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

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        <div xml:id="echoid-div694" type="section" level="1" n="408">
          <p>
            <s xml:id="echoid-s7004" xml:space="preserve">
              <pb o="288" file="0308" n="308" rhead="GEOMETRIÆ"/>
            lineæ erunt interſe, vtrectangula ſub partibus baſis ab ei-
              <lb/>
            ſdem æquidiſtantibus conſtitutis.</s>
            <s xml:id="echoid-s7005" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7006" xml:space="preserve">Sit ergo parabola, FCH, circa axim, vel diametrum, CG, ad
              <lb/>
            quam ordinatim applicetur recta linea vtcunq; </s>
            <s xml:id="echoid-s7007" xml:space="preserve">FH, ducantur dein-
              <lb/>
            de intra parabolam axi, vel diametro, CG, parallelæ vtcunque, A
              <lb/>
            N, MO, baſim, FH, in punctis, N, O, diuidentes. </s>
            <s xml:id="echoid-s7008" xml:space="preserve">Dico igitur re-
              <lb/>
            ctam, AN, ad rectam, MO, eſſe vt rectangulum, FNH, ad re-
              <lb/>
            ctangulum, FOH; </s>
            <s xml:id="echoid-s7009" xml:space="preserve">ducatur per, M, ipſi, FH, parallela, MI; </s>
            <s xml:id="echoid-s7010" xml:space="preserve">eſt
              <lb/>
            ergo, GC, ad, CI, vt quadratum, GH, ad quadratum, IM, vel
              <lb/>
              <note position="left" xlink:label="note-0308-01" xlink:href="note-0308-01a" xml:space="preserve">38. EtSch.
                <lb/>
              40. lib. 1.</note>
            ad quadratum, GO, ergo, perconuerſionem rationis, GC, ad, G
              <lb/>
              <figure xlink:label="fig-0308-01" xlink:href="fig-0308-01a" number="202">
                <image file="0308-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0308-01"/>
              </figure>
            I, vel ad, MO, erit vt quadratum, H
              <lb/>
            G, ad ſuireliquum, dempto quadrato,
              <lb/>
            GO, hoc autem reſiduum eſt rectan-
              <lb/>
            gulum ſub, GOH, bis, vna cum qua-
              <lb/>
            drato, OH, quod eſt æqualerectan-
              <lb/>
            gulo, FOH, nam rectangulum, GO
              <lb/>
            H, cum quadrato, OH, æquatur re-
              <lb/>
            ctangulo, GHO, .</s>
            <s xml:id="echoid-s7011" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7012" xml:space="preserve">rectangulo ſub,
              <lb/>
            FG, OH, cui ſi iunxeris rectangulum
              <lb/>
            ſub, GO, & </s>
            <s xml:id="echoid-s7013" xml:space="preserve">eadem, OH, conſurget
              <lb/>
            integrum rectangulum, FOH, æqualerectangulis ſub, GOH, bis,
              <lb/>
              <note position="left" xlink:label="note-0308-02" xlink:href="note-0308-02a" xml:space="preserve">4. 2. Elem.</note>
            vna cum quadrato, OH, ergo, CG, ad, MO, erit vt quadratum,
              <lb/>
              <note position="left" xlink:label="note-0308-03" xlink:href="note-0308-03a" xml:space="preserve">3.2. Elem.</note>
            GH, .</s>
            <s xml:id="echoid-s7014" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7015" xml:space="preserve">vt rectangulum, FGH, ad rectangulum, FOH, & </s>
            <s xml:id="echoid-s7016" xml:space="preserve">con-
              <lb/>
              <note position="left" xlink:label="note-0308-04" xlink:href="note-0308-04a" xml:space="preserve">1. 2. Elem.</note>
            uertendo, MO, ad, CG, erit vtrectang. </s>
            <s xml:id="echoid-s7017" xml:space="preserve">HOF, ad rectangulum, H
              <lb/>
            GF; </s>
            <s xml:id="echoid-s7018" xml:space="preserve">codem modo oſtendemus, CG, ad, AN, eſſe vt idem rectan-
              <lb/>
            gulum, HGF, ad rectangulum, FNH, ergo ex æquali, & </s>
            <s xml:id="echoid-s7019" xml:space="preserve">conuer-
              <lb/>
            tendo, AN, ad, MO, erit vt rectangulum, FNH, ad rectangulum,
              <lb/>
            FOH, quod oſtendere oportebat. </s>
            <s xml:id="echoid-s7020" xml:space="preserve">Poſſunt autem vocari &</s>
            <s xml:id="echoid-s7021" xml:space="preserve">, AN,
              <lb/>
            MO, ordinatim applicatæ ad baſim parabolæ, FCH, ſcilicet ad
              <lb/>
            ipſam, FH.</s>
            <s xml:id="echoid-s7022" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div696" type="section" level="1" n="409">
          <head xml:id="echoid-head429" xml:space="preserve">THEOREMA IV. PROPOS. IV.</head>
          <p>
            <s xml:id="echoid-s7023" xml:space="preserve">SI ad baſim parabolæ ordinatim applicetur vtcunque re-
              <lb/>
            cta linea, ſiat autem parallelogrammum, & </s>
            <s xml:id="echoid-s7024" xml:space="preserve">triangulum
              <lb/>
            habentia circa communem angulum dictam applicatam, & </s>
            <s xml:id="echoid-s7025" xml:space="preserve">
              <lb/>
            abſciſſam à baſiab vtrauis extremitatum eiuſdem, vel ſint
              <lb/>
            duæ ad baſim vtcunque ordinatim applicatæ, ſub alterutra
              <lb/>
            quarum, & </s>
            <s xml:id="echoid-s7026" xml:space="preserve">ſub in cluſa ab ijſdem portione baſis ſiat paralle-
              <lb/>
            logrammum, & </s>
            <s xml:id="echoid-s7027" xml:space="preserve">triangulum; </s>
            <s xml:id="echoid-s7028" xml:space="preserve">dicti parallelogrammi, vel </s>
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