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

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          <p>
            <s xml:id="echoid-s2621" xml:space="preserve">
              <pb o="110" file="0130" n="130" rhead="GEOMETRIÆ"/>
            nium linearum figurę, GOQ, hac lege producta, complectetur eas,
              <lb/>
            quæ de ip. </s>
            <s xml:id="echoid-s2622" xml:space="preserve">a manent in figuris iam diſpoſitis, ergo omnes lineæ figu-
              <lb/>
            ræ, GOQ, ſic productæ complectentur omnes lineas figurarum ſic
              <lb/>
            diſpoſitarum, ergo erunt ad illas ſimul ſumptas, vt totum ad partem,
              <lb/>
            nam illæ in his reperientur, & </s>
            <s xml:id="echoid-s2623" xml:space="preserve">aliquid amplius, ergo erunt illis ma-
              <lb/>
            iores, omnes lineę autem figurarum ſic diſpoſitarum ſunt non mino-
              <lb/>
            res omnibus lineis figuræ, EAG, ex qua deſumptæ ſunt, ergo om-
              <lb/>
            nes lineę figurę, GOQ, ſic productæ ſunt, vt effectæ fuerint maio-
              <lb/>
            res omnibus lineis figurę, EAG; </s>
            <s xml:id="echoid-s2624" xml:space="preserve">eodem pacto oſtendemus nos poſ-
              <lb/>
            ſe vice verſa iſtas illis efficere maiores, ergo omnes lineæ figurarum,
              <lb/>
            EAG, GOQ, ſumptæ cum regulis vtcumque ſuppoſitis, cuiuſuis
              <lb/>
              <note position="left" xlink:label="note-0130-01" xlink:href="note-0130-01a" xml:space="preserve">Diffin. 4.
                <lb/>
              1.5. Elem.</note>
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                <image file="0130-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0130-01"/>
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            ſint altitudinis ſumptę iux-
              <lb/>
            ta eaſdem regulas, ſunt
              <lb/>
            magnitudines inter ſe ra-
              <lb/>
            tionem habentes, quod ſi
              <lb/>
            ſubter rectam, HQ, ad-
              <lb/>
            huc eſſent portiones con-
              <lb/>
            ſideratarum à nobis figu-
              <lb/>
            rarum, EAG, GOQ, eo-
              <lb/>
            dem modo oſtenderemus omnes lineas earundem ſumptas, cum ijſ-
              <lb/>
            dem regulis eſſe magnitudines rationem inter ſe habentes, vnde inte-
              <lb/>
            grarum figurarum omnes lineę eſſent magnitudines inter ſe rationem
              <lb/>
            habentes, quod in fig. </s>
            <s xml:id="echoid-s2625" xml:space="preserve">planis oſtendere opus erat.</s>
            <s xml:id="echoid-s2626" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2627" xml:space="preserve">In ſiguris autem ſolidis conſimiliter procedemus; </s>
            <s xml:id="echoid-s2628" xml:space="preserve">nam ſi in ſupe-
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            riori figura intellexerimus, EAG, GOQ, eſſe figuras ſolidas, & </s>
            <s xml:id="echoid-s2629" xml:space="preserve">
              <lb/>
            pro rectis lineis æquidiſtantibus intellexerimus plana æquidiſtantia,
              <lb/>
            vt pro rectis, EG, GQ, plana, EG, GQ, quibus plana, LM, N
              <lb/>
            S, ſint æquidiſtanter ducta, ſumptis pro regulis planis, EG, GQ,
              <lb/>
            ijſque in directum ſibi conſtitutis.</s>
            <s xml:id="echoid-s2630" xml:space="preserve">i. </s>
            <s xml:id="echoid-s2631" xml:space="preserve">ita vt iaceant regulæ in eodem
              <lb/>
            plano, oſtendemus nos poſſe ita producere omnia plana ſolidæ figu-
              <lb/>
            ræ, GOQ, vt eadem complectantur omnia plana figuræ, EAG,
              <lb/>
            (ſi ſint eiuſdem altitudinis dictæ figuræ) integræ exiſtentis, vel (ſi
              <lb/>
            non ſint) diuiſæ in figuras ſolidas, ex. </s>
            <s xml:id="echoid-s2632" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s2633" xml:space="preserve">EBDG, BAD, ſic di-
              <lb/>
            ſpoſitas, vt baſes, ſiue regulę iaceant in eodem plano, & </s>
            <s xml:id="echoid-s2634" xml:space="preserve">ita, vt om-
              <lb/>
            nia plana dictarum ſigurarum ſolidarum, vel ſint intra oppoſita pla-
              <lb/>
            na dictas figuras tangentia, vel nihil eorum extra, vnde omnia pla-
              <lb/>
            na figuræ ſolidæ, GOQ, ſic producta fient totum, & </s>
            <s xml:id="echoid-s2635" xml:space="preserve">portiones ab
              <lb/>
            eiſdem captæ in figura ſolida, EAG, integra, vel diuiſa, vt dictum
              <lb/>
            eſt.</s>
            <s xml:id="echoid-s2636" xml:space="preserve">i. </s>
            <s xml:id="echoid-s2637" xml:space="preserve">omnia plana figuræ, EAG, fient pars omnium planorum fi-
              <lb/>
            guræ, GOQ, ſic productorum, nam hæc in illis tota reperientur,
              <lb/>
            & </s>
            <s xml:id="echoid-s2638" xml:space="preserve">aliquid amplius, vnde omnia plana figuræ, GOQ, ſic producta
              <lb/>
            erunt, vt effecta ſint maiora omnibus planis figuræ, EAG; </s>
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