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

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          <p>
            <s xml:id="echoid-s13475" xml:space="preserve">
              <pb o="522" file="0542" n="542" rhead="GEOMETRIÆ"/>
            B. </s>
            <s xml:id="echoid-s13476" xml:space="preserve">Dico ſolidum rectangulum ſub duobus triangulis, ABC, ACD,
              <lb/>
            contentum, regulis, BC, CF, eſſe pyramidem, cuius baſis erit pa-
              <lb/>
            rallelogrammum rectangulum ſub prædictis baſibus, BC, CD, pa-
              <lb/>
            riter contentum, dummodo alterum dictorum triangulorum ſit in
              <lb/>
            ambitu ipſius contenti ſolidi. </s>
            <s xml:id="echoid-s13477" xml:space="preserve">Sit enim deſcriptum ipſum ſolidum
              <lb/>
            rectangulum ſub triangulis, ABC, ACD, contentum, nempè, AE
              <lb/>
              <figure xlink:label="fig-0542-01" xlink:href="fig-0542-01a" number="356">
                <image file="0542-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0542-01"/>
              </figure>
            BCF, ſit tamen alterum ip-
              <lb/>
            ſorum, vt, ABC, in ambitu
              <lb/>
            ipſius contenti, ſolidi, &</s>
            <s xml:id="echoid-s13478" xml:space="preserve">, AF
              <lb/>
            C, ſuperficies homologa ipſi,
              <lb/>
            ACD, iuxta regulam planũ,
              <lb/>
            BCF, erit ergo, ACF, trian-
              <lb/>
            gulum, eſto enim, quod vnũ
              <lb/>
            parallelorum ipſi, BF, plano-
              <lb/>
            rum, ſolidum, AEC, ſecanti-
              <lb/>
            um, in eo effecerit parallelo
              <lb/>
            grammum rectangulũ, GMIH, & </s>
            <s xml:id="echoid-s13479" xml:space="preserve">intriangulo, ACD, rectam, IY,
              <lb/>
            iam ſcimus, quod, HI, eſt in eodem plano cum, FC, cui eſt paral-
              <lb/>
            lela, & </s>
            <s xml:id="echoid-s13480" xml:space="preserve">ambo ſunt in eodem plano cum, AC, quod etiam de reli-
              <lb/>
            quis in ſuperficie, ACF, ipſi, FC, parallelis exiſtentibus eodem mo-
              <lb/>
            do oſtendetur, ergo iacent omnes in plano ipſarum, AC, CF, ergo,
              <lb/>
            ACF, eſt ſuperficies plana cum vero vt, CD, ad, IY, ita ſit, CA, ad,
              <lb/>
            AI, & </s>
            <s xml:id="echoid-s13481" xml:space="preserve">ita etiam, CF, ad, IH, erit, CF, ad, IH, vt, CA, ad, AI, er-
              <lb/>
            gotria puncta, FHA, erunt in recta linea, in eadem autem eſſe
              <lb/>
            oſtendemus etiam reliquarum ipſi, CF, parallelarum extrema pun-
              <lb/>
            cta ex hac parte, ergo, ACF, erit triangulum: </s>
            <s xml:id="echoid-s13482" xml:space="preserve">Conſimili autem
              <lb/>
              <note position="left" xlink:label="note-0542-01" xlink:href="note-0542-01a" xml:space="preserve">Lemwa 1.
                <lb/>
              22. l. 1.</note>
            modo pariter demonſtrabimus, ABE, AEF, eſſe triangula, & </s>
            <s xml:id="echoid-s13483" xml:space="preserve">eſt,
              <lb/>
            BF, parallelogrammum rectangulum, ergo ſolidum, ABF, eſt py-
              <lb/>
            ramis, & </s>
            <s xml:id="echoid-s13484" xml:space="preserve">eius baſis parallelogrammum, BF, quod oſtendere opus
              <lb/>
            erat.</s>
            <s xml:id="echoid-s13485" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1202" type="section" level="1" n="720">
          <head xml:id="echoid-head753" xml:space="preserve">COROLLARIVM I.</head>
          <p style="it">
            <s xml:id="echoid-s13486" xml:space="preserve">_E_X hoc pariter intelligipoteſt, quod ſolidum rectang. </s>
            <s xml:id="echoid-s13487" xml:space="preserve">contentum
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            ſub trapezijs ex.</s>
            <s xml:id="echoid-s13488" xml:space="preserve">g.</s>
            <s xml:id="echoid-s13489" xml:space="preserve">MBCI, ICDγ, in eiſdem parallelis, Sγ, ND,
              <lb/>
            exiſtentibus, regulis ijſdem, BC, CF, eſt fruſtum pyramidis abſciſſæ per
              <lb/>
            planum baſi, BF, æquidiſtans, vt, GECI, dummodo alterum dictorum
              <lb/>
            trapeziorum in ambitu contenti ſolidi conſiſtat.</s>
            <s xml:id="echoid-s13490" xml:space="preserve"/>
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