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

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        <div xml:id="echoid-div723" type="section" level="1" n="425">
          <p>
            <s xml:id="echoid-s7326" xml:space="preserve">
              <pb o="304" file="0324" n="324" rhead="GEOMETRIÆ"/>
            per punctum extremum alterius ſecundò ductæ, parallela
              <lb/>
            primò ductæ, incluſæ dicto puncto, & </s>
            <s xml:id="echoid-s7327" xml:space="preserve">alio eiuſdem paralle-
              <lb/>
            læ productæ, ſi opus ſit; </s>
            <s xml:id="echoid-s7328" xml:space="preserve">in quod cadit, quæ ducitur per
              <lb/>
            aliud extremum punctum ſecundò ductæ, parallela axi, vel
              <lb/>
            diametro parabolæ per primò ductam conſtitutæ.</s>
            <s xml:id="echoid-s7329" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7330" xml:space="preserve">Sit curua parabolæ, BAEC, intra quam ſint vtcumq; </s>
            <s xml:id="echoid-s7331" xml:space="preserve">ductæ in
              <lb/>
            eandem curuam hinc inde terminantes (.</s>
            <s xml:id="echoid-s7332" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7333" xml:space="preserve">quod non ſint ductæ pa-
              <lb/>
            rallelæ axi) primò, BC, ſecundò, AD; </s>
            <s xml:id="echoid-s7334" xml:space="preserve">ducatur deinde per vtrum
              <lb/>
              <figure xlink:label="fig-0324-01" xlink:href="fig-0324-01a" number="217">
                <image file="0324-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0324-01"/>
              </figure>
            libet extremorum punctorum ſecundò
              <lb/>
            ductæ, vt per, A, ipſa, AF, parallela
              <lb/>
            ipſi, BC, in quam productam, ſi opus
              <lb/>
            ſit, incidat parallela axi, quæ ducitur
              <lb/>
            per punctum, D, aliud extremum
              <lb/>
            ipſius, AD, occurrat autem illi in, F.
              <lb/>
            </s>
            <s xml:id="echoid-s7335" xml:space="preserve">Dico parabolam, BAEC, ad para-
              <lb/>
            bolam, AED, eſſe vt cubum, BC,
              <lb/>
            ad cubum, AF. </s>
            <s xml:id="echoid-s7336" xml:space="preserve">Eſt enim parabola,
              <lb/>
              <note position="left" xlink:label="note-0324-01" xlink:href="note-0324-01a" xml:space="preserve">@. huius.</note>
            BNC, ad parabolam, ANE, vt cubus, BC, ad cubum, AE,
              <lb/>
            item parabola, ANE, ad parabolam, ANED, eſt vt cubus, A
              <lb/>
              <note position="left" xlink:label="note-0324-02" xlink:href="note-0324-02a" xml:space="preserve">Exantec.</note>
            E, ad cubum, AF, ergo parabola, BNC, ad parabolam, AN
              <lb/>
            ED, eſt vt cubus, BC, ad cubum, AF, quod oſtendere opus
              <lb/>
            erat.</s>
            <s xml:id="echoid-s7337" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div725" type="section" level="1" n="426">
          <head xml:id="echoid-head446" xml:space="preserve">THEOREMA XIV. PROPOS. XV.</head>
          <p>
            <s xml:id="echoid-s7338" xml:space="preserve">IN eadem antecedentis figura, ſi ducatur intra parabo-
              <lb/>
            lam, BNC, à puncto, V, ſumpto vtcumque in curua, B
              <lb/>
            NC, verſus baſim, BC, ipſa, VX, incidens baſi in, X, pa-
              <lb/>
            rallela axi, vel diametro eiuſdem parabolæ. </s>
            <s xml:id="echoid-s7339" xml:space="preserve">Dico parabo-
              <lb/>
            lam, ANED, ad ſegmentum, VCX, eſſe vt cubum, AF,
              <lb/>
            ad parallelepipedum ter ſub, BX, & </s>
            <s xml:id="echoid-s7340" xml:space="preserve">quadrato, XC, cum
              <lb/>
            cubo, XC.</s>
            <s xml:id="echoid-s7341" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7342" xml:space="preserve">Nam parabola, ANED, ad parabolam, BNC, conuertendo,
              <lb/>
            eſt vt cubus, AF, ad cubum, BC, item parabola, BNC, ad
              <lb/>
            ſegmentum, VCX, eſt vt cubus, BC, ad parallelepipedum ter ſub
              <lb/>
              <note position="left" xlink:label="note-0324-03" xlink:href="note-0324-03a" xml:space="preserve">6.huius.</note>
            altitudine, BX, baſi quadrato, XC, cum cubo, XC, ergo, ex æ-
              <lb/>
            quali, parabola, ANED, ad ſegmentum, VXC, erit vt cubus,
              <lb/>
            AF, ad parallelepipedum terſub, BX, & </s>
            <s xml:id="echoid-s7343" xml:space="preserve">quadrato, XC, cum cu-
              <lb/>
            bo, XC, quod oſtendere oportebat.</s>
            <s xml:id="echoid-s7344" xml:space="preserve"/>
          </p>
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