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

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          <p>
            <s xml:id="echoid-s14259" xml:space="preserve">
              <pb o="542" file="0562" n="562" rhead="GEOMETRI Æ"/>
            libus figuris, in antecedentibus prop. </s>
            <s xml:id="echoid-s14260" xml:space="preserve">conſideratis. </s>
            <s xml:id="echoid-s14261" xml:space="preserve">Appendix au-
              <lb/>
            tem Cor 6 reſtauratione minimè indigere manifeſtum eſt. </s>
            <s xml:id="echoid-s14262" xml:space="preserve">Et hæc
              <lb/>
            circa prop.</s>
            <s xml:id="echoid-s14263" xml:space="preserve">lib.</s>
            <s xml:id="echoid-s14264" xml:space="preserve">4. </s>
            <s xml:id="echoid-s14265" xml:space="preserve">adnotaſſe ſufficiat, reliquum eſt, vt ad lib.</s>
            <s xml:id="echoid-s14266" xml:space="preserve">5. </s>
            <s xml:id="echoid-s14267" xml:space="preserve">exami-
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            nandum nos conferamus.</s>
            <s xml:id="echoid-s14268" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1252" type="section" level="1" n="757">
          <head xml:id="echoid-head790" xml:space="preserve">THEOREMA XXVII. PROPOS. XXVII.</head>
          <p>
            <s xml:id="echoid-s14269" xml:space="preserve">IN Schemate prop. </s>
            <s xml:id="echoid-s14270" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14271" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14272" xml:space="preserve">5. </s>
            <s xml:id="echoid-s14273" xml:space="preserve">regula eadem retenta, oſten-
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            demus quadratum ſolidum parallelogrammi, AF, ad
              <lb/>
            quadratum ſolidum hyperbolæ, DBF, eſſe vt, OE, ad com-
              <lb/>
            poſitam ex, NB, &</s>
            <s xml:id="echoid-s14274" xml:space="preserve">. {1/3}. </s>
            <s xml:id="echoid-s14275" xml:space="preserve">BE.</s>
            <s xml:id="echoid-s14276" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14277" xml:space="preserve">Aſſumatur .</s>
            <s xml:id="echoid-s14278" xml:space="preserve">n. </s>
            <s xml:id="echoid-s14279" xml:space="preserve">ex eo paral-
              <lb/>
              <figure xlink:label="fig-0562-01" xlink:href="fig-0562-01a" number="369">
                <image file="0562-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0562-01"/>
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            lelogrammum, CE, cum ſe-
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            mihyperbola, BEF, & </s>
            <s xml:id="echoid-s14280" xml:space="preserve">recta,
              <lb/>
            OE, necnon, MG, quæcum-
              <lb/>
            q; </s>
            <s xml:id="echoid-s14281" xml:space="preserve">ex ordinatim applicatis ad
              <lb/>
            diametrum, BE, extendantur
              <lb/>
            autem, CB, FE, & </s>
            <s xml:id="echoid-s14282" xml:space="preserve">fiant BD,
              <lb/>
            EQ, ſingulæ æquales ipſi, E
              <lb/>
            O, necnon, RE, AB, ſingulæ
              <lb/>
            æquales ipſi, EB, & </s>
            <s xml:id="echoid-s14283" xml:space="preserve">iungan-
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            tur, DQ, AR, AE, quas, GM,
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            indefinitè quoq; </s>
            <s xml:id="echoid-s14284" xml:space="preserve">producta ſecet in punctis, P, S, T. </s>
            <s xml:id="echoid-s14285" xml:space="preserve">Erunt ergo, D
              <lb/>
            R, DE, AE, parallelogramma. </s>
            <s xml:id="echoid-s14286" xml:space="preserve">Quoniam verò quad. </s>
            <s xml:id="echoid-s14287" xml:space="preserve">EF, ad quad.
              <lb/>
            </s>
            <s xml:id="echoid-s14288" xml:space="preserve">
              <note position="left" xlink:label="note-0562-01" xlink:href="note-0562-01a" xml:space="preserve">39, & ſch.
                <lb/>
              40. l. 1.</note>
            MH, eſt vt rectang. </s>
            <s xml:id="echoid-s14289" xml:space="preserve">OEB, ad, OMB, hoc eſt vt rectangulum, QER,
              <lb/>
            ad rectangulum, PTS, permutando quadratum, FE, ad rectangu-
              <lb/>
            lum, QER, erit vt quadratum, HM, ad rectangulum, PTS, quod
              <lb/>
            & </s>
            <s xml:id="echoid-s14290" xml:space="preserve">in cæteris oſten demus, ergo quadratum ſolidum, BEF, & </s>
            <s xml:id="echoid-s14291" xml:space="preserve">re-
              <lb/>
            ctangulum ſolidum ſub trapezio, DQEA, & </s>
            <s xml:id="echoid-s14292" xml:space="preserve">triangulo, AER, erunt
              <lb/>
            proportionaliter analoga, ac in proportione quadrati, FE, & </s>
            <s xml:id="echoid-s14293" xml:space="preserve">re-
              <lb/>
            ctanguli, QER, Conſimili modo probabimus quadratum ſolidum,
              <lb/>
            CE, eſſe æqualiter analogum rectangulo ſolido ſub, OB, BR, & </s>
            <s xml:id="echoid-s14294" xml:space="preserve">ad
              <lb/>
            ipſum pariter eſſe in proportione quadrati, EF, ad rectangulum, Q
              <lb/>
            ER, ergo dicta ſolida proportionalia erunt, & </s>
            <s xml:id="echoid-s14295" xml:space="preserve">permutãdo quadratũ
              <lb/>
            ſolidumCE, ad quad, ſolidũ, BEF, erit vt rectangulum ſolidum ſub,
              <lb/>
            QB, BR, ad rectangulum ſolidum ſub, DQEA, ARE, hoc eſt vt, QE,
              <lb/>
              <note position="left" xlink:label="note-0562-02" xlink:href="note-0562-02a" xml:space="preserve">17. huius.</note>
            ad cõpoſitam ex {1/2}. </s>
            <s xml:id="echoid-s14296" xml:space="preserve">QR, & </s>
            <s xml:id="echoid-s14297" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s14298" xml:space="preserve">RE, hoc eſt vt, OE; </s>
            <s xml:id="echoid-s14299" xml:space="preserve">ad compoſitãex, N
              <lb/>
            B, (quæ eſt dimidia, BO,) & </s>
            <s xml:id="echoid-s14300" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s14301" xml:space="preserve">BE, igitur, viſo ſchemate dictę prop.
              <lb/>
            </s>
            <s xml:id="echoid-s14302" xml:space="preserve">1 quadratum ſolidum, AF, ad quadratum ſolidum, DBF, erit vt, O
              <lb/>
            E, ad compoſitam ex, NB, & </s>
            <s xml:id="echoid-s14303" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s14304" xml:space="preserve">BE, quod demonſtrare oportebat.</s>
            <s xml:id="echoid-s14305" xml:space="preserve"/>
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