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А

LE ROY I).

TREATISE

WARREN B. BROWN,

ON

A L G E BRA.

BY ELIAS LOOMIS, LL.D.,

PROFESSOR OF NATURAL PHILOSOPHY AND ASTRONOMY IN YALE COLLEGE, AND AUTHOR

OF A "COURSE OF MATHEMATICS."

REVISED EDITION.

DEPARTMENT OF EDUCATION
LELAND STANFORD JUNIOR UNIVERSITY

NEW YORK:.
HARPER & BROTHERS, PUBLISHERS,

327 To 335 PEARL STREET,

TRANKLIN &QUARE.

A. 44957
LIBROMOSYRE

UNIVERSITY
TEMA

ELEMENTARY ARITHMETIC.. Elements of Arithmetic, Do

signed for Children. 16mo, 166 pages, Half Sheep, 40 cents. A TREATISE ON ARITHMETIC, Theoretical and Practical. Tenth

Edition. 12mo, 345 pages, Sheep extra, $1 25. ELEMENTS OF ALGEBRA. Designed for the Use of Beginners.

Twenty-third Edition. 12mo, 281 pages, Sheep extra, $1 25. A TREATISE ON ALGEBRA. New and Revised Edition. 8vo,

384 pages, Sheep extra, $2 00; 12mo, Sheep, $1 50. ELEMENTS OF GEOMETRY AND CONIC SECTIONS. Twen

ty-eighth Edition. 12mo, 234 pages, Sheep extra, $1 50. TRIGONOMETRY AND TABLES. Twenty-fifth Edition. Svo,

359 pages, Sheep extra, $200.

The Trigonometry and Tables, bound separately, $1 50 each. GEOMETRY AND TRIGONOMETRY. Consisting of the Au

thor's “Elements of Geometry and Conic Sections," and the first two Books of his "Plane Trigonometry,” bound in One Volume. Prepared for High Schools

and Academies. 12mo, 292 pages, Sheep, $1 50. ELEMENTS OF ANALYTICAL GEOMETRY, and of the Differ

ential and Integral Calculus. Nineteenth Edition. 8vo, 286 pages, Sheep extra,

$2 oo. ELEMENTS OF NATURAL PHILOSOPHY. Designed for Acad

emies and High Schools. Fifth Edition. 12mo, 352 pages, Sheep extra, $1 50. ELEMENTS OF ASTRONOMY. Designed for Academies and

High Schools. 12mo, 254 pages, Sheep, $1 50. PRACTICAL ASTRONOMY. An Introduction to Practical Astron

omy, with a Collection of Astronomical Tables. Seventh Edition. 8vo, 499 pages,

Sheep extra, $200. RECENT PROGRESS OF ASTRONOMY, especially in the United

States. A thoroughly revised Edition. Illustrations. 12mo, 396 pages, Cloth,

$1 50.

A TREATISE ON ASTRONOMY. With Illustrations. Svo, 352

pages, Sheep, $2 00. A TREATISE ON METEOROLOGY. For the Use of Academies

and High Schools.• 8vo, 308 pages, Sheep extra, $200.

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.

PRE FACE.

THE stereotype plates of my Treatise on Algebra having become 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.

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