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

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        <div xml:id="echoid-div784" type="section" level="1" n="465">
          <pb o="326" file="0346" n="346" rhead="GEOMETRIÆ"/>
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        <div xml:id="echoid-div786" type="section" level="1" n="466">
          <head xml:id="echoid-head486" xml:space="preserve">THEOREMA XXX. PROPOS. XXXII.</head>
          <p>
            <s xml:id="echoid-s7836" xml:space="preserve">SI parallelogrammum, & </s>
            <s xml:id="echoid-s7837" xml:space="preserve">parabola fuerint in eadem ba-
              <lb/>
            ſi, & </s>
            <s xml:id="echoid-s7838" xml:space="preserve">circa eundem axim, vel diametrum conſtituta,
              <lb/>
            baſiſque ſumatur pro regula: </s>
            <s xml:id="echoid-s7839" xml:space="preserve">Omnia quadrata dicti paral-
              <lb/>
            lelogrammi ad omnia quadrata figuræ compoſitæ ex para-
              <lb/>
            bola, & </s>
            <s xml:id="echoid-s7840" xml:space="preserve">alterutro trilineorum, qui fiunt extra parabolam,
              <lb/>
            demptis omnibus quadratis eiuſdem trilinei, erunt vt di-
              <lb/>
            ctum parallelogrammum ad dictam parabolam; </s>
            <s xml:id="echoid-s7841" xml:space="preserve">ad eadem
              <lb/>
            verò cum omnibus quadratis illius trilinci erunt, vt dictum
              <lb/>
            parallelogrammum ad dictam parabolam ſimul cum {@/2} {1/4}. </s>
            <s xml:id="echoid-s7842" xml:space="preserve">di-
              <lb/>
            ctiparallelogrammi .</s>
            <s xml:id="echoid-s7843" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7844" xml:space="preserve">vt 24. </s>
            <s xml:id="echoid-s7845" xml:space="preserve">ad 17.</s>
            <s xml:id="echoid-s7846" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7847" xml:space="preserve">Sit ergo parallelogrammum, AF, in eadem baſi, DF, & </s>
            <s xml:id="echoid-s7848" xml:space="preserve">circa
              <lb/>
            eundem axim, vel diametrum, BE, cum parabola, DBF, regula
              <lb/>
            ſit, DF. </s>
            <s xml:id="echoid-s7849" xml:space="preserve">Dico omnia quadrata, AF, ad omnia quadrat
              <unsure/>
            a figuræ,
              <lb/>
            CBDF, demptis omnibus quadratis trilinei, BCF, eſſe, vt, AF,
              <lb/>
            ad parabolam, DBF, eadem verò ad omnia quadrata fig. </s>
            <s xml:id="echoid-s7850" xml:space="preserve">CBD
              <lb/>
              <figure xlink:label="fig-0346-01" xlink:href="fig-0346-01a" number="233">
                <image file="0346-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0346-01"/>
              </figure>
            F, eſſe vt, AF, ad parabo-
              <lb/>
            lam, DBF, cum {@/2} {1/4}. </s>
            <s xml:id="echoid-s7851" xml:space="preserve">paral-
              <lb/>
            lelogrammi, AF; </s>
            <s xml:id="echoid-s7852" xml:space="preserve">quoniam
              <lb/>
            enim, BE, eſt axis, vel dia-
              <lb/>
            meter tum parabolæ, DBF,
              <lb/>
            tum parallelogrammi, AF,
              <lb/>
            ideò ſi ducatur intra paralle-
              <lb/>
            logrammum, AF, vtcunq-
              <lb/>
            recta linea parallelaipſi, D
              <lb/>
            F, portiones eiuſdem inclu-
              <lb/>
            ſæ trilineis, ADB, CFB, erunt inter ſe æquales, & </s>
            <s xml:id="echoid-s7853" xml:space="preserve">ideò para-
              <lb/>
            bola, DBF, erit figura, qualem poſtulat Prop. </s>
            <s xml:id="echoid-s7854" xml:space="preserve">29. </s>
            <s xml:id="echoid-s7855" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s7856" xml:space="preserve">3. </s>
            <s xml:id="echoid-s7857" xml:space="preserve">quapro-
              <lb/>
            pter omnia quadrata, AF, ad omnia quadrata figuræ, CBDF,
              <lb/>
            demptis omnibus quadratis trilinei, BCF, erunt vt, AF, ad para-
              <lb/>
            bolam, DBF.</s>
            <s xml:id="echoid-s7858" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7859" xml:space="preserve">Quoniam verò omnia quadrata, AF, ad omnia quadrata, BF,
              <lb/>
            ſunt vt quadratum, DF, ad quadratum, FE, .</s>
            <s xml:id="echoid-s7860" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7861" xml:space="preserve">quadrupla .</s>
            <s xml:id="echoid-s7862" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7863" xml:space="preserve">vt
              <lb/>
            24. </s>
            <s xml:id="echoid-s7864" xml:space="preserve">ad 6. </s>
            <s xml:id="echoid-s7865" xml:space="preserve">omnia verò quadrata, BF, ſunt ſexcupla omnium qua-
              <lb/>
            dratorum trilinei, BCF, .</s>
            <s xml:id="echoid-s7866" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7867" xml:space="preserve">vt 6. </s>
            <s xml:id="echoid-s7868" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s7869" xml:space="preserve">igitur omnia quadrata, AF,
              <lb/>
              <note position="left" xlink:label="note-0346-01" xlink:href="note-0346-01a" xml:space="preserve">30. huius.</note>
            ad omnia quadrata trilinei, BCF, erunt vt 24. </s>
            <s xml:id="echoid-s7870" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s7871" xml:space="preserve">ideſt vt, AF,
              <lb/>
            ad ſui ipſius {@/2} {1/4}. </s>
            <s xml:id="echoid-s7872" xml:space="preserve">ergo omnia quadrata, AF, ad omnia quadrata </s>
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