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

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            <s xml:id="echoid-s5873" xml:space="preserve">
              <pb o="239" file="0259" n="259" rhead="LIBER III."/>
            ad portionem, RCT, ergo ex æquali omnia quadrata, KG, adom-
              <lb/>
              <note position="right" xlink:label="note-0259-01" xlink:href="note-0259-01a" xml:space="preserve">Cor. 19.
                <lb/>
              huius.</note>
            nia quadrata figuræ, LCRT, demptis omnibus quadratis trilinei,
              <lb/>
            CLT, erunt vt, KG, ad portionem, RCT. </s>
            <s xml:id="echoid-s5874" xml:space="preserve">Eodem modo oſten-
              <lb/>
            demus omnia quadrata, KG, ad omnia quadrata figuræ, VEGY,
              <lb/>
            demptis omnibus quadratis trilinei, EGY, eſſe vt, KG, ad portio-
              <lb/>
            nem, VEY, quæ conſerua.</s>
            <s xml:id="echoid-s5875" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5876" xml:space="preserve">Omnia inſuper quadrata, KG, ad omnia quadrata, RY, vt
              <lb/>
              <note position="right" xlink:label="note-0259-02" xlink:href="note-0259-02a" xml:space="preserve">Coroll.
                <lb/>
              26. l. 2.</note>
            probauimus, ſunt vt, KG, ad, RY, item omnia quadrata, RY,
              <lb/>
            ad rectangula ſub, RY, R Φ, ſunt vt, RY, ad R Φ, & </s>
            <s xml:id="echoid-s5877" xml:space="preserve">tandem re-
              <lb/>
              <note position="right" xlink:label="note-0259-03" xlink:href="note-0259-03a" xml:space="preserve">Caroll. 1.
                <lb/>
              26. l. 2.</note>
            ctangula ſub, R Φ, RY, adrectangula ſub portione, RFV, & </s>
            <s xml:id="echoid-s5878" xml:space="preserve">
              <lb/>
            ſub, RY, ſunt vt, R Φ, ad portionem, RFV, ergo ex æquali
              <lb/>
            omnia quadrata, KG, adrectangula ſub portione, RFV, & </s>
            <s xml:id="echoid-s5879" xml:space="preserve">ſub,
              <lb/>
            RY, erunt vt, KG, ad portionem, RFV, ergo, colligendo, om-
              <lb/>
            nia quadrata, KG, ad omnia quadrata figurarum, LCRT, VE
              <lb/>
            GY, demptis omnibus quadratis trilineorum, CLT, EGY, & </s>
            <s xml:id="echoid-s5880" xml:space="preserve">ad
              <lb/>
            omnia quadrata, RY, & </s>
            <s xml:id="echoid-s5881" xml:space="preserve">ad rectangula ſemel ſub portione, RFV,
              <lb/>
            & </s>
            <s xml:id="echoid-s5882" xml:space="preserve">ſub, RY, erunt vt, KG, ad portiones, RCT, VEY, RFV,
              <lb/>
            & </s>
            <s xml:id="echoid-s5883" xml:space="preserve">ad rectangulum, RY, .</s>
            <s xml:id="echoid-s5884" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5885" xml:space="preserve">vt, KG, ad portionem, TCFEY.</s>
            <s xml:id="echoid-s5886" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5887" xml:space="preserve">Reliquum eſt, vt comparemus omnia quadrata, KG, ad omnia
              <lb/>
            quadrata portionis, RFV, & </s>
            <s xml:id="echoid-s5888" xml:space="preserve">ad rectangula ſub eadem, & </s>
            <s xml:id="echoid-s5889" xml:space="preserve">ſub, RY,
              <lb/>
            quia autem, RV, æquatur ipſi, TY, portio, RFV, æquatur por-
              <lb/>
            tioni, THY, etiam in ellipſi, quia, RV, TY, ſunt parallelæ,
              <lb/>
            ideò omnia quadrata portionis, RFV, ſunt rectangula ſub portio-
              <lb/>
            ne, RFV, & </s>
            <s xml:id="echoid-s5890" xml:space="preserve">ſub portione, THY, quibus ſi iunxeris rectangula
              <lb/>
              <note position="right" xlink:label="note-0259-04" xlink:href="note-0259-04a" xml:space="preserve">A. 23. l. 2.</note>
            ſub eadem portione, RFV, & </s>
            <s xml:id="echoid-s5891" xml:space="preserve">ſub, RY, componentur rectangu-
              <lb/>
            la ſub eadem portione, RFV, & </s>
            <s xml:id="echoid-s5892" xml:space="preserve">ſub quadrilineo, RTHYV.
              <lb/>
            </s>
            <s xml:id="echoid-s5893" xml:space="preserve">Nuncvel, RV, eſt æqualis ipſi, VY, & </s>
            <s xml:id="echoid-s5894" xml:space="preserve">ſic, RY, erit quadratum,
              <lb/>
            ſiue rhombus, vel, RV, non eſt æqualis ipſi, VY, & </s>
            <s xml:id="echoid-s5895" xml:space="preserve">tunc in ipſa,
              <lb/>
            VY, producta, ſi opus ſit ſumatur, VZ, æqualis, ipſi, VR, & </s>
            <s xml:id="echoid-s5896" xml:space="preserve">du-
              <lb/>
            cta per, Z, Z Π, ipſi, RV, parallela, ſit conſtitutum, RZ, qua-
              <lb/>
            dratum, vel rhombus ipſius, RV: </s>
            <s xml:id="echoid-s5897" xml:space="preserve">Omnia ergo quadrata, KG, ad
              <lb/>
            omnia quadrata, RZ, habent rationem compoſitam ex ratione
              <lb/>
              <note position="right" xlink:label="note-0259-05" xlink:href="note-0259-05a" xml:space="preserve">Diffin. 12.
                <lb/>
              l. 1.</note>
            quadrati, KL, ad quadratum, R Π, vel ad quadratum, RV, & </s>
            <s xml:id="echoid-s5898" xml:space="preserve">
              <lb/>
            ex ratione ipſius, KB, ad, RV, quæ duæ rationes componunt ra-
              <lb/>
              <note position="right" xlink:label="note-0259-06" xlink:href="note-0259-06a" xml:space="preserve">11. l. 2,</note>
            tionem parallelepipedi rectanguli ſub altitudine, BK, baſi autem
              <lb/>
              <note position="right" xlink:label="note-0259-07" xlink:href="note-0259-07a" xml:space="preserve">D. Cor. 4.</note>
            quadrato, KL, ad cubum, RV. </s>
            <s xml:id="echoid-s5899" xml:space="preserve">Siautem, CE, FH, ſint tantum
              <lb/>
              <note position="right" xlink:label="note-0259-08" xlink:href="note-0259-08a" xml:space="preserve">Gen. 34.
                <lb/>
              l. 2.</note>
            diametri, ſic dicemus, nempè, Omnia quadrata, KG, ad omnia
              <lb/>
            quadrata, RZ, rhombi habent rationem compoſitam ex ratione,
              <lb/>
            KL, ad, R Π, bis ſumpta, & </s>
            <s xml:id="echoid-s5900" xml:space="preserve">ex ratione, KB, ad, RV, quæ tres
              <lb/>
              <note position="right" xlink:label="note-0259-09" xlink:href="note-0259-09a" xml:space="preserve">23. huius.</note>
            rationes componunt rationem parallelepiped ſub altitudine, KL,
              <lb/>
            baſi parallelogrammo, KG, ad parallelepipedum ſub altitudine,
              <lb/>
            RV, baſi autem rhombo, RZ: </s>
            <s xml:id="echoid-s5901" xml:space="preserve">Omnia verò quadrata, RZ, </s>
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