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

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          <p style="it">
            <s xml:id="echoid-s8191" xml:space="preserve">
              <pb o="335" file="0355" n="355" rhead="LIBER IV."/>
            quadrata figuræ, CBNP, demptis omnibus quadratis quadrilinei, B
              <lb/>
            CPO; </s>
            <s xml:id="echoid-s8192" xml:space="preserve">& </s>
            <s xml:id="echoid-s8193" xml:space="preserve">vtraque eſſe, vt cubum, DF. </s>
            <s xml:id="echoid-s8194" xml:space="preserve">ad cubum, NO.</s>
            <s xml:id="echoid-s8195" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">_Ex 2. hu-_
            <lb/>
          _ius._</note>
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        <div xml:id="echoid-div809" type="section" level="1" n="479">
          <head xml:id="echoid-head499" xml:space="preserve">THEOREMA XXXIX. PROPOS. XLI</head>
          <p>
            <s xml:id="echoid-s8196" xml:space="preserve">INeiſdem figuris oſtendemus, regulis adhuc ipſis, DM,
              <lb/>
            DF, omnia quadrata figuræ, CBDF, ad omnia quadra-
              <lb/>
            ta figuræ, CBNP, eſſe vt parallelepipedum ſub, BE, & </s>
            <s xml:id="echoid-s8197" xml:space="preserve">
              <lb/>
            {1/2} {1/2}. </s>
            <s xml:id="echoid-s8198" xml:space="preserve">quadrati ipſius, DF, ad parallelepipedum ſub, BX, & </s>
            <s xml:id="echoid-s8199" xml:space="preserve">
              <lb/>
            his ſpatijs ſimul compoſitis .</s>
            <s xml:id="echoid-s8200" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8201" xml:space="preserve">quadrato, XP: </s>
            <s xml:id="echoid-s8202" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8203" xml:space="preserve">quadrati,
              <lb/>
            NX, & </s>
            <s xml:id="echoid-s8204" xml:space="preserve">rectangulo ſub ſexquitertia, NX, & </s>
            <s xml:id="echoid-s8205" xml:space="preserve">ſub, XP; </s>
            <s xml:id="echoid-s8206" xml:space="preserve">Om-
              <lb/>
            nia verò quadrata figuræ, HBDM, ad omnia quadrata fi-
              <lb/>
            guræ, HBNV, eſſe vt parallelepipedum ſub, BE, & </s>
            <s xml:id="echoid-s8207" xml:space="preserve">his
              <lb/>
            ſpatijs .</s>
            <s xml:id="echoid-s8208" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8209" xml:space="preserve">quadrato, ME, 1. </s>
            <s xml:id="echoid-s8210" xml:space="preserve">quadrati, ED, & </s>
            <s xml:id="echoid-s8211" xml:space="preserve">rectangulo
              <lb/>
            ſub ſexquitertia, DE, & </s>
            <s xml:id="echoid-s8212" xml:space="preserve">ſub, EM, ad parallelepipedum ſub,
              <lb/>
            BX, & </s>
            <s xml:id="echoid-s8213" xml:space="preserve">his ſpatijs .</s>
            <s xml:id="echoid-s8214" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8215" xml:space="preserve">quadrato, VX, 1. </s>
            <s xml:id="echoid-s8216" xml:space="preserve">quadrati, XN, & </s>
            <s xml:id="echoid-s8217" xml:space="preserve">re-
              <lb/>
            ctangulo, ſub ſexquitertia, NX, & </s>
            <s xml:id="echoid-s8218" xml:space="preserve">ſub, XV.</s>
            <s xml:id="echoid-s8219" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8220" xml:space="preserve">Ducatur per, N, ipſi, BE, parallela, NQ, in vtraq; </s>
            <s xml:id="echoid-s8221" xml:space="preserve">figura, igi-
              <lb/>
              <figure xlink:label="fig-0355-01" xlink:href="fig-0355-01a" number="240">
                <image file="0355-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0355-01"/>
              </figure>
            tur omnia quadrata
              <lb/>
            figuræ, CBDF, ad
              <lb/>
            omnia quadrata figu-
              <lb/>
            ræ, CBNP, habẽt ra-
              <lb/>
            tionem compoſitam
              <lb/>
            ex ea, quam habent
              <lb/>
            omnia quadrata figu-
              <lb/>
            ræ, CBDF, ad om-
              <lb/>
            nia quadrata, AF, .</s>
            <s xml:id="echoid-s8222" xml:space="preserve">i.
              <lb/>
            </s>
            <s xml:id="echoid-s8223" xml:space="preserve">ex ea, quam habent
              <lb/>
            {3/2} {7/4}. </s>
            <s xml:id="echoid-s8224" xml:space="preserve">quadrati, DF, ad
              <lb/>
            quadratum, DF, & </s>
            <s xml:id="echoid-s8225" xml:space="preserve">ex ratione omnium quadratorum, AF, ad om-
              <lb/>
              <note position="right" xlink:label="note-0355-02" xlink:href="note-0355-02a" xml:space="preserve">32. huius</note>
            nia quadrata, AP, .</s>
            <s xml:id="echoid-s8226" xml:space="preserve">i. </s>
            <s xml:id="echoid-s8227" xml:space="preserve">ex ratione, EB, ad, BX, & </s>
            <s xml:id="echoid-s8228" xml:space="preserve">ex ratione om-
              <lb/>
            nium quadratorum, AP, ad omnia quadrata, QP, .</s>
            <s xml:id="echoid-s8229" xml:space="preserve">i. </s>
            <s xml:id="echoid-s8230" xml:space="preserve">ex ratione
              <lb/>
            quadrati, GP, vel quadrati, DF, ad quadratum, PN, & </s>
            <s xml:id="echoid-s8231" xml:space="preserve">tandem
              <lb/>
            ex ratione omnium quadratorum, QP, ad omnia quadrata figurę, C
              <lb/>
              <note position="right" xlink:label="note-0355-03" xlink:href="note-0355-03a" xml:space="preserve">34. huius.</note>
            BNP, .</s>
            <s xml:id="echoid-s8232" xml:space="preserve">i. </s>
            <s xml:id="echoid-s8233" xml:space="preserve">ex ratione quadrati, NP, ad quadratum, PX, cum {1/2}. </s>
            <s xml:id="echoid-s8234" xml:space="preserve">quadra-
              <lb/>
            ti, XN, & </s>
            <s xml:id="echoid-s8235" xml:space="preserve">cum rectâgulo ſub ſexquitertia, NX, & </s>
            <s xml:id="echoid-s8236" xml:space="preserve">ſub, XP, harum au-
              <lb/>
            tem rat onum iſtæ .</s>
            <s xml:id="echoid-s8237" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8238" xml:space="preserve">quam habent {1/2} {7/4}. </s>
            <s xml:id="echoid-s8239" xml:space="preserve">quadrati, DF, ad quadratum,
              <lb/>
            DF, quadatum, DF, ad quadratum, NP, & </s>
            <s xml:id="echoid-s8240" xml:space="preserve">quadratum, NP, ad hęc
              <lb/>
            ſimul .</s>
            <s xml:id="echoid-s8241" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8242" xml:space="preserve">quadratum, PX, @. </s>
            <s xml:id="echoid-s8243" xml:space="preserve">quadrati, NX, & </s>
            <s xml:id="echoid-s8244" xml:space="preserve">rectangulum ſub ſex.</s>
            <s xml:id="echoid-s8245" xml:space="preserve"/>
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