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Topic: Jean Bernoulli

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	Bernoulli - LoveToKnow 1911
		Jean le Rond d'Alembert acknowledges with gratitude, that "whatever she knew of mathematics he owed to the works of Jean Bernoulli." He was a member of almost every learned society in Europe, and one of the first mathematicians of a mathematical age.
		Jean Bernoulli (1710-1790), the youngest of the three sons of Jean Bernoulli, was born at Basel on the 18th of May 1710.
		Nicolas Bernoulli (1687-1759), cousin of the three preceding, and son of Nicolas Bernoulli, one of the senators of Basel, was born in that city on the 10th of October 1687.
	www.1911encyclopedia.org /Bernoulli (3121 words)

	Leonhard Euler - LoveToKnow 1911
		His mathematical genius gained for him a high place in the 'esteem of Jean Bernoulli, who was at that time one of the first mathematicians in Europe, as well as of his sons Daniel and Nicolas Bernoulli.
		At the same time, by the advice of the younger Bernoullis, who had removed to St Petersburg in 1725, he applied himself to the study of physiology, to which he made a happy application of his mathematical knowledge; and he also attended the medical lectures at Basel.
		While he was engaged in physiological researches, he composed a dissertation on the nature and propagation of sound, and an answer to a prize question concerning the masting of ships, to which the French Academy of Sciences adjudged the second rank in the year 5727.
	www.1911encyclopedia.org /Leonhard_Euler (1730 words)

	CATHOLIC ENCYCLOPEDIA: Guillaume-Francois-Antoine de l'Hopital
		In 1692 he became acquainted with Jean Bernoulli, one of the three or four men of the day who understood the new methods of differential calculus.
		During four months he studied with Bernoulli, whom he had invited to his estate of Oucques near Vendôme, and learned from him this branch of the science of numbers.
		Leibniz, and the Bernoullis in the propounding and solving of problems involving the calculus.
	www.newadvent.org /cathen/07469a.htm (371 words)

	Johann (also John or Jean) Bernoulli (Site not responding. Last check: )
		Johann Bernoulli was born in Bale, Switzerland on August 7, 1667.
		Bernoulli was extremely competitive with his brother Jakob and his own son, Daniel with regards to mathematics.
		Bernoulli was a very successful teacher, however, and he inspired his students to have a zeal and a passion for mathematics, which he felt himself.
	www.geocities.com /mathladies/bios/johannb.html (291 words)

	Mathematicians - MathWiki (Site not responding. Last check: )
		Bernoulli, Jean (1667-1748 AD; also known as John or Johann) : the brother of Jacques, and also known for his work on the calculus.
		Jean Bernoulli had three sons, all of whom became professors of mathematics, the most prominent being Daniel.
		Bernoulli, Daniel (1700-1782 AD) : the son of Jean Bernoulli, noted for his book Hydrodynamica (1738 AD, Hydrodynamics) in which he laid the foundations of the modern discipline of hydrodynamics and introduced Bernoulli’s equation.
	www.mathsisfun.com /wiki/Mathematicians (5706 words)

	Bernoulli Equation: History of Daniel Bernoulli and his Equation (Site not responding. Last check: )
		The Bernoulli family is renowned for having produced several generations of mathematicians of historical importance as well as being partly responsible for the rapid spread and development of Leibniz's calculus in the eighteenth century.
		Daniel Bernoulli was born on February 8, 1700 in Groningen, Netherlands while his father Johannes I held a mathematics chair in the University of Groningen.
		In Hydrodynamica, Bernoulli was the first to give the correct analysis of the tank draining problem; the latter was derived using his ideas of energy conservation.
	www.fluidmech.net /tutorials/bernoulli/bernoulli-history.htm (1254 words)

	Johann Bernoulli - Wikipedia, the free encyclopedia
		Johann Bernoulli (Basel, July 27, 1667 - January 1, 1748) was a Swiss mathematician.
		He was the brother of Jakob Bernoulli, and the father of Daniel Bernoulli (for whom the Bernoulli's principle was named) and Nicolaus II Bernoulli.
		Bernoulli proposed a fluid energy perpetual motion machine.
	en.wikipedia.org /wiki/Johann_Bernoulli (210 words)

	The Helen of Geometers
		Incidentally, the Bernoulli's were partisans on the side of Leibniz in the famous priority dispute between Leibniz and Newton over the invention of calculus.
		Bernoulli supposedly said he knew who the anonymous author must be, "as the lion is recognized by his print".
		It's interesting that Jean Bernoulli apparently arrived at his result from his studies of the path of a light ray through a non-uniform medium.
	www.mathpages.com /rr/s8-03/8-03.htm (1364 words)

	modbio
		Bernoulli was a prolific publisher on analysis, as was his brother, using the calculus to good effect in studying curves, and in 1705 took over the chair in Basle left clear by his brother's death.
		However, Jean was an outstanding teacher and researcher, responsible for the quick dissemination of the calculus, and is frequently regarded as the inventor of the calculus of variations by his work on the brachistochrone, though many before him had studied similar problems without the aid of the calculus.
		Born in Basle, Euler was heavily influenced in his early years by the Bernoullis, Jean as a teacher and Jean's sons Daniel and Nicolaus as friends, and although Euler's father initially wanted his son to enter the ministry, he helped to instruct his son in mathematics, as he himself was a capable mathematician.
	www.glasgowg43.freeserve.co.uk /modbio.htm (7619 words)

	Daniel Bernoulli Biography \| Encyclopedia of World Biography
		Daniel Bernoulli was born on Jan. 29, 1700, in Gröningen, Netherlands.
		He was the second son of Jean Bernoulli, a noted mathematician who began the use of "g" for the acceleration of gravity.
		Bernoulli won or shared 10 prizes of the Paris Academy of Sciences, a feat equaled by only one other person, his friend and rival Leonhard Euler.
	www.bookrags.com /biography/daniel-bernoulli (359 words)

	10.3. Bernoulli, Johan (1667-1748)
		Johann Bernoulli was one of the pioneers in the field of calculus and helped apply the new tool to real problems.
		Johann (also known as Johannes, Jean or John, depending on the translation) Bernoulli was born in Basel, Switzerland, on August 6, 1667.
		Bernoulli was obviously enraged by the theft and ceased helping his freeloading friend.
	web01.shu.edu /projects/reals/history/bernoull.html (833 words)

	Bernoulli Bibliography
		The Bernoulli numbers are among the most interesting and important number sequences in mathematics.
		Bernoulli numbers are particularly important in number theory, especially in connection with Fermat's last theorem (see, e.g., Ribenboim (1979)).
		The same is true for the numerous generalizations and extensions of the Bernoulli and allied numbers and of the corresponding polynomials.
	www.mscs.dal.ca /~dilcher/bernoulli.html (997 words)

	Jean d'Alembert (Site not responding. Last check: )
		The Petersburg problem was introduced by Nicholas Bernoulli in correspondence to Montmort which occurred in September 1713.
		In an article written for the general reader published in June of 1760 and in a paper presented to the Academy of Sciences of Paris that same year, he stated that the two chief motives for inoculation are humanity and the interest of the state.
		Daniel Bernoulli earned a share of the prize in 1734 with his paper, "Physical and astronomical researches on the problem proposed for the second time by the Academie Royale des Sciences de Paris." Here he hypothesized that the solar atmosphere was the cause.
	www.cs.xu.edu /math/Sources/Dalembert/index.html (1106 words)

	AbeBooks: Search Results - Bernoulli and Opera Omnia
		This first edition of the collective works of Jean Bernoulli comprises 189 of his papers and 59 of his lectures.
		After Newton and Leibniz Bernoulli was the leading mathematician to work on and to develop the differential and integral calculus.
		First edition of Bernoulli's complete works, 1742 in 4 volumes containing nearly 200 writings by the famous Swiss mathematician Johann Bernoulli, published by Gabriel Cramer when Bernoulli was still living.
	www.abebooks.co.uk /search/sortby/3/an/Bernoulli+/tn/+Opera+Omnia (875 words)

	[No title]
		Instead, he and Jean Bernoulli, showed that even hitherto unknown curves could be discovered from their corresponding differential equations.
		Bernoulli had thrown out a challenge to determine the curve on which a body falling under the influence of gravity, travelled in the least time.
		In summary, Bernoulli's ingenious solution is as follows: Fermat had demonstrated that light, refracted by a change in the density of the medium, travelled the least time path.
	www.wlym.com /antidummies/part08.html (1806 words)

	Anecdote - Johann [Jean] Bernoulli - Bernoulli & L`Hôpital (Site not responding. Last check: )
		Anecdote - Johann [Jean] Bernoulli - Bernoulli & L`Hôpital
		[Bernoulli's allegations were lent credence by the discovery of documents in Basel in 1922.]
		Bernoulli, Johann [Jean] (1667-1748) Swiss mathematician [noted for his development of the calculus of variations]
	anecdotage.com /index.php?aid=6195 (217 words)

	Leonhard Euler Biography \| World of Scientific Discovery
		His teacher was Jean Bernoulli of the famous Bernoulli family that produced twelve mathematicians and scientists over five generations.
		Bernoulli assisted Euler in obtaining a position as professor of mathematics at the Petersburg Academy.
		Working along with Bernoulli, Euler introduced the algebraic symbols e, i, f(),, and he devised a number of trigonometric and geometric theorems and rules known by his name.
	www.bookrags.com /biography/leonhard-euler-wsd (465 words)

	[No title]
		At first Euler obtained the value of zeta(2), and at least the next few values of zeta(2v), by a somewhat reckless application of Newton's algebraic results, on the sums of powers of the roots for an equation of finite degree, to transcendental equations of the type 1 - sin(x/a) = 0.
		As to Goldbach, he was in Petersburg at the time of the discovery and surely must have heard of it at once.
		Bernoulli, de Moivre and Stirling, great authorities in such matters, were highly surprised when I told them that I had found the sum of zeta(2), and even of zeta(n) for n even": Eu.IV A-5.120].
	www.math.niu.edu /~rusin/known-math/99/zeta2 (2171 words)

	Biographies Info Science : Bernoulli Famille des
		De son côté, Jean Bernoulli se consacre à la diffusion du calcul infinitésimal à travers l'Europe ; il devient le correspondant privilégié de Leibniz et de nombreux autres scientifiques, à tel point qu'on lui discerne le titre de "praeceptor mathematicus Europae".
		Jean Bernoulli est également un remarquable professeur qui succèdera à son frère à l'université de Bâle en 1705 où il aura pour élève un certain
		Successivement professeur de physique, de botanique, d'anatomie et de philosophie, Daniel Bernoulli étudie les cordes vibrantes avec Euler et d'Alembert et propose les lois qui portent son nom, concernant les vibrations de l'air dans les tuyaux sonores.
	www.infoscience.fr /histoire/biograph/biograph.php3?Ref=10 (469 words)

	matematicos
		Así, Euler partió en 1727, año de la muerte de Newton, a San Petersburgo, para reunirse con sus amigos, los jóvenes Bernoulli, que le habían precedido allí algunos años antes.
		En el camino hacia Rusia, se enteró de que Nicolás Bernoulli había caído víctima del duro clima nórdico; y el mismo día que puso pie sobre suelo ruso murió la emperatriz Catalina, acontecimiento que amenazó con la disolución de la Academia, cuya fundación ella había dirigido.
		En 1733 sucedió a su amigo Daniel Bernoulli, que deseaba retirarse, y el mismo año se casó con Mademoiselle Gsell, una dama suiza, hija de un pintor que había sido llevado a Rusia por Pedro el Grande.
	www.mat.usach.cl /histmat/html/eule.html (1205 words)

	Fidelio Article - Schiller Institute- LEIBNIZ on the Catenary Spring 2001 issue
		Leibniz's paper on the catenary curve, was written at the instigation of Jacques Bernoulli for the Acta Eruditorum of Leipzig, June 1691.
		So, M. Bernoulli has made this profound remark, which is, that at each inflexion point, the proportion between t and y, that is to say, between dx and dy, takes the greatest or the smallest value that can be assigned.
		I would like M. Bernoulli to consent to examine closely the article on the measurement of forces, which I opposed to M. Papin, especially near the end, where I think I have noticed the origin of the common error.
	www.schillerinstitute.org /fid_97-01/011_catenary.html (3602 words)

	L'Hopital (Site not responding. Last check: )
		In 1692, L'H?pital met Jean Bernoulli, and thus began a rather difficult friendship.
		It is also used everyday in engineering: the automatic transmission of a car depends on differential calculus to decide when to shift gears, and the automatic pilot on an airplane relies on it for knowing how the plane is moving.
		Bernoulli was very upset because he didn't think he was properly credited, since much of the work in the book was apparently based off of his work.
	www.whyville.net /smmk/whytimes/article?id=106 (462 words)

	Teorema de Bernoulli. Bombas y turbinas (Site not responding. Last check: )
		Bernoulli nació en Groningen (Países Bajos), el 29 de enero de 1700 y desde muy pronto manifestó su interés por las matemáticas.
		Bernoulli promovió en Europa la aceptación de la nueva física del científico inglés Isaac Newton.
		Bernoulli murió el 17 de marzo de 1782 en Basilea.
	html.rincondelvago.com /teorema-de-bernoulli_bombas-y-turbinas.html (3796 words)

	The Galileo Project
		As soon as he was old enough to bear arms, he obtained a commission of captain in the cavalry, but he had already, by that time, acquired a passion for mathematics from his tutor.
		It is not clear that he taught l'Hospital, but after Bernoulli had been there a few months, l'Hospital returned to Ourques, Touraine, embued with the new mathematics.
		Correspondence with Leibniz, with Jean Bernoulli, and with Huygens.
	galileo.rice.edu /Catalog/NewFiles/lhopital.html (329 words)

	jean - Definition, Synonyms, and Reference from OnPedia.com
		jean - (usually plural) close-fitting pants of heavy denim for casual wear
		Levi's, levis - a popular brand of jeans
		jean - a coarse durable twill-weave cotton fabric
	www.onpedia.com /dictionary/jean (127 words)

	Braquistócrona
		Na solução original de Jean Bernoulli usou uma analogia com a lei da refracção em óptica.
		O problema de Jean Bernoulli tem por solução a ciclóide.
		Jean Bernoulli provou que a ciclóide tem a propriedade de ser braquistócrona, isto é, é a curva de descida mais rápida de um ponto material que se move entre dois pontos dados, num campo de gravidade.
	www.mat.uc.pt /~bebiano/Atractor/braq.htm (544 words)

	UCL Centre de philosophie des sciences -- Ed. Benvenuto & A. Mastrorilli (Site not responding. Last check: )
		In particular we analyse some important passages in modern hystory of physics, marking the rise and fall of the theory of vortex trough the work of Decartes, Leibniz, Newton and Bernoulli.
		The scientific debate on the point at issue was so much animated as the Academy of Sciences of Paris posed two questions to explain some physical problems trough vortex theory.
		Here we analyse Johann Bernoulli’s contribution to the topic, coming forward as a protagonist of both competitions announced in 1728 and 1730.
	www.lofs.ucl.ac.be /fisc/staff/stoffel/Descartes-5.htm (366 words)

	Leonhard Euler
		After receiving preliminary instructions in mathematics from his father, he was sent to the University of Basel, where geometry soon became his favorite study.
		While he was engaged in physiological researches, he composed a dissertation on the nature and propagation of souund, and an answer to a prize question concerning the masting of ships, to which the French Academy of Sciences adjudged the second rank in the year 1727.
		In 1735 a problem proposed by the academy, for the solution of which several eminent mathematicians had demanded the space of some months, was solved by Euler in three days, but the effort threw him into a fever which endangered his life and deprived him of the use of his right eye.
	www.nndb.com /people/954/000048810 (1451 words)

	The Bernoullis, IIHR, College of Engineering, The University of Iowa
		The Bernoullis: Jacques (Jakob), 1654-1705; Johann (Jean), 1667-1748; Daniel (1700-1782)
		Jacques and Johann Bernoulli of Basel, Switzerland, along with their descendents, became distinguished in the seventeenth and eighteenth centuries as mathematicians and physical scientists.
		Daniel, son of Johann, was trained as a physician and later taught anatomy, mathematics, and physics.
	www.iihr.uiowa.edu /products/history/hoh/bernoullis.html (370 words)

	Johann Or Jean Bernoulli Biography (1667–1748) Online Encyclopedia Article About Johann Or Jean Bernoulli Biography ...
		Mathematician, born in Basel, N Switzerland, the brother of Jakob Bernoulli.
		He did mathematical and chemical research, and became professor at Groningen (1695) and Basel (1705).
		He founded a dynasty of mathematicians which continued for two generations.
	encyclopedia.jrank.org /Cambridge/entries/072/Johann-or-Jean-Bernoulli.html (124 words)

	Leonhard Euler Biography - Biography.com
		He studied mathematics there under Jean Bernoulli, and became professor of physics (1731) and then of mathematics (1733) at the St Petersburg Academy of Sciences.
		In 1738 he lost the sight of one eye.
		Find your favorite celebrities, and mysteries on DVD at the BIOGRAPHY® store.
	www.biography.com /search/article.jsp?aid=9289255 (360 words)

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