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

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          <p>
            <s xml:id="echoid-s12748" xml:space="preserve">
              <pb o="500" file="0520" n="520" rhead="GEOMETRIÆ"/>
              <figure xlink:label="fig-0520-01" xlink:href="fig-0520-01a" number="349">
                <image file="0520-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0520-01"/>
              </figure>
            reſultantium figurarum termini ſint in ſuperficiebus, AMCG, A
              <lb/>
            MDG; </s>
            <s xml:id="echoid-s12749" xml:space="preserve">AMEG ſimiliter in alio ſolido eſto quod plana, quę produ-
              <lb/>
            xerũt in ſolido, AMEGF, figur. </s>
            <s xml:id="echoid-s12750" xml:space="preserve">MEGF, NSTV, genuerint figuras,
              <lb/>
            QRY, ΖλΩ, ad quas illæ habent eandem rationem, ductis autem,
              <lb/>
            vel aſſumptis rectis, QY, ΖΔ, inter ſe parallelis, illæ producantur
              <lb/>
            verſus eandem partem, ΔΥ, in ijſq; </s>
            <s xml:id="echoid-s12751" xml:space="preserve">productis accipiantur quæcũq;
              <lb/>
            </s>
            <s xml:id="echoid-s12752" xml:space="preserve">æquè multiplices, vel æquales, YX, Δ℟, & </s>
            <s xml:id="echoid-s12753" xml:space="preserve">idem fiat in cæteris
              <lb/>
            ipſis parallelis in figuris, QRY, ΖΩΔ, ſic productis, & </s>
            <s xml:id="echoid-s12754" xml:space="preserve">omnium
              <lb/>
            termini ſint in lineis, YXR, Δ℟Ω, hæ verò lineæ, ſicut & </s>
            <s xml:id="echoid-s12755" xml:space="preserve">reliqua-
              <lb/>
            rum figurarum eodem modo producibilium, ſint in ſuperficiebus,
              <lb/>
              <note position="left" xlink:label="note-0520-01" xlink:href="note-0520-01a" xml:space="preserve">Ex antec.</note>
            PYR, PYXR. </s>
            <s xml:id="echoid-s12756" xml:space="preserve">Manifeſtum eſt autem figuras, MEGF, MDGE, M
              <lb/>
            CGD, eſſe æqualiter analogas, & </s>
            <s xml:id="echoid-s12757" xml:space="preserve">ideò inter ſe æquales, ſicut etiã
              <lb/>
            figuræ, NSTV, NOTS, NBTO, pariter inter ſe ſunt æquales, & </s>
            <s xml:id="echoid-s12758" xml:space="preserve">
              <lb/>
            quecunq; </s>
            <s xml:id="echoid-s12759" xml:space="preserve">aliæ ſunt in eodem plano, ex quo habemus etiam ſoli-
              <lb/>
            da, AMEGF, AMDGE, AMCGD, eſſe æqualiter analoga, & </s>
            <s xml:id="echoid-s12760" xml:space="preserve">ideò
              <lb/>
            interſe æqualia. </s>
            <s xml:id="echoid-s12761" xml:space="preserve">Eodem modo oſtendemus ſolida, PQRY, PRX
              <lb/>
            Y, pariter inter ſe æqualia eſſe. </s>
            <s xml:id="echoid-s12762" xml:space="preserve">Quotupiex eſt ergo ſolidum, AM
              <lb/>
            CGF, extribus, AMCGD, AMDGE, AMEGF, compoſitum, to-
              <lb/>
            tuplex eſt figura, MCGF, ex tribus, MCGD, MDGE, MEGF, cõ-
              <lb/>
            poſita, figuræ, MEGF. </s>
            <s xml:id="echoid-s12763" xml:space="preserve">Similiter quotuplex eſt ſolidum, PQRX,
              <lb/>
            ex duobus, PQRY, PYRX, compoſitum ipſius, PQRY, totuplex
              <lb/>
            eſt baſis, QRX, ex duabus, QRY, YRX, compoſita, fig. </s>
            <s xml:id="echoid-s12764" xml:space="preserve">QRY; </s>
            <s xml:id="echoid-s12765" xml:space="preserve">ita
              <lb/>
            vt habeamus æquè multiplices primæ, & </s>
            <s xml:id="echoid-s12766" xml:space="preserve">tertiæ, necnon ſecundę,
              <lb/>
            & </s>
            <s xml:id="echoid-s12767" xml:space="preserve">quartę magnitudinis. </s>
            <s xml:id="echoid-s12768" xml:space="preserve">Cum autem figuræ, FMCG, VNBT,
              <lb/>
            ſint æquè multiplices figurarum, MEGF, NSTV, & </s>
            <s xml:id="echoid-s12769" xml:space="preserve">pariter figu-
              <lb/>
            ræ, QRX, ΖΩ℟, ſint æquè multiplices figurarum, QRY, </s>
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