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

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          <pb o="119" file="0139" n="139" rhead="LIBER II."/>
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        <div xml:id="echoid-div291" type="section" level="1" n="183">
          <head xml:id="echoid-head198" xml:space="preserve">THEOREMA VII. PROPOS. VII.</head>
          <p>
            <s xml:id="echoid-s2805" xml:space="preserve">PArallelogramma, quorum baſes altitudinibus, vellate-
              <lb/>
            ribus æqualiter baſibus inclinatis, reciprocantur, ſunt
              <lb/>
            æqualia, & </s>
            <s xml:id="echoid-s2806" xml:space="preserve">quæ ſunt æqualia, baſes habent altitudinibus,
              <lb/>
            vel lateribus æqualiter baſibus inclinatis, reciprocas.</s>
            <s xml:id="echoid-s2807" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2808" xml:space="preserve">Sint parallelogramma, HX, AD, quorum baſes, VX, BD, re-
              <lb/>
            ciprocentur eorum altitudinibus, CO, RZ, vel lateribus, CD, R
              <lb/>
            X, quotieſcunq; </s>
            <s xml:id="echoid-s2809" xml:space="preserve">ſint æqualiter baſibus inclinata. </s>
            <s xml:id="echoid-s2810" xml:space="preserve">Dico hæc paral-
              <lb/>
            lelogramma eſſe æqualia; </s>
            <s xml:id="echoid-s2811" xml:space="preserve">etenim parallelogrammum, HX, ad pa-
              <lb/>
            rallelogrammum, AD, habet rationem compoſitam ex ea, quam
              <lb/>
            habet, VX, ad, BD, &</s>
            <s xml:id="echoid-s2812" xml:space="preserve">, RZ, ad, CO, ſiue, RX, ad, CD, cum
              <lb/>
              <figure xlink:label="fig-0139-01" xlink:href="fig-0139-01a" number="79">
                <image file="0139-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0139-01"/>
              </figure>
            illa ſunt æquiangula, eſt autem, vt,
              <lb/>
            VX, ad, BD, ita, CO, ad, RZ,
              <lb/>
            vel, CD, ad, RX, cum illa ſunt
              <lb/>
              <note position="right" xlink:label="note-0139-01" xlink:href="note-0139-01a" xml:space="preserve">Ex ante-
                <lb/>
              ced.</note>
            æquiangula, ergo parallelogram-
              <lb/>
            mum, HX, ad parallelogrammum,
              <lb/>
            AD, habet rationem compoſitam
              <lb/>
            ex ea, quam habet, CO, ad, RZ,
              <lb/>
            &</s>
            <s xml:id="echoid-s2813" xml:space="preserve">, RZ, ad, CO, ſiue ex ea, quam
              <lb/>
            habet, CD, ad, RX, &</s>
            <s xml:id="echoid-s2814" xml:space="preserve">, RX, ad, CD, quæ eſt eadem ei, quam
              <lb/>
              <note position="right" xlink:label="note-0139-02" xlink:href="note-0139-02a" xml:space="preserve">Defin. 12.
                <lb/>
              lib. 1.</note>
            habet, CD, ad, CD, vt illa eſt eadem ei, quam habet, CO, ad,
              <lb/>
            CO, ſuntque proportiones æqualitatis, ergo parallelogrammum,
              <lb/>
            HX, erit æquale parallelogrammo, AD.</s>
            <s xml:id="echoid-s2815" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2816" xml:space="preserve">Sint nunc parallelogrammum, HX, æquale parallelogrammo, A
              <lb/>
            D. </s>
            <s xml:id="echoid-s2817" xml:space="preserve">Dico, vt, VX, ad, BD, ita eſſe, CO, ad, RZ, vel, CD, ad,
              <lb/>
            RX, cum ſunt æquiangula. </s>
            <s xml:id="echoid-s2818" xml:space="preserve">Quoniam ergo parallelogrammum, H
              <lb/>
            X, eſt æquale parallelogrammo, AD, erit ad illud, vt, CO, ad,
              <lb/>
            CO, vel vt, CD, ad, CD, ideſt (de foris ſumpto, RZ, vel pro
              <lb/>
            ſecunda ratione, RX,) inratione compoſita ex ea, quam habet, C
              <lb/>
              <note position="right" xlink:label="note-0139-03" xlink:href="note-0139-03a" xml:space="preserve">Defin. 12.
                <lb/>
              lib. 1.</note>
            O, ad, RZ, & </s>
            <s xml:id="echoid-s2819" xml:space="preserve">ex ea, quam habet, RZ, ad, CO, vel ex ea, quam
              <lb/>
            habet, CD, ad, RX, &</s>
            <s xml:id="echoid-s2820" xml:space="preserve">, RX, ad, CD, verum, HX, ad, AD,
              <lb/>
              <note position="right" xlink:label="note-0139-04" xlink:href="note-0139-04a" xml:space="preserve">Exantec.</note>
            habet etiam rationem compoſitam ex ea, quam habet, VX, ad, B
              <lb/>
            D, &</s>
            <s xml:id="echoid-s2821" xml:space="preserve">, RZ, ad, CO, vel, RX, ad, CD, cum ſunt æquiangula,
              <lb/>
            ergo duæ rationes, CO, ad, RZ, &</s>
            <s xml:id="echoid-s2822" xml:space="preserve">, RZ, ad, CO, vel, CD, ad,
              <lb/>
            RX, &</s>
            <s xml:id="echoid-s2823" xml:space="preserve">, RX, ad, CD, componunt eandem rationem, quam iſtę
              <lb/>
            duæ.</s>
            <s xml:id="echoid-s2824" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s2825" xml:space="preserve">VX, ad, BD, &</s>
            <s xml:id="echoid-s2826" xml:space="preserve">, RZ, ad, CO, vel, RX, ad, CD, eſt
              <lb/>
            autem communis ratio, quam habet, RZ, ad, CO, vel, RX, ad,
              <lb/>
            CD, ergo reliqua ratio .</s>
            <s xml:id="echoid-s2827" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s2828" xml:space="preserve">quam habet, VX, ad, BD, erit </s>
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