sict. i.] DISSERTATION SECOND. 27 



Viela was a very learned man, and an excellent mathe- 

 matician, 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 express- 

 ing general truths, and attained to that extension which 

 has since rendered it such a powerful instrument of in- 

 vestigation. He has also given new demonstrations of the 

 rule for resolving cubick, and even biquadratick 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 case where none of the terms are want- 

 ing, and where all the roots are real or positive. It is, in- 

 deed, extremely curious to remark, how gradually the 

 truths of this sort came in sight. This proposition belong- 

 ed to a general truth, the greater part ot which remained 

 yet to be discovered. Vieta's treatises were originally 

 published about the year 1600, and were afterwards col- 

 lected 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 re- 

 solve 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 indebt- 

 ed to Albert Girard, a Flemish mathematician, whose prin- 

 cipal work, Invention Nouvelle en Algebre, was printed 

 in 1669. This ingenious author perceived a greater ex- 

 tent, but not yet the whole of the truth, partially discov- 

 ered by Vieta, viz. the successive formation of the coeffi- 



