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

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        <div xml:id="echoid-div586" type="section" level="1" n="343">
          <p>
            <s xml:id="echoid-s5948" xml:space="preserve">
              <pb o="242" file="0262" n="262" rhead="GEOMETRIÆ"/>
            vel vtrectangulum, FMN, ad, {1/6}, quadratorum, RM, MV,.</s>
            <s xml:id="echoid-s5949" xml:space="preserve">.
              <lb/>
            ad, {1/3}, quadrati, RM, .</s>
            <s xml:id="echoid-s5950" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5951" xml:space="preserve">ad rectangulum ſub; </s>
            <s xml:id="echoid-s5952" xml:space="preserve">FM, &</s>
            <s xml:id="echoid-s5953" xml:space="preserve">, {1/3}, MH, .</s>
            <s xml:id="echoid-s5954" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5955" xml:space="preserve">vt,
              <lb/>
            MN, ad, {1/3}, MH, vel vt tripla, MN, ad, MH. </s>
            <s xml:id="echoid-s5956" xml:space="preserve">Inſuper eadem
              <lb/>
            rectangula ſub, Δ V, VT, ad rectangula ſub portione, RFV, & </s>
            <s xml:id="echoid-s5957" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0262-01" xlink:href="fig-0262-01a" number="162">
                <image file="0262-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0262-01"/>
              </figure>
            ſub, RY, ſunt vt parallelogrammum,
              <lb/>
            Δ V, ad portionem, RFV, ergo ſi
              <lb/>
            fiat, vt, Δ V, ad portionem, RFV,
              <lb/>
              <note position="left" xlink:label="note-0262-01" xlink:href="note-0262-01a" xml:space="preserve">Coroll. 1.
                <lb/>
              26. l. 2.</note>
            ita tripla, MN, ad, H ω; </s>
            <s xml:id="echoid-s5958" xml:space="preserve">rectangula
              <lb/>
            ſub, Δ V, VT, ad reliquum, demptis
              <lb/>
            rectangulis ſub portione, RFV, & </s>
            <s xml:id="echoid-s5959" xml:space="preserve">
              <lb/>
            ſub, RY; </s>
            <s xml:id="echoid-s5960" xml:space="preserve">à rectangulis ſub eadem por-
              <lb/>
            tione, & </s>
            <s xml:id="echoid-s5961" xml:space="preserve">ſub quadrilineo, RTHYV,
              <lb/>
            .</s>
            <s xml:id="echoid-s5962" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5963" xml:space="preserve">ad rectangula ſub portione, RFV,
              <lb/>
            & </s>
            <s xml:id="echoid-s5964" xml:space="preserve">portione, THY, .</s>
            <s xml:id="echoid-s5965" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5966" xml:space="preserve">ad omnia qua-
              <lb/>
            drata portionis, RFV, erunt vetripla,
              <lb/>
            MN, ad, M ω, omnia autem quadra-
              <lb/>
            ta, Δ V, ad rectangula ſub, Δ V, VT,
              <lb/>
            ſunt vt quadratum, FM, ad rectangu-
              <lb/>
            lum, FMI, .</s>
            <s xml:id="echoid-s5967" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5968" xml:space="preserve">vt, FM, ad, MI, vel
              <lb/>
            vt ſexquialtera, FM, ad ſexquialte-
              <lb/>
            ram, MI, .</s>
            <s xml:id="echoid-s5969" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5970" xml:space="preserve">ad triplam, MN, rectan-
              <lb/>
            gula autem ſub, Δ V, VT, ad omnia
              <lb/>
              <note position="left" xlink:label="note-0262-02" xlink:href="note-0262-02a" xml:space="preserve">@4. l. 2.</note>
            quadrata portionis, RFV, ſunt vt
              <lb/>
            tripla, MN, ad, M ω, ergo ex æqua-
              <lb/>
              <note position="left" xlink:label="note-0262-03" xlink:href="note-0262-03a" xml:space="preserve">@. l. 2.</note>
            li omnia quadrata, Δ V, ad omnia
              <lb/>
            quadrata portionis, RFV, erunt vt ſexquialtera ipſius, FM, ad,
              <lb/>
            M ω, quæ eſt reſiduumipſius, MH, dempta, H ω, ad quam tri-
              <lb/>
            pla, MN, eſt vt, Δ V, ad portionem, RFV, quod oſtendere
              <lb/>
            opus erat.</s>
            <s xml:id="echoid-s5971" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div588" type="section" level="1" n="344">
          <head xml:id="echoid-head361" xml:space="preserve">THEOREMA XXIII. PROPOS. XXIV.</head>
          <p>
            <s xml:id="echoid-s5972" xml:space="preserve">EXpoſita denuò figura circuli Th. </s>
            <s xml:id="echoid-s5973" xml:space="preserve">21. </s>
            <s xml:id="echoid-s5974" xml:space="preserve">oſtendendum eſt
              <lb/>
            omnia quadrata portionis minoris, RFV, vtcunque
              <lb/>
            ſumptæ regula diametro. </s>
            <s xml:id="echoid-s5975" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5976" xml:space="preserve">FM, ad omnia quadrata eiuſ-
              <lb/>
            dem regula baſi. </s>
            <s xml:id="echoid-s5977" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5978" xml:space="preserve">RV, eſſe vt rectangulum ſub, M, & </s>
            <s xml:id="echoid-s5979" xml:space="preserve">ſub
              <lb/>
            baſi, RV, ad tria quadrata lineæ, RM, cum quad. </s>
            <s xml:id="echoid-s5980" xml:space="preserve">MF.</s>
            <s xml:id="echoid-s5981" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5982" xml:space="preserve">Omnia .</s>
            <s xml:id="echoid-s5983" xml:space="preserve">n. </s>
            <s xml:id="echoid-s5984" xml:space="preserve">quadrata portionis, RFV, regula, FM, ad omnia
              <lb/>
              <note position="left" xlink:label="note-0262-04" xlink:href="note-0262-04a" xml:space="preserve">ex antec.</note>
            quadrata, Δ V, regula eadem, ſunt vt, ω M, ad ſexquialteram, F
              <lb/>
            M, .</s>
            <s xml:id="echoid-s5985" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5986" xml:space="preserve">vt, {2/3}, M ω, ad, FM; </s>
            <s xml:id="echoid-s5987" xml:space="preserve">omnia item quadrata, Δ V, </s>
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