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

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          <p>
            <s xml:id="echoid-s5930" xml:space="preserve">
              <pb o="241" file="0261" n="261" rhead="LIBER III."/>
            collectis) ad omnia quadrata figuræ, LCFEG, demptis omnibus
              <lb/>
            quadratis trilineorum, CLT, EGY, erunt vt parallelepipedum ſub
              <lb/>
            altitudine, KL, baſi parallelogrammo, KG, ad cylindricum ſub
              <lb/>
            altitudine, KL, baſi portione, TCFEY, vna cum, {1/6}, cubi, RV,
              <lb/>
              <note position="right" xlink:label="note-0261-01" xlink:href="note-0261-01a" xml:space="preserve">36. Lib. 2.</note>
            in circulo. </s>
            <s xml:id="echoid-s5931" xml:space="preserve">In ellipſi autem, vt idem parallepipedum ad eundem cy-
              <lb/>
            lindricum, vna cum ea parte cubi, RV, vel parallelepipedi ſub, R
              <lb/>
            V, & </s>
            <s xml:id="echoid-s5932" xml:space="preserve">rhombo, RZ, ad quam eiuſdem cubi, vel parallelepipedis ſex-
              <lb/>
            ta pars ſit, vt quadratum, CE, ad quadratum, FH: </s>
            <s xml:id="echoid-s5933" xml:space="preserve">Omnia autem
              <lb/>
            quadrata, AG, ad omnia quadrata, KG, ſunt vt parallelepipedum
              <lb/>
            ſub altitudine, AL, baſi parallelogrammo, AG, ad parallelepipe-
              <lb/>
            dum ſub altitudine, LK, baſi parallelogrammo, KG, ergo ex ęqua-
              <lb/>
            li pariter omnia quadrata, AG, ad omnia quadrata figurę, LCFE
              <lb/>
            G, demptis omnibus quadratis trilineorum, CLT, EGY, erunt in
              <lb/>
            circulo, vt parallelepipedum ſub altitudine, AL, vel, FI, baſi au-
              <lb/>
            tem parallelogrammo, AG, ad cylindricum ſub altitudine, LK, vel,
              <lb/>
            MI, baſi autem portione, TCFEY, vna cum, {1/6}, cubi, RV, vel,
              <lb/>
            TY. </s>
            <s xml:id="echoid-s5934" xml:space="preserve">In ellipſi verò erunt, vt parallelepipedum ſub altitudine, FI,
              <lb/>
            baſi autem parallelogrammo, AG, ad cylindricum ſub altitudine,
              <lb/>
            MI, baſi autem ipſa portione, TCFEY, vna cum ea parte cubi,
              <lb/>
            RV, vel, TY, ſiue parallelepipedi ſub altitudine, TY, & </s>
            <s xml:id="echoid-s5935" xml:space="preserve">baſi rhom-
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            bo, RZ, ad quam eiuſdem cubi, vel parallelepipedi ſexta pars ſit, vt
              <lb/>
            quadra@um, CE, ad quadratum, FH; </s>
            <s xml:id="echoid-s5936" xml:space="preserve">quod oſtendere oportebat.</s>
            <s xml:id="echoid-s5937" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div586" type="section" level="1" n="343">
          <head xml:id="echoid-head360" xml:space="preserve">THEOREMA XXII. PROPOS. XXIII.</head>
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            <s xml:id="echoid-s5938" xml:space="preserve">EXpoſita figura circuli Theorematis ſuperioris, & </s>
            <s xml:id="echoid-s5939" xml:space="preserve">in eo
              <lb/>
            ſumpta vtcunq;</s>
            <s xml:id="echoid-s5940" xml:space="preserve">portione minori, RFV, cæteris, prout
              <lb/>
            ſtant, ſuppoſitis. </s>
            <s xml:id="echoid-s5941" xml:space="preserve">Dico omnia quadrata, Δ V, ad omnia qua-
              <lb/>
            drata portionis, RFV, eſſe, vt ſexquialtera, FM, ad reli-
              <lb/>
            quum diametri, MH, maioris portionis, ab eodem dempta
              <lb/>
            recta linea, ad quam tripla, MN, ſit, vt parallelogrammum,
              <lb/>
            Δ V, ad portionem, RFV.</s>
            <s xml:id="echoid-s5942" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5943" xml:space="preserve">Rectangula enim ſub, Δ V, VT, ad omnia quadrata, RZ, ſunt vt
              <lb/>
              <note position="right" xlink:label="note-0261-02" xlink:href="note-0261-02a" xml:space="preserve">5. Lib. 2.</note>
            vnum ad vnum. </s>
            <s xml:id="echoid-s5944" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5945" xml:space="preserve">vt rectangulum, FMI, ad quadratum, VZ, vel
              <lb/>
            ad quadratum, RV, omnia item quadrata, RZ, ſunt ſexcupla re-
              <lb/>
              <note position="right" xlink:label="note-0261-03" xlink:href="note-0261-03a" xml:space="preserve">Corol. 21.
                <lb/>
              huius.</note>
            ctangulorum ſub portione, RFV, & </s>
            <s xml:id="echoid-s5946" xml:space="preserve">quadrilineo, RTHYV, ideſt
              <lb/>
            ſunt ad illa, vt quadratum, RV, ad ſui, {1/6}, ergo ex æquali rectan-
              <lb/>
            gula ſub, Δ V, VT, ad rectangula ſub portione, RFV, & </s>
            <s xml:id="echoid-s5947" xml:space="preserve">quadri-
              <lb/>
            lineo, RTHYV, erunt vt rectang. </s>
            <s xml:id="echoid-s5948" xml:space="preserve">FMI, ad, {1/6}, quadrati, </s>
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