TRACT 33 .

History of algebra.

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words : like as ly and •/, derived from the letters R, r,became the signs of radicality.

Later authors, and other nations, used some the one ofthose names, and some another. It was also called speciousarithmetic by Vieta, on account of the species, or lettersof the alphabet, which he brought into general use ; andby Newton it was called universal arithmetic, from themanner in which it performs all arithmetical operations bygeneral symbols, or indeterminate quantities.

Some authors define algebra to be the art of resolvingmathematical problems: but this is the idea of analysis, orthe analytic art in general, rather than of algebra, which isonly one particular species of it.

Indeed algebra properly consists of two 'parts: first, themethod of calculating magnitudes or quantities, as repre-sented by letters or other characters; and secondly themanner of applying these calculations in the solution ofproblems.

In algebra, as applied to the resolution of problems, thefirst business is to translate the problem out of the commoninto the algebraic language, by expressing all the conditionsand quantities, both known and unknown, bjr their propercharacters, arranged in an equation, or several equations ifnecessary, and treating the unknown quantity, whether itbe number, or line, or any other thing, in the same wayas if it were a known one: this forms the composition.Then the resolution, or analytic part, is the disentanglingthe unknown quantity from the several others with which itis connected, so as to retain it alone on one side of theequation, while all the other, or known quantities, are col-lected on the other side, and so giving the value of the un-known one. And as this disentangling of the quantitysought, is performed by the converse of the operations bywhich it is connected with the others, taking them alwaysbackwards in the contrary order, it hence becomes a speciesof the analytic art, and is called the modern analysis, in

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VOL. II.