Analysis:

Vedas

Vedas, F(Viete, Franco), 1540 was born in Boitu, France [Boitu, Fontenet-leconte, modern province]; 1603 12 13 died in Paris.

Vedas are the most influential mathematicians in France in the16th century. His achievements mainly include:

Plane trigonometry and sphericity

Mathematical Laws Applied to Triangle is one of David's earliest mathematical monographs, and it is also one of the earliest works that systematically discuss planes and spheres. 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 multi-angle equation, gave the function that would be expressed as, and gave the multi-angle expression when n is equal to any positive integer.

Symbolic Algebra and Equation Theory

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. To represent a known quantity, the vowel A (later n) represents an unknown quantity X, a square and a cubus. 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. 159 1 year has an outline, and 1600 was published with the title "Numerical Solution of Power".

Contribution of geometry

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 about 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 representation 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.