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

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              <pb o="507" file="0527" n="527" rhead="LIBER VII."/>
            ptis,, ergo ſunt figuræ proportionaliter analogæ, ergo dicti cy-
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            lindrici erunt inter ſe, vt baſes, KLM, SQTR, quod erat demon-
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              <note position="right" xlink:label="note-0527-01" xlink:href="note-0527-01a" xml:space="preserve">3.huius.</note>
            ſtrandum.</s>
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        <div xml:id="echoid-div1169" type="section" level="1" n="699">
          <head xml:id="echoid-head732" xml:space="preserve">COROLLARIV M.</head>
          <p style="it">
            <s xml:id="echoid-s13046" xml:space="preserve">_C_Vm verò etiam cylindrici in eiſdem baſibus, & </s>
            <s xml:id="echoid-s13047" xml:space="preserve">altitudinibus
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            prædictis æqualibus, ſint inter ſe, vt ipſæ baſes, propterea erũt
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            etiam inter ſe, vt ipſi conici, vnde ſi in vna ſpecie cylindricorum, & </s>
            <s xml:id="echoid-s13048" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0527-02" xlink:href="note-0527-02a" xml:space="preserve">_5. huius._</note>
            conicorum oſtenſum fuerit, cylindricum triplum eſſe conici in eadem
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            baſi, & </s>
            <s xml:id="echoid-s13049" xml:space="preserve">altitudine cum eo exiſtentis, illicò hoc etiam de reliquis ſpe-
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            crebus cylindricorum, & </s>
            <s xml:id="echoid-s13050" xml:space="preserve">conicorum facilè colligemus.</s>
            <s xml:id="echoid-s13051" xml:space="preserve"/>
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        <div xml:id="echoid-div1171" type="section" level="1" n="700">
          <head xml:id="echoid-head733" xml:space="preserve">THEOREMA VIII. PROPOS. VIII.</head>
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            <s xml:id="echoid-s13052" xml:space="preserve">QVilibet Cylindricus triplus eſt Conici in eadem ba-
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            ſi, & </s>
            <s xml:id="echoid-s13053" xml:space="preserve">altitudine, cum eo exiſtentis.</s>
            <s xml:id="echoid-s13054" xml:space="preserve"/>
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            <s xml:id="echoid-s13055" xml:space="preserve">Sit quicunq; </s>
            <s xml:id="echoid-s13056" xml:space="preserve">cylindricus, GO, & </s>
            <s xml:id="echoid-s13057" xml:space="preserve">conicus in eadem baſi, IMNO,
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            & </s>
            <s xml:id="echoid-s13058" xml:space="preserve">eadem altitudine cum ipſo. </s>
            <s xml:id="echoid-s13059" xml:space="preserve">Dico cylindricum, GO, triplum
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              <figure xlink:label="fig-0527-01" xlink:href="fig-0527-01a" number="351">
                <image file="0527-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0527-01"/>
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            eſſe conici, HIMNO.
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            </s>
            <s xml:id="echoid-s13060" xml:space="preserve">Exponatur enim pri-
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            ſma, AFDE, triangu-
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            lares habens baſes, A
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            BC, FDE; </s>
            <s xml:id="echoid-s13061" xml:space="preserve">altitudinis
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            æqualis altitudini cy-
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            lindrici, GO, in baſi
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            verò, FDE, ſit pyra-
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            mis, CDFE; </s>
            <s xml:id="echoid-s13062" xml:space="preserve">erit er-
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            go priſma, ADEF,
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            triplum pyramidis, C
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            DEF, cum reſoluatur in tres pyramides æquales, FDBC, FDEC,
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            FBAC, vt oſtendit Euclides Vnd. </s>
            <s xml:id="echoid-s13063" xml:space="preserve">Element. </s>
            <s xml:id="echoid-s13064" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s13065" xml:space="preserve">7. </s>
            <s xml:id="echoid-s13066" xml:space="preserve">vt autem ſe
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              <note position="right" xlink:label="note-0527-03" xlink:href="note-0527-03a" xml:space="preserve">EX ant.</note>
            habet priſma, ADEF, ad pyramidem, CDEF, ita ſe habet cylin-
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            dricus, GO, ad conicum, HIMNO, ergo, GO, triplus eſt conici, H
              <lb/>
            MO, vnde omnis cylindricus triplus eſt conici in eadem baſi, & </s>
            <s xml:id="echoid-s13067" xml:space="preserve">al-
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            titudine cum eo conſtituti, illi enim conici, qui ſunt in eadem ba-
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            ſi, & </s>
            <s xml:id="echoid-s13068" xml:space="preserve">altitudine ex ant. </s>
            <s xml:id="echoid-s13069" xml:space="preserve">omnes inter ſe ſunt æquales, quod oſten-
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            dendum erat.</s>
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