THE ELEMENTS OF PLANE AND SPHERICAL TRIGONOMETRY, WITH THE NATURE AND PROPERTIES OF LOGARITHMS, AND THE CONSTRUCTION AND USE OF MATHEMATICAL TABLES. DESIGNED FOR THE USE OF STUDENTS IN THE UNIVERSITY. BY JOHN HIND, M.A. F.C.P.S. F.R.A.S. LATE FELLOW AND TUTOR OF SIDNEY SUSSEX COLLEGE, CAMBRIDGE. FIFTH EDITION. CAMBRIDGE: DEIGHTON, BELL & CO. LONDON: BELL AND DALDY, 186, FLEET STREET. 1855. 183. c. 29. ADVERTISEMENT. THE following pages are designed to enable the Student to become acquainted with the Principles and Applications of Trigonometry, without requiring of him any thing more than a knowledge of the Elements of Geometry, and a facility in the common operations of Arithmetic and Algebra. The first four chapters of the Plane Trigonometry, contain what is most essentially necessary for the study of the best modern works on Science; and pains have been taken to render the demonstrations of the fundamental propositions as concise as possible, without at all affecting their logical accuracy. The remaining chapters take a more extensive and analytical view of the Nature and Applications of Trigonometry and Logarithms, the particulars of which, as well as of those in Spherical Trigonometry, may be seen in the Table of Contents. In the Appendices will be found many interesting Theorems and Problems with their Solutions, as well as Collections of Examples for Practice with their Answers annexed; and the Reader, who may be desirous of arriving at a proficiency in Mathematical Science, will scarcely neglect to avail himself of some of their suggestions. CAMBRIDGE, May 21, 1855. TABLE OF CONTENTS. PAGE The Divisions of a Right Angle........... The Foreign Division of the Right Angle The Genesis of Angular Magnitude The Connection between an Angle and its Arc. The Trigonometrical Functions of an Arc ...... 8 The Sine and Cosine of (m+1) A, with Deductions The Values of the Sines and Cosines of 18°, 36°, &c......... The Sines and Cosines of A and B in terms of } (A ± B). The Tangents and Cotangents of A± B, with Deductions....... 38 The Continued Product of m Factors of the form, cosa +V-1 sin a. 41 The Sides of a Triangle proportional to the Sines of the oppo- site Angles.. |