HIGH SCHOOL MATHEMATICS

FIRST BOOK

BY

E. H. TAYLOR, PH.D.

INSTRUCTOR IN MATHEMATICS

AND

FISKE ALLEN, A.M.

PRINCIPAL OF THE TRAINING SCHOOL

EASTERN ILLINOIS STATE

NORMAL SCHOOL

NEW YORK

HENRY HOLT AND COMPANY

PREFACE

THIS is the first of a series of two books in mathematics for the seventh and eighth grades. These books assume that the pupil has mastered the work in arithmetic usually given in the first six grades. They continue the work in arithmetic by drill to obtain speed and accuracy, a study of percentage and its applications in ordinary business and in other everyday affairs, and a study of mensuration. They extend the mathematical content of the course of the seventh and eighth grades by including those parts of elementary algebra and geometry that are adapted to the abilities of the pupils of these grades. This extension is made possible by the omission of the more difficult and technical applications of arithmetic found in the traditional course. It is believed that these books contain enough of algebra and geometry so that a year may be gained in the later course in the high school.

Algebra is approached through the formula which is its most practical aspect for the beginning pupil. Throughout the course the pupil is given practice in stating rules as formulas and formulas as rules until the formula comes to be a natural expression for mathematical truths. Other algebraic notions included are the equation, negative numbers, and the graph. Common geometric notions-angle, perpendicular, triangle, polygon are introduced and used in constructions and various problems in mensuration. Many of the important theorems of elementary geometry are developed from observation and construction and are used in applied problems. It is believed that the familiarity thus obtained with geometric truths will appreciably shorten