The universal notation among civilized nations at the present time is the Hindu or Arabic, the symbols of which, except the zero, originated in India before the beginning of the Christian era, and seem to have been the initial letters of the early numerals. The system derives its intrinsic importance, however, from the zero, which renders possible the distinctive feature known as place value. Thus, in the number 302, the 3 stands for hundreds because it is in hundreds' place, a fact which could not be conveniently indicated without the symbol 0 or its equivalent. The zero ' appeared about the fifth century a.d., and somewhat later the Arabs, coming from the East after the conquest of Spain, brought the new system with them. About the year 1200 these Hindu numerals began to be known in Christian Europe, but it was not until the fifteenth century that they were generally taught and used. The decimal point appeared about the opening of the seventeenth century, and through its influence Table of Contents Preface iii; Tatile of Contents' v; Definitions and Etymologies vn; SVMnOLS AND AbDHEVJATIONSXVU; CHAPTER I-Notation and the Fundamental Operations 1; I Writing and Reading Numbers 1; IT Checks 3; III Addition 4; IV Subtraction 5; V Multiplication 6; VI Division 10; Axioms 13; Fundamental Laws 14; CHATTER II- Factors and Multiples 15; I Tfsts of Divisibility 15; II Casting out Nines 19; III Greatest Common Divisor 21; IV Least Common Multiple 24; CHAPTER III-Common Fractions 26; CHAPTER IV-Powers and Roots 32; I Involution 32; II Square Root 34; III Cube Root 39; CHAPTER V-The Formal Solution of Phohlums 41; I Symbols 42; II Language 44; III Methods 44; IV Checks 49; CHAPTER VI- Measures 51; I Compound Numbers 54; II The Metric System 59; III measukes op TlSMPEHATUKE 64; CHAPTER VII - Mensuration GO; CIIAPTEE VIII-Longitude and Time 80; CHAPTER IX - Ratio and Proportion 87; I Ratio 87; II pROrORTION 9G; CHAPTER