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

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              <figure xlink:label="fig-0500-01" xlink:href="fig-0500-01a" number="337">
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            A, ad parallelepipe-
              <lb/>
            dum ſub compoſita
              <lb/>
            ex ſexquialteraeiuſ-
              <lb/>
            dem tranſuerſi late-
              <lb/>
            ris, &</s>
            <s xml:id="echoid-s12305" xml:space="preserve">, KA, & </s>
            <s xml:id="echoid-s12306" xml:space="preserve">qua-
              <lb/>
            drato, KA. </s>
            <s xml:id="echoid-s12307" xml:space="preserve">Conus
              <lb/>
            verò, DAF, ad co-
              <lb/>
            num, MAI, vt cu-
              <lb/>
            bus, EA, ad cubum,
              <lb/>
            AK.</s>
            <s xml:id="echoid-s12308" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12309" xml:space="preserve">Nunc intelliga-
              <lb/>
              <note position="left" xlink:label="note-0500-01" xlink:href="note-0500-01a" xml:space="preserve">F. H.
                <lb/>
              Cor. gen.
                <lb/>
              34. l. 2.</note>
            tur demptum à cy-
              <lb/>
            lindro, BF, hæmi-
              <lb/>
            ſphærium, vel hæ-
              <lb/>
            miſphæroides, DVATF. </s>
            <s xml:id="echoid-s12310" xml:space="preserve">Igitur per demonſtrata patet reliquum
              <lb/>
            cylindri ab abſciſſam ab eo portionem per ductum planum eſſe, vt
              <lb/>
              <note position="left" xlink:label="note-0500-02" xlink:href="note-0500-02a" xml:space="preserve">Coroll. 5.
                <lb/>
              34. l. 3.</note>
            cubus, AE, eſt ad cubum, EK. </s>
            <s xml:id="echoid-s12311" xml:space="preserve">Dempto autem conoide parabo-
              <lb/>
            lico ab eodem cylindro; </s>
            <s xml:id="echoid-s12312" xml:space="preserve">reliquum cylindri ab abſciſſam portionẽ
              <lb/>
            erit, vt quadratum, AE, ad quadratum, EK. </s>
            <s xml:id="echoid-s12313" xml:space="preserve">Dempto verò co-
              <lb/>
              <note position="left" xlink:label="note-0500-03" xlink:href="note-0500-03a" xml:space="preserve">Coroll. 9.
                <lb/>
              51. l. 4.</note>
            noide hyperbolico ab eodem cylindro, reliquum cylindri ad ab-
              <lb/>
            ſciſſam portionem erit, vt parallelepipedum ſub compoſita ex
              <lb/>
            ſexquialtera tranſuerſi lateris, & </s>
            <s xml:id="echoid-s12314" xml:space="preserve">dupla axis eiuſdem, & </s>
            <s xml:id="echoid-s12315" xml:space="preserve">ſub qua-
              <lb/>
            drato eiuſdem axis, ad parallelepipedum ſub compoſita ex ſex-
              <lb/>
              <note position="left" xlink:label="note-0500-04" xlink:href="note-0500-04a" xml:space="preserve">Coroll. 5.
                <lb/>
              30. l. 5.</note>
            quialtera eiuſdem tranſuerſi lateris, & </s>
            <s xml:id="echoid-s12316" xml:space="preserve">axibus vtriuſq; </s>
            <s xml:id="echoid-s12317" xml:space="preserve">portionis,
              <lb/>
            & </s>
            <s xml:id="echoid-s12318" xml:space="preserve">ſub quadrato exceſſus maioris axis ſuper minorem. </s>
            <s xml:id="echoid-s12319" xml:space="preserve">Tandem
              <lb/>
            dempto cono, DAF, à cylindro, BF, reſiduum cylindri ad abſciſsã
              <lb/>
            portionem erit, vt cubus, AE, ad parallelepipedum ſub ſexquialte-
              <lb/>
              <note position="left" xlink:label="note-0500-05" xlink:href="note-0500-05a" xml:space="preserve">Defin. 12.
                <lb/>
              l. 1.</note>
            ra, kE, & </s>
            <s xml:id="echoid-s12320" xml:space="preserve">ſub rectangulo, AKE, cum {2/3}. </s>
            <s xml:id="echoid-s12321" xml:space="preserve">quadrati, KE. </s>
            <s xml:id="echoid-s12322" xml:space="preserve">Nam cy-
              <lb/>
            lindrus, BF, ad reliquum cylindri, CF, dempto fruſto coni, DMIF,
              <lb/>
              <note position="left" xlink:label="note-0500-06" xlink:href="note-0500-06a" xml:space="preserve">C. Cor. 4.
                <lb/>
              gener. 34.
                <lb/>
              l. 2.</note>
            habet rationem compoſitam ex ea, quam habet cylindrus, BF, ad
              <lb/>
            cylindrum, CF, ideſt ex ea, quam habet, AE, ad, EK, & </s>
            <s xml:id="echoid-s12323" xml:space="preserve">ex ratio-
              <lb/>
              <note position="left" xlink:label="note-0500-07" xlink:href="note-0500-07a" xml:space="preserve">Collig. ex
                <lb/>
              L. Coroll.
                <lb/>
              4. gener.
                <lb/>
              34. l. 2.</note>
            ne cylindri, CF, ad reliquum, dempto à cylindro, CF, fruſto, DM
              <lb/>
            IF, quæ eſt ea, quam habet quadratum, DE, ad rectangulum, CM
              <lb/>
            K, cum {2/3}. </s>
            <s xml:id="echoid-s12324" xml:space="preserve">quadrati, CM, vel quadratum, EA, ad rectangulum, E
              <lb/>
            KA, cum {2/3}. </s>
            <s xml:id="echoid-s12325" xml:space="preserve">quadrati, EK, eſt autem reliquum cylindri, BF, dem-
              <lb/>
            pto cono, DAF, {2/3}. </s>
            <s xml:id="echoid-s12326" xml:space="preserve">eiuſdem cylindri, ergo reliquum cylindri, BF,
              <lb/>
            dempto cono, DAF, ad reliquum cylindri, CF, dempto fruſto, D
              <lb/>
            MIF, erit in ratione compoſita ex ea, quam habẽt {2/3}. </s>
            <s xml:id="echoid-s12327" xml:space="preserve">AE, ad, EK,
              <lb/>
            ideſt, AE, ad ſexquialteram, EK, & </s>
            <s xml:id="echoid-s12328" xml:space="preserve">quadratum, AE, ad rectangu-
              <lb/>
              <note position="left" xlink:label="note-0500-08" xlink:href="note-0500-08a" xml:space="preserve">D. G.
                <lb/>
              Cor. gen.
                <lb/>
              34. l. 2.</note>
            lum, AKE, cum {2/3}. </s>
            <s xml:id="echoid-s12329" xml:space="preserve">quadrati, kE, quæ duæ rationes componunt
              <lb/>
            rationem cubi, AE, ad parallelepipedum ſub ſexquialtera, Ek, &</s>
            <s xml:id="echoid-s12330" xml:space="preserve"/>
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