A BRIEF HISTORY OF MATHEMATICS - AN AUTHORIZED TRANSLATION OP DR. KARL - FINK'S GESCHICHTE DER ELEMENTAR-MATHEMATIK - DAVID EUGENE SMITH - 1900 - CONTENTS - Translators Preface ............. iii Authors Preface. ............... v General Survey . . . . . . . . . . . . . . . . I I. NUJIBER-SYSTEMS AND NUMBER-SYMBOLS. 6 11. ARITHMETIC. X. General Survey . . . . . . . . . . . . . n First Period. The Arithmetic of the Oldest Nations to the Time of the Arabs. I. The Arithmetic of Whole Numbers . . . . . . . 24 2. The .Irithmetic of Fractions . . . . . . . . . 31 3. Applied Arithmetic . . . . . . . . . . . . 34 C. Second Ieriod. From the Eighth to the Fourteenth Century. I. The Arithmetic of Whole Numbers . . . . . . . 36 2. The Arithmetic of Fractions . . . . . . . . . 40 3. Applied Arithmetic . . . . . . . . . . . . 41 I. Third Period. From the Fifteenth to the Nineteenth Century. I. The Arithmetic of Whole Numbers . ...... 41 2. The Arithmetic of Fractions . . 49 3. Applied Arithmetic ........... 51 111. ALGEBRA. A. General Survey . . . . . . . . . . . . . . . 61 U. First Period. From the Earliest Times to the Arabs. I. General Zrithmetic . . . . . . . . . . . . 63 Egyptian Synbolisrn 63. Greek Arithmetic 64 Symbolism 65 Theory of Kullbers 6G Series 67 tle Irrational 68 Keg- 18 xii HISTORY OF MATHEMATICS. PAGE C Second Period. From the Middle Ages to the Middle of the Seventeenth Century . . . . . . . . . 287 Vieta and Regiomontanus 287 Trigonometric Tables 289 Logarithms 290. L. Third Period. From the Middle of the Seventeenth Cen- tury to the Present . . . . . . . . . . . 294 Biographical Notes . . . . . . . . . . . . . . 29 Index. . . . . . . ,. . . . . . . . . . . 323