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Topic: Francois Vieta

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18th century

	François Viète - Wikipedia, the free encyclopedia
		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.
		Vieta's writings became very quickly known; but, when Franciscus van Schooten issued a general edition of his works in 1646, some were lost.
		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 Gallus (1600).
	en.wikipedia.org /wiki/Francois_Vieta (1066 words)

	Franciscus Vieta
		Vieta did however spend his free time in mathematical studies; and he was able to make significant contributions to mathematics in the areas of arithmetic, algebra, trigonometry, and geometry (Eves, p.
		Vieta was not looking at trigonometry as an independent branch of mathematics; rather, he felt that trigonometry could be used to help solve algebraic problems that had resisted the older methods of algebra.
		Vieta's pioneering work, the development of a set of literal notations that enabled him to write both parameters and unknowns in the same equation, became the building blocks for the notation that we use today.
	www.math.rutgers.edu /~cherlin/History/Papers1999/ploe.html (1536 words)

	History of Algebra - Franciscus Vieta (François Viète) (1540-1603). Albert Girard.
		The older algebraists had indeed resolved geometrical problems, but each solution was particular; whereas Vieta, by introducing general symbols, produced general formulae, which were applicable to all problems of the same kind, without the trouble of going over the same process of analysis for each.
		This happy application of algebra to geometry produced great improvements: it led Vieta to the doctrine of angular sections, one of the most important of his discoveries, which is now expanded into the arithmetic of sines or analytical trigonometry.
		He extended the theory of equations somewhat further than Vieta, but he did not completely unfold their composition; he was the first that showed the use of the negative sign in the resolution of geometrical problems, and the first to speak of imaginary quantities.
	www.1902-encyclopedia.com /A/ALG/algebra-10.html (439 words)

	Vieta (crater) - Wikipedia, the free encyclopedia
		Vieta is a lunar impact crater that lies due north of the Schickard walled plain, in the southwestern part of the Moon.
		About a half crater diameter to the southeast is the smaller Fourier crater, and to the north-northeast lies Cavendish crater.
		By convention these features are identified on lunar maps by placing the letter on the side of the crater mid-point that is closest to Vieta crater.
	en.wikipedia.org /wiki/Vieta_(crater) (193 words)

	François Viète (Site not responding. Last check: 2007-10-23)
		While letters had been used to describe an unknown quantity by earlier writers, Vieta was the first to also use letters for the parameters or constant coefficients in an equation.
		Vieta's algebra was significantly more systematic in the formal manipulation of equations than that of his predecessors, but it still does not reach the facility of modern techniques, because he did not consider negative numbers, and did not yet have a symbol for equality.
		In geometry Vieta gave a solution of the problem of Apollonius referred to above, and also made a study of ``solid" problems such as the trisection of the angle and the construction of the regular heptagon, which use a marked ruler in addition to the Euclidean tools of ruler and compass.
	math.berkeley.edu /~robin/Viete/work.html (285 words)

	Table of Contents
		II The formalism of Vieta and the transformation of the arithmos concept.
		B. Vieta's point of departure: the concept of synthetic apodeixis in Pappus and in Diophantus.
		C. The reinterpretation of the Diophantine procedure by Vieta: I. "The procedure for solutions "in the indeterminate form" as an analogue to geometric analysis" 2.
	www.doverpublications.com /cgi-bin/toc.pl/0486272893 (306 words)

	ALGEBRA (Site not responding. Last check: 2007-10-23)
		The principle underlying this expression is probably to be found in the fact that it measured the limits of their attainments in algebra, for they were unable to solve equations of a higher degree than the quadratic or square.
		Franciscus Vieta (Francois Viete) named it Specious Arithmetic, on account of the species of the quantities involved, which he represented symbolically by the various letters of the alphabet.
		Vieta, who does not avail himself of the discoveries of his predecessors--the negative roots of Cardan, the revised notation of Stifel and Stevin, &c.--introduced or popularized many new terms and symbols, some of which are still in use.
	simplestartpage.com /2301_ALGEBRA.HTML (5420 words)

	VIETA (or VIETE), FRAN... - Online Information article about VIETA (or VIETE), FRAN... (Site not responding. Last check: 2007-10-23)
		hand, Vieta was well skilled in most modern artifices, aiming at a simplification of equations by the substitution of new quantities having a certain connexion with the See also:
		Vieta himself, of course, did,not see so far as that; nevertheless the merit cannot be denied him of having indirectly suggested the thought.
		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 See also:
	encyclopedia.jrank.org /VAN_VIR/VIETA_or_VIETE_FRANCOIS_SEIGNEU.html (2107 words)

	François Viète
		However, I would like to describe here some of his work in geometry, which seems to be less well known: the trisection of the angle, the solution of the ``casus irreducibilis'' of the cubic equation, and the construction of the regular heptagon.
		Vieta also allows the same where a line and a circle are given instead of two lines.
		Vieta gives the general rule for this case of the cubic equation in De Recognitione Equationum [Opera p.91], but without proof, referring to his book Theoremata ad sectiones angulares [Opera pp 287-304] for explanation.
	math.berkeley.edu /~robin/Viete/construction.html (1493 words)

	Mathematicians - François Vieta
		Vieta lived in a time of violent religious wars between Catholics and Protestants called Huguenots.
		Even though Vieta was a Catholic, he also worked as a lawyer for a Protestant family.
		Mathematics was only a hobby of his, but nevertheless Vieta was of great importance and influence.
	mathematica.ludibunda.ch /mathematicians11.html (197 words)

	Franciscus Vista (Site not responding. Last check: 2007-10-23)
		Vieta was born 1540, Fontenay-le-Comte, France and died December 13
		FRANCISCUS VIETA, mathematician who introduced the first systematic algebraic notation and contributed to the theory of equations.
		He knew the connection between the positive roots of an equation (which, in his time, were thought of as the only roots) and the coefficients of the different powers of the unknown quantity.
	web.ukonline.co.uk /mathematians.history/franciscus_vista.htm (237 words)

	Phenomenon of Science: Chap. 11
		Vieta also introduced the term "coefficient.'' In external appearance Vieta's symbols are still rather far from modern ones.
		In Vieta only similar quantities can be added and subtracted and coefficients must include an indication of their geometric nature.
		Vieta and Fermat are intellectual prisoners of the Greek geometric algebra.
	pespmc1.vub.ac.be /POS/Turchap11.html (6499 words)

	CATHOLIC ENCYCLOPEDIA: Francois Vieta, Seigneur de la Bigottiere
		To the latter, as king, Vieta, while councilor of the Parlement in Tours, rendered signal service by discovering the key to the Spanish cipher.
		During his last years, spent mainly in Paris, he was maître des requêtes (master of requests) and royal privy councillor.
		To Vieta as a mathematician Huygens, Halley, Chasles, and Fourier have given high rank.
	www.newadvent.org /cathen/15425b.htm (481 words)

	Earliest Uses of Grouping Symbols (Site not responding. Last check: 2007-10-23)
		Ball (page 242) says the vinculum was introduced by Francois Vieta (1540-1603) in 1591.
		Braces { } are found in the 1593 edition of Francois Vieta's Zetetica (Cajori vol.
		In the writing of large numbers, various methods have been used to separate numerals into groups, including dots, vertical bars, commas, arcs, colons, and accent marks.
	members.aol.com /Jeff570/grouping.html (478 words)

	The Galileo Project
		Ritter, "Francois Viète, inventeur de l'algebre moderne, 1540-1603, essai sur sa vie et son oeuvre," Revue occidentale philosophique sociale et politique, 2nd ser., 10 (1895) 234-74.
		J.M. Dunoyer de Segonzac, "Deux hommes de sciences dans les pays de la Loire aux XVIe et XVIIe siècles: Francois Viète et René Descartes," in 97e congres national des sociétés savantes, (Nantes, 1972) 1, 123-33.
		Grisard, "Francois Viète, mathematicien de la fin du seizième siecle," These de 3e cycle Ecole pratique des hautes etudes, (Paris, 1968).
	galileo.rice.edu /Catalog/NewFiles/viete.html (925 words)

	François Viète (also known as Franciscus Vieta) Biography / Biography of François Viète ...
		Among Viète's other significant mathematical accomplishments are: using algebra to solve longstanding geometrical problems; calculating to 10 places, an important accomplishment of his time; playing a role in the improvements brought by the development of Julian calendars; and having a public hand in the mathematical controversies of his era.
		Get the complete François Viète (also known as Franciscus Vieta) Biography— pages in all.
		Each Biography is written by a biographical expert or professional educator and is a complete resource on the individual.
	www.bookrags.com /biography-francois-viete-also-known-as-franciscus-vieta-wom (278 words)

	Power Page
		There are quite a few polynomials known that generate cubic quartets.
		Vieta's formulas yield large numbers that are often not relatively prime.
		Elementary reasoning suggests that if it takes two variables to create a Pythagorean triple, it should take at least three to make the cubic analogue, so Vieta's solution is not complete.
	www.uwgb.edu /dutchs/RECMATH/rmpowers.htm (2442 words)

	What They Don't Tell You About Pi in High School
		In the sixteenth century, Francois Vieta of Paris found pi to nine decimal places using polygons of 393,216 sides.
		This degree of accuracy was beyond all practical use, but nevertheless, mathematicians continued to calculate pi to more and more decimal places.
		Vieta had a much more significant contribution to the determination of pi.
	www.ms.uky.edu /~lee/ma502/pi/MA502piproject.html (1821 words)

	COMP101 - PRACTICAL SESSION 5 (Site not responding. Last check: 2007-10-23)
		Francois Vieta (1540-1603), a French mathematician who proposed the sequence:
		You should allow for a "number of terms" value to be supplied by the user.
		Although the exchange of ideas between students is encouraged, student collaboration should not extend to the submitting of identical, or near identical, pieces of work.
	www.csc.liv.ac.uk /~frans/COMP101/week8/practical5.html (790 words)

	A look to the past
		We should thank Bombelli for discovering that imaginary numbers play an important role in the development of algebra.
		The French mathematician François Vieta (1540-1603) proposed a new focus for the solution of cubic equations.
		He also began the study of the relationship between the roots and the coefficients of an equation.
	ued.uniandes.edu.co /servidor/em/recinf/tg18/Vizmanos/Vizmanos-2.html (1340 words)

	Vieta and Cardano
		In Germany advances were made in astronomy and trigonometry, while brilliant contributions to algebra were made in Italy.
		(Cajori) Among the various Renaissance scholars, two significant mathematicians are worth special mention because of their important contributions to the mathematical field of algebra: the French mathematician of the 16th century, Francois Viéte; and the Italian mathematician Girolamo Cardano.
		Throughout Viéte's lifetime, he gained the acquaintance of highly respectable clients and friends such as the Huguenots, Coligny, Condés, the Queen of Navarre, Henry Navarre, and Francois de Rohan; all significant political figures.
	www.math.rutgers.edu /~cherlin/History/Papers1999/tumminelli.html (4396 words)

	CHAPTER 3: The Nature of Current Mathematical Research.
		In other cases the authors state why the results they have obtained are important, so that the work can be more readily judged.
		When Vieta introduced letters for classes of numbers he stated that he could now make the distinction between numerical algebra and a science of algebra (to use modern terminology).
		Perhaps many a seemingly worthless paper has merit, but if that merit is not apparent to knowledgeable mathematicians, only an adverse judgment is in order.
	www.marco-learningsystems.com /pages/kline/prof/profchap3.html (7816 words)

	Amazon.com: Greek Mathematical Thought and the Origin of Algebra: Books: Jacob Klein (Site not responding. Last check: 2007-10-23)
		Beginning from the classical foundations of mathematics, he follows the subject carefully through every turn of ideation until he has completed his thesis.
		On the basis of this thorough-going evaluation and exegesis of mathematical thought, he identifies Francois Viete as the true founder of this modern symbolic intentionality.
		But he does not rest with this, proceeding to show how Descartes, Stevin, and Wallis each draw out of this foundation conclusions which are familiar to the modern thinker.
	www.amazon.com /exec/obidos/tg/detail/-/0262610221?v=glance (1465 words)

	Earliest Uses of Symbols of Operation and Grouping
		In 1636 James Hume brought out an edition of the algebra of Vieta, in which he introduced a superior notation, writing down the base and elevating the exponent to a position above the regular line and a little to the right.
		Except for the use of Roman numerals, one has here our modern notation.
		The factorial symbol (!) was introduced by Christian Kramp (1760-1826) in 1808 as a convenience to the printer.
	www.veling.nl /anne/templars/operation.html (2019 words)

	New Catholic Dictionary: Francois Vieta, Seigneur de la Bigottiere
		New Catholic Dictionary: Francois Vieta, Seigneur de la Bigottiere
		Made the initial application of algebraic transformation to trigonometry.
		Popularized reduction as a method of solving equations and the use of letters of the alphabet in algebra to denote quantity.
	www.catholic-forum.com /saints/ncd05158.htm (39 words)

	more word origins 9
		When two things were joined to make something more effective, we add co, the root for with, to form coefficient.
		The math historian Cajori credits 16th Century mathematician Francois Vieta for the creation of the word, but suggest that it did not become common until near the beginning of the 18th century.
		Two or more points are said to be collinear if they lie on the same line.
	www.pballew.net /arithme9.html (5498 words)

	Wilmott Forums - Cubes 3^3 + 4^3 + 5^3 = 6^3 (Site not responding. Last check: 2007-10-23)
		I haven't a particle of confidence in a man who has no redeeming petty vices.
		Thanks to Francois Vieta for his really elegant solution, but we're looking for "ALL triplets of POSITIVE integers {x,y,z)".
		There are some solutions, for example {3,4,5}, that could not be represented in the Vieta's form.
	www.wilmott.com /messageview.cfm?catid=26&threadid=19602 (442 words)

	Lonergan Web Site:The Joseph Flanagan Interview© (Site not responding. Last check: 2007-10-23)
		(As I discuss in my second chapter of Quest for Self-Knowledge, Francois Vieta, the mathematian who was only discovered twenty or thirty years ago, is the key figure before Descartes.
		Everyone thinks that Descartes is the key figure in mathematics, but the first person to say, "Let x equal the unknown" was Vieta.
		So the shift from knowns to unknowns is a crucial step.) But even more important for mathematics was that once it discovered the method to approaching problems it took off.
	www.lonergan.on.ca /interviews/flanagan.htm (2514 words)

	Inwit Publishing, Inc. and Inwit, LLC -- Writings, Links and Software Demonstrations - History and Oddities of the ...
		The method employed by Tsu Ch’ung-chih for his six correct digits is not known for sure, but may have been similar to Archimedes’ (20).
		In 1579 Francois Vieta, the man who introduced literal quantities into algebra, used polygons of 393,216 sides to obtain
		Vieta in 1593 gave the first non-geometrical method for finding
	www.inwit.com /inwit/writings/historyandodditiesofpi.html (5713 words)

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