TRACT 33.

HISTORY OF ALGEBRA.

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predecessors ; as, for instance, where he neglects to availhimself of the negative roots of Cardan ; the numeral expo-nents of Stifelius, instead of which he uses the names of thepowers themselves ; or the fractional exponents of Stevinus;or the commodious way of prefixing the coefficient beforethe quantity or factor; and such like circumstances ; thewant of which gives his Algebra the appearance of an agemuch earlier than its own. But his real inventions ofthings before not known, may be reduced to the followingparuculars.

1st. Vieta introduced the general use of the letters of thealphabet, to denote indefinite given quantities ; which hadonly been done on some particular occasions before his time.But the general use of letters, for the. unknown quantities,was before pretty common with Stifelius and his successors.Vieta uses the vou'els a, e, i, o, u, y for the unknown quan-tities, and the consonants b, c, d, &c, for known ones.

2d. He invented, and introduced many expressions orterms, several of which are in use to this day : such as coeffi-cient, affirmative and negative, pure and adfected or affected,unciae, homogeneum adfectionis, homogeneum compara-tionis, tlie line or vinculum over compound quantities, thusa + b. And his method of setting down his equations, is toplace the homogeneum comparationis, or absolute knownterm, on the right-hand side alone, and on the other sideall the terms which contain the unknown quantity, withtheir proper signs.

3d. In' most of the rules and reductions for cubic andother equations, he made some improvements, and varia-tions in the modes.

4th. He showed how to change the root of an equation ina given proportion.

5. He derived or raised the cubic and biquadratic, &eequations, from quadratics ; not by composition in Harriot’swav, but by squaring and otherwise multiplying certainparts of the quadratic. And as some quadratic equationshave two roots, therefore the cubic^ and others raised from

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