PREFACE. IT has been attempted in this work to give a thoroughly modern account of those portions of Plane Trigonometry, which an intelligent student may be expected to read as his first course of the subject. In the execution of it, two principal aims have been kept in view. In the first place, it has been sought to preserve clearness throughout-clearness of expression, and of demonstration. But to accomplish this, it has not been thought advisable to banish all detail in the text, and to give outline only, except in cases where the student could not fairly expect more. An air of greater simplicity might perhaps thus have been given to the book; but that, of course, would soon have vanished on its being read. On the other hand, it is hoped that it will seldom, if ever, be found to occur, that a multitude of words has been allowed to render a difficulty in the nature of the subject still more difficult. The second main endeavour has been to place, group, |