084" xml:space="preserve">21. </s>
            <s xml:id="echoid-s11085" xml:space="preserve">intelligantur deſcri-
              <lb/>
            ptæ ſectiones, BIG, kMP, quæ dicuntur coniugatæ ſectioni-
              <lb/>
            bus, DAF, CVE, ex quibus in reuolutione genitæ fuerint oppoſi-
              <lb/>
            tæ conoides, B G, kMP, patet igitur cylindrum, DE, ad tympa-
              <lb/>
            num hyperbolicum, DAF, EVC, demptis oppoſitis conoidibus,
              <lb/>
            BIG, KMP, eſſe vt parallelepipedum ſub, ZC, & </s>
            <s xml:id="echoid-s11086" xml:space="preserve">ſub quadrato, Z
              <lb/>
            Q (quæ habetur extenſa, ZC, ad aſymptoton producta .</s>
            <s xml:id="echoid-s11087" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s11088" xml:space="preserve">ad, OS,
              <lb/>
            cu@occurrat in, Q,) a@ parallele ipedum bis ſub, XM, & </s>
            <s xml:id="echoid-s11089" xml:space="preserve">quadra-
              <lb/>
            to, MO, cum cubo, MO, & </s>
            <s xml:id="echoid-s11090" xml:space="preserve">amplius {1/3}. </s>
            <s xml:id="echoid-s11091" xml:space="preserve">eiuſdem cubi; </s>
            <s xml:id="echoid-s11092" xml:space="preserve">& </s>
            <s xml:id="echoid-s11093" xml:space="preserve">ſic eſſe
              <lb/>
            quodlibet ſolidum ſimilare genitum ex, FC, ad ſibi ſimlare g@nitũ
              <lb/>
            ex figura, DAFEVC, demptis ſolidis ſimilaribus genitis ex oppo-
              <lb/>
            ſitis hyperbolis, BIG, KMP, iuxta cõmunẽ regulam, FE, vel, AV.</s>
            <s xml:id="echoid-s11094" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1013" type="section" level="1" n="606">
          <head xml:id="echoid-head631" xml:space="preserve">COROLL. XXVIII. SECTIO PRIOR.</head>
          <p>
            <s xml:id="echoid-s11095" xml:space="preserve">IN Prop. </s>
            <s xml:id="echoid-s11096" xml:space="preserve">28. </s>
            <s xml:id="echoid-s11097" xml:space="preserve">illius aſſumpta figu-
              <lb/>
              <figure xlink:label="fig-0444-01" xlink:href="fig-0444-01a" number="307">
                <image file="0444-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0444-01"/>
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            ra, eadem reuoluatur circa axẽ,
              <lb/>
            &</s>
            <s xml:id="echoid-s11098" xml:space="preserve">Y, vel, GZ, ſit autem reuolutio
              <lb/>
            circa, &</s>
            <s xml:id="echoid-s11099" xml:space="preserve">Y; </s>
            <s xml:id="echoid-s11100" xml:space="preserve">patet ergo cylindrum ge-
              <lb/>
            nitum ex, TV, nempè, TV, ad reli-
              <lb/>
            quum, ab eodem demptis ſolidis ge
              <lb/>
            nitis ex quatuor hyperbolis coniu-
              <lb/>
            gatis, BFH, PIQ, AEC, MON, eſſe
              <lb/>
            vt cubus, ZV, vel, SY, ad parallele-
              <lb/>
            pipedum ſub, QV, & </s>
            <s xml:id="echoid-s11101" xml:space="preserve">quad. </s>
            <s xml:id="echoid-s11102" xml:space="preserve">ZV, vna
              <lb/>
            cum parallelepipedo ſub, ZQ, & </s>
            <s xml:id="echoid-s11103" xml:space="preserve">ſub
              <lb/>
            compoſito ex {1/3}. </s>
            <s xml:id="echoid-s11104" xml:space="preserve">quadrati, ZQ, & </s>
            <s xml:id="echoid-s11105" xml:space="preserve">
              <lb/>
            qua@rato, SO, ab his tamen dempto
              <lb/>
            parallelepipedo ſub, SO, & </s>
            <s xml:id="echoid-s11106" xml:space="preserve">quadra
              <lb/>
            to, OY, cum {1/3}. </s>
            <s xml:id="echoid-s11107" xml:space="preserve">cubi, OY, & </s>
            <s xml:id="echoid-s11108" xml:space="preserve">ſic </s>
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