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

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          <p>
            <s xml:id="echoid-s1953" xml:space="preserve">
              <pb o="77" file="0097" n="97" rhead="LIBER I."/>
            E, ED, erunt æquales, eodem pacto oſtendemus quaſcumque du-
              <lb/>
            ctas à puncto, E, ad lineam ambientem, MBND, eſſe æquales
              <lb/>
            cuilibet ipſarum, BE, EN, ED, EM, ergo figura, MBND, erit
              <lb/>
            circulus, cuius centrum, E, in axe reperitur, quod erat oſtendendum.</s>
            <s xml:id="echoid-s1954" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div190" type="section" level="1" n="123">
          <head xml:id="echoid-head134" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s1955" xml:space="preserve">_C_olligimus autem ipſas, BD, MN, communes ſectiones figurã-
              <lb/>
            rum per axem ductarum, & </s>
            <s xml:id="echoid-s1956" xml:space="preserve">circulorum, qui per ſectionem dicti
              <lb/>
            ſolidi per plana ad axem recta in eo produsuntur, eſſe eorum diametros,
              <lb/>
            cum per centrum tranſeant.</s>
            <s xml:id="echoid-s1957" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div191" type="section" level="1" n="124">
          <head xml:id="echoid-head135" xml:space="preserve">THEOREMA XXXII. PROPOS. XXXV.</head>
          <p>
            <s xml:id="echoid-s1958" xml:space="preserve">SI quicunq; </s>
            <s xml:id="echoid-s1959" xml:space="preserve">conus ſecetur plano baſi æquidiſtante conce-
              <lb/>
            pta in cono figura erit circulus centrum in axe habens.</s>
            <s xml:id="echoid-s1960" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1961" xml:space="preserve">Si conus ſit rectus patet hoc ex antecedenti Propoſ. </s>
            <s xml:id="echoid-s1962" xml:space="preserve">cæterum ſi ſit
              <lb/>
            ſcalenus, qualis ſit conus, ACFD, qui ſecetur plano baſi, CFD,
              <lb/>
            æquidiſtante, quod in eo producat figuram, BRE. </s>
            <s xml:id="echoid-s1963" xml:space="preserve">Dico ipſam eſſe
              <lb/>
            circulum, centrum in axe habentem. </s>
            <s xml:id="echoid-s1964" xml:space="preserve">Secetur ergo plano per axem,
              <lb/>
              <note position="right" xlink:label="note-0097-01" xlink:href="note-0097-01a" xml:space="preserve">16. huius.</note>
            quod in eo producat triangulum, ACD, cuius & </s>
            <s xml:id="echoid-s1965" xml:space="preserve">circuli, CFD,
              <lb/>
            communis ſectio ſit, CD, quę erit diameter dicti circuli; </s>
            <s xml:id="echoid-s1966" xml:space="preserve">eius autem
              <lb/>
            & </s>
            <s xml:id="echoid-s1967" xml:space="preserve">figuræ, BRE, communis ſectio, BE; </s>
            <s xml:id="echoid-s1968" xml:space="preserve">ſunt igitur trianguli, AB
              <lb/>
              <note position="right" xlink:label="note-0097-02" xlink:href="note-0097-02a" xml:space="preserve">4. Sex. El.</note>
            l, ACN, ſimiles, quia, BI, ęquidiſtat ipſi, C
              <lb/>
            N, ergo, CN, ad, NA, erit vt, BI, ad, IA,
              <lb/>
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            eodem modo oſtendemus, AN, ad, ND, eſſe
              <lb/>
            vt, BI, ad, IE, ergo, ex æquo, CN, ad, N
              <lb/>
            D, erit vt, BI, ad, IE, ſed, CN, eſt ęqualis,
              <lb/>
            ND, ergo &</s>
            <s xml:id="echoid-s1969" xml:space="preserve">, BI, ipſi, IE. </s>
            <s xml:id="echoid-s1970" xml:space="preserve">Ducatur nunc
              <lb/>
            aliud planum per axem, quod producat trian-
              <lb/>
            gulum, ANF, quodq; </s>
            <s xml:id="echoid-s1971" xml:space="preserve">ſecet figuram, BRE,
              <lb/>
            in, IR, fient ergo trianguli, AIR, ANF, æ-
              <lb/>
            quianguli, ergo, FN, NA, NC, erunt lineæ
              <lb/>
            in eadem proportione cum ipſis, RI, IA, IB,
              <lb/>
            ergo, ex ęquo, FN, ad, NC, erit vt, RI, ad,
              <lb/>
            IB, ſed, FN, eſt æqualis ipſi, NC, ergo, R
              <lb/>
            I, erit æqualis ipſi, IB, eodem modo oſtende
              <lb/>
            mus quaſcunque ductas à puncto, I, ad lineam ambientem, BRE,
              <lb/>
            eſſe æquales ipſi, BI, ergo figura, BRE, erit circulus, cuius, cen-
              <lb/>
            trum, I, quod oſtendere oportebat.</s>
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