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

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        <div xml:id="echoid-div824" type="section" level="1" n="487">
          <pb o="344" file="0364" n="364" rhead="GEOMETRIÆ"/>
        </div>
        <div xml:id="echoid-div826" type="section" level="1" n="488">
          <head xml:id="echoid-head508" xml:space="preserve">THEOREMA XLVIII. PROPOS. L.</head>
          <p>
            <s xml:id="echoid-s8617" xml:space="preserve">IN eadem figura, ducta per, I, IL, æquidiſtante ipſi, A
              <lb/>
            Q, adhuc oſtendemus omnia quadrata trilinei, DGP,
              <lb/>
            ad omnia quadrata trilinei, DTI, habere rationem compo-
              <lb/>
            ſitam ex ea, quam habet rectangulum, ZPG, cum. </s>
            <s xml:id="echoid-s8618" xml:space="preserve">qua-
              <lb/>
            drati, PG, ad rectangulum, STI, cum quadrati, TI, & </s>
            <s xml:id="echoid-s8619" xml:space="preserve">ex ea,
              <lb/>
            quam habet quadratum, PG, ad quadratum TI.</s>
            <s xml:id="echoid-s8620" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8621" xml:space="preserve">Nam omnia quadrata, DGP, ad omnia quadrata, DIT, ha-
              <lb/>
            bent rationem compoſitam ex ea, quam habent omnia quadrata,
              <lb/>
            DGP, ad omnia quadrata, DG, .</s>
            <s xml:id="echoid-s8622" xml:space="preserve">i. </s>
            <s xml:id="echoid-s8623" xml:space="preserve">ex ea, quam habet {1/3}. </s>
            <s xml:id="echoid-s8624" xml:space="preserve">ZP, cũ
              <lb/>
              <note position="left" xlink:label="note-0364-01" xlink:href="note-0364-01a" xml:space="preserve">41. huius.</note>
            {1/6}. </s>
            <s xml:id="echoid-s8625" xml:space="preserve">PG, ad, ZP, .</s>
            <s xml:id="echoid-s8626" xml:space="preserve">i. </s>
            <s xml:id="echoid-s8627" xml:space="preserve">ſumpta, PG, communi altitudine, ex ea, quam
              <lb/>
            habet rectangulum ſub {1/3}. </s>
            <s xml:id="echoid-s8628" xml:space="preserve">ZP, & </s>
            <s xml:id="echoid-s8629" xml:space="preserve">{1/6}. </s>
            <s xml:id="echoid-s8630" xml:space="preserve">PG, & </s>
            <s xml:id="echoid-s8631" xml:space="preserve">ſub, PG, ad rectangu-
              <lb/>
            lum, ZPG, item ex ratione omnium quadratorum, DG, ad om-
              <lb/>
            nia quadrata, DI, ſcilicet compoſita ex ea, quam habet, PD, ad, D
              <lb/>
            T, & </s>
            <s xml:id="echoid-s8632" xml:space="preserve">quadratum, PG, ad quadratum, TI, eſt autem, vt, PD, ad,
              <lb/>
            DT, ita rectangulum, ZPG, ad rectangulum, STI; </s>
            <s xml:id="echoid-s8633" xml:space="preserve">Tandem
              <lb/>
            verò componitur ex ea, quam habent omnia quadrata, DI,
              <lb/>
              <figure xlink:label="fig-0364-01" xlink:href="fig-0364-01a" number="246">
                <image file="0364-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0364-01"/>
              </figure>
            ad omnia quadrata, DIT,
              <lb/>
            ideſt ex ratione, ST, ad {1/3}.
              <lb/>
            </s>
            <s xml:id="echoid-s8634" xml:space="preserve">ST, cum {1/6}. </s>
            <s xml:id="echoid-s8635" xml:space="preserve">TI, ideſt ſum-
              <lb/>
            pta, TI, communi altitudi-
              <lb/>
            ne, ex ea, quam habet rectan-
              <lb/>
            gulum, STI, ad rectangulum
              <lb/>
            fub, TI, & </s>
            <s xml:id="echoid-s8636" xml:space="preserve">compoſita ex {1/3}. </s>
            <s xml:id="echoid-s8637" xml:space="preserve">S
              <lb/>
            T, & </s>
            <s xml:id="echoid-s8638" xml:space="preserve">{1/6}. </s>
            <s xml:id="echoid-s8639" xml:space="preserve">TI, iſtæ autem ratio-
              <lb/>
              <note position="left" xlink:label="note-0364-02" xlink:href="note-0364-02a" xml:space="preserve">47. huius.</note>
            nes .</s>
            <s xml:id="echoid-s8640" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8641" xml:space="preserve">quam habet rectangu-
              <lb/>
            lum ſub {1/3}. </s>
            <s xml:id="echoid-s8642" xml:space="preserve">ZP, & </s>
            <s xml:id="echoid-s8643" xml:space="preserve">{1/6}, PG, & </s>
            <s xml:id="echoid-s8644" xml:space="preserve">
              <lb/>
            ſub, PG, ad rectangulum, ZPG, & </s>
            <s xml:id="echoid-s8645" xml:space="preserve">huius ad rectangulum, STI,
              <lb/>
            & </s>
            <s xml:id="echoid-s8646" xml:space="preserve">taudem rectanguli, STI, ad rectangulum ſub, TI, & </s>
            <s xml:id="echoid-s8647" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s8648" xml:space="preserve">ST,
              <lb/>
            cum {1/6}. </s>
            <s xml:id="echoid-s8649" xml:space="preserve">TI, componunt rationem rectanguli fub {1/3}. </s>
            <s xml:id="echoid-s8650" xml:space="preserve">ZP, & </s>
            <s xml:id="echoid-s8651" xml:space="preserve">{1/6}. </s>
            <s xml:id="echoid-s8652" xml:space="preserve">PG,
              <lb/>
            & </s>
            <s xml:id="echoid-s8653" xml:space="preserve">ſub, PG, ad rectangulum ſub {1/3}. </s>
            <s xml:id="echoid-s8654" xml:space="preserve">ST, & </s>
            <s xml:id="echoid-s8655" xml:space="preserve">{1/6}. </s>
            <s xml:id="echoid-s8656" xml:space="preserve">TI, & </s>
            <s xml:id="echoid-s8657" xml:space="preserve">ſub, TI
              <emph style="sub">6</emph>
            .</s>
            <s xml:id="echoid-s8658" xml:space="preserve">i, tri-
              <lb/>
            plicatis terminis, componunt rationem rectanguli ſub, ZP, PG,
              <lb/>
            cum rectangulo, ſub {3/6}. </s>
            <s xml:id="echoid-s8659" xml:space="preserve">PG, & </s>
            <s xml:id="echoid-s8660" xml:space="preserve">ſub, PG, .</s>
            <s xml:id="echoid-s8661" xml:space="preserve">i. </s>
            <s xml:id="echoid-s8662" xml:space="preserve">cum {1/2}. </s>
            <s xml:id="echoid-s8663" xml:space="preserve">quadrati, PG,
              <lb/>
            ad rectangulum ſub, ST, TI, cum rectanguio ſub {3/6}. </s>
            <s xml:id="echoid-s8664" xml:space="preserve">TI, & </s>
            <s xml:id="echoid-s8665" xml:space="preserve">ſub, T
              <lb/>
            I, .</s>
            <s xml:id="echoid-s8666" xml:space="preserve">i. </s>
            <s xml:id="echoid-s8667" xml:space="preserve">cum {1/2}. </s>
            <s xml:id="echoid-s8668" xml:space="preserve">quadrati, TI, & </s>
            <s xml:id="echoid-s8669" xml:space="preserve">remanſit ſola ratio quadrati, PG, ad
              <lb/>
            quadratum, TI, ergo omnia quadrata trilinei, DGP, ad om-
              <lb/>
            nia quadrata trilinei, DIT, habebunt rationem compoſitam </s>
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