Vieta, François

(also Vietè). Born 1540 in Fontenayle-Comte; died Dec. 13, 1603, in Paris. French mathematician. A lawyer by profession.

In 1591, Vieta introduced literal designations not only for unknown quantities but also for coefficients in equations. Owing to this it became possible for the first time to express the properties of equations and their roots by general formulas. He also established uniform methods for the solution of equations of the second, third, and fourth degree. Among his discoveries Vieta himself valued especially highly the establishment of the relationship between the roots and the coefficients of equations. For the approximate solution of equations with numerical coefficients Vieta proposed a method that is analogous to Newton’s later method. In trigonometry Vieta provided the complete solution to the problem of determining all the elements of a plane or spherical triangle on the basis of three quantities, and he found important expansions of cos nx and sin nx in powers of cos x and sin x. He was the first to study infinite products. His works are written in a language difficult to follow and therefore received less widespread attention than they deserved.