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

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        <div xml:id="echoid-div256" type="section" level="1" n="170">
          <pb o="108" file="0128" n="128" rhead="GEOMETRIÆ"/>
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        <div xml:id="echoid-div265" type="section" level="1" n="171">
          <head xml:id="echoid-head185" xml:space="preserve">POSTVLATA</head>
          <head xml:id="echoid-head186" xml:space="preserve">I.</head>
          <p>
            <s xml:id="echoid-s2583" xml:space="preserve">COngruentium planarum figurarum omnes lineæ, ſum-
              <lb/>
              <note position="left" xlink:label="note-0128-01" xlink:href="note-0128-01a" xml:space="preserve">Def. 1. &
                <lb/>
              2. huius.</note>
            ptæ vna earundem vt regula communi, ſunt congruen-
              <lb/>
            tes; </s>
            <s xml:id="echoid-s2584" xml:space="preserve">Et congruentium ſolidorum omnia plana, ſumpta eorum
              <lb/>
            vno, vt regula communi, ſunt pariter congruentia.</s>
            <s xml:id="echoid-s2585" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div267" type="section" level="1" n="172">
          <head xml:id="echoid-head187" xml:space="preserve">II.</head>
          <p>
            <s xml:id="echoid-s2586" xml:space="preserve">Omnes figuræ ſimiles alicuius figuræ planæ ſunt omnia
              <lb/>
            plana ſolidi, quod terminatur ſuperficie, in qua iacent peri-
              <lb/>
              <note position="left" xlink:label="note-0128-02" xlink:href="note-0128-02a" xml:space="preserve">A. Def. 8.
                <lb/>
              huius.</note>
            metri omnium dictarum ſimilium figurarum.</s>
            <s xml:id="echoid-s2587" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div269" type="section" level="1" n="173">
          <head xml:id="echoid-head188" xml:space="preserve">THEOREMA I. PROPOS. I.</head>
          <p>
            <s xml:id="echoid-s2588" xml:space="preserve">QVarumlibet planarum figurarum omnes lineæ recti
              <lb/>
            tranſitus; </s>
            <s xml:id="echoid-s2589" xml:space="preserve">& </s>
            <s xml:id="echoid-s2590" xml:space="preserve">quarumlibet ſolidarum omnia plana, ſunt
              <lb/>
            magnitudines inter ſe rationem habentes.</s>
            <s xml:id="echoid-s2591" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2592" xml:space="preserve">Sint duæ planæ vtcumque figuræ, EAG, GOQ, quarum re-
              <lb/>
            gulæ, EG, GQ, vtcumq; </s>
            <s xml:id="echoid-s2593" xml:space="preserve">ſit autem figuræ, EAG, altitudo ſum-
              <lb/>
            pta reſpectu, EG, ipſa, A ℟, & </s>
            <s xml:id="echoid-s2594" xml:space="preserve">figuræ, GOQ, altitudo ſumpta
              <lb/>
            reſpectu, GQ, ipſa, OP. </s>
            <s xml:id="echoid-s2595" xml:space="preserve">Dico ergo omnes lineas recti tranſitus fi-
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            guræ, EAG, ſumptas cum regula, EG, ad omnes lineas rectitran-
              <lb/>
              <figure xlink:label="fig-0128-01" xlink:href="fig-0128-01a" number="70">
                <image file="0128-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0128-01"/>
              </figure>
            ſitus figuræ, GOQ, ſum-
              <lb/>
            ptas cum regula, GQ, ra-
              <lb/>
            tionem habere. </s>
            <s xml:id="echoid-s2596" xml:space="preserve">Conſtitu-
              <lb/>
            antur regulæ, EG, GQ,
              <lb/>
            ſibi in directum, & </s>
            <s xml:id="echoid-s2597" xml:space="preserve">ſint to-
              <lb/>
            tæ figuræ ſupra ipſas regu-
              <lb/>
            las in eodem plano, vel igi-
              <lb/>
            tur altitudines, A ℟, OP,
              <lb/>
            ſunt æquales, vel non, ſupponamus primò ipſas eſſe ęquales, abſcin-
              <lb/>
            dantur nuncab altitudinibus, A ℟, OP, ex hypoteſi ęqualibus, por-
              <lb/>
            tiones, I ℟, RP, æquales verſus regulas, EG, GQ, ſi ergo per
              <lb/>
            punctum, I, duxerimus regulæ, EG, parallelam, LM, hæc pro-
              <lb/>
            ducta tranſibit per punctum, R, fiet ergo, LM, quę clauditur </s>
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