GIVEN. SOUGHT. 12 A, B, C. Fig. 7. See Fig. 7. In the triangle DEF, DE, EF, FD are refpectively the fupplements of the measures The of the given angles B, A, C in the triangle fides. BAC; the fides of the triangle DEF are therefore given, and by the preceding cafe the angles D, E, F may be found, and the fides BC, BA, AC are the fupplements of the measures of these angles. The 3d, 5th, 7th, 9th, 10th, cafes, which are commonly called ambiguous, admit of two folutions, either of which will answer the conditions required; for, in these cases, the measure of the angle or fide fought, may be either greater or less than a quadrant, and the two folutions will be fupplements to each other. (cor. to def. 4. 6. Pl. Tr.) If from any of the angles of an oblique-angled fpherical triangle, a perpendicular arch be drawn upon the oppofite fide, most of the cafes of oblique-angled triangles may be refolved by means of Napier's Rules. FINIS. PRINTED BY J. & M. ROBERTSON, 1803. |