François Viète.

François Viète (or Vieta), seigneur de la Bigotière (1540 - December 13, 1603), generally known as Franciscus Vieta, was a French mathematician. Download high resolution version (1000x1568, 286 KB) This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... Download high resolution version (1000x1568, 286 KB) This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... Events January 6 - King Henry VIII of England marries Anne of Cleves, his fourth Queen consort. ... December 13 is the 347th day of the year (348th in leap years) in the Gregorian calendar. ... Events March 24 - Elizabeth I of England dies and is succeeded by her cousin King James VI of Scotland, uniting the crowns of Scotland and England April 28 – Funeral of Elizabeth I of England in Westminster Abbey July 17 or July 19 - Sir Walter Raleigh arrested for treason. ... The French Republic or France (French: République française or France) is a country whose metropolitan territory is located in western Europe, and which is further made up of a collection of overseas islands and territories located in other continents. ... A mathematician is a person whose area of study and research is mathematics. ...

He was born at Fontenay-le-Comte, in Poitou, and is believed to have been brought up as a Roman Catholic; but there is no doubt that he was a Huguenot for several years. On the completion of his studies in law at Poitiers Vieta began his career as an advocate in his native town. He left in about 1567, and later became a councillor of the parlement of Brittany, at Rennes. The religious troubles drove him out, and Henri, duc de Rohan, a well-known leader of the Huguenots, took him under his special protection, recommending him in 1580 as a "maître des requetes" (master of requests). Henry of Navarre, at Rohan's instigation, addressed two letters to King Henry III of France on March 3 and April 26, 1585, in an attempt to obtain Vieta's restoration to his former office; he failed. After Henry of Navarre became King of France, Vieta was given the position of councillor of the parlement at Tours (1589). He afterwards became a royal privy councillor, and remained so till his death, which took place suddenly at Paris in February 1603. The cause of his death is unknown. Alexander Anderson, the editor of his scientific writings, speaks of a "praeceps et immaturum autoris fatum." Fontenay-le-Comte is a commune of western France. ... Poitou was a province of France whose capital city was Poitiers. ... The Roman Catholic Church, most often spoken of simply as the Catholic Church, is the largest Christian church, with over one billion members. ... In the 16th and 17th centuries, the name of Huguenots came to apply to members of the Protestant Reformed Church of France. ... Law (a loanword from Danish- Norwegian lov), in politics and jurisprudence, is a set of rules or norms of conduct which mandate, proscribe or permit specified relationships among people and organizations, provide methods for ensuring the impartial treatment of such people, and provide punishments for those who do not follow... Location within France Poitiers (population 85,000) is a city and commune in central France, préfecture (capital) of the Vienne département. ... Parlements (pronounced in French) in ancien régime France — contrary to what their name would suggest to the modern reader — were not democratic or political institutions, but law courts . ... Traditional coat of arms This article is about the historical duchy and French province, as well as the cultural area of Brittany. ... Location within France The Parlement de Bretagne (Parliament of Brittany), the most famous building in Rennes, was rebuilt after a terrible fire in 1994. ... Henri, duc de Rohan (1579 - April 13, 1638), French soldier, writer and leader of the Huguenots, was born at the château of Blain, in Brittany. ... By Frans Pourbus the younger. ... Henry III (French: Henri III; Polish: Henryk III Walezy; September 19, 1551 - August 2, 1589) was King of Poland (1573-1574) and subsequently King of France (1574-1589). ... March 3 is the 62nd day of the year in the Gregorian Calendar (63rd in leap years). ... April 26 is the 116th day of the year in the Gregorian Calendar (117th in leap years). ... Events January 12 - The Netherlands adopts the Gregorian calendar Beginning of the Eighth War of Religion in France (also known as the War of the Three Henrys) August 8 - John Davis enters Cumberland Sound in quest for the North West Passage. ... Location within France Tours is a city in France, the préfecture (capital city) of the Indre-et-Loire département, on the lower reaches of the river Loire, between Orléans and the Atlantic coast. ... Events Rebellion of the Catholic League against King Henry III of France, in revenge for his murder of Duke Henry of Guise. ... February is the second month of the year in the Gregorian Calendar. ... Events March 24 - Elizabeth I of England dies and is succeeded by her cousin King James VI of Scotland, uniting the crowns of Scotland and England April 28 – Funeral of Elizabeth I of England in Westminster Abbey July 17 or July 19 - Sir Walter Raleigh arrested for treason. ... Alexander Anderson (c. ...

While at Tours, Vieta discovered the key to a Spanish cipher, consisting of more than 500 characters, and this meant that all dispatches in that language which fell into the hands of the French could be easily read. However, his fame now rests entirely on his achievements in mathematics. Being wealthy, he printed numerous papers at his own expense, in which he wrote on various branches of the science, and sent them to scholars in almost every country of Europe. Evidence of his character is found in the fact that he entertained as a guest, for a whole month, a scientific adversary, Adriaan van Roomen, and then paid the expenses of his journey home. Vieta's writings became very quickly known; but, when Franciscus van Schooten issued a general edition of his works in 1646, some were lost. This article is about the international language known as Spanish. ... This article is about algorithms for encryption and decryption. ... Adriaan van Roomen (29 September 1561 _ 4 May 1615), also known as Adrianus Romanus, was a Belgian mathematician. ... Franciscus Schooten (1615 - May 29, 1660) was a Dutch mathematician who is most known for popularizing the analytic geometry of René Descartes. ... Events Ongoing events English Civil War (1642-1649) Births April 15 - King Christian V of Denmark April 26 - King Peter II of Portugal July 1 - Gottfried Leibniz, German philosopher, scientist, mathematician, diplomat and lawyer. ...

Vieta's writings lacked discipline. In devising technical terms derived from the Greek he seems to have aimed at making them as unintelligible as possible. None of them has held its ground, and even his proposal to denote unknown quantities by the vowels A, E, I, O, U, Y--the consonants B, C, etc., being reserved for general known quantities--was not taken up. In this denotation he followed, perhaps, some older contemporaries, such as Petrus Ramus, who designated the points in geometrical figures by vowels, making use of consonants, R, S, T, etc., only when these were exhausted. Vieta is sometimes called the father of modern algebra. This does not mean that nobody before him had ever thought of choosing symbols different from numerals, such as the letters of the alphabet, to denote the quantities of arithmetic, but that he made the custom popular. All that is wanting in his writings, especially in his Isagoge in artem analyticam (1591), in order to make them look like a modern school algebra, is the sign of equality--an absence which is more striking because Robert Recorde had made use of the present symbol for this purpose since 1557 and Guilielmus Xylander had employed vertical parallel lines since 1575. Petrus Ramus. ... Algebra is a branch of mathematics which may be roughly characterized as a generalization and extension of arithmetic, in which symbols are employed to denote operations, and letters to represent number and quantity; it also refers to a particular kind of abstract algebra structure, the algebra over a field. ... Events June - Capture of Zutphen by the Dutch under Maurice of Nassau. ... Robert Recorde (c. ... Events Spain is effectively bankrupt. ... Guilielmus Xylander (Wilhelm Holtzman, according to his own spelling) (December 26, 1532 - February 10, 1576) was a German classical scholar. ... Events August 5 - Henry Sidney is appointed Lord Lieutenant of Ireland. ...

On the other hand, Vieta was well skilled in most modern artifices, aiming at the simplification of equations by the substitution of new quantities having a certain connection with the primitive unknown quantities. Another of his works, Recensio canonica effectionum geometricarum, bears a modern stamp, being what was later called an algebraic geometry-- a collection of precepts how to construct algebraic expressions with the use of ruler and compass only. While these writings were generally intelligible, and therefore of the greatest didactic importance, the principle of homogeneity, first enunciated by Vieta, was so far in advance of his times that most readers seem to have passed it over without adverting to its value. That principle had been made use of by the Greek authors of the classic age; but of later mathematicians only Hero, Diophantus, etc., ventured to regard lines and surfaces as mere numbers that could be joined to give a new number, their sum. Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. ... Heros aeolipile Hero (or Heron) of Alexandria (c. ... Diophantus of Alexandria - Διόφαντος ο Αλεξανδρεύς - (circa 200/214 - circa 284/298) was an ancient Greek mathematician. ...

The study of such sums, found in the works of Diophantus, may have prompted Vieta to lay down the principle that quantities occurring in an equation ought to be homogeneous, all of them lines, or surfaces, or solids, or supersolids--an equation between mere numbers being inadmissible. During the centuries that have elapsed between Vieta's day and the present, several changes of opinion have taken place on this subject. Modern mathematicians like to make homogeneous such equations as are not so from the beginning, in order to get values of a symmetrical shape. Vieta himself did not see that far; nevertheless he indirectly suggested the thought. He also conceived methods for the general resolution of equations of the second, third and fourth degrees different from those of Scipione dal Ferro and Lodovico Ferrari, with which he must have been acquainted. He devised an approximate numerical solution of equations of the second and third degrees, wherein Leonardo of Pisa must have preceded him, but by a method which is completely lost. Lodovico Ferrari (February 2, 1522 - October 5, 1565) was an Italian mathematician. ... Drawing of Leonardo Pisano Leonardo of Pisa or Leonardo Pisano (c. ...

He knew the connexion existing between the positive roots of an equation (which, by the way, were alone thought of as roots) and the coefficients of the different powers of the unknown quantity. He found out the formula for deriving the sine of a multiple angle, knowing that of the simple angle with due regard to the periodicity of sines. This formula must have been known to Vieta in 1593. In that year Adriaan van Roomen gave out as a problem to all mathematicians an equation of the 45th degree, which, being recognized by Vieta as depending on the equation between sin and sin 4>/45, was resolved by him at once, all the twenty-three positive roots of which the said equation was capable being given at the same time (see trigonometry), Such was the first encounter of the two scholars. A second took place when Vieta pointed to Apollonius's problem of taction as not yet being mastered, and Adriaan van Roomen gave a solution by the hyperbola. Vieta, however, did not accept it, as there existed a solution by means of the rule and the compass only, which he published himself in his Apollonius Callus (1600). In this paper Vieta made use of the centre of similitude of two circles. Lastly he gave an infinite product for the number x (see squaring the circle). In mathematics, a root (or a zero) of a function f is an element x in the domain of f such that f(x) = 0. ... In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ... Trigonometry (from the Greek trigonon = three angles and metro = measure) is a branch of mathematics dealing with angles, triangles and trigonometric functions such as sine and cosine. ... Apollonius may refer to: Apollonius Dyscolus Apollonius of Perga; Apollonius of Rhodes; or Apollonius of Tyana. ... Events January January 1 - Scotland adopts January 1st as being New Years Day February February 17 - Giordano Bruno burned in a stake for heresy July July 2 - Battle of Nieuwpoort: Dutch forces under Maurice of Nassau defeat Spanish forces under Archduke Albert in a battle on the coastal dunes. ... Squaring the circle is the impossible task of using ruler-and-compass constructions to make a square with the same area as a given circle. ...

Vieta's collected works were issued under the title of Opera Mathematica by F van Schooten at Leiden in 1646. Events Ongoing events English Civil War (1642-1649) Births April 15 - King Christian V of Denmark April 26 - King Peter II of Portugal July 1 - Gottfried Leibniz, German philosopher, scientist, mathematician, diplomat and lawyer. ...

Reference

• This entry incorporates public domain text originally from the 1911 Encyclopaedia Britannica.