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

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            <s xml:id="echoid-s13966" xml:space="preserve">
              <pb o="536" file="0556" n="556" rhead="GEOMETRIE"/>
            ptam ab, HM, prædictæ homologa, habet duplicatam rationem
              <lb/>
            eius, quam, EF, habet ad, HM, ergo vt quadratum, EF, ad qua-
              <lb/>
            dratum, HM, ita eſt figura, EF, ad ſibi ſimilem figuram deſcriptã
              <lb/>
            ab, HM, & </s>
            <s xml:id="echoid-s13967" xml:space="preserve">permutando vt quadratum, EF, ad figuram quamcuq;
              <lb/>
            </s>
            <s xml:id="echoid-s13968" xml:space="preserve">
              <figure xlink:label="fig-0556-01" xlink:href="fig-0556-01a" number="364">
                <image file="0556-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0556-01"/>
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            aliam deſcriptam ab, EF, ita erit quadratum,
              <lb/>
            HM, ad figuram prędictæ ſimilem deſcriptam
              <lb/>
            ab, HM, prædictæ homologa, ergo quadratũ
              <lb/>
            ſolidum figuræ, DEF, & </s>
            <s xml:id="echoid-s13969" xml:space="preserve">ſolidum ſimilare quo-
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            dcumq; </s>
            <s xml:id="echoid-s13970" xml:space="preserve">genitum ex figura, DEF, luxta comu
              <lb/>
            nem regulam, EF, ſunt ſolida proportionaliter
              <lb/>
            analoga ſecundum communem regulã, EF, ergo erunt inter ſe vt fi-
              <lb/>
              <note position="left" xlink:label="note-0556-01" xlink:href="note-0556-01a" xml:space="preserve">3. huius.</note>
            guræ planæ ab eodem latere, vt ab, EF, deſcriptę. </s>
            <s xml:id="echoid-s13971" xml:space="preserve">Eodẽ modo oſtẽ-
              <lb/>
            demus quadratum ſolidũ, ABC, & </s>
            <s xml:id="echoid-s13972" xml:space="preserve">ſolidũ aliud quodcumq; </s>
            <s xml:id="echoid-s13973" xml:space="preserve">ſimilare
              <lb/>
            genitum ex figura, ABC, iuxta cõmunẽ regulam, BC, eſſe inter ſe, vt
              <lb/>
            figuræ à, BC, deſcriptæ, ſunt autem duo quadrata, BC, EF, & </s>
            <s xml:id="echoid-s13974" xml:space="preserve">duæ
              <lb/>
            aliæ quæcumq; </s>
            <s xml:id="echoid-s13975" xml:space="preserve">ſimiles figuræ planæ deſcriptæ ab homologis, BC,
              <lb/>
            EF, proportionales, ergo & </s>
            <s xml:id="echoid-s13976" xml:space="preserve">dicta ſolida proportionalia erunt, nẽpè
              <lb/>
            vt quadratũ, BC, ad figuram, BC, ſic erat quadratum ſolidũ, ABC,
              <lb/>
            ad ſolidum ſimilare genitũ ex, ABC, ſed vt quadratũ, BC, ad figurã,
              <lb/>
            BC, ita eſt qua dratum, EF, ad figuram, EF, prædictæ ſimilem, & </s>
            <s xml:id="echoid-s13977" xml:space="preserve">ita
              <lb/>
            etiam quadratum ſolidum, DEF, ad ſolidum prædicto ſimilare ge-
              <lb/>
            nitum ex, DEF, ergo quadratum ſolidum, ABC, ad ſolidum ſimi-
              <lb/>
            lare, ABC, eſt vt quadratum ſolidum, DEF, ad ſolidum præ dicto
              <lb/>
            ſimilare genitũ ex, DEF, & </s>
            <s xml:id="echoid-s13978" xml:space="preserve">permutando quad. </s>
            <s xml:id="echoid-s13979" xml:space="preserve">ſolidũ, ABC, ad qua-
              <lb/>
            dratũ ſolidũ, DEF, erit vt ſolidũ quodcũq; </s>
            <s xml:id="echoid-s13980" xml:space="preserve">ſimilare genitũ ex, ABC,
              <lb/>
            ad ſibi ſimilare gen tũ ex, DEF, luxta dictas regulas, quod oſtendere
              <lb/>
            opus erat.</s>
            <s xml:id="echoid-s13981" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1239" type="section" level="1" n="748">
          <head xml:id="echoid-head781" xml:space="preserve">ANNOTATIO.</head>
          <p>
            <s xml:id="echoid-s13982" xml:space="preserve">HVius demonſtratio ſimilis eſt demonſtrationi Prop. </s>
            <s xml:id="echoid-s13983" xml:space="preserve">33. </s>
            <s xml:id="echoid-s13984" xml:space="preserve">1. </s>
            <s xml:id="echoid-s13985" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13986" xml:space="preserve">cui
              <lb/>
            per hanc ſuppletur, Coro laria autem iuxta methodum ibi
              <lb/>
            adhibitam facilè quoq; </s>
            <s xml:id="echoid-s13987" xml:space="preserve">deducentur, illam vero huc reſeruaui, vt
              <lb/>
            promptiorem pro colligendis ſequentibus Corollarijs lib. </s>
            <s xml:id="echoid-s13988" xml:space="preserve">3. </s>
            <s xml:id="echoid-s13989" xml:space="preserve">ex hac
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            pendentibus eam haberemus. </s>
            <s xml:id="echoid-s13990" xml:space="preserve">Adhibuit quidem nomen ſolidi ſi-
              <lb/>
            milaris, quod per indefinitum numerum parallelorum planorum
              <lb/>
            fuit pariter explicatum lib. </s>
            <s xml:id="echoid-s13991" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13992" xml:space="preserve">ad B. </s>
            <s xml:id="echoid-s13993" xml:space="preserve">Defin. </s>
            <s xml:id="echoid-s13994" xml:space="preserve">8. </s>
            <s xml:id="echoid-s13995" xml:space="preserve">attamen ſi vice om-
              <lb/>
            nium planorum, ſeu deſcriptarum figurarum, ſubſtituamus quot-
              <lb/>
            cumq; </s>
            <s xml:id="echoid-s13996" xml:space="preserve">plana, ſeu deſcriptas figuras, ita vt perimetri deſcriptarum
              <lb/>
            figurarum iacere intelligantur in ſuperficie ipſum ſolidum ambiẽ-
              <lb/>
            te, intelligemus nihilominus, licet nonnihil diuerſo modo, eſſe idẽ
              <lb/>
            ſolidum, quod dicitur ſimilare, ac à propria genitrice </s>
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