OF PLANE AND SPHERICAL TRIGONOMETRY, THEORETICAL AND PRACTICAL, DESIGNED CHIEFLY FOR THE USE OF JUNIOR BY A. C. JOHNSON, M. A., Naval Instructor, Royal Navy. (FOURTH EDITION, REVISED AND ENLARGED.) LONDON: HARRISON, 59, PALL MALL. PORTSEA: JAMES GRIFFIN. 1871. 183. e. 28. PREFAC E. THE following pages have been designed with the view of placing before the young Student, in a simple and concise form, all the most important rules of Plane and Spherical Trigonometry, and to afford him a clear and intelligible exposition of the principles upon which those rules are founded; and although, for the sake of convenience, the theoretical parts of these subjects have been first considered, yet, where it is necessary that the Student should, in the first instance, confine himself to the practice, it will suffice that he make himself acquainted with the contents of the first four pages, and with the Chapter on Logarithms, working out the Examples as far as Division: he may then proceed with the practical Solution of Triangles, taking the rules either as they come, or in any other order that may be deemed expedient; after which, he can direct his attention to the remaining portions of the book. PLANE TRIGONOMETRY. CHAPTER I I. PLANE TRIGONOMETRY* is that branch of Mathematics which treats of the measurement of the sides and angles of plane triangles. 2. A triangle consists of six parts, viz., three sides and three angles. The numerical values of any three of these parts being given, provided that one of them is a side, the values of the remaining parts may be found by Plane Trigonometry. 3. This science, while retaining the name that limits it to the triangle, now embraces all figures that may be divided into triangles, and all cases in which angular measurement is the subject of investigation. 4. An angle, according to the Geometrical definition, cannot exceed two right angles, but in Trigonometry it may have any value whatever. Trigonometry is derived from two Greek words, trigonon a triangle, and metreo I measure. B |