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

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            <s xml:id="echoid-s5383" xml:space="preserve">
              <pb o="221" file="0241" n="241" rhead="LIBER III."/>
            micirculo, vel ſemiellipſi, FQB, diuiduntur per curuam, FQB, in
              <lb/>
              <note position="right" xlink:label="note-0241-01" xlink:href="note-0241-01a" xml:space="preserve">Per C.23.
                <lb/>
              lib. 2.</note>
            rectangula fub quadrilineo, FQBDZ, & </s>
            <s xml:id="echoid-s5384" xml:space="preserve">ſemicirculo, vel ſemiel-
              <lb/>
            lipſi, FQB, & </s>
            <s xml:id="echoid-s5385" xml:space="preserve">in omnia quadrata ſemicirculi, vel ſemiellipſis, FQ
              <lb/>
            B, videndum ergo nunceſt, quamrationem habeant omnia quadra-
              <lb/>
            ta, FD, ad omnia quadrata ſemicirculi, vel ſemiellipſis, FQB,
              <lb/>
              <note position="right" xlink:label="note-0241-02" xlink:href="note-0241-02a" xml:space="preserve">9. Lib. 2.</note>
            quod fic patet; </s>
            <s xml:id="echoid-s5386" xml:space="preserve">omnia quadrata, FD, ad omnia quadrata, FC,
              <lb/>
              <note position="right" xlink:label="note-0241-03" xlink:href="note-0241-03a" xml:space="preserve">Elici etiã
                <lb/>
              poteſt ex
                <lb/>
              12. lib. 2.</note>
            ſunt vt quadratum, DB, ad quadratum, BC, .</s>
            <s xml:id="echoid-s5387" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5388" xml:space="preserve">ad rectangulum ſub,
              <lb/>
            DB, BI, nam tres, DB, BC, BI, ſunt continuè proportionales,
              <lb/>
            omnia item quadrata, FC, omnium quadratorum ſemicirculi, vel
              <lb/>
              <note position="right" xlink:label="note-0241-04" xlink:href="note-0241-04a" xml:space="preserve">Coroll. 1.
                <lb/>
              huius.
                <lb/>
              5. Lib. 2.</note>
            ſemiellipſis, FQB, ſunt ſexquialtera .</s>
            <s xml:id="echoid-s5389" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5390" xml:space="preserve">ſunt vt rectangulum, DBI,
              <lb/>
            ad rectangulum, DBR, quia, BR, eſt, {2/3}, BI, ergo ex æquali om
              <lb/>
            nia quadrata, FD, ad omnia quadrata ſemicirculi, vel ſemiellipfis,
              <lb/>
            FQB, ſunt vt quadratum, DB, ad rectangulum ſub, DB, BR,
              <lb/>
            omnia autem quadrata, FD, ad rectangula ſub, FD, & </s>
            <s xml:id="echoid-s5391" xml:space="preserve">ſemicircu-
              <lb/>
            lo, vel ſemiellipſi, FQB, erant vt idem quadratum, DB, ad rectan-
              <lb/>
            gulum ſub, DB, BE, ergo omnia quadrata, FD, ad rectangula ſub
              <lb/>
            ſemicirculo, vel ſemiell pſi, FQB, & </s>
            <s xml:id="echoid-s5392" xml:space="preserve">ſub quadrilineo, FQBDZ,
              <lb/>
            erunt vt idem quadratum, DB, ad rectangulum ſub, DB, &</s>
            <s xml:id="echoid-s5393" xml:space="preserve">, RE,
              <lb/>
            ad eadem verò bis ſumpta, vt idem quadratum, DB, ad rectangu-
              <lb/>
            lum ſub, DB, &</s>
            <s xml:id="echoid-s5394" xml:space="preserve">, RV, quia verò omnia quadrata, FD, ad omnia
              <lb/>
            quadrata ſemicirculi, vel ſemiellipſis, FQB, ſunt vt quadratum, D
              <lb/>
            B, ad rectangulum ſub, DB, BR, ergo colligendo omnia quadra-
              <lb/>
            ta, FD, ad omnia quadrata ſemicirculi, vel ſemiellipſis, FQB, vna
              <lb/>
            cum rectangulis ſub ſemicirculo, vel ſemiellipſi, FQB, & </s>
            <s xml:id="echoid-s5395" xml:space="preserve">quadri-
              <lb/>
            lineo, FQBDZ, bis ſumptis, erunt vt quadratum, DB, ad rectan-
              <lb/>
            gula ſub, DB, BR, DB, RV, .</s>
            <s xml:id="echoid-s5396" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5397" xml:space="preserve">ad rectangulum ſub, DB, BV;
              <lb/>
            </s>
            <s xml:id="echoid-s5398" xml:space="preserve">quia verò ſiab omnibus quadratis, FD, ſubtraxeris omnia quadrata
              <lb/>
            ſemicirculi, vel ſemiellipſis, FQB, vna cum rectangulis bis ſub eo-
              <lb/>
            dem ſemicirculo, vel ſemiellipſi, FQB, & </s>
            <s xml:id="echoid-s5399" xml:space="preserve">ſub quadrilineo, FQB
              <lb/>
              <note position="right" xlink:label="note-0241-05" xlink:href="note-0241-05a" xml:space="preserve">PerD.23.
                <lb/>
              lib, 2.</note>
            DZ, remanent omnia quadrata quadrilinei, FQBDZ, ideò, per
              <lb/>
            conuerſionem rationis, omnia quadrata parallelogrammi, FD, ad
              <lb/>
              <note position="right" xlink:label="note-0241-06" xlink:href="note-0241-06a" xml:space="preserve">5. Lib. 2.</note>
            omnia quadrata quadrilinei, FQBDZ, erunt vt quadratum, BD,
              <lb/>
            ad rectangulum ſub, BD, DV, .</s>
            <s xml:id="echoid-s5400" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5401" xml:space="preserve">vt, BD, ad, DV, quod tantum
              <lb/>
            proximè verificatur, non .</s>
            <s xml:id="echoid-s5402" xml:space="preserve">n. </s>
            <s xml:id="echoid-s5403" xml:space="preserve">parallelogrammum, FC, ad ſemicir-
              <lb/>
            culum, vel ſemiellipſim, FQB, eſt pręcisè, vt 14. </s>
            <s xml:id="echoid-s5404" xml:space="preserve">ad 11. </s>
            <s xml:id="echoid-s5405" xml:space="preserve">ſed tantum
              <lb/>
            proximè, ideò, &</s>
            <s xml:id="echoid-s5406" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5407" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5408" xml:space="preserve">Defiderari nunctantum videtur in hac demonſtratione, quod pro.
              <lb/>
            </s>
            <s xml:id="echoid-s5409" xml:space="preserve">betur punctum, R, non identificari puncto, E, ſed cadere inter, B
              <lb/>
            E, quod ſic facilè patet, cum .</s>
            <s xml:id="echoid-s5410" xml:space="preserve">n. </s>
            <s xml:id="echoid-s5411" xml:space="preserve">oſtenſum ſit omnia quadrata, FD,
              <lb/>
            ad rectangula ſub parallelogrammo, FD, & </s>
            <s xml:id="echoid-s5412" xml:space="preserve">ſemicirculo, vel ſemiel-
              <lb/>
            lipſi, FQB, eſſe vt quadratum, DB, ad rectangulum ſub, DB, B
              <lb/>
            E, inſuper oſtenſum ſit omnia quadrata, FD, ad omnia </s>
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