STEREOTYPED EDITION REVISED 1883. Cambridge: AT THE UNIVERSITY PRESS. Beman 4-4-2.4 10207 PREFACE. The present Work on ELEMENTARY TRIGONOMETRY contains that part of the subject which can conveniently be explained without the use of infinite series. It is intended either for class-teaching or for private study. Accordingly the Examples are numerous and for the most part easy. Those which are not original have been selected from the Cambridge and Army Examination Papers of the last few years. The Miscellaneous Examples are somewhat more difficult, and should in most cases be postponed until the student reads the subject for the second time. The order in which the chapters are read may be varied at the discretion of the Teacher. The last three Chapters are not required in the Previous Examination of Candidates for Honours at Cambridge. J. B. L. March, 1882. IN the SECOND EDITION a short course has been indicated for the use of Students who wish to read the Solution of Triangles as early as possible. Such Students are advised to omit every article that is marked with an asterisk. A double asterisk has been placed before those articles which should be omitted by all Students until they are reading the subject for the second time. At the suggestion of Mr H. S. Hall, Master at Clifton College, an Appendix has been added containing examples of a kind which occurs frequently in Examination Papers and which illustrates the principles explained in Chapters XVI. and XVII. GONVILLE AND CAIUS COLLEGE, August, 1884. CONTENTS II. ON INCOMMENSURABLE QUANTITIES III. ON THE RELATION BETWEEN THE CIRCUMFERENCE OF IV. ON THE MEASUREMENT OF ANGLES VI. ON THE RATIOS OF CERTAIN ANGLES VII. ON THE TRIGONOMETRICAL RATIOS OF THE SAME VIII. ON THE USE OF THE SIGNS + AND IX. ON THE USE OF + AND IN TRIGONOMETRY X. ON ANGLES UNLIMITED IN MAGNITUDE. I. XI. ON THE RATIOS OF Two ANGLES XII. ON THE RATIOS OF MULTIPLE ANGLES XIII. ON ANGLES UNLIMITED IN MAGNITUDE. II. XV. ON THE USE OF MATHEMATICAL TABLES XVI. ON THE RELATIONS BETWEEN THE SIDES AND ANGLES XVII. ON THE SOLUTION OF TRIANGLES XVIII. ON THE MEASUREMENT OF HEIGHTS AND DISTANCES XX. ON THE AREA OF THE CIRCLE, THE CONSTRUCTION 259 273 |