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

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            T CFEY, regula, TY, ſunt vt rectangulum ſub, FN, & </s>
            <s xml:id="echoid-s6156" xml:space="preserve">tripla,
              <lb/>
            N H, .</s>
            <s xml:id="echoid-s6157" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6158" xml:space="preserve">vt, {3/4}, quadrati, FH, ad rectangulum ſub, FI, & </s>
            <s xml:id="echoid-s6159" xml:space="preserve">ſub, I
              <lb/>
            H N, .</s>
            <s xml:id="echoid-s6160" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6161" xml:space="preserve">vt totum quadratum, FH, ad rectangulum ſub, FI, & </s>
            <s xml:id="echoid-s6162" xml:space="preserve">
              <lb/>
            ſub ſexquitertia ipſarum, IHN, .</s>
            <s xml:id="echoid-s6163" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6164" xml:space="preserve">in circulo, vt quadratum, AP,
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              <figure xlink:label="fig-0268-01" xlink:href="fig-0268-01a" number="165">
                <image file="0268-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0268-01"/>
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            (quod æquatur quadrato, FH, ) ad
              <lb/>
            idem rectangulum ideſt ſumpta, FI,
              <lb/>
            communi altitudine, vt parallelepipe-
              <lb/>
            dum ſub, FI, & </s>
            <s xml:id="echoid-s6165" xml:space="preserve">quadrato, AP, .</s>
            <s xml:id="echoid-s6166" xml:space="preserve">i.
              <lb/>
            </s>
            <s xml:id="echoid-s6167" xml:space="preserve">vt parallelepipedum ſub, AP. </s>
            <s xml:id="echoid-s6168" xml:space="preserve">vel, L
              <lb/>
            G, & </s>
            <s xml:id="echoid-s6169" xml:space="preserve">parallelogrammo rectangulo
              <lb/>
            ſub, FI, ſiue, AL, &</s>
            <s xml:id="echoid-s6170" xml:space="preserve">, LG, ad pa-
              <lb/>
            rallelepipedum ſub, FI, & </s>
            <s xml:id="echoid-s6171" xml:space="preserve">ſub baſi
              <lb/>
            rectangulo ſub, FI, & </s>
            <s xml:id="echoid-s6172" xml:space="preserve">ſub ſexquiter-
              <lb/>
            tia, IHN, ergo ex æquali omnia
              <lb/>
            quadrata figuræ, LCFE G, dem-
              <lb/>
            ptis omnibus quadratis trilineorum,
              <lb/>
            CLT, YGE, regula, FI, ad omnia
              <lb/>
            quadrata portionis, TCFE Y, regu-
              <lb/>
            la, TY, erunt vt cylindricus ſub, M
              <lb/>
            I, & </s>
            <s xml:id="echoid-s6173" xml:space="preserve">ſub portione, TCFE Y, vna
              <lb/>
            cum, {1/6}, cubi, TY, ad parallelepipe-
              <lb/>
            dum ſub, FI, & </s>
            <s xml:id="echoid-s6174" xml:space="preserve">ſub rectangulo ſub,
              <lb/>
            F I, & </s>
            <s xml:id="echoid-s6175" xml:space="preserve">ſexquitertia, IHN; </s>
            <s xml:id="echoid-s6176" xml:space="preserve">& </s>
            <s xml:id="echoid-s6177" xml:space="preserve">hoc in
              <lb/>
            circulo.</s>
            <s xml:id="echoid-s6178" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6179" xml:space="preserve">In ellipſi autem eadem habebunt
              <lb/>
            rationem compoſitam exiam dicta ratione .</s>
            <s xml:id="echoid-s6180" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s6181" xml:space="preserve">ex ratione cylindrici
              <lb/>
            ſub, MI, & </s>
            <s xml:id="echoid-s6182" xml:space="preserve">ſub portione, TGFE Y, vna cum ea parte cubi, vel
              <lb/>
            parallelepipedi ſub, RV, & </s>
            <s xml:id="echoid-s6183" xml:space="preserve">rhombo, RZ, ad quam eiuſdem, {1/6}, ſit
              <lb/>
            vt quadratum, CE, ad quadratum, FH, ad parallelepipedum,
              <lb/>
            ſub, LG, & </s>
            <s xml:id="echoid-s6184" xml:space="preserve">parallelogrammo, AG, & </s>
            <s xml:id="echoid-s6185" xml:space="preserve">ex ratione quadrati, FH,
              <lb/>
            ad rectangulum ſub, FI, & </s>
            <s xml:id="echoid-s6186" xml:space="preserve">ſub ſexquitertia ipſarum, IHN; </s>
            <s xml:id="echoid-s6187" xml:space="preserve">quas
              <lb/>
            duas rationes in circulo in vna reſoluimus, quia in eo quadratum,
              <lb/>
            F H, æquatur quadrato, AP, quod cum in ellipſi non verificetur,
              <lb/>
            ideò has duas rationes componentes pro ipſa ellipſi retinuimus;
              <lb/>
            </s>
            <s xml:id="echoid-s6188" xml:space="preserve">quod oſtendere oportebat.</s>
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        <div xml:id="echoid-div598" type="section" level="1" n="348">
          <head xml:id="echoid-head365" xml:space="preserve">THEOREMA XXVII. PROPOS. XXVIII.</head>
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            <s xml:id="echoid-s6190" xml:space="preserve">IN eadem ſuperioris figura oſtendemus, tum in circulo,
              <lb/>
            tum in ellipſi, omnia quadrata figuræ, LCFEG, dem-
              <lb/>
            ptis omnibus quadratis trilineorum, CLT, YGE, </s>
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