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ALGEBRA

FOR COLLEGES AND SCHOOLS

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FOR COLLEGES AND SCHOOLS

BY

H. S. HALL, M.A., AND S. R. KNIGHT, B.A.

REVISED AND ENLARGED

FOR THE USE OF AMERICAN SCHOOLS

BY

F. L. SEVENOAK, A.M.
ASSISTANT PRINCIPAL OF THE ACADEMIC DEPARTMENT,

STEVENS INSTITUTE OF TECHNOLOGY

New York
THE MACMILLAN COMPANY

LONDON : MACMILLAN & CO., LTD.

1902

All rights reserved

COPYRIGHT, 1896,

BY THE MACMILLAN COMPANY.

COPYRIGHT, 1897,

BY THE MACMILLAN COMPANY.

First edition, 1895. Second edition, revised and enlarged, 1896.
Reprinted with corrections, January, 1897; August, October, 1897;
August, 1898 ; October, 1898; July, August, 1899: September, 1899;
January, July, 1900; July, 1901 ; April, August, October, 1902.

LIBRARY
Leland Stanford, Jr.
UNIVERSITY

Norwood Press
J. 8. Cushing & Co. - Berwick & Smith

Norwood Mass. U.S.A.

PREFACE.

WITHIN a comparatively short time, the algebra requirement for admission to many of our Colleges and Schools of Science has been much increased in both thoroughness of preparation and amount of subject matter. This increase has made necessary the rearrangement and extension of elementary algebra, and it is for this reason that the present revision of Hall and Knight's Elementary Algebra has been undertaken.

The marked success of the work, and the hearty endorsement by many of our ablest educators of the treatment of the subject as therein presented, warrant the belief that the present edition, with its additional subject-matter, will be found a desirable arrangement and satisfactory treatment of every part of the subject required for admission to any of our Colleges or Schools of Technology.

Many changes in the original chapters have been made, among which we would call attention to the following: A proof, by mathematical induction, of the binomial theorem for positive integral index has been added to Chapter XXXIX.; a method of finding a factor that will rationalize any binomial surd follows the treatment of binomial quadratic surds; Chapter XLII. has been re-written in part, and appears as a chapter on equations in quadratic form; and the chapter

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