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

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            <s xml:id="echoid-s2639" xml:space="preserve">
              <pb o="111" file="0131" n="131" rhead="LIBER II."/>
            modo oſtendemus nos poſſe ſic producere omnia plana figuræ, EA
              <lb/>
            G, vt fiant maiora omnibus planis figuræ, GOQ, ita productis, & </s>
            <s xml:id="echoid-s2640" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0131-01" xlink:href="note-0131-01a" xml:space="preserve">Diffin. 4.
                <lb/>
              1. 5. Elem.</note>
            ſic deinceps; </s>
            <s xml:id="echoid-s2641" xml:space="preserve">ergo omnia plana ſolidarum figurarum, EAG, GO
              <lb/>
            Q, ſunt magnitudines inter ſe rationem habentes, quod oſtendere
              <lb/>
            opus erat.</s>
            <s xml:id="echoid-s2642" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div273" type="section" level="1" n="174">
          <head xml:id="echoid-head189" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s2643" xml:space="preserve">_P_Oſſet fortè quis circa hanc demonſtrationem dubitare, nonrectè per-
              <lb/>
            cipiens quomodo ind finitæ numero lineæ, vel plana, quales eſſe
              <lb/>
            exiſtimari poſſunt, quæà me vocantur, omnes linea, vel omnia plana
              <lb/>
            talium, vel talium figurarum poſſint ad inuicem comparari: </s>
            <s xml:id="echoid-s2644" xml:space="preserve">Propter
              <lb/>
            quod innuendum mihi videtur, dum conſidero omnes lineas, vel omnia
              <lb/>
            plana alicuius figuræ, me non numerum ipſarum comparare, quem igno-
              <lb/>
            ramus, ſed tantum magnitudinem, quæ adæquatur ſpatio ab eiſdem li-
              <lb/>
            neis occupato, cum illi congruat, & </s>
            <s xml:id="echoid-s2645" xml:space="preserve">quoniam illud ſpatium terminis
              <lb/>
            comprehenditur, ideò & </s>
            <s xml:id="echoid-s2646" xml:space="preserve">earum magnitudo eſt terminis eiſdem compre-
              <lb/>
            henſa, quapropter illi poteſt fieri additio, vel ſubtractio, licet numerum
              <lb/>
            earundem ignoremus; </s>
            <s xml:id="echoid-s2647" xml:space="preserve">quod ſufficere dico, vt illa ſint ad inuicem compa-
              <lb/>
            rabilia, alioquin neque ipſa ſpatia figurarum eſſent ad inuicem compa-
              <lb/>
            rabilia: </s>
            <s xml:id="echoid-s2648" xml:space="preserve">Vel enim continuum nihil ali ud eſt pręter ipſa indiuiſibilia, vel
              <lb/>
            aliquid aliud, ſi nihil eſt præter indiuiſibilia, profectò ſi eorum conge-
              <lb/>
            ries nequit comparari, neque ſpatium, ſiue continuum, erit comparabi-
              <lb/>
            le, cum illud nihil aliud eſſe ponatur, quam ipſa indiuiſibilia: </s>
            <s xml:id="echoid-s2649" xml:space="preserve">Si Verò
              <lb/>
            continuum eſt aliquid aliud præter ipſa indiuiſibilia, fateri æquum eſt hoc
              <lb/>
            aliquid aliud interiacere ipſa indiuiſibilia, habemus ergo continuum,
              <lb/>
            diſſeparabile in quædam, quæ continuum componunt, numero adbuc in-
              <lb/>
            definita, inter quælibet enim duo indiuiſibilia æquum eſt interiacere ali-
              <lb/>
            quid illius, quod dictum eſt eſſe aliquid aliud in ipſo continuo præter in-
              <lb/>
            diuiſibilia, qua enim ratione tolleretur à medio duarum, à medijs quo-
              <lb/>
            que oæterarum tolleretur; </s>
            <s xml:id="echoid-s2650" xml:space="preserve">hoc cum ita ſit comparare nequibimus ipſa,
              <lb/>
            continua, ſiue ſpatia adinuicem, cum ea, quæ colliguntur, & </s>
            <s xml:id="echoid-s2651" xml:space="preserve">ſimul col-
              <lb/>
            lecta comparantur, ſcilicet, quæ continuum componunt, ſint numero in-
              <lb/>
            definita, abſurdum, autem eſt dicere coutinua terminis comprehenſa non
              <lb/>
            eſſe ad muicem comparabilia, ergo abſurdum eſt dicere congeriem om-
              <lb/>
            nium linearum ſiue planorum, duarum quarumlibet figurarum non eſſe
              <lb/>
            ad inuicem comparabilem, non obſtante, quod quæ colliguntur, & </s>
            <s xml:id="echoid-s2652" xml:space="preserve">il-
              <lb/>
            lam congeriem componunt ſint numero indefinita, veluti hoc non obſtat
              <lb/>
            in continuo, ſiue ergo continuum ex indiuiſibilibus componatur, ſiue,
              <lb/>
            non, indiuiſibilium congeries ſunt adinuicem comparabiles, & </s>
            <s xml:id="echoid-s2653" xml:space="preserve">propor-
              <lb/>
            tionem habent.</s>
            <s xml:id="echoid-s2654" xml:space="preserve"/>
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