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

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        <div xml:id="echoid-div1233" type="section" level="1" n="745">
          <p>
            <s xml:id="echoid-s13842" xml:space="preserve">
              <pb o="534" file="0554" n="554" rhead="GEOMETR I Æ"/>
            quatur quoq; </s>
            <s xml:id="echoid-s13843" xml:space="preserve">rectangulo, DTA, ergo vt rectangulum, GQR, ad
              <lb/>
            rectangulum, POT, ita rectangulum, DRA, erit ad rectangulum,
              <lb/>
            DTA, hoc eſt ita quadratum, RF, ad quadratum, TX, ergo per-
              <lb/>
            mutando rectangulum, GQR, ad quadratum, RF, erit vt rectan-
              <lb/>
            gulum, POT, ad quadratum, TX, quod & </s>
            <s xml:id="echoid-s13844" xml:space="preserve">in reliquis huiuſmodi
              <lb/>
              <note position="left" xlink:label="note-0554-01" xlink:href="note-0554-01a" xml:space="preserve">3. huius.</note>
            oſtendetur ſpatijs ergo rectangulum ſolidum ſub trapezijs, LHG
              <lb/>
              <note position="left" xlink:label="note-0554-02" xlink:href="note-0554-02a" xml:space="preserve">Coroll. 2.
                <lb/>
              13. huius.</note>
            Q, LMRQ, & </s>
            <s xml:id="echoid-s13845" xml:space="preserve">quadratum ſolidum, MSXFR, erunt, vel æqualiter
              <lb/>
            in circulo, vel proportionaliter analoga in ellipſi, ergo erunt inter
              <lb/>
            ſe vt rectangulum, GQR, & </s>
            <s xml:id="echoid-s13846" xml:space="preserve">quadratum, RF, ſunt quoq; </s>
            <s xml:id="echoid-s13847" xml:space="preserve">inter ſe,
              <lb/>
            ſed vt rectangulum, GQR, ad quadratum, RF, ſic etiam eſſe oſtẽ-
              <lb/>
            demus rectangulum ſolidum ſub, HQ, QM, ad quadratum ſolidũ,
              <lb/>
            NR, ergo rectangulum ſolidum ſub, HQ, QM, ad quadratum ſo-
              <lb/>
            lidum, NR, erit vt rectang. </s>
            <s xml:id="echoid-s13848" xml:space="preserve">ſolidum ſub, LHGQ, LMRQ, ad qua-
              <lb/>
            dratum ſolidum, MSXFR, & </s>
            <s xml:id="echoid-s13849" xml:space="preserve">permutando rectangulum iolidum
              <lb/>
            ſub, HQ, QM, ad rectangulum ſolidum ſub, LHGQ, LMRQ, erit
              <lb/>
            vt quadratum ſolidum, NR, ad quadratum ſolidum, MSXFR, eſt
              <lb/>
            autem rectangulum ſolidum ſub, HQ, QM, ad rectangulum ſoli-
              <lb/>
            dum ſub, HGQL, LQRM, vt rectangulum ſub, GQR, ad rectan-
              <lb/>
              <note position="left" xlink:label="note-0554-03" xlink:href="note-0554-03a" xml:space="preserve">19. huius.</note>
            gulum ſub, GQ; </s>
            <s xml:id="echoid-s13850" xml:space="preserve">& </s>
            <s xml:id="echoid-s13851" xml:space="preserve">ſub compoſita ex {1/2}. </s>
            <s xml:id="echoid-s13852" xml:space="preserve">QY, & </s>
            <s xml:id="echoid-s13853" xml:space="preserve">ex, YR; </s>
            <s xml:id="echoid-s13854" xml:space="preserve">vna cum
              <lb/>
            rectangulo ſub, QY, & </s>
            <s xml:id="echoid-s13855" xml:space="preserve">ſub compoſita ex {1/6}. </s>
            <s xml:id="echoid-s13856" xml:space="preserve">QY, & </s>
            <s xml:id="echoid-s13857" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s13858" xml:space="preserve">YR, hoc eſt
              <lb/>
            vt rectangulum, DRA, ad rectangulum ſub, DR, & </s>
            <s xml:id="echoid-s13859" xml:space="preserve">ſub compoſi-
              <lb/>
            ta ex {1/2}. </s>
            <s xml:id="echoid-s13860" xml:space="preserve">RM, & </s>
            <s xml:id="echoid-s13861" xml:space="preserve">ex, MA, vna cum rectangulo ſub, RM, & </s>
            <s xml:id="echoid-s13862" xml:space="preserve">ſub cõ-
              <lb/>
            poſita ex {1/6}. </s>
            <s xml:id="echoid-s13863" xml:space="preserve">RM, & </s>
            <s xml:id="echoid-s13864" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s13865" xml:space="preserve">MA, ergo ſic etiam erit quadratum ſolidum
              <lb/>
            NR, ad quadratum ſolidum ſemiportionis, MSXFR, & </s>
            <s xml:id="echoid-s13866" xml:space="preserve">ita etiam
              <lb/>
            quadratum ſolidum, BF, ad quadratum ſolidum ipſius, ICFS, con-
              <lb/>
            ſpecta figura dìctæ prop. </s>
            <s xml:id="echoid-s13867" xml:space="preserve">3. </s>
            <s xml:id="echoid-s13868" xml:space="preserve">quod oſtendere opus erat.</s>
            <s xml:id="echoid-s13869" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1235" type="section" level="1" n="746">
          <head xml:id="echoid-head779" xml:space="preserve">ANNOTATIO.</head>
          <p>
            <s xml:id="echoid-s13870" xml:space="preserve">POſterior pars dictæ Prop. </s>
            <s xml:id="echoid-s13871" xml:space="preserve">3. </s>
            <s xml:id="echoid-s13872" xml:space="preserve">oſtendetur vt ibi, ſolita nominum
              <lb/>
            mutatione facta, ſicut etiam Prop. </s>
            <s xml:id="echoid-s13873" xml:space="preserve">4. </s>
            <s xml:id="echoid-s13874" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s13875" xml:space="preserve">5. </s>
            <s xml:id="echoid-s13876" xml:space="preserve">reſtauratione
              <lb/>
            non indiget; </s>
            <s xml:id="echoid-s13877" xml:space="preserve">Cor. </s>
            <s xml:id="echoid-s13878" xml:space="preserve">autem deducetur eodem modo, vt ibi mutatis
              <lb/>
            tantum dictis nominibus, fiunt enim quadrata ſolida figurarum
              <lb/>
            ijſdem parallelis in eiuſdem ſchemate interceptarum, figuræ ſolidę
              <lb/>
              <note position="left" xlink:label="note-0554-04" xlink:href="note-0554-04a" xml:space="preserve">3. huius.</note>
            æqualiter analogæ, vnde etiam ſunt æquales, ex quo concluditur
              <lb/>
            deinde Corollarium eodem modo, quo ibi factum eſt. </s>
            <s xml:id="echoid-s13879" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s13880" xml:space="preserve">6.
              <lb/>
            </s>
            <s xml:id="echoid-s13881" xml:space="preserve">cum Cor. </s>
            <s xml:id="echoid-s13882" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s13883" xml:space="preserve">7. </s>
            <s xml:id="echoid-s13884" xml:space="preserve">8. </s>
            <s xml:id="echoid-s13885" xml:space="preserve">9. </s>
            <s xml:id="echoid-s13886" xml:space="preserve">cum Cor. </s>
            <s xml:id="echoid-s13887" xml:space="preserve">pariter vt ibi oſtendentur, muta-
              <lb/>
            tis nominibus, vt ſupra Prop. </s>
            <s xml:id="echoid-s13888" xml:space="preserve">10. </s>
            <s xml:id="echoid-s13889" xml:space="preserve">ſic patebit probabuntur enim fi-
              <lb/>
            guræ, AFH, AGH, eſſe proportionaliter analogæ, & </s>
            <s xml:id="echoid-s13890" xml:space="preserve">ideò eſſe inter
              <lb/>
            ſe, vt, FH, HG, eodem modo, quo ibi factum eſt, ex quo ſimiliterr
              <lb/>
            concludetur, AFVT, ad, AGVS, eſſe vt, FT, ad, GS; </s>
            <s xml:id="echoid-s13891" xml:space="preserve">& </s>
            <s xml:id="echoid-s13892" xml:space="preserve">non </s>
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