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

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              <pb o="117" file="0137" n="137" rhead="LIBER II."/>
            conſequentium, iuxta quæ, tanquam regulas, dictæ omnes lineæ, vel
              <lb/>
            omnia plana intelliguntur aſſumpta.</s>
            <s xml:id="echoid-s2765" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div286" type="section" level="1" n="181">
          <head xml:id="echoid-head196" xml:space="preserve">THEOREMA V. PROPOS. V.</head>
          <p>
            <s xml:id="echoid-s2766" xml:space="preserve">PArallelogramma in eadem altitudine exiſtentia inter ſe
              <lb/>
            ſunt, vt baſes; </s>
            <s xml:id="echoid-s2767" xml:space="preserve">& </s>
            <s xml:id="echoid-s2768" xml:space="preserve">quę in eadem baſi, vt altitudines, vel,
              <lb/>
            vt latera æqualiter baſibus inclinata.</s>
            <s xml:id="echoid-s2769" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2770" xml:space="preserve">Sint parallelogramma quæcunque, AM, MC, in eadem altitu-
              <lb/>
            dine conftituta, ſumpta altitudine iuxta baſes, GM, MH. </s>
            <s xml:id="echoid-s2771" xml:space="preserve">Dico
              <lb/>
            parallelogrammum, AM, ad parallelogrammum, MC, eſſe vt, G
              <lb/>
            M, ad, MH. </s>
            <s xml:id="echoid-s2772" xml:space="preserve">Ducatur quęcunq; </s>
            <s xml:id="echoid-s2773" xml:space="preserve">intra parallelogramma, AM, M
              <lb/>
              <figure xlink:label="fig-0137-01" xlink:href="fig-0137-01a" number="77">
                <image file="0137-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0137-01"/>
              </figure>
            C, parallela ipſis, GM, MH, cu-
              <lb/>
            ius portiones parallelogrammis,
              <lb/>
            AM, MC, interceptę ſint, DE,
              <lb/>
            EI. </s>
            <s xml:id="echoid-s2774" xml:space="preserve">Quoniam ergo, DM, eſt
              <lb/>
            parallelogrammum, ſicut &</s>
            <s xml:id="echoid-s2775" xml:space="preserve">, E
              <lb/>
            H, erit, DE, ęqualis ipſi, GM,
              <lb/>
            &</s>
            <s xml:id="echoid-s2776" xml:space="preserve">, EI, ipſi, MH, erit igitur, G
              <lb/>
            M, ad, MH, vt, DE, ad, EI, & </s>
            <s xml:id="echoid-s2777" xml:space="preserve">DE, EI, ductæ ſunt vtcunq;
              <lb/>
            </s>
            <s xml:id="echoid-s2778" xml:space="preserve">parallelæ ipſis, GM, MH, ergo parallelogramma, AM, MC, e-
              <lb/>
            runt ex genere figurarum Theorematis anteced. </s>
            <s xml:id="echoid-s2779" xml:space="preserve">ergo, AM, ad, M
              <lb/>
            C, erit vt, DE, ad, EI, vel vt, GM, ad, MH, quæ ſunt eorun-
              <lb/>
            dem baſes. </s>
            <s xml:id="echoid-s2780" xml:space="preserve">Hæc autem verificabuntur etiam ſi altitudines æquales
              <lb/>
            fuerint, vt facilè patet.</s>
            <s xml:id="echoid-s2781" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2782" xml:space="preserve">Sint nunc parallelogramma, QP, LP, in eadem baſi, NP, con-
              <lb/>
            ſtituta. </s>
            <s xml:id="echoid-s2783" xml:space="preserve">Dico eadem eſſe, vt altitudines ſumptæ iuxta baſim, NP,
              <lb/>
            demittantur ergo, OR, TS, altitudines in, NP, productam, in
              <lb/>
            punctis, RS, illi occurrentes (niſi fortè, TP, OP, eſſent ipſæ alti-
              <lb/>
            tudines, vel intra parallelogramma inciderent baſi, NP,) & </s>
            <s xml:id="echoid-s2784" xml:space="preserve">à pun-
              <lb/>
            ctis, Q, L, illis parallelæ, QX, LV, in punctis, V, X, baſi, NP,
              <lb/>
            incidentes, ſuntigitur parallelogramma, QS, LR, in ęqualibus al-
              <lb/>
            titudinibus, QT, LO, ſumptis iuxta baſes, TS, OR, ergo paral-
              <lb/>
              <note position="right" xlink:label="note-0137-01" xlink:href="note-0137-01a" xml:space="preserve">Ex prima
                <lb/>
              parte hu-
                <lb/>
              ius Prop.</note>
            lelogramma, QS, LR, erunt inter ſe, vt baſes, TS, OR, eſt au-
              <lb/>
            tem parallelogrammum, QS, æquale parallelogrammo, QP, &</s>
            <s xml:id="echoid-s2785" xml:space="preserve">,
              <lb/>
            LR, ipſi, LP, ergo parallelogramma, QP, LP, erunt inter ſe, vt,
              <lb/>
            TS, OR, quæ pro ipſis ſunt altitudines ſumptæ iuxta baſim, NP.
              <lb/>
            </s>
            <s xml:id="echoid-s2786" xml:space="preserve">Si autem latus, OP, extenderetur ſuper latus, PT, ideſt latera, O
              <lb/>
            P, PT, eſſent ęqualiter inclinata communi baſi, NP, tunc ſumptis
              <lb/>
            pro baſibus ipſis, TP, OP, haberemus parallelogramma, QP, </s>
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