# Page:Popular Science Monthly Volume 17.djvu/532

Algebra has been and still is defined as universal arithmetic, and is most commonly thought of as simply a generalized statement of the truths about natural numbers. And historically such it was; as such it started, and was indeed a very gradual growth. In the first known treatise on the subject by Diophantus, in the third or fourth century, the few symbols employed are mere abbreviations for ordinary words. The Arabians, who obtained their algebra from the Hindoos, did little or nothing toward its extension, though it retains in its name an Arabic touch, and the word algorithm, always, and now more than ever, associated with it, has the Arabic al. It was after their treatises had been carried into Italy by a merchant of Pisa, about 1200, that important improvements began. About 1500 the first problem of the third degree is said to have been solved. After that, Cardan first gave the general solution of a cubic equation, and employed letters to denote the unknown quantities, the given ones being still mere numbers. Toward the middle of the sixteenth century algebra was introduced into Germany, France, and England, by Stifel, Peletarius, and Robert Recorde, respectively. Recorde endowed it with the symbol of relation ${\displaystyle =}$, and Stifel with the far more important symbols of operation,