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THE CHOSEN. EE W.

RAY'S

NEW HIGHER

ARITHMETIC

A REVISED EDITION OF THE HIGHER ARITHMETIC

BY

JOSEPH RAY, M. D.

Late Professor in Woodward College.

VAN ANTWERP, BRAGG & CO.

CINCINNATI AND NEW YORK.

RAY'S MATHEMATICAL SERIES.

ARITHMETIC.

Ray's New Primary Arithmetic.
Ray's New Intellectual Arithmetic.
Ray's New Practical Arithmetic.
Ray's New Higher Arithmetic.

TWO-BOOK SERIES.

Kay's New Elementary Arithmetic.
Ray's New Practical Arithmetic.

ALGEBRA.

Ray's New Elementary Algebra.
Ray's New Higher Algebra.

HIGHER MATHEMATICS

Ray's Plane and Solid Geometry.
Ray's Geometry and Trigonometry.

Ray's Analytic Geometry.

Ray's Elements of Astronomy.

Ray's Surveying and Navigation.

Ray's Differential and Integral Calculus.

COPYRIGHT,
1880,

BY VAN ANTWERP, BRAGG & Co.

HARVARD
UNIVERSITY
LIBRARY

48*137

PREFACE.

RAY'S HIGHER ARITHMETIC was published nearly twenty-five years ago. Since its publication it has had a more extensive circulation than any other similar treatise issued in this country. To adapt it more perfectly to the wants of the present and future, it has been carefully revised.

It has been the aim of the revision to make RAY'S NEW HIGHER ARITHMETIC thoroughly practical, useful, and teachable. To this end the greatest care has been given to securing concise definitions and explanations, and, at the same time, the systematic and thorough presentation of each subject. The pupil is taught to think for himself correctly, and to attain his results by the shortest and best methods. Special attention is given to modern business transactions, and all obsolete matter has been discarded.

Almost every chapter of the book has been entirely rewritten, without materially changing the general plan of the former edition, although much new, and some original matter has been introduced. Many of the original exercises are retained.

Particular attention is called to the rational treatment of the Arithmetical Signs, to the prominence given to the Metric System, and to the comprehensive, yet practical, presentation of Percentage and its various Applications. The method of combining the algebraic and geometric processes in explaining square and cube root will commend itself to teachers. The chapter on Mensuration is unusually full and varied, and contains a vast amount of useful information.

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