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

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          <p>
            <s xml:id="echoid-s9873" xml:space="preserve">
              <pb o="384" file="0404" n="404" rhead="GEOMETRIÆ"/>
            dratum, HP, ad rectangulum, MPX, ideò quadratum, BC, ad re-
              <lb/>
              <note position="left" xlink:label="note-0404-01" xlink:href="note-0404-01a" xml:space="preserve">21 primi
                <lb/>
              Co 1.</note>
            ctangulum, ACG, erit vt quadratum, HP, ad rectangulum, MPX;
              <lb/>
            </s>
            <s xml:id="echoid-s9874" xml:space="preserve">quia autem ratio, quam habet, BC, ad, CA, &</s>
            <s xml:id="echoid-s9875" xml:space="preserve">, BC, ad, CG, com-
              <lb/>
              <note position="left" xlink:label="note-0404-02" xlink:href="note-0404-02a" xml:space="preserve">Iuxta def.
                <lb/>
              Cõmand.
                <lb/>
              & dicta
                <lb/>
              ad Schol.
                <lb/>
              28. l. 1.</note>
            ponit rationem quadrati, BC, ad rectangulum, ACG, & </s>
            <s xml:id="echoid-s9876" xml:space="preserve">item ra-
              <lb/>
            tio, quam habet, HP, ad, PM, &</s>
            <s xml:id="echoid-s9877" xml:space="preserve">, HP, ad PX, componit rationem
              <lb/>
              <figure xlink:label="fig-0404-01" xlink:href="fig-0404-01a" number="275">
                <image file="0404-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0404-01"/>
              </figure>
            quadrati, HP, ad rectã-
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            gulum, MPX, harum
              <lb/>
            autem rationum com-
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            ponentium ea, quam
              <lb/>
            habet, BC, ad, CA, eſt
              <lb/>
            eadem, ei, quam ha-
              <lb/>
            bet, HP, ad, PM, ideò
              <lb/>
            reliquæ componentiũ
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            erunt eædem .</s>
            <s xml:id="echoid-s9878" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s9879" xml:space="preserve">BC, ad
              <lb/>
            CG, erit vt, HP, ad, P
              <lb/>
            X, eſt autem etiam, A
              <lb/>
            C, ad, CB, conuerten.
              <lb/>
            </s>
            <s xml:id="echoid-s9880" xml:space="preserve">do, vt, MP, ad PH,
              <lb/>
            ergo, ex æquali, & </s>
            <s xml:id="echoid-s9881" xml:space="preserve">con-
              <lb/>
            uertendo, GC, ad CA,
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            erit vt, XP, ad PM, & </s>
            <s xml:id="echoid-s9882" xml:space="preserve">
              <lb/>
            diuidendo, GA, ad, A
              <lb/>
            C, erit vt, XM, ad MP, & </s>
            <s xml:id="echoid-s9883" xml:space="preserve">antecedentium dimidia .</s>
            <s xml:id="echoid-s9884" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s9885" xml:space="preserve">VG, ad AC,
              <lb/>
            erit vt, RX, ad, MP, eſt autem eadem, VG, ad, GA, vt eadem, R
              <lb/>
            X, ad, XM, ergo, VG, ad, GC, erit vt, RX, ad, XP, & </s>
            <s xml:id="echoid-s9886" xml:space="preserve">componen-
              <lb/>
            do, VC, ad, CG, erit vt, RP, ad PX, eſt autem, VC, ad, CG, vt om-
              <lb/>
            nia quadrata hyperbolæ, BAD, ad omnia quadrata trianguli, B
              <lb/>
            AD, &</s>
            <s xml:id="echoid-s9887" xml:space="preserve">, RP, ad PX, vt omnia quadrata hyperbolę, HMQ, ad om-
              <lb/>
            nia quadrata trianguli, HMQ, ergo omnia quadrata hyperbolę,
              <lb/>
              <note position="left" xlink:label="note-0404-03" xlink:href="note-0404-03a" xml:space="preserve">1. huius.</note>
            BAD, ad omnia quadrata trianguli, BAD, erunt vt omnia qua-
              <lb/>
            drata hyperbolæ, HMQ, ad omnia quadrata trianguli, HMQ, & </s>
            <s xml:id="echoid-s9888" xml:space="preserve">
              <lb/>
            permutando, omnia quadrata hyperbolę, BAD, ad omnia gua-
              <lb/>
            drata hyperbolę, HMQ, erunt vt omnia quadrata trianguli, BA
              <lb/>
            D, ad omnia quadrata trianguli, HMQ, .</s>
            <s xml:id="echoid-s9889" xml:space="preserve">@. </s>
            <s xml:id="echoid-s9890" xml:space="preserve">in tripla ratione eius,
              <lb/>
              <note position="left" xlink:label="note-0404-04" xlink:href="note-0404-04a" xml:space="preserve">F Cor. 22.
                <lb/>
              l. 2.</note>
            quam habet, AC, ad, MP, quod oſtendere opus erat.</s>
            <s xml:id="echoid-s9891" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div918" type="section" level="1" n="547">
          <head xml:id="echoid-head571" xml:space="preserve">THEOREMA XIII, PROPOS. XIV.</head>
          <p>
            <s xml:id="echoid-s9892" xml:space="preserve">SIexponatur ſemiperbola, quæ per axem, vel diametrũ
              <lb/>
            integrę ſit abſciſſa, habens pro baſi dimidiam </s>
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