pence soterzi magés, denoted as tommi the other zrgirangle, girea "4, 5%. other parts. 2. GATEC; to find the other 3m 6 = 78°.2=5745,c=6356. A... Gm7=4%%. =46"; to find the other parts. Ansa=6440, or its supplement, <=5444, or its supplement, c=6435, or is supplement. C & Gomen = 48, c=6435; red the other Aus 1=48°18, c=5444, 64°40' Ex. Or drantal opposi Ex the t to fin H In the quadrantal triangle ABC, given the quaide a 90°, an adjacent angle c = 42° 12', and the angle A 64°40'; required the other parts of the ? In an oblique-angled spherical triangle are given e sides, viz, a = 56°40', b = 83°13', c = 114°30'; he angles. by the fifth case of table 2, we have sin (Is—b) . sin (Is—c). sin Asin sin b. sin c sin A log sin (s-b)+log sin (s-c)+ar. comp. sin bar. comp. log sin c: where s = a+b+c. = = sin (s-b) log sin 43°58' = 9.8415749 Sum of the four logs = log sina log sin 24°15' quently the angle A is 48°31'. the common analogy, 9.3418385 0.0030508 0.0409771 sin 48°31' sin a... sin 56°40′ log = 9.9219401 sin 83°13′ sin 62°56' = 9.9969492 log = 9.9495770 log = 9.9590229 log =9-9116507. he remaining angles are, B=62°56', and c=125°19'. By way of comparison of methods, let us find the by the analogies of Napier, according to case 5 In order to which, suppose a perpendicular demitthe angle c on the opposite side c. Then shall we diff. seg. of c = garithms, is tan (b+a). tan (b-a) tan c an (ba) = log tan 69°56' in (b-a) = log tan 13°16' = 10.4375601 Their sum = 19.8103420 log tan c= log tan 57°15′ = 10-1916394 = geos dif. seg. log cos 22°34′ = 9.6187026 the segments of the base are 79°49' and 34°41'. Therefore, The side opp. to other angle. By the common analogy. Sines of angles are as sines of oppos. sides. Tan 1 seg. of this side cos adj. angle x tan given side. the side contain-i ed between the given angles. Sin 2 seg. tan ang. opp. given side ngles Third side. and a side opposite to one of them. H. Two sides and an Third angle. The angle opp. to the other side. Angle included between the given sides. sin 1 seg. x tan ang. adj. given side Let fall a per. as Cot 1 seg. of this ang. = cos giv. side × tan adj. angle. Sines of sides are as sines of their opposite angles. Cot 1 seg. ang. req. dicular from the included angle. Cos 2 seg= tan given ang. x cos adj. side. cos 1 seg. x tan giv, side a lj, giv, angle tan side opp. given angle TABLE II.-For the Solution of Oblique-Angled Spherical Triangles. An angle or a side being divided by a perpendicular, the first and second segments are denoted by 1 seg, and 2 seg. ities required. Values of the Ju Given. Reprred. Let fall a per. on angle to one of them. Third side. cos ang. adj. given side Let fall a perpendicular as before. Tan 1 seg. side req. Cos 2 seg. cos given ang. x tan adj. side. cos 1 seg. x cos side opp. given angle cos si e aij. given angle Let fall a perpen. Tan 1 seg. of div. side = cos giv. ang. x tan side opp. ang. sought. Tan sought ang. tan giv, ang. x sin 1 scg. sin 2 seg. of div. side V. An angle by the The み of its halt Les fall a perpen.) Cot 1 seg. ang. from one of the Cos angle sought An angle oppos. to one of the given sides. from the third cos giv. ang. x tan other given side. angle. Afides Let fall a perpen. Tan 1 seg. of div. side chided) angle. Third side. on one of the giv. sides. Cos side sought IV. A side and the to one of the third side. two ad A side opposite Let fall a perpen-Cot 1 seg. of div. ang. = cos giv. side a tan ang opp. side sought given angless Third angles jacent angles. sine or dicular on the Tan side sought div. tan giv. side at yunan diy cos & Bog. of divide of angl cos giv. side a ton mber pl be the sides; A, B, C, the angles, and, uskoling de angle at Then, siu (4-() . Nu c of its half, Given. I. Two TABLE II.-For the Solution of Oblique-Angled Spherical Triangles. An angle or a side being divided by a perpendicular, the first and second segments are denoted by 1 seg. and 2 seg. Reuered. The side opp. to By the common other angle. angles Third side. and a side opposite Valves of the Ju 'ities required. Sines of angles are as sines of oppos. sides. analogy. Let fall a per. on the side contain Sin 2 seg. ed between the given angles. Tan 1 seg. of this side = cos adj. angle x tan given side. = sin 1 seg. x tan ang. adj. given side tan ang. opp. given side Cot 1 seg. of this ang. = cos giv. side x tan adj. angle. sin 1 seg. x cos ang. opp. given side cos ang. adj. given side Third angle. Let fall a per. as before. Sin 2 seg. = The angle opp. ( By the common to the other side. analogy. Sines of sides are as sines of their opposite angles. Two and an given sides. dicular from the included angle. of them. sides angle opposite to one of them. Let fall a perpen-Cot 1 seg. ang. req = tan given ang. x cos adj. side. Let fall a perpen- Third side. dicular as before. (Cos 2 seg. cos 1 seg. x tan giv, side adj. giv. angle tan side opp. given angle req. = cos given ang. x tan adj. side. cos 1 seg. x cos side opp. given angle cos sie adj. given angle |