0 A TREATISE ON ALGEBRA. BY ELIAS LOOMIS, LLD, PROFESSOR OF NATURAL PHILOSOPHY AND ASTRONOMY IN YALE COLLEGE, AND AUTHOR REVISED EDITION. NEW YORK: HARPER & BROTHERS, PUBLISHERS, 327 TO 335 PEARL STREET, FRANKLIN SQUARE. ALGEBRAIC PROBLEMS AND EXAMPLES. 258 pp., $1 05. ELEMENTS OF GEOMETRY. Revised Edition. 388 pp., $1 17. ELEMENTS OF TRIGONOMETRY, SURVEYING, AND NAVIGATION. 194 pp., $1 17. The Trigonometry and Tables, bound in one volume. 360 pp., $1 75. ELEMENTS OF ANALYTICAL GEOMETRY. Revised Edition. 261 pp., $1 17. ELEMENTS OF ASTRONOMY. 254 pp., $1 17. PRACTICAL ASTRONOMY. 499 pp., $1 75. TREATISE ON ASTRONOMY. 351 pp., $175. Entered, according to Act of Congress, in the year one thousand eight hundred and sixty-eight by HARPER & BROTHERS, In the Clerk's Office of the District Court of the Southern District of New York. PREFACE. THE stereotype plates of my Treatise on Algebra having be come so much worn in the printing of more than 60,000 copies that it had become necessary to cast them aside, I decided to improve the opportunity to make a thorough revision of the work. I therefore solicited criticisms from several college professors who had had much experience in the use of this book, and in reply have received numerous suggestions. The book has been almost entirely rewritten, nearly every page of it having been given to the printer in manuscript. The general plan of the original work has not been materially altered, but the changes of arrangement and of execution are numerous. In the former editions, in place of abstruse demonstrations, I sometimes employed numerical illustrations, or deductions from particular examples. In the present edition such methods have been discarded, and I have aimed to demonstrate with conciseness and elegance every principle which is propounded. This book therefore aims to exhibit in logical order all those principles of Algebra which are most important as a preparation for the subsequent branches of a college course of mathematics. I have retained, with but slight alteration, a feature which was made prominent in the former editions, that of stating each problem twice: first as a restricted numerical problem, and then in a more general form, aiming thereby to lead the student to cultivate the faculty of generalization. At the same time I have very much increased the number of examples incorporated with each chapter of the book, and at the close have given a large collection of examples, to which the teacher may resort whenever occasion may require. The proofs of the work have all been examined by Prof. H. A. Newton, to whom I am indebted for numerous and important suggestions. |