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

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          <p>
            <s xml:id="echoid-s13524" xml:space="preserve">
              <pb o="524" file="0544" n="544" rhead="GEOMETRIE"/>
            ra autem fuerit indiuiſa: </s>
            <s xml:id="echoid-s13525" xml:space="preserve">Solidum rectangulum ſub indi-
              <lb/>
            uiſa, & </s>
            <s xml:id="echoid-s13526" xml:space="preserve">ſub diuiſa contentum, æquabitur ſolidis rectangu-
              <lb/>
            lis ſub eadem indiuiſa, & </s>
            <s xml:id="echoid-s13527" xml:space="preserve">ſub partibus diuiſæ, regulis ijſ-
              <lb/>
            dem, contentis.</s>
            <s xml:id="echoid-s13528" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13529" xml:space="preserve">Sint duæ expoſitæ ſuperficies, AC, CH, ſolidum recrangulum,
              <lb/>
            FC, iuxca regulas, kC, CB, continentes, earum autem altera, vt,
              <lb/>
            AC, ſit diuila in quotcumq; </s>
            <s xml:id="echoid-s13530" xml:space="preserve">partes, vt per lineam, DEC, ſecan-
              <lb/>
            tem quaſcumq; </s>
            <s xml:id="echoid-s13531" xml:space="preserve">intra ſuperficiem, AC, ipſiregulæ, BC, parallelas,
              <lb/>
              <figure xlink:label="fig-0544-01" xlink:href="fig-0544-01a" number="357">
                <image file="0544-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0544-01"/>
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            in duas partes, DEC, ADECB, ipſa
              <lb/>
            verò, HC, ſit indiuiſa. </s>
            <s xml:id="echoid-s13532" xml:space="preserve">Dico ſolidum
              <lb/>
            contentum ſub indiuiſa, HC, & </s>
            <s xml:id="echoid-s13533" xml:space="preserve">ſub
              <lb/>
            diuiſa, AC, ideſt, FC, æquari ſolidis
              <lb/>
            contentis ſub, DEC, CH, & </s>
            <s xml:id="echoid-s13534" xml:space="preserve">ſub, DE
              <lb/>
            CBA, & </s>
            <s xml:id="echoid-s13535" xml:space="preserve">ſub eadem, CH. </s>
            <s xml:id="echoid-s13536" xml:space="preserve">Intelliga-
              <lb/>
            tur ergo quandam rectam lineam fer-
              <lb/>
            ri peripſam, CED, indefinitè produ
              <lb/>
            ctam, donec totam percurrerit, ac
              <lb/>
            ſemper moueri ipſi regulæ, KC, æqui-
              <lb/>
            diſtanter, deſcribet ergo ſuperficiem
              <lb/>
            cylindraceam, quæ ſit, KEH, & </s>
            <s xml:id="echoid-s13537" xml:space="preserve">ab-
              <lb/>
            ſcindet à ſuperſiciebus, FK, AC, ſu-
              <lb/>
            perficies cylindraceas, HIK, DEC, &</s>
            <s xml:id="echoid-s13538" xml:space="preserve">, HC, eſt cylindracea, & </s>
            <s xml:id="echoid-s13539" xml:space="preserve">hoc
              <lb/>
            ſiue ſit in ambitu contenti ſolidi, ſiue non, alioquin non poſſent
              <lb/>
            latera, quæ per ſolidum, FC, ſecantia plana, ipſi, GC, æquidiſtã-
              <lb/>
            tia ſignantur in ipſa ſuperficie, HC, omnia vni regulæ, kC, æqui-
              <lb/>
            diſtare, ergo ſolidum, HIKCED, ſuperficiebus cylindraceis com-
              <lb/>
            prehenditur, quarum regulæ ſunt, kC, CB, inuicem perpendicula-
              <lb/>
            res ergo ſi ſolidum, HIKCED, ſecetur planis ipſi, kB, parallelis fiẽt
              <lb/>
            in ſolido parallelogramina ipſi, kB, æquiangula, hoc eſt rectangu-
              <lb/>
            la, & </s>
            <s xml:id="echoid-s13540" xml:space="preserve">ideò dictum ſolidum erit ſolidum rectangulum contentum
              <lb/>
            ſub, HC, CED, ſuperficiebus: </s>
            <s xml:id="echoid-s13541" xml:space="preserve">Eodem modo oſtendemus, HIKC
              <lb/>
            EDAG, eſſe ſolidum rectangulum contentum ſub ſuperficie, DIC,
              <lb/>
            hoe eſt, Dk, il i homologa iuxta planum, BK, ac ſub, DECBA, eſt
              <lb/>
            autem ſolidum, FC, æquale duobus ſolidis, HIC, CIHFB, ſimul
              <lb/>
            ſumptis, ergo ſolidum rectangulum contentum ſub indiuiſa ſuperö
              <lb/>
            ficie, HC, & </s>
            <s xml:id="echoid-s13542" xml:space="preserve">ſub diuiſa, AC, æquale eſt ſolidis rectangulis conten-
              <lb/>
            tis ſub eadem indiuiſa, HC, & </s>
            <s xml:id="echoid-s13543" xml:space="preserve">ſub partibus diuiſæ, DEC, DECB
              <lb/>
            A, regulis ſemper ijſdem, BC, CK, retentis, quod oſtendere opus
              <lb/>
            erat.</s>
            <s xml:id="echoid-s13544" xml:space="preserve"/>
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