François Viète

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François Viète

François Viète or Franciscus Vieta , as he called himself in Latinized form (* 1540 in Fontenay-le-Comte ; † December 13 , according to other sources February 23, 1603 in Paris ), was a French lawyer and mathematician . He introduced the use of letters as variables in modern mathematical notation. He is considered to be the actual founder of algebra in modern Europe.



François Viète was born in Fontenay-le-Comte (in today's Vendée department in western France) in 1540 as the son of the respected lawyer Étienne Viète. He came from a wealthy middle-class background. Viète attended a convent school and began studying law in Poitiers at the age of 18 with the aim of pursuing a university career.

After graduating, he settled in his hometown as a lawyer . First (1564) he took up a position as secretary and legal advisor to the very influential and wealthy Protestant family Soubise . In addition, he taught the family's daughter, Catherine Parthenay, as a private tutor, whose interest in astronomy, astrology and mathematics is likely to have strongly influenced him. In this way a work by Viète on the representation of the planetary theory on the basis of the Ptolemaic geocentric system was created .

From 1570 he worked as a lawyer in Paris and soon enjoyed an excellent reputation. After the death of his father, he inherited his title Sieur de la Bigotière. In 1574 he was appointed a member of the Parliament in Rennes . From 1580 Viète lived again in Paris, where he also worked in the parliament and as a personal advisor to the king. He was adviser to the kings Henry III. (1551–1589) and Heinrich IV. (1553–1610), for whom he deciphered intercepted messages from the enemy Spain. He signed as “interprète et déchiffreur du roi”.

Due to political intrigue - mainly through the influence of the Catholic League and the Guise family - he was dismissed in 1584 and retired to the country, where he mainly occupied himself with mathematics. After the murder of Heinrich III. However, in 1589 he was reappointed to his previous office by his successor Heinrich IV.

Around this time he gained an international reputation as a mathematician. The anecdote of his meeting with Adriaan van Roomen (Adrianus Romanus; 1561–1615) is known and is told in numerous sources, including the “Historiettes” by Tallemant des Réaux . Van Roomen was a mathematician from Leuven who was teaching in Würzburg at the time . He had set a task as a challenge for all mathematicians in Europe and was so enthusiastic about Viète's solution that he immediately left for France to meet him. Viète, who later dryly commented on the speed of his solution with Ut legi, ut solvi (as read, so solved), for his part set van Roomen the task of finding all circles that touch three given circles ( Apollonian problem ). This problem had already been solved in antiquity by Apollonios of Perge , but Apollonios' writing was lost. Van Roomen solved the problem with the help of a hyperbola. Viète considered this solution to be inadequate because it was not limited to the classic method with compasses and ruler . Viète later published an improved solution himself in his Apollonius Gallus .

Since Viète's health was getting worse and worse, he asked the king in 1602 for his release in order to recover. But he did not recover and died on December 13, 1603 in Paris.

Viète lived in a time that was marked by bitter religious battles between the Catholics and the Protestant Huguenots. He himself was a Catholic, like the king, but also frequented Protestant circles and was close to the "politiques" who, in contrast to the Catholic League, sought to overcome religious differences and achieve national unity.

Merits as a mathematician

Actually, mathematics was just a sideline for Viète, but he became one of the most important and influential mathematicians of his time.

He is sometimes also called the "father of algebra " because he introduced arithmetic with letters in modern times and systematically used symbols for arithmetic operations, especially since he recognized that this opened up far more possibilities than before. Already in ancient mathematics , Diophantus of Alexandria used letter symbolism (Viète studied Diophant). Viète finally introduced arithmetic with (capital Latin) letters, which is based on the same principles as arithmetic with numbers. He distinguished the "logistica numerosa" as pure numerical calculation from the more abstract "logistica speciosa", the "letter arithmetic" and can thus be described as the founder of modern algebra. Our current spelling is largely due to him. He was the first to consistently (with a few exceptions) use symbols for mathematical operations and reduced entire mathematical complexes to formulas:

  • So he used the characters + and -, first used by Johannes Widmann in a book in 1489, in his works. Previously, these were usually written out as plus and minus in arithmetic operations.
  • He also used the fraction line as a symbol for division and the word "in" as a fixed symbol for multiplication .
  • Viète expressed the equality of two terms with the word "aequabitur" and thus invented the first equal sign . Vieta wrote related terms under each other and connected them with curly brackets.

In addition, he has achieved excellent results in the field of trigonometry and made valuable preparatory work for the subsequent elaboration of the calculus . In this context he was the first to describe a closed formula for the circle number π in 1593 in the form of an infinite product (see main article Vieta's product representation of the circle number ).

Today we know Vieta's theorem about the solutions to a quadratic equation .

He attacked the work of Christophorus Clavius and others on the Gregorian calendar from 1600 in a series of pamphlets and accused them of arbitrariness and errors. He published his own proposal, which Clavius ​​rejected in a publication in 1603 after Viète's death.

The asteroid (31823) Viète and the lunar crater Vieta were named after him.


Opera , 1646

Viète has published numerous works, most of which, however, only appeared in small editions and were intended for his circle of friends. The first complete edition was published by Frans van Schooten in Leiden near Elsevier after his death in 1646 under the title Opera mathematica, in unum volumen congesta, ac recognita, opera atque studio Francisci Schooten (reprint Hildesheim: Olms 1970). The Scottish mathematician Alexander Anderson , who also wrote commentaries, had begun editing it in Paris as early as 1612 . He had access to the estate kept by Viète's pupil Jacques Aleaume (his father had been Viète's secretary). Viète's most important works include:

  • Canon mathematicus seu ad triangula (1579)
  • Liber singularis (1579)
  • Isagogue in artem analyticam (1591)
  • Apollonius Gallus (1600)
  • Relatio Kalendarii vere gregoriani (1600)
  • Apud Christophorum Clavium expostulatio (1602)

Some writings were published by Alexander Anderson around 1615 such as:

The edition of the works of Frans van Schooten 1646:

  • Francisci Vietae opera mathematica / in unum volumen congesta, ac recognita, opera atque studio Francisci a Schooten Leydensis, Matheseos Professoris . Viète's works published by Frans van Schooten , Leiden 1646, doi : 10.3931 / e-rara-9151

Newer editions:

  • Karin Reich , Helmuth Gericke Francois Viète: Introduction to the New Algebra , Historiae scientiarum elementa, Volume 5, Munich: Fritsch 1973 (translation of the Isagoge from 1591)
  • Francois Viète, Albert Girard, Florimond de Beaune: The early theory of equations: on their nature and constitution (translation of 3 treatises), Annapolis: Golden Hind Press 1986 (Translator Robert Schmidt, von Viète: De aequationum recognitione et emendatione)
  • The analytic art: nine studies in algebra, geometry and trigonometry from the Opus Restitutae Mathematicae Analyzes, seu Algebrâ Novâ , Kent State University Press 1983 (translator T. Richard Witmer), reprint Dover


  • Hubert LL Busard : Viète, François . In: Charles Coulston Gillispie (Ed.): Dictionary of Scientific Biography . tape 14 : Addison Emery Verrill - Johann Zwelfer . Charles Scribner's Sons, New York 1976, p. 18-25 .
  • Evelyne Barbin et al. a .: François Viète: Un mathématicien sous la Renaissance , Vuibert 2005
  • Ivo Schneider : François Viète , in: Exempla historica. Epochs of World History in Biographies, Vol. 27. Fischer Tb .: Frankfurt / M. 1984, pp. 57-84.
  • Jacob Klein : Greek logistics and the emergence of algebra in: Sources and studies on the history of mathematics, astronomy and physics, Department B: Studies, Volume 3, First Booklet, Berlin 1934, pp. 18-105 and Second Booklet, Berlin 1936 , Pp. 122-235; Republished in English under the title: Greek Mathematical Thought and the Origin of Algebra . Cambridge, Mass. 1968, ISBN 0-486-27289-3
  • David Kahn : The Codebreakers , 1967 (about Viète as a cryptographer)
  • Philippe PA Henry: La solution de François Viète au Genealogie d'Adriaan van Roomen (PDF, 2.2 MB, French)

See also

Web links

Commons : François Viète  - Collection of images, videos and audio files