Introduction to Veda (Viete, Francois, seigneurdeLa Bigotiere) is one of the most influential mathematicians in France in the16th century. He was the first to introduce algebraic symbols of systems and improved the theory of equations. He was born in Boitu on 1540. 1603 12 13 died in Paris. When I was young, I studied law, worked as a lawyer, later engaged in political activities, worked as a member of parliament, and deciphered the enemy's code for the government in the war against Spain. David is also devoted to mathematical research. He was the first to consciously and systematically use letters to represent known numbers, unknowns and their powers, which brought great progress to the theoretical research of algebra. David discussed various rational transformations of the roots of the equation, and found the relationship between the roots of the equation and the coefficients (so people call the conclusion describing the relationship between the roots and the coefficients of a quadratic equation in one variable "Vieta Theorem"). Vedas are honored as "the father of algebra" in Europe. David's most important contribution is the development of algebra. He introduced algebraic symbols systematically for the first time and promoted the development of equation theory. David used the word "analysis" to summarize the contents and methods of algebra at that time. He created a large number of algebraic symbols, replaced unknowns with letters, systematically expounded and perfected the solutions of cubic and quartic equations, and pointed out the relationship between roots and coefficients. The triangular solution of irreducible cubic equation is given. He has written many books, such as Introduction to Analytical Methods and Identification and Correction of Equations. David engaged in mathematical research only out of love, but he accomplished masterpieces in algebra and trigonometry. His Mathematical Laws Applied to Triangles (1579) is one of David's earliest mathematical monographs, and it may be the first book in Western Europe that systematically discusses six methods for trigonometric functions to solve planar and spherical triangles. He is called the father of modern algebraic symbols. David also specially wrote a paper "Tangent Angle", which preliminarily discussed the general formulas of sine, cosine and tangent chord, and applied algebraic transformation to trigonometry for the first time. He considered the equation with multiple angles, gave the function of expressing COS(nx) as COS(x), and gave the expression of multiple angles when n≤ 1 1 equals any positive integer. His book Introduction to Analytic Methods (159 1) concentrates his previous achievements in algebra, making algebra truly an excellent branch of mathematics. His contribution to equation theory is that he proposed the solutions of quadratic, cubic and quartic equations in the book "Arrangement and Revision of Equations". Introduction to Analytical Methods is the most important Vedic algebraic work and the earliest monograph on symbolic algebra. Chapter 1 of this book combines two Greek documents: Chapter 7 of Papos's Mathematics Collection and the steps to solve problems in Diophantine's works. He believes that algebra is a logical analysis technique to obtain conditions from known results. He is confident that Greek mathematicians have applied this analysis technique, but he just reorganized this analysis method. David was not satisfied with Diophantine's idea of solving every problem with a special solution. He tried to create a universal symbolic algebra. He introduced letters to represent quantities, consonants B, C, D and so on. As a known quantity, vowel A (later n) is regarded as an unknown quantity X, square number and acubus are regarded as x2 and x3, and this algebra is called "class operation" to distinguish it from "number operation" used to determine numbers. When David put forward the difference between class operation and number operation, he had already drawn the boundary between algebra and arithmetic. In this way, algebra becomes the knowledge of general classes and equations. This innovation is regarded as an important progress in the history of mathematics, which opens the way for the development of algebra. Therefore, David is called "the father of algebra" by the west. 1593, David published another monograph on algebra-Five Articles of Analysis (5 volumes, about 159 1 year); On the Determination and Correction of Equations was published by his friend A. Anderson in Paris after the death of Vedas, but it was completed as early as 159 1 year. Among them, a series of formulas about equation transformation are obtained, and the improved solutions of G cardano's cubic equation and L Ferrari's quartic equation are given. Another achievement is to record the famous Vieta theorem, that is, the relationship between the roots and coefficients of an equation. David also discussed the numerical solution of algebraic equations, which was published in 1600 with the title "Numerical solution of power". In 1593, David explained how to use rulers and compasses to solve geometric problems, which led to some quadratic equations in five analyses. In the same year, his "Supplement to Geometry" was published in tours, which gave some knowledge of the algebraic equations involved in drawing rulers and rulers. In addition, David gave the infinite expression of pi for the first time, and created a set of decimal notation of 10, which promoted the reform of notation. Later, the Vedas thought of solving geometric problems by algebraic method was inherited by Descartes and developed into analytic geometry. To some extent, David is also an authority on geometry. He calculated pi through a polygon with 393,465,438+06 sides, accurate to 9 decimal places, and has been in the leading position in the world for a long time. David also specially wrote a paper "Tangent Angle", which preliminarily discussed the general formulas of sine, cosine and tangent chord, and applied algebraic transformation to trigonometry for the first time. He considered the equation with multiple angles, gave the function of expressing COS(nx) as COS(x), and gave the expression of multiple angles when n≤ 1 1 equals any positive integer. David's most important contribution is the development of algebra. He introduced algebraic symbols systematically for the first time and promoted the development of equation theory. David used the word "analysis" to summarize the contents and methods of algebra at that time. He created a large number of algebraic symbols, replaced unknowns with letters, systematically expounded and perfected the solutions of cubic and quartic equations, and pointed out the relationship between roots and coefficients. The triangular solution of irreducible cubic equation is given. He has written many books, such as Introduction to Analytical Methods and Identification and Correction of Equations. Because the Vedas made many important contributions, he became one of the most outstanding mathematicians in France in the16th century. Content of Vieta's Theorem [Edit this paragraph] In the unary quadratic equation AX 2+BX+C = 0 (A ≠ 0 and △ = B 2-4ac ≥ 0), let two roots be X 1 and X 2, then X 1+X2 =-B/. Generally, for a univariate equation with degree n ∑ AIX I = 0, its roots are expressed as X 1, X2…, Xn, and we have ∑ xi = (-1)1* a (n-1)/a (n) ∑ xixj = This theorem was obtained by David in16th century. The proof of this theorem depends on the basic theorem of algebra, but Gauss first demonstrated it in 1799. It can be inferred from the basic theorem of algebra that any unary equation of degree n must have roots in a complex set. So the left end of the equation can be decomposed into the product of linear factors in the range of complex numbers: where is the root of the equation. Vieta's theorem is obtained by comparing the coefficients at both ends. Vieta theorem is widely used in equation theory. Proof of Vieta Theorem [Edit this paragraph] Let x 1 and x2 be two solutions of the unary quadratic equation ax 2+bx+c = 0. If: a(x-x 1)(x-x2)=0, then we can get ax 2-a (x1+x2) x+ax1x 2 = 0:-a (x/kloc-0). Then: an (x-x1) (x-x2) ... (x-xn) = 0, So: an (x-x1) (x-x2) ... (x-xn) = ∑ aixi (when open (x-x1) a (n-2) = an (∑ xixj) ... A0 = = (-/)

Go to the next level and wish the landlord, hoping that the landlord will adopt it.