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Written by a distinguished educator, this survey for upper-level undergraduates and graduate students traces the development of arithmetic, algebra, geometry, and trigonometry in the ancient world; the influence of Hindu and Arabic mathematicians on medieval European thought; and the trends that led to modern mathematics. 1917 edition.

Antiquity 1
Number-Systems and Numerals 1
Arithmetic and Algebra 19
Egypt 19
Greece 26
Rome 37
Geometry and Trigonometry 43
Egypt and Babylonia 43
Greece 46
Rome 89
Middle Ages 93
Arithmetic and Algebra 93
Hindus 93
Arabs 103
Europe during the Middle Ages 111
Introduction of Roman Arithmetic 111
Translation of Arabic Manuscripts 118
The First Awakening 119
Geometry and Trigonometry 122
Hindus 122
Arabs 125
Europe during the Middle Ages 131
Introduction of Roman Geometry 131
Translation of Arabic Manuscripts 132
The First Awakening 134
Modern Times 139
Arithmetic 139
Its Development as a Science and Art 139
English Weights and Measures 167
Rise of the Commercial School in England 179
Causes which Checked the Growth of Demonstrative Arithmetic in England 204
Reforms in Arithmetical Teaching 211
Arithmetic in the United States 215
"Pleasant and Diverting Questions" 219
Algebra 224
The Renaissance 224
The Last Three Centuries 234
Geometry and Trigonometry 245
Editions of Euclid. Early Researches 245
The Beginning of Modern Synthetic Geometry 252
Modern Elementary Geometry 256
Modern Synthetic Geometry 257
Modern Geometry of the Triangle and Circle 259
Non-Euclidean Geometry 266
Text-books on Elementary Geometry 275
Recent Movements in Teaching 290
The Perry Movement 291
International Commission 297
American Associations 301
Attacks upon the Study of Mathematics as a Training of the Mind 304
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