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

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          <p>
            <s xml:id="echoid-s9646" xml:space="preserve">
              <pb o="375" file="0395" n="395" rhead="LIBER V."/>
            ptoti datæ hyperbolæ. </s>
            <s xml:id="echoid-s9647" xml:space="preserve">Dico igitur omnia quadrata hyperbolę,
              <lb/>
            SOX, ad omnia quadrata trianguli, HCR, habere rationem com-
              <lb/>
              <figure xlink:label="fig-0395-01" xlink:href="fig-0395-01a" number="270">
                <image file="0395-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0395-01"/>
              </figure>
            poſitam ex ea, quam habet quadratum,
              <lb/>
            SX, ad quadratum, HR, & </s>
            <s xml:id="echoid-s9648" xml:space="preserve">rectangulũ,
              <lb/>
            AVO, ad rectangulum, BVC, inngan-
              <lb/>
            tur, OS, OX: </s>
            <s xml:id="echoid-s9649" xml:space="preserve">Omnia ergo quadrata hy-
              <lb/>
              <note position="right" xlink:label="note-0395-01" xlink:href="note-0395-01a" xml:space="preserve">Defin .12.
                <lb/>
              l. 1.
                <lb/>
              1. huius.
                <lb/>
              D. Cor.
                <lb/>
              22. l. 2.</note>
            perbolæ, SOX, ad omnia quadrata triã-
              <lb/>
            guli, HCR, habent rationem compoſi-
              <lb/>
            tam ex ea, quam habent omnia quadra-
              <lb/>
            ta hyperbolæ, SOX, ad omnia quadra-
              <lb/>
            ta trianguli, SOX, .</s>
            <s xml:id="echoid-s9650" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9651" xml:space="preserve">ex ea, quam Habet,
              <lb/>
            AV, ad, VB, & </s>
            <s xml:id="echoid-s9652" xml:space="preserve">ex ea, quam habent om-
              <lb/>
            nia quadrata trianguli, SOX, ad omnia
              <lb/>
            quadrata trianguli, HCR, quæ eſt com-
              <lb/>
            poſita ex ea, quam habet quadratum, S
              <lb/>
              <note position="right" xlink:label="note-0395-02" xlink:href="note-0395-02a" xml:space="preserve">6 ſec.</note>
            X, ad quadratum, HR, & </s>
            <s xml:id="echoid-s9653" xml:space="preserve">ex ea, quam
              <lb/>
            habet, OV, ad, VC, habemus ergo has tres rationes componen-
              <lb/>
            tes rationem, quam habent omnia quadrata hyperbolæ, SOX, ad
              <lb/>
            omnia quadrata trianguli, HCR, ſcilicet eam, quam habet qua-
              <lb/>
            dratum, SX, ad quadratum, HR, & </s>
            <s xml:id="echoid-s9654" xml:space="preserve">quam habet, AV, ad, VB, & </s>
            <s xml:id="echoid-s9655" xml:space="preserve">
              <lb/>
            tandem, quam habet, OV, ad, VC, harum autem iſtæ duæ .</s>
            <s xml:id="echoid-s9656" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s9657" xml:space="preserve">quã
              <lb/>
            habet, AV, ad, VB, &</s>
            <s xml:id="echoid-s9658" xml:space="preserve">, OV, ad; </s>
            <s xml:id="echoid-s9659" xml:space="preserve">VC, componunt rationem rectã-
              <lb/>
            guli, AVO, ad rectangulum, BVC, ergo omnia quadrata hyper-
              <lb/>
            bolæ, SOX, ad omnia quadrata trianguli, HCR, habent rationẽ
              <lb/>
            compoſitam ex ea, quam habet quadratum, SX, ad quadratum,
              <lb/>
            HR, & </s>
            <s xml:id="echoid-s9660" xml:space="preserve">rectangulum, AVO, ad rectangulum, BVC, quod oſten-
              <lb/>
            dere opus erat.</s>
            <s xml:id="echoid-s9661" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div906" type="section" level="1" n="541">
          <head xml:id="echoid-head565" xml:space="preserve">THEOREMA VII. PROPOS. VIII.</head>
          <p>
            <s xml:id="echoid-s9662" xml:space="preserve">IN eadem anteced. </s>
            <s xml:id="echoid-s9663" xml:space="preserve">figura, regula eadem, retenta, oſten-
              <lb/>
            demus (ducta intra hyperbolam, SOX ipſa, IY, occur-
              <lb/>
            rente aſymptotis, CH, CR, in, T, P,) omnia quadrata tra-
              <lb/>
            pezij, THRP, ad omnia quadrata fruſti hyperbolæ, ISXY,
              <lb/>
            eſſe in ratione compoſita ex ea, quam habet rectangulum
              <lb/>
            ſub, GP, VR, cum .</s>
            <s xml:id="echoid-s9664" xml:space="preserve">quadrati, PM, ad quadratum, VX, & </s>
            <s xml:id="echoid-s9665" xml:space="preserve">
              <lb/>
            ex ea, quam habet rectangulum, BVO, ad rectangulum
              <lb/>
            ſub, BV, OG, vna cum rectangulo ſub compoſita ex .</s>
            <s xml:id="echoid-s9666" xml:space="preserve">BO,
              <lb/>
            & </s>
            <s xml:id="echoid-s9667" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s9668" xml:space="preserve">GV, & </s>
            <s xml:id="echoid-s9669" xml:space="preserve">ſub, GV.</s>
            <s xml:id="echoid-s9670" xml:space="preserve"/>
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