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

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          <p>
            <s xml:id="echoid-s2905" xml:space="preserve">
              <pb o="124" file="0144" n="144" rhead="GEOMETRIÆ"/>
            poſitam ex ea, quam habet, BV, ad, ON, vel, BD, ad, OM, cum
              <lb/>
            ſunt æquiangula, & </s>
            <s xml:id="echoid-s2906" xml:space="preserve">ex ea, quem habet quadratum, CD, ad qua-
              <lb/>
            dratum, GM, quod oſtendendum erat.</s>
            <s xml:id="echoid-s2907" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div309" type="section" level="1" n="191">
          <head xml:id="echoid-head206" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s2908" xml:space="preserve">_H_Inc patet, ſi vice quadratorum ſumamus alias figuras planas ſimi-
              <lb/>
            les, quod eodem pacto oſtendemus omnes figuras ſimiles, AD, F
              <lb/>
            M, habere inter ſerationem compoſitam ex ratione quadratorum, CD,
              <lb/>
            GM, & </s>
            <s xml:id="echoid-s2909" xml:space="preserve">altitudinum, BV, ON, vel laterum, BD, OM, æqualiter
              <lb/>
            baſibus inclinatorum, cum parallelogramma ſunt æquiangula.</s>
            <s xml:id="echoid-s2910" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div310" type="section" level="1" n="192">
          <head xml:id="echoid-head207" xml:space="preserve">THEOREMA XII. PROPOS. XII.</head>
          <p>
            <s xml:id="echoid-s2911" xml:space="preserve">P Arallelogrammorum, quorum baſium quadrata altitu-
              <lb/>
            dinibus iuxta eaſdem baſes ſumptis reciprocantur, vel
              <lb/>
            lateribus æqualiter dictis baſibus inclinatis; </s>
            <s xml:id="echoid-s2912" xml:space="preserve">omnia quadra-
              <lb/>
            ta, regulis eiſdem baſibus, ſunt æqualia: </s>
            <s xml:id="echoid-s2913" xml:space="preserve">Et quorum paral-
              <lb/>
            lelogrammorum, regulis baſibus, omnia quadrata ſunt æ-
              <lb/>
            qualia, baſium quadrata altitudinibus, vellateribus æqua-
              <lb/>
            liter dictis baſibus inclinatis, reciprocantur.</s>
            <s xml:id="echoid-s2914" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2915" xml:space="preserve">Sint parallelogramma, HX, AD, quorum baſium, VX, BD,
              <lb/>
            quadrata altitudinibus iuxta ipſas baſes ſumptis, vel lateribus, RX,
              <lb/>
            CD, ſi hæc baſibus, VX, BD, æqualiter ſint inclinata, recipro-
              <lb/>
              <figure xlink:label="fig-0144-01" xlink:href="fig-0144-01a" number="84">
                <image file="0144-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0144-01"/>
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            centur. </s>
            <s xml:id="echoid-s2916" xml:space="preserve">Dico omnia quadrata pa-
              <lb/>
            rallelogrammorum, HX, AD, eſſe
              <lb/>
            inter ſe æqualia. </s>
            <s xml:id="echoid-s2917" xml:space="preserve">Nam omnia qua-
              <lb/>
              <note position="left" xlink:label="note-0144-01" xlink:href="note-0144-01a" xml:space="preserve">Ex auce-
                <lb/>
              ced.</note>
            drara, HX, ad omnia quadrata, A
              <lb/>
            D, habent rationem compoſitam ex
              <lb/>
            ea, quam habet quadratum, VX, ad
              <lb/>
            quadratum, BD, .</s>
            <s xml:id="echoid-s2918" xml:space="preserve">i. </s>
            <s xml:id="echoid-s2919" xml:space="preserve">ex ea, quam
              <lb/>
            habet, CO, ad, RZ, vel, CD, ad,
              <lb/>
            RX, cum ſunt æquiangula, & </s>
            <s xml:id="echoid-s2920" xml:space="preserve">ex ea, quam habet, RZ, ad, CO,
              <lb/>
            vel, RX, ad, CD, quæ duæ rationes componunt rationem, CO,
              <lb/>
            ad, CO, vel, CD, ad, CD, quæ eſt ratio æqualitatis, & </s>
            <s xml:id="echoid-s2921" xml:space="preserve">ideò om-
              <lb/>
            nia quadrata, HX, erunt æqualia omnibus quadratis, AD.</s>
            <s xml:id="echoid-s2922" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2923" xml:space="preserve">Sint nunc omnia quadrata, HX, æqualia omnibus quadratis, A
              <lb/>
            D, regulis eiſdem, VX, BD. </s>
            <s xml:id="echoid-s2924" xml:space="preserve">Dico quadratum, VX, ad quadra-
              <lb/>
            tum, BD, eſſe vt, CO, ad, RZ, vel, CD, ad, RX, cum ſunt </s>
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