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

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            <s xml:id="echoid-s7310" xml:space="preserve">
              <pb o="303" file="0323" n="323" rhead="LIBER IV."/>
            ſit ab illis tribus æquale eſt cubo mediæ ideſt parallelepipedum ſub
              <lb/>
              <note position="right" xlink:label="note-0323-01" xlink:href="note-0323-01a" xml:space="preserve">45.1.2.</note>
            altitudine, CE, & </s>
            <s xml:id="echoid-s7311" xml:space="preserve">ſub baſi rectangulo ipſius, BC, ductæ in tri-
              <lb/>
            plam, CH, æquabitur cubo, BC, remanet adhuc parallelepipe-
              <lb/>
            dum ſub altitudine, HB, baſi t@ibus rectangulis, BCH, quod (al-
              <lb/>
            titudinem, BH, diuidentes in duas ſilicet in, BC, CH,) diuidi-
              <lb/>
            mus in parallelepipedum ſub altitudine, HC, baſirectangulo, H
              <lb/>
              <note position="right" xlink:label="note-0323-02" xlink:href="note-0323-02a" xml:space="preserve">35.1.2.</note>
            CB, ter ſumpto ideſt in parallelepipedum ſub altitudine, BC, baſi
              <lb/>
            quadrato, CH, ter ſumpto, & </s>
            <s xml:id="echoid-s7312" xml:space="preserve">in parallelepipedum ſub altitudine,
              <lb/>
              <note position="right" xlink:label="note-0323-03" xlink:href="note-0323-03a" xml:space="preserve">36.1.2.</note>
            BC, baſi rectangulo, BCH, terſumpto ideſt in parallelep pedum
              <lb/>
            ſub altitudine, HC, baſi quadrato, BC, ter ſumpto; </s>
            <s xml:id="echoid-s7313" xml:space="preserve">parallepipe-
              <lb/>
              <note position="right" xlink:label="note-0323-04" xlink:href="note-0323-04a" xml:space="preserve">36.1.2.</note>
            dum ergo ſub altitudine compoſita ex, HB, CE, baſi rec@angu-
              <lb/>
            lo, HCB, ter ſumpto, æquatur parallelepipedis ter ſub, BC, & </s>
            <s xml:id="echoid-s7314" xml:space="preserve">
              <lb/>
            quadrato, CH, terſub, HC, & </s>
            <s xml:id="echoid-s7315" xml:space="preserve">quadrato, CB, cum cubo, CB,
              <lb/>
            ad hæc ergo ſimul ſumpta cubus, HB, erit vt parabola, HNB,
              <lb/>
            ad trilineum, HASB; </s>
            <s xml:id="echoid-s7316" xml:space="preserve">quia verò parallelepipedum ter ſub, BC,
              <lb/>
              <note position="right" xlink:label="note-0323-05" xlink:href="note-0323-05a" xml:space="preserve">38.1.2.</note>
            & </s>
            <s xml:id="echoid-s7317" xml:space="preserve">quadrato, CH, cum parallelepipedo ter ſub, HC, & </s>
            <s xml:id="echoid-s7318" xml:space="preserve">quadrato,
              <lb/>
            CB, cum cubo, CB, deficiunt à cubo, BH, quantitate cubi, HC,
              <lb/>
            ideo, per conuerſionem rationis, parabola, HNB, ad ſegmentum,
              <lb/>
            HNA, erit vt cubus, BH, ad cubum, HC.</s>
            <s xml:id="echoid-s7319" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7320" xml:space="preserve">Nuncdico parabolam, HNB, ad ſegmentum, HNBV, eſſe
              <lb/>
            vt cubum, BH, ad cubum, HX; </s>
            <s xml:id="echoid-s7321" xml:space="preserve">ducatur per, V, ipſi, BH, pa-
              <lb/>
            rallela, VZ, ſecans curuam parabolæ productam in, Z, & </s>
            <s xml:id="echoid-s7322" xml:space="preserve">à
              <lb/>
              <note position="right" xlink:label="note-0323-06" xlink:href="note-0323-06a" xml:space="preserve">@. huius.</note>
            puncto, H, ipſi, NO, vel, XV, demittatur parallela, HI, oc-
              <lb/>
            currens ipſi, VZ, in, I, eſt ergo parabola, BNH, ad parabo-
              <lb/>
            lam, VBNHZ, vt cubus, BH, ad cubum, VZ, item parabo-
              <lb/>
            la, VBNHZ, ad ſegmentum, VBNH, (quia, VH, eſt ſupra
              <lb/>
            baſim, VZ,) eſt vt cubus, ZV, ad cubum, VI, vel, XH; </s>
            <s xml:id="echoid-s7323" xml:space="preserve">æqua-
              <lb/>
            lis, VI, quia, XI, eſt parallelogrammum; </s>
            <s xml:id="echoid-s7324" xml:space="preserve">ergo, ex æquali, pa-
              <lb/>
            rabola, HNB, ad ſegmentum, HNBV, conſtitutum per lineam
              <lb/>
            ductam à puncto extremo, H, baſis, BH, properantem infra
              <lb/>
            eandem baſim, BH, erit vt cubus, BH, ad cubum, HX, quæ o-
              <lb/>
            ſtendenda erant.</s>
            <s xml:id="echoid-s7325" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div723" type="section" level="1" n="425">
          <head xml:id="echoid-head445" xml:space="preserve">THEOREMA XIII. PROPOS. XIV.</head>
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            <s xml:id="echoid-s7326" xml:space="preserve">SIintra curuam parabolæ ducantur vtcunque duæ rectæ
              <lb/>
            lineæ in eandem curuam terminantes, parabola ab vna
              <lb/>
            ductarum conſtituta ad parabolam ab alia conſtitutam erit,
              <lb/>
            vt cubus primò ductæ ad cubum rectæ lineæ, quæ, </s>
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