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0 <br />IV <br />TABLE IV. - Tancrcnts and .Externals to a 10.0uvk.. . <br />. Angle <br />I Tangent <br />I Exturnal <br />II .Angle <br />I Tangent <br />I External <br />II Angle I Tangent <br />I }internal <br />31° <br />I -599,0 <br />210::3 <br />41° • <br />2142.2 <br />38'.4 <br />51° <br />2732,9 <br />4803.6 <br />10' <br />.1598.0 <br />218.7 <br />10' <br />2151.7 <br />I <br />300.7 <br />10' <br />2743.1 <br />C22.R <br />20 <br />1606.9 <br />221.1 <br />20 <br />2161..2 <br />394.1 <br />20 <br />2753,4 <br />'627.2 <br />30 <br />1615.9 <br />223.5 <br />302170.3 <br />30 <br />397.4 <br />80 <br />2763.7 <br />631.7 <br />40.. <br />.1624.9 <br />226.0 <br />40 <br />'180.3 <br />400.8 <br />40 <br />2773.9 <br />. 636,2 <br />50 <br />.1633.9 <br />228.4 <br />50 <br />'2189:9 <br />404.2 <br />50 <br />2781.2 <br />640.7 <br />32. <br />;1643.0230.9 <br />3442.7 <br />421. <br />2199.4 <br />407.6 <br />52 <br />2794.5. <br />04"u:2 <br />10 <br />1.652,0 <br />233,4 <br />10 <br />2209.0 <br />41.1,1 <br />.'10 <br />2304.9 <br />640,7 <br />:20 <br />_1661.0 <br />235.9 <br />20 <br />'2218,6 <br />. 414,5 <br />20 <br />2815.2 <br />654.8 <br />30 . <br />"1670:0 <br />235.4 <br />30 <br />2228:1 <br />418.0 <br />30 <br />2325.6 <br />6.5R.S <br />- 4U <br />X1679:1 <br />241.0 <br />.: 40 <br />2237 <br />421,4 <br />- t40 <br />233.5.9 <br />- 063.4 <br />50 <br />'16881 <br />243.5'- <br />50 <br />2,'47:3 <br />425.0 <br />50 <br />2546.3 <br />668.0 <br />• 33 <br />' <br />1697:2 , <br />'1706:3 <br />246,1 <br />43 : <br />2257:0 <br />428.5 <br />53 <br />2856.7 <br />672:7 <br />' 10 <br />10 <br />248.1 <br />10 <br />2266:6 <br />432.0 <br />10 <br />2367.1 <br />677.3 <br />3U <br />7715:3 <br />,. 251.3 <br />20 <br />2276 2 <br />435.6 <br />..20 <br />2877.5 <br />632.0 <br />80 <br />' <br />7724:4. <br />. 253.9 <br />30 <br />•2+85.9 <br />439.2 <br />30 <br />2888.0 <br />656.7 <br />40 <br />.1733.5 <br />256.5 <br />40 <br />2295.6 <br />442,3 <br />40 <br />29AR.4 <br />f,9 L.4 <br />50 <br />1;42:6 ' <br />259.1 <br />50 <br />2305,2 <br />446.4 <br />5U <br />2908.9 <br />696.1 <br />34 - <br />• 10 <br />1151:7 <br />261.8 <br />44 <br />2314.9 <br />450,0 <br />54 <br />2919.9 <br />700.9 <br />20 <br />;1760.8 <br />264,5 <br />10 <br />2324.6 <br />453.6 <br />to <br />2929.9 <br />.705.7 <br />. <br />30 <br />1770.0 <br />267.2 <br />20 <br />2334,3 <br />457.8 <br />20 <br />.2940.4 <br />510,6 <br />2000.6 <br />1779.1 <br />269.9 <br />30 <br />2344.1 <br />4fi1,0 <br />30 <br />2951.0 <br />715,3 <br />. 40 <br />50 <br />1788:2 <br />272.6 <br />40 <br />2853,8 <br />464.6 <br />90•2961.5 <br />-40 <br />72.1 <br />2021.1 <br />.1797:4 <br />275.3 <br />50 <br />2363.5 <br />468.4 <br />50 <br />2972,1 ' <br />7255.0 <br />35 <br />1806!6 <br />278.1 <br />45 <br />-373,9 <br />472.1 <br />55 <br />2932.; <br />729,9 <br />10 <br />20 <br />1815:'; <br />280.8 <br />10 <br />23,93.1 <br />475.8 <br />10 <br />299:3.3 <br />5:34.8 <br />.. <br />30 <br />.1824:9 <br />283,6 <br />20 <br />2392.3 <br />479,6 <br />20 <br />3003.9 <br />739.7 <br />40 <br />1534.1 <br />266.4 <br />30 <br />-2402.6 <br />483.8 <br />30 <br />3014.5 <br />744.6 <br />50 <br />7893.3 <br />259.2 <br />40 <br />2412.4 <br />'481.2 <br />40 <br />3025.2 <br />749.6 <br />2089.5 <br />1852.5 <br />292.0 <br />50 <br />2422.3 <br />491.0 <br />-b0 <br />3035.8 <br />754.6 <br />:36 <br />1581.7 <br />294,9 <br />41. " <br />2432.1 <br />494.8 <br />56 <br />3016.5 <br />759.6 <br />10 <br />20 <br />1870.9 <br />297.7 <br />..10• <br />2441.9 <br />498.7 <br />10 <br />3057.2 <br />764 6 <br />30 <br />1880.1 <br />'1889.4 <br />300.6 <br />20 <br />2451.8 <br />502,5 <br />20 <br />3067.9 <br />',69,7 <br />2115.3 <br />' 26' <br />303.5 <br />30 <br />2461,7 <br />506.4 ' <br />30 <br />307S.7 <br />77417 <br />'10 <br />50 <br />1893:6 . <br />306.4 <br />40 <br />2471,5 <br />510.3 <br />40 <br />3069.4 <br />779.9 <br />21311.' <br />1907.9 <br />309.3 <br />-50 <br />2481.4 <br />514,3 <br />50 <br />3100.2 <br />784.9 <br />X37 <br />10 <br />1917.1 <br />312:2 <br />47 <br />2491:9 <br />518.2 <br />57 <br />3110,9 <br />790,1 <br />. <br />20 <br />.1926.4 <br />315.2 <br />10 <br />2501.2 <br />522.2 <br />10 <br />3131,1 <br />495.2 <br />- <br />30 <br />-1935.1 <br />318.1 <br />- 20 <br />251 .2 <br />526.1 <br />20 <br />3132.6 <br />800.4 <br />40 <br />1945.0 <br />321.1 <br />30 <br />2521.1 <br />530.1 <br />30 <br />3143.4' <br />805.6 <br />- <br />50 <br />MA .3 <br />324.1 <br />40 <br />25.91.:1 <br />534.2 <br />40 <br />:3154.2 <br />810,9 <br />2202.2 <br />,1963.6 <br />327,1 <br />50 <br />2541,0 <br />536.2 <br />50 <br />3165.1 <br />816.1 <br />'38' <br />LO <br />1972.9 <br />330.2 <br />4S <br />2551.0 <br />542:2 <br />58 <br />3116:0 <br />621.4 <br />20 <br />1932.2 <br />383.'2 <br />10 <br />2561:0 <br />546.3 <br />10 <br />3186,9 <br />826.7 <br />30 <br />1991,5 <br />2000.9 <br />336.3 <br />*89.3 <br />20 <br />2571:0 <br />550.4 <br />20 <br />3197.8 <br />332.0 <br />40 <br />•2010.2 <br />342.4 <br />30 <br />40 <br />2531.0 <br />554,5 <br />30 <br />3209.5 <br />537.3 <br />50 <br />2019.6 <br />345.5 <br />50 <br />2591.0 <br />553.6 <br />40 <br />3219.7 <br />842.7 <br />2269.3 <br />40 <br />3913.4 <br />1208.9 <br />2G0.1.1 <br />562,8 <br />50 <br />3230.7 <br />848,1 <br />'39 ' <br />10 <br />2029.0 <br />343.6 <br />49 <br />261.1.2 <br />566,9 <br />59 <br />3241,7 <br />553,5 <br />,' <br />:20 <br />2038.4 <br />2047.8 <br />351,8 <br />10 <br />`l0 <br />2621.2 <br />571,1 <br />10 <br />8252.- <br />853.9 <br />30 <br />- 10 <br />354.9 <br />1229.7 <br />2631.3 <br />575.3 <br />20 <br />32-53.7 <br />864.9 <br />.i 90 <br />2057.2 <br />2 OG6.6 <br />358.1 <br />361.3 <br />30 <br />40 <br />2641.4 <br />579.5 <br />30 <br />27 <br />3..:x,8 <br />88,9,6 <br />50 <br />2076.0 <br />364.5 <br />50 <br />2651.5 <br />2661.6 <br />583,3 <br />40 <br />3255.8 <br />875.3 <br />2338.2 <br />40 <br />3987.2 <br />1250,9 <br />40 <br />598.0 <br />50 <br />329G.9 <br />690.8 <br />'40 <br />10 <br />2055,4 <br />367.7 <br />50 <br />2671.8 <br />593.8 <br />60 <br />3308.0 <br />886.4 <br />. <br />20 <br />2094,9 <br />2104.* <br />871.0 <br />374.2 <br />10 <br />20 <br />2GS1,9 <br />596.6 <br />10 <br />'3819.1 <br />392.0 <br />30 <br />21.13 <br />375.5 <br />30 <br />2692.1 <br />60(1.9 <br />20 <br />3330.3 <br />897.5 <br />40 <br />.8 <br />2123,3 I <br />380.8 <br />40 <br />2702.3 <br />2712.5 <br />605,3 <br />609.6 <br />30 <br />40 <br />3341.4 <br />903.2 <br />u b0 <br />2132 7 <br />384.1 <br />50 <br />272' <br />l.7 <br />614,0 <br />50 <br />*352.6 <br />3363.8 <br />908.8 <br />914.5 <br />A, <br />"'v <br />TABLE IV. - Tangents and Externals to a 1e Curve. <br />Angle I <br />Tangent <br />External <br />Angle I <br />Tangent <br />External <br />.Angle <br />Tangent <br />I External <br />61° I <br />8375.0 <br />920.2 <br />71° <br />4036.9 <br />1308.2 <br />SI" ' <br />4803.6 <br />18115.3 <br />10' I <br />3336.3 <br />925.9 <br />10' <br />4099.5 <br />1315.6 <br />- .10' <br />4903.0 <br />1814.7 <br />20 <br />3397.5 <br />931.6 <br />-20 <br />4112.1 <br />1322.9 <br />20 <br />4922.5 <br />1924.1 <br />308405.3 <br />997.3 <br />30 <br />4124.8 <br />1330.3 <br />30 <br />4937.0 <br />1333.6 <br />'9U <br />3420.1 <br />948, 1. <br />41) <br />4137.4 <br />1337,7 <br />40 <br />4051.5 <br />1313.1 <br />50 <br />343L.4 <br />948.9 <br />50 <br />4150.1 <br />1345.1 <br />60 <br />49G6.1 <br />1852.6 <br />62 <br />3442.7 <br />954.3 <br />72 <br />4162.3 <br />1852.6 <br />82 <br />4980., <br />1862.2 <br />10 <br />3454.1 <br />960.6 <br />10 <br />4175.6 <br />1360.1 <br />7.10 <br />4995.4 <br />1871.3 <br />20 <br />3465.4 <br />966.5 <br />20 <br />4188.5 <br />1867,6 <br />20 <br />5010.0 <br />1831.5 <br />30 . <br />3470,3 <br />972.4 <br />30 <br />4201.2 <br />1375.2 <br />30' <br />5024:8 <br />1891,2 <br />40 <br />3488.3 <br />978.3 <br />40 <br />4214:0 <br />1392.9 <br />40 <br />5039.5 <br />1900.9 <br />50 <br />3499.7 <br />984.3 <br />50 <br />4226.8 <br />1390.4 <br />50 <br />5034,3 <br />1910.7 <br />63 ' <br />3511.1 <br />990.2 <br />73 <br />4239.7 <br />1398.0 <br />83 <br />5069.2 <br />1920, 5. <br />10 <br />3522.6 <br />996.2 <br />10 <br />4252.6 <br />1405.7 <br />10 <br />5084.0 <br />1990.4 <br />20 <br />3534,1 <br />1002.3 <br />20 <br />4265.6 <br />1413.5 <br />20 <br />5099,0 <br />1940,3 <br />30 <br />3545.6 <br />1008.3 <br />30 <br />4278.5 <br />1421,2 <br />30 <br />5113,9 <br />1950.3 <br />40 <br />3557:2 <br />1014.4 <br />40 <br />4291..5 <br />1429.0 <br />40 <br />51.28.9 <br />1960.2 <br />50 <br />3563.7 <br />1020.5 <br />50 <br />4304.6 <br />1436.8 <br />50 <br />5143:9 <br />1470.3 <br />6 1 <br />3550.3 <br />1026.6 <br />74 <br />4317.6 <br />1444.6 <br />84 <br />5159.0 <br />1930:4 <br />10 <br />3591.9 <br />1032,8 <br />10 <br />.4330.7 <br />1.452.5 <br />10 <br />5174.1 <br />1990.5 <br />2.^, <br />3603.5 <br />1039.0 <br />120 <br />4343.8 <br />1460.4 <br />20 <br />5189,3 <br />2000.6 <br />30 <br />3615.1 <br />•104.1,2 <br />30 <br />4356.9 <br />14GS.4 <br />30 <br />5204.4 <br />2010.8 <br />40 <br />3626.8 <br />1051.4 <br />40 <br />4270.1 <br />1476.4 <br />-40 <br />5219.: <br />2021.1 <br />60 <br />3639.6 <br />1057.7 <br />50 <br />4393.3 <br />1484.4 <br />50 <br />5-34.9 <br />2031.4 <br />65 <br />3050.2 <br />1063.9 <br />75 <br />439615 <br />1492,4 <br />85 <br />55250.3 <br />2041:7 <br />10 <br />3661.9 <br />1070.2 <br />10 <br />4409.3 <br />1500.5 <br />10 <br />5265.6 <br />2052.1 <br />20 <br />3673.7 <br />1076.6 <br />20 <br />4428.1 <br />1508.6 <br />20 <br />5291.0 <br />206.2.5 <br />30, <br />3685.4 <br />1082.9 <br />30 <br />4436:4 <br />1616.7 <br />30 <br />5296 4 <br />2073.0 <br />40 <br />3697.2 <br />1089.3 <br />- 40 <br />4449.7 <br />'1524.9 <br />40 <br />5311.9 <br />2089.5 <br />50 <br />3709.0 ' <br />1095.7 <br />50 <br />4463.1 <br />1533.1 <br />50 <br />5327.4 <br />2091,1 <br />CIO <br />3720:) <br />1102.2 <br />76 <br />4476.5 <br />1541.4 <br />86 <br />5343.0 <br />2104.7 <br />10 <br />3732,1, <br />1108.6 <br />10 <br />4489.9 <br />1549,7 <br />10 <br />535.9.6 <br />2115.3 <br />' 26' <br />3744.6 <br />1115.1 <br />20 <br />4503.4 <br />1553.0 <br />20 <br />5374,2 <br />2126.0 <br />30 <br />3756.5 <br />1121.7. <br />30 <br />4516.9 <br />1566.3 <br />30 <br />5389.9 <br />21311.' <br />40 <br />3768.5 <br />1128.2 <br />40 <br />4580.4 <br />1574.7 <br />40 <br />5405.6 <br />2147,5 <br />50 <br />37,30.4 <br />1134.8 <br />50 <br />4544.0 <br />1583.1 <br />50 <br />5421.4 <br />2158.4 <br />67 <br />9792.4 <br />1141.4 <br />77 <br />4557.6 <br />1591.6 <br />S7- <br />543;.2 <br />2169:'2 <br />10 <br />3804.4 <br />1148.0 <br />10 <br />4571.2 <br />1600.1 <br />10 <br />5453,1 <br />2180.2 <br />20 <br />3316.4 <br />1154.7 <br />20 <br />4584,8 <br />1608.6 <br />20 <br />5469.0 <br />2191.1 <br />30 <br />3328.4 <br />1161.3 <br />30 <br />4598.5 <br />1G17.1 <br />30 <br />5484,9 <br />2202.2 <br />40 <br />3840.5 <br />1168.1 <br />40 <br />4612.2 <br />1625.7 <br />40 <br />5500.9 <br />2213.2 <br />50 <br />3852.6 <br />1174.8 <br />50 <br />4626.0 <br />1634.4 <br />50 <br />5517.0 <br />2224.3 <br />68 <br />3864.7 <br />1181,6 <br />78 <br />4639.8 <br />1643.0 <br />SS <br />5533.1 <br />2235;6 <br />•10 <br />3876.8 <br />1188.4 <br />10 <br />4653.6 <br />1651.7 <br />10 <br />5549.2 <br />2246.7 <br />20 <br />3989.0 <br />1195.2 <br />20 <br />4667.4 <br />1660.5 <br />20 <br />;5565.4 <br />2258.0 <br />30 <br />3901,2 <br />1202.0 <br />30 <br />4631.3 <br />1669.2 <br />30 <br />5581.G <br />2269.3 <br />40 <br />3913.4 <br />1208.9 <br />. 40 <br />4695.2 <br />1678.1 <br />40 <br />5597,8 <br />2280.6 <br />50 <br />3925.6 <br />1215.8 <br />50 <br />4709.2 <br />1656.9 <br />'50 <br />5614.2 <br />2292.0 <br />69 <br />'- 3937.9 <br />1222.7 <br />79 <br />4723.2 <br />1695.8 <br />S9 <br />5630.5 <br />2303.5 <br />- 10 <br />3950.2 <br />1229.7 <br />10 <br />4737.2 <br />1704.7 <br />10 <br />5646.9 <br />2315.0 <br />.20 <br />3962'.5 <br />1236.7 <br />20 <br />4751.2 <br />1713.; <br />20 <br />5663.4 <br />2326.6 <br />30 <br />3974.8 <br />1243.7 <br />30 <br />4765.3 <br />1722,7 <br />30 <br />- 5679.9 <br />2338.2 <br />40 <br />3987.2 <br />1250,9 <br />40 <br />4779.4 <br />1731.7 <br />40 <br />5696.4 <br />2349.8 <br />50 <br />3999.5 <br />157.9 <br />50 <br />4793.6 <br />1740.8 <br />50 <br />5713.0 <br />2381.5 <br />70 <br />4011.9 <br />1265.0 <br />so <br />4807.7 <br />1749.9 <br />90 <br />5729.7 <br />2373:9 <br />10 <br />4024.4 <br />1.272.1 <br />10 <br />4822:0 <br />1759.0 <br />10 <br />5746.3 <br />2385.1 <br />20 <br />4036.8 <br />1279.3 <br />20 <br />4386.2 <br />1763.2 <br />20 <br />5763.1 <br />2397.0 <br />30 <br />4049.3 <br />1256.5 <br />30 <br />4350.5 <br />1777.4 <br />30 <br />5779.9 <br />2408.9 <br />40 <br />4061.8 <br />1293.6 <br />40 <br />4864.8 <br />1736.7 <br />40 <br />57981,7 <br />2420.9 <br />50 <br />4074.4 <br />1300.9 <br />50 <br />4879.2 <br />1796.0 <br />11 <br />50 <br />5813.6 <br />2432.9• <br />