PREFACE For some years abbreviated texts in Trigonometry have had the field almost to themselves. It is the feeling of the present writers that brevity has been carried to an extreme. Many books now attempt to give in a hundred pages or less essentially the same material that was formerly given in two hundred pages. Brevity has been obtained by cutting explanation to the bone- or deeper. The instructor trying to cover the ground in half the time once allowed must use the class hour to supply suggestions and illustrative examples that the text omits. This procedure, which tends toward the lecture method, is wasteful of time and relatively ineffective. In the present volume the authors have tried to meet the needs of the shorter as well as of the longer course. This is done, not by omitting explanation, but by arranging the material so that it is possible to give a satisfactory shorter course by using limited portions of the text. In assigning lessons in this book it is to be borne in mind that, on account of the greater amount of explanatory material, five or six pages here often correspond to two or three in the hundred page style of presentation. The authors have, however, been on their guard against diffuseness and the inclusion of unnecessary detail. Material for longer courses. A course of about forty lessons will cover the portion of the book devoted to plane trigonometry if the sections marked by stars are omitted. In a slightly longer course, or with an honor class, the starred sections may be included. An additional twelve to fifteen lessons would be required for the chapter on spherical trigonometry. iii |