CHAMBERS'S EDUCATIONAL COURSE-EDITED BY W. AND R. CHAMBERS. WILLIAM AND ROBERT CHAMBERS, LONDON AND EDINBURGH. 1854. In this introductory treatise on Arithmetic, the utmost simplicity of language has been studied in expressing the rules; and in every instance their meaning is shewn by examples wrought out at length before the eye of the pupil, accompanied with detailed explanations of the mode of working the questions. In the present edition, the exercises and explanatory notes have been greatly extended, and many new rules have been added, that were not given in the former edition ; such as Equation, Partnership, the Square and Cube Roots, Duodecimals, &c. The work will be found to contain all the ordinary rules taught at school. An account of the proposed Decimal System of reckoning 'money, with examples and exercises, has been given as an Appendix. CONTENTS. Page . . · · BARTER, ACCOUNTS, BILLS, GREATEST COMMON MEASURE OR DIVISOR, INTRODUCTION TO ARITHMETIC. ARITHMETIC is the art of counting or reckoning by means of Numbers. Number expresses either a unit—that is, one of anything—or a collection of units of the same kind, as two horsemen, five books, a thousand feet. NOTATION AND NUMERATION. NOTATION is the method of expressing numbers by means of certain signs or figures; thus-1, 2, 3. - NUMERATION is the art of reading or expressing numbers in words; thus-1, one ; 2, two. THE FIGURES used to express numbers are the following:one, two, three, four, five, six, scven, eight, nine, nothing or nought. 1 2 3 4 5 6 7 8 9 0 The first nine of these figures, when standing separately or singly, thus-3, 6, are termed units, and each of them represents one of the numbers from one to nine. The last, 0, called a nothing or nought, when standing by itself, expresses no number, or nothing; but when annexed to any of the other figures, it increases their value tenfold. Thus 1 with O annexed becomes 10, or ten; 2 with 0 annexed, thus— 20, represents twenty; 10 with O annexed represents one hundred; and so on. These figures, besides the value they have when standing singly, have also, when standing in connection with other figures, a local value, depending on the place they occupy in the number; thus 2 by itself means two, but if it becomes the second figure from the right by another figure having been placed after it, thus-23, the 2 counts as 2 tens, or twenty; and if a third figure is annexed, so as to make it the third from the right, thus-236, the 2 counts as 2 hundreds; and so on, the addition of each figure increasing tenfold the local value of those before it. It is by means of these ten figures and their combinations that all numbers are expressed. |