Arithmetic

Arithmetic, the science of numbers. The systematic representation of numbers is termed notation. With a bad system of notation, such as that of the Greeks and Romans, arithmetical processes were laborious, and the progress of the science very slow. It was not till the introduction of the decimal system of notation in the tenth century that arithmetic began to develop much, though there had been writers on the subject from the time of Euclid. The elementary operations in arithmetic are addition and subtraction, converse processes that in the extension of the science in algebra are regarded as identical; and the other two converse processes, multiplication and division. The theory of numbers supplies us with different modes of operating. Thus ordinary multiplication is effected by a method of continued addition, and division by subtraction; but these may also be effected by logarithms (q.v.). The various subjects to which arithmetical rules are applied, are noticed separately.