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

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            <s xml:id="echoid-s12514" xml:space="preserve">
              <pb o="489" file="0509" n="509" rhead="LIBER VII."/>
            adæquari. </s>
            <s xml:id="echoid-s12515" xml:space="preserve">Nunc aſſumpto trilineo, ECG, & </s>
            <s xml:id="echoid-s12516" xml:space="preserve">poſito, C, in, D, &</s>
            <s xml:id="echoid-s12517" xml:space="preserve">,
              <lb/>
            CG, in, DH, cadet, G, in, H, quia, CG, DH, ſunt æquales, ca-
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            dente verò trilineo, ECG, ſuper, FDH, extendetur, CE, ſuper, D
              <lb/>
            F, cum angulus, FDH, exterior fit æqualis interiori, ECG; </s>
            <s xml:id="echoid-s12518" xml:space="preserve">paral-
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            lelarum, DH, CG, & </s>
            <s xml:id="echoid-s12519" xml:space="preserve">punctum, E, erit in, F, ambituſque, ENG,
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            cadet ſuper ambitum, FOH, ſi enim non, eſto quod aliquod pun-
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            ctum ambitus, ENG, non cadat ſuper, FOH, cadet ergo, vel extra
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            trilineum, FDH, vel intra, cadat extra, vt in, R, ita vt ambitus, E
              <lb/>
            NGH, cadat vt, FRH, erit ergo, MR, maior, MO, ſed, MR, eſt
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            æqualis, LN, ergo, LN, erit maior, MO, ſed eſt etiam æqualis ei-
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            dem, MO, ex demonſtratis, ergo eſſet æqualis, & </s>
            <s xml:id="echoid-s12520" xml:space="preserve">maior eadem,
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            MO, quod eſt abſurdum, non ergo aliquod punctum ambitus, EN
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            G, cadit extra trilineum, FDH, eodem modo probabitur, nec ca-
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            dere intra eundem trilineum, ergo ambitus, ENG, cadet ſuper am-
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            bitum, FOH, congruens totus toti, & </s>
            <s xml:id="echoid-s12521" xml:space="preserve">conſequenter etiam trili-
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            neus, ECG, congruet trilineo, FDH, & </s>
            <s xml:id="echoid-s12522" xml:space="preserve">illi æqualis erit, vnde abla-
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            to communi trilineo, DIE, & </s>
            <s xml:id="echoid-s12523" xml:space="preserve">addito communi trilineo, GIH, fiet,
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            EGHF, figura æqualis parallelogrammo, CH. </s>
            <s xml:id="echoid-s12524" xml:space="preserve">Eodem modo
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            oſtendemus figuram, AGHB, æquari eidem, CH, ergo figuræ, A
              <lb/>
            GHB, EGHF, inter ſe æquales erunt. </s>
            <s xml:id="echoid-s12525" xml:space="preserve">Cum autem dictæ figuræ
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            fuerint in æqualibus baſibus, tum conſtituentes ſuper vnamquãq;
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            </s>
            <s xml:id="echoid-s12526" xml:space="preserve">parallelogrammum in eiſdem parallelis cum ijidem poſitum, con-
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            cludemus etiam dictas figuras æquales eſſe, probantes eodem mo-
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            do deſcriptis parallelogrammis adæquari, quę quidem inter ſe erũt
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            æqualia, quod demonſtrare opus erat. </s>
            <s xml:id="echoid-s12527" xml:space="preserve">Hæcautem vocentur pa-
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            rallelogramma curuilinea, cum, AG, BH, EG, FH, fuerint curuæ
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            lineæ, cum verò fuerint rectæ lineæ, parallelogramma rectilinea
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            ad illorum differentiam eadem appeliabimus, ſed vtraq; </s>
            <s xml:id="echoid-s12528" xml:space="preserve">in gene-
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            re, ſi libuerit, nomine parallelogrammi tantum ctiam nuncupa-
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            bimus.</s>
            <s xml:id="echoid-s12529" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1141" type="section" level="1" n="684">
          <head xml:id="echoid-head717" xml:space="preserve">LEMMA II.</head>
          <p>
            <s xml:id="echoid-s12530" xml:space="preserve">SI in æqualibus rectis lineis, tamqũam in baſibus, & </s>
            <s xml:id="echoid-s12531" xml:space="preserve">iu
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            eiſdem parallelis, fuerint quæcunq; </s>
            <s xml:id="echoid-s12532" xml:space="preserve">planæ figuræ, æ-
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            qualiter analogæ iuxta dictas baſes; </s>
            <s xml:id="echoid-s12533" xml:space="preserve">portiones autem æ-
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            quidiſtantium quotcunq; </s>
            <s xml:id="echoid-s12534" xml:space="preserve">ipſis baſibus linearum in figuris
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            conceptæ integræ fuerint, ac in altera dictarum figurarum
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            ſic ſe habentes, vt quælibet propinquior baſi ſit maior re-
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            motiori, dictæ figuræ interſe æquales erunt.</s>
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