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HISTORICAL VIEW OP THE

trisection of a circular arc. He also mentions a ma-nuscript of Diophantus in the Vatican , in which theinvention of algebra is ascribed to the Indians. Nothingof this, however, appears in the works of Diophantus assubsequently printed. This point remains without ex-planation.

Among the mathematicians of the 16th century, none,perhaps, has secured a more lasting reputation thanVieta, a native of Fontenoy, who is entitled by Ricciolithe great ornament of French science. He was equallyremarkable for industry and originality. He advancedthe algebraic notation by the introduction of letters tostand for the known as well as the unknown quantities,so that it was in his hands that the language of algebrafirst became capable of expressing general truths. Hedelivered a rule for solving some cases of biquadraticequations. And in the case of an equation of any degree,complete with all its terms (that is, containing in se-parate terms all the powers of the unknown quantity upto the highest, by which the degree of the equation isdesignated) ; and when the roots are all positive, hediscovered the relation between the roots and the co-efficients of the terms. Thus was another step slowlytaken towards the complete theory.

Vieta was not less celebrated for the improvements heintroduced into trigonometry: and in his treatise onangular sections, made a most important application ofalgebra to the theorems and problems of geometry. Herestored some of the books of Apollonius in a mannerhighly creditable to his own ingenuity, though not pre-cisely accordant with the taste and style of his author.He also directed his attention to astronomical subjects,and submitted to Pope Clement VIII . a plan for reform-ing the Calendar. He is said also to have composed animportant astronomical work, called “ Harmonicon Cse-leste,” which being lent to a friend, was, by some un-principled rival, surreptitiously taken from him, anddestroyed or suppressed. His mathematical treatises