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

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            <s xml:id="echoid-s6063" xml:space="preserve">
              <pb o="245" file="0265" n="265" rhead="LIBER III."/>
            culo, tum in ellipſi) eſt vt quadratum, CN, ad quadratum, NF, vel
              <lb/>
            vt quadratum, CE, ad quadratum, FH, ideò ſex rectangula, RMV,
              <lb/>
            ad rectangulum, FMH, erunt vt ſex quadrata, CE, ad vnum qua-
              <lb/>
            dra um, FH, .</s>
            <s xml:id="echoid-s6064" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6065" xml:space="preserve">erunt vt omnia quadrata, RZ, ad rectangula ſub
              <lb/>
            portione, RFV, & </s>
            <s xml:id="echoid-s6066" xml:space="preserve">quadrilineo, RTHY V, vt autem ſunt ſex re-
              <lb/>
            ctangula, RMV, ad rectangulum, FMH, ita quatuor rectangu-
              <lb/>
            la, RMV, ad, {2/3}, rectanguli, FMH, .</s>
            <s xml:id="echoid-s6067" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6068" xml:space="preserve">ad rectangulum ſub, FM,
              <lb/>
            &</s>
            <s xml:id="echoid-s6069" xml:space="preserve">, {2/3}, MH, ergo omnia quadrata, RZ, ad rectangula ſub portio-
              <lb/>
            ne, RFV, & </s>
            <s xml:id="echoid-s6070" xml:space="preserve">quadrilineo, RTHY V, erunt vt quatuor rectangu-
              <lb/>
            la, RMV, ad rectangulum ſub, FM, &</s>
            <s xml:id="echoid-s6071" xml:space="preserve">, {2/3}, MH, erant autem om-
              <lb/>
            nia quadrata, Δ V, ad omnia quadrata, RZ, vt quadratum, FM,
              <lb/>
            ad quatuor rectangula ſub, RMV, ergo ex æquali omnia quadra-
              <lb/>
            ta, Δ V, ad rectangula ſub portione, RFV, & </s>
            <s xml:id="echoid-s6072" xml:space="preserve">quadrilineo, RTH
              <lb/>
            YV, erunt vt quadratum, FM, ad rectangulum ſub, FM, & </s>
            <s xml:id="echoid-s6073" xml:space="preserve">ſub, {2/3}, MH,
              <lb/>
            eadem verò omnia quadrata, Δ V, ad rectangula ſub portione, R
              <lb/>
            F V, & </s>
            <s xml:id="echoid-s6074" xml:space="preserve">ſub, VT, oſtenſa ſunt eſſe, vt quadratum, FM, ad rectan-
              <lb/>
            gulum, ΓΜΙ, (ex quibus habemus rectangulum ſub, ΓΜΙ, mi-
              <lb/>
            nus eſſe rectangulo ſub, FM, & </s>
            <s xml:id="echoid-s6075" xml:space="preserve">ſub, {2/3}, MH, nam rectangula ſub
              <lb/>
            portione, RFV, & </s>
            <s xml:id="echoid-s6076" xml:space="preserve">ſub, VT, minora ſunt rectangulis ſub eadem
              <lb/>
            portione, RFV, & </s>
            <s xml:id="echoid-s6077" xml:space="preserve">quadrilineo, RTHY V,) ergo omnia quadra-
              <lb/>
            ta, Δ V, ad reſiduum omnium rectangulorum ſub portione, RFV,
              <lb/>
            & </s>
            <s xml:id="echoid-s6078" xml:space="preserve">quadrilineo, RTHY V, demptis rectangulis ſub portione, RF
              <lb/>
            V, & </s>
            <s xml:id="echoid-s6079" xml:space="preserve">ſub, VT, .</s>
            <s xml:id="echoid-s6080" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6081" xml:space="preserve">ad rectangula ſub vtriſq; </s>
            <s xml:id="echoid-s6082" xml:space="preserve">portionibus, RFV, THY,
              <lb/>
            .</s>
            <s xml:id="echoid-s6083" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6084" xml:space="preserve">ad omnia quadrata portionis, RFV, erunt vt quadratum, FM,
              <lb/>
            ad reſiduum ſpatium, dempto rectangulo, ΓΜΙ, a rectangulo ſub,
              <lb/>
            F M, & </s>
            <s xml:id="echoid-s6085" xml:space="preserve">ſub, {2/3}, MH, (hoc autem vocetur reſiduum rectangulum
              <lb/>
            huius Theor.) </s>
            <s xml:id="echoid-s6086" xml:space="preserve">quod oſtendere opus erat.</s>
            <s xml:id="echoid-s6087" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div593" type="section" level="1" n="346">
          <head xml:id="echoid-head363" xml:space="preserve">THEOREMA XXV. PROPOS. XXVI.</head>
          <p>
            <s xml:id="echoid-s6088" xml:space="preserve">EXpoſita adhuc figura Theor. </s>
            <s xml:id="echoid-s6089" xml:space="preserve">antecedentis, oſtendemus
              <lb/>
            omnia quadrata portionis, RFV, regula, FM, ad om-
              <lb/>
            nia quadrata eiuſdem portionis, regula baſi, eſſe vt paralle-
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            lepipedum ſub b ſireſiduo rectangulo antecedentis Theor-
              <lb/>
            altitudine tripla, MH, ad parallelepipedum ſub baſi rectan-
              <lb/>
            gulo ipſius, FM, ductæ in, RV, altitudine linea compoſita
              <lb/>
            ex, MH, HN.</s>
            <s xml:id="echoid-s6090" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6091" xml:space="preserve">Omnia .</s>
            <s xml:id="echoid-s6092" xml:space="preserve">n. </s>
            <s xml:id="echoid-s6093" xml:space="preserve">quadrata portionis, RFV, regula, FM, ad omnia
              <lb/>
            quacrata eluidem, regula, RV, habent rationem compoſitam ex
              <lb/>
              <note position="right" xlink:label="note-0265-01" xlink:href="note-0265-01a" xml:space="preserve">Defin. 12.
                <lb/>
              lib. 1.</note>
            ea, quam habent omnia quadrata, RFV, ad omnia quadrata, </s>
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