Francois Viète
Born: 1540 in Fontenay-le-Comte, France
Died: 13 Dec 1603 in Paris, France
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Viète introduced the first systematic algebraic notation
Viète trained as a lawyer at the University of Poitiers, receiving his degree in 1560. He began publication of Canon mathematicus, seu ad triangula cum appendicibus in 1571. The first two books on plane and spherical trigonometry were completed by 1579. The last two books on astronomy have never been published.
In 1573 Viète was appointed to the parliament of Brittany and in 1589 he worked for the French state as a parliamentary councillor.
During the war with Spain (1590), Viète served Henry IV of France and deciphered the Spanish code in intercepted messages.
Viète introduced the first systematic algebraic notation in his book In artem analyticam isagoge (1591). He demonstrated the value of symbols by using plus + and minus - signs for operations, and 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. The convention where letters near the beginning of the alphabet represent known quantities while letters near the end represent unknown quantities was introduced later by Descartes in La Gèometrie . This convention is used today, often without people realising that a convention is being used at all. (If asked to solve ax = b nobody asks which quantity do I solve for?.)
Viète made many improvements in the theory of equations. He presented methods for solving equations of second, third and fourth degree. He knew the connection between the positive roots of equations and the coefficients of the different powers of the unknown quantity.
He also wrote books on trigonometry and geometry such as Supplementum geometriae (1593). He gave geometrical solutions to doubling a cube and trisecting an angle in this book.
In 1593 Viète published a second book examining various problems such as doubling the cube, trisecting an angle and he constructed the tangent at any point on an Archimedian spiral. Also, in this book, he calculated 
to 9 places using a polygon of 6.2
= 393216 sides. He also represented as an infinite product.
Viète also did important work in trigonometry and left an unpublished manuscript on mathematical astronomy.
References elsewhere in this archive:
Tell me about approximations for
Show me the Archimedian spiral
Other Web sites:
References:
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