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

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        <div xml:id="echoid-div106" type="section" level="1" n="75">
          <p>
            <s xml:id="echoid-s894" xml:space="preserve">
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            BD, ęquidiſtante, & </s>
            <s xml:id="echoid-s895" xml:space="preserve">quia latus, AB, indefinitè productum oc-
              <lb/>
            currit baſi, etiam dictum baſi ęquidiſtans planum occurret indefini-
              <lb/>
            tè productum ipſi baſi, quod eſt abſurdum, non igitur planum du-
              <lb/>
            ctum per, A, baſi, BD, ęquidiſtans conicum tangit vel ſecat in a-
              <lb/>
            lio, quam in puncto, A, ergo, A, erit illius vnicus vertex reſpectu
              <lb/>
            baſis, BD, quod erat oſtendendum.</s>
            <s xml:id="echoid-s896" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div108" type="section" level="1" n="76">
          <head xml:id="echoid-head87" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s897" xml:space="preserve">_C_Vm autem dicemus verticem alicuius conici, intelligemus ſemper
              <lb/>
            ipſum reſpectu baſis aſſumptum, ideſt punctum, curin reuolutie-
              <lb/>
            ne innititur latus cylindrict, niſi aliud explicetur.</s>
            <s xml:id="echoid-s898" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div109" type="section" level="1" n="77">
          <head xml:id="echoid-head88" xml:space="preserve">THEOREMA XIII. PROPOS. XVI.</head>
          <p>
            <s xml:id="echoid-s899" xml:space="preserve">SI conicus ſecetur vtcumque per verticem ducto plano,
              <lb/>
            concepta in ipſo ſigura, vel figuræ, erit triangulus, vel
              <lb/>
            trianguli.</s>
            <s xml:id="echoid-s900" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s901" xml:space="preserve">Secetur quilibet conicus, ABF, plano vtcumque per verticem
              <lb/>
            ducto, quod in eo producat figuram, ſiue figuras, ABC, AEF.
              <lb/>
            </s>
            <s xml:id="echoid-s902" xml:space="preserve">
              <figure xlink:label="fig-0052-01" xlink:href="fig-0052-01a" number="25">
                <image file="0052-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0052-01"/>
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            Dico eas eſſe triangulos, Sit com-
              <lb/>
            munis ſectio illius, & </s>
            <s xml:id="echoid-s903" xml:space="preserve">baſis pro-
              <lb/>
            ducti plani, tota, BF, cuius, CE,
              <lb/>
            portio maneat extra baſim, eſt igi-
              <lb/>
            tur, BF, recta linea, dico etiam
              <lb/>
            eſſe rectas ipſas, AB, AC, AE,
              <lb/>
            AF, ſienim non eſt, AB, recta,
              <lb/>
            ducatur in plano figurę, ABC, re-
              <lb/>
            cta, AOB, igitur, AOB, quę
              <lb/>
            iungit punctum, B, & </s>
            <s xml:id="echoid-s904" xml:space="preserve">verticem coni eſt latus conici, ABF, ergo
              <lb/>
            eſt in ſuperficie coniculari, & </s>
            <s xml:id="echoid-s905" xml:space="preserve">eſt etiam in plano figurę, ABC, ergo
              <lb/>
            eſt in eorum communi ſectione, ideſt cadit ſuper, AB, igitur, AB,
              <lb/>
            erit recta linea, eodem modo oſtendemus ipſas, AC, AE, AF, eſſe
              <lb/>
            rectas, & </s>
            <s xml:id="echoid-s906" xml:space="preserve">ideò erit, ABC, triangulus, vt etiam, AEF, quod erat
              <lb/>
            oſtendendum.</s>
            <s xml:id="echoid-s907" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div111" type="section" level="1" n="78">
          <head xml:id="echoid-head89" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s908" xml:space="preserve">_E_Odem modo nobis innoteſcit figuras, quæ extra conicum fiunt eſſe
              <lb/>
            triangulos, ideſt, ACE, eſſe triangulum, & </s>
            <s xml:id="echoid-s909" xml:space="preserve">qui ex ipſis inte-
              <lb/>
            gratur, ſcilicet, ABF, pariter eſſe triangulum.</s>
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