ว

NEW

HIGHER ALGEBRA;

AN

ANALYTICAL COURSE

DESIGNED FOR

HIGH SCHOOLS, ACADEMIES, AND COLLEGES.

BY BENJAMIN GREENLEAF, A. M.,

AUTHOR OF A MATHEMATICAL SERIES.

BOSTON:

PUBLISHED BY ROBERT S. DAVIS & CO.

NEW YORK: OAKLEY & MASON, AND A. S. BARNES & CO.

PHILADELPHIA: J. A. BANCROFT & COMPANY.

ST. LOUIS: KEITH AND WOODS.

CHICAGO: S. C. GRIGGS & CO.

1871.

PUBLIC LIBRARY 281275

ASTOR, LENOX AND

GREENLEAF'S

TILDEN FOUNDATIONS. NEW COMPREHENSIVE SERIES.

1903

An ENTIRELY NEW MATHEMATICAL COURSE, fully adapted to the best methods of Modern Instruction.

GREENLEAF'S NEW PRIMARY ARITHMETIC.

GREENLEAF'S NEW INTELLECTUAL ARITHMETIC.

GREENLEAF'S NEW ELEMENTARY ARITHMETIC.

GREENLEAF'S NEW PRACTICAL ARITHMETIC.

GREENLEAF'S NEW ELEMENTARY ALGEBRA.

GREENLEAF'S NEW HIGHER ALGEBRA.

GREENLEAF'S ELEMENTS OF GEOMETRY.

GREENLEAF'S ELEMENTS OF TRIGONOMETRY.

GREENLEAF'S GEOMETRY AND TRIGONOMETRY.

Other Books of a Complete Series, in preparation.

**KEYS to the PRACTICAL ARITHMETIC, ALGEBRAS, GEOMETRY and TRIGONOMETRY, in separate volumes.

PREFACE.

THE author's New Elementary Algebra having now, after several years' trial, proved a great success, many teachers, acquainted with the practical results accomplished by the use of that book, have been very urgent in their demands for a work on the same plan, for advanced students.

The aim of this treatise is to meet, more fully than has been done heretofore, the requirements of the highest standard of mathematical instruction in the best high schools and seminaries. To this end, great care has been taken to include all the more important parts of analysis, to treat each topic with as much conciseness as is consistent with clearness and elegance, to introduce valuable original processes, and to secure throughout an arrangement most conducive to a philosophical development of the science.

The work, therefore, is very comprehensive in its scope, ample in its range for the curriculum of the college, yet furnishing a course not too extended for the higher order of academies.

The Examples have been selected with a view to a full illustration of principles. While complicated and puzzling problems have been excluded, a proper regard has been had to such exercises as promote mental discipline, or tend to make expert practical analysts.

Each subject, as far as possible, has been made complete in itself, so that certain parts can be omitted by the student when desirable, at the option of the teacher.