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

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          <p>
            <s xml:id="echoid-s10440" xml:space="preserve">
              <pb o="402" file="0422" n="422" rhead="GEOMETRIÆ"/>
            VS; </s>
            <s xml:id="echoid-s10441" xml:space="preserve">componunt ergo rationem trium quadratorum, OV, cum
              <lb/>
            rectangulo, OVZ, bis, & </s>
            <s xml:id="echoid-s10442" xml:space="preserve">quadrato, VZ, .</s>
            <s xml:id="echoid-s10443" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10444" xml:space="preserve">duorum quadratorum,
              <lb/>
            OV, cum quadrato, OZ, ad tria quadrata, OV, cum rectangulo,
              <lb/>
            OVS, bis & </s>
            <s xml:id="echoid-s10445" xml:space="preserve">quadrato, VS, .</s>
            <s xml:id="echoid-s10446" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10447" xml:space="preserve">ad duo quadrata, OV, cum quadra-
              <lb/>
            to, OS, hæc autem ratio ſimul cum ea, quæ remanſit .</s>
            <s xml:id="echoid-s10448" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10449" xml:space="preserve">cum ra-
              <lb/>
            tione, EC, ad, MN, componit rationem parallelepipedi ſub, EC,
              <lb/>
            & </s>
            <s xml:id="echoid-s10450" xml:space="preserve">baſi quadrato, ZO, cum duplo quadrati, OV, ad parallelepipe-
              <lb/>
            dum ſub, MN, & </s>
            <s xml:id="echoid-s10451" xml:space="preserve">baſi quadrato, SO, cum duplo quadrati, OV;
              <lb/>
            </s>
            <s xml:id="echoid-s10452" xml:space="preserve">vel parallelepipedi ſub, XL, baſi quadrato, RZ, cum duplo qua-
              <lb/>
            drati, AV, ad parallelepipedum ſub, HG, baſi quadrato, BS, cum
              <lb/>
            duplo quadrati, AV, quod nobis erat oſtendendum.</s>
            <s xml:id="echoid-s10453" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div949" type="section" level="1" n="566">
          <head xml:id="echoid-head591" xml:space="preserve">THEOREMA XXIV. PROPOS. XXV.</head>
          <p>
            <s xml:id="echoid-s10454" xml:space="preserve">IN eadem figura Prop. </s>
            <s xml:id="echoid-s10455" xml:space="preserve">23. </s>
            <s xml:id="echoid-s10456" xml:space="preserve">oſtendemus omnia quadrata
              <lb/>
            figuræ, FADCVE, (regula eadem, AV,) demptis omni-
              <lb/>
            bus quadratis triangulorum kOI, POQ, ad omnia quadra-
              <lb/>
            ta figuræ, TAYNVM, demptis omnibus quadratis trian-
              <lb/>
            gulorum, &</s>
            <s xml:id="echoid-s10457" xml:space="preserve">O, ΩΠ, eſſe vt, EC, ad, MN, vel, XL, ad, H
              <lb/>
            G, qui ſuntſecundiaxes, vel diametri.</s>
            <s xml:id="echoid-s10458" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10459" xml:space="preserve">Nam omnia quadrata figuræ, FADCVE, demptis omnibus
              <lb/>
              <figure xlink:label="fig-0422-01" xlink:href="fig-0422-01a" number="286">
                <image file="0422-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0422-01"/>
              </figure>
            quadratis triangulorum, kOI, POQ, ad
              <lb/>
            omnia quadrata figuræ, TAYNVM, dẽ
              <lb/>
            ptis omnibus quadratis triangulorum, & </s>
            <s xml:id="echoid-s10460" xml:space="preserve">
              <lb/>
            O℟, ΩΟΠ, habent rationem compoſitã
              <lb/>
            ex ratione omnium quadratorum figuræ,
              <lb/>
            FADCVE, demptis omnibus quadratis
              <lb/>
            triangulorum, KOI, POQ, ad omnia qua-
              <lb/>
            drata, FC, .</s>
            <s xml:id="echoid-s10461" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s10462" xml:space="preserve">ex ratione quadrati, AV, ad
              <lb/>
              <note position="left" xlink:label="note-0422-01" xlink:href="note-0422-01a" xml:space="preserve">Coroll. 1.
                <lb/>
              22. huius.</note>
            quadratum, DC, item ex ratione omniũ
              <lb/>
            quadratorum, FC, ad omnia quadrata, T
              <lb/>
            N, quæ eſt compoſita ex ratione quadra-
              <lb/>
            ti, DC, ad quadratum, YN, & </s>
            <s xml:id="echoid-s10463" xml:space="preserve">ex ratione,
              <lb/>
            CE, ad, NM, & </s>
            <s xml:id="echoid-s10464" xml:space="preserve">tandem componitur ex
              <lb/>
            ratione omnium quadratorum, TN, ad
              <lb/>
            omnia quadrata figurę, TAYNVM, dẽ-
              <lb/>
            ptis omnibus quadratis triangulorum, & </s>
            <s xml:id="echoid-s10465" xml:space="preserve">
              <lb/>
            O℟, ΩΟΠ, .</s>
            <s xml:id="echoid-s10466" xml:space="preserve">i. </s>
            <s xml:id="echoid-s10467" xml:space="preserve">ex ea, quam habet quadratum, YN, ad quadratũ
              <lb/>
              <note position="left" xlink:label="note-0422-02" xlink:href="note-0422-02a" xml:space="preserve">Coroll. 1.
                <lb/>
              22. huius.</note>
            AV, ex his autem rationibus illa, quam habet quadratum, AV, </s>
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