VIETE, F.(1540-1603)

    The greatest French mathematician of the sixteenth century was Francois Viete, frequently called by his semi-Latin name of Vieta, a lawyer and member of parliament who devoted most of his leisure time to mathematics.  He was born in 1540 at Fontenay and died in 1603 in Paris.
    Some entertaining anecdotes are told about Viete.  There is a story about an ambassador from the low Countries who boasted to king Henry IV that

France had no mathematician capable of solving a problem proposed in 1593 by his countryman Adrianus Romanus (1561-1615), which required the solution of a rorty-fifth degree eqration.     Viete was summoned and shown the equation.   Recognizing an underlying trigonometric cinnection, he was able, in a few minutes, to give two roots and later gave twenty-one more.  The negative roots escaped him.  In return, Viete challenged Romanus to solve the problem of Apollonius (see Section 6-4), but Romanus was unable to lbtain a solution using Euclidean tools.  When he was shoun the proposer's elegant solution, he traveled to Fontenay to meet Viete, and a warm friendship developed.  There is also a story of how Viete successfully deciphered a Spanish code containing war against Spain.  So certain was King Philip II that the code was undecipherable that he complained to the Pope that the French were employing magic against his country, "contrary to the practice of the Christian faith."  It is said that when absorbed with mathematics, Viete would closet himself in his study for days.
Viete wrote a number of works on trigonometry, algebre, and geometry, chief of which are the Canon mathematicus seu ad triangula (1579), the In
artem analyticam isagoge (1591), the Supplementum geometriae (1593), De numerosa poteatatum resolutione (1600), and De aequationum recognitione et emendatione (published posthuously in 1615).  These works, except the last, were printed and distributed at Viete's own expense.
    viete was an outstanding algebraist, so it is no surprise to learn that he applied algebra and trigonometry to his geometry.  He contributed to the three famous problems of antiquity by showing that both the trisection and the duplication problems depend upon the solution of cubic equations.   We have mantioned Viete's calculation of ¥ð and his interesting infinite product converging to 2/¥ð.  We mentioned his attempted restoration of Apollonius lost work on Tangencies.
    In 1594, Viete acquired nome unfortunate notoridty by conducting an angry controverwy with clavius on the Gregorian reform of the calendar.  Viete's attitude in the matter was wholly unscientific.