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

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          <p>
            <s xml:id="echoid-s1934" xml:space="preserve">
              <pb o="76" file="0096" n="96" rhead="GEOMETRIÆ"/>
            perſiciei dictum ſolidum ambientis, quia gitur, B, non eſt in commu-
              <lb/>
            ni ſectione iam dicta, & </s>
            <s xml:id="echoid-s1935" xml:space="preserve">eſt in plano figuræ, ACDFG, igitur erit
              <lb/>
            intra, vel extra ſuperficiem ambientem dictum ſolidum, eſt autem in
              <lb/>
            ambitu figuræ, quæ tali ambitu dictam ſuperficiem deſcribit, ergo
              <lb/>
            erit in ipſa ſuperficie ambiente, & </s>
            <s xml:id="echoid-s1936" xml:space="preserve">non erit, quod eſt abſurdum, non
              <lb/>
            igitur aliquis punctus ambitus figuræ, quæ dictam ſolidum per reuo-
              <lb/>
            lutionem generat eſt extra ambitum figuræ, ACDFG, igitur iſti
              <lb/>
            ambitus, & </s>
            <s xml:id="echoid-s1937" xml:space="preserve">conſequenter ipſæ figuræ ſibi inuicem congruunt, & </s>
            <s xml:id="echoid-s1938" xml:space="preserve">fit
              <lb/>
            vna figura, ea ſcilicet, quæ per reuolutionem dictum ſolidum rotun-
              <lb/>
            dum generat, quod erat demonſtrandum.</s>
            <s xml:id="echoid-s1939" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div188" type="section" level="1" n="122">
          <head xml:id="echoid-head133" xml:space="preserve">THEOREMA XXXI. PROPOS. XXXIV.</head>
          <p>
            <s xml:id="echoid-s1940" xml:space="preserve">SI ſolidum rotũdum ſecetur plano ad axem recto, fiet con-
              <lb/>
            cepta in ipſo figura circulus, cuius centrum erit in axe.</s>
            <s xml:id="echoid-s1941" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1942" xml:space="preserve">Sit ſolidum rotundum, cuius axis, AC, & </s>
            <s xml:id="echoid-s1943" xml:space="preserve">figura, quæ ipſum per
              <lb/>
            reuolut onem genuit ipſa, ABCD, ſecetur autem plano ad axem
              <lb/>
            recto, ex quo in ipſo producatur figura, MBND. </s>
            <s xml:id="echoid-s1944" xml:space="preserve">Dico hanc eſſe
              <lb/>
            circulum, cuius centrum erit in axe, vt, E, ſit autem communis ſe-
              <lb/>
            ctio plani recti ad axem, & </s>
            <s xml:id="echoid-s1945" xml:space="preserve">figuræ, ABCD, recta, BD, quia er-
              <lb/>
            go figura, ABCD, eſt circa axem, ipſa autem, BD, quæ rectè a-
              <lb/>
              <note position="left" xlink:label="note-0096-01" xlink:href="note-0096-01a" xml:space="preserve">Defin. 6.</note>
            xim ſecat, vna eſt ex ordinatim ad ipſam
              <lb/>
            axim applicatis, ideò ab ea bifariam diui-
              <lb/>
              <figure xlink:label="fig-0096-01" xlink:href="fig-0096-01a" number="52">
                <image file="0096-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0096-01"/>
              </figure>
            ditur in puncto, E, ducatur nunc aliud pla-
              <lb/>
            num per axem, quod in dicto ſolido pro-
              <lb/>
            ducat figuram, AMCN, quæ ſecet figu-
              <lb/>
              <note position="left" xlink:label="note-0096-02" xlink:href="note-0096-02a" xml:space="preserve">Exantec.</note>
            ram, MBND, in recta, MN, erit ergo
              <lb/>
            hæc figura eadem ei, quæ per reuolutio-
              <lb/>
            nem dictum genuit ſolidum, & </s>
            <s xml:id="echoid-s1946" xml:space="preserve">ideò erit fi-
              <lb/>
            gura circa axem, ad quam ordinatim ap-
              <lb/>
            plicatur, MN, cum ipſa rectè axem, AC,
              <lb/>
            diu dat, ergo, MN, bifariam diuiditur in,
              <lb/>
            E, eodem pacto quaſcumq; </s>
            <s xml:id="echoid-s1947" xml:space="preserve">alias commu-
              <lb/>
            nes ſectiones figurarum per axem, AC,
              <lb/>
            tranſeuntium, & </s>
            <s xml:id="echoid-s1948" xml:space="preserve">figurę, BNDM, oſten-
              <lb/>
            demus bifariam diuidi in, E. </s>
            <s xml:id="echoid-s1949" xml:space="preserve">Vlterius, quia figuræ, ABCD, AM
              <lb/>
            CN, ſunt eædem illi, quæ per reuolutionem generat ſolidum, AB
              <lb/>
            CD, &</s>
            <s xml:id="echoid-s1950" xml:space="preserve">, BD, MN, tranſeunt per idem punctum axis, AC, rectè
              <lb/>
            eundem ſecantes, ideo ſi ipſa, AMCN, reuolueretur, donec eſſet
              <lb/>
            in plano figurę, ABCD, illi congrueret, &</s>
            <s xml:id="echoid-s1951" xml:space="preserve">, MN, ipſi, BD, vn-
              <lb/>
            de, MN, BD, ſunt æquales, & </s>
            <s xml:id="echoid-s1952" xml:space="preserve">ideò earum dimidię, NE, EB; </s>
            <s xml:id="echoid-s1953" xml:space="preserve"/>
          </p>
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