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\\frac{\\overline{SA_2}}{\\overline{SA_1}}",[568,1123,1125,1454],{"className":1124,"ariaHidden":598},[597],[568,1126,1128,1132,1442,1447,1451],{"className":1127},[602],[568,1129],{"className":1130,"style":1131},[606],"height:2.4837em;vertical-align:-0.9233em;",[568,1133,1135,1140,1438],{"className":1134},[611],[568,1136],{"className":1137},[1138,1139],"mopen","nulldelimiter",[568,1141,1143],{"className":1142},[1045],[568,1144,1146,1429],{"className":1145},[668,669],[568,1147,1149,1426],{"className":1148},[673],[568,1150,1153,1288,1298],{"className":1151,"style":1152},[677],"height:1.5603em;",[568,1154,1156,1160],{"style":1155},"top:-2.2267em;",[568,1157],{"className":1158,"style":1159},[685],"height:3em;",[568,1161,1163],{"className":1162},[611],[568,1164,1167],{"className":1165},[611,1166],"overline",[568,1168,1170,1280],{"className":1169},[668,669],[568,1171,1173,1277],{"className":1172},[673],[568,1174,1177,1266],{"className":1175,"style":1176},[677],"height:0.8833em;",[568,1178,1180,1183],{"style":1179},"top:-3em;",[568,1181],{"className":1182,"style":1159},[685],[568,1184,1186,1226],{"className":1185},[611],[568,1187,1189,1192],{"className":1188},[611],[568,1190,637],{"className":1191},[611,612],[568,1193,1195],{"className":1194},[664],[568,1196,1198,1218],{"className":1197},[668,669],[568,1199,1201,1215],{"className":1200},[673],[568,1202,1204],{"className":1203,"style":678},[677],[568,1205,1206,1209],{"style":681},[568,1207],{"className":1208,"style":686},[685],[568,1210,1212],{"className":1211},[690,691,692,693],[568,1213,641],{"className":1214},[611,693],[568,1216,701],{"className":1217},[700],[568,1219,1221],{"className":1220},[673],[568,1222,1224],{"className":1223,"style":708},[677],[568,1225],{},[568,1227,1229,1232],{"className":1228},[611],[568,1230,728],{"className":1231,"style":749},[611,612],[568,1233,1235],{"className":1234},[664],[568,1236,1238,1258],{"className":1237},[668,669],[568,1239,1241,1255],{"className":1240},[673],[568,1242,1244],{"className":1243,"style":678},[677],[568,1245,1246,1249],{"style":764},[568,1247],{"className":1248,"style":686},[685],[568,1250,1252],{"className":1251},[690,691,692,693],[568,1253,641],{"className":1254},[611,693],[568,1256,701],{"className":1257},[700],[568,1259,1261],{"className":1260},[673],[568,1262,1264],{"className":1263,"style":708},[677],[568,1265],{},[568,1267,1269,1272],{"style":1268},"top:-3.8033em;",[568,1270],{"className":1271,"style":1159},[685],[568,1273],{"className":1274,"style":1276},[1275],"overline-line","border-bottom-width:0.04em;",[568,1278,701],{"className":1279},[700],[568,1281,1283],{"className":1282},[673],[568,1284,1286],{"className":1285,"style":708},[677],[568,1287],{},[568,1289,1291,1294],{"style":1290},"top:-3.23em;",[568,1292],{"className":1293,"style":1159},[685],[568,1295],{"className":1296,"style":1276},[1297],"frac-line",[568,1299,1301,1304],{"style":1300},"top:-3.677em;",[568,1302],{"className":1303,"style":1159},[685],[568,1305,1307],{"className":1306},[611],[568,1308,1310],{"className":1309},[611,1166],[568,1311,1313,1418],{"className":1312},[668,669],[568,1314,1316,1415],{"className":1315},[673],[568,1317,1319,1407],{"className":1318,"style":1176},[677],[568,1320,1321,1324],{"style":1179},[568,1322],{"className":1323,"style":1159},[685],[568,1325,1327,1367],{"className":1326},[611],[568,1328,1330,1333],{"className":1329},[611],[568,1331,637],{"className":1332},[611,612],[568,1334,1336],{"className":1335},[664],[568,1337,1339,1359],{"className":1338},[668,669],[568,1340,1342,1356],{"className":1341},[673],[568,1343,1345],{"className":1344,"style":678},[677],[568,1346,1347,1350],{"style":681},[568,1348],{"className":1349,"style":686},[685],[568,1351,1353],{"className":1352},[690,691,692,693],[568,1354,804],{"className":1355},[611,693],[568,1357,701],{"className":1358},[700],[568,1360,1362],{"className":1361},[673],[568,1363,1365],{"className":1364,"style":708},[677],[568,1366],{},[568,1368,1370,1373],{"className":1369},[611],[568,1371,728],{"className":1372,"style":749},[611,612],[568,1374,1376],{"className":1375},[664],[568,1377,1379,1399],{"className":1378},[668,669],[568,1380,1382,1396],{"className":1381},[673],[568,1383,1385],{"className":1384,"style":678},[677],[568,1386,1387,1390],{"style":764},[568,1388],{"className":1389,"style":686},[685],[568,1391,1393],{"className":1392},[690,691,692,693],[568,1394,804],{"className":1395},[611,693],[568,1397,701],{"className":1398},[700],[568,1400,1402],{"className":1401},[673],[568,1403,1405],{"className":1404,"style":708},[677],[568,1406],{},[568,1408,1409,1412],{"style":1268},[568,1410],{"className":1411,"style":1159},[685],[568,1413],{"className":1414,"style":1276},[1275],[568,1416,701],{"className":1417},[700],[568,1419,1421],{"className":1420},[673],[568,1422,1424],{"className":1423,"style":708},[677],[568,1425],{},[568,1427,701],{"className":1428},[700],[568,1430,1432],{"className":1431},[673],[568,1433,1436],{"className":1434,"style":1435},[677],"height:0.9233em;",[568,1437],{},[568,1439],{"className":1440},[1441,1139],"mclose",[568,1443],{"className":1444,"style":1446},[1445],"mspace","margin-right:0.2778em;",[568,1448,1088],{"className":1449},[1450],"mrel",[568,1452],{"className":1453,"style":1446},[1445],[568,1455,1457,1460],{"className":1456},[602],[568,1458],{"className":1459,"style":1131},[606],[568,1461,1463,1466,1677],{"className":1462},[611],[568,1464],{"className":1465},[1138,1139],[568,1467,1469],{"className":1468},[1045],[568,1470,1472,1669],{"className":1471},[668,669],[568,1473,1475,1666],{"className":1474},[673],[568,1476,1478,1568,1576],{"className":1477,"style":1152},[677],[568,1479,1480,1483],{"style":1155},[568,1481],{"className":1482,"style":1159},[685],[568,1484,1486],{"className":1485},[611],[568,1487,1489],{"className":1488},[611,1166],[568,1490,1492,1560],{"className":1491},[668,669],[568,1493,1495,1557],{"className":1494},[673],[568,1496,1498,1549],{"className":1497,"style":1176},[677],[568,1499,1500,1503],{"style":1179},[568,1501],{"className":1502,"style":1159},[685],[568,1504,1506,1509],{"className":1505},[611],[568,1507,589],{"className":1508,"style":613},[611,612],[568,1510,1512,1515],{"className":1511},[611],[568,1513,637],{"className":1514},[611,612],[568,1516,1518],{"className":1517},[664],[568,1519,1521,1541],{"className":1520},[668,669],[568,1522,1524,1538],{"className":1523},[673],[568,1525,1527],{"className":1526,"style":678},[677],[568,1528,1529,1532],{"style":681},[568,1530],{"className":1531,"style":686},[685],[568,1533,1535],{"className":1534},[690,691,692,693],[568,1536,641],{"className":1537},[611,693],[568,1539,701],{"className":1540},[700],[568,1542,1544],{"className":1543},[673],[568,1545,1547],{"className":1546,"style":708},[677],[568,1548],{},[568,1550,1551,1554],{"style":1268},[568,1552],{"className":1553,"style":1159},[685],[568,1555],{"className":1556,"style":1276},[1275],[568,1558,701],{"className":1559},[700],[568,1561,1563],{"className":1562},[673],[568,1564,1566],{"className":1565,"style":708},[677],[568,1567],{},[568,1569,1570,1573],{"style":1290},[568,1571],{"className":1572,"style":1159},[685],[568,1574],{"className":1575,"style":1276},[1297],[568,1577,1578,1581],{"style":1300},[568,1579],{"className":1580,"style":1159},[685],[568,1582,1584],{"className":1583},[611],[568,1585,1587],{"className":1586},[611,1166],[568,1588,1590,1658],{"className":1589},[668,669],[568,1591,1593,1655],{"className":1592},[673],[568,1594,1596,1647],{"className":1595,"style":1176},[677],[568,1597,1598,1601],{"style":1179},[568,1599],{"className":1600,"style":1159},[685],[568,1602,1604,1607],{"className":1603},[611],[568,1605,589],{"className":1606,"style":613},[611,612],[568,1608,1610,1613],{"className":1609},[611],[568,1611,637],{"className":1612},[611,612],[568,1614,1616],{"className":1615},[664],[568,1617,1619,1639],{"className":1618},[668,669],[568,1620,1622,1636],{"className":1621},[673],[568,1623,1625],{"className":1624,"style":678},[677],[568,1626,1627,1630],{"style":681},[568,1628],{"className":1629,"style":686},[685],[568,1631,1633],{"className":1632},[690,691,692,693],[568,1634,804],{"className":1635},[611,693],[568,1637,701],{"className":1638},[700],[568,1640,1642],{"className":1641},[673],[568,1643,1645],{"className":1644,"style":708},[677],[568,1646],{},[568,1648,1649,1652],{"style":1268},[568,1650],{"className":1651,"style":1159},[685],[568,1653],{"className":1654,"style":1276},[1275],[568,1656,701],{"className":1657},[700],[568,1659,1661],{"className":1660},[673],[568,1662,1664],{"className":1663,"style":708},[677],[568,1665],{},[568,1667,701],{"className":1668},[700],[568,1670,1672],{"className":1671},[673],[568,1673,1675],{"className":1674,"style":1435},[677],[568,1676],{},[568,1678],{"className":1679},[1441,1139],[564,1681,1682,1683,1711,1712,1740],{},"Beide Sätze gelten auch, wenn sich zwei Geraden in ",[568,1684,1686,1699],{"className":1685},[571],[568,1687,1689],{"className":1688},[575],[577,1690,1691],{"xmlns":579},[581,1692,1693,1697],{},[584,1694,1695],{},[587,1696,589],{},[591,1698,589],{"encoding":593},[568,1700,1702],{"className":1701,"ariaHidden":598},[597],[568,1703,1705,1708],{"className":1704},[602],[568,1706],{"className":1707,"style":607},[606],[568,1709,589],{"className":1710,"style":613},[611,612]," kreuzen und die Parallelen auf verschiedenen Seiten von ",[568,1713,1715,1728],{"className":1714},[571],[568,1716,1718],{"className":1717},[575],[577,1719,1720],{"xmlns":579},[581,1721,1722,1726],{},[584,1723,1724],{},[587,1725,589],{},[591,1727,589],{"encoding":593},[568,1729,1731],{"className":1730,"ariaHidden":598},[597],[568,1732,1734,1737],{"className":1733},[602],[568,1735],{"className":1736,"style":607},[606],[568,1738,589],{"className":1739,"style":613},[611,612]," liegen (X-Figur statt V-Figur).",[564,1742,1743,1744,711,1865,1986,1987,1990],{},"Der Grund: Die Dreiecke ",[568,1745,1747,1773],{"className":1746},[571],[568,1748,1750],{"className":1749},[575],[577,1751,1752],{"xmlns":579},[581,1753,1754,1770],{},[584,1755,1756,1758,1764],{},[587,1757,589],{},[633,1759,1760,1762],{},[587,1761,637],{},[639,1763,641],{},[633,1765,1766,1768],{},[587,1767,728],{},[639,1769,641],{},[591,1771,1772],{"encoding":593},"SA_1B_1",[568,1774,1776],{"className":1775,"ariaHidden":598},[597],[568,1777,1779,1782,1785,1825],{"className":1778},[602],[568,1780],{"className":1781,"style":654},[606],[568,1783,589],{"className":1784,"style":613},[611,612],[568,1786,1788,1791],{"className":1787},[611],[568,1789,637],{"className":1790},[611,612],[568,1792,1794],{"className":1793},[664],[568,1795,1797,1817],{"className":1796},[668,669],[568,1798,1800,1814],{"className":1799},[673],[568,1801,1803],{"className":1802,"style":678},[677],[568,1804,1805,1808],{"style":681},[568,1806],{"className":1807,"style":686},[685],[568,1809,1811],{"className":1810},[690,691,692,693],[568,1812,641],{"className":1813},[611,693],[568,1815,701],{"className":1816},[700],[568,1818,1820],{"className":1819},[673],[568,1821,1823],{"className":1822,"style":708},[677],[568,1824],{},[568,1826,1828,1831],{"className":1827},[611],[568,1829,728],{"className":1830,"style":749},[611,612],[568,1832,1834],{"className":1833},[664],[568,1835,1837,1857],{"className":1836},[668,669],[568,1838,1840,1854],{"className":1839},[673],[568,1841,1843],{"className":1842,"style":678},[677],[568,1844,1845,1848],{"style":764},[568,1846],{"className":1847,"style":686},[685],[568,1849,1851],{"className":1850},[690,691,692,693],[568,1852,641],{"className":1853},[611,693],[568,1855,701],{"className":1856},[700],[568,1858,1860],{"className":1859},[673],[568,1861,1863],{"className":1862,"style":708},[677],[568,1864],{},[568,1866,1868,1894],{"className":1867},[571],[568,1869,1871],{"className":1870},[575],[577,1872,1873],{"xmlns":579},[581,1874,1875,1891],{},[584,1876,1877,1879,1885],{},[587,1878,589],{},[633,1880,1881,1883],{},[587,1882,637],{},[639,1884,804],{},[633,1886,1887,1889],{},[587,1888,728],{},[639,1890,804],{},[591,1892,1893],{"encoding":593},"SA_2B_2",[568,1895,1897],{"className":1896,"ariaHidden":598},[597],[568,1898,1900,1903,1906,1946],{"className":1899},[602],[568,1901],{"className":1902,"style":654},[606],[568,1904,589],{"className":1905,"style":613},[611,612],[568,1907,1909,1912],{"className":1908},[611],[568,1910,637],{"className":1911},[611,612],[568,1913,1915],{"className":1914},[664],[568,1916,1918,1938],{"className":1917},[668,669],[568,1919,1921,1935],{"className":1920},[673],[568,1922,1924],{"className":1923,"style":678},[677],[568,1925,1926,1929],{"style":681},[568,1927],{"className":1928,"style":686},[685],[568,1930,1932],{"className":1931},[690,691,692,693],[568,1933,804],{"className":1934},[611,693],[568,1936,701],{"className":1937},[700],[568,1939,1941],{"className":1940},[673],[568,1942,1944],{"className":1943,"style":708},[677],[568,1945],{},[568,1947,1949,1952],{"className":1948},[611],[568,1950,728],{"className":1951,"style":749},[611,612],[568,1953,1955],{"className":1954},[664],[568,1956,1958,1978],{"className":1957},[668,669],[568,1959,1961,1975],{"className":1960},[673],[568,1962,1964],{"className":1963,"style":678},[677],[568,1965,1966,1969],{"style":764},[568,1967],{"className":1968,"style":686},[685],[568,1970,1972],{"className":1971},[690,691,692,693],[568,1973,804],{"className":1974},[611,693],[568,1976,701],{"className":1977},[700],[568,1979,1981],{"className":1980},[673],[568,1982,1984],{"className":1983,"style":708},[677],[568,1985],{}," sind ",[616,1988,1989],{},"ähnlich",". Das große Dreieck ist eine maßstäbliche Vergrößerung des kleinen.",[559,1992,1994],{"id":1993},"beispiele","Beispiele",[564,1996,1997,1998,2161,2162,711,2318,2474],{},"Gegeben sind ",[568,1999,2001,2039],{"className":2000},[571],[568,2002,2004],{"className":2003},[575],[577,2005,2006],{"xmlns":579},[581,2007,2008,2036],{},[584,2009,2010,2024,2026,2029,2033],{},[1048,2011,2012,2022],{"accent":598},[584,2013,2014,2016],{},[587,2015,589],{},[633,2017,2018,2020],{},[587,2019,637],{},[639,2021,641],{},[1065,2023,1067],{"stretchy":598},[1065,2025,1088],{},[639,2027,2028],{},"4",[2030,2031,2032],"mtext",{}," ",[2030,2034,2035],{},"cm",[591,2037,2038],{"encoding":593},"\\overline{SA_1} = 4\\,\\text{cm}",[568,2040,2042,2140],{"className":2041,"ariaHidden":598},[597],[568,2043,2045,2049,2131,2134,2137],{"className":2044},[602],[568,2046],{"className":2047,"style":2048},[606],"height:1.0333em;vertical-align:-0.15em;",[568,2050,2052],{"className":2051},[611,1166],[568,2053,2055,2123],{"className":2054},[668,669],[568,2056,2058,2120],{"className":2057},[673],[568,2059,2061,2112],{"className":2060,"style":1176},[677],[568,2062,2063,2066],{"style":1179},[568,2064],{"className":2065,"style":1159},[685],[568,2067,2069,2072],{"className":2068},[611],[568,2070,589],{"className":2071,"style":613},[611,612],[568,2073,2075,2078],{"className":2074},[611],[568,2076,637],{"className":2077},[611,612],[568,2079,2081],{"className":2080},[664],[568,2082,2084,2104],{"className":2083},[668,669],[568,2085,2087,2101],{"className":2086},[673],[568,2088,2090],{"className":2089,"style":678},[677],[568,2091,2092,2095],{"style":681},[568,2093],{"className":2094,"style":686},[685],[568,2096,2098],{"className":2097},[690,691,692,693],[568,2099,641],{"className":2100},[611,693],[568,2102,701],{"className":2103},[700],[568,2105,2107],{"className":2106},[673],[568,2108,2110],{"className":2109,"style":708},[677],[568,2111],{},[568,2113,2114,2117],{"style":1268},[568,2115],{"className":2116,"style":1159},[685],[568,2118],{"className":2119,"style":1276},[1275],[568,2121,701],{"className":2122},[700],[568,2124,2126],{"className":2125},[673],[568,2127,2129],{"className":2128,"style":708},[677],[568,2130],{},[568,2132],{"className":2133,"style":1446},[1445],[568,2135,1088],{"className":2136},[1450],[568,2138],{"className":2139,"style":1446},[1445],[568,2141,2143,2147,2150,2154],{"className":2142},[602],[568,2144],{"className":2145,"style":2146},[606],"height:0.6444em;",[568,2148,2028],{"className":2149},[611],[568,2151],{"className":2152,"style":2153},[1445],"margin-right:0.1667em;",[568,2155,2158],{"className":2156},[611,2157],"text",[568,2159,2035],{"className":2160},[611],", ",[568,2163,2165,2200],{"className":2164},[571],[568,2166,2168],{"className":2167},[575],[577,2169,2170],{"xmlns":579},[581,2171,2172,2197],{},[584,2173,2174,2188,2190,2193,2195],{},[1048,2175,2176,2186],{"accent":598},[584,2177,2178,2180],{},[587,2179,589],{},[633,2181,2182,2184],{},[587,2183,637],{},[639,2185,804],{},[1065,2187,1067],{"stretchy":598},[1065,2189,1088],{},[639,2191,2192],{},"10",[2030,2194,2032],{},[2030,2196,2035],{},[591,2198,2199],{"encoding":593},"\\overline{SA_2} = 10\\,\\text{cm}",[568,2201,2203,2300],{"className":2202,"ariaHidden":598},[597],[568,2204,2206,2209,2291,2294,2297],{"className":2205},[602],[568,2207],{"className":2208,"style":2048},[606],[568,2210,2212],{"className":2211},[611,1166],[568,2213,2215,2283],{"className":2214},[668,669],[568,2216,2218,2280],{"className":2217},[673],[568,2219,2221,2272],{"className":2220,"style":1176},[677],[568,2222,2223,2226],{"style":1179},[568,2224],{"className":2225,"style":1159},[685],[568,2227,2229,2232],{"className":2228},[611],[568,2230,589],{"className":2231,"style":613},[611,612],[568,2233,2235,2238],{"className":2234},[611],[568,2236,637],{"className":2237},[611,612],[568,2239,2241],{"className":2240},[664],[568,2242,2244,2264],{"className":2243},[668,669],[568,2245,2247,2261],{"className":2246},[673],[568,2248,2250],{"className":2249,"style":678},[677],[568,2251,2252,2255],{"style":681},[568,2253],{"className":2254,"style":686},[685],[568,2256,2258],{"className":2257},[690,691,692,693],[568,2259,804],{"className":2260},[611,693],[568,2262,701],{"className":2263},[700],[568,2265,2267],{"className":2266},[673],[568,2268,2270],{"className":2269,"style":708},[677],[568,2271],{},[568,2273,2274,2277],{"style":1268},[568,2275],{"className":2276,"style":1159},[685],[568,2278],{"className":2279,"style":1276},[1275],[568,2281,701],{"className":2282},[700],[568,2284,2286],{"className":2285},[673],[568,2287,2289],{"className":2288,"style":708},[677],[568,2290],{},[568,2292],{"className":2293,"style":1446},[1445],[568,2295,1088],{"className":2296},[1450],[568,2298],{"className":2299,"style":1446},[1445],[568,2301,2303,2306,2309,2312],{"className":2302},[602],[568,2304],{"className":2305,"style":2146},[606],[568,2307,2192],{"className":2308},[611],[568,2310],{"className":2311,"style":2153},[1445],[568,2313,2315],{"className":2314},[611,2157],[568,2316,2035],{"className":2317},[611],[568,2319,2321,2356],{"className":2320},[571],[568,2322,2324],{"className":2323},[575],[577,2325,2326],{"xmlns":579},[581,2327,2328,2353],{},[584,2329,2330,2344,2346,2349,2351],{},[1048,2331,2332,2342],{"accent":598},[584,2333,2334,2336],{},[587,2335,589],{},[633,2337,2338,2340],{},[587,2339,728],{},[639,2341,641],{},[1065,2343,1067],{"stretchy":598},[1065,2345,1088],{},[639,2347,2348],{},"3",[2030,2350,2032],{},[2030,2352,2035],{},[591,2354,2355],{"encoding":593},"\\overline{SB_1} = 3\\,\\text{cm}",[568,2357,2359,2456],{"className":2358,"ariaHidden":598},[597],[568,2360,2362,2365,2447,2450,2453],{"className":2361},[602],[568,2363],{"className":2364,"style":2048},[606],[568,2366,2368],{"className":2367},[611,1166],[568,2369,2371,2439],{"className":2370},[668,669],[568,2372,2374,2436],{"className":2373},[673],[568,2375,2377,2428],{"className":2376,"style":1176},[677],[568,2378,2379,2382],{"style":1179},[568,2380],{"className":2381,"style":1159},[685],[568,2383,2385,2388],{"className":2384},[611],[568,2386,589],{"className":2387,"style":613},[611,612],[568,2389,2391,2394],{"className":2390},[611],[568,2392,728],{"className":2393,"style":749},[611,612],[568,2395,2397],{"className":2396},[664],[568,2398,2400,2420],{"className":2399},[668,669],[568,2401,2403,2417],{"className":2402},[673],[568,2404,2406],{"className":2405,"style":678},[677],[568,2407,2408,2411],{"style":764},[568,2409],{"className":2410,"style":686},[685],[568,2412,2414],{"className":2413},[690,691,692,693],[568,2415,641],{"className":2416},[611,693],[568,2418,701],{"className":2419},[700],[568,2421,2423],{"className":2422},[673],[568,2424,2426],{"className":2425,"style":708},[677],[568,2427],{},[568,2429,2430,2433],{"style":1268},[568,2431],{"className":2432,"style":1159},[685],[568,2434],{"className":2435,"style":1276},[1275],[568,2437,701],{"className":2438},[700],[568,2440,2442],{"className":2441},[673],[568,2443,2445],{"className":2444,"style":708},[677],[568,2446],{},[568,2448],{"className":2449,"style":1446},[1445],[568,2451,1088],{"className":2452},[1450],[568,2454],{"className":2455,"style":1446},[1445],[568,2457,2459,2462,2465,2468],{"className":2458},[602],[568,2460],{"className":2461,"style":2146},[606],[568,2463,2348],{"className":2464},[611],[568,2466],{"className":2467,"style":2153},[1445],[568,2469,2471],{"className":2470},[611,2157],[568,2472,2035],{"className":2473},[611],". Mit dem ersten Strahlensatz:",[568,2476,2478],{"className":2477},[1030],[568,2479,2481,2575],{"className":2480},[571],[568,2482,2484],{"className":2483},[575],[577,2485,2486],{"xmlns":579,"display":1039},[581,2487,2488,2572],{},[584,2489,2490,2496,2498,2522,2525,2528,2530,2544,2546,2559,2561,2563,2565,2568,2570],{},[1045,2491,2492,2494],{},[639,2493,2192],{},[639,2495,2028],{},[1065,2497,1088],{},[1045,2499,2500,2514],{},[1048,2501,2502,2512],{"accent":598},[584,2503,2504,2506],{},[587,2505,589],{},[633,2507,2508,2510],{},[587,2509,728],{},[639,2511,804],{},[1065,2513,1067],{"stretchy":598},[584,2515,2516,2518,2520],{},[639,2517,2348],{},[2030,2519,2032],{},[2030,2521,2035],{},[1445,2523],{"width":2524},"1em",[1065,2526,2527],{},"⇒",[1445,2529],{"width":2524},[1048,2531,2532,2542],{"accent":598},[584,2533,2534,2536],{},[587,2535,589],{},[633,2537,2538,2540],{},[587,2539,728],{},[639,2541,804],{},[1065,2543,1067],{"stretchy":598},[1065,2545,1088],{},[1045,2547,2548,2557],{},[584,2549,2550,2552,2555],{},[639,2551,2348],{},[1065,2553,2554],{},"⋅",[639,2556,2192],{},[639,2558,2028],{},[2030,2560,2032],{},[2030,2562,2035],{},[1065,2564,1088],{},[639,2566,2567],{},"7,5",[2030,2569,2032],{},[2030,2571,2035],{},[591,2573,2574],{"encoding":593},"\\frac{10}{4} = \\frac{\\overline{SB_2}}{3\\,\\text{cm}}\n\\quad\\Rightarrow\\quad\n\\overline{SB_2} = \\frac{3 \\cdot 10}{4}\\,\\text{cm} = 7{,}5\\,\\text{cm}",[568,2576,2578,2659,2832,2929,3029],{"className":2577,"ariaHidden":598},[597],[568,2579,2581,2585,2650,2653,2656],{"className":2580},[602],[568,2582],{"className":2583,"style":2584},[606],"height:2.0074em;vertical-align:-0.686em;",[568,2586,2588,2591,2647],{"className":2587},[611],[568,2589],{"className":2590},[1138,1139],[568,2592,2594],{"className":2593},[1045],[568,2595,2597,2638],{"className":2596},[668,669],[568,2598,2600,2635],{"className":2599},[673],[568,2601,2604,2616,2624],{"className":2602,"style":2603},[677],"height:1.3214em;",[568,2605,2607,2610],{"style":2606},"top:-2.314em;",[568,2608],{"className":2609,"style":1159},[685],[568,2611,2613],{"className":2612},[611],[568,2614,2028],{"className":2615},[611],[568,2617,2618,2621],{"style":1290},[568,2619],{"className":2620,"style":1159},[685],[568,2622],{"className":2623,"style":1276},[1297],[568,2625,2626,2629],{"style":1300},[568,2627],{"className":2628,"style":1159},[685],[568,2630,2632],{"className":2631},[611],[568,2633,2192],{"className":2634},[611],[568,2636,701],{"className":2637},[700],[568,2639,2641],{"className":2640},[673],[568,2642,2645],{"className":2643,"style":2644},[677],"height:0.686em;",[568,2646],{},[568,2648],{"className":2649},[1441,1139],[568,2651],{"className":2652,"style":1446},[1445],[568,2654,1088],{"className":2655},[1450],[568,2657],{"className":2658,"style":1446},[1445],[568,2660,2662,2666,2816,2820,2823,2826,2829],{"className":2661},[602],[568,2663],{"className":2664,"style":2665},[606],"height:2.2463em;vertical-align:-0.686em;",[568,2667,2669,2672,2813],{"className":2668},[611],[568,2670],{"className":2671},[1138,1139],[568,2673,2675],{"className":2674},[1045],[568,2676,2678,2805],{"className":2677},[668,669],[568,2679,2681,2802],{"className":2680},[673],[568,2682,2684,2704,2712],{"className":2683,"style":1152},[677],[568,2685,2686,2689],{"style":2606},[568,2687],{"className":2688,"style":1159},[685],[568,2690,2692,2695,2698],{"className":2691},[611],[568,2693,2348],{"className":2694},[611],[568,2696],{"className":2697,"style":2153},[1445],[568,2699,2701],{"className":2700},[611,2157],[568,2702,2035],{"className":2703},[611],[568,2705,2706,2709],{"style":1290},[568,2707],{"className":2708,"style":1159},[685],[568,2710],{"className":2711,"style":1276},[1297],[568,2713,2714,2717],{"style":1300},[568,2715],{"className":2716,"style":1159},[685],[568,2718,2720],{"className":2719},[611],[568,2721,2723],{"className":2722},[611,1166],[568,2724,2726,2794],{"className":2725},[668,669],[568,2727,2729,2791],{"className":2728},[673],[568,2730,2732,2783],{"className":2731,"style":1176},[677],[568,2733,2734,2737],{"style":1179},[568,2735],{"className":2736,"style":1159},[685],[568,2738,2740,2743],{"className":2739},[611],[568,2741,589],{"className":2742,"style":613},[611,612],[568,2744,2746,2749],{"className":2745},[611],[568,2747,728],{"className":2748,"style":749},[611,612],[568,2750,2752],{"className":2751},[664],[568,2753,2755,2775],{"className":2754},[668,669],[568,2756,2758,2772],{"className":2757},[673],[568,2759,2761],{"className":2760,"style":678},[677],[568,2762,2763,2766],{"style":764},[568,2764],{"className":2765,"style":686},[685],[568,2767,2769],{"className":2768},[690,691,692,693],[568,2770,804],{"className":2771},[611,693],[568,2773,701],{"className":2774},[700],[568,2776,2778],{"className":2777},[673],[568,2779,2781],{"className":2780,"style":708},[677],[568,2782],{},[568,2784,2785,2788],{"style":1268},[568,2786],{"className":2787,"style":1159},[685],[568,2789],{"className":2790,"style":1276},[1275],[568,2792,701],{"className":2793},[700],[568,2795,2797],{"className":2796},[673],[568,2798,2800],{"className":2799,"style":708},[677],[568,2801],{},[568,2803,701],{"className":2804},[700],[568,2806,2808],{"className":2807},[673],[568,2809,2811],{"className":2810,"style":2644},[677],[568,2812],{},[568,2814],{"className":2815},[1441,1139],[568,2817],{"className":2818,"style":2819},[1445],"margin-right:1em;",[568,2821],{"className":2822,"style":1446},[1445],[568,2824,2527],{"className":2825},[1450],[568,2827],{"className":2828,"style":2819},[1445],[568,2830],{"className":2831,"style":1446},[1445],[568,2833,2835,2838,2920,2923,2926],{"className":2834},[602],[568,2836],{"className":2837,"style":2048},[606],[568,2839,2841],{"className":2840},[611,1166],[568,2842,2844,2912],{"className":2843},[668,669],[568,2845,2847,2909],{"className":2846},[673],[568,2848,2850,2901],{"className":2849,"style":1176},[677],[568,2851,2852,2855],{"style":1179},[568,2853],{"className":2854,"style":1159},[685],[568,2856,2858,2861],{"className":2857},[611],[568,2859,589],{"className":2860,"style":613},[611,612],[568,2862,2864,2867],{"className":2863},[611],[568,2865,728],{"className":2866,"style":749},[611,612],[568,2868,2870],{"className":2869},[664],[568,2871,2873,2893],{"className":2872},[668,669],[568,2874,2876,2890],{"className":2875},[673],[568,2877,2879],{"className":2878,"style":678},[677],[568,2880,2881,2884],{"style":764},[568,2882],{"className":2883,"style":686},[685],[568,2885,2887],{"className":2886},[690,691,692,693],[568,2888,804],{"className":2889},[611,693],[568,2891,701],{"className":2892},[700],[568,2894,2896],{"className":2895},[673],[568,2897,2899],{"className":2898,"style":708},[677],[568,2900],{},[568,2902,2903,2906],{"style":1268},[568,2904],{"className":2905,"style":1159},[685],[568,2907],{"className":2908,"style":1276},[1275],[568,2910,701],{"className":2911},[700],[568,2913,2915],{"className":2914},[673],[568,2916,2918],{"className":2917,"style":708},[677],[568,2919],{},[568,2921],{"className":2922,"style":1446},[1445],[568,2924,1088],{"className":2925},[1450],[568,2927],{"className":2928,"style":1446},[1445],[568,2930,2932,2935,3011,3014,3020,3023,3026],{"className":2931},[602],[568,2933],{"className":2934,"style":2584},[606],[568,2936,2938,2941,3008],{"className":2937},[611],[568,2939],{"className":2940},[1138,1139],[568,2942,2944],{"className":2943},[1045],[568,2945,2947,3000],{"className":2946},[668,669],[568,2948,2950,2997],{"className":2949},[673],[568,2951,2953,2964,2972],{"className":2952,"style":2603},[677],[568,2954,2955,2958],{"style":2606},[568,2956],{"className":2957,"style":1159},[685],[568,2959,2961],{"className":2960},[611],[568,2962,2028],{"className":2963},[611],[568,2965,2966,2969],{"style":1290},[568,2967],{"className":2968,"style":1159},[685],[568,2970],{"className":2971,"style":1276},[1297],[568,2973,2974,2977],{"style":1300},[568,2975],{"className":2976,"style":1159},[685],[568,2978,2980,2983,2987,2991,2994],{"className":2979},[611],[568,2981,2348],{"className":2982},[611],[568,2984],{"className":2985,"style":2986},[1445],"margin-right:0.2222em;",[568,2988,2554],{"className":2989},[2990],"mbin",[568,2992],{"className":2993,"style":2986},[1445],[568,2995,2192],{"className":2996},[611],[568,2998,701],{"className":2999},[700],[568,3001,3003],{"className":3002},[673],[568,3004,3006],{"className":3005,"style":2644},[677],[568,3007],{},[568,3009],{"className":3010},[1441,1139],[568,3012],{"className":3013,"style":2153},[1445],[568,3015,3017],{"className":3016},[611,2157],[568,3018,2035],{"className":3019},[611],[568,3021],{"className":3022,"style":1446},[1445],[568,3024,1088],{"className":3025},[1450],[568,3027],{"className":3028,"style":1446},[1445],[568,3030,3032,3036,3040,3048,3052,3055],{"className":3031},[602],[568,3033],{"className":3034,"style":3035},[606],"height:0.8389em;vertical-align:-0.1944em;",[568,3037,3039],{"className":3038},[611],"7",[568,3041,3043],{"className":3042},[611],[568,3044,3047],{"className":3045},[3046],"mpunct",",",[568,3049,3051],{"className":3050},[611],"5",[568,3053],{"className":3054,"style":2153},[1445],[568,3056,3058],{"className":3057},[611,2157],[568,3059,2035],{"className":3060},[611],[564,3062,3063,3064,3260],{},"Ist in derselben Figur ",[568,3065,3067,3105],{"className":3066},[571],[568,3068,3070],{"className":3069},[575],[577,3071,3072],{"xmlns":579},[581,3073,3074,3102],{},[584,3075,3076,3094,3096,3098,3100],{},[1048,3077,3078,3092],{"accent":598},[584,3079,3080,3086],{},[633,3081,3082,3084],{},[587,3083,637],{},[639,3085,641],{},[633,3087,3088,3090],{},[587,3089,728],{},[639,3091,641],{},[1065,3093,1067],{"stretchy":598},[1065,3095,1088],{},[639,3097,804],{},[2030,3099,2032],{},[2030,3101,2035],{},[591,3103,3104],{"encoding":593},"\\overline{A_1B_1} = 2\\,\\text{cm}",[568,3106,3108,3242],{"className":3107,"ariaHidden":598},[597],[568,3109,3111,3114,3233,3236,3239],{"className":3110},[602],[568,3112],{"className":3113,"style":2048},[606],[568,3115,3117],{"className":3116},[611,1166],[568,3118,3120,3225],{"className":3119},[668,669],[568,3121,3123,3222],{"className":3122},[673],[568,3124,3126,3214],{"className":3125,"style":1176},[677],[568,3127,3128,3131],{"style":1179},[568,3129],{"className":3130,"style":1159},[685],[568,3132,3134,3174],{"className":3133},[611],[568,3135,3137,3140],{"className":3136},[611],[568,3138,637],{"className":3139},[611,612],[568,3141,3143],{"className":3142},[664],[568,3144,3146,3166],{"className":3145},[668,669],[568,3147,3149,3163],{"className":3148},[673],[568,3150,3152],{"className":3151,"style":678},[677],[568,3153,3154,3157],{"style":681},[568,3155],{"className":3156,"style":686},[685],[568,3158,3160],{"className":3159},[690,691,692,693],[568,3161,641],{"className":3162},[611,693],[568,3164,701],{"className":3165},[700],[568,3167,3169],{"className":3168},[673],[568,3170,3172],{"className":3171,"style":708},[677],[568,3173],{},[568,3175,3177,3180],{"className":3176},[611],[568,3178,728],{"className":3179,"style":749},[611,612],[568,3181,3183],{"className":3182},[664],[568,3184,3186,3206],{"className":3185},[668,669],[568,3187,3189,3203],{"className":3188},[673],[568,3190,3192],{"className":3191,"style":678},[677],[568,3193,3194,3197],{"style":764},[568,3195],{"className":3196,"style":686},[685],[568,3198,3200],{"className":3199},[690,691,692,693],[568,3201,641],{"className":3202},[611,693],[568,3204,701],{"className":3205},[700],[568,3207,3209],{"className":3208},[673],[568,3210,3212],{"className":3211,"style":708},[677],[568,3213],{},[568,3215,3216,3219],{"style":1268},[568,3217],{"className":3218,"style":1159},[685],[568,3220],{"className":3221,"style":1276},[1275],[568,3223,701],{"className":3224},[700],[568,3226,3228],{"className":3227},[673],[568,3229,3231],{"className":3230,"style":708},[677],[568,3232],{},[568,3234],{"className":3235,"style":1446},[1445],[568,3237,1088],{"className":3238},[1450],[568,3240],{"className":3241,"style":1446},[1445],[568,3243,3245,3248,3251,3254],{"className":3244},[602],[568,3246],{"className":3247,"style":2146},[606],[568,3249,804],{"className":3250},[611],[568,3252],{"className":3253,"style":2153},[1445],[568,3255,3257],{"className":3256},[611,2157],[568,3258,2035],{"className":3259},[611],", folgt mit dem zweiten Strahlensatz:",[568,3262,3264],{"className":3263},[1030],[568,3265,3267,3323],{"className":3266},[571],[568,3268,3270],{"className":3269},[575],[577,3271,3272],{"xmlns":579,"display":1039},[581,3273,3274,3320],{},[584,3275,3276,3294,3296,3308,3310,3312,3314,3316,3318],{},[1048,3277,3278,3292],{"accent":598},[584,3279,3280,3286],{},[633,3281,3282,3284],{},[587,3283,637],{},[639,3285,804],{},[633,3287,3288,3290],{},[587,3289,728],{},[639,3291,804],{},[1065,3293,1067],{"stretchy":598},[1065,3295,1088],{},[1045,3297,3298,3306],{},[584,3299,3300,3302,3304],{},[639,3301,804],{},[1065,3303,2554],{},[639,3305,2192],{},[639,3307,2028],{},[2030,3309,2032],{},[2030,3311,2035],{},[1065,3313,1088],{},[639,3315,3051],{},[2030,3317,2032],{},[2030,3319,2035],{},[591,3321,3322],{"encoding":593},"\\overline{A_2B_2} = \\frac{2 \\cdot 10}{4}\\,\\text{cm} = 5\\,\\text{cm}",[568,3324,3326,3460,3558],{"className":3325,"ariaHidden":598},[597],[568,3327,3329,3332,3451,3454,3457],{"className":3328},[602],[568,3330],{"className":3331,"style":2048},[606],[568,3333,3335],{"className":3334},[611,1166],[568,3336,3338,3443],{"className":3337},[668,669],[568,3339,3341,3440],{"className":3340},[673],[568,3342,3344,3432],{"className":3343,"style":1176},[677],[568,3345,3346,3349],{"style":1179},[568,3347],{"className":3348,"style":1159},[685],[568,3350,3352,3392],{"className":3351},[611],[568,3353,3355,3358],{"className":3354},[611],[568,3356,637],{"className":3357},[611,612],[568,3359,3361],{"className":3360},[664],[568,3362,3364,3384],{"className":3363},[668,669],[568,3365,3367,3381],{"className":3366},[673],[568,3368,3370],{"className":3369,"style":678},[677],[568,3371,3372,3375],{"style":681},[568,3373],{"className":3374,"style":686},[685],[568,3376,3378],{"className":3377},[690,691,692,693],[568,3379,804],{"className":3380},[611,693],[568,3382,701],{"className":3383},[700],[568,3385,3387],{"className":3386},[673],[568,3388,3390],{"className":3389,"style":708},[677],[568,3391],{},[568,3393,3395,3398],{"className":3394},[611],[568,3396,728],{"className":3397,"style":749},[611,612],[568,3399,3401],{"className":3400},[664],[568,3402,3404,3424],{"className":3403},[668,669],[568,3405,3407,3421],{"className":3406},[673],[568,3408,3410],{"className":3409,"style":678},[677],[568,3411,3412,3415],{"style":764},[568,3413],{"className":3414,"style":686},[685],[568,3416,3418],{"className":3417},[690,691,692,693],[568,3419,804],{"className":3420},[611,693],[568,3422,701],{"className":3423},[700],[568,3425,3427],{"className":3426},[673],[568,3428,3430],{"className":3429,"style":708},[677],[568,3431],{},[568,3433,3434,3437],{"style":1268},[568,3435],{"className":3436,"style":1159},[685],[568,3438],{"className":3439,"style":1276},[1275],[568,3441,701],{"className":3442},[700],[568,3444,3446],{"className":3445},[673],[568,3447,3449],{"className":3448,"style":708},[677],[568,3450],{},[568,3452],{"className":3453,"style":1446},[1445],[568,3455,1088],{"className":3456},[1450],[568,3458],{"className":3459,"style":1446},[1445],[568,3461,3463,3466,3540,3543,3549,3552,3555],{"className":3462},[602],[568,3464],{"className":3465,"style":2584},[606],[568,3467,3469,3472,3537],{"className":3468},[611],[568,3470],{"className":3471},[1138,1139],[568,3473,3475],{"className":3474},[1045],[568,3476,3478,3529],{"className":3477},[668,669],[568,3479,3481,3526],{"className":3480},[673],[568,3482,3484,3495,3503],{"className":3483,"style":2603},[677],[568,3485,3486,3489],{"style":2606},[568,3487],{"className":3488,"style":1159},[685],[568,3490,3492],{"className":3491},[611],[568,3493,2028],{"className":3494},[611],[568,3496,3497,3500],{"style":1290},[568,3498],{"className":3499,"style":1159},[685],[568,3501],{"className":3502,"style":1276},[1297],[568,3504,3505,3508],{"style":1300},[568,3506],{"className":3507,"style":1159},[685],[568,3509,3511,3514,3517,3520,3523],{"className":3510},[611],[568,3512,804],{"className":3513},[611],[568,3515],{"className":3516,"style":2986},[1445],[568,3518,2554],{"className":3519},[2990],[568,3521],{"className":3522,"style":2986},[1445],[568,3524,2192],{"className":3525},[611],[568,3527,701],{"className":3528},[700],[568,3530,3532],{"className":3531},[673],[568,3533,3535],{"className":3534,"style":2644},[677],[568,3536],{},[568,3538],{"className":3539},[1441,1139],[568,3541],{"className":3542,"style":2153},[1445],[568,3544,3546],{"className":3545},[611,2157],[568,3547,2035],{"className":3548},[611],[568,3550],{"className":3551,"style":1446},[1445],[568,3553,1088],{"className":3554},[1450],[568,3556],{"className":3557,"style":1446},[1445],[568,3559,3561,3564,3567,3570],{"className":3560},[602],[568,3562],{"className":3563,"style":2146},[606],[568,3565,3051],{"className":3566},[611],[568,3568],{"className":3569,"style":2153},[1445],[568,3571,3573],{"className":3572},[611,2157],[568,3574,2035],{"className":3575},[611],[564,3577,3578,3579,3622,3623,3651,3652,3694,3695,3738],{},"Höhe eines Baumes: Man stellt einen ",[568,3580,3582,3601],{"className":3581},[571],[568,3583,3585],{"className":3584},[575],[577,3586,3587],{"xmlns":579},[581,3588,3589,3598],{},[584,3590,3591,3593,3595],{},[639,3592,804],{},[2030,3594,2032],{},[2030,3596,3597],{},"m",[591,3599,3600],{"encoding":593},"2\\,\\text{m}",[568,3602,3604],{"className":3603,"ariaHidden":598},[597],[568,3605,3607,3610,3613,3616],{"className":3606},[602],[568,3608],{"className":3609,"style":2146},[606],[568,3611,804],{"className":3612},[611],[568,3614],{"className":3615,"style":2153},[1445],[568,3617,3619],{"className":3618},[611,2157],[568,3620,3597],{"className":3621},[611]," hohen Stab senkrecht so auf, dass die Spitze seines Schattens genau auf die Spitze des Baumschattens fällt. Dieser gemeinsame Punkt ist ",[568,3624,3626,3639],{"className":3625},[571],[568,3627,3629],{"className":3628},[575],[577,3630,3631],{"xmlns":579},[581,3632,3633,3637],{},[584,3634,3635],{},[587,3636,589],{},[591,3638,589],{"encoding":593},[568,3640,3642],{"className":3641,"ariaHidden":598},[597],[568,3643,3645,3648],{"className":3644},[602],[568,3646],{"className":3647,"style":607},[606],[568,3649,589],{"className":3650,"style":613},[611,612],". Der erste Strahl ist der Boden, der zweite der Sonnenstrahl, der über die Spitze des Stabes und die Spitze des Baumes läuft. Stab und Baum stehen beide senkrecht, sind also parallel. Der Schatten des Stabes ist ",[568,3653,3655,3673],{"className":3654},[571],[568,3656,3658],{"className":3657},[575],[577,3659,3660],{"xmlns":579},[581,3661,3662,3670],{},[584,3663,3664,3666,3668],{},[639,3665,2348],{},[2030,3667,2032],{},[2030,3669,3597],{},[591,3671,3672],{"encoding":593},"3\\,\\text{m}",[568,3674,3676],{"className":3675,"ariaHidden":598},[597],[568,3677,3679,3682,3685,3688],{"className":3678},[602],[568,3680],{"className":3681,"style":2146},[606],[568,3683,2348],{"className":3684},[611],[568,3686],{"className":3687,"style":2153},[1445],[568,3689,3691],{"className":3690},[611,2157],[568,3692,3597],{"className":3693},[611]," lang, der des Baumes ",[568,3696,3698,3717],{"className":3697},[571],[568,3699,3701],{"className":3700},[575],[577,3702,3703],{"xmlns":579},[581,3704,3705,3714],{},[584,3706,3707,3710,3712],{},[639,3708,3709],{},"18",[2030,3711,2032],{},[2030,3713,3597],{},[591,3715,3716],{"encoding":593},"18\\,\\text{m}",[568,3718,3720],{"className":3719,"ariaHidden":598},[597],[568,3721,3723,3726,3729,3732],{"className":3722},[602],[568,3724],{"className":3725,"style":2146},[606],[568,3727,3709],{"className":3728},[611],[568,3730],{"className":3731,"style":2153},[1445],[568,3733,3735],{"className":3734},[611,2157],[568,3736,3597],{"className":3737},[611],". Mit dem zweiten Strahlensatz:",[568,3740,3742],{"className":3741},[1030],[568,3743,3745,3848],{"className":3744},[571],[568,3746,3748],{"className":3747},[575],[577,3749,3750],{"xmlns":579,"display":1039},[581,3751,3752,3845],{},[584,3753,3754,3780,3782,3800,3802,3804,3806,3818,3820,3832,3834,3836,3838,3841,3843],{},[1045,3755,3756,3772],{},[584,3757,3758,3761,3769],{},[2030,3759,3760],{},"Baumh",[1048,3762,3763,3766],{"accent":598},[2030,3764,3765],{},"o",[1065,3767,3768],{},"¨",[2030,3770,3771],{},"he",[584,3773,3774,3776,3778],{},[639,3775,804],{},[2030,3777,2032],{},[2030,3779,3597],{},[1065,3781,1088],{},[1045,3783,3784,3792],{},[584,3785,3786,3788,3790],{},[639,3787,3709],{},[2030,3789,2032],{},[2030,3791,3597],{},[584,3793,3794,3796,3798],{},[639,3795,2348],{},[2030,3797,2032],{},[2030,3799,3597],{},[1445,3801],{"width":2524},[1065,3803,2527],{},[1445,3805],{"width":2524},[584,3807,3808,3810,3816],{},[2030,3809,3760],{},[1048,3811,3812,3814],{"accent":598},[2030,3813,3765],{},[1065,3815,3768],{},[2030,3817,3771],{},[1065,3819,1088],{},[1045,3821,3822,3830],{},[584,3823,3824,3826,3828],{},[639,3825,804],{},[1065,3827,2554],{},[639,3829,3709],{},[639,3831,2348],{},[2030,3833,2032],{},[2030,3835,3597],{},[1065,3837,1088],{},[639,3839,3840],{},"12",[2030,3842,2032],{},[2030,3844,3597],{},[591,3846,3847],{"encoding":593},"\\frac{\\text{Baumhöhe}}{2\\,\\text{m}} = \\frac{18\\,\\text{m}}{3\\,\\text{m}}\n\\quad\\Rightarrow\\quad\n\\text{Baumhöhe} = \\frac{2 \\cdot 18}{3}\\,\\text{m} = 12\\,\\text{m}",[568,3849,3851,3980,4081,4137,4235],{"className":3850,"ariaHidden":598},[597],[568,3852,3854,3858,3971,3974,3977],{"className":3853},[602],[568,3855],{"className":3856,"style":3857},[606],"height:2.0574em;vertical-align:-0.686em;",[568,3859,3861,3864,3968],{"className":3860},[611],[568,3862],{"className":3863},[1138,1139],[568,3865,3867],{"className":3866},[1045],[568,3868,3870,3960],{"className":3869},[668,669],[568,3871,3873,3957],{"className":3872},[673],[568,3874,3877,3897,3905],{"className":3875,"style":3876},[677],"height:1.3714em;",[568,3878,3879,3882],{"style":2606},[568,3880],{"className":3881,"style":1159},[685],[568,3883,3885,3888,3891],{"className":3884},[611],[568,3886,804],{"className":3887},[611],[568,3889],{"className":3890,"style":2153},[1445],[568,3892,3894],{"className":3893},[611,2157],[568,3895,3597],{"className":3896},[611],[568,3898,3899,3902],{"style":1290},[568,3900],{"className":3901,"style":1159},[685],[568,3903],{"className":3904,"style":1276},[1297],[568,3906,3907,3910],{"style":1300},[568,3908],{"className":3909,"style":1159},[685],[568,3911,3913],{"className":3912},[611],[568,3914,3916,3919,3954],{"className":3915},[611,2157],[568,3917,3760],{"className":3918},[611],[568,3920,3923],{"className":3921},[611,3922],"accent",[568,3924,3926],{"className":3925},[668],[568,3927,3929],{"className":3928},[673],[568,3930,3933,3941],{"className":3931,"style":3932},[677],"height:0.6679em;",[568,3934,3935,3938],{"style":1179},[568,3936],{"className":3937,"style":1159},[685],[568,3939,3765],{"className":3940},[611],[568,3942,3943,3946],{"style":1179},[568,3944],{"className":3945,"style":1159},[685],[568,3947,3951],{"className":3948,"style":3950},[3949],"accent-body","left:-0.25em;",[568,3952,3768],{"className":3953},[611],[568,3955,3771],{"className":3956},[611],[568,3958,701],{"className":3959},[700],[568,3961,3963],{"className":3962},[673],[568,3964,3966],{"className":3965,"style":2644},[677],[568,3967],{},[568,3969],{"className":3970},[1441,1139],[568,3972],{"className":3973,"style":1446},[1445],[568,3975,1088],{"className":3976},[1450],[568,3978],{"className":3979,"style":1446},[1445],[568,3981,3983,3986,4066,4069,4072,4075,4078],{"className":3982},[602],[568,3984],{"className":3985,"style":2584},[606],[568,3987,3989,3992,4063],{"className":3988},[611],[568,3990],{"className":3991},[1138,1139],[568,3993,3995],{"className":3994},[1045],[568,3996,3998,4055],{"className":3997},[668,669],[568,3999,4001,4052],{"className":4000},[673],[568,4002,4004,4024,4032],{"className":4003,"style":2603},[677],[568,4005,4006,4009],{"style":2606},[568,4007],{"className":4008,"style":1159},[685],[568,4010,4012,4015,4018],{"className":4011},[611],[568,4013,2348],{"className":4014},[611],[568,4016],{"className":4017,"style":2153},[1445],[568,4019,4021],{"className":4020},[611,2157],[568,4022,3597],{"className":4023},[611],[568,4025,4026,4029],{"style":1290},[568,4027],{"className":4028,"style":1159},[685],[568,4030],{"className":4031,"style":1276},[1297],[568,4033,4034,4037],{"style":1300},[568,4035],{"className":4036,"style":1159},[685],[568,4038,4040,4043,4046],{"className":4039},[611],[568,4041,3709],{"className":4042},[611],[568,4044],{"className":4045,"style":2153},[1445],[568,4047,4049],{"className":4048},[611,2157],[568,4050,3597],{"className":4051},[611],[568,4053,701],{"className":4054},[700],[568,4056,4058],{"className":4057},[673],[568,4059,4061],{"className":4060,"style":2644},[677],[568,4062],{},[568,4064],{"className":4065},[1441,1139],[568,4067],{"className":4068,"style":2819},[1445],[568,4070],{"className":4071,"style":1446},[1445],[568,4073,2527],{"className":4074},[1450],[568,4076],{"className":4077,"style":2819},[1445],[568,4079],{"className":4080,"style":1446},[1445],[568,4082,4084,4088,4128,4131,4134],{"className":4083},[602],[568,4085],{"className":4086,"style":4087},[606],"height:0.6944em;",[568,4089,4091,4094,4125],{"className":4090},[611,2157],[568,4092,3760],{"className":4093},[611],[568,4095,4097],{"className":4096},[611,3922],[568,4098,4100],{"className":4099},[668],[568,4101,4103],{"className":4102},[673],[568,4104,4106,4114],{"className":4105,"style":3932},[677],[568,4107,4108,4111],{"style":1179},[568,4109],{"className":4110,"style":1159},[685],[568,4112,3765],{"className":4113},[611],[568,4115,4116,4119],{"style":1179},[568,4117],{"className":4118,"style":1159},[685],[568,4120,4122],{"className":4121,"style":3950},[3949],[568,4123,3768],{"className":4124},[611],[568,4126,3771],{"className":4127},[611],[568,4129],{"className":4130,"style":1446},[1445],[568,4132,1088],{"className":4133},[1450],[568,4135],{"className":4136,"style":1446},[1445],[568,4138,4140,4143,4217,4220,4226,4229,4232],{"className":4139},[602],[568,4141],{"className":4142,"style":2584},[606],[568,4144,4146,4149,4214],{"className":4145},[611],[568,4147],{"className":4148},[1138,1139],[568,4150,4152],{"className":4151},[1045],[568,4153,4155,4206],{"className":4154},[668,669],[568,4156,4158,4203],{"className":4157},[673],[568,4159,4161,4172,4180],{"className":4160,"style":2603},[677],[568,4162,4163,4166],{"style":2606},[568,4164],{"className":4165,"style":1159},[685],[568,4167,4169],{"className":4168},[611],[568,4170,2348],{"className":4171},[611],[568,4173,4174,4177],{"style":1290},[568,4175],{"className":4176,"style":1159},[685],[568,4178],{"className":4179,"style":1276},[1297],[568,4181,4182,4185],{"style":1300},[568,4183],{"className":4184,"style":1159},[685],[568,4186,4188,4191,4194,4197,4200],{"className":4187},[611],[568,4189,804],{"className":4190},[611],[568,4192],{"className":4193,"style":2986},[1445],[568,4195,2554],{"className":4196},[2990],[568,4198],{"className":4199,"style":2986},[1445],[568,4201,3709],{"className":4202},[611],[568,4204,701],{"className":4205},[700],[568,4207,4209],{"className":4208},[673],[568,4210,4212],{"className":4211,"style":2644},[677],[568,4213],{},[568,4215],{"className":4216},[1441,1139],[568,4218],{"className":4219,"style":2153},[1445],[568,4221,4223],{"className":4222},[611,2157],[568,4224,3597],{"className":4225},[611],[568,4227],{"className":4228,"style":1446},[1445],[568,4230,1088],{"className":4231},[1450],[568,4233],{"className":4234,"style":1446},[1445],[568,4236,4238,4241,4244,4247],{"className":4237},[602],[568,4239],{"className":4240,"style":2146},[606],[568,4242,3840],{"className":4243},[611],[568,4245],{"className":4246,"style":2153},[1445],[568,4248,4250],{"className":4249},[611,2157],[568,4251,3597],{"className":4252},[611],[559,4254,4256],{"id":4255},"typische-fehler","Typische Fehler",[4258,4259,4260,4264,4579],"ul",{},[4261,4262,4263],"li",{},"Die Strahlensätze anwenden, obwohl die Geraden nicht parallel sind.",[4261,4265,4266,4267,4428,4429,4549,4550,4578],{},"Beim zweiten Strahlensatz die Teilstrecke ",[568,4268,4270,4300],{"className":4269},[571],[568,4271,4273],{"className":4272},[575],[577,4274,4275],{"xmlns":579},[581,4276,4277,4297],{},[584,4278,4279],{},[1048,4280,4281,4295],{"accent":598},[584,4282,4283,4289],{},[633,4284,4285,4287],{},[587,4286,637],{},[639,4288,641],{},[633,4290,4291,4293],{},[587,4292,637],{},[639,4294,804],{},[1065,4296,1067],{"stretchy":598},[591,4298,4299],{"encoding":593},"\\overline{A_1A_2}",[568,4301,4303],{"className":4302,"ariaHidden":598},[597],[568,4304,4306,4309],{"className":4305},[602],[568,4307],{"className":4308,"style":2048},[606],[568,4310,4312],{"className":4311},[611,1166],[568,4313,4315,4420],{"className":4314},[668,669],[568,4316,4318,4417],{"className":4317},[673],[568,4319,4321,4409],{"className":4320,"style":1176},[677],[568,4322,4323,4326],{"style":1179},[568,4324],{"className":4325,"style":1159},[685],[568,4327,4329,4369],{"className":4328},[611],[568,4330,4332,4335],{"className":4331},[611],[568,4333,637],{"className":4334},[611,612],[568,4336,4338],{"className":4337},[664],[568,4339,4341,4361],{"className":4340},[668,669],[568,4342,4344,4358],{"className":4343},[673],[568,4345,4347],{"className":4346,"style":678},[677],[568,4348,4349,4352],{"style":681},[568,4350],{"className":4351,"style":686},[685],[568,4353,4355],{"className":4354},[690,691,692,693],[568,4356,641],{"className":4357},[611,693],[568,4359,701],{"className":4360},[700],[568,4362,4364],{"className":4363},[673],[568,4365,4367],{"className":4366,"style":708},[677],[568,4368],{},[568,4370,4372,4375],{"className":4371},[611],[568,4373,637],{"className":4374},[611,612],[568,4376,4378],{"className":4377},[664],[568,4379,4381,4401],{"className":4380},[668,669],[568,4382,4384,4398],{"className":4383},[673],[568,4385,4387],{"className":4386,"style":678},[677],[568,4388,4389,4392],{"style":681},[568,4390],{"className":4391,"style":686},[685],[568,4393,4395],{"className":4394},[690,691,692,693],[568,4396,804],{"className":4397},[611,693],[568,4399,701],{"className":4400},[700],[568,4402,4404],{"className":4403},[673],[568,4405,4407],{"className":4406,"style":708},[677],[568,4408],{},[568,4410,4411,4414],{"style":1268},[568,4412],{"className":4413,"style":1159},[685],[568,4415],{"className":4416,"style":1276},[1275],[568,4418,701],{"className":4419},[700],[568,4421,4423],{"className":4422},[673],[568,4424,4426],{"className":4425,"style":708},[677],[568,4427],{}," statt ",[568,4430,4432,4458],{"className":4431},[571],[568,4433,4435],{"className":4434},[575],[577,4436,4437],{"xmlns":579},[581,4438,4439,4455],{},[584,4440,4441],{},[1048,4442,4443,4453],{"accent":598},[584,4444,4445,4447],{},[587,4446,589],{},[633,4448,4449,4451],{},[587,4450,637],{},[639,4452,804],{},[1065,4454,1067],{"stretchy":598},[591,4456,4457],{"encoding":593},"\\overline{SA_2}",[568,4459,4461],{"className":4460,"ariaHidden":598},[597],[568,4462,4464,4467],{"className":4463},[602],[568,4465],{"className":4466,"style":2048},[606],[568,4468,4470],{"className":4469},[611,1166],[568,4471,4473,4541],{"className":4472},[668,669],[568,4474,4476,4538],{"className":4475},[673],[568,4477,4479,4530],{"className":4478,"style":1176},[677],[568,4480,4481,4484],{"style":1179},[568,4482],{"className":4483,"style":1159},[685],[568,4485,4487,4490],{"className":4486},[611],[568,4488,589],{"className":4489,"style":613},[611,612],[568,4491,4493,4496],{"className":4492},[611],[568,4494,637],{"className":4495},[611,612],[568,4497,4499],{"className":4498},[664],[568,4500,4502,4522],{"className":4501},[668,669],[568,4503,4505,4519],{"className":4504},[673],[568,4506,4508],{"className":4507,"style":678},[677],[568,4509,4510,4513],{"style":681},[568,4511],{"className":4512,"style":686},[685],[568,4514,4516],{"className":4515},[690,691,692,693],[568,4517,804],{"className":4518},[611,693],[568,4520,701],{"className":4521},[700],[568,4523,4525],{"className":4524},[673],[568,4526,4528],{"className":4527,"style":708},[677],[568,4529],{},[568,4531,4532,4535],{"style":1268},[568,4533],{"className":4534,"style":1159},[685],[568,4536],{"className":4537,"style":1276},[1275],[568,4539,701],{"className":4540},[700],[568,4542,4544],{"className":4543},[673],[568,4545,4547],{"className":4546,"style":708},[677],[568,4548],{}," einsetzen. Die Strecken auf den Strahlen beginnen dort immer bei ",[568,4551,4553,4566],{"className":4552},[571],[568,4554,4556],{"className":4555},[575],[577,4557,4558],{"xmlns":579},[581,4559,4560,4564],{},[584,4561,4562],{},[587,4563,589],{},[591,4565,589],{"encoding":593},[568,4567,4569],{"className":4568,"ariaHidden":598},[597],[568,4570,4572,4575],{"className":4571},[602],[568,4573],{"className":4574,"style":607},[606],[568,4576,589],{"className":4577,"style":613},[611,612],".",[4261,4580,4581],{},"Brüche verschieden aufstellen: Steht links die längere Strecke im Zähler, muss das auch rechts so sein.",{"title":4583,"searchDepth":4584,"depth":4584,"links":4585},"",2,[4586,4587,4588],{"id":561,"depth":4584,"text":562},{"id":1993,"depth":4584,"text":1994},{"id":4255,"depth":4584,"text":4256},[4590,4593,4596,4598],{"lhs":4591,"rhs":4592},"10 \u002F 4","7.5 \u002F 3",{"lhs":4594,"rhs":4595},"3 * 10 \u002F 4","7.5",{"lhs":4597,"rhs":3051},"2 * 10 \u002F 4",{"lhs":4599,"rhs":3840},"2 * 18 \u002F 3","A_1B_1 \\parallel A_2B_2","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>A\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>B\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>∥\u003C\u002Fmo>\u003Cmsub>\u003Cmi>A\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>B\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A_1B_1 \\parallel A_2B_2\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0502em;\">B\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0502em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0502em;\">B\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0502em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md",{"caption":4605,"x":4606,"y":4609,"unit":4612,"items":4613},"Zwei Strahlen mit dem Scheitelpunkt S, geschnitten von den Parallelen A₁B₁ und 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