PREFACE. THIS Volume contains only those portions of Plane and Spherical Trigonometry which are essential in the practical applications of the subject to problems in surveying, geodesy, and navigation. The attention of teachers and others is invited to the following, which may be regarded as constituting the salient features of the work: 1. The proofs of the functions of 0°, 90°, 180°, and 270°; Arts. 38 to 41. 2. The figures, and the tabular arrangement of the work, in the discussions of Arts. 42 and 44. 3. The solution of problems in Art. 56 by the construction of a diagram, in a manner analogous to that of Art. 15. 4. The proofs of the fundamental formulæ for any angle; Arts. 57 to 59. 5. The discussion of the line values of the trigonometric functions, and their application in tracing the changes in the functions as the angle increases from 0° to 360°; Arts. 62 to 64. 6. The proofs of the formulæ for the sines and cosines of x + y and x y for any values of x and y; Arts. 68 to 70. -- 7. The discussion of the ambiguous case in the solution of plane oblique triangles; Arts. 124 to 126. 184018 |