Given. Sought.

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

See FIG. 7.

In the triangle DEF, DE, EF, FD are refpectively the fupplements of the meafures 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 meafures of thefe angles.

The 3d, 5th, 7th, 9th, 10th, cafes, which are commonly called ambiguous, admit of two folutions, either of which will anfwer the conditions required; for, in these cafes, 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 tri angle, a perpendicular arch be drawn upon the oppofite fide, moft of the cafes of oblique angled triangles may be resolved by means of Napier's rules.

FIN I S.