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THE

N O R M AL

HIGHER ARITHMETIC,

DESIGNED FOR

COMMON SCHOOLS, HIGH SCHOOLS, NORMAL SCHOOLS,

ACADEMIES, ETC.

BY

EDWARD BROOKS, A. M., Ph. D.,

PRINCIPAL AND PROFESSOR OF MATHEMATICS IN PENNSYLVANIA STATE NORMAL
SCHOOL, AND AUTHOR OF "THE NORMAL SERIES OF ARIT
ELEMENTARY ALGEBRA," "NORMAL GEOMETRY AND TRIGONOMETRY,"

“PHILOSOPHY OF ARITHMETIC," ETC.

" Theory and Practice, properly combined, give the desirable results of mental

power and business capacity."

PHILADELPHIA
SOWER, POTTS & COMPANY

530 MARKET ST. AND 523 MINOR ST.

GAYAPO COLLEGE LIBRARY

GIFT OF THE
NAUDATE 3 POOL OF EDUCATION

COPYRIGHT
BY EDWARD BROOKS, A. M.

1877.

STEREOTYPED & PRINTED

BY
THE INQUIRER P. & P. CO.,

LANCASTER, PA.

CONTENTS.

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PAGE.

PAGE.

PREFACE, :

: : :V

Subtraction of Circulates, . 149.

INTRODUCTION.

Multiplication of Circulates, 150

Nature of Arithmetic, . 9 Division of Circulates, 150

Greatest Common Divisor, 151

SECTION I.

Least Common Multiple, . 152

ARITIIMETICAL LANGUAGE.

Principles of Circulates, 153

Numeration,

Complementary Repetends, 155

.

Notation, . . . 14 Continued Fractions, . 157

SECTION II.

SECTION VI.

FUNDAMENTAL OPERATIONS.

DENOMINATE NUMBERS. . . 160

Addition,

Measures of

Value, .

. 161

Subtraction,

.

Multiplication,

Weight, .

166

..
. .

Division,

Length, .

170

General Principles, . . 54 Surface, . .

Volume, .

SECTION III.

Capacity,

. 176

SECONDARY OPERATIONS.

Angles, . ..

Composition, ,

180

. . 57

Time, .

Factoring,

Miscellaneous Tables,

.

Greatest Common Divisor, . 69

The Metric System, .

Reduction,

.

Least Common Multiple, .

192

Cancellation, . . . 80

Addition, . . . .

Subtraction,

. 197

SECTION IV.

Multiplication, . .

COMMON FRACTIONS,

Division, :

200

.

Numeration and Notation, . 84 Difference between Dates, . 202

Longitude and Time : 204

Reduction, . . .

DENOMINATE FRACTIONS.

Addition, . .

Reduction, ·

Subtraction,

·

207

·

.

Addition, . . .

211

Multiplication, .

Subtraction, .

Division, . . . .

Multiplication, . . 212

Complex Fractions,. . 103

Division, . .-

213

Relation of Numbers, . . 104

:

Greatest Common Divisor, 214

Greatest Common Divisor, 106

Least Common Multiple, . 215

Least Common Multiple, . 107

SECTION V.

SECTION VII.

DECIMAL FRACTIONS, . . 112 PRACTICAL MEASUREMENTS.

Reduction

Rectangle, Triangle, Circle, 219

Addition, . .

: 222

.

Measurement of Land,

Subtraction, . .

.

.

119 Artificers' Work, .

Multiplication, . . .

Carpeting, Papering, etc., . 2:25

Division, . . .

Cube and Cylinder, . 226

United States Money,. .

Wood Measure, . . . .

Commercial Transactions,

Boards and Timber, .. 229

Bills and Accounts, . . 135

231

Masonry, Brickwork, etc.,

Circulating Decimals, . 143 Capacity of Cisterns, etc., 234

Reduction of Circulates, . 144 Capacity of Bins, etc., . 235

Addition of Circulates, . 148 1 Comparison of Measures, 237

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