ARITHMETIC. NUMBER is the abstract ratio of one quantity to another of the same kind, taken for unity. Theoretic Arithmetic is the science of numbers. Practical Arithmetic is the art of numbering. In Arithmetic there are five principal or fundamental rules for its operations, namely, Notation, Addition, Subtraction, Multiplication, and Division. NOTATION.* NOTATION teaches how to read any proposed number, expressed in characters, and to write any proposed number in characters. * As it is absolutely necessary to have a perfect knowledge of our excellent method of notation, in order to understand the reasoning made use of in the following Notes, I shall endeavour to explain it in as clear and concise a manner as possible. 1. It may then be observed, that the characters, by which all numbers are expressed, are these ten; 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; 0 is called a cypher, and the rest, or rather all of them, are called figures or digits. The names and signification of these characters, and the origin or generation of the numbers they stand for, are as follow; O nothing; 1 one, or a single I. To read Numbers. RULE. To the simple value of each figure join the name of its place, beginning at the left and reading toward the right. thing, called an unit; 1 and 1 are 2 two; 2 and 1 are 3 three ; 3 and 1 are 4 four; 4 and 1 are 5 five; 5 and 1 are 6 six; 6 and 1 are 7 seven; 7 and 1 are 8 eight; 8 and I are 9 nine; and 9 and 1 are ten, which has no single character; and thus by con tinual addition of one, all numbers are generated. 2. Besides the simple value of the figures, as above noted, they have each a local value according to the following law, namely, in a combination of figures, reckoning from right to left, the figure in the first place represents its primitive simple value; that in the second place, ten times its simple value; that in the third place, a hundred times its simple value, and so on; the value of the figure in each place being ten times the value of it in that immediately preceding it. 3. The names of the places are denominated according to their order. The first is called the place of units; the second, that of tens; the third, of hundreds; the fourth, of thousands; the fifth, of ten thousands; the sixth, of hundred thousands; the seventh, of millions, and so on. Thus, in the number 3456789; 9 in the first place signifies only nine; 8 in the second place signifies eight tens, or eighty; 7 in the third place is seven hundred; 6 in the fourth place is six thousand; 5 in the fifth place is fifty thousand; 4 in the sixth place is four hundred thousand; and 3 in the seventh place is three million; and the whole number is read thus, three million, four hundred and fifty six thousand, seven hundred and eighty nine. |