OF PLANE AND SPHERICAL TRIGONOMETRY; WITH PRACTICAL APPLICATIONS. BY BENJAMIN GREENLEAF, A. M., AUTHOR OF A MATHEMATICAL SERIES. IMPROVED ELECTROTYPE EDITION. BOSTON: PUBLISHED BY ROBERT S. DAVIS & CO. NEW YORK: BAKER, PRATT, & CO., 142 & 144 GRAND STREET. PHILADELPHIA: J. A. BANCROFT & COMPANY. ST. LOUIS: GRAY, BAKER, & COMPANY. CHICAGO: JANSEN, MCCLURG, & CO. Edue T168.76.435 idue NEW COMPREHENSIVE SERIES. An ENTIRELY NEW MATHEMATICAL COURSE, fully adapted to the best methods of Modern Instruction. GREENLEAF'S NEW PRIMARY ARITHMETIC. GREENLEAF'S NEW INTELLECTUAL ARITHMETIC. GREENLEAF'S NEW ELEMENTARY ARITHMETIC. GREENLEAF'S NEW PRACTICAL ARITHMETIC. GREENLEAF'S NEW ELEMENTARY ALGEBRA. GREENLEAF'S NEW HIGHER ALGEBRA. GREENLEAF'S NEW ELEMENTARY GEOMETRY. GREENLEAF'S ELEMENTS OF GEOMETRY. GREENLEAF'S ELEMENTS OF TRIGONOMETRY. GREENLEAF'S GEOMETRY AND TRIGONOMETRY. * Other Books of a Complete Series, in preparation. KEYS to the PRACTICAL ARITHMETIC, Algebras, GEOMETRY and TRIGONOMETRY, in separate volumes. Entered according to Act of Congress, in the year 1863, by in the Clerk's Office of the District Court for the District of Massachusetts. THE preparation of this treatise was undertaken at the earnest solicitation of many teachers, who, having used the author's Arithmetics, Algebras, and Elements of Geometry with satisfaction, were desirous of seeing his series rendered more nearly complete by the addition of the Elements of Plane and Spherical Trigonometry. It is hoped that the present work will be found to be a complete system, theoretical and practical, fully adapted to the wants of advanced classes. The trigonometric functions, in this treatise, have been regarded as ratios, since this improved method has not only now superseded the ancient method in English and French works, but has been approved and adopted generally by the best American mathematicians. Reference, however, is made to whatever is especially valuable in the old method. In the preparation of this work the author has received valuable suggestions from many eminent teachers, to whom he would here express his sincere thanks. Especially would he acknowledge his great obligations to H. B. Maglathlin, A. M., who for many months has been associated with him in his labors, and to whose experience as a teacher, skill as a mathematician, and ability as a writer, the value of this treatise is largely due. BENJAMIN GREENLEAF. BRADFORD, Mass., July 25, 1861. NOTICE. THIS System of Trigonometry was designed to be published in connection with the author's Elements of Geometry. It is now published separately, to accommodate those teachers who desire to use it in that form. January 1, 1863. |