Developmental College Mathematics
... was banished by his political enemies from the court. He left Paris and moved to Beauvoir-sur-Mer where he was able to devote himself entirely to his mathematical studies. During this period, Viete’s best mathematical work was done (O’Connor and Robertson). In 1589, Henry III brought Vičte back into his parliament. After the assassination of Hernry III, Viete worked for Henry IV as a Protestant supporter. Viete’s mathematical abilities were excellent by this time and Henry IV, who acquired coded messages sent to Philip II of Spain, asked Vičte decoding messages. It took him time to decode all of messages, eventually; he completed it (O’ Connor and Robertson). “In 1593, Henry IV converted back to Roman Catholicism who was supported by Spain due to political problems. Vičte also converted to Roman Catholicism”(O’Connor and Robertson). Henry IV declared war on Philip II of Spain in 1595. During this time, Vičte saved King by solving a mathematical problem which involved solving an equation of degree 45. “Vičte solved the problem by realizing that there was an underlying trigonometric connection” (O’Connor and Robertson). In return, Vičte challenged Van Roomen to solve the problem of Apollonian, but Van Roomen was unable to find a solution using Euclidean tools. When he received the proposer’s solution, he traveled to Fontenay to meet Vičte and the two men developed their warm friendship (Vičte, F.). Vičte continued to serve Henry IV as a royal privy councilor and master of requests until 1597 and he was dismissed in 1602. He died one year later on Feb. 23, 1603 in Paris (O’Connor and Robertson). “Viete’s mathematical work covers a wide range, but his most important work is the In artem analytical isagoge” (Hollingdale 120). Vičte introduced the first systematic algebraic notaion in his book In artem analytical isagoge published at Tours in 1591. It means “Introduction to the analytic art”. In his treatise In artem analytical isagoge, Vičte demonstrated the value of symbols introducing letters to represent unknowns. He suggested using letters as symbols for quantities both known and unknown. He used vowels for the unknowns and consonants for known quantities. He also introduced the plus(+), minus(-) symbols and square brackets (O’Connor and Robertson). He knew the relation between the positive roots of equations and the coefficients of unknown quantity. “Vičte made many improvements in the theory of equations. He presented methods for solving equations of second, third and fourth degree” (O’Conner and Robertson). “The notion of using letters systematically, not just to represent unknown quantities but also as general coefficients, is Vičte’s most important contribution to algebraic theory” (Hollingdale 121). Vičte represented π as an infinite product. His substitution method for the solution of polynomials still goes by his name. In addition, he was the first to describe the law of cosines and he developed formulas for the sine and cosine of a multiple angle (Cramer). Vičte wrote a number of books on trigonometry and geometry such as S...