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

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              <pb o="34" file="0054" n="54" rhead="GEOMETRIÆ"/>
            communem ſectionem borum duorum planorum fore intra figuram in,
              <lb/>
            conico productan à plano omnibus eiuſdem lateribus coincidente, vt
              <lb/>
            patet in conico, ACD qui ſecatur plano, ACD, & </s>
            <s xml:id="echoid-s930" xml:space="preserve">alio, BNEO,
              <lb/>
            quorum com nunis ſectio ſit, BE. </s>
            <s xml:id="echoid-s931" xml:space="preserve">Dico n. </s>
            <s xml:id="echoid-s932" xml:space="preserve">ſi, CD, ſit intra figuram, C
              <lb/>
            MDV, etiam, BE, fore intra figuram, BNEO, nam, ACVD, e§t
              <lb/>
            conicus, & </s>
            <s xml:id="echoid-s933" xml:space="preserve">quia latera non vniuntur, niſi in puncto, A, ideo, BOE,
              <lb/>
            eſt aliqua figura, vt etiam, BNE, & </s>
            <s xml:id="echoid-s934" xml:space="preserve">ideò, BE, cadit intra figuram,
              <lb/>
            BNEO.</s>
            <s xml:id="echoid-s935" xml:space="preserve"/>
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        <div xml:id="echoid-div115" type="section" level="1" n="81">
          <head xml:id="echoid-head92" xml:space="preserve">THEOREMA XV. PROPOS. XVIII.</head>
          <p>
            <s xml:id="echoid-s936" xml:space="preserve">SI per verticem conici, & </s>
            <s xml:id="echoid-s937" xml:space="preserve">rectam tangentem eius baſim
              <lb/>
            extendatur planum, hoc tanget ipſum conicum in vna,
              <lb/>
            vel pluribus rectis lineis, quę erunt latera conici, velin pla-
              <lb/>
            no tranſeunte per eiuſdem latera, quod erit triangulum, ſiue
              <lb/>
            in plurib us triangulis.</s>
            <s xml:id="echoid-s938" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s939" xml:space="preserve">Sit conicus, cuius vertex, A, baſis, BCE, quam tangat recta,
              <lb/>
            DF, in puncto, vel punctis, ſiue in linea. </s>
            <s xml:id="echoid-s940" xml:space="preserve">Dico planum, ADF,
              <lb/>
            tangere dictum conicum in recta linea, ſiue in pluribus rectis lineis,
              <lb/>
            ſiue in plano, quod erit triangulum per eiuſdem latera tranſiens.
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            </s>
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              <figure xlink:label="fig-0054-01" xlink:href="fig-0054-01a" number="27">
                <image file="0054-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0054-01"/>
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            Tangat igitur, DF, figuram, BCE,
              <lb/>
            in puncto, B, & </s>
            <s xml:id="echoid-s942" xml:space="preserve">iungatur, AB, perq;
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            </s>
            <s xml:id="echoid-s943" xml:space="preserve">AB, &</s>
            <s xml:id="echoid-s944" xml:space="preserve">, DF, dictum ſit extenſum pla-
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            num, ergo, AB, erit latus conici, A
              <lb/>
            CE, nam latus, quod reuoluitur tran-
              <lb/>
            ſiens per, B, congruit rectę, AB, alio-
              <lb/>
            quin duæ rectæ lineæ clauderent ſuper-
              <lb/>
            ficiem, eſt ergo, AB, in ſuperficie co-
              <lb/>
            niculari, eſt etiam in plano per, A, &</s>
            <s xml:id="echoid-s945" xml:space="preserve">,
              <lb/>
            DF, tranſeunte, ergo, AB, eſt com-
              <lb/>
            munis tum ſuperſiciei coniculari, tum
              <lb/>
            plano per, A, &</s>
            <s xml:id="echoid-s946" xml:space="preserve">, DF, ducto, nullus
              <lb/>
            autem punctus rectę, AB, eſt intra ſu-
              <lb/>
            perſiciem cylindraceam, ergo planum
              <lb/>
            per, AB, DF, ductum tangit conicum
              <lb/>
            in recta, AB: </s>
            <s xml:id="echoid-s947" xml:space="preserve">Eodem pacto oſtendemus idem tangere conicum in
              <lb/>
            quibuſuis alijs lateribus, quæ ducuntur à punctis contactus rectæ li-
              <lb/>
            neæ, DF, qui fi ſint plures, fit etiam contactus in omnibus lineis,
              <lb/>
            fi vero contactus rectæ, DF, fiat in recta linea tunc contactus plani
              <lb/>
            per, AB, DF, fit in ſingulis rectis lineis, quæ à recta talis </s>
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