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THE

NORMAL

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 “TAE NORMAL SERIES OF ARITHMETICS," “ NORMAL
ELEMENTARY ALGEBRA," "NORMAL GEOMETRY AND TRIGONOMETRY,”

PHILOSOPHY OF ARITHMETIC," ETC.

66

" 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.

HAYARD CCLLEGE LIBRARY

GIFT OF THE
GRADUATE SCHOOL OF EDUCATION

28

my: 1

COPYRIGHT
BY EDWARD BROOKS, A. M.

1877.

STEREOTYPED & PRINTED

BY

THE INQUIRER P. & P. CO.,

LANCASTER, PA.

CONTENTS.

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

ARITHMETICAL LANGUAGE.

Principles of Circulates, 153

Numeration,

13 Complementary Repetends, 155

Notation,

14 Continued Fractions,

157

SECTION II.

SECTION VI.

FUNDAMENTAL OPERATIONS.

DENOMINATE NUMBERS.

. 160

Addition,

23 Measures of

Subtraction,

Value,

161

Multiplication,

Weight,

166

Division,

Length,

170

General Principles,

54 Surface,

. 173

Volume,

175

SECTION III.

Capacity,

. 176

SECONDARY OPERATIONS.

Angles,

179

Composition,

Time,

180

Factoring,

63

Miscellaneous Tables, 185

Greatest Common Divisor, 69

The Metric System,

. 186

Least Common Multiple, 73 Reduction,

192

Cancellation,

80 Addition,

196

Subtraction,

197

SECTION IV.

Multiplication,

199

COMMON FRACTIONS,

82

Division,

200

Numeration and Nota

rotation, 84 Difference between Dates, . 202

Principles,

85

Longitude and Time, 204

Reduction,

87

DENOMINATE FRACTIONS.

Addition,

93

Reduction,

207

Subtraction,

94

Addition,

211

Multiplication,

97

Division,

Subtraction,

211

100

Complex Fractions,.

Multiplication,

212

103

Relation of Numbers, :

Division,

213

104

Greatest Common Divisor, 214

Greatest Common Divisor, 106

Least Common Multiple,

Least Common Multiple, 215

107

SECTION V.

SECTION VII.

DECIMAL FRACTIONS,

112 PRACTICAL MEASUREMENTS.

Reduction,

115 Rectangle, Triangle, Circle, 219

Addition,

118

Measurement of Land,

Subtraction,

119 Artificers' Work,

224

Multiplication,

120 Carpeting, Papering, etc., 225

Division,

122

Cube and Cylinder,

226

United States Money, . 129 Wood Measure,

Commercial Transactions, 132 Boards and Timber,

229

Bills and Accounts,

135 Masonry, Brickwork, etc., 231

Circulating Decimals,

143 Capacity of Cisterns, etc., 234

Reduction of Circulates,

144 Capacity of Bins, etc., 235

Addition of Circulates, 148 Comparison of Measures,

237

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228

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