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

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          <p>
            <s xml:id="echoid-s9152" xml:space="preserve">
              <pb o="362" file="0382" n="382" rhead="GEOMETRIÆ"/>
            regulam, ZG, vt in poſteriore dicti Theor. </s>
            <s xml:id="echoid-s9153" xml:space="preserve">parte dictum eſt.</s>
            <s xml:id="echoid-s9154" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div883" type="section" level="1" n="529">
          <head xml:id="echoid-head549" xml:space="preserve">COROLLARIVM XXV.</head>
          <p>
            <s xml:id="echoid-s9155" xml:space="preserve">IN Propoſitione 48: </s>
            <s xml:id="echoid-s9156" xml:space="preserve">ſumatur de figura Propoſit. </s>
            <s xml:id="echoid-s9157" xml:space="preserve">46. </s>
            <s xml:id="echoid-s9158" xml:space="preserve">parabola.
              <lb/>
            </s>
            <s xml:id="echoid-s9159" xml:space="preserve">ZAG, cum baſi, ZG, & </s>
            <s xml:id="echoid-s9160" xml:space="preserve">axi, AQ, & </s>
            <s xml:id="echoid-s9161" xml:space="preserve">axi, AQ, & </s>
            <s xml:id="echoid-s9162" xml:space="preserve">reſecto eius minori fruſto,
              <lb/>
            DPG, de eiuſdem figura adnuc ſumatur, AXG, trilineum, in quo
              <lb/>
            ducitur, DE, æquidiſtans ipſi, AX, & </s>
            <s xml:id="echoid-s9163" xml:space="preserve">ſeorſim ponatur, vt autem fiat
              <lb/>
              <figure xlink:label="fig-0382-01" xlink:href="fig-0382-01a" number="261">
                <image file="0382-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0382-01"/>
              </figure>
            ſolitum exemplum, reuoluatur parabola, ZAG, circa manentem
              <lb/>
            axim, AQ, & </s>
            <s xml:id="echoid-s9164" xml:space="preserve">fruſtum minus eiuſdem, quod eſt, DPG, circa, DP,
              <lb/>
            ex quo fiat aceruus minor, RDG. </s>
            <s xml:id="echoid-s9165" xml:space="preserve">Inſuper trilineum, AXG, reuo-
              <lb/>
            luatur circa, GX, vt fiat apex parabolicus, AGZ, & </s>
            <s xml:id="echoid-s9166" xml:space="preserve">ex GDE, eius
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            fruſtum, GDY; </s>
            <s xml:id="echoid-s9167" xml:space="preserve">patet igitur ex ipſa Prop. </s>
            <s xml:id="echoid-s9168" xml:space="preserve">48. </s>
            <s xml:id="echoid-s9169" xml:space="preserve">aceruum minorem,
              <lb/>
            RDG, ad conoidem parabolicam, ZAG, habere rationem compo-
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            ſitam ex ea, quam habet compoſita ex {1/3}. </s>
            <s xml:id="echoid-s9170" xml:space="preserve">ZP, & </s>
            <s xml:id="echoid-s9171" xml:space="preserve">{1/6}. </s>
            <s xml:id="echoid-s9172" xml:space="preserve">PG, ad, ZP, & </s>
            <s xml:id="echoid-s9173" xml:space="preserve">
              <lb/>
            ex ratione parallelepipedi ſub, DP, & </s>
            <s xml:id="echoid-s9174" xml:space="preserve">quadrato, PG, ad dimidium
              <lb/>
            parallelepipedi ſub, AQ & </s>
            <s xml:id="echoid-s9175" xml:space="preserve">quadrato, QG; </s>
            <s xml:id="echoid-s9176" xml:space="preserve">& </s>
            <s xml:id="echoid-s9177" xml:space="preserve">ſic etiã eſſe quodlibet
              <lb/>
            ſolidum ſimilare genitum ex fruſto parabolæ, DGP, ad ſibi ſimila-
              <lb/>
            re genitum ex ſemiparabola, AQG; </s>
            <s xml:id="echoid-s9178" xml:space="preserve">iuxta communem regulam,
              <lb/>
            ZG. </s>
            <s xml:id="echoid-s9179" xml:space="preserve">Item ex eadem Prop. </s>
            <s xml:id="echoid-s9180" xml:space="preserve">patet apicem parabolicum, AGZ, ad
              <lb/>
            eius fruſtum, DGY, habere rationem compoſitam ex ea, quam
              <lb/>
            habet ſexta pars parallelepipedi ſub AQ, & </s>
            <s xml:id="echoid-s9181" xml:space="preserve">quadrato, QG, ad pa-
              <lb/>
            rallelepipedum ſub, DP, & </s>
            <s xml:id="echoid-s9182" xml:space="preserve">quadrato, PG, & </s>
            <s xml:id="echoid-s9183" xml:space="preserve">ex ea, quam habet,
              <lb/>
            ZP, ad reſiduum, demptis ab eadem, ZP, {2/3}. </s>
            <s xml:id="echoid-s9184" xml:space="preserve">ZP, cum {1/6}. </s>
            <s xml:id="echoid-s9185" xml:space="preserve">PG: </s>
            <s xml:id="echoid-s9186" xml:space="preserve">Sic
              <lb/>
            autem quoque erit quodcunque ſolidum ſimilare genitum ex trili-
              <lb/>
            neo, AXG, ad ſibi ſimilare genitum ex trilineo, GDE, iuxta com-
              <lb/>
            munem regulam, AX.</s>
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