Careful consideration has been given both to the early difficulties and to the possible future needs of the beginner. The book differs somewhat from other text-books on this branch of mathematics both in the arrangement and in the manner of presentation. The oldest and simplest part of trigonometry, namely, the solution of triangles and the associated practical problems, is concluded before the more general and abstract portions of the study are introduced. The first chapters of the book contain little more about trigonometric ratios and angular analysis than is sufficient to enable the beginner to understand clearly the arithmetical part of the science, and its simple practical applications. This arrangement seems to have several advantages. The subject is rendered far less strange at the beginning, and, by means of practical, concrete examples, the student becomes familiar with the trigonometric functions before proceeding to the more general treatment. His progress is thus made easier and more rapid. Teachers who prefer a wider generality of treatment at the outset, however, can select the chapters in a different order from that followed in the text. An endeavour has been made to introduce the several topics in such a way that the pupil may have, from the very start, an intelligent idea of each step in advance, as well as of the ultimate purpose of the study. In some cases, especially in Chapter II. (the first chapter on trigonometry), care has been taken to prepare the mind of the learner for the reception of new ideas, by the preliminary solution of easy familiar exercises. Throughout the work the author has endeavoured to make each step clear, and thus to prevent the appearance of that puzzled feeling which has such a depressing influence on those entering upon a new study. On the other hand, he has sought to develop independence of mind and the power of mental initiative on the part of the student. Suggestions as to practical methods of work are frequently introduced, and summaries are made in several places for the purpose of helping the pupil to get a better idea of the subject as a whole. In the practical applications, marked attention has been given to the graphical method of solution, as well as to the method of computation. The former method serves as a check upon the latter, and affords practice in neat and careful drawing. What is perhaps more important, however, is that the students will thus become accustomed to a method which will be used by them in other studies, and which is often employed in practical work by engineers and others. Logarithms are used almost at the beginning of the study as here presented. For this reason, and in order to avoid making a digression later on, an introductory chapter is devoted to a review on logarithms. Examples, simple ones as a rule, are given in the several articles. Questions and exercises suitable for practice and review on the separate chapters are placed at the end of the book instead of at the ends of the chapters. These collections will be found useful, both in the short reviews that may be required on the completion of each chapter and in the larger and more general reviews. Many of the examples have been taken from examination papers set in Great Britain and the United States. Throughout the work there are many historical and other notes; and an historical sketch is given in the Appendix. It is believed that some knowledge of the historical development of trigonometry, and of the men of various times and races who have helped to advance the subject, will interest and stimulate those who are entering upon its study. While writing this book, the author has received many valuable suggestions from Mr. J. A. Clark, B.S., of the Ithaca High School, and from several of his colleagues in the departments of mathematics and of engineering at Cornell University. He is indebted to Dr. G. A. Miller and Dr. J. V. Westfall, of the department of mathematics at Cornell University, for their kind assistance in the revision of the proof-sheets, and to Mr. E. A. Miller, B.S., for his friendly aid in working examples. The drawings have been made by Mr. A. T. Bruegel, M.M.E., formerly instructor in the kinematics of machinery at Cornell University, now of the Pratt Institute, Brooklyn, N.Y. The author uses this opportunity to express his thanks for the pains taken by Mr. Bruegel to make the figures a pleasing feature of the book. D. A. MURRAY. CORNELL UNIVERSITY, |