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

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          <pb o="197" file="0217" n="217" rhead="GEOMETRIÆ"/>
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        <div xml:id="echoid-div494" type="section" level="1" n="299">
          <head xml:id="echoid-head315" xml:space="preserve">CAVALERII
            <lb/>
          LIBER TERTIVS.</head>
          <head xml:id="echoid-head316" xml:space="preserve">In quo de circulo, & Ellipſi, ac ſolidis ab
            <lb/>
          eiſdem genitis, traditur doctrina.</head>
          <figure number="131">
            <image file="0217-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0217-01"/>
          </figure>
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        <div xml:id="echoid-div495" type="section" level="1" n="300">
          <head xml:id="echoid-head317" xml:space="preserve">THEOREMA I. PROPOS. I.</head>
          <p>
            <s xml:id="echoid-s4848" xml:space="preserve">OMnia quadrata portionis circuli, vel El-
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            lipſis, ad omnia quadrata parallelo-
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            grammi in eadem baſi, & </s>
            <s xml:id="echoid-s4849" xml:space="preserve">altitudine
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            cum portione conſtituti, regula baſi,
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            erunt, vt compoſita ex ſexta parte axis,
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            vel diametri eiuſdem, & </s>
            <s xml:id="echoid-s4850" xml:space="preserve">dimidia reli-
              <lb/>
            quæ portionis, ad axim, vel diame-
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            trum reliquæ portionis: </s>
            <s xml:id="echoid-s4851" xml:space="preserve">Eadem verò
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            ad omnia quadrata trianguli in ijſdem
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            exiſtentis erunt, vt compoſita ex dimidia totius, & </s>
            <s xml:id="echoid-s4852" xml:space="preserve">reliquæ
              <lb/>
            portionis axi, vel diametro, ad axim, vel diametrum reliquæ
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            portionis.</s>
            <s xml:id="echoid-s4853" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4854" xml:space="preserve">Sit circulus, vel ellipſis, EDRP, cuius axis, vel diameter, ER,
              <lb/>
            ad quem ordinatim applicetur, DP, abſcindens vtcumque portio-
              <lb/>
            nem, DEP, quæ ſumatur quoq; </s>
            <s xml:id="echoid-s4855" xml:space="preserve">pro regula, & </s>
            <s xml:id="echoid-s4856" xml:space="preserve">centrum ſit, A, ac
              <lb/>
            parallelogrammum, FP, in eadem baſi, DP, cum portione, & </s>
            <s xml:id="echoid-s4857" xml:space="preserve">ea-
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            dem altitudine; </s>
            <s xml:id="echoid-s4858" xml:space="preserve">ſint autem primò, DF, PH, latera parallelogram-
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            mi, FP, parallela ipſi, ER. </s>
            <s xml:id="echoid-s4859" xml:space="preserve">Dico ergo omnia quadrata portionis,
              <lb/>
            DEP, ad omnia quadrata parallelogrammi, FP, eſſe, vt compo-
              <lb/>
            ſita ex ſexta parte, EB, & </s>
            <s xml:id="echoid-s4860" xml:space="preserve">dimidia, BR, adipſam, BR. </s>
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