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

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              <pb o="473" file="0491" n="491" rhead="LIBER VI."/>
            H, vel, LK, altituto, ad, FE, vt verò, CD, ad, M, ita quadratum
              <lb/>
            CD, ad quadratum, GH, vel circulus, CD, ad circulum, GH, er-
              <lb/>
            go vt, LK, ad, FE, ſic circulus, CD, ad circulum, GH, ergo cy-
              <lb/>
              <note position="right" xlink:label="note-0491-01" xlink:href="note-0491-01a" xml:space="preserve">E. G.
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              Coroll. 4.
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              gene. 34.
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              l. 2.</note>
            lindri, CFD, GLH, ſunt æquales, eſt autem cylindrus, CFD, ſex-
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            quialter cylindri, A, ergo cylindrus, GLH, erit ſexquialter cylin-
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            dri, A, eſt autem cylindrus, GLH, etiam ſexquialter ſphæræ circa
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            diametrum, GH, vel illi æqualem, NO, deſcriptæ ideſt ſphæræ, B,
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              <note position="right" xlink:label="note-0491-02" xlink:href="note-0491-02a" xml:space="preserve">Coroll. 1.
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              34. l. 3.</note>
            ergo ſphæra, B, erit æqualis dato cylindro, A.</s>
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          <p>
            <s xml:id="echoid-s12077" xml:space="preserve">Sit nunc datus axis, NO, circa quem ſit conſtituenda ſphærois
              <lb/>
            æqualis dato cylindro, A, ſi igitur ſphæra circa diametrum, NO,
              <lb/>
            eſſet æqualis dato cylindro, non poſſet circa hanc diametrum fie-
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            ri alia ſphærois ęqualis dato cylindro, ſed talis ſphęrois eſſet eadẽ
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            ſphęra. </s>
            <s xml:id="echoid-s12078" xml:space="preserve">Non ſit autem ęqualis ſphęra, B, cylindro, A, tunc fiat
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            ſphęra ęqualis cylindro, A, quę ſit circa diametrum, ST, deinde
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            fiat, vt, NO, ad, ST, ſic quadratum, ST, ad, X1, bifariam diuiſam
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            in, B, centro, & </s>
            <s xml:id="echoid-s12079" xml:space="preserve">fiat ſphęrois circa diametros, NO, XI, igitur pri.
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            </s>
            <s xml:id="echoid-s12080" xml:space="preserve">miaxes, NO, ST, reciprocè reſpondent ſecundorum axium, ST,
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            vel, 34, XI, quadratis ergo ſphęra, ST, erit ęqualis ſphęroidis, NX
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              <note position="right" xlink:label="note-0491-03" xlink:href="note-0491-03a" xml:space="preserve">Corol. 10.
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              Prop. 34.
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              l. 3. ſect. 4.</note>
            OI, ergo ſphęrois, NXOI, circa datum axim, erit ęqualis dato cy-
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            lindro, A, quod erat inueniendum.</s>
            <s xml:id="echoid-s12081" xml:space="preserve"/>
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        <div xml:id="echoid-div1108" type="section" level="1" n="663">
          <head xml:id="echoid-head693" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s12082" xml:space="preserve">_H_Inc colligitur cuicunq; </s>
            <s xml:id="echoid-s12083" xml:space="preserve">ex ſolidis in antecedenti, & </s>
            <s xml:id="echoid-s12084" xml:space="preserve">Corolla.
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            </s>
            <s xml:id="echoid-s12085" xml:space="preserve">rijs eiuſdem nominatis ſphæram æqualem nos ſcire conſtitue-
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            re, necnon ſphæroidem æqualem circa datum axem, ſphæramque, ac
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            ſphæoidem, quæ ad quodcunq; </s>
            <s xml:id="echoid-s12086" xml:space="preserve">ex ipſis datam rationem habeat. </s>
            <s xml:id="echoid-s12087" xml:space="preserve">Pro-
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              <note position="right" xlink:label="note-0491-04" xlink:href="note-0491-04a" xml:space="preserve">25. huius.</note>
            poſito enim ex illis quocunque ſolido, inuenietur primò cylindrus,
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            qui ad ipſum datam rationem habeat, deinde fiet ſphæra, vel ſphærois
              <lb/>
            circa datum axim, æqualis inuento c ylindro, quæ ſubinde ad datum
              <lb/>
            ſolidum datam rationem habebit: </s>
            <s xml:id="echoid-s12088" xml:space="preserve">Et vniuerſaliter patet ſi diſcamus,
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            dato cylindro æquale ſolidum ex iam @onſideratorum genere construe-
              <lb/>
            re, conſequenter eiuſmodi ſolidum nos ſcire conſtruere, quod ad ali-
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            quod ex nominatis in antecedenti Propoſitione, & </s>
            <s xml:id="echoid-s12089" xml:space="preserve">eiuſdem Corolla-
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            rijs, datam rationem habeat.</s>
            <s xml:id="echoid-s12090" xml:space="preserve"/>
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        <div xml:id="echoid-div1110" type="section" level="1" n="664">
          <head xml:id="echoid-head694" xml:space="preserve">PROBLEMA IV. PROPOS. XXVII.</head>
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            <s xml:id="echoid-s12091" xml:space="preserve">DAto cylindro apicem ſphæralem æqualem conſtitue-
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            re, vel ſphæroidalem, & </s>
            <s xml:id="echoid-s12092" xml:space="preserve">hunc circa datum axem.</s>
            <s xml:id="echoid-s12093" xml:space="preserve"/>
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