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

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            <s xml:id="echoid-s9821" xml:space="preserve">
              <pb o="382" file="0402" n="402" rhead="GEOMETRIÆ"/>
            ſimilia, & </s>
            <s xml:id="echoid-s9822" xml:space="preserve">ex ratione, quæ in huius Theorematis ſupradi-
              <lb/>
            ctis caſibusinter illa duorectangula primò loco expoſita
              <lb/>
            fuit.</s>
            <s xml:id="echoid-s9823" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9824" xml:space="preserve">Sint aſſumptę quęcunq; </s>
            <s xml:id="echoid-s9825" xml:space="preserve">hyperbolę, BAD, HMQ, circa axes,
              <lb/>
            vel diametros, AC, MP, circa quas ſint quoq; </s>
            <s xml:id="echoid-s9826" xml:space="preserve">triangula, BAD, H
              <lb/>
            MQ, & </s>
            <s xml:id="echoid-s9827" xml:space="preserve">in baſibus, BD, HQ, latus autem tranſuerſum hyperbolę,
              <lb/>
            BAD, ſit, GA, cuius ſexquialtera, VA; </s>
            <s xml:id="echoid-s9828" xml:space="preserve">& </s>
            <s xml:id="echoid-s9829" xml:space="preserve">larus tranſuerſum hy-
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            perbolę, HMQ, ſit, MX, cuius ſexquialtera, MR, ſint autem ex-
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            poſitæ duæ vtcunque rectæ lineæ, FY, EN. </s>
            <s xml:id="echoid-s9830" xml:space="preserve">Dico omnia qua-
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            drata hyperbolę, BAD, regula, BD, ad omnia quadrata hyper.
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            </s>
            <s xml:id="echoid-s9831" xml:space="preserve">
              <figure xlink:label="fig-0402-01" xlink:href="fig-0402-01a" number="274">
                <image file="0402-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0402-01"/>
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            perbolę, HMQ, regu-
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            la, HQ, habereratio-
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            nem compoſitã ex ea,
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            quam habet rectangu-
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            lum ſub, VC, XP, adre-
              <lb/>
            ctangulum ſub RP, C
              <lb/>
            G, & </s>
            <s xml:id="echoid-s9832" xml:space="preserve">ex ea, quam ha-
              <lb/>
            bet parallelepipedum
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            ſub altitudinehyperbo-
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            lę, BAD, & </s>
            <s xml:id="echoid-s9833" xml:space="preserve">ſub qua-
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            drato, BD, ad paralle-
              <lb/>
            lepipedum ſub altitu-
              <lb/>
            dine hyperbolę, HMQ,
              <lb/>
            baſi quadrato, HQ;
              <lb/>
            </s>
            <s xml:id="echoid-s9834" xml:space="preserve">quod oſtendemus ad
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            modum Propoſ. </s>
            <s xml:id="echoid-s9835" xml:space="preserve">10. </s>
            <s xml:id="echoid-s9836" xml:space="preserve">Si
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            verò comparentur om-
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            nia quadrata hyperbolæ, BAD, ad omnia rectangula hyperbolæ,
              <lb/>
            HMQ, ſimilia rectangulo ſub, HQ, EN, oſtendemus illa ad hæc
              <lb/>
            habere rationem compoſitam ex ratione primò dicta inter illa re-
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            ctangula, & </s>
            <s xml:id="echoid-s9837" xml:space="preserve">ex ratione parallelepipedi ſub altitud ne hyperpolæ,
              <lb/>
            BAD, baſiquad ato, BD, ad parallelepipedum ſub altitudine hy-
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            perbolæ, HMQ, baſi rectangulo ſub, HQ, EN; </s>
            <s xml:id="echoid-s9838" xml:space="preserve">hocq; </s>
            <s xml:id="echoid-s9839" xml:space="preserve">oſtende-
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            mus iuxta methodum Propol. </s>
            <s xml:id="echoid-s9840" xml:space="preserve">antecedentis. </s>
            <s xml:id="echoid-s9841" xml:space="preserve">Sitandem compa. </s>
            <s xml:id="echoid-s9842" xml:space="preserve">
              <lb/>
            rentur omnia rectangula hyperbolæ, BAD, ſimilia rectangulo ſub,
              <lb/>
            BD, FY, ad omnia rectangula hy perbolæ, HMQ, ſimilia rectan-
              <lb/>
            gulo ſub, HQ, EN, oſten demus propoſitum de his hoc pacto: </s>
            <s xml:id="echoid-s9843" xml:space="preserve">Nã
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            omnia rectangula hyperbolæ, BAD, ſimilia rectangulo ſub, BD,
              <lb/>
            FY, ad omnia quadrata eiuſdem, BAD, ſunt vt rectangulum ſub,
              <lb/>
            BD, FY, ad?</s>
            <s xml:id="echoid-s9844" xml:space="preserve">? quadratum, BD, .</s>
            <s xml:id="echoid-s9845" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9846" xml:space="preserve">vt parallelepipedum ſub </s>
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