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

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        <div xml:id="echoid-div595" type="section" level="1" n="347">
          <head xml:id="echoid-head364" xml:space="preserve">THEOREMA XXVI. PROPOS. XXVII.</head>
          <p>
            <s xml:id="echoid-s6125" xml:space="preserve">ADhucetiam exponatur figura circuli, & </s>
            <s xml:id="echoid-s6126" xml:space="preserve">ellipſis Theor.
              <lb/>
            </s>
            <s xml:id="echoid-s6127" xml:space="preserve">21. </s>
            <s xml:id="echoid-s6128" xml:space="preserve">oſtendemus, .</s>
            <s xml:id="echoid-s6129" xml:space="preserve">n. </s>
            <s xml:id="echoid-s6130" xml:space="preserve">omnia quadrata figuræ, LCFE
              <lb/>
            G, demptis omnibus quadratis trilineorum, CLT, YGE,
              <lb/>
            regula, FI, ad omnia quadrata portionis, TCFEY, regu-
              <lb/>
            la baſi, TY, eſſe, in circulo, vt cylindricus ſub, IM, & </s>
            <s xml:id="echoid-s6131" xml:space="preserve">por-
              <lb/>
            tione, TCFE Y, vna cum, {1/@}, cubi, TY, ad parallelepipe-
              <lb/>
            dum ſub altitudine, FI, baſi verò rectangulo ſub, FI, & </s>
            <s xml:id="echoid-s6132" xml:space="preserve">
              <lb/>
            ſexquitertia duarum, IH, HN. </s>
            <s xml:id="echoid-s6133" xml:space="preserve">In ellipſi verò habere ra-
              <lb/>
            tionem compoſitam ex ea, quam habet cylindricus ſub, IM,
              <lb/>
            & </s>
            <s xml:id="echoid-s6134" xml:space="preserve">portione, TCFE Y, vna cum ea parte cubi, TY, vel pa-
              <lb/>
            rallelepipedi ſub, RV, & </s>
            <s xml:id="echoid-s6135" xml:space="preserve">rhombo, RZ, ad quam eiuſdem
              <lb/>
            cubi, vel parallelepipedi ſexta pars fit, vt quadratum, CE,
              <lb/>
            ad quadratum, FH, ad parallclepipedum ſub altitudine, L
              <lb/>
            G, baſi parallelogrammo, AG; </s>
            <s xml:id="echoid-s6136" xml:space="preserve">& </s>
            <s xml:id="echoid-s6137" xml:space="preserve">ex ea, quam habet qua-
              <lb/>
            dratum, FH, ad rectangulum ſub, FI, & </s>
            <s xml:id="echoid-s6138" xml:space="preserve">ſub ſexquitertia
              <lb/>
            duarum, IH, HN.</s>
            <s xml:id="echoid-s6139" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6140" xml:space="preserve">Omnia quadrata namq; </s>
            <s xml:id="echoid-s6141" xml:space="preserve">figuræ, LCFG, demptis omnibus qua-
              <lb/>
              <note position="right" xlink:label="note-0267-01" xlink:href="note-0267-01a" xml:space="preserve">22. huius.</note>
            dratis trilineorum, CLT, YGE, oſtenſa ſunt eſſe ad omnia qua-
              <lb/>
            drata, AG, regula, FI, vt cylindricum ſub, MI, & </s>
            <s xml:id="echoid-s6142" xml:space="preserve">ſub baſi por-
              <lb/>
            tione, TCFE Y, vna cum, {1/6}, cubi, TY, in circulo (in ellipſi ve-
              <lb/>
            rò vna cum ea parte cubi, TY, vel parallelepipedi ſub, RV, & </s>
            <s xml:id="echoid-s6143" xml:space="preserve">
              <lb/>
            rhombo, RZ, ad quam eiuſdem, {1/6}, ſit vt quadratum, CE, ad
              <lb/>
            quadratum, FH,) ad parallelepipedum ſub, LA, & </s>
            <s xml:id="echoid-s6144" xml:space="preserve">parallelo-
              <lb/>
            grammo, AG. </s>
            <s xml:id="echoid-s6145" xml:space="preserve">Vlterius omnia quadrata, AG, regula, FI, ad
              <lb/>
              <note position="right" xlink:label="note-0267-02" xlink:href="note-0267-02a" xml:space="preserve">29. l. 2.</note>
            omnia quadrata eiuſdem, AG, regula, LG, ſunt vt, AL, ad, L
              <lb/>
            G, .</s>
            <s xml:id="echoid-s6146" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6147" xml:space="preserve">vt parallelepipedum ſub, AL, & </s>
            <s xml:id="echoid-s6148" xml:space="preserve">parallelogrammo, ALG,
              <lb/>
            ad parallelepipedum ſub, LG, & </s>
            <s xml:id="echoid-s6149" xml:space="preserve">parallelogrammo eodem; </s>
            <s xml:id="echoid-s6150" xml:space="preserve">AL
              <lb/>
            G, ergo ex æquali omnia quadrata figuræ, LCFEG, demptis
              <lb/>
            omnibus quadratis trilineorum, CLT, YGE, regula, FI, ad om-
              <lb/>
            nia quadrata, AG, regula, TY, erunt vt cylindricus ſub, MI, & </s>
            <s xml:id="echoid-s6151" xml:space="preserve">
              <lb/>
            portione, TCFEY, vna cum, {1/6}, cubi, TY, in circulo, in ellipſi
              <lb/>
            verò vna cum dicta parte cubi, TY, vel parallelepipedi ſub, RV,
              <lb/>
            & </s>
            <s xml:id="echoid-s6152" xml:space="preserve">rhombo, RZ, ad parallelepipedum ſub, LG, & </s>
            <s xml:id="echoid-s6153" xml:space="preserve">parallelogram-
              <lb/>
            mo, ALG.</s>
            <s xml:id="echoid-s6154" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6155" xml:space="preserve">Tandem omnia quadrata, AG, ad omnia quadrata portionis,
              <lb/>
              <note position="right" xlink:label="note-0267-03" xlink:href="note-0267-03a" xml:space="preserve">2. huius.</note>
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