Studying On The Vieta's Numerical Solutions Of The High-Degree Equations

French mathematician Vieta (1540-1630) is famous of his symbolic algebra,Vieta's theorem and the achievement of trigonometry. His work "On the Numerical Resolution of Powers by Exegetics(Paris,1600)" has an important influence on later generations. Through talk about the examples in the chapter of numerial solution from his book "The Analytic Art". We understand the essence of Vieta's methods which is based on the binomial expansion theory, by the begining of the valution, we can get the results from successive interation. Vieta lists every key intermedate results by using table lists and he explain the related results, so it makes the solution clearly. Another feature of his method is reflected in the valution techniques, that is a different way from formers of the processing method in dealing with the highest. We talk about the specific procedures of solving the higher equation numerical solution and discuss the characteristics and universalities.To discuss the numerical solution of the general program and to analyze the root estimation method.Vitea's numerical solution of this equation has a general category, which also has a general method for estimating root correctness, but also has some limitations.