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c^2",[572,1166,1168,1215,1259,1277,1300,1322],{"className":1167,"ariaHidden":602},[601],[572,1169,1171,1175,1206,1209,1212],{"className":1170},[606],[572,1172],{"className":1173,"style":1174},[610],"height:0.8974em;vertical-align:-0.0833em;",[572,1176,1178,1181],{"className":1177},[615],[572,1179,730],{"className":1180},[615,616],[572,1182,1184],{"className":1183},[885],[572,1185,1187],{"className":1186},[889],[572,1188,1190],{"className":1189},[893],[572,1191,1194],{"className":1192,"style":1193},[897],"height:0.8141em;",[572,1195,1197,1200],{"style":1196},"top:-3.063em;margin-right:0.05em;",[572,1198],{"className":1199,"style":905},[904],[572,1201,1203],{"className":1202},[909,910,911,912],[572,1204,833],{"className":1205},[615,912],[572,1207],{"className":1208,"style":940},[846],[572,1210,1049],{"className":1211},[944],[572,1213],{"className":1214,"style":940},[846],[572,1216,1218,1221,1250,1253,1256],{"className":1217},[606],[572,1219],{"className":1220,"style":1193},[610],[572,1222,1224,1227],{"className":1223},[615],[572,1225,791],{"className":1226},[615,616],[572,1228,1230],{"className":1229},[885],[572,1231,1233],{"className":1232},[889],[572,1234,1236],{"className":1235},[893],[572,1237,1239],{"className":1238,"style":1193},[897],[572,1240,1241,1244],{"style":1196},[572,1242],{"className":1243,"style":905},[904],[572,1245,1247],{"className":1246},[909,910,911,912],[572,1248,833],{"className":1249},[615,912],[572,1251],{"className":1252,"style":919},[846],[572,1254,837],{"className":1255},[923],[572,1257],{"className":1258,"style":919},[846],[572,1260,1262,1265,1268,1271,1274],{"className":1261},[606],[572,1263],{"className":1264,"style":933},[610],[572,1266,633],{"className":1267},[615,616],[572,1269],{"className":1270,"style":940},[846],[572,1272,842],{"className":1273},[944],[572,1275],{"className":1276,"style":940},[846],[572,1278,1280,1284,1288,1291,1294,1297],{"className":1279},[606],[572,1281],{"className":1282,"style":1283},[610],"height:1em;vertical-align:-0.25em;",[572,1285,1144],{"className":1286},[1287],"mopen",[572,1289,563],{"className":1290},[615,616],[572,1292],{"className":1293,"style":940},[846],[572,1295,1049],{"className":1296},[944],[572,1298],{"className":1299,"style":940},[846],[572,1301,1303,1306,1309,1313,1316,1319],{"className":1302},[606],[572,1304],{"className":1305,"style":1283},[610],[572,1307,760],{"className":1308,"style":775},[615,616],[572,1310,1153],{"className":1311},[1312],"mclose",[572,1314],{"className":1315,"style":919},[846],[572,1317,837],{"className":1318},[923],[572,1320],{"className":1321,"style":919},[846],[572,1323,1325,1328],{"className":1324},[606],[572,1326],{"className":1327,"style":1193},[610],[572,1329,1331,1334],{"className":1330},[615],[572,1332,633],{"className":1333},[615,616],[572,1335,1337],{"className":1336},[885],[572,1338,1340],{"className":1339},[889],[572,1341,1343],{"className":1342},[893],[572,1344,1346],{"className":1345,"style":1193},[897],[572,1347,1348,1351],{"style":1196},[572,1349],{"className":1350,"style":905},[904],[572,1352,1354],{"className":1353},[909,910,911,912],[572,1355,833],{"className":1356},[615,912],". Das passt zum Satz des Pythagoras.",[558,1359,1361],{"id":1360},"herleitung","Herleitung",[563,1363,1364,1365,745,1394,1422,1423,1451,1452,1616,1617,1701],{},"Im Teildreieck mit den Seiten ",[572,1366,1368,1382],{"className":1367},[575],[572,1369,1371],{"className":1370},[579],[581,1372,1373],{"xmlns":583},[585,1374,1375,1380],{},[588,1376,1377],{},[591,1378,1379],{},"h",[595,1381,1379],{"encoding":597},[572,1383,1385],{"className":1384,"ariaHidden":602},[601],[572,1386,1388,1391],{"className":1387},[606],[572,1389],{"className":1390,"style":803},[610],[572,1392,1379],{"className":1393},[615,616],[572,1395,1397,1410],{"className":1396},[575],[572,1398,1400],{"className":1399},[579],[581,1401,1402],{"xmlns":583},[585,1403,1404,1408],{},[588,1405,1406],{},[591,1407,563],{},[595,1409,563],{"encoding":597},[572,1411,1413],{"className":1412,"ariaHidden":602},[601],[572,1414,1416,1419],{"className":1415},[606],[572,1417],{"className":1418,"style":711},[610],[572,1420,563],{"className":1421},[615,616]," und ",[572,1424,1426,1439],{"className":1425},[575],[572,1427,1429],{"className":1428},[579],[581,1430,1431],{"xmlns":583},[585,1432,1433,1437],{},[588,1434,1435],{},[591,1436,730],{},[595,1438,730],{"encoding":597},[572,1440,1442],{"className":1441,"ariaHidden":602},[601],[572,1443,1445,1448],{"className":1444},[606],[572,1446],{"className":1447,"style":645},[610],[572,1449,730],{"className":1450},[615,616]," gilt nach Pythagoras ",[572,1453,1455,1489],{"className":1454},[575],[572,1456,1458],{"className":1457},[579],[581,1459,1460],{"xmlns":583},[585,1461,1462,1486],{},[588,1463,1464,1470,1472,1478,1480],{},[826,1465,1466,1468],{},[591,1467,730],{},[831,1469,833],{},[835,1471,837],{},[826,1473,1474,1476],{},[591,1475,1379],{},[831,1477,833],{},[835,1479,1049],{},[826,1481,1482,1484],{},[591,1483,563],{},[831,1485,833],{},[595,1487,1488],{"encoding":597},"a^2 = h^2 + p^2",[572,1490,1492,1536,1580],{"className":1491,"ariaHidden":602},[601],[572,1493,1495,1498,1527,1530,1533],{"className":1494},[606],[572,1496],{"className":1497,"style":1193},[610],[572,1499,1501,1504],{"className":1500},[615],[572,1502,730],{"className":1503},[615,616],[572,1505,1507],{"className":1506},[885],[572,1508,1510],{"className":1509},[889],[572,1511,1513],{"className":1512},[893],[572,1514,1516],{"className":1515,"style":1193},[897],[572,1517,1518,1521],{"style":1196},[572,1519],{"className":1520,"style":905},[904],[572,1522,1524],{"className":1523},[909,910,911,912],[572,1525,833],{"className":1526},[615,912],[572,1528],{"className":1529,"style":919},[846],[572,1531,837],{"className":1532},[923],[572,1534],{"className":1535,"style":919},[846],[572,1537,1539,1542,1571,1574,1577],{"className":1538},[606],[572,1540],{"className":1541,"style":1174},[610],[572,1543,1545,1548],{"className":1544},[615],[572,1546,1379],{"className":1547},[615,616],[572,1549,1551],{"className":1550},[885],[572,1552,1554],{"className":1553},[889],[572,1555,1557],{"className":1556},[893],[572,1558,1560],{"className":1559,"style":1193},[897],[572,1561,1562,1565],{"style":1196},[572,1563],{"className":1564,"style":905},[904],[572,1566,1568],{"className":1567},[909,910,911,912],[572,1569,833],{"className":1570},[615,912],[572,1572],{"className":1573,"style":940},[846],[572,1575,1049],{"className":1576},[944],[572,1578],{"className":1579,"style":940},[846],[572,1581,1583,1587],{"className":1582},[606],[572,1584],{"className":1585,"style":1586},[610],"height:1.0085em;vertical-align:-0.1944em;",[572,1588,1590,1593],{"className":1589},[615],[572,1591,563],{"className":1592},[615,616],[572,1594,1596],{"className":1595},[885],[572,1597,1599],{"className":1598},[889],[572,1600,1602],{"className":1601},[893],[572,1603,1605],{"className":1604,"style":1193},[897],[572,1606,1607,1610],{"style":1196},[572,1608],{"className":1609,"style":905},[904],[572,1611,1613],{"className":1612},[909,910,911,912],[572,1614,833],{"className":1615},[615,912],". Mit dem Höhensatz ",[572,1618,1620,1644],{"className":1619},[575],[572,1621,1623],{"className":1622},[579],[581,1624,1625],{"xmlns":583},[585,1626,1627,1641],{},[588,1628,1629,1635,1637,1639],{},[826,1630,1631,1633],{},[591,1632,1379],{},[831,1634,833],{},[835,1636,837],{},[591,1638,563],{},[591,1640,760],{},[595,1642,1643],{"encoding":597},"h^2 = pq",[572,1645,1647,1691],{"className":1646,"ariaHidden":602},[601],[572,1648,1650,1653,1682,1685,1688],{"className":1649},[606],[572,1651],{"className":1652,"style":1193},[610],[572,1654,1656,1659],{"className":1655},[615],[572,1657,1379],{"className":1658},[615,616],[572,1660,1662],{"className":1661},[885],[572,1663,1665],{"className":1664},[889],[572,1666,1668],{"className":1667},[893],[572,1669,1671],{"className":1670,"style":1193},[897],[572,1672,1673,1676],{"style":1196},[572,1674],{"className":1675,"style":905},[904],[572,1677,1679],{"className":1678},[909,910,911,912],[572,1680,833],{"className":1681},[615,912],[572,1683],{"className":1684,"style":919},[846],[572,1686,837],{"className":1687},[923],[572,1689],{"className":1690,"style":919},[846],[572,1692,1694,1697],{"className":1693},[606],[572,1695],{"className":1696,"style":711},[610],[572,1698,1700],{"className":1699,"style":775},[615,616],"pq"," folgt:",[572,1703,1705],{"className":1704},[811],[572,1706,1708,1764],{"className":1707},[575],[572,1709,1711],{"className":1710},[579],[581,1712,1713],{"xmlns":583,"display":820},[585,1714,1715,1761],{},[588,1716,1717,1723,1725,1727,1729,1731,1737,1739,1741,1743,1745,1747,1749,1751,1753,1755,1757,1759],{},[826,1718,1719,1721],{},[591,1720,730],{},[831,1722,833],{},[835,1724,837],{},[591,1726,563],{},[591,1728,760],{},[835,1730,1049],{},[826,1732,1733,1735],{},[591,1734,563],{},[831,1736,833],{},[835,1738,837],{},[591,1740,563],{},[835,1742,842],{},[835,1744,1144],{"stretchy":1143},[591,1746,760],{},[835,1748,1049],{},[591,1750,563],{},[835,1752,1153],{"stretchy":1143},[835,1754,837],{},[591,1756,563],{},[835,1758,842],{},[591,1760,633],{},[595,1762,1763],{"encoding":597},"a^2 = pq + p^2 = p \\cdot (q + p) = p \\cdot c",[572,1765,1767,1811,1829,1873,1892,1913,1934,1952],{"className":1766,"ariaHidden":602},[601],[572,1768,1770,1773,1802,1805,1808],{"className":1769},[606],[572,1771],{"className":1772,"style":875},[610],[572,1774,1776,1779],{"className":1775},[615],[572,1777,730],{"className":1778},[615,616],[572,1780,1782],{"className":1781},[885],[572,1783,1785],{"className":1784},[889],[572,1786,1788],{"className":1787},[893],[572,1789,1791],{"className":1790,"style":875},[897],[572,1792,1793,1796],{"style":900},[572,1794],{"className":1795,"style":905},[904],[572,1797,1799],{"className":1798},[909,910,911,912],[572,1800,833],{"className":1801},[615,912],[572,1803],{"className":1804,"style":919},[846],[572,1806,837],{"className":1807},[923],[572,1809],{"className":1810,"style":919},[846],[572,1812,1814,1817,1820,1823,1826],{"className":1813},[606],[572,1815],{"className":1816,"style":1068},[610],[572,1818,1700],{"className":1819,"style":775},[615,616],[572,1821],{"className":1822,"style":940},[846],[572,1824,1049],{"className":1825},[944],[572,1827],{"className":1828,"style":940},[846],[572,1830,1832,1835,1864,1867,1870],{"className":1831},[606],[572,1833],{"className":1834,"style":954},[610],[572,1836,1838,1841],{"className":1837},[615],[572,1839,563],{"className":1840},[615,616],[572,1842,1844],{"className":1843},[885],[572,1845,1847],{"className":1846},[889],[572,1848,1850],{"className":1849},[893],[572,1851,1853],{"className":1852,"style":875},[897],[572,1854,1855,1858],{"style":900},[572,1856],{"className":1857,"style":905},[904],[572,1859,1861],{"className":1860},[909,910,911,912],[572,1862,833],{"className":1863},[615,912],[572,1865],{"className":1866,"style":919},[846],[572,1868,837],{"className":1869},[923],[572,1871],{"className":1872,"style":919},[846],[572,1874,1876,1880,1883,1886,1889],{"className":1875},[606],[572,1877],{"className":1878,"style":1879},[610],"height:0.6389em;vertical-align:-0.1944em;",[572,1881,563],{"className":1882},[615,616],[572,1884],{"className":1885,"style":940},[846],[572,1887,842],{"className":1888},[944],[572,1890],{"className":1891,"style":940},[846],[572,1893,1895,1898,1901,1904,1907,1910],{"className":1894},[606],[572,1896],{"className":1897,"style":1283},[610],[572,1899,1144],{"className":1900},[1287],[572,1902,760],{"className":1903,"style":775},[615,616],[572,1905],{"className":1906,"style":940},[846],[572,1908,1049],{"className":1909},[944],[572,1911],{"className":1912,"style":940},[846],[572,1914,1916,1919,1922,1925,1928,1931],{"className":1915},[606],[572,1917],{"className":1918,"style":1283},[610],[572,1920,563],{"className":1921},[615,616],[572,1923,1153],{"className":1924},[1312],[572,1926],{"className":1927,"style":919},[846],[572,1929,837],{"className":1930},[923],[572,1932],{"className":1933,"style":919},[846],[572,1935,1937,1940,1943,1946,1949],{"className":1936},[606],[572,1938],{"className":1939,"style":1879},[610],[572,1941,563],{"className":1942},[615,616],[572,1944],{"className":1945,"style":940},[846],[572,1947,842],{"className":1948},[944],[572,1950],{"className":1951,"style":940},[846],[572,1953,1955,1958],{"className":1954},[606],[572,1956],{"className":1957,"style":645},[610],[572,1959,633],{"className":1960},[615,616],[558,1962,1964],{"id":1963},"beispiele","Beispiele",[563,1966,1967,1968,2039,2040,2119,2120,2276],{},"Ein rechtwinkliges Dreieck hat die Hypotenuse ",[572,1969,1971,1997],{"className":1970},[575],[572,1972,1974],{"className":1973},[579],[581,1975,1976],{"xmlns":583},[585,1977,1978,1994],{},[588,1979,1980,1982,1984,1987,1991],{},[591,1981,633],{},[835,1983,837],{},[831,1985,1986],{},"10",[1988,1989,1990],"mtext",{}," ",[1988,1992,1993],{},"cm",[595,1995,1996],{"encoding":597},"c = 10\\,\\text{cm}",[572,1998,2000,2018],{"className":1999,"ariaHidden":602},[601],[572,2001,2003,2006,2009,2012,2015],{"className":2002},[606],[572,2004],{"className":2005,"style":645},[610],[572,2007,633],{"className":2008},[615,616],[572,2010],{"className":2011,"style":919},[846],[572,2013,837],{"className":2014},[923],[572,2016],{"className":2017,"style":919},[846],[572,2019,2021,2025,2028,2032],{"className":2020},[606],[572,2022],{"className":2023,"style":2024},[610],"height:0.6444em;",[572,2026,1986],{"className":2027},[615],[572,2029],{"className":2030,"style":2031},[846],"margin-right:0.1667em;",[572,2033,2036],{"className":2034},[615,2035],"text",[572,2037,1993],{"className":2038},[615]," und den Abschnitt ",[572,2041,2043,2066],{"className":2042},[575],[572,2044,2046],{"className":2045},[579],[581,2047,2048],{"xmlns":583},[585,2049,2050,2063],{},[588,2051,2052,2054,2056,2059,2061],{},[591,2053,563],{},[835,2055,837],{},[831,2057,2058],{},"3,6",[1988,2060,1990],{},[1988,2062,1993],{},[595,2064,2065],{"encoding":597},"p = 3{,}6\\,\\text{cm}",[572,2067,2069,2087],{"className":2068,"ariaHidden":602},[601],[572,2070,2072,2075,2078,2081,2084],{"className":2071},[606],[572,2073],{"className":2074,"style":711},[610],[572,2076,563],{"className":2077},[615,616],[572,2079],{"className":2080,"style":919},[846],[572,2082,837],{"className":2083},[923],[572,2085],{"className":2086,"style":919},[846],[572,2088,2090,2094,2098,2106,2110,2113],{"className":2089},[606],[572,2091],{"className":2092,"style":2093},[610],"height:0.8389em;vertical-align:-0.1944em;",[572,2095,2097],{"className":2096},[615],"3",[572,2099,2101],{"className":2100},[615],[572,2102,2105],{"className":2103},[2104],"mpunct",",",[572,2107,2109],{"className":2108},[615],"6",[572,2111],{"className":2112,"style":2031},[846],[572,2114,2116],{"className":2115},[615,2035],[572,2117,1993],{"className":2118},[615],". Dann ist ",[572,2121,2123,2163],{"className":2122},[575],[572,2124,2126],{"className":2125},[579],[581,2127,2128],{"xmlns":583},[585,2129,2130,2160],{},[588,2131,2132,2134,2136,2138,2140,2142,2145,2147,2149,2151,2153,2156,2158],{},[591,2133,760],{},[835,2135,837],{},[831,2137,1986],{},[1988,2139,1990],{},[1988,2141,1993],{},[835,2143,2144],{},"−",[831,2146,2058],{},[1988,2148,1990],{},[1988,2150,1993],{},[835,2152,837],{},[831,2154,2155],{},"6,4",[1988,2157,1990],{},[1988,2159,1993],{},[595,2161,2162],{"encoding":597},"q = 10\\,\\text{cm} - 3{,}6\\,\\text{cm} = 6{,}4\\,\\text{cm}",[572,2164,2166,2184,2212,2248],{"className":2165,"ariaHidden":602},[601],[572,2167,2169,2172,2175,2178,2181],{"className":2168},[606],[572,2170],{"className":2171,"style":711},[610],[572,2173,760],{"className":2174,"style":775},[615,616],[572,2176],{"className":2177,"style":919},[846],[572,2179,837],{"className":2180},[923],[572,2182],{"className":2183,"style":919},[846],[572,2185,2187,2191,2194,2197,2203,2206,2209],{"className":2186},[606],[572,2188],{"className":2189,"style":2190},[610],"height:0.7278em;vertical-align:-0.0833em;",[572,2192,1986],{"className":2193},[615],[572,2195],{"className":2196,"style":2031},[846],[572,2198,2200],{"className":2199},[615,2035],[572,2201,1993],{"className":2202},[615],[572,2204],{"className":2205,"style":940},[846],[572,2207,2144],{"className":2208},[944],[572,2210],{"className":2211,"style":940},[846],[572,2213,2215,2218,2221,2227,2230,2233,2239,2242,2245],{"className":2214},[606],[572,2216],{"className":2217,"style":2093},[610],[572,2219,2097],{"className":2220},[615],[572,2222,2224],{"className":2223},[615],[572,2225,2105],{"className":2226},[2104],[572,2228,2109],{"className":2229},[615],[572,2231],{"className":2232,"style":2031},[846],[572,2234,2236],{"className":2235},[615,2035],[572,2237,1993],{"className":2238},[615],[572,2240],{"className":2241,"style":919},[846],[572,2243,837],{"className":2244},[923],[572,2246],{"className":2247,"style":919},[846],[572,2249,2251,2254,2257,2263,2267,2270],{"className":2250},[606],[572,2252],{"className":2253,"style":2093},[610],[572,2255,2109],{"className":2256},[615],[572,2258,2260],{"className":2259},[615],[572,2261,2105],{"className":2262},[2104],[572,2264,2266],{"className":2265},[615],"4",[572,2268],{"className":2269,"style":2031},[846],[572,2271,2273],{"className":2272},[615,2035],[572,2274,1993],{"className":2275},[615]," und",[572,2278,2280],{"className":2279},[811],[572,2281,2283,2348],{"className":2282},[575],[572,2284,2286],{"className":2285},[579],[581,2287,2288],{"xmlns":583,"display":820},[585,2289,2290,2345],{},[588,2291,2292,2298,2300,2302,2304,2306,2308,2310,2312,2314,2316,2319,2321,2327,2330,2333,2335,2337,2339,2341,2343],{},[826,2293,2294,2296],{},[591,2295,730],{},[831,2297,833],{},[835,2299,837],{},[831,2301,1986],{},[1988,2303,1990],{},[1988,2305,1993],{},[835,2307,842],{},[831,2309,2058],{},[1988,2311,1990],{},[1988,2313,1993],{},[835,2315,837],{},[831,2317,2318],{},"36",[1988,2320,1990],{},[826,2322,2323,2325],{},[1988,2324,1993],{},[831,2326,833],{},[1988,2328,2329],{},"  ",[835,2331,2332],{},"⇒",[1988,2334,2329],{},[591,2336,730],{},[835,2338,837],{},[831,2340,2109],{},[1988,2342,1990],{},[1988,2344,1993],{},[595,2346,2347],{"encoding":597},"a^2 = 10\\,\\text{cm} \\cdot 3{,}6\\,\\text{cm} = 36\\,\\text{cm}^2 \\;\\Rightarrow\\; a = 6\\,\\text{cm}",[572,2349,2351,2395,2422,2458,2517,2535],{"className":2350,"ariaHidden":602},[601],[572,2352,2354,2357,2386,2389,2392],{"className":2353},[606],[572,2355],{"className":2356,"style":875},[610],[572,2358,2360,2363],{"className":2359},[615],[572,2361,730],{"className":2362},[615,616],[572,2364,2366],{"className":2365},[885],[572,2367,2369],{"className":2368},[889],[572,2370,2372],{"className":2371},[893],[572,2373,2375],{"className":2374,"style":875},[897],[572,2376,2377,2380],{"style":900},[572,2378],{"className":2379,"style":905},[904],[572,2381,2383],{"className":2382},[909,910,911,912],[572,2384,833],{"className":2385},[615,912],[572,2387],{"className":2388,"style":919},[846],[572,2390,837],{"className":2391},[923],[572,2393],{"className":2394,"style":919},[846],[572,2396,2398,2401,2404,2407,2413,2416,2419],{"className":2397},[606],[572,2399],{"className":2400,"style":2024},[610],[572,2402,1986],{"className":2403},[615],[572,2405],{"className":2406,"style":2031},[846],[572,2408,2410],{"className":2409},[615,2035],[572,2411,1993],{"className":2412},[615],[572,2414],{"className":2415,"style":940},[846],[572,2417,842],{"className":2418},[944],[572,2420],{"className":2421,"style":940},[846],[572,2423,2425,2428,2431,2437,2440,2443,2449,2452,2455],{"className":2424},[606],[572,2426],{"className":2427,"style":2093},[610],[572,2429,2097],{"className":2430},[615],[572,2432,2434],{"className":2433},[615],[572,2435,2105],{"className":2436},[2104],[572,2438,2109],{"className":2439},[615],[572,2441],{"className":2442,"style":2031},[846],[572,2444,2446],{"className":2445},[615,2035],[572,2447,1993],{"className":2448},[615],[572,2450],{"className":2451,"style":919},[846],[572,2453,837],{"className":2454},[923],[572,2456],{"className":2457,"style":919},[846],[572,2459,2461,2464,2467,2470,2502,2505,2508,2511,2514],{"className":2460},[606],[572,2462],{"className":2463,"style":875},[610],[572,2465,2318],{"className":2466},[615],[572,2468],{"className":2469,"style":2031},[846],[572,2471,2473,2479],{"className":2472},[615],[572,2474,2476],{"className":2475},[615,2035],[572,2477,1993],{"className":2478},[615],[572,2480,2482],{"className":2481},[885],[572,2483,2485],{"className":2484},[889],[572,2486,2488],{"className":2487},[893],[572,2489,2491],{"className":2490,"style":875},[897],[572,2492,2493,2496],{"style":900},[572,2494],{"className":2495,"style":905},[904],[572,2497,2499],{"className":2498},[909,910,911,912],[572,2500,833],{"className":2501},[615,912],[572,2503],{"className":2504,"style":919},[846],[572,2506],{"className":2507,"style":919},[846],[572,2509,2332],{"className":2510},[923],[572,2512],{"className":2513,"style":919},[846],[572,2515],{"className":2516,"style":919},[846],[572,2518,2520,2523,2526,2529,2532],{"className":2519},[606],[572,2521],{"className":2522,"style":645},[610],[572,2524,730],{"className":2525},[615,616],[572,2527],{"className":2528,"style":919},[846],[572,2530,837],{"className":2531},[923],[572,2533],{"className":2534,"style":919},[846],[572,2536,2538,2541,2544,2547],{"className":2537},[606],[572,2539],{"className":2540,"style":2024},[610],[572,2542,2109],{"className":2543},[615],[572,2545],{"className":2546,"style":2031},[846],[572,2548,2550],{"className":2549},[615,2035],[572,2551,1993],{"className":2552},[615],[572,2554,2556],{"className":2555},[811],[572,2557,2559,2623],{"className":2558},[575],[572,2560,2562],{"className":2561},[579],[581,2563,2564],{"xmlns":583,"display":820},[585,2565,2566,2620],{},[588,2567,2568,2574,2576,2578,2580,2582,2584,2586,2588,2590,2592,2595,2597,2603,2605,2607,2609,2611,2613,2616,2618],{},[826,2569,2570,2572],{},[591,2571,791],{},[831,2573,833],{},[835,2575,837],{},[831,2577,1986],{},[1988,2579,1990],{},[1988,2581,1993],{},[835,2583,842],{},[831,2585,2155],{},[1988,2587,1990],{},[1988,2589,1993],{},[835,2591,837],{},[831,2593,2594],{},"64",[1988,2596,1990],{},[826,2598,2599,2601],{},[1988,2600,1993],{},[831,2602,833],{},[1988,2604,2329],{},[835,2606,2332],{},[1988,2608,2329],{},[591,2610,791],{},[835,2612,837],{},[831,2614,2615],{},"8",[1988,2617,1990],{},[1988,2619,1993],{},[595,2621,2622],{"encoding":597},"b^2 = 10\\,\\text{cm} \\cdot 6{,}4\\,\\text{cm} = 64\\,\\text{cm}^2 \\;\\Rightarrow\\; b = 8\\,\\text{cm}",[572,2624,2626,2670,2697,2733,2792,2810],{"className":2625,"ariaHidden":602},[601],[572,2627,2629,2632,2661,2664,2667],{"className":2628},[606],[572,2630],{"className":2631,"style":875},[610],[572,2633,2635,2638],{"className":2634},[615],[572,2636,791],{"className":2637},[615,616],[572,2639,2641],{"className":2640},[885],[572,2642,2644],{"className":2643},[889],[572,2645,2647],{"className":2646},[893],[572,2648,2650],{"className":2649,"style":875},[897],[572,2651,2652,2655],{"style":900},[572,2653],{"className":2654,"style":905},[904],[572,2656,2658],{"className":2657},[909,910,911,912],[572,2659,833],{"className":2660},[615,912],[572,2662],{"className":2663,"style":919},[846],[572,2665,837],{"className":2666},[923],[572,2668],{"className":2669,"style":919},[846],[572,2671,2673,2676,2679,2682,2688,2691,2694],{"className":2672},[606],[572,2674],{"className":2675,"style":2024},[610],[572,2677,1986],{"className":2678},[615],[572,2680],{"className":2681,"style":2031},[846],[572,2683,2685],{"className":2684},[615,2035],[572,2686,1993],{"className":2687},[615],[572,2689],{"className":2690,"style":940},[846],[572,2692,842],{"className":2693},[944],[572,2695],{"className":2696,"style":940},[846],[572,2698,2700,2703,2706,2712,2715,2718,2724,2727,2730],{"className":2699},[606],[572,2701],{"className":2702,"style":2093},[610],[572,2704,2109],{"className":2705},[615],[572,2707,2709],{"className":2708},[615],[572,2710,2105],{"className":2711},[2104],[572,2713,2266],{"className":2714},[615],[572,2716],{"className":2717,"style":2031},[846],[572,2719,2721],{"className":2720},[615,2035],[572,2722,1993],{"className":2723},[615],[572,2725],{"className":2726,"style":919},[846],[572,2728,837],{"className":2729},[923],[572,2731],{"className":2732,"style":919},[846],[572,2734,2736,2739,2742,2745,2777,2780,2783,2786,2789],{"className":2735},[606],[572,2737],{"className":2738,"style":875},[610],[572,2740,2594],{"className":2741},[615],[572,2743],{"className":2744,"style":2031},[846],[572,2746,2748,2754],{"className":2747},[615],[572,2749,2751],{"className":2750},[615,2035],[572,2752,1993],{"className":2753},[615],[572,2755,2757],{"className":2756},[885],[572,2758,2760],{"className":2759},[889],[572,2761,2763],{"className":2762},[893],[572,2764,2766],{"className":2765,"style":875},[897],[572,2767,2768,2771],{"style":900},[572,2769],{"className":2770,"style":905},[904],[572,2772,2774],{"className":2773},[909,910,911,912],[572,2775,833],{"className":2776},[615,912],[572,2778],{"className":2779,"style":919},[846],[572,2781],{"className":2782,"style":919},[846],[572,2784,2332],{"className":2785},[923],[572,2787],{"className":2788,"style":919},[846],[572,2790],{"className":2791,"style":919},[846],[572,2793,2795,2798,2801,2804,2807],{"className":2794},[606],[572,2796],{"className":2797,"style":803},[610],[572,2799,791],{"className":2800},[615,616],[572,2802],{"className":2803,"style":919},[846],[572,2805,837],{"className":2806},[923],[572,2808],{"className":2809,"style":919},[846],[572,2811,2813,2816,2819,2822],{"className":2812},[606],[572,2814],{"className":2815,"style":2024},[610],[572,2817,2615],{"className":2818},[615],[572,2820],{"className":2821,"style":2031},[846],[572,2823,2825],{"className":2824},[615,2035],[572,2826,1993],{"className":2827},[615],[563,2829,2830,2831,2999],{},"Zur Kontrolle: ",[572,2832,2834,2868],{"className":2833},[575],[572,2835,2837],{"className":2836},[579],[581,2838,2839],{"xmlns":583},[585,2840,2841,2865],{},[588,2842,2843,2849,2851,2857,2859],{},[826,2844,2845,2847],{},[831,2846,2109],{},[831,2848,833],{},[835,2850,1049],{},[826,2852,2853,2855],{},[831,2854,2615],{},[831,2856,833],{},[835,2858,837],{},[826,2860,2861,2863],{},[831,2862,1986],{},[831,2864,833],{},[595,2866,2867],{"encoding":597},"6^2 + 8^2 = 10^2",[572,2869,2871,2915,2959],{"className":2870,"ariaHidden":602},[601],[572,2872,2874,2877,2906,2909,2912],{"className":2873},[606],[572,2875],{"className":2876,"style":1174},[610],[572,2878,2880,2883],{"className":2879},[615],[572,2881,2109],{"className":2882},[615],[572,2884,2886],{"className":2885},[885],[572,2887,2889],{"className":2888},[889],[572,2890,2892],{"className":2891},[893],[572,2893,2895],{"className":2894,"style":1193},[897],[572,2896,2897,2900],{"style":1196},[572,2898],{"className":2899,"style":905},[904],[572,2901,2903],{"className":2902},[909,910,911,912],[572,2904,833],{"className":2905},[615,912],[572,2907],{"className":2908,"style":940},[846],[572,2910,1049],{"className":2911},[944],[572,2913],{"className":2914,"style":940},[846],[572,2916,2918,2921,2950,2953,2956],{"className":2917},[606],[572,2919],{"className":2920,"style":1193},[610],[572,2922,2924,2927],{"className":2923},[615],[572,2925,2615],{"className":2926},[615],[572,2928,2930],{"className":2929},[885],[572,2931,2933],{"className":2932},[889],[572,2934,2936],{"className":2935},[893],[572,2937,2939],{"className":2938,"style":1193},[897],[572,2940,2941,2944],{"style":1196},[572,2942],{"className":2943,"style":905},[904],[572,2945,2947],{"className":2946},[909,910,911,912],[572,2948,833],{"className":2949},[615,912],[572,2951],{"className":2952,"style":919},[846],[572,2954,837],{"className":2955},[923],[572,2957],{"className":2958,"style":919},[846],[572,2960,2962,2965,2969],{"className":2961},[606],[572,2963],{"className":2964,"style":1193},[610],[572,2966,2968],{"className":2967},[615],"1",[572,2970,2972,2976],{"className":2971},[615],[572,2973,2975],{"className":2974},[615],"0",[572,2977,2979],{"className":2978},[885],[572,2980,2982],{"className":2981},[889],[572,2983,2985],{"className":2984},[893],[572,2986,2988],{"className":2987,"style":1193},[897],[572,2989,2990,2993],{"style":1196},[572,2991],{"className":2992,"style":905},[904],[572,2994,2996],{"className":2995},[909,910,911,912],[572,2997,833],{"className":2998},[615,912],".",[563,3001,3002,3003,3031,3032,1422,3097,3162],{},"Gesucht ist umgekehrt der Abschnitt ",[572,3004,3006,3019],{"className":3005},[575],[572,3007,3009],{"className":3008},[579],[581,3010,3011],{"xmlns":583},[585,3012,3013,3017],{},[588,3014,3015],{},[591,3016,563],{},[595,3018,563],{"encoding":597},[572,3020,3022],{"className":3021,"ariaHidden":602},[601],[572,3023,3025,3028],{"className":3024},[606],[572,3026],{"className":3027,"style":711},[610],[572,3029,563],{"className":3030},[615,616],", wenn ",[572,3033,3035,3058],{"className":3034},[575],[572,3036,3038],{"className":3037},[579],[581,3039,3040],{"xmlns":583},[585,3041,3042,3055],{},[588,3043,3044,3046,3048,3051,3053],{},[591,3045,730],{},[835,3047,837],{},[831,3049,3050],{},"5",[1988,3052,1990],{},[1988,3054,1993],{},[595,3056,3057],{"encoding":597},"a = 5\\,\\text{cm}",[572,3059,3061,3079],{"className":3060,"ariaHidden":602},[601],[572,3062,3064,3067,3070,3073,3076],{"className":3063},[606],[572,3065],{"className":3066,"style":645},[610],[572,3068,730],{"className":3069},[615,616],[572,3071],{"className":3072,"style":919},[846],[572,3074,837],{"className":3075},[923],[572,3077],{"className":3078,"style":919},[846],[572,3080,3082,3085,3088,3091],{"className":3081},[606],[572,3083],{"className":3084,"style":2024},[610],[572,3086,3050],{"className":3087},[615],[572,3089],{"className":3090,"style":2031},[846],[572,3092,3094],{"className":3093},[615,2035],[572,3095,1993],{"className":3096},[615],[572,3098,3100,3123],{"className":3099},[575],[572,3101,3103],{"className":3102},[579],[581,3104,3105],{"xmlns":583},[585,3106,3107,3120],{},[588,3108,3109,3111,3113,3116,3118],{},[591,3110,633],{},[835,3112,837],{},[831,3114,3115],{},"13",[1988,3117,1990],{},[1988,3119,1993],{},[595,3121,3122],{"encoding":597},"c = 13\\,\\text{cm}",[572,3124,3126,3144],{"className":3125,"ariaHidden":602},[601],[572,3127,3129,3132,3135,3138,3141],{"className":3128},[606],[572,3130],{"className":3131,"style":645},[610],[572,3133,633],{"className":3134},[615,616],[572,3136],{"className":3137,"style":919},[846],[572,3139,837],{"className":3140},[923],[572,3142],{"className":3143,"style":919},[846],[572,3145,3147,3150,3153,3156],{"className":3146},[606],[572,3148],{"className":3149,"style":2024},[610],[572,3151,3115],{"className":3152},[615],[572,3154],{"className":3155,"style":2031},[846],[572,3157,3159],{"className":3158},[615,2035],[572,3160,1993],{"className":3161},[615]," bekannt sind:",[572,3164,3166],{"className":3165},[811],[572,3167,3169,3219],{"className":3168},[575],[572,3170,3172],{"className":3171},[579],[581,3173,3174],{"xmlns":583,"display":820},[585,3175,3176,3216],{},[588,3177,3178,3180,3182,3193,3195,3202,3204,3206,3209,3212,3214],{},[591,3179,563],{},[835,3181,837],{},[3183,3184,3185,3191],"mfrac",{},[826,3186,3187,3189],{},[591,3188,730],{},[831,3190,833],{},[591,3192,633],{},[835,3194,837],{},[3183,3196,3197,3200],{},[831,3198,3199],{},"25",[831,3201,3115],{},[1988,3203,1990],{},[1988,3205,1993],{},[835,3207,3208],{},"≈",[831,3210,3211],{},"1,92",[1988,3213,1990],{},[1988,3215,1993],{},[595,3217,3218],{"encoding":597},"p = \\frac{a^2}{c} = \\frac{25}{13}\\,\\text{cm} \\approx 1{,}92\\,\\text{cm}",[572,3220,3222,3240,3356,3444],{"className":3221,"ariaHidden":602},[601],[572,3223,3225,3228,3231,3234,3237],{"className":3224},[606],[572,3226],{"className":3227,"style":711},[610],[572,3229,563],{"className":3230},[615,616],[572,3232],{"className":3233,"style":919},[846],[572,3235,837],{"className":3236},[923],[572,3238],{"className":3239,"style":919},[846],[572,3241,3243,3247,3347,3350,3353],{"className":3242},[606],[572,3244],{"className":3245,"style":3246},[610],"height:2.1771em;vertical-align:-0.686em;",[572,3248,3250,3254,3344],{"className":3249},[615],[572,3251],{"className":3252},[1287,3253],"nulldelimiter",[572,3255,3257],{"className":3256},[3183],[572,3258,3261,3335],{"className":3259},[889,3260],"vlist-t2",[572,3262,3264,3330],{"className":3263},[893],[572,3265,3268,3281,3292],{"className":3266,"style":3267},[897],"height:1.4911em;",[572,3269,3271,3275],{"style":3270},"top:-2.314em;",[572,3272],{"className":3273,"style":3274},[904],"height:3em;",[572,3276,3278],{"className":3277},[615],[572,3279,633],{"className":3280},[615,616],[572,3282,3284,3287],{"style":3283},"top:-3.23em;",[572,3285],{"className":3286,"style":3274},[904],[572,3288],{"className":3289,"style":3291},[3290],"frac-line","border-bottom-width:0.04em;",[572,3293,3295,3298],{"style":3294},"top:-3.677em;",[572,3296],{"className":3297,"style":3274},[904],[572,3299,3301],{"className":3300},[615],[572,3302,3304,3307],{"className":3303},[615],[572,3305,730],{"className":3306},[615,616],[572,3308,3310],{"className":3309},[885],[572,3311,3313],{"className":3312},[889],[572,3314,3316],{"className":3315},[893],[572,3317,3319],{"className":3318,"style":1193},[897],[572,3320,3321,3324],{"style":1196},[572,3322],{"className":3323,"style":905},[904],[572,3325,3327],{"className":3326},[909,910,911,912],[572,3328,833],{"className":3329},[615,912],[572,3331,3334],{"className":3332},[3333],"vlist-s","​",[572,3336,3338],{"className":3337},[893],[572,3339,3342],{"className":3340,"style":3341},[897],"height:0.686em;",[572,3343],{},[572,3345],{"className":3346},[1312,3253],[572,3348],{"className":3349,"style":919},[846],[572,3351,837],{"className":3352},[923],[572,3354],{"className":3355,"style":919},[846],[572,3357,3359,3363,3426,3429,3435,3438,3441],{"className":3358},[606],[572,3360],{"className":3361,"style":3362},[610],"height:2.0074em;vertical-align:-0.686em;",[572,3364,3366,3369,3423],{"className":3365},[615],[572,3367],{"className":3368},[1287,3253],[572,3370,3372],{"className":3371},[3183],[572,3373,3375,3415],{"className":3374},[889,3260],[572,3376,3378,3412],{"className":3377},[893],[572,3379,3382,3393,3401],{"className":3380,"style":3381},[897],"height:1.3214em;",[572,3383,3384,3387],{"style":3270},[572,3385],{"className":3386,"style":3274},[904],[572,3388,3390],{"className":3389},[615],[572,3391,3115],{"className":3392},[615],[572,3394,3395,3398],{"style":3283},[572,3396],{"className":3397,"style":3274},[904],[572,3399],{"className":3400,"style":3291},[3290],[572,3402,3403,3406],{"style":3294},[572,3404],{"className":3405,"style":3274},[904],[572,3407,3409],{"className":3408},[615],[572,3410,3199],{"className":3411},[615],[572,3413,3334],{"className":3414},[3333],[572,3416,3418],{"className":3417},[893],[572,3419,3421],{"className":3420,"style":3341},[897],[572,3422],{},[572,3424],{"className":3425},[1312,3253],[572,3427],{"className":3428,"style":2031},[846],[572,3430,3432],{"className":3431},[615,2035],[572,3433,1993],{"className":3434},[615],[572,3436],{"className":3437,"style":919},[846],[572,3439,3208],{"className":3440},[923],[572,3442],{"className":3443,"style":919},[846],[572,3445,3447,3450,3453,3459,3463,3466],{"className":3446},[606],[572,3448],{"className":3449,"style":2093},[610],[572,3451,2968],{"className":3452},[615],[572,3454,3456],{"className":3455},[615],[572,3457,2105],{"className":3458},[2104],[572,3460,3462],{"className":3461},[615],"92",[572,3464],{"className":3465,"style":2031},[846],[572,3467,3469],{"className":3468},[615,2035],[572,3470,1993],{"className":3471},[615],[558,3473,3475],{"id":3474},"typische-fehler","Typische 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",[572,3540,3542,3555],{"className":3541},[575],[572,3543,3545],{"className":3544},[579],[581,3546,3547],{"xmlns":583},[585,3548,3549,3553],{},[588,3550,3551],{},[591,3552,563],{},[595,3554,563],{"encoding":597},[572,3556,3558],{"className":3557,"ariaHidden":602},[601],[572,3559,3561,3564],{"className":3560},[606],[572,3562],{"className":3563,"style":711},[610],[572,3565,563],{"className":3566},[615,616]," gehört zur Kathete ",[572,3569,3571,3584],{"className":3570},[575],[572,3572,3574],{"className":3573},[579],[581,3575,3576],{"xmlns":583},[585,3577,3578,3582],{},[588,3579,3580],{},[591,3581,730],{},[595,3583,730],{"encoding":597},[572,3585,3587],{"className":3586,"ariaHidden":602},[601],[572,3588,3590,3593],{"className":3589},[606],[572,3591],{"className":3592,"style":645},[610],[572,3594,730],{"className":3595},[615,616],": Es ist der Abschnitt, der direkt an 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