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

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          <pb o="525" file="0545" n="545" rhead="LIBER VII."/>
        </div>
        <div xml:id="echoid-div1209" type="section" level="1" n="725">
          <head xml:id="echoid-head758" xml:space="preserve">COROLLARIVM I.</head>
          <p style="it">
            <s xml:id="echoid-s13545" xml:space="preserve">_E_Xpoſita figura plana quacumq; </s>
            <s xml:id="echoid-s13546" xml:space="preserve">BGEO, in parallelis, AC, DF, & </s>
            <s xml:id="echoid-s13547" xml:space="preserve">
              <lb/>
            aſſumptis pro regulis, DF, FH, inuicem perpendicularibus, ita
              <lb/>
              <figure xlink:label="fig-0545-01" xlink:href="fig-0545-01a" number="358">
                <image file="0545-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0545-01"/>
              </figure>
            tamen vt, FH, ſit extra planum parallelarum,
              <lb/>
            AC, DF, primò colligitur, ſi ipſa figura per
              <lb/>
            ſolam lineam, BE, (ſecantem quaſcumq; </s>
            <s xml:id="echoid-s13548" xml:space="preserve">in-
              <lb/>
            tra eandem figuram, ipſiregulæ, DF, para l-
              <lb/>
            lelas deſcriptibiles) diutdatur vtcunq; </s>
            <s xml:id="echoid-s13549" xml:space="preserve">qua-
              <lb/>
            dratum ſolidum ſubindiuiſa, BGEO, & </s>
            <s xml:id="echoid-s13550" xml:space="preserve">ſub
              <lb/>
            eadem, BGEO, quatenus diuiſa, æquari rectangulis ſolidis ſub eadem
              <lb/>
            indiuiſa, BGEO, & </s>
            <s xml:id="echoid-s13551" xml:space="preserve">ſub partibus, BGE, BOE.</s>
            <s xml:id="echoid-s13552" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1211" type="section" level="1" n="726">
          <head xml:id="echoid-head759" xml:space="preserve">COROLLARIVM II.</head>
          <p style="it">
            <s xml:id="echoid-s13553" xml:space="preserve">_C_olligitur ſecundò rectangulum ſolidum ſub indiuiſa, BEO, & </s>
            <s xml:id="echoid-s13554" xml:space="preserve">ſub
              <lb/>
            diuiſa, BGEO, æquarirectangulis ſolidis ſub eadem indiuiſa, BE
              <lb/>
            O, & </s>
            <s xml:id="echoid-s13555" xml:space="preserve">ſub parte, BEO, hoc eſt quadrato ſolido, BEO, & </s>
            <s xml:id="echoid-s13556" xml:space="preserve">rectangulo ſo-
              <lb/>
            lido ſub, BEO, BEG.</s>
            <s xml:id="echoid-s13557" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1212" type="section" level="1" n="727">
          <head xml:id="echoid-head760" xml:space="preserve">COROLLARIVM III.</head>
          <p style="it">
            <s xml:id="echoid-s13558" xml:space="preserve">_C_olligitur tertiò quadratum ſolidum ipſius, BGEO, æquari rectã-
              <lb/>
            gulis ſolidis ſub, BGEO, ac, viriuſq; </s>
            <s xml:id="echoid-s13559" xml:space="preserve">partibus, BEG, BEO, per
              <lb/>
            Cor. </s>
            <s xml:id="echoid-s13560" xml:space="preserve">prim. </s>
            <s xml:id="echoid-s13561" xml:space="preserve">& </s>
            <s xml:id="echoid-s13562" xml:space="preserve">ſubinde æquari quadratis partium, BEG, BEO, vnacum
              <lb/>
            rectangulobis ſub eiſdem partibus, BEG, BEO, per Cor. </s>
            <s xml:id="echoid-s13563" xml:space="preserve">ant.</s>
            <s xml:id="echoid-s13564" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1213" type="section" level="1" n="728">
          <head xml:id="echoid-head761" xml:space="preserve">COROLLARIVM. IV.</head>
          <p style="it">
            <s xml:id="echoid-s13565" xml:space="preserve">_C_olligitur quartò, ſi linea, BIE, bifariam, BNE, verò non bifari@
              <lb/>
            ſecent dictas ipſi, DF, parallelas: </s>
            <s xml:id="echoid-s13566" xml:space="preserve">Rectangulum ſolidum ſub in
              <lb/>
            diuiſa, BNEO, & </s>
            <s xml:id="echoid-s13567" xml:space="preserve">ſub diuiſa, BGEN, per ipſam, BIE, æquari rectan-
              <lb/>
            gulo ſolido ſub eadem indiuiſa, BNEO, & </s>
            <s xml:id="echoid-s13568" xml:space="preserve">ſub partibus, BIEN, BGEI,
              <lb/>
            diuiſæ, hoc eſt æquari rectangulo ſub eadem, BNEO, & </s>
            <s xml:id="echoid-s13569" xml:space="preserve">ſub, BIEO, cum
              <lb/>
            ſolido rectangulo ſub, BOEN, BNEI, cui (i addatur quad. </s>
            <s xml:id="echoid-s13570" xml:space="preserve">ſolidum, BI
              <lb/>
            EN, (ex quibus integratur rectang ſolidum ſub, BIEO, BIEN, per
              <lb/>
            Cor. </s>
            <s xml:id="echoid-s13571" xml:space="preserve">primum) fiet quadratum ſolidum, BEO, cui æquabitur rectangu-
              <lb/>
            lum ſolidum ſub, BGEN, BNEO, cum quadrato ſolido figuræ, BIEN,
              <lb/>
            intermediæ ſec intibus lineis, BIE, BNE, liceat autem, curn dicimus
              <lb/>
            v
              <unsure/>
            ectangulum ſolidum ſub duabus figuris, ſubintelligere ſemper con-
              <lb/>
            tentum, breuitatis gratia, etiam ſi non exprimatur, vt in planis fieri
              <lb/>
            conſacuit.</s>
            <s xml:id="echoid-s13572" xml:space="preserve"/>
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