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

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        <div xml:id="echoid-div196" type="section" level="1" n="127">
          <p>
            <s xml:id="echoid-s2023" xml:space="preserve">
              <pb o="81" file="0101" n="101" rhead="LIBER I."/>
            terminans in ambientem ſuperficiem bifariam diuidetur ab ipſa, BD,
              <lb/>
              <note position="right" xlink:label="note-0101-01" xlink:href="note-0101-01a" xml:space="preserve">Ex antec.</note>
            vtin, N; </s>
            <s xml:id="echoid-s2024" xml:space="preserve">Sie oſtendemus, BD, diuidere cæteras omnes ipfi, EM,
              <lb/>
            æquidiſtantes in ſuperficiem ambientem hinc inde terminatas, & </s>
            <s xml:id="echoid-s2025" xml:space="preserve">
              <lb/>
            quia, BD, ſecat, EM, adangulos rectos, cæteras omnes iam di-
              <lb/>
            ctas bifariam, & </s>
            <s xml:id="echoid-s2026" xml:space="preserve">ad angulos rectos ſecabit, igitur tunc figura, BED
              <lb/>
            M, erit circa axem, BD, ſiue in ſolido rotundo, ſiue in cono: </s>
            <s xml:id="echoid-s2027" xml:space="preserve">Siau-
              <lb/>
            tem triangulus, APQ, non tranſeat per ductam ipſi plano perpen-
              <lb/>
            dicularem, tunc eodem modo, quoſupra oſtendemus, BD, ſecare
              <lb/>
            omnes ęquidiſtantes ipſi, EM, bifariam, & </s>
            <s xml:id="echoid-s2028" xml:space="preserve">quia triangulus, APQ,
              <lb/>
            non tranſit per perpendicularem baſi, neque erit erectus ipſi baſi, P
              <lb/>
            EQM, ergo angulus, EDB, non erit rectus, nam ſi eſſet rectus,
              <lb/>
            cum ſit etiam rectus, EDP, planum circuli, PEQM, eſſet erectum
              <lb/>
            triangulo, APQ, & </s>
            <s xml:id="echoid-s2029" xml:space="preserve">ille huic, quod eſt contra ſuppoſitum, igitur,
              <lb/>
              <note position="right" xlink:label="note-0101-02" xlink:href="note-0101-02a" xml:space="preserve">4. Vndec.
                <lb/>
              Elem.</note>
            BD, ſecabit, EM, & </s>
            <s xml:id="echoid-s2030" xml:space="preserve">conſequenter cæteras iam dictas illi æquidi-
              <lb/>
            ſtantes bifariam, & </s>
            <s xml:id="echoid-s2031" xml:space="preserve">ad angulos non rectos, igitur figura, EBM, tunc
              <lb/>
            erit circa diametrum, & </s>
            <s xml:id="echoid-s2032" xml:space="preserve">erit diameter ipſa, BD, ſiue axis, in ſupra-
              <lb/>
            dicto caſu tum in cono, tum etiam in ſolido rotundo, quod erat oſten-
              <lb/>
            dendum.</s>
            <s xml:id="echoid-s2033" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div198" type="section" level="1" n="128">
          <head xml:id="echoid-head139" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s2034" xml:space="preserve">_H_Inc colligitur in cono, ſi triangulus per axem ductus ſit erectus
              <lb/>
            baſi, fieri dictam figuram circa axem; </s>
            <s xml:id="echoid-s2035" xml:space="preserve">ſi verò non ſit erectus, ſed
              <lb/>
            inclinatus eidem, fieri figuram circa diametrum; </s>
            <s xml:id="echoid-s2036" xml:space="preserve">in ſolido rotundo au-
              <lb/>
            tem fieri ſemper figuram circa axem.</s>
            <s xml:id="echoid-s2037" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div199" type="section" level="1" n="129">
          <head xml:id="echoid-head140" xml:space="preserve">THEOREMA XXXV. PROPOS. XXXVIII.</head>
          <p>
            <s xml:id="echoid-s2038" xml:space="preserve">SI conus ſecetur plano per axem, ſecetur deinde altero pla-
              <lb/>
            no ſecante baſim coni ſecundum rectam lineam, quę ad
              <lb/>
            baſim trianguli per axem ſit perpendicularis, cuius & </s>
            <s xml:id="echoid-s2039" xml:space="preserve">trian-
              <lb/>
            guli per axem cõmunis ſectio ſit parallela vni laterum trian-
              <lb/>
            guli per axem; </s>
            <s xml:id="echoid-s2040" xml:space="preserve">quadrata ordinatim applicatarum ad axim,
              <lb/>
            vel diametrum figurę in cono ſecundo plano productę, æqui-
              <lb/>
            diſtantium eiuſdem, & </s>
            <s xml:id="echoid-s2041" xml:space="preserve">baſis communi ſe ctioni erunt inter fe,
              <lb/>
            vt abíciſſæ per eaidem ordinatim applicatas verſus verticem
              <lb/>
            ſumptæ ab eiſdem axibus, vel diametris iam dictis.</s>
            <s xml:id="echoid-s2042" xml:space="preserve"/>
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