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

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        <div xml:id="echoid-div132" type="section" level="1" n="92">
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            <s xml:id="echoid-s1137" xml:space="preserve">
              <pb o="43" file="0063" n="63" rhead="LIBERI."/>
            E, ad, BD, ita, CA, ad, AB, ergo vt, CM, ad, MB, ita erit, C
              <lb/>
            A, ad, AB, diuidendo, CB, ad, BM, erit vt, CB, ad, BA, er-
              <lb/>
            go, MB, erit æqualis ipſi, BA, totum parti, quod eſt abiurdum,
              <lb/>
            non igitur, ED, producta tranſit ſupra, A, eodem modo oſtende-
              <lb/>
            mus non tranfire infra, A, ergo tranſibit per, A, ergo tria puncta,
              <lb/>
            A, D, E, erunt in recta linea, AE, quod erat oſtendendum.</s>
            <s xml:id="echoid-s1138" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div134" type="section" level="1" n="93">
          <head xml:id="echoid-head104" xml:space="preserve">THEOREMA XX. PROPOS. XXIII.</head>
          <p>
            <s xml:id="echoid-s1139" xml:space="preserve">SI duarum quarumlibet ſimilium figurarum habeamus
              <lb/>
            homologas cum duabus quibuſdam regulis, habebi-
              <lb/>
            mus etiam homologas earundem cum duabus quibuſuis a-
              <lb/>
            lijs, cum prædictis angulos æquales ad eandem partem fa-
              <lb/>
            cientibus.</s>
            <s xml:id="echoid-s1140" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1141" xml:space="preserve">Patet hęc propoſitio, nam quæcunq; </s>
            <s xml:id="echoid-s1142" xml:space="preserve">figuræ planę ſimiles, ſi ſint
              <lb/>
            æquales, & </s>
            <s xml:id="echoid-s1143" xml:space="preserve">ſimiliter poſitæ, poſſunt eſſe cuiuſdam cylindrici oppo-
              <lb/>
              <note position="right" xlink:label="note-0063-01" xlink:href="note-0063-01a" xml:space="preserve">14. Huius.</note>
            ſitæ baſes, ſi ſint inæquales, oppoſitæ bales fruſti conici, in his au-
              <lb/>
              <note position="right" xlink:label="note-0063-02" xlink:href="note-0063-02a" xml:space="preserve">22. Huius</note>
            tem contingit, ſi habeamus homologas cum duabus quibuſdam re-
              <lb/>
              <note position="right" xlink:label="note-0063-03" xlink:href="note-0063-03a" xml:space="preserve">Corol. 9.
                <lb/>
              & 11. hus
                <lb/>
              ius.</note>
            gulis, nos eaſdem habere cum alijs duabus quibuſcumque cum præ-
              <lb/>
            dictis angulos æquales ad eandem partem conſtituentibus, ergo hoc
              <lb/>
            in quibuſcumque planis ſimilibus figuris verificatur, quod eſt pro-
              <lb/>
            poſitum.</s>
            <s xml:id="echoid-s1144" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div136" type="section" level="1" n="94">
          <head xml:id="echoid-head105" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s1145" xml:space="preserve">_E_T quia incidentes ad homologarum ſimilium figurarum regulas an-
              <lb/>
              <note position="right" xlink:label="note-0063-04" xlink:href="note-0063-04a" xml:space="preserve">_B. Def. 10._</note>
            gulos ad eandem partem efficiunt æquales, ideò & </s>
            <s xml:id="echoid-s1146" xml:space="preserve">ipſæ incidentes
              <lb/>
            erunt homologarum earundem ſimilium figurarum regulæ, & </s>
            <s xml:id="echoid-s1147" xml:space="preserve">vice verſa
              <lb/>
            in quibuſdam regulis homologarum poterunt ſumi earum incidentes.</s>
            <s xml:id="echoid-s1148" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div138" type="section" level="1" n="95">
          <head xml:id="echoid-head106" xml:space="preserve">THEOREMA XXI. PROPOS. XXIV.</head>
          <p>
            <s xml:id="echoid-s1149" xml:space="preserve">SI in duarum ſimilium figurarum oppoſitas tangentes, quę
              <lb/>
            earundem homologarum ſint regulæ, incidant duæ re-
              <lb/>
            ctæ lineæ ad eundem angulum ex eadem parte eaſdem ſe-
              <lb/>
            cantes, ductis verò quibuſdam duabus, prædictis tangenti-
              <lb/>
            bus parallelis, in dictis figuris, quæ ſecantes diuidant ſimi-
              <lb/>
            liter ad eandem partem, vel aſſumptis ipſis oppoſitis tangen-
              <lb/>
            tibus, reperiamus harum portiones inter incidentes, & </s>
            <s xml:id="echoid-s1150" xml:space="preserve"/>
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