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

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            <s xml:id="echoid-s12609" xml:space="preserve">
              <pb o="494" file="0514" n="514" rhead="GEOMETRIÆ"/>
            in ambitu, ANE, vel enim tanget in linea, aut lineis, vel in pun-
              <lb/>
            ctis, & </s>
            <s xml:id="echoid-s12610" xml:space="preserve">lineis, vel tantum in punctis, eſto quod fiat contactus in re-
              <lb/>
            cta, LM, & </s>
            <s xml:id="echoid-s12611" xml:space="preserve">in puncto, N, tranſeantq; </s>
            <s xml:id="echoid-s12612" xml:space="preserve">per puncta, L, M, N, rectæ
              <lb/>
            lineæ regulæ, FE, parallelæ, HD, QC, PB, ſecantes ambitum fi-
              <lb/>
            guræ, SPFR, in punctis, P, Q, H, I, O, R, & </s>
            <s xml:id="echoid-s12613" xml:space="preserve">rectam, AE, in pun-
              <lb/>
              <figure xlink:label="fig-0514-01" xlink:href="fig-0514-01a" number="344">
                <image file="0514-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0514-01"/>
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            ctis, B, C, D, nulluſque alius
              <lb/>
            factus fuerit contactus in am-
              <lb/>
            bitu, ANMLE. </s>
            <s xml:id="echoid-s12614" xml:space="preserve">Quoniam er-
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            go a puncto, N, ad, A, nullus
              <lb/>
            datur contactus, erit, ANB, fi-
              <lb/>
            gura in alteram partem, nem-
              <lb/>
            pè verſus, A, deficiens, hoc eſt
              <lb/>
            quælibet in figura, ANB, pa-
              <lb/>
            rallela, NB, erit maior remo-
              <lb/>
            tiori, ſi enim non, eſto quod
              <lb/>
            aliqua vt, YT, non ſit maior remotiori, XV, ad ambitum termina-
              <lb/>
            ta, vel ergo erit illi æqualis, vel eadem maior, ſit illi æqualis, & </s>
            <s xml:id="echoid-s12615" xml:space="preserve">
              <lb/>
            iungatur, YX, hæc ergo erit paralſela, AE, & </s>
            <s xml:id="echoid-s12616" xml:space="preserve">occurrit ambitui in
              <lb/>
            duobus punctis, Y, X, ergo poſſibile erit ducere rectam lineam ipſi,
              <lb/>
            YX, ſeu, AE, parallelam, tangentem portionem curuæ lineæ, hoc
              <lb/>
              <note position="left" xlink:label="note-0514-01" xlink:href="note-0514-01a" xml:space="preserve">Ex antec.
                <lb/>
              Lem.</note>
            eſt ambitus, AN, inter duos occurſus, Y, X, continuatam, quod
              <lb/>
            eſt contra ſuppoſitum: </s>
            <s xml:id="echoid-s12617" xml:space="preserve">quod ſi dicatur, YT, eſſe minorem, XV,
              <lb/>
            multò magis conuincetur præfatum abſurdum, ergo, YT, erit ma-
              <lb/>
            ior, XV, & </s>
            <s xml:id="echoid-s12618" xml:space="preserve">quælibet, NB, propinquior remotiore maior, ergo fi-
              <lb/>
            gura, ANB, erit in alteram partem deficiens: </s>
            <s xml:id="echoid-s12619" xml:space="preserve">eodem modo autem
              <lb/>
            oſtendemus etiam, NMCB, LED, eſſe figuras in alteram partem
              <lb/>
            deficientes, LMCD, autem manifeſtum eſt eſſe parallelogrammũ
              <lb/>
            rectilineum, ergo in figura, SPFR, ipſa, SPR, quæ eſt æqualiter
              <lb/>
            analoga ipſi, ANB, erit figura in alteram partem deficiens, ſic etiã,
              <lb/>
            PQOR, HFI, QHIO, verò erit paralle@ @grammum rectilineum,
              <lb/>
            ſeu curuilineum, prout, QH, OI, rectæ, vel curuæ, eſſe poſſunt,
              <lb/>
            ergo figura, SPFR, componitur ex figuris in alteram partem defi-
              <lb/>
            cientibus, ac ex parallelogrammo rectilineo, ſeu curuilineo, re-
              <lb/>
            gula, FE, quod oſtendere opus erat.</s>
            <s xml:id="echoid-s12620" xml:space="preserve"/>
          </p>
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          <head xml:id="echoid-head722" xml:space="preserve">COROLLARIVM.</head>
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            <s xml:id="echoid-s12621" xml:space="preserve">_H_Inc habetur figuram, SPFR, ipſi, ANE, æqualem eſſe, & </s>
            <s xml:id="echoid-s12622" xml:space="preserve">vni-
              <lb/>
            uerſaliter figuras planas æqualit er analogas, in quibus earum
              <lb/>
            regula æquidiſtantium quotcunq; </s>
            <s xml:id="echoid-s12623" xml:space="preserve">linearum concepta portiones inte-
              <lb/>
            graſunt, inter ſe æquales eſſe.</s>
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