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

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        <div xml:id="echoid-div536" type="section" level="1" n="320">
          <pb o="216" file="0236" n="236" rhead="GEOMETRIÆ"/>
        </div>
        <div xml:id="echoid-div537" type="section" level="1" n="321">
          <head xml:id="echoid-head338" xml:space="preserve">E. SECTIO V.</head>
          <note position="left" xml:space="preserve">E.</note>
          <p style="it">
            <s xml:id="echoid-s5252" xml:space="preserve">_S_Imiles ellipſes ſunt in dupla ratione ſuorum axium, vel diametrc-
              <lb/>
            rum homologarum, vel vt corundem quadrata.</s>
            <s xml:id="echoid-s5253" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div538" type="section" level="1" n="322">
          <head xml:id="echoid-head339" xml:space="preserve">F. SECTIO VI.</head>
          <note position="left" xml:space="preserve">F.</note>
          <p style="it">
            <s xml:id="echoid-s5254" xml:space="preserve">_P_Ro circulis autem (vt ſupra dictum eſt) hoc tantum habetur, quod
              <lb/>
            ſint vt diametrorum quadrata, vel in dupla ratione diametrorum;
              <lb/>
            </s>
            <s xml:id="echoid-s5255" xml:space="preserve">neque illis alia variatio contingit, ſicuti ellipſibus competere ex ſupe-
              <lb/>
            rioribus compertum eſt.</s>
            <s xml:id="echoid-s5256" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div539" type="section" level="1" n="323">
          <head xml:id="echoid-head340" xml:space="preserve">THEOREMA XI. PROPOS. XII.</head>
          <p>
            <s xml:id="echoid-s5257" xml:space="preserve">QVęcunq; </s>
            <s xml:id="echoid-s5258" xml:space="preserve">de omnibus quadratis parallelogrammorum,
              <lb/>
            appoſitas ibi conditiones habentium, oſtenſa ſunt in
              <lb/>
            Theor. </s>
            <s xml:id="echoid-s5259" xml:space="preserve">9.</s>
            <s xml:id="echoid-s5260" xml:space="preserve">10.</s>
            <s xml:id="echoid-s5261" xml:space="preserve">11.</s>
            <s xml:id="echoid-s5262" xml:space="preserve">12.</s>
            <s xml:id="echoid-s5263" xml:space="preserve">13. </s>
            <s xml:id="echoid-s5264" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s5265" xml:space="preserve">2 eadem de omnibus quadratis
              <lb/>
            circulorum, vel ellipſium illis inſcriptorum (regula in
              <lb/>
            vtriſque altero axium, vel diametrorum coniugatarum) ve-
              <lb/>
            rificabuntur.</s>
            <s xml:id="echoid-s5266" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5267" xml:space="preserve">Patet hæc propoſitio, nam omnia quadrata circulorum, vel el-
              <lb/>
            lipſium (regula altero axium, vel diametrorum) ſunt ſubſexquial-
              <lb/>
              <note position="left" xlink:label="note-0236-03" xlink:href="note-0236-03a" xml:space="preserve">Coroll.1.
                <lb/>
              buius.</note>
            tera omnium quadratorum parallelogrammorum, quibus inſcri-
              <lb/>
            buntur, latera habentium dictis axibus, vel diametris parallela; </s>
            <s xml:id="echoid-s5268" xml:space="preserve">ha-
              <lb/>
            bentibus autem illis appoſitas ibi conditiones in ſuis lateribus, eędem
              <lb/>
            adſunt in axibus, vel diametris circulorum, vel ellipſium, quibus
              <lb/>
            circumſcribuntur, & </s>
            <s xml:id="echoid-s5269" xml:space="preserve">è contra; </s>
            <s xml:id="echoid-s5270" xml:space="preserve">& </s>
            <s xml:id="echoid-s5271" xml:space="preserve">ideò concluſiones, quæ collectæ
              <lb/>
            ſunt pro illis in dictis Theor. </s>
            <s xml:id="echoid-s5272" xml:space="preserve">etiam pro omnibus quadratis circulo-
              <lb/>
            rum, vel ellipſium illis inſcriptorum, vt demonſtratę recipi poſſunt,
              <lb/>
            cum fint eorum partes proportionales, ijſdem regulis pro omnibus
              <lb/>
            quadratis circulorum, vel ellipſium, & </s>
            <s xml:id="echoid-s5273" xml:space="preserve">pro omnibus quadra-
              <lb/>
            tis parallelogrammorum illis circumſeriptorum, aſſumptis,
              <lb/>
            quod, &</s>
            <s xml:id="echoid-s5274" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5275" xml:space="preserve"/>
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          <figure number="147">
            <image file="0236-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0236-01"/>
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