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

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              <pb o="387" file="0407" n="407" rhead="LIBER V."/>
            fe vt, FD, ad hyperbolã, CBD, quod patet nam, CBD, eſt ſigura
              <lb/>
            qualem poſtulat Prop. </s>
            <s xml:id="echoid-s9957" xml:space="preserve">29. </s>
            <s xml:id="echoid-s9958" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s9959" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9960" xml:space="preserve">eſt enim, BE, communis axis,
              <lb/>
            vel diameter, FD, parallelogrammi, & </s>
            <s xml:id="echoid-s9961" xml:space="preserve">hyperbolæ, CBD, vnde
              <lb/>
            patet propoſitum.</s>
            <s xml:id="echoid-s9962" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div923" type="section" level="1" n="550">
          <head xml:id="echoid-head574" xml:space="preserve">THEOREMA XV. PROPOS. XVI.</head>
          <p>
            <s xml:id="echoid-s9963" xml:space="preserve">IN eadem anteced. </s>
            <s xml:id="echoid-s9964" xml:space="preserve">Prepoſ. </s>
            <s xml:id="echoid-s9965" xml:space="preserve">figura, ſi producatur, CD,
              <lb/>
            vtcunq; </s>
            <s xml:id="echoid-s9966" xml:space="preserve">in, M, & </s>
            <s xml:id="echoid-s9967" xml:space="preserve">compleatur parallelogrammum, HC,
              <lb/>
            regula, CM: </s>
            <s xml:id="echoid-s9968" xml:space="preserve">Omnia quadrata, FM. </s>
            <s xml:id="echoid-s9969" xml:space="preserve">demptis omnibus qua-
              <lb/>
            dratis, GM, ad omnia quadrata figuræ, HBCM, dem-
              <lb/>
            ptis omnibus quadratis figuræ, HBDM, erunt vt, FD, ad
              <lb/>
            hyperbolam, CBD.</s>
            <s xml:id="echoid-s9970" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9971" xml:space="preserve">Patet hoc Theor. </s>
            <s xml:id="echoid-s9972" xml:space="preserve">nam, CBD, eſt ſigura, qualem poſtulat Prop.
              <lb/>
            </s>
            <s xml:id="echoid-s9973" xml:space="preserve">30. </s>
            <s xml:id="echoid-s9974" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s9975" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9976" xml:space="preserve">quia, BE, eſt communis ax@s, vel diameter, parallelo-
              <lb/>
            grammi, FD, & </s>
            <s xml:id="echoid-s9977" xml:space="preserve">hyperbolæ, CBD, vnde, &</s>
            <s xml:id="echoid-s9978" xml:space="preserve">c.</s>
            <s xml:id="echoid-s9979" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div924" type="section" level="1" n="551">
          <head xml:id="echoid-head575" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s9980" xml:space="preserve">_H_Inc babetur omnia quadrata, FD ad omnia quad ſigura, GBCD,
              <lb/>
            demptis omnibus quadratis trilmet, BGD, eſſe vt omnia qua-
              <lb/>
            drata FM, demptis omnibus quadratis, GM, ad omnia quadrata figu-
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            ræ, HBCM, demptis omnibus quadratis ſig. </s>
            <s xml:id="echoid-s9981" xml:space="preserve">HBDM, quia vtraq; </s>
            <s xml:id="echoid-s9982" xml:space="preserve">ſunt,
              <lb/>
            vt, FD, ad byperbolam, CBD.</s>
            <s xml:id="echoid-s9983" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div925" type="section" level="1" n="552">
          <head xml:id="echoid-head576" xml:space="preserve">THEOREMA XVI. PROPOS. XVII.</head>
          <p>
            <s xml:id="echoid-s9984" xml:space="preserve">IN eadem Prop. </s>
            <s xml:id="echoid-s9985" xml:space="preserve">15. </s>
            <s xml:id="echoid-s9986" xml:space="preserve">figura ſi intelligamus ductam vt-
              <lb/>
            cunq; </s>
            <s xml:id="echoid-s9987" xml:space="preserve">axi, vel diametro, BE, parallelam, RS, fiat au-
              <lb/>
            tẽ, vt oia quad FE, ad oia q uad. </s>
            <s xml:id="echoid-s9988" xml:space="preserve">ſemihyperb BCE, regula,
              <lb/>
            CD, .</s>
            <s xml:id="echoid-s9989" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9990" xml:space="preserve">vt, AE, ad compoſitam ex. </s>
            <s xml:id="echoid-s9991" xml:space="preserve">AB, & </s>
            <s xml:id="echoid-s9992" xml:space="preserve">BE, ita quadra-
              <lb/>
            tum, CE, ad quadratum, EI, & </s>
            <s xml:id="echoid-s9993" xml:space="preserve">vt FE, ad ſemihyperbolã,
              <lb/>
            BCE, ita eſſe ſupponatur, CE, ad, EV, vbicunq; </s>
            <s xml:id="echoid-s9994" xml:space="preserve">cadatpũ-
              <lb/>
            ctum, V. </s>
            <s xml:id="echoid-s9995" xml:space="preserve">Dico omnia quadrata, FS, ad omnia quadrata
              <lb/>
            figuræ, RBCS, regula, CD, eſſe vt quadratum, CD, ad
              <lb/>
            quadratum, SE, quadratum, EI, & </s>
            <s xml:id="echoid-s9996" xml:space="preserve">rectangulum bis ſub,
              <lb/>
            VE, ES.</s>
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