VIETA (or VIITE), FRANcOIS, SEIGNEUR DE LA BIGOTIERE (1540-1603 ) , more generally known as FRAN CISCUS VIETA, French mathematician, was born at Fontenay-le-Comte, in Poitou. Ac cording to F. Ritter, Bolletino Boncompagni (1868), Vieta was brought up as a Catholic, and died in the same creed ; but there can be no doubt that he belonged to the Huguenots for several years. On the completion of his studies in law at Poitiers Vieta became an advocate in his native town, and later councillor of the parlement of Brittany. Rohan, the well-known chief of the Huguenots, took Vieta under his special protection. After the accession of Henry IV., Vieta became in 1589 councillor of the parlement at Tours, and subsequently a royal privy councillor.
We know of one important service rendered by Vieta as a royal officer. While at Tours he discovered the key to a Spanish cipher, consisting of more than 5oo characters, and thenceforward all the despatches in that language which fell into the hands of the French could be easily read. Philip II. was so convinced that his cipher was a safe one that when he found the French were aware of the contents of his letters he complained to the pope that the French were using sorcery against him.
Vieta printed at his own expense the numerous papers which he wrote on various branches of this science, and communicated them to scholars in almost every country of Europe.
Vieta has been called the father of modern algebra. All that is wanting in his writings, especially in his Isagoge in artem analyti cam (1591), in order to make them look like a modern school algebra, is merely the sign of equality. His Recensio canonica effectionum geometricarum is what we now call an algebraic geometry.
He conceived methods for the general resolution of equations of the second, third and fourth degrees different from those of Ferro and Ferrari, with which, however, it is difficult to believe him to have been unacquainted. He knew the connection existing between the positive roots of an equation (which, in his day, were alone thought of as roots) and the coefficients of the different powers of the unknown quantity. He found out the formula for deriving the sine of a multiple angle, knowing that of the simple angle with due regard to the periodicity of sines. This formula must have been known to Vieta in 1593. In his Apollonius Gallus (i600) Vieta made use of the centre of similitude of two circles. Lastly he gave an infinite product for the number r. (See article on CIRCLE.) Vieta's collected works were issued under the title of Opera Mathe matica by F. van Schooten at Leyden in 1646.