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	Albert Girard Summary
		A mathematician who contributed to a number of areas ranging from arithmetic to algebra, Albert Girard enjoyed little recognition during his lifetime.
		In addition, Girard developed a simplified means for demarking the cube root still in use today.
		Also a widely published translator, Girard was responsible for translating a number of works from French into Flemish, the language of Holland, and from Flemish into French.
	www.bookrags.com /Albert_Girard (484 words)

	[No title] (Site not responding. Last check: 2007-10-26)
		Girard attended the Univeristy of Leiden at age 22 where he studied music and his interest of choice was the lute.
		Girard, like many of the mathematicians of his time, was primarily interested in military applications of mathematics.
		Girard died on December 8, 1632. References "Albert Girard", MacTutor Biography
	feeds.feedburner.com /FermatsLastTheorem (1722 words)

	EQUATIONS, THEORY OF,
		In 1629 the French mathematician Albert Girard (1595–1632) recognized both negative and complex roots of equations and so was able to complete the partial insight of François Viète (1540–1603) into the relation between the roots of an algebraic equation and its coefficients.
		Albert Einstein (1879 - 1955) In 1915, Einstein perfected his general theory of relativity, summing up his theory with the mathematical equation E=mc squared.
		Albert Einstein is born, the son of a Jewish electrical engineer in Ulm, Germany.
	www.history.com /encyclopedia.do?vendorId=FWNE.fw..eq051300.a (1408 words)

	Girard_Albert
		Albert Girard was French but went as a religious refugee to the Netherlands.
		Like many mathematicians of his day Albert Girard was interested in military applications of mathematics and in particular studied fortifications.
		It appears that Girard spent some time as an engineer in the Dutch army although this was probably after he published his work on trigonometry.
	www.educ.fc.ul.pt /icm/icm2003/icm14/Girard_Albert.htm (199 words)

	Arnold Schoenberg
		Another of his most important works from this period is Pierrot Lunaire[?] of 1912, a cycle of songs set to a text by Albert Girard that was unlike anything that preceded it.
		It was the equivalent in music of Albert Einstein’s discoveries in Physics, and Schoenberg announced it characteristically, during a walk with his friend Josef Rufer, when he said "I have today made a discovery which will ensure the supremacy of German music for the next hundred years".
		This remark, much misquoted and misunderstood, was probably made with Schoenberg’s customary wry and ironic humour, referring to the collapse of the dominant political position of the German-speaking world in previous years, and also emphasising his desire to stand with Mozart and Bach.
	www.ebroadcast.com.au /lookup/encyclopedia/ar/Arnold_Schoenberg.html (1153 words)

	Girard_Albert biography
		Albert Girard worked on algebra, trigonometry and arithmetic.
		In 1626 he published a treatise on trigonometry containing the first use of the abbreviations sin, cos, tan.
		Gassendi, writing to a friend, talks about Girard and refers to his position in the Dutch army.
	www-history.mcs.st-andrews.ac.uk /history/Biographies/Girard_Albert.html (227 words)

	McCook Daily Gazette: Story: Louis A. Girard
		They later opened Girard's Automotive, which he operated until retirement in 1976.
		He was preceded in death by his wife, Eva June 19, 1994; one daughter, Rochelle Cox March 1, 2003; three brothers, Edmond, Elmer and George Girard; and one sister, Eva Morris; two grandsons and two great-grandchildren.
		Mass of Christian burial is Saturday, 10:30 a.m., at St. Patrick's Catholic Church in McCook with the Rev. Jerel Scholl officiating.
	www.mccookgazette.com /story/1071142.html (221 words)

	de Girard De Saint Gerand à Giroulet
		• Girard De Saint Gerand Marie Charles Claude Ferdinand
		• Girard La Barcerie Joseph Louis Frederic Gaston
		• de Girard De Saint Gerand à Giroulet
	www.patrimoine-de-france.org /hommes/honneurs-196.html (938 words)

	Albert Girard (I) (Site not responding. Last check: 2007-10-26)
		Albert Girard (I) Now Playing Movie/TV News My Movies DVD New Releases IMDbTV Message Boards Showtimes and Tickets IMDbPro IMDb Resume
		Discuss this name with other users on IMDb message board for Albert Girard (I)
		Find where Albert Girard is credited alongside another name
	imdb.com /name/nm0320625 (130 words)

	Australian Information from Wikipedia
		Girard is the name of several places in the United States of America:
		Girard (MFL station), a rapid transit station on SEPTA's Market-Frankford Line in Philadelphia, Pennsylvania
		If an internal link led you here, you may wish to change the link to point directly to the intended article.
	www.thinkingaustralia.com /thinking_australia/wikipedia/default.php?title=Girard (184 words)

	The Ice Age Challenge > Free novel online > Agape Book > author Rolf A. F. Witzsche
		Girard's theorem was that polynomial equations with powers of n must have n solutions.
		Girard's discovery in 1629, as you say, was made smack in the middle of the Thirty Years War.
		Girard was probably caught up in this deep reaching search as to what we are as human beings, and what we are capable of as people with a godlike intellect.
	members.shaw.ca /rolfwitzsche/novels/book2a/book2053.html (757 words)

	TriploV - Albert Girard
		GIRARD, Albert A. (1890) - Révision des céphalopodes du Muséum de Lisbonne.
		GIRARD, Albert Alexandre (1893) - Révision de la faune malacologique des îles St. Thomé et du Prince.
		GIRARD, Albert Alexandre (1895) - Sur le "Tyrophorella thomensis", Greeff, gastéropode terrestre muni d'un faux opercule à charnière.
	www.triplov.com /biblos/albert_girard.htm (517 words)

	The Galileo Project
		De Waard cites a passage from Girard's edition of Stevin in which he complained of being in a foreign country without a maecenas and burdened with a family.
		He said that he had to postpone the publication of his mathematics until a time when the pursuit of the sciences would be more highly esteemed than it was at that time.
		Paul Tannery, "Albert Girard di Saint-Mihiel," Bulletin des sciences mathematiques et astronomiques, 2nd ser.
	galileo.rice.edu /Catalog/NewFiles/girard.html (326 words)

	girard - Ask.com Web Search
		He was born in Bordeaux, France, and became a sailor at the age of 13.
		Girard Township is a township in Erie County, Pennsylvania, United States.
		Girard, the forthcoming issue of Anthropoetics is devoted to your work and I would like to take the opportunity of this interview to...
	www.ask.com /web?q=girard (302 words)

	Fermat's Last Theorem
		Albert Girard was born in France in 1595.
		Girard made numerous original contributions that had a lasting impact on the history of mathematics.
		Van Roomen's problem established François Viète as one of the most important mathematicians of his day, showed the relevance of trigonometry to solving algebraic equations, and finally paved the way to Albert Girard's insight (and Carl Friedrich Gauss's brilliant proof) of the Fundamental Theorem of Algebra.
	fermatslasttheorem.blogspot.com (3130 words)

	Complex Numbers
		For years after Bombelli's work, many still thought complex numbers were a waste of time, but there were others who used complex numbers extensively and through their work, much more was discovered.
		Albert Girard suggested that an equation may have as many roots as its degree in 1620.
		René Descartes, who contributed the term "imaginary" for these numbers, said that even though one can imagine that every equation has as many roots as its degree, real numbers may not correspond to all of these imagined roots.
	www.und.edu /instruct/lgeller/complex.html (779 words)

	The Serial Music Arnold Schoenberg [Biography] (Site not responding. Last check: 2007-10-26)
		Schoenberg's music had made a break from tonality, which greatly polarised responses to it: his followers and students saw him as one of the most important figures in music, while critics hated his work, on the whole.
		It was the equivalent in music of Albert Einstein's discoveries in Physics, and Schoenberg announced it characteristically, during a walk with his friend Josef Rufer, when he said "I have today made a discovery which will ensure the supremacy of German music for the next hundred years".
		This remark, much misquoted and misunderstood, was probably made with Schoenberg's customary wry and ironic humour, referring to the collapse of the dominant political position of the German-speaking world in previous years, and also emphasising his desire to stand with Mozart and Bach.
	humanitiesweb.org /human.php?s=c&p=c&a=b&ID=65 (1330 words)

	Musica Leopolis - Albert Krywolt
		Albert Krywolt, pianist, is one of Canada’s foremost opera musicians.
		Albert has a special affinity for contemporary repertoire, and has helped launch the world premieres of several Canadian operas, including Nosferatu and The Golden Ass by Randolph Peters, and Mario and the Magician by Harry Somers.
		Leading up to the COC’s inaugural season in the Four Seasons Centre for the Performing Arts in 2006/07, Albert is serving as head coach for all four productions in Wagner’s Ring Cycle, directed by Atom Egoyan, François Girard, Tim Albery and Michael Levine, and conducted by Richard Bradshaw.
	www.musicaleopolis.com /artists/albertKrywolt.cfm (191 words)

	Portsmouth Herald Obituaries from: Tuesday, November 25, 2003
		He is survived by his wife of 55 years, Laurette (Pelchat) Girard of York; two brothers: Raymond Girard Sr.
		and his wife, Patricia, of Brewster, Mass., and Albert Girard and his wife, Geraldine, of Windham, N.H.; two sisters: Rachel Mitchell of North Eastham, Mass., and Jeanne and her husband, William Godsey, of Bay St. Louis, Miss.; 18 nieces and nephews; and one great-grandniece.
		GIRARD - Andrew J. Girard Jr., of Lindsay Road, York, Maine, died Sunday, Nov. 23, 2003, at York Hospital.
	www.seacoastonline.com /2003news/11252003/obituari/62125.htm (1129 words)

	NewStandard: 8/10/98
		FALL RIVER -- Josephine Girard, 91, of Marigold Avenue, Somerset, formerly of Plymouth Avenue, Fall River, died unexpectedly Saturday, Aug. 8, 1998, at Charlton Memorial Hospital.
		Girard was employed for 10 years as an inspector for the former Firestone Tire & Rubber Co.
		Girard was a member of the Somerset Senior Citizens Group.
	www.s-t.com /daily/08-98/08-10-98/zzzddobi.htm (1702 words)

	Discover the Wisdom of Mankind on Blinkbits.com
		Albert Edward Harry Mayer Archibald Primrose, 6th Earl of Rosebery (en)
		Albert Edward Harry Meyer Archibald Primrose, 6th Earl of Rosebery (en)
		Albert Edward John Spencer, 7th Earl Spencer (en)
	www.blinkbits.com /wikifeeds/AL?from=12000 (182 words)

	Sketching the History of Hypercomplex Numbers (Site not responding. Last check: 2007-10-26)
		Albert Girard (1595-1632) publishes Invention nouvelle en l'algebre, stating clearly the relations between roots and coefficients, allowing of negative and imaginary roots to equations.
		(Girard's conceptualization of negative solutions also paves the way toward the idea of the number line, interpreting negative numbers as a kind of relative orientation.) Girard retained all imaginary roots because they show the general principles in the formation of an equation from its roots.
		Rene Descartes (1596-1650) coins the term "imaginary" for expressions involving square roots of negative numbers, and takes their occurrence as a sign that the problem is insoluble.
	history.hyperjeff.net /hypercomplex.html (2109 words)

	A look to the past
		He also began the study of the relationship between the roots and the coefficients of an equation.
		That work was completed by the Flemish mathematician Albert Girard (1590-1633) with the publication of Invention nouvelle en l'algèbre in 1629.
		Girard, facing the problem of taking square roots of negative numbers, was, in 1629, the first to dare to conjecture the following: "An equation of degree n has exactly n roots, as long as you count the impossible ones".
	ued.uniandes.edu.co /servidor/em/recinf/tg18/Vizmanos/Vizmanos-2.html (1340 words)

	Fundamental Theorem of Algebra (Site not responding. Last check: 2007-10-26)
		Descartes said that one can "imagine" for every equation of degree n, n roots, but these imagined roots do not correspond to any real quantity.
		Albert Girard, a Flemish mathematiciam, was the first to claim that there are always n solutions to a polynomial of degree n in 1629 in L'invention en algèbre.
		Many mathematicians accepted Girard's claim that a polynomial equation must have n roots, and proceeded to try to show that these roots were of the form a + bi, a, b real, instead of first showing that they actually existed.
	www.und.nodak.edu /dept/math/history/fundalg.htm (451 words)

	Early Attempts to Prove FTA
		A glance into early attempts even to formulate the Fundamental Theorem of Algebra correctly, demonstrates how much development of mathematics has been impeded by the absence of a proper language to describe mathematical concepts.
		The first formulation of the theorem was due to Albert Girard (1595-1632), a native of Lorraine who worked in Holland and was the editor of the works of Simon Stevin.
		His L'invention nouvelle en l'algèbre (Amsterdam, 1629) bases its fame on its formulation of the fundamental theorem of algebra, which also shows that he already took complex number seriously.
	www.cut-the-knot.org /fta/early.shtml (726 words)

	History - Page Two
		Later he gives a solution of the general cubic that needs the extraction of only a single cube root.
		Albert Girard (1595-1632) conjectures that the nth degree equation has
		Rene Descartes (1596-1650) gives his rule of signs to determine the number of positive roots of a given polynomial.
	www.vimagic.de /hope/1/history_two.html (144 words)

	Convergence \| On This Day...
		Euler gives the first clear statement of the fundamental theorem of algebra; every algebraic equation of degree n has exactly n complex roots.
		Imprecise statements of the result were given earlier by Peter Rothe (1608) and Albert Girard (1629).
		Incorrect proofs were given by d'Alembert (1746), Euler (1749), Foncenex (1759), Lagrange (1772) and Laplace (1795), but a correct proof (and the name) had to await Gauss's doctoral dissertation of 1799, who discovered it in the fall of 1797 when he was 20.
	mathdl.maa.org /convergence/1/?pa=historicalEvent&sa=browseFrontEnd&month=11&day=15 (276 words)

	E514 -- De mensura angulorum solidorum
		He also notes that a very clever geometer, Albert Girard (1595-1632), suggests measuring solid angles in the same way, by the part of a sphere that they subtend.
		He also defines the "area of an angle" of a sphere to be the area of the wedge-shaped region bounded by semicircles intersecting at the given angle: If the angle in radians measures a, then the area is 2ar
		Euler then states and proves (with attribution) Girard's Theorem: The area of a spherical triangle is always equal to the angle by which the sum of all three angles of the triangle exceeds two right angles.
	www.math.dartmouth.edu /~euler/pages/E514.html (285 words)

	E514 -- De mensura angulorum solidorum (Site not responding. Last check: 2007-10-26)
		He also notes that a very clever geometer, Albert Girard (1595-1632), suggests measuring solid angles in the same way, by the part of a sphere that they subtend.
		He also defines the "area of an angle" of a sphere to be the area of the wedge-shaped region bounded by semicircles intersecting at the given angle: If the angle in radians measures a, then the area is 2ar
		Euler then states and proves (with attribution) Girard's Theorem: The area of a spherical triangle is always equal to the angle by which the sum of all three angles of the triangle exceeds two right angles.
	math.dartmouth.edu /~euler/pages/E514.html (285 words)

	Mumma, Moomaw, Mumaw & Muma Database Index
		Mumma, Albert Girard (2 JUN 1906 - 15 JUL 1997)
		Mumma, Albert J. Mumma, Albert Lewis (23 MAR 1893 -)
		Mumma, Albert Stanley (4 JUL 1854 - 11 JAN 1922)
	www.mumma.org /databases/mumma/mumma175.html (1024 words)

	Fund theorem of algebra
		Viète gave equations of degree n with n roots but the first claim that there are always n solutions was made by a Flemish mathematician Albert Girard in 1629 in L'invention en algèbre.
		In fact this was to become the whole problem of the FTA for many years since mathematicians accepted Albert Girard's assertion as self-evident.
		Now Harriot knew that a polynomial which vanishes at t has a root x - t but this did not become well known until stated by Descartes in 1637 in La géométrie, so Albert Girard did not have much of the background to understand the problem properly.
	physics.rug.ac.be /fysica/Geschiedenis/HistTopics/Fund_theorem_of_algebra.html (1516 words)

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