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

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        <div xml:id="echoid-div703" type="section" level="1" n="413">
          <pb o="295" file="0315" n="315" rhead="LIBER IV."/>
        </div>
        <div xml:id="echoid-div705" type="section" level="1" n="414">
          <head xml:id="echoid-head434" xml:space="preserve">COROLLARIV M.</head>
          <p style="it">
            <s xml:id="echoid-s7157" xml:space="preserve">_H_Inc patet, quod, diuidendo, portio parabolæ, SGAT, ad por-
              <lb/>
            tionem, SHT, erit bt omnia quadrata ſemiportionis, AMVT,
              <lb/>
            ad omnia quadrata ſemiportionis, HVT, .</s>
            <s xml:id="echoid-s7158" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s7159" xml:space="preserve">bt parallelepipedum ſub
              <lb/>
            altitudine linea compoſita ex, OH, HT, baſi quadrato, TA, ad paral-
              <lb/>
            lelepipedum ſub altitudine, XT, baſi quadrato, HT, bt patet in Coroll.
              <lb/>
            </s>
            <s xml:id="echoid-s7160" xml:space="preserve">ſupradictæ Propoſ. </s>
            <s xml:id="echoid-s7161" xml:space="preserve">6. </s>
            <s xml:id="echoid-s7162" xml:space="preserve">eiuſdem Libri 3.</s>
            <s xml:id="echoid-s7163" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div706" type="section" level="1" n="415">
          <head xml:id="echoid-head435" xml:space="preserve">THEOREMA VII. PROPOS. VII.</head>
          <p>
            <s xml:id="echoid-s7164" xml:space="preserve">SI duæ ad baſim parabolæ applicentur vtcunque rectæ li-
              <lb/>
            neæ, abſciſſæ portiones parabolæ eruntinterſe, vt pa-
              <lb/>
            rallelepipeda ſub baſibus quadratis abſciſſarum à baſi per
              <lb/>
            eaſdem applicatas ab eadem extremitate, à qua portiones
              <lb/>
            abſciſſæ intelliguntur, altitudinibus compoſitis ex reſiduis
              <lb/>
            dictæ baſis (demptis abſciſſis) & </s>
            <s xml:id="echoid-s7165" xml:space="preserve">dimidia totius.</s>
            <s xml:id="echoid-s7166" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7167" xml:space="preserve">Sit ergo parabola, HGA, in baſi, HA, ad quam ordinatim ap-
              <lb/>
            plicentur duæ vtcunque lineæ, ST, RV, abſcindentes portiones, R
              <lb/>
              <figure xlink:label="fig-0315-01" xlink:href="fig-0315-01a" number="209">
                <image file="0315-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0315-01"/>
              </figure>
            HV, SHT. </s>
            <s xml:id="echoid-s7168" xml:space="preserve">Dico portionem, RHV, ad
              <lb/>
            portionem, SHT, eſſe (ſi producatur, AX,
              <lb/>
            æqualis ipſius baſis, AH, medietati) vt pa-
              <lb/>
            rallelepipedum ſub altitudine, XV, baſi qua-
              <lb/>
            drato, VH, ad parallelepipedum ſub altitudi-
              <lb/>
            ne, XT, baſi quadrato, TH. </s>
            <s xml:id="echoid-s7169" xml:space="preserve">Eſt enim por-
              <lb/>
            tio, RHV, ad parabolam, AGH, vt paral-
              <lb/>
            lelepipedum ſub altitudine, XV, baſi quadra-
              <lb/>
              <note position="right" xlink:label="note-0315-01" xlink:href="note-0315-01a" xml:space="preserve">Exantec.</note>
            to, VH, ad parallelepipedum ſub altitudine,
              <lb/>
            XA, baſi quadrato, AH, item parabola, A
              <lb/>
            GH, ad portionem, HST, eſt vt parallele-
              <lb/>
            pipedum ſub altitudine, XA, baſi quadrato,
              <lb/>
            AH, ad parall elepipedum ſub altitudine, XT,
              <lb/>
            baſi quadrato, TH, ergo exæquali portio, R
              <lb/>
            HV, ad portionem, SHT, eſt vt parallele-
              <lb/>
            pipedum ſub altitudine, XV, baſi quadrato,
              <lb/>
            VH, ad parallelepipedum ſub altitudine, X
              <lb/>
            T, baſi quadrato, TH, quod oſtendere opor-
              <lb/>
            tebar.</s>
            <s xml:id="echoid-s7170" xml:space="preserve"/>
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