Fellow of St Peter's College, Cambridge; and late Professor of Mathematics in the East India College, Herts. FIRST AMERICAN, REVISED AND CORRECTED FROM THE SIXTH LONDON EDITION. Philadelphia: KEY, MIELKE & BIDDLE, 181 MARKET STREET. 1832. Entered according to the act of congress, in the year 1832, by Key, Mielke & Biddle, in the clerk's office of the district court of the eastern district of Pennsylvania. Philadelphia: 3-13-45 ÅDE Lulft 3-8-45 52001 ADVERTISEMENT TO THE LONDON EDITION. THE favourable reception which this Treatise has met with from the public has induced the author, in this sixth edition, to make some considerable additions and alterations. By contracting the letter-press, more particularly in the early part of the work, these improvements have been effected in such a manner as to render it unnecessary to enlarge the size, or increase the price of the volume. The whole has also been revised, and the press corrected, by a friend on whose judgment and accuracy the author has the greatest reliance: it is hoped, therefore, that it may still retain its character, as a useful elementary work on this branch of mathematical science. A* ADVERTISEMENT TO THE AMERICAN EDITION. THE rapid sale of six editions of Bridge's Algebra in England has induced the publishers to furnish a revised edition for the use of American students. Their object has been to simplify the work, and to adapt it to the capacity of beginners. With this view some of the most abstruse chapters and formulæ have been omitted, some examples for practice have been added, and the whole has been made more popular, and more useful for schools and academies. The long processes of reasoning which might embarrass the learner have either been omitted or inserted in a note. The text has been brought to the form of rules, illustrations, and examples for practice. Thus modified, it is believed that this treatise will bear comparison with any of the text books now in use, for perspicuity, simplicity of method, and adaptation to the comprehension of learners; and will enable the young pupil to acquire a thorough knowledge of the elements of algebra, and a practical skill in the solution of algebraic questions, as rapidly and with as little perplexity as any of the treatises extant. CONTENTS. SECT. I. Explanation of the algebraic method of nota- tion |