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

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          <pb o="50" file="0070" n="70" rhead="GEOMETRIÆ"/>
          <p>
            <s xml:id="echoid-s1286" xml:space="preserve">Sint duæ vtcumque figuræ rectilineæ, ABDEH, MTRPN;
              <lb/>
            </s>
            <s xml:id="echoid-s1287" xml:space="preserve">
              <note position="left" xlink:label="note-0070-01" xlink:href="note-0070-01a" xml:space="preserve">Prima
                <lb/>
              Def. Sex-
                <lb/>
              ti Elem.</note>
            ſimiles iuxta definitionem E@clidis, ideſt ſingulos habentes angulos
              <lb/>
            æquales, A, M; </s>
            <s xml:id="echoid-s1288" xml:space="preserve">B, T; </s>
            <s xml:id="echoid-s1289" xml:space="preserve">D, R; </s>
            <s xml:id="echoid-s1290" xml:space="preserve">P, E; </s>
            <s xml:id="echoid-s1291" xml:space="preserve">HN, & </s>
            <s xml:id="echoid-s1292" xml:space="preserve">circa æquales angu-
              <lb/>
            los latera proportionalia. </s>
            <s xml:id="echoid-s1293" xml:space="preserve">Dico eaidem eſſe ſimiles iuxta meam de-
              <lb/>
            finitionem: </s>
            <s xml:id="echoid-s1294" xml:space="preserve">Ducantur duæ vtcum que oppoſitæ earum tangentes,
              <lb/>
            quæ cum duobus ex lateribus homologis earumdem angulos æqua-
              <lb/>
            les ab eadem parte contineant, ſint autem ex vna parte tangentes
              <lb/>
            ipſæ, AH, MN, quæ cum ipſis, HE, NP, lateribus homologis
              <lb/>
            angulos continent ęquales, AHG, MNO, & </s>
            <s xml:id="echoid-s1295" xml:space="preserve">ſint ex alia parte tan-
              <lb/>
            gentes ipſæ, DF, RQ, quæ cum ipſis, HE, NP, productis con-
              <lb/>
              <figure xlink:label="fig-0070-01" xlink:href="fig-0070-01a" number="35">
                <image file="0070-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0070-01"/>
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            currant in punctis, F, Q, ducantur deinde à
              <lb/>
            punctis angulorum, qui ſunt, B, E; </s>
            <s xml:id="echoid-s1296" xml:space="preserve">TP, di-
              <lb/>
            ctis tangentibus parallelæ, BG, CE, TO, S
              <lb/>
            P, & </s>
            <s xml:id="echoid-s1297" xml:space="preserve">iungantur, BH, BE, TN, TP. </s>
            <s xml:id="echoid-s1298" xml:space="preserve">Quia
              <lb/>
            ergo anguli, MNQ, AHF, ſunt æquales,
              <lb/>
            etiam anguli, NQR, HFD, erunt ęquales,
              <lb/>
            & </s>
            <s xml:id="echoid-s1299" xml:space="preserve">quia anguli, NPR, HED, ſunt quoque
              <lb/>
            æquales, etiam anguli, RPQ, DEF, erunt
              <lb/>
            æquales, & </s>
            <s xml:id="echoid-s1300" xml:space="preserve">reliqu reliquis, vnde trianguli, R
              <lb/>
            PQ, DEF, erunt æquianguli, & </s>
            <s xml:id="echoid-s1301" xml:space="preserve">ideò, QP,
              <lb/>
              <note position="left" xlink:label="note-0070-02" xlink:href="note-0070-02a" xml:space="preserve">4. Sexti
                <lb/>
              Elem.</note>
            ad, PR, erit vt, FE, ad, ED, eſt autem, R
              <lb/>
            P, ad, PN, vt, DE, ad, EH, ergo, ex ęquali,
              <lb/>
              <note position="left" xlink:label="note-0070-03" xlink:href="note-0070-03a" xml:space="preserve">Ex Defin.
                <lb/>
              Eucl.</note>
            QP, ad, PN, erit vt, FE, ad, EH, igitur,
              <lb/>
            NQ, HF, ſunt ſimiliter ad eandem partem
              <lb/>
            diuiſæ in punctis, E, P, quia verò angulus, NPS, æquatur angu-
              <lb/>
            lo, NQR.</s>
            <s xml:id="echoid-s1302" xml:space="preserve">. HFD.</s>
            <s xml:id="echoid-s1303" xml:space="preserve">. HEC, &</s>
            <s xml:id="echoid-s1304" xml:space="preserve">, NPR, ipſi, HED, ideo reli-
              <lb/>
            quus, SPR, æquabitur reliquo, CED, eſt autem angulus, TR
              <lb/>
            P, ęqualis angulo, BDE, ergo trianguli, PSR, ECD, erunt æ-
              <lb/>
            quianguli, & </s>
            <s xml:id="echoid-s1305" xml:space="preserve">ideò, CE, ad, ED, erit vt, SP, ad, PR, &</s>
            <s xml:id="echoid-s1306" xml:space="preserve">, ED,
              <lb/>
            ad, EF, erit vt, RP, ad, PQ; </s>
            <s xml:id="echoid-s1307" xml:space="preserve">ergo ex æquali, & </s>
            <s xml:id="echoid-s1308" xml:space="preserve">permutando, C
              <lb/>
            E, ad, SP, erit vt, EF, ad, PQ .</s>
            <s xml:id="echoid-s1309" xml:space="preserve">i. </s>
            <s xml:id="echoid-s1310" xml:space="preserve">vt, HF, ad, NQ. </s>
            <s xml:id="echoid-s1311" xml:space="preserve">S militer
              <lb/>
              <note position="left" xlink:label="note-0070-04" xlink:href="note-0070-04a" xml:space="preserve">6. Sexti
                <lb/>
              Elem.</note>
            quia anguli, BDE, TRP, ſunt æquales, & </s>
            <s xml:id="echoid-s1312" xml:space="preserve">circa eos latera ſunt
              <lb/>
            proportionalia, ideò trianguli, BDE, TRP, erunt æquianguli,
              <lb/>
            vnde anguli, DBE, RTP, &</s>
            <s xml:id="echoid-s1313" xml:space="preserve">, BED, TPR, erunt ęquales, ſunt
              <lb/>
            autem ęquales ipſi, CED, SPR, ergo reliqui, BEC, TPS, erunt
              <lb/>
            æquales, & </s>
            <s xml:id="echoid-s1314" xml:space="preserve">ideò trianguli, BCE, TSP, erunt ęquianguli, & </s>
            <s xml:id="echoid-s1315" xml:space="preserve">quia
              <lb/>
            angulus, BEF, eſt ęqualis ipſi, TPQ, reliquns, BEH, erit ęqua-
              <lb/>
            lis reliquo, TPN, eſt autem, BGE, ęqual sipſi, TOP, ergo trian-
              <lb/>
            guli, BGE, TOP, erunt ęquianguli, ergo, BG, ad, TO, erit vt,
              <lb/>
            BE, ad, TP, ideſt vt, CE, ad, SP, ideſt vt, HF, ad, NQ, per-
              <lb/>
            mucando, & </s>
            <s xml:id="echoid-s1316" xml:space="preserve">conuertendo, HF, ad, GB, erit vt, NQ, ad, OT;
              <lb/>
            </s>
            <s xml:id="echoid-s1317" xml:space="preserve">quia verò anguli, HAB, NMT, ſunt ęquales, & </s>
            <s xml:id="echoid-s1318" xml:space="preserve">circa eoſdem </s>
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