COPYRIGHT, 1914, 1915, BY GEORGE WENTWORTH AND DAVID EUGENE SMITII ALL RIGHTS RESERVED 318.10 EDUCATION DEPT. The Athenæum Press PREFACE In preparing a work to replace the Wentworth Trigonometry, which has dominated the teaching of the subject in America for a whole generation, some words of explanation are necessary as to the desirability of the changes that have been made. Although the great truths of mathematics are permanent, educational policy changes from generation to generation, and the time has now arrived when some rearrangement of matter is necessary to meet the legitimate demands of the schools. The principal changes from the general plan of the standard texts in use in America relate to the sequence of material and to the number and nature of the practical applications. With respect to sequence the rule has been followed that the practical use of every new feature should be clearly set forth before the abstract theory is developed. For example, it will be noticed that the definite uses of each of the natural functions are given as soon as possible, that the need for logarithmic computation follows, that thereafter the secant and cosecant assume a minor place, and that a wide range of practical applications of the right triangle awakens an early interest in the subject. The study of the functions of larger angles, and of the sum and difference of two angles, now becomes necessary to further progress in trigonometry, after which the oblique triangle is considered, together with a large number of practical, nontechnical applications. The decimal division of the degree is explained and is used enough to show its value, but it is recognized that this topic has, as yet, only a subordinate place. It seems probable that the decimal fraction will in due time supplant the sexagesimal here as it has in other fields of science, and hence the student should be familiar with its advantages. Such topics as the radian, graphs of the various functions, the applications of trigonometry to higher algebra, and the theory of trigonometric equations properly find place at the end of the course in plane trigonometry. They are important, but their value is best appreciated after a good course in the practical uses of the subject. ✓ iii M187515 They may be considered briefly or at length as the circumstances may warrant. In the spherical trigonometry the same principles have been followed, the practical preceding the theoretical, and the number of applications being increased, but the technical work on astronomy is relegated to textbooks on that subject. The authors have sought to give teachers and students all the material needed for a thorough study of plane and spherical trigonometry, with more problems than any one class will use, thus offering opportunity for a new selection of examples from year to year, and allowing for the omission of the more theoretical portions of Chapters IX-XII of the Plane Trigonometry if desired. The tables have been arranged with great care, every practical device having been adopted to save eye strain, all tabular material being furnished that the student will need, and an opportunity being afforded to use angles divided either sexagesimally or decimally, as the occasion demands. The answers have been placed at the back of the book, experience having shown that, in trigonometry as well as in other subjects, this is better than to incorporate them in the text. It is hoped that the care that has been taken to arrange all matter in the order of difficulty and of actual need, to place the practical before the theoretical, to eliminate all that is not necessary to a clear understanding of the subject, and to present a page that is at the same time pleasing to the eye and inviting to the mind will commend itself to and will meet with the approval of the many friends of the series of which this work is a part. GEORGE WENTWORTH |