. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. sm. .r = sm. a sin. (e + x) But, sin. j: -\- cos. e. â¢. sin. (o + b) sin. c = sin. a sin. d (sin. e cot. x -f cos. e) ; sin. (a + b) sin. c ^ sin. a sin. d = sin. a sin. d sin. e cot. x. ⢠.cot. sin. (n 4- ') sin. e X â :; âcot. e; or, ^ sin. (a-fo) sin. ccosec. sin. a sin. o sin. e ' ' \ i / rfc osec. e â cot. c. Rcle.âAdd together, the log. cosec. »fa, the log. sin. of the »um of a und b, the tog. sin. of]c, the log. cosec. ofd, and the log. cuse
. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. sm. .r = sm. a sin. (e + x) But, sin. j: -\- cos. e. â¢. sin. (o + b) sin. c = sin. a sin. d (sin. e cot. x -f cos. e) ; sin. (a + b) sin. c ^ sin. a sin. d = sin. a sin. d sin. e cot. x. ⢠.cot. sin. (n 4- ') sin. e X â :; âcot. e; or, ^ sin. (a-fo) sin. ccosec. sin. a sin. o sin. e ' ' \ i / rfc osec. e â cot. c. Rcle.âAdd together, the log. cosec. »fa, the log. sin. of the »um of a und b, the tog. sin. of]c, the log. cosec. ofd, and the log. cusec. of e; the natural number corresponding to this sum, rejecting 50 in the index, mide less by the natural co-tangent of e, will give the natural co-tangent of X. log, (« + *) = 75° 50' = 120 â 75 = 40 = 19 65 , log. 30 , log. 20 , log. 05 , log. cosec. sin. sin. cosec. cosec. The natural number corresponding =: The natural cot. of 19° 05' (e) =: = 100134127 = 9 0334445 = 99S59416 = 10-1889391 = 10-4855279 0-6072758 4-0483290 2-8905407 Natural cot. of x = 1-1577823 . ⢠. ir = 40' 49' 04" = ABO ; and c -f x = 59" 54' 04" = OBC. Hence, OC = 1JS4-49, and OB = 1493-34 chains respectively, which may be found by Plane Trigonometry. Suppose the angles a, b, c, d, remain as before, but it is found impossible to measure AC with any degree of accuracy, OB being on a plane it is measured and found to be 18G09 links. Required the angle x, and the distance AC in feet? In this instance, x = 40" 49'04" ; and 4C = 4112-227 feet. This could not be solved by the rules of pla'ne trigonome- try. (6.) There are four stations on the same plane, the linear distance be- tween every two of any three of them being given, as well as the angular distance of the fourth from each of the other three ; to find the remaining parts. Let A, B, and C, be the three stations whose distances are known ; ^en<:e the three angles a, b, and c, of the triangle ABC may
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