Given. Sought.

12 A, B, C. The Fig. 7. fides.

See Fig. 7.

In the triangles DEF, DE, EF, FD are refpectively the fupplements of the measures of the given angles B, A, C in the triangle 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 thefe angles.

The 3d, 5th, 7th, 9th, 10th, cafes which are commonly called ambiguous, admit of two folutions, either of which will aħfwer 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 spherical tri angle, a perpendicular arch be drawn upon the opposite fide, most of the cafes of oblique-angled triangles may be refolved by means of Napier's rules.

FINI S.