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

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            <s xml:id="echoid-s7913" xml:space="preserve">
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            bus quadratis, BF, ad omnia quadrata, AF, vt 11. </s>
            <s xml:id="echoid-s7914" xml:space="preserve">ad 24. </s>
            <s xml:id="echoid-s7915" xml:space="preserve">ergo,
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            exæquali, omnia quadrata figuræ, CBDF, demptis omnibus qua-
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            dratis BF, ad omnia quadrata, BF, demptis omnibus quadratis tri-
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            linei, BCF, erunt vt 11. </s>
            <s xml:id="echoid-s7916" xml:space="preserve">ad 5. </s>
            <s xml:id="echoid-s7917" xml:space="preserve">quod erat oſtendendum.</s>
            <s xml:id="echoid-s7918" xml:space="preserve"/>
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        <div xml:id="echoid-div793" type="section" level="1" n="469">
          <head xml:id="echoid-head489" xml:space="preserve">THEOREMA XXXII. PROPOS. XXXIV.</head>
          <p>
            <s xml:id="echoid-s7919" xml:space="preserve">ASſumpta eadem anteced. </s>
            <s xml:id="echoid-s7920" xml:space="preserve">Theor. </s>
            <s xml:id="echoid-s7921" xml:space="preserve">figura, ſiproducatur
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            baſis, DF, (quæ retineatur pro regula) vtcunq; </s>
            <s xml:id="echoid-s7922" xml:space="preserve">in,
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            M, & </s>
            <s xml:id="echoid-s7923" xml:space="preserve">per M, ipſi, BE, parallela ducatur, MH, cui occur-
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            rat, AC, producta, in ipſo, H. </s>
            <s xml:id="echoid-s7924" xml:space="preserve">Omnia quadrata, AM,
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            demptis omnibus quadratis, CM, ad omnia quadrata figu-
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            ræ, HBDM, demptis omnibus quadratis quadrilinei, H
              <lb/>
            BFM, erunt vt, AF, ad parabolam, DBF, ideſt erunt
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            eorum ſexquialtera: </s>
            <s xml:id="echoid-s7925" xml:space="preserve">Quod facilè patebit, quia parabola, D
              <lb/>
            BF, inſcripta parallegrammo, AF, eſt figura, qualem po-
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            ſtulat Propoſit. </s>
            <s xml:id="echoid-s7926" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7927" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s7928" xml:space="preserve">3. </s>
            <s xml:id="echoid-s7929" xml:space="preserve">Vlterius autem dico omnia qua-
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            drat’a, AM, ad omnia quadrata figuræ, BDMH, eſſe vt
              <lb/>
            quadratum, DM, ad quadratum, ME, dimidium qua-
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            drati, ED, cum rectangulo ſub ſexquitértia, DE, & </s>
            <s xml:id="echoid-s7930" xml:space="preserve">
              <lb/>
            ſub, EM.</s>
            <s xml:id="echoid-s7931" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7932" xml:space="preserve">In conſtructa figura igitur omnia quadrata figuræ, HBDM, per
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            rectam, BE, diuiduntur in omnia quadrata ſemiparabolæ, BDC,
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            in omnia quadrata, BM, & </s>
            <s xml:id="echoid-s7933" xml:space="preserve">in rectangula bis ſub ſemiparabola, B
              <lb/>
              <note position="left" xlink:label="note-0348-01" xlink:href="note-0348-01a" xml:space="preserve">D. 23. l. 2.</note>
            DE, & </s>
            <s xml:id="echoid-s7934" xml:space="preserve">ſub EH, nunc ad horum ſingula comparemus omnia qua-
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              <figure xlink:label="fig-0348-01" xlink:href="fig-0348-01a" number="235">
                <image file="0348-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0348-01"/>
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            drata, AM: </s>
            <s xml:id="echoid-s7935" xml:space="preserve">Om-
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            nia igitur quadr@@-
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            ta, AM, ad om-
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            nia quadrata, BM,
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            ſunt vt quadra-
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            tum, DM, ad
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            quadratum, ME,
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            quod ſerua. </s>
            <s xml:id="echoid-s7936" xml:space="preserve">Item
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            omnia quadrata,
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            AM, ad omnia quadrata, AE, ſunt vt quadratum, MD, ad qua-
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            dratum, DE, omnia verò quadrata, AE, ſunt dupla omnium qua-
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            dratorum ſemiparabolæ, BDE, ergo omnia quadrata, AM, ad
              <lb/>
            omnia quadrata ſemiparabolæ, BDE, ſunt vt quadratum, MD,
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            ad dimidium quadrati, DE, quod etiam ſerua. </s>
            <s xml:id="echoid-s7937" xml:space="preserve">Tandem </s>
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