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

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            <s xml:id="echoid-s13598" xml:space="preserve">
              <pb o="527" file="0547" n="547" rhead="LIBER VII."/>
            hoc eſt quadratis ſolidis, BGEN, BNEO, additis communibus duobus
              <lb/>
            adbuc rectangulis ſub, BGEN, BIEN, ſeu, BNEO, quæ ſuperſunt, fi-
              <lb/>
            eut quatuor rectangula ſolida ſub, BGEN, BIEN, cum quadrato ſo-
              <lb/>
            lido, BGEI, æqualia duobus quadratis ſolidis, BGEN, BNEO, cum
              <lb/>
            duobus rectangulis ſolidis ſub, BGEN, BNEO, hoc eſt quadrato ſoli-
              <lb/>
            do, BGEO, per Cor. </s>
            <s xml:id="echoid-s13599" xml:space="preserve">Tertium.</s>
            <s xml:id="echoid-s13600" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1218" type="section" level="1" n="732">
          <head xml:id="echoid-head765" xml:space="preserve">COROLLARIVM VIII.</head>
          <p style="it">
            <s xml:id="echoid-s13601" xml:space="preserve">_C_olligitur octauò, ſi figuræ, BGEO, ſecetur vt in Cor. </s>
            <s xml:id="echoid-s13602" xml:space="preserve">4. </s>
            <s xml:id="echoid-s13603" xml:space="preserve">quadrata
              <lb/>
            ſolida figurarum, BGEN, BNEO, dupla eſſe quadratorum ſoli-
              <lb/>
            dorum, BGEI, BIEN. </s>
            <s xml:id="echoid-s13604" xml:space="preserve">Nam quad. </s>
            <s xml:id="echoid-s13605" xml:space="preserve">ſolidum, BGEN, æquatur quadra-
              <lb/>
            tis ſolidis, BGEI, BIEN cum duobus rectangulis ſolidis ſub, BGEI, BI
              <lb/>
            EN, per Cor. </s>
            <s xml:id="echoid-s13606" xml:space="preserve">Tertium, ideſt cum duobus rectangulis ſolidis ſub, BIEO,
              <lb/>
            (homologa ipſi, BGEI,) &</s>
            <s xml:id="echoid-s13607" xml:space="preserve">, BIEN, quibus ſi addatur reſiduum qua-
              <lb/>
            dratum ſolidum, BNEO fiunt duo rect angula ſolida ſub, BIEO, BIE
              <lb/>
            N, cum quadrato ſolido, BNEO, æqualia quadrato ſolido, BIEO, ſeu,
              <lb/>
            BGEI, cum quadrato ſolido, BIEN, igitur quadrata ſolida, BGEN, B
              <lb/>
            NEO, dupla ſunt quadratorum ſolidorum; </s>
            <s xml:id="echoid-s13608" xml:space="preserve">BGEI, BIEN.</s>
            <s xml:id="echoid-s13609" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1219" type="section" level="1" n="733">
          <head xml:id="echoid-head766" xml:space="preserve">COROLLARIVM IX.</head>
          <p style="it">
            <s xml:id="echoid-s13610" xml:space="preserve">_C_olligitur nonò, ſuppoſitis in figura ſectionibus ipſius Cor. </s>
            <s xml:id="echoid-s13611" xml:space="preserve">5. </s>
            <s xml:id="echoid-s13612" xml:space="preserve">qua-
              <lb/>
            drata ſolida, BGEO, BNEO, dupla eſſe quadratorum ſolidorum,
              <lb/>
            BGEI, BIEO. </s>
            <s xml:id="echoid-s13613" xml:space="preserve">Etenim quadratum ſolidum, BGEO, æquatur per Cor 3.
              <lb/>
            </s>
            <s xml:id="echoid-s13614" xml:space="preserve">quadratis ſolidis, BGEI, BIEO, cum duobus rectangulis ſolidis ſub, BG
              <lb/>
            EI, ſeu, BIEN, illi homologa, &</s>
            <s xml:id="echoid-s13615" xml:space="preserve">, BIEO, quæ duo rectangula ſolida fa-
              <lb/>
            ciunt cum quadrato ſolido, BNEO, reſiduo, quadrata ſolida, BIEO, BI
              <lb/>
            EN, ſeu, BGEI, BIEO, ergo quadrata ſolida, BGEO, BNEO, dupla
              <lb/>
            ſunt quadratorum ſolidorum, BGEI, BIEO.</s>
            <s xml:id="echoid-s13616" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1220" type="section" level="1" n="734">
          <head xml:id="echoid-head767" xml:space="preserve">COROLLARIVM X.</head>
          <p style="it">
            <s xml:id="echoid-s13617" xml:space="preserve">_C_olligitur decimò, & </s>
            <s xml:id="echoid-s13618" xml:space="preserve">vltimò, ſi tandem ex. </s>
            <s xml:id="echoid-s13619" xml:space="preserve">g. </s>
            <s xml:id="echoid-s13620" xml:space="preserve">lineæ, BNE, ſecet
              <lb/>
            quaſcumq; </s>
            <s xml:id="echoid-s13621" xml:space="preserve">intra figuram, BNE, ipſi, DF, æquidiſtantes, ſecun-
              <lb/>
            dum extremam, ac mediam rationem, ita vt maior portio cuiuſcumq;
              <lb/>
            </s>
            <s xml:id="echoid-s13622" xml:space="preserve">ſectæ lineæ ſit ex. </s>
            <s xml:id="echoid-s13623" xml:space="preserve">g. </s>
            <s xml:id="echoid-s13624" xml:space="preserve">in figura, BGEN, rectangulum ſolidum ſub, BGE
              <lb/>
            O, BNEO, æquari quadrato ſolido, BGEN, bæc enim ſolida erunt
              <lb/>
            æqualiter analogaiuxta regulam planum, DFH, ex eo quod in vnoquo-
              <lb/>
            que eidem parallelorũ planorum ipſa ſolida ſecantiũ, ac capientiũ vnũ
              <lb/>
            rectangulum, & </s>
            <s xml:id="echoid-s13625" xml:space="preserve">vnum quadratum, ſemper rectangulum eſt æquale,
              <lb/>
            quadrato in eodem plano exiſtenti.</s>
            <s xml:id="echoid-s13626" xml:space="preserve"/>
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