TRIGONOMETRY, SURVEYING AND TABLES BY G. A. WENTWORTH, A.M. AUTHOR OF A SERIES OF TEXT-BOOKS IN MATHEMATICS REVISED EDITION BOSTON, U.S.A., AND LONDON GINN & COMPANY, PUBLISHERS 1895 HARVARD COLLEGE LIBRARY GIFT OF MISS ELLEN L. WENTWORTH MAY 8 1939 Entered, according to Act of Congress, in the year 1882, by G. A. WENTWORTH in the Office of the Librarian of Congress, at Washington. Copyright, 1895, by G. A. WENTWORTH. отраву IN N preparing this work the aim has been to furnish just so much of Trigonometry as is actually taught in our best schools and colleges. Consequently, all investigations that are important only for the special student have been omitted, except the development of functions in series. The principles have been unfolded with the utmost brevity consistent with simplicity and clearness, and interesting problems have been selected with a view to awaken a real love for the study. Much time and labor have been spent in devising the simplest proofs for the propositions, and in exhibiting the best methods of arranging the logarithmic work. The object of the work on Surveying is to present this subject in a clear and intelligible way, according to the best methods in actual use; and also to present it in so small a compass that students in general may find the time to acquire a competent knowledge of this very interesting and important study. The author is under particular obligation for assistance to G. A. Hill, A.M., of Cambridge, Mass., to Prof. James L. Patterson, of Schenectady, N.Y., to Dr. F. N. Cole, of Ann Arbor, Mich., and to Prof. S. F. Norris, of Baltimore, Md. G. A. WENTWORTH. EXETER, N.H., July, 1895 PLANE TRIGONOMETRY. Angular measure, page 1; trigonometric functions, 3; representation of functions by lines, 7; changes in the functions as the angle changes, functions of complementary angles, 11; relations of the functions of an angle, 12; formulas for finding all the other functions of an Given parts of a triangle, 19. Case I., when an acute angle and the hypotenuse are given, 19; Case II., when an acute angle and the opposite leg are given, 20; Case III., when an acute angle and an adjacent leg are given, 20; Case IV., when the hypotenuse and a leg are given, 21; Case V., when the two legs are given, 21. General method of solving a right triangle, 22; solutions by logarithms, 24; area of the right triangle, 26; the isosceles triangle, 31; the regular polygon, 33. Definition of goniometry, 36; angles of any magnitude, 36; general definitions of the functions of angles, 37; algebraic signs of the func- tions, 39; functions of a variable angle, 40; functions of angles greater than 360°, 42; formulas for acute angles extended to all angles, 43; reduction of the function of all angles to the functions of angles in the first quadrant, 46; functions of angles that differ by 90°, 48; functions of a negative angle, 49; functions of the sum of two angles, 51; func- tions of the difference of two angles, 53; functions of twice an angle, 55; functions of half an angle, 55; sums and differences of functions, 56. CHAPTER IV. THE OBLIQUE TRIANGLE: Law of sines, 60; law of cosines, 62; law of tangents, 64. Solu- tions: Case I., when one side and two angles are given, 64; Case II., |