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

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            <s xml:id="echoid-s1255" xml:space="preserve">
              <pb o="49" file="0069" n="69" rhead="LIBER I."/>
            quadrata, AE, EG, (quia etiam, AEG, rectus eſt) æquabuntur
              <lb/>
            tribus quadratis, AE, EF, FG, vnde, ablato communiquadrato,
              <lb/>
              <note position="right" xlink:label="note-0069-01" xlink:href="note-0069-01a" xml:space="preserve">48. Primi
                <lb/>
              El. Def. 6.</note>
            AE, quadratum, GE, ęquabitur duobus quadratis, GF, FE; </s>
            <s xml:id="echoid-s1256" xml:space="preserve">pari
              <lb/>
            ratione autem probabimus quadratum, YT, æquari quadratis, Y
              <lb/>
              <note position="right" xlink:label="note-0069-02" xlink:href="note-0069-02a" xml:space="preserve">Vndec.</note>
            Z, ZT, vnde anguli, GFE, YZT, recti erunt; </s>
            <s xml:id="echoid-s1257" xml:space="preserve">& </s>
            <s xml:id="echoid-s1258" xml:space="preserve">eodem modo
              <lb/>
              <note position="right" xlink:label="note-0069-03" xlink:href="note-0069-03a" xml:space="preserve">Elem.</note>
            probabimus eſſe rectos, EPG, TXY, ergo anguli, AFE, KZT,
              <lb/>
              <note position="right" xlink:label="note-0069-04" xlink:href="note-0069-04a" xml:space="preserve">Defin. 6.
                <lb/>
              Vnd. El.</note>
            erunt anguli inclinationis primorum planorum, BG, LY, cum iu-
              <lb/>
            biectis planis, HV, & </s>
            <s xml:id="echoid-s1259" xml:space="preserve">Λ, & </s>
            <s xml:id="echoid-s1260" xml:space="preserve">ideò inter ſe æquales: </s>
            <s xml:id="echoid-s1261" xml:space="preserve">Similiter anguli,
              <lb/>
            APE, KXT, erunt inclinationes ſecundorum planorum, AV, K
              <lb/>
            Λ, cum eiſdem ſubiectis planis. </s>
            <s xml:id="echoid-s1262" xml:space="preserve">Quia ergo anguli, AFE, KZT,
              <lb/>
            ſunt æquales, &</s>
            <s xml:id="echoid-s1263" xml:space="preserve">, AEF, KTZ, recti, erunt triangula, AFE, K
              <lb/>
            ZT, inter ſe ſimilia, vt etiam triangula, AFG, KZY, inter ſe,
              <lb/>
            nam anguli, AGF, KYZ, ſunt quoque æquales, &</s>
            <s xml:id="echoid-s1264" xml:space="preserve">, AFG, KZ
              <lb/>
            Y, recti; </s>
            <s xml:id="echoid-s1265" xml:space="preserve">erit ergo, vt, EF, ad, FA, ſic, TZ, ad, ZK, & </s>
            <s xml:id="echoid-s1266" xml:space="preserve">vt, A
              <lb/>
            F, ad, FG, ſic, KZ, ad, ZY, ergo ex æquali, vt, EF, ad, FG,
              <lb/>
            itaerit, TZ, ad, ZY, & </s>
            <s xml:id="echoid-s1267" xml:space="preserve">ſunt circa rectos, nempè æquales angu-
              <lb/>
              <note position="right" xlink:label="note-0069-05" xlink:href="note-0069-05a" xml:space="preserve">6. Sexti
                <lb/>
              Elem.</note>
            los, GFE, YZT, ergo triangula, GFE, YZT, pariter ſimilia
              <lb/>
            erunt, anguli igitur, EGF, TYZ, adæquabuntur, totus autem,
              <lb/>
            PGF, toti, XYZ, æquatur, ergo reliquus, EGP, erit ęqualis re-
              <lb/>
            liquo, TYX, & </s>
            <s xml:id="echoid-s1268" xml:space="preserve">ſunt recti, EPG, TXY, vt probatum eſt, ergo
              <lb/>
            erunt, GPE, YXT, ſimilia triangula, igitur, vt, PG, ad, GE,
              <lb/>
            ſic erit, XY, ad, YT, vt verò, GE, ad, GF, ſic eſt, YT, ad, YZ,
              <lb/>
            & </s>
            <s xml:id="echoid-s1269" xml:space="preserve">vt, GF, ad, GA, ſic, YZ, ad, YK, ergo ex æquali, PG, ad,
              <lb/>
            GA, erit vt, XY, ad, YK, habemus ergo duo triangula, APG,
              <lb/>
            KXY, habentia duos angulos, APG, KXY, ęquales, ſunt. </s>
            <s xml:id="echoid-s1270" xml:space="preserve">n. </s>
            <s xml:id="echoid-s1271" xml:space="preserve">re-
              <lb/>
            cti, circa verò duos, PGA, XYK, latera proportionalia, & </s>
            <s xml:id="echoid-s1272" xml:space="preserve">reli-
              <lb/>
            quorum vtrumq; </s>
            <s xml:id="echoid-s1273" xml:space="preserve">ſimul, PAG, XKY, minorem recto, ergo erunt
              <lb/>
              <note position="right" xlink:label="note-0069-06" xlink:href="note-0069-06a" xml:space="preserve">7. Sexti
                <lb/>
              Elem.</note>
            ſimilia, & </s>
            <s xml:id="echoid-s1274" xml:space="preserve">anguli, PGA, XYK, ęquales, vnde reliqui, AGV, Κ
              <lb/>
            Υ Λ, pariter æquales erunt, quod eſt vnum propoſitorum.</s>
            <s xml:id="echoid-s1275" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1276" xml:space="preserve">Rurſus, quia, PE, ad, EF, eſt vt, XT, ad, TZ; </s>
            <s xml:id="echoid-s1277" xml:space="preserve">EF, autem
              <lb/>
            ad, EA, vt, TZ, ad, TK, ergo ex æquali, PE, ad, EA, erit vt,
              <lb/>
            XT, ad; </s>
            <s xml:id="echoid-s1278" xml:space="preserve">TK, & </s>
            <s xml:id="echoid-s1279" xml:space="preserve">ſunt circa ęquales angulos, PEA, XTK, latera
              <lb/>
              <note position="right" xlink:label="note-0069-07" xlink:href="note-0069-07a" xml:space="preserve">6. Sexti
                <lb/>
              Elem.</note>
            proportionalia, ergo triangula, APE, KXT, ſimil a erunt, nec-
              <lb/>
            non anguli, APE, KXT, inclinationis ſecundorum planorum, A
              <lb/>
            V, Κ Λ, cum ſubiectis planis inter ſe æquales, & </s>
            <s xml:id="echoid-s1280" xml:space="preserve">ad eandem partem
              <lb/>
            quod etiam demonſtrare propoſitum fuit.</s>
            <s xml:id="echoid-s1281" xml:space="preserve"/>
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        </div>
        <div xml:id="echoid-div147" type="section" level="1" n="100">
          <head xml:id="echoid-head111" xml:space="preserve">THEOREMA XXIV. PROPOS XXVII.</head>
          <p>
            <s xml:id="echoid-s1282" xml:space="preserve">POſita definitione, quam affert Euclides lib 6. </s>
            <s xml:id="echoid-s1283" xml:space="preserve">El. </s>
            <s xml:id="echoid-s1284" xml:space="preserve">de ſimi-
              <lb/>
            libus figuris rectilineis, ſequitur pro ipſis etiam defini-
              <lb/>
            tio geneneralis, quam de omnibus ſimilibus figuris planis
              <lb/>
            ipſe attuli.</s>
            <s xml:id="echoid-s1285" xml:space="preserve"/>
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