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

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        <div xml:id="echoid-div1062" type="section" level="1" n="638">
          <pb o="451" file="0471" n="471" rhead="LIBER VI."/>
          <figure number="323">
            <image file="0471-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0471-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s11569" xml:space="preserve">Inſuper omnia quadrata, FP, ſunt tripla omnium quadratorum
              <lb/>
              <note position="right" xlink:label="note-0471-01" xlink:href="note-0471-01a" xml:space="preserve">24. l. 2.</note>
            trianguli, OHP, & </s>
            <s xml:id="echoid-s11570" xml:space="preserve">ideo ſunt ad illa, vt triangulus, ABD, ad ſe-
              <lb/>
            ctionem, AIB, cuius eſt triplus, quod etiam ſerua. </s>
            <s xml:id="echoid-s11571" xml:space="preserve">Vlterius om-
              <lb/>
              <note position="right" xlink:label="note-0471-02" xlink:href="note-0471-02a" xml:space="preserve">Elicitur
                <lb/>
              ex prima
                <lb/>
              l. 4.</note>
            nia quadrata trianguli, OHP, ad omnia quadrata trianguli, OMN,
              <lb/>
            ſunt vt cubus, PO, ad cubum, ON, ideſt vt cubus, DA, ad cubum,
              <lb/>
            AE, ideſt vt ſectio, AIB, ad ſectionem, AXI, (ſunt enim tertiæ par-
              <lb/>
              <note position="right" xlink:label="note-0471-03" xlink:href="note-0471-03a" xml:space="preserve">F. Cor. 22.
                <lb/>
              l. 2.</note>
            tes triangulorum, ABD, AIE, qui inter ſe ſunt, vt cubi, DA, AE,)
              <lb/>
            ergo ex &</s>
            <s xml:id="echoid-s11572" xml:space="preserve">quali omnia quadrata, GP, ad omnia quadrata trianguli,
              <lb/>
            OMN, erunt vt triangulus, ABC, ad ſectionem, AXI, ſed omnia
              <lb/>
            quadrata, GP, ad omnia quadrata trianguli, OHP, erant vt idem
              <lb/>
            triangulum, ABC, ad ſectionem, AIB, ergo omnia quadrata, G
              <lb/>
            P, ad reliquum, demptis omnibus quadratis trianguli, OMN, ab
              <lb/>
              <note position="right" xlink:label="note-0471-04" xlink:href="note-0471-04a" xml:space="preserve">28. l. 2.</note>
            omnibus quadratis trianguli, OHP, ſcilicet ad omnia quadrati tra-
              <lb/>
            pezij, MHPN, erunt vt triangulus, ABC, ad reliquum, dempta
              <lb/>
            ſectione, AXI, a ſectione, AIB, ſcilicet ad trilineum, AIB, ſed om-
              <lb/>
            nia quadrata, GP, ad omnia quadrata trapezij, MHPN, ſunt vt
              <lb/>
            quadratum, HP, ad rectangulum, ſub, HP, MN, vna cum {1/5}. </s>
            <s xml:id="echoid-s11573" xml:space="preserve">qua-
              <lb/>
            drati, GM, ideſt vt quadratum, PO, ad rectangulum ſub, PO, ON,
              <lb/>
            vna cum {1/3}. </s>
            <s xml:id="echoid-s11574" xml:space="preserve">quadrati, PN, ergo triangulus, ABC, ad trilineum, A
              <lb/>
            BI, eric vt quadratum, PO, ad rectangulum, PON, vna cum {1/3}. </s>
            <s xml:id="echoid-s11575" xml:space="preserve">qua-
              <lb/>
            drati, PN, ideſt vt quadratum, DA, ad rectangulum, DAE, vna
              <lb/>
            cum {1/3}. </s>
            <s xml:id="echoid-s11576" xml:space="preserve">quadrati, DE, quod erat oſtendendum.</s>
            <s xml:id="echoid-s11577" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1065" type="section" level="1" n="639">
          <head xml:id="echoid-head669" xml:space="preserve">THEOREMA XV. PROPOS. XV.</head>
          <p>
            <s xml:id="echoid-s11578" xml:space="preserve">SPatium ſub ſpirali ex quacunq; </s>
            <s xml:id="echoid-s11579" xml:space="preserve">reuolutione genita,
              <lb/>
            præterquam ex prima, & </s>
            <s xml:id="echoid-s11580" xml:space="preserve">recta eiuſdem numeri </s>
          </p>
        </div>
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