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

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            <s xml:id="echoid-s13375" xml:space="preserve">
              <pb o="517" file="0537" n="537" rhead="LIBER VII."/>
            parallelogrammum, &</s>
            <s xml:id="echoid-s13376" xml:space="preserve">, F℟&</s>
            <s xml:id="echoid-s13377" xml:space="preserve">, eſt angulus rectus, eſt enim exterior
              <lb/>
            parallelarum, F℟, XT, & </s>
            <s xml:id="echoid-s13378" xml:space="preserve">ideòipſi interiori, XT&</s>
            <s xml:id="echoid-s13379" xml:space="preserve">, æqualis, erit,
              <lb/>
            E℟, etiam rectangulum, & </s>
            <s xml:id="echoid-s13380" xml:space="preserve">quia, & </s>
            <s xml:id="echoid-s13381" xml:space="preserve">℟, æquatur ipſi, TV, ſunt. </s>
            <s xml:id="echoid-s13382" xml:space="preserve">n.
              <lb/>
            </s>
            <s xml:id="echoid-s13383" xml:space="preserve">
              <figure xlink:label="fig-0537-01" xlink:href="fig-0537-01a" number="354">
                <image file="0537-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0537-01"/>
              </figure>
            ΔΜ, OI, figuræ homologæ,
              <lb/>
            ſicut etiam, F℟, æquatur ip-
              <lb/>
            ſi, YV, ideò rectangulum, E
              <lb/>
            ℟, erit æquale rectangulo, X
              <lb/>
            V. </s>
            <s xml:id="echoid-s13384" xml:space="preserve">Eadem ratione oſtende-
              <lb/>
            mus, quæcunq; </s>
            <s xml:id="echoid-s13385" xml:space="preserve">alia duo re-
              <lb/>
            ctangula ab eodem dictorum
              <lb/>
            ęquidiſtantium plano in ipſis
              <lb/>
            ſolidis producta ęqualia eſie,
              <lb/>
            ergo cum ſolida, CM, PI, ſint
              <lb/>
            in eadem altitudine ſumpta
              <lb/>
            regulis eiſdem æqualibus re-
              <lb/>
            ctangulis, cõcluduntur enim
              <lb/>
            inter extrema plana parallela, quorum contactus eſt in planis, N
              <lb/>
            M, RI; </s>
            <s xml:id="echoid-s13386" xml:space="preserve">Cλ, PB, ideò dicta ſolida erunt æqualiter analoga iuxta di-
              <lb/>
              <note position="right" xlink:label="note-0537-01" xlink:href="note-0537-01a" xml:space="preserve">1. huius.</note>
            ctas regulas, ergo inter ſe æqualia erunt; </s>
            <s xml:id="echoid-s13387" xml:space="preserve">& </s>
            <s xml:id="echoid-s13388" xml:space="preserve">cum ſuperficies, ΔΜ,
              <lb/>
            ſit homologa ipſi, OI, &</s>
            <s xml:id="echoid-s13389" xml:space="preserve">, DM, ipſi, QI, regula plano, RI, propte-
              <lb/>
            rea & </s>
            <s xml:id="echoid-s13390" xml:space="preserve">erit, CM, ſolidum rectangulum æquale ipſi, PI, & </s>
            <s xml:id="echoid-s13391" xml:space="preserve">ſub eiſdẽ
              <lb/>
            ſuperficiebus, QI, IO, continebitur, & </s>
            <s xml:id="echoid-s13392" xml:space="preserve">eius regulæ erunt pariter
              <lb/>
            ipſæ, HI, IS. </s>
            <s xml:id="echoid-s13393" xml:space="preserve">Cum verò in ſuperficie, OI, indefinitè producta, in-
              <lb/>
            definitæ numero figuræ ipſi, OI, homologæ, regula plano, RI,
              <lb/>
            ſupponi poſſint, vt facillimè apparet, ideò ſupradicta methodo tot
              <lb/>
            ſolida rectangula ijſdem ſuperexſtrui poterunt, regulis eiſdẽ, quot
              <lb/>
            erunt figuræ ipſi, HP, homologæ, iuxta dictas regulas, ideſt nu-
              <lb/>
            mero indefinita, quorum vnumquodq; </s>
            <s xml:id="echoid-s13394" xml:space="preserve">ipſi, PI, adæquari, ac ſub
              <lb/>
            eiſdem ſuperficiebus, QI, IO, contineri, vt ſupra oſtendemus.
              <lb/>
            </s>
            <s xml:id="echoid-s13395" xml:space="preserve">Quemadmodũ ſi etiã indefinitè ſuperficies, PH, HS, SB, BP, ſupra,
              <lb/>
            vel infra producerentur, alia indefinita numero ſolida rectangula
              <lb/>
            inueniri eodem modo poſſent, quorum vnumquodque ipſi, PI,
              <lb/>
            adæquari, ac ſub eiſdem ſuperficiebus, QI, IO, contineri, regulis
              <lb/>
            eiſdem, HI, IS, pari ratione probaremus. </s>
            <s xml:id="echoid-s13396" xml:space="preserve">Hæc autem oſtenden-
              <lb/>
            da proponebantur.</s>
            <s xml:id="echoid-s13397" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1190" type="section" level="1" n="711">
          <head xml:id="echoid-head744" xml:space="preserve">COROLL ARIVM I.</head>
          <p style="it">
            <s xml:id="echoid-s13398" xml:space="preserve">_E_X ſupra demonſtratis manifeſtum eſt, quomodo ſolidum rectan-
              <lb/>
            gulum ſub duabus datis ſuperficiebus contentum, iuxta datas
              <lb/>
            regulas, in data ſuperficie cylindracea, quæ continentium altera </s>
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