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

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            <s xml:id="echoid-s13453" xml:space="preserve">
              <pb o="521" file="0541" n="541" rhead="LIBER VII."/>
            vt rect angulum, BCD, ad rectangulum, SCV, ſunt enim hæc plana ré
              <lb/>
            ctangula baſes dictorum rectangulorum ſolidorum, quæ ex dictis ſunt
              <lb/>
            parallelepipeda, ſeu cylindrici eiuſdem altitudinis ſumptæ reſpectu
              <lb/>
            dict arum baſium, & </s>
            <s xml:id="echoid-s13454" xml:space="preserve">ideò ſunt vt ipſæ baſes, hoc eſt vt dicta rectangu-
              <lb/>
            la, ſuppoſito tamen quod continentia parallelogramma ſint in ambitu
              <lb/>
            contentorum ſolidorum.</s>
            <s xml:id="echoid-s13455" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1199" type="section" level="1" n="718">
          <head xml:id="echoid-head751" xml:space="preserve">ANNOTATIO.</head>
          <p>
            <s xml:id="echoid-s13456" xml:space="preserve">POterant quidem exhiberi parallelogramma, AC, RC, in eodē
              <lb/>
            plano cum figuris, EHC, CHD, & </s>
            <s xml:id="echoid-s13457" xml:space="preserve">in eiſdem cum ipſis paral-
              <lb/>
            lelis, vt, HY, proipſo, AC, &</s>
            <s xml:id="echoid-s13458" xml:space="preserve">, HR, proipſo, RC, & </s>
            <s xml:id="echoid-s13459" xml:space="preserve">intelligi me-
              <lb/>
            taliter deſcripta ſolida rectang. </s>
            <s xml:id="echoid-s13460" xml:space="preserve">iam dicta ſub iſtis in eodem plano
              <lb/>
            iacentibus fig. </s>
            <s xml:id="echoid-s13461" xml:space="preserve">prout dictum eſt, quo pacto eadem intelligi potuiſ-
              <lb/>
            ſent, ſed cum nonnihil difficile captu initio huius nouæ doctrinæ
              <lb/>
            hoc mihi fore videretur, eadem vt ſupra exhibere malui, verunta-
              <lb/>
            men valde expediet pro ſequentibus aſſuefieri dictorum ſolidorum
              <lb/>
            mentali deſcriptioni, exhibitis continentibus eadem fig. </s>
            <s xml:id="echoid-s13462" xml:space="preserve">(quæ, pu-
              <lb/>
            to, ſemper planæ erunt ) in eiſdem parallelis conſtitutis, quemad-
              <lb/>
            modum duabus quibuſcung; </s>
            <s xml:id="echoid-s13463" xml:space="preserve">rectis lineis exhibitis, illico rectangu-
              <lb/>
            lum ſub ipſis mentaliter deſcribere ſolemus, ſicuti & </s>
            <s xml:id="echoid-s13464" xml:space="preserve">quadratum
              <lb/>
            datæ rectæ lineæ cuiuſcumq; </s>
            <s xml:id="echoid-s13465" xml:space="preserve">abſque eo, quod ſemper in ſchema-
              <lb/>
            tibus ipſa deſcripta exhibeantur, ſic ergo & </s>
            <s xml:id="echoid-s13466" xml:space="preserve">ſolida rectang. </s>
            <s xml:id="echoid-s13467" xml:space="preserve">& </s>
            <s xml:id="echoid-s13468" xml:space="preserve">ſolida
              <lb/>
            quadrata, ſub duabus planis figuris in eiſdem parallelis exiſtentibus
              <lb/>
            iuxta datas regulas contenta, ad figurarum confuſionem euitan-
              <lb/>
            dam & </s>
            <s xml:id="echoid-s13469" xml:space="preserve">nos quoq; </s>
            <s xml:id="echoid-s13470" xml:space="preserve">mentaliter vt plurimum deſcribemus.</s>
            <s xml:id="echoid-s13471" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1200" type="section" level="1" n="719">
          <head xml:id="echoid-head752" xml:space="preserve">THEOREMA XIV. PROPOS. XIV.</head>
          <p>
            <s xml:id="echoid-s13472" xml:space="preserve">SI duo triangula fuerint in eiſdem parallelis conſtituta.
              <lb/>
            </s>
            <s xml:id="echoid-s13473" xml:space="preserve">Solidum rectangolum ſub eiſdem contentum, regula
              <lb/>
            altera dictarum parallelarum, ac alia quadam illi in ſubli-
              <lb/>
            mi perpendiculari, erit pyramis, habens in baſi parallelo-
              <lb/>
            grammum rectangulum, ſub dictorum triangulorum baſi-
              <lb/>
            bus contentum, dummodo alterum dictorum triangulorũ
              <lb/>
            ſit in ambitu contentiſolidi.</s>
            <s xml:id="echoid-s13474" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13475" xml:space="preserve">Sint duo triangula in eiſdem parallelis conſtituta, LK, ND, nẽ
              <lb/>
            pè, ABC, ACD, in baſibus, BC, CD, in parallela, ND, diſpoſitis,
              <lb/>
            eleuetur autem à puncto, C, quædam, CF, perpendicularis ipſi, </s>
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