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

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            <s xml:id="echoid-s2924" xml:space="preserve">
              <pb o="125" file="0145" n="145" rhead="LIBER II."/>
            quiangula, etenim, CO, ad, CO, habet rationem compoſitam ex
              <lb/>
              <note position="right" xlink:label="note-0145-01" xlink:href="note-0145-01a" xml:space="preserve">Defin. 13.
                <lb/>
              lib. 1.</note>
            ea, quam habet, CO, ad, RZ, & </s>
            <s xml:id="echoid-s2925" xml:space="preserve">RZ, ad, CO, & </s>
            <s xml:id="echoid-s2926" xml:space="preserve">ſic, CD, ad,
              <lb/>
            CD, ex ea, quam habet, CD, ad, RX, &</s>
            <s xml:id="echoid-s2927" xml:space="preserve">, RX, ad, CD, quia
              <lb/>
            verò omnia quadrata, HX, ſunt æqualia omnibus quadratis, AD,
              <lb/>
            ideò ſunt ad illa, vt, CO, ad, CO, vel vt, CD, ad, CD, .</s>
            <s xml:id="echoid-s2928" xml:space="preserve">i. </s>
            <s xml:id="echoid-s2929" xml:space="preserve">in ra-
              <lb/>
            tione compoſita ex ratione, CO, ad, RZ, &</s>
            <s xml:id="echoid-s2930" xml:space="preserve">, RZ, ad, CO, vel,
              <lb/>
            CD, ad, RX, &</s>
            <s xml:id="echoid-s2931" xml:space="preserve">, RX, ad, CD, ſunt autem omnia quadrata, H
              <lb/>
            X, ad omnia quadrata, AD, in ratione compoſita ex ea, quam ha-
              <lb/>
              <note position="right" xlink:label="note-0145-02" xlink:href="note-0145-02a" xml:space="preserve">Exantec.</note>
            bet quadratum, VX, ad quadratum, BD, &</s>
            <s xml:id="echoid-s2932" xml:space="preserve">, RZ, ad, CO, ſiue,
              <lb/>
            RX, ad, CD, cum ſunt æquiangula, ideò duæ rationes, CO, ad,
              <lb/>
            RZ, &</s>
            <s xml:id="echoid-s2933" xml:space="preserve">, RZ, ad, CO, ſiue aliæ duę rationes, CD, ad, RX, &</s>
            <s xml:id="echoid-s2934" xml:space="preserve">,
              <lb/>
            RX, ad, CD, componunt eandem rationem, quam iſtę duę .</s>
            <s xml:id="echoid-s2935" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s2936" xml:space="preserve">ra-
              <lb/>
            tio quadrati, VX, ad quadratum, BD, &</s>
            <s xml:id="echoid-s2937" xml:space="preserve">, RZ, ad, CO, vel, R
              <lb/>
            X, ad, CD, eſt autem communis ratio, RZ, ad, CO, vel, RX,
              <lb/>
            ad, CD, ergo reliqua ratio, quam habet quadratum, VX, ad qua-
              <lb/>
            dratum, BD, erit eadem reliquę, quam nempè habet, CO, ad,
              <lb/>
            RZ, vel, CD, ad, RX, cum ſunt æquiangula, quod erat oſten-
              <lb/>
            dendum.</s>
            <s xml:id="echoid-s2938" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div313" type="section" level="1" n="193">
          <head xml:id="echoid-head208" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s2939" xml:space="preserve">_I_Dem eodem modo de omnibus figuris ſimilibus quibuſuis parallelo-
              <lb/>
            grammorum, HX, AD, regulis ijſdem, VX, BD, oſtendi poſſe ex
              <lb/>
            ſuperiori methodo colligitur.</s>
            <s xml:id="echoid-s2940" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div314" type="section" level="1" n="194">
          <head xml:id="echoid-head209" xml:space="preserve">THEOREMA XIII. PROPOS. XIII.</head>
          <p>
            <s xml:id="echoid-s2941" xml:space="preserve">SImilium parallelogrammorum omnia quadrata, regulis
              <lb/>
            homologis lateribus, ſunt in tripla ratione laterum ho-
              <lb/>
            mologorum.</s>
            <s xml:id="echoid-s2942" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2943" xml:space="preserve">Sint ſimilia parallelogramma, AC, EG, quorum latera homo-
              <lb/>
              <note position="right" xlink:label="note-0145-03" xlink:href="note-0145-03a" xml:space="preserve">Tux. diff. 1.
                <lb/>
              Sex. El.</note>
            loga, BC, FG, ſint ſumpta pro regula. </s>
            <s xml:id="echoid-s2944" xml:space="preserve">Dico omnia quadrata, A
              <lb/>
              <figure xlink:label="fig-0145-01" xlink:href="fig-0145-01a" number="85">
                <image file="0145-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0145-01"/>
              </figure>
            C, ad omnia quadr. </s>
            <s xml:id="echoid-s2945" xml:space="preserve">EG, eſſe in tripla ra-
              <lb/>
            tione eius, quam habet, BC, ad, FG. </s>
            <s xml:id="echoid-s2946" xml:space="preserve">Quo-
              <lb/>
              <note position="right" xlink:label="note-0145-04" xlink:href="note-0145-04a" xml:space="preserve">Ex def. 1.
                <lb/>
              Sex. El.</note>
            niam enim parallelogramma, AC, EG,
              <lb/>
            ſunt ſimilia, ideò ſunt æquiangula, & </s>
            <s xml:id="echoid-s2947" xml:space="preserve">circa
              <lb/>
            æquales angulos latera habent proportio-
              <lb/>
            nalia, &</s>
            <s xml:id="echoid-s2948" xml:space="preserve">, BC, CD; </s>
            <s xml:id="echoid-s2949" xml:space="preserve">FG, GH, ſunt late-
              <lb/>
            ra ad inuicem æqualiter inclinata, quorum,
              <lb/>
            BC, FG, ſunt regulę, ideò omnia quadrata, AC, regula, BC, </s>
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