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

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          <pb o="83" file="0103" n="103" rhead="LIBERI."/>
        </div>
        <div xml:id="echoid-div201" type="section" level="1" n="130">
          <head xml:id="echoid-head141" xml:space="preserve">THEOREMA XXXVI. PROPOS. XXXIX.</head>
          <p>
            <s xml:id="echoid-s2054" xml:space="preserve">IIſdem poſitis, præterquamquod, BV, ſit parallela ipſi, A
              <lb/>
            F, ſed poſito, quod concurrat cum eodem latere, FA, ver-
              <lb/>
            ſus verticem producto, vt in, Z. </s>
            <s xml:id="echoid-s2055" xml:space="preserve">Dico quadratum, ED, ad
              <lb/>
            quadratum, MO, eſſe vt rectangulum, ZVB, ad rectangu-
              <lb/>
            lum, ZNB.</s>
            <s xml:id="echoid-s2056" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2057" xml:space="preserve">Quia enim quadratum, EV, eſt æquale rectangulo, CVF, & </s>
            <s xml:id="echoid-s2058" xml:space="preserve">
              <lb/>
            quadratum, MN, rectangulo, HNR, ideò quadratum, EV, ad
              <lb/>
              <note position="right" xlink:label="note-0103-01" xlink:href="note-0103-01a" xml:space="preserve">14. Secun.
                <lb/>
              Elem.</note>
              <figure xlink:label="fig-0103-01" xlink:href="fig-0103-01a" number="57">
                <image file="0103-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0103-01"/>
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            quadratum, MN, erit vt rectangulum, CV
              <lb/>
            F, HNR, rectangulum verò, CVF, ad,
              <lb/>
            HNR, habet rationem compoſitam ex ea,
              <lb/>
            quam habet, CV, ad, HN, (vt infra inde-
              <lb/>
            pendenter ab hac Propoſit. </s>
            <s xml:id="echoid-s2059" xml:space="preserve">probatur) .</s>
            <s xml:id="echoid-s2060" xml:space="preserve">i. </s>
            <s xml:id="echoid-s2061" xml:space="preserve">VB,
              <lb/>
              <note position="right" xlink:label="note-0103-02" xlink:href="note-0103-02a" xml:space="preserve">Ex Sexta
                <lb/>
              lib. 2. ſeq.
                <lb/>
              vel ex 23.
                <lb/>
              Sexti El.</note>
            ad, BN, quia trianguli, CVB, HNB, ſunt
              <lb/>
            æquianguli, & </s>
            <s xml:id="echoid-s2062" xml:space="preserve">ex ea, quam habet, VF, ad,
              <lb/>
            NR, ideſt, VZ, ad, ZN, quia trianguli, V
              <lb/>
            FZ, NRZ, ſunt æquianguli, duę verò ra-
              <lb/>
            tiones, VB, ad, BN, &</s>
            <s xml:id="echoid-s2063" xml:space="preserve">, VZ, ad, ZN,
              <lb/>
              <note position="right" xlink:label="note-0103-03" xlink:href="note-0103-03a" xml:space="preserve">Ex Sexta
                <lb/>
              lib. 2. ſeq.
                <lb/>
              velex 23.
                <lb/>
              Sexti El.</note>
            componunt rationem rectanguli, ZVB, ad
              <lb/>
            rectangulum, ZNB, ergo rectangulum, C
              <lb/>
            VF, ad rectangulum, HNR, .</s>
            <s xml:id="echoid-s2064" xml:space="preserve">i. </s>
            <s xml:id="echoid-s2065" xml:space="preserve">quadratum,
              <lb/>
            EV, ad quadratum, MN, vel quadratum, ED, ad quadratum, M
              <lb/>
            O, erit vt rectangulum, ZVB, ad rectangulum, ZNB, quod oſten-
              <lb/>
            dere opus erat; </s>
            <s xml:id="echoid-s2066" xml:space="preserve">hæc autem ab Apollonio vocatur Hyperbola.</s>
            <s xml:id="echoid-s2067" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div203" type="section" level="1" n="131">
          <head xml:id="echoid-head142" xml:space="preserve">THEOREMA XXXVII. PROPOS. XL.</head>
          <p>
            <s xml:id="echoid-s2068" xml:space="preserve">TAndem eiſdem poſitis, preterquam dicto concurſu, po-
              <lb/>
            ſito, inquam, BV, concurrere cum vtroq; </s>
            <s xml:id="echoid-s2069" xml:space="preserve">latere trian-
              <lb/>
            guli per axem, & </s>
            <s xml:id="echoid-s2070" xml:space="preserve">productum, etiam cum baſi trianguli per
              <lb/>
            axem conuenire, vt in, 2. </s>
            <s xml:id="echoid-s2071" xml:space="preserve">Dico quadratum, RD, ad qua-
              <lb/>
            dratum, MO, eſſe vt rectangulum, VSB, ad rectangulum,
              <lb/>
            VNB.</s>
            <s xml:id="echoid-s2072" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2073" xml:space="preserve">Sit ergo talis hic appoſitum ſchema, in quo planum figuræ B ℟
              <lb/>
            VD, (cuius axis, vel diameter ſecat vtraque latera, AC, AF, & </s>
            <s xml:id="echoid-s2074" xml:space="preserve">
              <lb/>
            producta incidit in baſim, CF, productam in, 2,) extenſum </s>
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