146 Division of Decimals 148 Jaring Decimals... ing Decimals...... lating Decimals... 161 } EXPLANATION of certain CHARACTERS used in the following Work. +P LUS, or more, is the Mark of Addition; and denotes the Numbers it stands between are to be ad. ded together. -Signifies Minus, or less, is the Sign of Subtraction; and when it stands between two Numbers, it denotes that the latter is to be taken from the former. x Is the Mark of Multiplication; and denotes that the Numbers betwixt which it stands are to be, multiplied together. Is the Mark of Division; and when two Numbers are placed in the same manner as the points are here, it denotes, that the Number above the Line is to be divided by that below. Is the Mark of Equality ; which being set between two Numerical Expressions, denotes they are equal between themselves. :::: Are marks of Proportionality; and denote that the Numbers betwixt which they are placed, are proportional Numbers. Eramples. For 4+3=7; read, 4 more 3 is equal to 7. / For 4—3=1; read, when 3 is taken from 4, the rea mainder is equal to 1. For 4x3=12; read, 4 multiplied by 3 produces 12. For 24"; read, 12 being divided by 3, the quotient is equal to 4. For 4::3:12; read, as I is to 4, 50 is 3 to 12. A TREATISE OF ARITHMETIC. BOOK I. RITHMETIC is that Part of Mathematics which exhibits the Doctrine of NUMBERS, explains their Properties, and teaches the Art of calculating them. A CHAP. I. NOTATION OF NUMBERS. Notation is the writing of Numbers properly. 1. All Numbers are expressed by the different dispo, sition of the following ten Characters, called Figures : 2. The value of these figures appears above at the first view; but we must observe, that besides their simple value, there expressed, they receive a new value from the place they possess in numbers expressed by several figures. 3. The value of the places encreases in a tenfold proportion infinite. 4. The first place is that next the right hand; the second the next on the left of it, and so on. 5. Every 5. Every figure standing alone expresses its own value, as 7 expresses the number seven, 9 nine, &c. 6. If a number be expressed by more figures than ones (as every number above nine is) then the first figure signifies its own value or units, the second ten times its own value, or as many tens as singly it expresses units, &c. Thus in the following numbers: 17 Seventeen The first figures 7, 1, 4, signify simply their own value, viz. 7 seven, 1 one, and 4 four; but the second figures 1, 7, 6, receive a new value from their place, and stand for ten times their simple value, viz. 1 signifies ten, 7 seventy, (seven tens) and 6 sixty, (or 6 lens.) 7. In like manner, a figure in the 3d place signifies ten times ten times, or a hundred times as much as it would in the first, as in the numbers : 317 Three Hundred and Seventeen. And so continually every figure to the left-hand has ten times the value it would have in the next place to the right, and signifies ten times its own value, so often repeated as its place is distant from the first or units place. 8. Whence it follows, and is easy to be conceived, that every ten of the value of a lower place is equal to 1 of the next higher. 9. But as the frequent repetition of tens would occasion obscurity and confusion, different terms are used to express the local value of figures, as by the following: TABLE |