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

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          <p>
            <s xml:id="echoid-s2698" xml:space="preserve">
              <pb o="114" file="0134" n="134" rhead="GEOMETRIÆ"/>
            nes lineas figurę, D, tunc enim comparare continuum ad continuum
              <lb/>
            non eſſet niſi ipſa indiuiſibilia comparare; </s>
            <s xml:id="echoid-s2699" xml:space="preserve">ſed eſto, quod hoc ſit fal-
              <lb/>
            ſum, vel quod, etiamſi verum ſit, tamen legitima ratione ad hoc pro-
              <lb/>
            bandum nondum peruenerimus; </s>
            <s xml:id="echoid-s2700" xml:space="preserve">nihilominus adhuc dico ipſa indi-
              <lb/>
            uiſibilia. </s>
            <s xml:id="echoid-s2701" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s2702" xml:space="preserve">omnes lineas figurę, A, ad omnes lineas figuræ, D, eſſe
              <lb/>
            vt figuram, A, ad figuram, D. </s>
            <s xml:id="echoid-s2703" xml:space="preserve">Quoniam ergo aſſumpſimus figu-
              <lb/>
            ras, B, C, ſingulas æquales figuræ, A, &</s>
            <s xml:id="echoid-s2704" xml:space="preserve">, E, æqualem figuræ, D,
              <lb/>
            omnes lineæ ſingularum figurarum, A, B, C, erunt æquales omni-
              <lb/>
              <note position="left" xlink:label="note-0134-01" xlink:href="note-0134-01a" xml:space="preserve">Perante-
                <lb/>
              ctd.</note>
            bus lineis figuræ, A, ſumptis iuxta dictam regulam (quacunque re-
              <lb/>
            gula dictæ omnes lineæ ſint aſſumptæ) & </s>
            <s xml:id="echoid-s2705" xml:space="preserve">ideò quotuplex erit com-
              <lb/>
            poſitum ex figuris, ABC, figuræ, A, totuplex erit compoſitum ex
              <lb/>
            omnibus lineis figurarum, ABC, omnium linearum figuræ, A, & </s>
            <s xml:id="echoid-s2706" xml:space="preserve">
              <lb/>
            ideò habebimus æquè multiplicia primæ, & </s>
            <s xml:id="echoid-s2707" xml:space="preserve">tertiæ vtcunq; </s>
            <s xml:id="echoid-s2708" xml:space="preserve">ſumpta;
              <lb/>
            </s>
            <s xml:id="echoid-s2709" xml:space="preserve">ſimiliter oſtendemus compoſitum ex figuris, E, D, æquè multiplex
              <lb/>
              <figure xlink:label="fig-0134-01" xlink:href="fig-0134-01a" number="74">
                <image file="0134-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0134-01"/>
              </figure>
            eſſe figuræ, D, ac compoſitum ex omnibus li-
              <lb/>
            neis figurarum, E, D, multiplex eſt omnium
              <lb/>
            linearum figuræ, D, quæ ſunt æquè multipli-
              <lb/>
            cia ſecundæ, & </s>
            <s xml:id="echoid-s2710" xml:space="preserve">quartę vtcunque ſumpta, quia
              <lb/>
            ergo ſi multiplex primę. </s>
            <s xml:id="echoid-s2711" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s2712" xml:space="preserve">compoſitum ex figu
              <lb/>
            ris, ABC, ſuperauerit multiplex ſecundę, ſci-
              <lb/>
            licet compoſitum ex figuris, DE, etiam mul-
              <lb/>
            tiplex tertiæ. </s>
            <s xml:id="echoid-s2713" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s2714" xml:space="preserve">compoſitum ex omnibus lineis
              <lb/>
            figurarum, ABC, ſuperabit multiplex quartæ
              <lb/>
            .</s>
            <s xml:id="echoid-s2715" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s2716" xml:space="preserve">compoſitum ex omnibus lineis figurarum, DE, & </s>
            <s xml:id="echoid-s2717" xml:space="preserve">ſi multiplex pri-
              <lb/>
              <note position="left" xlink:label="note-0134-02" xlink:href="note-0134-02a" xml:space="preserve">Elicitur
                <lb/>
              ex antec.</note>
            mæ fuerit æquale multiplici ſecundæ, etiam multiplex tertię erit æ-
              <lb/>
            quale multiplici quarte, ſcilicet ſi compoſitum ex figuris, ABC,
              <lb/>
            fuerit æquale compoſito ex figuris, DE, etiam eorundem compo-
              <lb/>
            ſitorum omnes lineæ erunt æquales, & </s>
            <s xml:id="echoid-s2718" xml:space="preserve">ſi minus, minus, ideò prima
              <lb/>
              <note position="left" xlink:label="note-0134-03" xlink:href="note-0134-03a" xml:space="preserve">Defin. 5.
                <lb/>
              Qui. El.</note>
            ad ſecundam erit, vt tertia ad quartam, ſcilicet figura, A, ad figu-
              <lb/>
            ram, D, erit vt omnes lineæ figuræ, A, ad omnes lineas figuræ, D,
              <lb/>
            ſumptas iuxta datas regulas. </s>
            <s xml:id="echoid-s2719" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s2720" xml:space="preserve">iuxta quaſcunq; </s>
            <s xml:id="echoid-s2721" xml:space="preserve">regulas, quod in fig.
              <lb/>
            </s>
            <s xml:id="echoid-s2722" xml:space="preserve">
              <note position="left" xlink:label="note-0134-04" xlink:href="note-0134-04a" xml:space="preserve">Coroll. I.
                <lb/>
              huius.</note>
            planis erat oſtendendum.</s>
            <s xml:id="echoid-s2723" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2724" xml:space="preserve">Verum ſi intellexerimus, A, D, eſſe figuras ſolidas, aſſumentes,
              <lb/>
            C, B, ſingulas æquales ipſi, A, &</s>
            <s xml:id="echoid-s2725" xml:space="preserve">, E, ipſi, D, oſtendemus com-
              <lb/>
            poſitum ex figuris, ABC, tam multiplex eſſe figurę, A, ac compo-
              <lb/>
            ſitum ex omnibus planis figurarum, A, B, C, multiplex eſt omnium
              <lb/>
            planorum figurę, A, & </s>
            <s xml:id="echoid-s2726" xml:space="preserve">ſic compoſitum ex figuris, D, E, tam mul-
              <lb/>
            tiplex eſſe figuræ, D, ac compoſitum ex omnibus planis figurarum,
              <lb/>
            DE, multiplex eſt omnium planorum figuræ, D, & </s>
            <s xml:id="echoid-s2727" xml:space="preserve">tandem per
              <lb/>
            antecedentem Propoſitionem oſtendemus, ſi multiplex primæ ſupe-
              <lb/>
            rauerit multiplex ſecundę, etiam multiplex tertiæ ſuperaturum mul-
              <lb/>
            tiplex quartæ, & </s>
            <s xml:id="echoid-s2728" xml:space="preserve">ſi minus, minus, vel ſi æquale, & </s>
            <s xml:id="echoid-s2729" xml:space="preserve">ęquale fore, </s>
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