Elements of geometry and trigonometry . e two adjacent anglesA and B are given, we are enabled to find the two other sidesa and b. These four proportions are known by the name ofNapier^s Analogies, X. In the case in which there are given tw^o sides and anangle opposite one of them, there will in general be two solu-tions corresponding to the two results in Case II. of rectilinealtriangles. It is also plain that this ambiguity will extend itselfto the corresponding case of the polar triangle, that is, to thecase in which there are given two angles and a side oppositeone of them. In evçry case w
Elements of geometry and trigonometry . e two adjacent anglesA and B are given, we are enabled to find the two other sidesa and b. These four proportions are known by the name ofNapier^s Analogies, X. In the case in which there are given tw^o sides and anangle opposite one of them, there will in general be two solu-tions corresponding to the two results in Case II. of rectilinealtriangles. It is also plain that this ambiguity will extend itselfto the corresponding case of the polar triangle, that is, to thecase in which there are given two angles and a side oppositeone of them. In evçry case we shall avoid all false solutionsby recollecting, 1st. That every angle, and every side of a spherical triangleis less than 180°. 2d. That the greater angle lies opposite the greater side, andthe least an^le oj^pasite the least side, and Ieciprocally, NAPIER^S CIRCULAR PARTS. XI. Besides the analogies of Napier already demonstrated,that Geometer also invented rules for the solution of all thecases of right angled spherical SPHERICAL TRIGOxNOMETRY. 251) In even right angled sphericaltriangle B AC, there are six j)arts :three sides and three angles. Ifwe omit the consideration of iIkjright angle, which is alwaysknown, tliere will be five remain-ing parts, two of which mustbe given before the others canbe determined. The circular parts, as they are called, are the two sidesc and b,about the right angle, the complements of the oblique angles Band C, and tlie complement of the hypothenuse a. Hence thereare five circular parts. The right angle A not being a circularpart, is supposed not to separate tlve circular parts c and b, sothat these parts are considered as adjacent to each other. If any two [)arts of the triangle be given, their correspondingcircular parts will also be known, and these together with arequired part, will make three parts under consideration. Now,these three parts ivilt all lie together, or one of them will be sepa-rated from both of the others. Fo
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