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

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            <s xml:id="echoid-s2743" xml:space="preserve">
              <pb o="116" file="0136" n="136" rhead="GEOMETRIÆ"/>
            AM, BR, ad eam, quæ illi indirectum iacet in figura, CME, erit
              <lb/>
            vt, BR, ad, RD, vel vt, AM, ad, ME, vt igitur, AM, ad, M
              <lb/>
            E, vnum .</s>
            <s xml:id="echoid-s2744" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s2745" xml:space="preserve">antecedentium ad vnum conſequentium, ita erunt om-
              <lb/>
            nia antecedentia, nempè omnes lineę figurę, CAM, regula, AM
              <lb/>
              <figure xlink:label="fig-0136-01" xlink:href="fig-0136-01a" number="76">
                <image file="0136-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0136-01"/>
              </figure>
            ad omnia conſequentia, ſcilicet
              <lb/>
            ad omnes lineas figuræ, CME,
              <lb/>
            regula, ME; </s>
            <s xml:id="echoid-s2746" xml:space="preserve">indefinitus .</s>
            <s xml:id="echoid-s2747" xml:space="preserve">n. </s>
            <s xml:id="echoid-s2748" xml:space="preserve">nu-
              <lb/>
            merus omnium antecedentium,
              <lb/>
            & </s>
            <s xml:id="echoid-s2749" xml:space="preserve">conſequentium, qui pro vtriſ-
              <lb/>
            que hic idem eſt, quicunque ſit
              <lb/>
            (& </s>
            <s xml:id="echoid-s2750" xml:space="preserve">hoc nam figuræ ſunt in ea-
              <lb/>
            dem altitudine, & </s>
            <s xml:id="echoid-s2751" xml:space="preserve">cuilibet ante-
              <lb/>
            cedenti in figura, CAM, aſſumpto reſpondet ſuum conſequens illi
              <lb/>
            in directum in alia figura conſtitutum) non obſtat quin omnes lineę
              <lb/>
            figurę, CAM, ſint comparabiles omnibus lineis figurę, CME, cum
              <lb/>
              <note position="left" xlink:label="note-0136-01" xlink:href="note-0136-01a" xml:space="preserve">1. huius.</note>
            ad illas rationem habeant, vt probatum eſt, & </s>
            <s xml:id="echoid-s2752" xml:space="preserve">ideò omnes lineæ fi-
              <lb/>
            guræ, CAM, regula, AM, ad omnes lineas figurę, CME, regu-
              <lb/>
            la, ME, erunt vt, AM, ad, ME, verum, vt omnes lineæ figuræ,
              <lb/>
            CAM, ad omnes lineas figurę, CME, ita fig. </s>
            <s xml:id="echoid-s2753" xml:space="preserve">CAM, eſt ad figu-
              <lb/>
              <note position="left" xlink:label="note-0136-02" xlink:href="note-0136-02a" xml:space="preserve">3. huius.</note>
            ram, CME, ergo figura, CAM, ad figuram, CME, erit vt, B
              <lb/>
            R, ad, RD, vel, AM, ad, ME, quod in figuris planis oſtendere
              <lb/>
            opus erat.</s>
            <s xml:id="echoid-s2754" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2755" xml:space="preserve">Si verò ſupponamus, CAM, CME, eſſe figuras ſolidas, & </s>
            <s xml:id="echoid-s2756" xml:space="preserve">vice
              <lb/>
            rectarum, AM, BR, ME, RD, plana intelligamus figuris, CA
              <lb/>
            M, CME, intercepta inuicem parallela, & </s>
            <s xml:id="echoid-s2757" xml:space="preserve">ita conſtituta, vt plana,
              <lb/>
            AM, ME, iaceant in eodem plano, veluti ſe habeant etiam plana,
              <lb/>
            BR, RD, reſpectu quorum præfata altitudo aſſumpta quoq; </s>
            <s xml:id="echoid-s2758" xml:space="preserve">intel-
              <lb/>
            ligatur, eadem methodo procedentes oſtendemus omnia plana figu-
              <lb/>
            ræ, CAM, ad omnia plana figuræ, CME, ideſt figuram ſolidam,
              <lb/>
            CAM, ad figuram ſolidam, CME, eſſe vt planum, BR, ad pla-
              <lb/>
              <note position="left" xlink:label="note-0136-03" xlink:href="note-0136-03a" xml:space="preserve">3. huius.</note>
            num, RD, vel vt planum, AM, ad planum, ME, quod & </s>
            <s xml:id="echoid-s2759" xml:space="preserve">in ſoli-
              <lb/>
            dis oſtendere opus erat.</s>
            <s xml:id="echoid-s2760" xml:space="preserve"/>
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        <div xml:id="echoid-div285" type="section" level="1" n="180">
          <head xml:id="echoid-head195" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s2761" xml:space="preserve">_C_Olligitur ex hoc in figuris planis, vel ſolidis, ſi magnitudines com-
              <lb/>
            paratæ ſint lineæ rectæ, vel plana, ſint autem illæ, quæ dicuntur
              <lb/>
            omnes lineæ, vel omnia plana dictarum figurarum, de illis quoq; </s>
            <s xml:id="echoid-s2762" xml:space="preserve">verifi-
              <lb/>
            cari, vt vnum antecedentium ad vnum conſequentium, ita eſſe omnia,
              <lb/>
            antecedentia ad omnia conſequentia; </s>
            <s xml:id="echoid-s2763" xml:space="preserve">& </s>
            <s xml:id="echoid-s2764" xml:space="preserve">in ſupradictis figuris planis
              <lb/>
            omnes lineas vnius ad omnes lineas alterius, vel in ſolidis omnia plana
              <lb/>
            vnius ad omnia plana alterius, eſſe vt vnum antecedentium ad </s>
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