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

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            <s xml:id="echoid-s1318" xml:space="preserve">
              <pb o="51" file="0071" n="71" rhead="LIBER I."/>
            tera proportionalia, ideòtriang. </s>
            <s xml:id="echoid-s1319" xml:space="preserve">HAB, NMT, ſuntæquiangun,
              <lb/>
              <note position="right" xlink:label="note-0071-01" xlink:href="note-0071-01a" xml:space="preserve">6. Sexei
                <lb/>
              Elem.</note>
            & </s>
            <s xml:id="echoid-s1320" xml:space="preserve">anguli, AHB, MNT; </s>
            <s xml:id="echoid-s1321" xml:space="preserve">ABH, MTN, interſe ęquales, ergo
              <lb/>
            cum anguli, AHG, MNO, ſint æquales, reliqui, BHG, TN
              <lb/>
            O, erunt æquales, ſunt etiam æquales anguli, HGB, NOT, ergo
              <lb/>
            trianguli, HBG, NTO, ſunt æquianguli, ergo, BG, ad, GH,
              <lb/>
            erit vt, TO, ad, ON, erat autem, FH, ad, GB, vt, QN, ad, O
              <lb/>
            T, ergo ex ęquali, FH, ad, HG, erit vt, QN, ad, NO, ſunt@gi-
              <lb/>
            tur ipiæ, HF, NQ, ſimiliter diuiſæ, & </s>
            <s xml:id="echoid-s1322" xml:space="preserve">ad eandem partem in pun-
              <lb/>
            ctis, G, O, & </s>
            <s xml:id="echoid-s1323" xml:space="preserve">ipſæ diuidentes, BG, TO, ſunt vt ipſæ, HF, NQ.</s>
            <s xml:id="echoid-s1324" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1325" xml:space="preserve">Ducantur nunc inter dictas oppoſitas tangentes elſdem parallelæ
              <lb/>
            duæ v@cumque, VK, XY, inter circuitum figurarum iam propoſi-
              <lb/>
            tarum, & </s>
            <s xml:id="echoid-s1326" xml:space="preserve">rectas, HF, NQ, comprehenſę, ſimiliter ad eandem par-
              <lb/>
            tem diu@dentes ipſas, HF, NQ, in punctis, K, Y, ſecanteſque ip-
              <lb/>
            ſas, BE, TP, in punctis, 3, 4, eſt ergo, FK, ad, QY, permutan-
              <lb/>
            do, vt, HF, ad, QN, ideſt vt, FE, ad, QP, ergo, FK, ad, Q
              <lb/>
            Y, erit vt, FE, ad, QP, & </s>
            <s xml:id="echoid-s1327" xml:space="preserve">reliqua, EK, ad reliquam, PY, vt, F
              <lb/>
            K, ad, QY, ideſt vt, FH, ad, QN; </s>
            <s xml:id="echoid-s1328" xml:space="preserve">Similiter oſtendenius, vt, F
              <lb/>
            H, ad, QN, ſic eſſe, GK, ad, OY, ergo, GK, ad, OY, erit vt,
              <lb/>
            KE, ad, YP, &</s>
            <s xml:id="echoid-s1329" xml:space="preserve">, permutando, GK, ad, KE, erit vt, OY, ad, Y
              <lb/>
            P, componendoque, GE, ad, FK, erit vt, OP, ad, PY, eſt verò,
              <lb/>
            vt, GE, ad, EK, ita, BG, ad, 3K, & </s>
            <s xml:id="echoid-s1330" xml:space="preserve">vt, OP, ad, PY, ita, T
              <lb/>
            O, ad, Y4, ergo, BG, ad, 3K, erit vt, TO, ad, Y4, & </s>
            <s xml:id="echoid-s1331" xml:space="preserve">permu-
              <lb/>
            tando, BG, ad, TO, erit vt, 3K, ad, 4Y, eſt verò vt, BG, ad, T
              <lb/>
            O, ita, HF, ad, NQ, ergo, 3K, ad, 4Y, erit vt, HF, ad, NQ,
              <lb/>
            ſimiliter, quia ipſæ, VK, XY, diuidunt ſimiliter ad eandem partem
              <lb/>
            ipſas, BC, TS, in punctis, V, X, ac diuiduntur ipſę, GE, OP, in
              <lb/>
            punctis, K, Y, ideò eodem modo oſtendemus ipſas, V3, X4, eſſe
              <lb/>
            vt ipſas, CE, SP, ideſt vt ipſas, HF, NQ, erant autem, 3K, 4
              <lb/>
            X, vt ipſæ, HF, NQ, ergo totæ, VK, XY, erunt vt ipiæ, HF,
              <lb/>
            NQ, habemus igitur figuras, ADE, MRP, in quibus ductę ſunt
              <lb/>
            oppoſitæ tangentes, AH, DF, MN, RQ, quibus inciderunt ip-
              <lb/>
            ſæ, HF, NQ, ad eundem angulum ex eadem parte, inuentum eſt
              <lb/>
            autem eas, quæ inter dictas, HF, NQ, & </s>
            <s xml:id="echoid-s1332" xml:space="preserve">circuitum figurarum ei-
              <lb/>
            ſdem tangentibus vtcumq; </s>
            <s xml:id="echoid-s1333" xml:space="preserve">ducuntur ęquidiſtantes, & </s>
            <s xml:id="echoid-s1334" xml:space="preserve">ſecant dictas,
              <lb/>
            HF, NQ, ſimiliter ad eandem partem, eodem ordine ſumptas, eſſe
              <lb/>
            vt ipſas, HF, NQ, ergo figuræ, ADE, MRP, quæ erant ſimi-
              <lb/>
            les iuxta definitionem Euclidis, erunt etiam ſimiles iuxta definitio-
              <lb/>
            nem meam, & </s>
            <s xml:id="echoid-s1335" xml:space="preserve">erunt dictæ tangentes regulæ homologarum earum-
              <lb/>
              <note position="right" xlink:label="note-0071-02" xlink:href="note-0071-02a" xml:space="preserve">Deſin. 10,
                <lb/>
              huius.</note>
            dem, & </s>
            <s xml:id="echoid-s1336" xml:space="preserve">ipſarum, ac dictarum ſimilium figurarum incidentes ipſę, H
              <lb/>
            F, NQ, quod erat oſtendendum.</s>
            <s xml:id="echoid-s1337" xml:space="preserve"/>
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