ARITHMETIC (Gr. ἀριθμητική, from ἀριθμεῖν, to
count), the science of the properties and
relations of numbers when expressed with figures
or relations of figures. The accepted opinion
is that we have derived this science from the
Greeks, who obtained it from the Phœnicians; but if we consider that the Chaldeans, one of the oldest nations, have given us the knowledge of certain astronomical cycles or periods, of which the determination required an advanced knowledge of arithmetic, it is evident that its origin is of much earlier date. The Hebrews and Greeks used the first nine letters of their alphabet for the numbers 1 to 9; the next nine letters for 10, 20, &c., to 90; and the others for hundreds; while for thousands they recommenced the alphabet and added to each letter a mark or iota. The Romans followed a similar system, of which our Roman numerals are a specimen. But arithmetic did not reach its more modern state of progress until the introduction of the Arabic figures now used by all civilized nations. The Arabs admit that they obtained these figures from Hindostan in the 10th century. They call them Indian figures, and arithmetic the Indian science. Boëthius, in his work De Geometria, informs us that the disciples of Pythagoras used in their calculations nine peculiar figures, while others used the letters of the alphabet; and it is probable that this philosopher, who had travelled considerably, had obtained this knowledge in Hindostan, and communicating it as a secret to his disciples, caused it to remain sterile in their hands. The Greeks in the ordinary way of writing expressed the fractions thus: while β, γ, δ, &c., stood for 2, 3, 4, &c., β', γ', δ', represented ½, ⅓, ¼, &c. The oldest text book