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

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          <pb o="227" file="0247" n="247" rhead="LIBER III."/>
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        <div xml:id="echoid-div558" type="section" level="1" n="331">
          <head xml:id="echoid-head348" xml:space="preserve">THEOREMA XVI. PROPOS. XVII.</head>
          <p>
            <s xml:id="echoid-s5541" xml:space="preserve">OMnia quadrata parallelogrammi circulo, vel ellipſi
              <lb/>
            circumſcripti (regula baſi) ad omnia quadrata figuræ
              <lb/>
            compoſitæ ex circulo, vel ellipſi, & </s>
            <s xml:id="echoid-s5542" xml:space="preserve">ex duobus trilineis ad-
              <lb/>
            iacentibus lateri, quod non eſt regula, nec ipſi parallelum,
              <lb/>
            veluti dicitur in Th. </s>
            <s xml:id="echoid-s5543" xml:space="preserve">14. </s>
            <s xml:id="echoid-s5544" xml:space="preserve">erunt, vt idem parallelogrammum
              <lb/>
            ad circulum, vel ellipſim, cui circumſcribitur, vna cum eo
              <lb/>
            ſpatio, quod relinquitur, dempto à quarta parte dicti paral-
              <lb/>
            lelogrammi circuli, vel ellipſis quadrante, ſimul cum exceſ-
              <lb/>
            ſu, quo idem quadrans ſuperat duas tertias dicti parallelo-
              <lb/>
            grammi ideſt erit, proximè, vt 21. </s>
            <s xml:id="echoid-s5545" xml:space="preserve">ad 17.</s>
            <s xml:id="echoid-s5546" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5547" xml:space="preserve">Exponatur denuò figura Theor.</s>
            <s xml:id="echoid-s5548" xml:space="preserve">14. </s>
            <s xml:id="echoid-s5549" xml:space="preserve">Dico omnia quadrata paral-
              <lb/>
            lelogrammi, HF, ad omnia quadrata figuræ compoſitæ ex circulo,
              <lb/>
            vel ellipſi, MBEG, & </s>
            <s xml:id="echoid-s5550" xml:space="preserve">trilineis, MGN, EGF, eſſe vt, HF, ad
              <lb/>
            circulum, vel ellipſim, MBEG, vna cum reſiduo, dempto à paral-
              <lb/>
            lelogrammo, MG, circuli, vel ellipſis, quadrante, MGA, ſimul
              <lb/>
            cum eo exceſſu, quo idem quadrans ſuperat duas tertias parallelo-
              <lb/>
            grammi, MG. </s>
            <s xml:id="echoid-s5551" xml:space="preserve">Etenim oſtenſum eſt omnia quadrata, HF, ad om-
              <lb/>
              <note position="right" xlink:label="note-0247-01" xlink:href="note-0247-01a" xml:space="preserve">15. huius.</note>
            nia quadrata circuli, vel ellipſis, MBEG, vna cum rectangulis bis
              <lb/>
            ſub eodem, & </s>
            <s xml:id="echoid-s5552" xml:space="preserve">ſub trilineis, MNG, GFE, eſſe vt, HF, ad circu-
              <lb/>
            lum, vel ellipſim, MBEG, quod lerua.</s>
            <s xml:id="echoid-s5553" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5554" xml:space="preserve">Vlterius, quia omnia quadrata, HG, ad omnia quadrata, MG,
              <lb/>
              <note position="right" xlink:label="note-0247-02" xlink:href="note-0247-02a" xml:space="preserve">9. Lib. 2.</note>
            ſunt vt quadratum, BG, ad quadratum, GA, .</s>
            <s xml:id="echoid-s5555" xml:space="preserve">@. </s>
            <s xml:id="echoid-s5556" xml:space="preserve">vt parallelogram-
              <lb/>
            mum, HF, ad parallelogrammum, MG; </s>
            <s xml:id="echoid-s5557" xml:space="preserve">inſuper omnia quadrata,
              <lb/>
              <note position="right" xlink:label="note-0247-03" xlink:href="note-0247-03a" xml:space="preserve">13. huius.</note>
            MG, ad omnia quadrata trilinei, MGN, ſunt vt, MG, ad reſi-
              <lb/>
              <figure xlink:label="fig-0247-01" xlink:href="fig-0247-01a" number="154">
                <image file="0247-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0247-01"/>
              </figure>
            duum dempto quadrante, MAG, ſimul
              <lb/>
            cum eo ſpatio, quo idem ſuperat duas
              <lb/>
            tertias rectanguli, MG, ab eodem re-
              <lb/>
            ctangulo, MG, ergo ex æquali omnia
              <lb/>
            quadrata, HG, ad omnia quadrata tri-
              <lb/>
            linei, MGN, erunt vt, HF, ad reſi-
              <lb/>
            duum, dempto quadrante, MAG, ſimul
              <lb/>
            cum eo ſpatio, quo idem ſuperat, {2/3}, re-
              <lb/>
            ctanguli, MG, ab eodem rectangulo, M
              <lb/>
              <note position="right" xlink:label="note-0247-04" xlink:href="note-0247-04a" xml:space="preserve">10.Lib.2.</note>
            G, &</s>
            <s xml:id="echoid-s5558" xml:space="preserve">, duplicatis proportionis terminis,
              <lb/>
            omnia quadrata, HF, ad omnia quadra-
              <lb/>
            ta trilineorum, MNG, GFE, erunt vt duplum, HF, ad </s>
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