Fran ç ois Vi è te (1540-1603) was born in Poitiers, France, in 1540 and died in Paris on December 13, 1603.When he was young, he studied law and became a lawyer. Later, he engaged in political activities. He was a member of parliament. In the war against Spain, he cracked the enemy's code for the government.Veda is also committed toMathematical research, the first to use letters consciously and systematicallyKnown number、unknown numberAndPower, broughtAlgebraSignificant progress in theoretical research.
Veda is honored as the "father of algebra" in Europe.Weida's most important contribution is to promote algebra. He was the first to systematically introduce algebraic symbols, which promoted the development of equation theory.Veda used the word "analysis" to summarize the contents and methods of algebra at that time.[1]He created a large number of algebraic symbols, replaced unknown numbers with letters, systematically expounded and improved the solution of cubic and quartic equations, and pointed out the relationship between roots and coefficients.giveCubic equationTriangular solution of irreducible case.Compiled《Introduction to Analytical Methods》, On the Identification and Correction of Equations, etc.
Veda is engaged inMathematical researchJust out of love, however, he completed algebra andTrigonometryA great work in this field.His Mathematical Laws Applied to Triangles (1579) is one of Veda's earliest mathematical monographs, probablyWestern EuropePart I: Six TrianglesShape functionSolve plane andspherical trigonometryA systematic work on the method of shape.He is called the father of modern algebraic symbols.Weida also wrote a special paper, "Intercept", which preliminarily discussedsine（sin）、cosine(cos), the general formula of tangent chord, the algebraic transformation is applied to trigonometry for the first time.He considered the equation containing double angle, specifically gave the function of COS (nx) expressed as COS (x), and gave the double angle when n ≤ 11 is equal to any positive integerexpressionHas.
His book "Introduction to Analytic Methods" (1591) concentrated his previous achievements in algebra, making algebra really an excellent branch of mathematics.His contribution to equation theory is that he proposed the solution of quadratic, cubic and quartic equations in the book "On the Arrangement and Correction of Equations".
Algebraic works
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《Introduction to Analytical Methods》It is the most important algebra work of Veda and the earliest monograph on symbolic algebra. Chapter 1 of the book uses two kinds of Greek literature:pappus Chapter 7 andDifantuCombining the steps of solving problems in the book, it is believed that algebra is a way of finding conditions from known resultslogic analysisHe was confident that the Greek mathematician had applied this analytical technique, and he just reorganized this analytical method.Veda is not satisfied with the idea that Diophantine uses a special solution to every problem and tries to create a general symbolic algebra.He introduced letters to express quantities, using consonant letters B, C, D, etc. to express known quantities, and vowel letters A (later used N), etcUnknown quantityx，While A quadratus and A cubus are used to represent x2 and x3, and this algebra is called the "operation of this class" to distinguish it from the "operation of numbers" used to determine numbers.When Veda proposed the difference between the operation of class and the operation of number, he had stipulated the boundary between algebra and arithmetic.In this way, algebra becomes the study of general classes and equations. This innovation is considered to beHistory of mathematicsIt opened up the way for the development of algebra, so Veda was called "the father of algebra" in the West.In 1593, Weida published another monograph on algebra - Five Chapters of Analysis (five volumes, completed in about 1591);On the Identification and Correction of Equations was written by his friend AAndersonPublished in Paris, but completed as early as 1591.Among them, a series of formulas related to equation transformation are obtained, and G. Kaldano cubic equation and LFerrariThe improved solution formula of quartic equation solution.The other is to record the famousVeda's theoremThat is, the relationship between the root of the equation and the coefficient.Veda also discussedalgebraic equationNumerical solutionIn 1600, it was published under the title of "Numerical Solution of Power".
In 1593, Weida explained how to userulerandcompassesMake certainQuadratic equationThe solution of the geometric problem.In the same year, his Supplementum geometriae was published in Tours, in which he gave some algebraic equation knowledge involved in the problem of drawing with ruler and gauge.In addition, Veda was the first to explicitly give the infinite formula of pi value, and created a set of decimal fractionsRepresentation, promotedNumerationReform.Later, Veda usedalgebraic methodThe idea of solving geometric problems comes fromDescartesInherit and develop into analysisgeometry。[2]In a way, Veda is also an authority in geometrypolygonCalculate pi, accurate to 9 decimal places, which has been in the leading position in the world for a long time.
Main contributions
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Veda's most important contribution is to promote algebra. He was the first to systematically introduce algebraic symbols, which promotedEquation theoryDevelopment of.Veda used the word "analysis" to summarize the contents and methods of algebra at that time.He created a large number of algebraic symbols, replaced unknown numbers with letters, and systematically expounded and improved threeQuartic equationThe relationship between root and coefficient is pointed out.giveCubic equationTriangular solution of irreducible case.Author《Introduction to Analytical Methods》, On the Identification and Correction of Equations, etc.
Because Veda made many important contributions, he later became one of the most outstanding mathematicians in France in the sixteenth century.
