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Rh a mathematician of that country, gave a regular treatise on Algebra, and considered, with very particular attention, the irreducible case of Cardan’s rule. He was the first who made the remark, that the problems belonging to that case can always be resolved by the trisection of an arch.

Vieta was a very learned man, and an excellent mathematician, remarkable both for industry and invention. He was the first who employed letters to denote the known as well as the unknown quantities, so that it was with him that the language of algebra first became capable of expressing general truths, and attained to that extension which has since rendered it such a powerful instrument of investigation. He has also given new demonstrations of the rule for resolving cubic, and even biquadratic equations. He also discovered the relation between the roots of an equation of any degree, and the coefficients of its terms, though only in the ease where none of the terms are wanting, and where all the roots are real or positive. It is, indeed, extremely curious to remark, how gradually the truths of this sort came in sight. This proposition belonged to a general truth, the greater part of which remained yet to be discovered. Vieta’s treatises were originally published about the year 1600, and were afterwards collected into one volume by Schooten, in 1646.

In speaking of this illustrious man, Vieta, we must not omit his improvements in trigonometry, and still less his treatise on angular sections, which was a most important application of Algebra to investigate the theorems, and resolve the problems of geometry. He also restored some of the books of Apollonius, in a manner highly creditable to his own ingenuity, but not perfectly in the taste of the Greek geometry; because, though the constructions are elegant, the demonstrations are all synthetical.

About the same period, Algebra became greatly indebted to Albert Girard, a Flemish mathematician, whose principal work, Invention Nouvelle en Algebre, was printed