FOR THE USE OF SCHOOLS: WITH TABLES FOR THE REDUCTION OF COMPOUND NUMBERS TO DECIMALS; EXAMINER, IN MATHEMATICS, AND PROFESSOR OF MATHEMATICS IN THE ROYAL MILITARY COLLEGE, SANDHURST. LONDON: PREFACE. This little Treatise contains Numeration; Addition, Subtrac- tion, Multiplication, and Division of Whole Numbers; the Decomposition of Numbers into Prime Factors ; the greatest Common Measure and least Common Multiple of two or more Numbers'; the reductions necessary to be made on Vulgar Fractions; Addition, Subtraction, Multiplication, and Division of Vulgar and Decimal Fractions; Extraction of the Square and Cube Roots of Numbers; Different Systems of Numera- tion ; Tables of Money, Weights, and Measures ; Observations on the Advantage of substituting a Decimal System of Money, Weights, and Measures, for the existing System of Compound Numbers; Tables for reducing Compound Numbers to Equiva- lent Decimal Numbers expressed in terms of a Principal Unit; and, conversely, for reducing such Decimal Numbers to Com- pound Numbers; Reduction, Addition, Subtraction, Multipli- cation, and Division of Compound Numbers; Aliquot Parts ; Duodecimals; and Proportion, with the Rules of Commercial Arithmetic depending on Proportion. An attempt has been made to give simple and intelligible in- vestigations of all the processes and rules, and to show that the A copious set of examples is annexed to each rule. The A more detailed Table of Contents is subjoined. Verifications of Addition and Subtraction Multiplication of Whole Numbers Verifications of Multiplication and Division Decomposition of Numbers into Prime Factors. Greatest Common Measure, and least Common Multiple of Two or more Numbers Reductions of Vulgar Fractions Reduction of a Vulgar to a Decimal Fraction and of a Periodic Decimal to a Abbreviations of Multiplication and Division of Decimal Fractions 121 Of the Powers and Roots of Numbers Of different Systems of Numeration Notation and Tables of Compound Numbers. Remarks on the Inconveni- ence of the existing form of Compound Numbers, with Tables of equivalent Decimal Numbers. Nomenclature of the French System of Multiplication of Duodecimal Numbers ARITHMETIC. ARTICLE 1. Arithmetic is the science of Numberg. Magnitude and quantity are terms employed to describe whatever is susceptible of increase or diminution. Unity is any quantity with which other quantities of the same kind are compared for the purpose of determining their measures or values. Number is the result of the combination of units of the same kind, or the relation which expresses how often a quantity contains that other quantity of the same kind which has been taken as unity. 2. By comparing different quantities of the same kind with the same unit, different numbers are obtained. To each of these a different name: must, for the sake of distinction, be assigned The name employed to denote a single individual is one. All whole numbers are formed by the combination of one with itself, then with the result of this combination, and so on indefinitely. The series of numbers being unlimited, to give every number a simple name would be inconvenient and even impossible. By means, however, of a few simple names and other expressions compounded of these simple names, a nomenclature is formed sufficiently copious to serve erery requirement, whether of theory or practice. The simple names of number are one, two, three, four, five, six, seven, eight, nine, ten, hundred, thousand, million, billion, trillion, quadrillion, quintillion, &c. The number formed of B |