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89-624: Viète was born at Fontenay-le-Comte in present-day Vendée . His grandfather was a merchant from La Rochelle . His father, Etienne Viète, was an attorney in Fontenay-le-Comte and a notary in Le Busseau . His mother was the aunt of Barnabé Brisson , a magistrate and the first president of parliament during the ascendancy of the Catholic League of France . Viète went to a Franciscan school and in 1558 studied law at Poitiers , graduating as

178-410: A putain publique ("public whore") and made ridiculous remarks about their difference in age (he was 18 years younger at a time when such large age differences between spouses were not at all uncommon). In November 1567, upon the death of Anne de Montmorency , Henry assumed the role of Lieutenant-General of France, placing him in nominal control of France's military. Henry served as a leader of

267-476: A Bachelor of Laws in 1559. A year later, he began his career as an attorney in his native town. From the outset, he was entrusted with some major cases, including the settlement of rent in Poitou for the widow of King Francis I of France and looking after the interests of Mary, Queen of Scots . In 1564, Viète entered the service of Antoinette d'Aubeterre , Lady Soubise, wife of Jean V de Parthenay-Soubise , one of

356-511: A better order which was scattered and confused in early writings. In 1596, Scaliger resumed his attacks from the University of Leyden. Viète replied definitively the following year. In March that same year, Adriaan van Roomen sought the resolution, by any of Europe's top mathematicians, to a polynomial equation of degree 45. King Henri IV received a snub from the Dutch ambassador, who claimed that there

445-451: A book of two trigonometric tables ( Canon mathematicus, seu ad triangula , the "canon" referred to by the title of his Universalium inspectionum , and Canonion triangulorum laterum rationalium ). A year later, he was appointed maître des requêtes to the parliament of Paris, committed to serving the king. That same year, his success in the trial between the Duke of Nemours and Françoise de Rohan, to

534-526: A bribe, but this would increase to 100,000 each. On 16 May 1573, Polish nobles chose Henry as the first elected monarch of the Polish–Lithuanian Commonwealth . The Lithuanian nobles boycotted this election, however, and it was left to the Lithuanian ducal council to confirm his election. The commonwealth elected Henry, rather than Habsburg candidates, partly in order to be more agreeable to

623-513: A clash of cultures between the Polish and the French. The young king and his followers were astonished by several Polish practices and disappointed by the rural poverty and harsh climate of the country. The Poles, on the other hand, wondered if all Frenchmen were as concerned with their appearance as their new king appeared to be. In many aspects, Polish culture had a positive influence on France. At Wawel,

712-515: A councillor of the Parlement of Rennes , at Rennes , and two years later, he obtained the agreement of Antoinette d'Aubeterre for the marriage of Catherine of Parthenay to Duke René de Rohan, Françoise's brother. In 1576, Henri, duc de Rohan took him under his special protection, recommending him in 1580 as " maître des requêtes ". In 1579, Viète finished the printing of his Universalium inspectionum (Mettayer publisher), published as an appendix to

801-565: A descendant of Louis IX (Saint Louis). The possibility of a Protestant on the throne led to the War of the Three Henrys . Under pressure from the duke of Guise, Henry III issued an edict suppressing Protestantism and annulling Henry of Navarre's right to the throne. Henry III, stung by the open disobedience of Guise, attempted a coup in May 1588 and sent royal Swiss troops into several neighbourhoods. This had

890-401: A few friends and scholars in almost every country of Europe, the systematic presentation of his mathematic theory, which he called " species logistic " (from species: symbol) or art of calculation on symbols (1591). He described in three stages how to proceed for solving a problem: Among the problems addressed by Viète with this method is the complete resolution of the quadratic equations of

979-422: A kind of "King of Times" as the historian of mathematics, Dhombres, claimed. It is true that Viète held Clavius in low esteem, as evidenced by De Thou: He said that Clavius was very clever to explain the principles of mathematics, that he heard with great clarity what the authors had invented, and wrote various treatises compiling what had been written before him without quoting its references. So, his works were in

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1068-504: A pencil. By the evening he had sent many other solutions to the ambassador." This suggests that the Adrien van Roomen problem is an equation of 45°, which Viète recognized immediately as a chord of an arc of 8° ( 1 45 {\displaystyle {\tfrac {1}{45}}} turn ). It was then easy to determine the following 22 positive alternatives, the only valid ones at the time. When, in 1595, Viète published his response to

1157-465: A population of 41,273. The river Vendée flows through the town. The town has an area of 34 km (13 sq mi). Fontenay was in existence as early as the time of the Gauls . The affix of comte is said to have been applied to it when it was taken by King Louis IX from the family of Lusignan and given to his brother Alphonse, count of Poitou , under whom it became capital of Bas-Poitou. Ceded to

1246-638: A protector of Catholicism, and tried to arrange his marriage to Mary, Queen of Scots ; however neither project took off. While still Duke of Anjou, he helped plot the St. Bartholomew's Day Massacre of 1572. Though Henry did not participate directly, historian Thierry Wanegffelen sees him as the royal most responsible for the massacre, which involved the targeted killing of many Huguenot leaders. Henry III's reign as King of France, like those of his elder brothers Francis and Charles, would see France in constant turmoil over religion. Henry continued to take an active role in

1335-417: A secret message to deliver. The king signaled for his attendants to step back for privacy, and Clément whispered in his ear while plunging a knife into his abdomen. Clément was then killed on the spot by the guards. At first, the king's wound did not appear fatal, but he enjoined all the officers around him, in case he did not survive, to be loyal to Henry of Navarre as their new king. The following morning, on

1424-405: A series of pamphlets (1600), of introducing corrections and intermediate days in an arbitrary manner, and misunderstanding the meaning of the works of his predecessor, particularly in the calculation of the lunar cycle. Viète gave a new timetable, which Clavius cleverly refuted, after Viète's death, in his Explicatio (1603). It is said that Viète was wrong. Without doubt, he believed himself to be

1513-518: Is a product of six factors (which, with this method, makes the actual construction humanly impossible). Fontenay-le-Comte Fontenay-le-Comte ( IPA: [fɔ̃tənɛ lə kɔ̃t] ; Poitevin : Funtenaes or Fintenè ) is a commune and subprefecture in the Vendée department in the Pays de la Loire region of Western France . In 2018, it had a population of 13,302, while its functional area had

1602-421: Is more striking because Robert Recorde had used the present symbol for this purpose since 1557, and Guilielmus Xylander had used parallel vertical lines since 1575. Note also the use of a 'u' like symbol with a number above it for an unknown to a given power by Rafael Bombelli in 1572. Viète had neither much time, nor students able to brilliantly illustrate his method. He took years in publishing his work (he

1691-486: Is so logically strategic with the man who goes to pieces when one of them dies." Katherine Crawford, by contrast, emphasizes the problems Henry's reputation encountered because of his failure to produce an heir and the presence of his powerful mother at court, combined with his enemies' insistence on conflating patronage with favouritism and luxury with decadence. In 1570, discussions commenced arranging for Henry to court Queen Elizabeth I of England . Elizabeth, almost 37,

1780-576: The Château of Blois , he invited Guise to the council chamber where the duke's brother Louis II, Cardinal of Guise , already waited. The duke was told that the king wished to see him in the private room adjoining the royal bedroom. There, royal guardsmen murdered the duke, then the cardinal. To make certain that no contender for the French throne was free to act against him, the king had the duke's son imprisoned. The duke of Guise had been very popular in France, and

1869-537: The Henrician Articles into law, recognizing the szlachta 's right to freely elect their monarch. Aged 22, Henry abandoned Poland–Lithuania upon inheriting the French throne when his brother, Charles IX , died without issue. France was at the time plagued by the Wars of Religion , and Henry's authority was undermined by violent political factions funded by foreign powers: the Catholic League (supported by Spain and

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1958-564: The Order of the Holy Spirit to commemorate his becoming first King of Poland and later King of France on the Feast of Pentecost and gave it precedence over the earlier Order of St. Michael , which had lost much of its original prestige by being awarded too frequently and too readily. The Order would retain its prestige as the premier chivalric order of France until the end of the French monarchy. Henry

2047-671: The Ottoman Empire (a traditional ally of France through the Franco-Ottoman alliance ) and strengthen a Polish-Ottoman alliance that was in effect. In addition to this, Henry was not a powerful ruler in his own right, as he was only a Prince, nor did France border the Commonwealth, so he wouldn't have the capacity to strip the Polish Nobility of their historic rights . A Polish delegation went to La Rochelle to meet with Henry, who

2136-682: The Pope ), the Protestant Huguenots (supported by England and the Dutch) and the Malcontents (led by Henry's own brother the Duke of Anjou and Alençon , a party of Catholic and Protestant aristocrats who jointly opposed the absolutist ambitions of the king). Henry III was himself a politique , arguing that a strong and centralised yet religiously tolerant monarchy would save France from collapse. After

2225-577: The Catholic Charles, Cardinal of Bourbon , as Henry III's heir. Henry had the Duke of Guise murdered in 1588 and was in turn assassinated by Jacques Clément , a Catholic fanatic, in 1589. He was succeeded by the King of Navarre who, as Henry IV , assumed the throne of France as the first king of the House of Bourbon and eventually converted to Catholicism. Henry was born at the royal Château de Fontainebleau ,

2314-549: The French army's position in Spain , threw the Emperor into a deep rage. If word is to be believed, the Emperor smashed an earthenware vase placed in front of him. Fontenay-le-Comte was the birthplace of: Fontenay-le-Comte is twinned with: Henry III of France Henry III ( French : Henri III, né Alexandre Édouard ; Polish : Henryk Walezy ; Lithuanian : Henrikas Valua ; 19 September 1551 – 2 August 1589)

2403-459: The French people. The portrait of a self-indulgent homosexual, incapable of fathering an heir to the throne, proved useful in efforts by the Catholic League to secure the succession for Cardinal Charles de Bourbon after 1585. However, French Renaissance scholar Gary Ferguson considers such interpretations to be unconvincing: "It is difficult to reconcile the king whose use of favourites

2492-455: The French were introduced to new technologies of septic facilities, in which litter (excrement) was taken outside the castle walls. On returning to France, Henry wanted to order the construction of such facilities at the Louvre and other palaces. Other inventions introduced to the French by the Polish included a bath with regulated hot and cold water as well as dining forks. In 1578, Henry created

2581-679: The Huguenots. His action resulted in Henry I, Duke of Guise , forming the Catholic League . After much posturing and negotiations, Henry was forced to rescind most of the concessions that had been made to the Protestants in the edict. After 1582, Henry became convinced of the need for fiscal reform to break the cycle of expedients upon which he had relied. To this end he summoned an Assembly of Notables which met from November 1583 to February 1584. While he failed to convince them of his most radical tax plans,

2670-478: The King of Spain. The contents of this letter, read by Viète, revealed that the head of the League in France, Charles, Duke of Mayenne , planned to become king in place of Henry IV. This publication led to the settlement of the Wars of Religion . The King of Spain accused Viète of having used magical powers. In 1593, Viète published his arguments against Scaliger. Beginning in 1594, he was appointed exclusively deciphering

2759-789: The Plantagenets by the Treaty of Brétigny , in 1360 it was retaken in 1372 by Duguesclin . It suffered repeated capture during the Religious Wars of the 16th century, was dismantled in 1621 and was occupied both by the Republicans and the Royalist Vendeans during the Revolt in the Vendée (1793). From 1790 to 1806 it was capital of the Vendée department. At Maison Laval on rue Rabelais , a townhouse built at

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2848-533: The Polish delegation handed over the "certificate of election to the throne of Poland-Lithuania". Henry also gave up any claims to succession and he "recognized the principle of free election" under the Henrician Articles and the pacta conventa . It was not until January 1574 that Henry was to reach the borders of Poland. On 21 February, Henry's coronation was held in Kraków . In mid-June 1574, upon learning of

2937-570: The Polish–Lithuanian Commonwealth. Henry chafed at the restrictions on monarchic power under the Polish-Lithuanian political system of " Golden Liberty ". The Polish-Lithuanian parliament had been urged by Anna Jagiellon , the sister of the recently deceased king Sigismund II Augustus, to elect him based on the understanding that Henry would wed Anna afterward. At a ceremony before the Parlement of Paris on 13 September,

3026-581: The Wars of Religion, and in 1572/1573 led the siege of La Rochelle , a massive military assault on the Huguenot-held city. At the end of May 1573, Henry learned that the Polish szlachta had elected him King of Poland (a country with a large Protestant minority at the time) and political considerations forced him to negotiate an end to the siege. Negotiators reached an agreement on 24 June 1573, and Catholic troops ended

3115-407: The admiration of many mathematicians over the centuries. Viète did not deal with cases (circles together, these tangents, etc.), but recognized that the number of solutions depends on the relative position of the three circles and outlined the ten resulting situations. Descartes completed (in 1643) the theorem of the three circles of Apollonius, leading to a quadratic equation in 87 terms, each of which

3204-474: The algebra of procedures ( al-Jabr and al-Muqabala ), creating the first symbolic algebra, and claiming that with it, all problems could be solved ( nullum non problema solvere ). In his dedication of the Isagoge to Catherine de Parthenay, Viète wrote: "These things which are new are wont in the beginning to be set forth rudely and formlessly and must then be polished and perfected in succeeding centuries. Behold,

3293-453: The ambassador, 'you have no mathematician, according to Adrianus Romanus, who didn't mention any in his catalog.' 'Yes, we have,' said the King. 'I have an excellent man. Go and seek Monsieur Viette,' he ordered. Vieta, who was at Fontainebleau, came at once. The ambassador sent for the book from Adrianus Romanus and showed the proposal to Vieta, who had arrived in the gallery, and before the King came out, he had already written two solutions with

3382-406: The art which I present is new, but in truth so old, so spoiled and defiled by the barbarians, that I considered it necessary, in order to introduce an entirely new form into it, to think out and publish a new vocabulary, having gotten rid of all its pseudo-technical terms..." Viète did not know "multiplied" notation (given by William Oughtred in 1631) or the symbol of equality, =, an absence which

3471-423: The beginning, in order to get values of a symmetrical shape. Viète 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 had not been acquainted. He devised an approximate numerical solution of equations of

3560-440: The behest of Jacques, Duke of Nemours , to run away from court to be a figurehead for the ultra-Catholics. However, the plot was uncovered before any action could be taken. Henry was known as a flaneur , who relished leisurely strolls through Paris and partook in the sociability in the busiest of neighbourhoods. He revelled in fairs, music, bilboquet and court masques . His extravagance in court entertainments cut him off from

3649-803: The benefit of the latter, earned him the resentment of the tenacious Catholic League. Between 1583 and 1585, the League persuaded king Henry III to release Viète, Viète having been accused of sympathy with the Protestant cause. 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 Viète's restoration to his former office, but he failed. Viète retired to Fontenay and Beauvoir-sur-Mer , with François de Rohan. He spent four years devoted to mathematics, writing his New Algebra (1591). In 1589, Henry III took refuge in Blois. He commanded

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3738-575: The center of similitude of two circles. His friend De Thou said that Adriaan van Roomen immediately left the University of Würzburg , saddled his horse and went to Fontenay-le-Comte, where Viète lived. According to De Thou, he stayed a month with him, and learned the methods of the new algebra . The two men became friends and Viète paid all van Roomen's expenses before his return to Würzburg. This resolution had an almost immediate impact in Europe and Viète earned

3827-671: The citizenry turned against Henry for the murders. The Parlement instituted criminal charges against the king, and he was compelled to join forces with his heir, the Protestant Henry of Navarre, by setting up the Parliament of Tours . By 1589 Henry's popularity hit a new low. Preachers were calling for his assassination and labelling him a tyrant. The people of Paris disdained him for his court extravagances, allowing corruption to grow rife, high taxes and having relied extensively on Italian financiers. But what most Parisians hated most about him

3916-458: The coefficients of the different powers of the unknown quantity (see Viète's formulas and their application on quadratic equations ). He discovered 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 Viète in 1593. In 1593, based on geometrical considerations and through trigonometric calculations perfectly mastered, he discovered

4005-470: The common people. He was also a devout Catholic who introduced pious reforms into the city and he encouraged the French church to follow the edicts of the Council of Trent . Reports that Henry engaged in same-sex relations with his court favourites, known as the mignons , date back to his own time. He was known to have enjoyed intense relationships with them. The scholar Louis Crompton maintains that all of

4094-514: The contemporary rumours were true. However, some modern historians dispute this: Jean-Francois Solnon, Nicolas Le Roux, and Jacqueline Boucher have noted that Henry had many famous mistresses, that he was well known for his taste in beautiful women, and that no male sex partners have been identified. They concluded that the idea he was homosexual was promoted by his political opponents (both Protestant and Catholic) who used his dislike of war to depict him as effeminate and undermine his reputation with

4183-519: The day that he was to have launched his assault to retake Paris, Henry III died. Chaos swept the attacking army, most of it quickly melting away; the proposed attack on Paris was postponed. Inside the city, joy at the news of Henry III's death was near delirium; some hailed the assassination as an act of God . Henry III was interred at the Saint Denis Basilica . Childless, he was the longest-living of Henry II's sons to have become king and also

4272-427: The death of Henry's younger brother Francis, Duke of Anjou , and when it became apparent that Henry would not produce an heir, the Wars of Religion developed into a succession crisis, the War of the Three Henrys . Henry III's closest heir was his distant cousin, King Henry III of Navarre , a Protestant. The Catholic League, led by Henry I, Duke of Guise , sought to exclude Protestants from the succession and championed

4361-513: The death of his brother Charles IX, Henry left Poland and headed back to France. Henry's absence provoked a constitutional crisis that the Parliament attempted to resolve by notifying Henry that his throne would be lost if he did not return from France by 12 May 1575. His failure to return caused Parliament to declare his throne vacant. The short reign of Henry at Wawel Castle in Poland was marked by

4450-526: The elliptic orbit of the planets, forty years before Kepler and twenty years before Giordano Bruno 's death. John V de Parthenay presented him to King Charles IX of France . Viète wrote a genealogy of the Parthenay family and following the death of Jean V de Parthenay-Soubise in 1566 his biography. In 1568, Antoinette, Lady Soubise, married her daughter Catherine to Baron Charles de Quellenec and Viète went with Lady Soubise to La Rochelle, where he mixed with

4539-572: The end of the 16th century, mathematics was placed under the dual aegis of Greek geometry and the Arabic procedures for resolution. At the time of Viète, algebra therefore oscillated between arithmetic, which gave the appearance of a list of rules; and geometry, which seemed more rigorous. Meanwhile, Italian mathematicians Luca Pacioli , Scipione del Ferro , Niccolò Fontana Tartaglia , Gerolamo Cardano , Lodovico Ferrari , and especially Raphael Bombelli (1560) all developed techniques for solving equations of

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4628-597: The end of the 18th Century, Emperor Napoleon 1st and his wife, Joséphine, spent the night of 7–8 August 1808. On their way from Rochefort to Nantes , they had stopped off in the Bas-Poitou capital of Fontenay-le-Comte where they were the guests of Mayor Laval who, to give them a dignified welcome, had prepared a triumphal arch over the Pont Neuf bridge. That night, the Emperor learned of the defeat of General Dupont at Bailem. The General's surrender, which seriously compromised

4717-553: The enemy's secret codes. In 1582, Pope Gregory XIII published his bull Inter gravissimas and ordered Catholic kings to comply with the change from the Julian calendar, based on the calculations of the Calabrian doctor Aloysius Lilius , aka Luigi Lilio or Luigi Giglio. His work was resumed, after his death, by the scientific adviser to the Pope, Christopher Clavius . Viète accused Clavius, in

4806-493: The first infinite product in the history of mathematics by giving an expression of π , now known as Viète's formula : He provides 10 decimal places of π by applying the Archimedes method to a polygon with 6 × 2 = 393,216 sides. This famous controversy is told by Tallemant des Réaux in these terms (46th story from the first volume of Les Historiettes. Mémoires pour servir à l’histoire du XVIIe siècle ): "In

4895-459: The first letters of the alphabet to designate the parameters and the latter for the unknowns. Viète also remained a prisoner of his time in several respects. First, he was heir of Ramus and did not address the lengths as numbers. His writing kept track of homogeneity, which did not simplify their reading. He failed to recognize the complex numbers of Bombelli and needed to double-check his algebraic answers through geometrical construction. Although he

4984-399: The form X 2 + X b = c {\displaystyle X^{2}+Xb=c} and third-degree equations of the form X 3 + a X = b {\displaystyle X^{3}+aX=b} (Viète reduced it to quadratic equations). He knew the connection between the positive roots of an equation (which, in his day, were alone thought of as roots) and

5073-596: The fourth son of King Henry II and Catherine de' Medici. He was a grandson of Francis I of France and Claude of France . His older brothers were Francis II of France , Charles IX of France , and Louis of Valois . He was made Duke of Angoulême and Duke of Orléans in 1560, then Duke of Anjou in 1566. He was his mother's favourite; she called him chers yeux ("precious eyes") and lavished fondness and affection upon him for most of his life. His elder brother, Charles, grew to detest him, partially because he resented his better health. The royal children were raised under

5162-501: The greatest didactic importance, the principle of homogeneity, first enunciated by Viète, was so far in advance of his times that most readers seem to have passed it over. 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. The study of such sums, found in

5251-915: The highest Calvinist aristocracy, leaders like Coligny and Condé and Queen Jeanne d’Albret of Navarre and her son, Henry of Navarre, the future Henry IV of France . In 1570, he refused to represent the Soubise ladies in their infamous lawsuit against the Baron De Quellenec, where they claimed the Baron was unable (or unwilling) to provide an heir. In 1571, he enrolled as an attorney in Paris, and continued to visit his student Catherine. He regularly lived in Fontenay-le-Comte, where he took on some municipal functions. He began publishing his Universalium inspectionum ad Canonem mathematicum liber singularis and wrote new mathematical research by night or during periods of leisure. He

5340-403: The letters and the results can be obtained at the end of the calculations by a simple replacement. This approach, which is the heart of contemporary algebraic method, was a fundamental step in the development of mathematics. With this, Viète marked the end of medieval algebra (from Al-Khwarizmi to Stevin) and opened the modern period. Being wealthy, Viète began to publish at his own expense, for

5429-679: The main Huguenot military leaders and accompanied him to Lyon to collect documents about his heroic defence of that city against the troops of Jacques of Savoy, 2nd Duke of Nemours just the year before. The same year, at Parc-Soubise, in the commune of Mouchamps in present-day Vendée , Viète became the tutor of Catherine de Parthenay , Soubise's twelve-year-old daughter. He taught her science and mathematics and wrote for her numerous treatises on astronomy and trigonometry , some of which have survived. In these treatises, Viète used decimal numbers (twenty years before Stevin 's paper) and he also noted

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5518-468: The nephew of Jacques Cartier , privileges over fishing, fur trading, and mining in New France . On 1 August 1589, Henry III lodged with his army at Saint-Cloud , and was preparing to attack Paris, when a young fanatical Dominican friar , Jacques Clément , carrying false papers, was granted access to deliver important documents to the king. The friar gave the king a bundle of papers and stated that he had

5607-405: The notables forwarded a series of proposals to him which would be embodied in his legislation during 1584. As a result of these policies the royal budget was almost balanced in 1585, before it was subject to political shock. In 1584, the king's youngest brother and heir presumptive , Francis, Duke of Anjou , died. Under Salic Law , the next heir to the throne was Protestant Henry of Navarre ,

5696-428: The other 22 problems to the ambassador. "Ut legit, ut solvit," he later said. Further, he sent a new problem back to Van Roomen, for resolution by Euclidean tools (rule and compass) of the lost answer to the problem first set by Apollonius of Perga . Van Roomen could not overcome that problem without resorting to a trick (see detail below). In 1598, Viète was granted special leave. Henry IV, however, charged him to end

5785-415: The problem set by Adriaan van Roomen, he proposed finding the resolution of the old problem of Apollonius , namely to find a circle tangent to three given circles. Van Roomen proposed a solution using a hyperbola , with which Viète did not agree, as he was hoping for a solution using Euclidean tools . Viète published his own solution in 1600 in his work Apollonius Gallus . In this paper, Viète made use of

5874-564: The revolt of the Notaries, whom the King had ordered to pay back their fees. Sick and exhausted by work, he left the King's service in December 1602 and received 20,000 écus , which were found at his bedside after his death. A few weeks before his death, he wrote a final thesis on issues of cryptography, which essay made obsolete all encryption methods of the time. He died on 23 February 1603, as De Thou wrote, leaving two daughters, Jeanne, whose mother

5963-531: The royal army, taking part in the victories over the Huguenots at the Battle of Jarnac (March 1569) and at the Battle of Moncontour (October 1569). At this time he was a rallying point for the ultra-Catholics at court, who saw him as an opposition figure to the tolerant line being taken by the King, with Charles, Cardinal of Lorraine guiding his council. Lorraine offered him 200,000 Francs of Church revenue to become

6052-419: The royal officials to be at Tours before 15 April 1589. Viète was one of the first who came back to Tours. He deciphered the secret letters of the Catholic League and other enemies of the king. Later, he had arguments with the classical scholar Joseph Juste Scaliger . Viète triumphed against him in 1590. After the death of Henry III, Viète became a privy councillor to Henry of Navarre, now Henry IV of France. He

6141-449: The second and third degrees, wherein Leonardo of Pisa must have preceded him, but by a method which was completely lost. Above all, Viète was the first mathematician who introduced notations for the problem (and not just for the unknowns). As a result, his algebra was no longer limited to the statement of rules, but relied on an efficient computational algebra, in which the operations act on

6230-520: The siege on 6 July 1573. Following the death of the Polish ruler Sigismund II Augustus on 7 July 1572, Jean de Monluc was sent as the French envoy to Poland to negotiate the election of Henry to the Polish throne in exchange for military support against Russia, diplomatic assistance in dealing with the Ottoman Empire , and financial subsidies. Charles IX allowed Henry’s envoys to give up to 50,000 écus to important people in Poland-Lithuania as

6319-415: 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

6408-556: The supervision of Diane de Poitiers , his father's mistress. Although he was skilled and fond of fencing, he preferred to indulge his tastes for the arts and reading. These predilections were attributed to his Italian mother. Henry's favourite interests were hunting and riding. At one point in his youth Henry showed a tendency towards Protestantism as a means of rebelling. At the age of nine, he called himself "a little Huguenot", attended Mass only to please his mother, sang Protestant psalms to his sister Margaret (exhorting her all

6497-644: The third degree, which heralded a new era. On the other hand, from the German school of Coss, the Welsh mathematician Robert Recorde (1550) and the Dutchman Simon Stevin (1581) brought an early algebraic notation: the use of decimals and exponents. However, complex numbers remained at best a philosophical way of thinking. Descartes , almost a century after their invention, used them as imaginary numbers. Only positive solutions were considered and using geometrical proof

6586-463: The times of Henri the fourth, a Dutchman called Adrianus Romanus , a learned mathematician, but not so good as he believed, published a treatise in which he proposed a question to all the mathematicians of Europe, but did not ask any Frenchman. Shortly after, a state ambassador came to the King at Fontainebleau. The King took pleasure in showing him all the sights, and he said people there were excellent in every profession in his kingdom. 'But, Sire,' said

6675-652: The unintended effect of rallying the people against him and in favor of the more popular Guise during the Day of the Barricades . Henry III fled the city; he later sought support from the Parlement of Paris and propped up an anti-League establishment throughout France. Following the defeat of the Spanish Armada that summer, the king's fear of Spanish support for the Catholic League apparently waned. Accordingly, on 23 December 1588, at

6764-438: The while to change her religion and cast her Book of Hours into the fire), and even bit the nose off a statue of Saint Paul . His mother firmly cautioned him against such behaviour, and he would never again show any Protestant tendencies. Instead, he became staunchly Catholic. In the factional dispute that engulfed France in the wake of Henry II's death in 1559, Henry was solicited by Henry, son of Francis, Duke of Guise , at

6853-471: The works of Diophantus, may have prompted Viète 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 Viète'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

6942-456: Was King of France from 1574 until his assassination in 1589, as well as King of Poland and Grand Duke of Lithuania from 1573 to 1575. As the fourth son of King Henry II of France , he was not expected to inherit the French throne and thus was a good candidate for the vacant throne of the Polish–Lithuanian Commonwealth , where he was elected monarch in 1573. During his brief rule, he signed

7031-470: Was Barbe Cottereau, and Suzanne, whose mother was Julienne Leclerc. Jeanne, the eldest, died in 1628, having married Jean Gabriau, a councillor of the parliament of Brittany . Suzanne died in January 1618 in Paris. The cause of Viète's death is unknown. Alexander Anderson , student of Viète and publisher of his scientific writings, speaks of a "praeceps et immaturum autoris fatum" (meeting an untimely end). At

7120-400: Was appreciated by the king, who admired his mathematical talents. Viète was given the position of councillor of the parlement at Tours . In 1590, Viète broke 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. Henry IV published a letter from Commander Moreo to

7209-425: Was common. The mathematician's task was in fact twofold. It was necessary to produce algebra in a more geometrical way (i.e. to give it a rigorous foundation), and it was also necessary to make geometry more algebraic, allowing for analytical calculation in the plane. Viète and Descartes solved this dual task in a double revolution. Firstly, Viète gave algebra a foundation as strong as that of geometry. He then ended

7298-460: Was crowned king of France on 13 February 1575 at Reims Cathedral . Although he was expected to produce an heir after he married the 21-year-old Louise of Lorraine on 14 February 1575, no issue resulted from their union. In 1574, Henry renewed letters that gave Portuguese New Christians the right of settling in France. In 1576, Henry signed the Edict of Beaulieu , which granted many concessions to

7387-470: Was expected by many parties in her country to marry and produce an heir. However, nothing came of these discussions. In initiating them, Elizabeth is viewed by historians as having intended only to arouse the concern of Spain, rather than contemplate marriage seriously. Henry's mother felt the chance of marriage despite differing religious views (Henry was Catholic, Elizabeth Protestant) simply required personal sacrifice. Henry tactlessly referred to Elizabeth as

7476-423: Was fully aware that his new algebra was sufficient to give a solution, this concession tainted his reputation. However, Viète created many innovations: the binomial formula , which would be taken by Pascal and Newton, and the coefficients of a polynomial to sums and products of its roots , called Viète's formula . Viète was well skilled in most modern artifices, aiming at the simplification of equations by

7565-637: Was his alleged sexuality. Under Henry, France named Guillaume Bérard as the first Consul of France in Morocco . The request came from the Moroccan prince Abd al-Malik , who had been saved by Bérard, a doctor by profession, during an epidemic in Constantinople and wished to retain Bérard in his service. Henry III encouraged the exploration and development of New World territories. In 1588, he granted Jacques Noël,

7654-496: Was known to dwell on any one question for up to three days, his elbow on the desk, feeding himself without changing position (according to his friend, Jacques de Thou ). In 1572, Viète was in Paris during the St. Bartholomew's Day massacre . That night, Baron De Quellenec was killed after having tried to save Admiral Coligny the previous night. The same year, Viète met Françoise de Rohan, Lady of Garnache, and became her adviser against Jacques, Duke of Nemours . In 1573, he became

7743-502: Was leading the Siege of La Rochelle. Henry left the siege following their visit. In Paris, on 10 September, the Polish delegation asked Henry to take an oath, at Notre Dame Cathedral , to "respect traditional Polish liberties and the law on religious freedom that had been passed during the interregnum ". As a condition of his election, he was compelled to sign the pacta conventa and the Henrician Articles , pledging religious tolerance in

7832-413: Was no mathematician in France. He said it was simply because some Dutch mathematician, Adriaan van Roomen, had not asked any Frenchman to solve his problem. Viète came, saw the problem, and, after leaning on a window for a few minutes, solved it. It was the equation between sin (x) and sin(x/45). He resolved this at once, and said he was able to give at the same time (actually the next day) the solution to

7921-482: Was very meticulous), and most importantly, he made a very specific choice to separate the unknown variables, using consonants for parameters and vowels for unknowns. In this notation he perhaps followed 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. This choice proved unpopular with future mathematicians and Descartes, among others, preferred

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