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

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          <p>
            <s xml:id="echoid-s12277" xml:space="preserve">
              <pb o="479" file="0499" n="499" rhead="LIBER VI."/>
              <figure xlink:label="fig-0499-01" xlink:href="fig-0499-01a" number="336">
                <image file="0499-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0499-01"/>
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            noides 63: </s>
            <s xml:id="echoid-s12278" xml:space="preserve">conus 42. </s>
            <s xml:id="echoid-s12279" xml:space="preserve">apex para-
              <lb/>
              <note position="right" xlink:label="note-0499-01" xlink:href="note-0499-01a" xml:space="preserve">Corol. 10.
                <lb/>
              51. l. 4. ſec.
                <lb/>
              poſterior.</note>
            bolicus 21. </s>
            <s xml:id="echoid-s12280" xml:space="preserve">apex ſphæralis 12.
              <lb/>
            </s>
            <s xml:id="echoid-s12281" xml:space="preserve">vnde patet hæmiſphęrium, vel
              <lb/>
            hæmiſphæroides ſexquitertium
              <lb/>
              <note position="right" xlink:label="note-0499-02" xlink:href="note-0499-02a" xml:space="preserve">Coroll. 1.
                <lb/>
              51. l. 4.</note>
            eſſe conoidis parabolici, quadru-
              <lb/>
              <note position="right" xlink:label="note-0499-03" xlink:href="note-0499-03a" xml:space="preserve">I. Corol. 4.
                <lb/>
              gener. 34.
                <lb/>
              l. 2.</note>
            plum apicis parabolici, & </s>
            <s xml:id="echoid-s12282" xml:space="preserve">ſe-
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            ptuplum apicis ſphæralis. </s>
            <s xml:id="echoid-s12283" xml:space="preserve">Co-
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            noides verò parabolicum tri-
              <lb/>
              <note position="right" xlink:label="note-0499-04" xlink:href="note-0499-04a" xml:space="preserve">Coroll. 8.
                <lb/>
              51. l. 4. ſe-
                <lb/>
              ctio 1.</note>
            plum eſſe apicis parabolici, & </s>
            <s xml:id="echoid-s12284" xml:space="preserve">
              <lb/>
            quintuplum ſexquiquartum apicis ſphæralis, quæ ex ipſis nume-
              <lb/>
              <note position="right" xlink:label="note-0499-05" xlink:href="note-0499-05a" xml:space="preserve">Coroll. 11.
                <lb/>
              34. l. 3.</note>
            ris colliguntur, ſimiliter conum, FCE, duplum eſſe apicis para
              <lb/>
            bolici, triplum ſexquialterum proximè apicis ſpæralis, quoad api-
              <lb/>
            cem ſphæralem enim ſemper proximam dictam rationẽ intellige,
              <lb/>
            & </s>
            <s xml:id="echoid-s12285" xml:space="preserve">tandem apex parabolicus ad ſphæralem erit ſexquiſupertripar-
              <lb/>
            tiens quartas.</s>
            <s xml:id="echoid-s12286" xml:space="preserve"/>
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        <div xml:id="echoid-div1130" type="section" level="1" n="677">
          <head xml:id="echoid-head707" xml:space="preserve">THEOREMA XXVII. PROPOS. XXXIV.</head>
          <p>
            <s xml:id="echoid-s12287" xml:space="preserve">SI in baſi cylindri, & </s>
            <s xml:id="echoid-s12288" xml:space="preserve">circa eundem axim, fuerint hæ-
              <lb/>
            miſphærium, vel hæmiſphæroides, conoides parabo-
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            licum, hyperbolicum, & </s>
            <s xml:id="echoid-s12289" xml:space="preserve">conus, ſecto verò axi vtcunque,
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            ducatur planum per punctum ſectionis baſi æquidiſtans.
              <lb/>
            </s>
            <s xml:id="echoid-s12290" xml:space="preserve">Abſciſſæ per ductum planum à dictis ſolidis portiones erũt
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            ad ſolida, à quibus abſcinduntur in ratione infraſcripta. </s>
            <s xml:id="echoid-s12291" xml:space="preserve">
              <lb/>
            Similiter demptis dictis ſolidis ſingillatim à cylindro, ab-
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            ſciſſæ per ductum planum portiones ad reſiduum cylindri,
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            demptis ſolidis iam dictis, erunt in ratione infraſcripta.</s>
            <s xml:id="echoid-s12292" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12293" xml:space="preserve">Sit cylindrus, BF, in baſi circulo, DF, & </s>
            <s xml:id="echoid-s12294" xml:space="preserve">circa axim, AE, circa
              <lb/>
            quem in eadem baſi ſit hæmiſphærium, vel hæmiſphæroides, DV
              <lb/>
            ATF, conoides parabolicum DOARF, hyperbolicum, DNASF,
              <lb/>
            & </s>
            <s xml:id="echoid-s12295" xml:space="preserve">conus, DMAIF, ſumpto autẽ vtcunq; </s>
            <s xml:id="echoid-s12296" xml:space="preserve">puncto in, AE, quod ſit, k,
              <lb/>
            per, k, ducatur planũ, CG, baſi, DF, æquidiſtans. </s>
            <s xml:id="echoid-s12297" xml:space="preserve">Igitur hæmiſphę-
              <lb/>
              <note position="right" xlink:label="note-0499-06" xlink:href="note-0499-06a" xml:space="preserve">Coroll. 7.
                <lb/>
              34. l. 3.</note>
            riũ, vel hæmiſphæroides, DVATF, ad portionẽ, VAT, erit vt pa-
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            ralle lepipedũ ſub dupla, AE, & </s>
            <s xml:id="echoid-s12298" xml:space="preserve">quadrato, AE, ad parallelepipedum
              <lb/>
            ſub compoſita ex dupla, AE, & </s>
            <s xml:id="echoid-s12299" xml:space="preserve">ex, EK, & </s>
            <s xml:id="echoid-s12300" xml:space="preserve">@ub quadrato, kA. </s>
            <s xml:id="echoid-s12301" xml:space="preserve">Co-
              <lb/>
            noides parabolicum, DOARF, ad conoides, OAR, erit vt qua-
              <lb/>
              <note position="right" xlink:label="note-0499-07" xlink:href="note-0499-07a" xml:space="preserve">Coroll. 3.
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              51. l. 4.</note>
            dratum, EA, ad quadratum, AK. </s>
            <s xml:id="echoid-s12302" xml:space="preserve">Conoides hyperbolicum, DN
              <lb/>
            ASF, ad conoides, NAS, vt parallelepipedum ſub compoſita ex
              <lb/>
              <note position="right" xlink:label="note-0499-08" xlink:href="note-0499-08a" xml:space="preserve">Coroll. 2.
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              30. l. 5.</note>
            ſexquialtera tranſuerſi eiuldem lateris, &</s>
            <s xml:id="echoid-s12303" xml:space="preserve">, EA, & </s>
            <s xml:id="echoid-s12304" xml:space="preserve">ſub quadrato, </s>
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