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	Bernoulli
		Nicolaus Bernoulli was an important citizen of Basel, being a member of the town council and a magistrate.
		Jacob Bernoulli was the brother of Johann Bernoulli and the uncle of Daniel Bernoulli.
		Jacob Bernoulli was appointed professor of mathematics in Basel in 1687 and the two brothers began to study the calculus as presented by Leibniz in his 1684 paper on the differential calculus in Nova Methodus pro Maximis et Minimis, itemque Tangentibus...
	www.thocp.net /biographies/bernoulli.html (1926 words)

	Bernoulli - HighBeam Encyclopedia (Site not responding. Last check: 2007-10-11)
		One of the chief developers both of the ordinary calculus and of the calculus of variations, he was the first to use the word integral in solving Leibniz's problem of the isochronous curve.
		He was succeeded at Basel by his brother, Johann, Jean, or John Bernoulli, 1667-1748, who earlier had been professor at Gröningen and who was famous for his work in the field of integral and exponential calculus and was also a founder of the calculus of variations.
		His greatest work was his Hydrodynamica (1738), which included the principle now known as Bernoulli's principle, and anticipated the law of conservation of energy and the kinetic-molecular theory of gases developed more than 100 years later.
	www.encyclopedia.com /doc/1E1-bernoulf1am.html (462 words)

	Johann Bernoulli
		Nicolaus and Margaretha Bernoulli tried to set Johann on the road to a business career but, despite his father's strong pushing, Johann seemed to be totally unsuited to a future in business.
		Bernoulli's course is virtually identical with de l'Hôpital's book but it is worth pointing out that de l'Hôpital had corrected a number of errors such as Bernoulli's mistaken belief that the integral of 1/x is infinite.
		Bernoulli also made important contributions to mechanics with his work on kinetic energy, which, not surprisingly, was another topic on which mathematicians argued over for many years.
	www.mathematik.ch /mathematiker/johann_bernoulli.php (2449 words)

	Bernoulli Equation: History of Daniel Bernoulli and his Equation (Site not responding. Last check: 2007-10-11)
		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)

	Reference.com/Encyclopedia/Daniel Bernoulli
		Bernoulli's principle is of critical use in aerodynamics.
		Born as the son of Johann Bernoulli, nephew of Jakob Bernoulli, younger brother of Nicolaus II Bernoulli, and older brother of Johann II, Daniel Bernoulli was by far the ablest of the younger Bernoullis.
		Bernoulli also wrote a large number of papers on various mechanical questions, especially on problems connected with vibrating strings, and the solutions given by Brook Taylor and by d'Alembert.
	reference.com /browse/wiki/Daniel_Bernoulli (619 words)

	THE BERNOULLI FAMILY
		One of the most distinguished families in the history of mathematics and science is the Bernoulli family of Switzerland, which from the late secenteenth century on, producced an unusual number of capable mathematicians and scientists.
		Johann Bernoulli was an even more prolific contributor to mathematics than was his brother Jakob, Though he was a jealous and cantankerous man, he was one of the most successful teachers of his time.
		Nicolaus, who showed great promise in the field of mathematics, was called to the St.Petersburg Academy, where he unfortunately died by drowining, only eight months later.
	library.thinkquest.org /22584/temh3007.htm (830 words)

	Jacob Bernoulli
		Jacob Bernoulli was appointed professor of mathematics in Basel in 1687 and the two brothers began to study the calculus as presented by Leibniz in his 1684 paper on the differential calculus.
		Jacob Bernoulli's first important contributions were a pamphlet on the parallels of logic and algebra published in 1685, work on probability in 1685 and geometry in 1687.
		Jacob Bernoulli continued to hold the chair of mathematics at Basel until his death in 1705 when the chair was filled by his brother Johann.
	www.stetson.edu /~efriedma/periodictable/html/Br.html (785 words)

	Daniel Bernoulli
		Daniel Bernoulli was the son of Johann Bernoulli.
		His older brother was Nicolaus(II) Bernoulli and his uncle was Jacob Bernoulli so he was born into a family of leading mathematicians but also into a family where there was unfortunate rivalry, jealousy and bitterness.
		Another important aspect of Daniel Bernoulli's work that proved important in the development of mathematical physics was his acceptance of many of Newton's theories and his use of these together with the tolls coming from the more powerful calculus of Leibniz.
	www.mathematik.ch /mathematiker/daniel_bernoulli.php (2115 words)

	Daniel Bernoulli
		His older brother was Nicolaus (II) Bernoulli and his uncle was Jacob Bernoulli so he was born into a family of leading mathematicians but also into a family where there was unfortunate rivalry, jealousy and bitterness.
		From 1728, Daniel Bernoulli and Leonard Euler dominated the mechanics of flexible and elastic bodies, in that year deriving the equilibrium curves for these bodies.
		Bernoulli determined the shape that a perfectly flexible thread assumes when acted upon by forces of which one component is vertical to the curve and the other is parallel to a given direction.
	www.economyprofessor.com /theorists/danielbernoulli.php (2180 words)

	Bernoulli_Nicolaus(I) (Site not responding. Last check: 2007-10-11)
		Nicolaus(I) Bernoulli was a nephew of Jacob Bernoulli and Johann Bernoulli.
		Nicolaus(I) Bernoulli was appointed to Galileo's chair at Padua in 1716 which Hermann had filled immediately prior to Nicolaus's appointment.
		As might be expected Nicolaus supported Leibniz but he did produce some good arguments in his favour such as observing that Newton failed to understand higher derivatives properly which had led him into errors in the problem of inverse central force in a resisting medium.
	mirror.math.nankai.edu.cn /mirror/www-history.mcs.st-and.ac.uk/history/Mathematicians/Bernoulli_Nicolaus(I).html (527 words)

	HENRI PITOT TUBE SPEED MEASURING INSTRUMENT \| DANIEL BERNOULLI'S LAW FLUID FLOW AIRFOIL LIFT
		Bernoulli discovered some fairly simple relationships between fluid velocity and pressure which are the fundamental basis for the design of wings.
		Born as the son of Johann Bernoulli,nephew of Jakob Bernoulli, younger brother of Nicolaus Bernoulli II,and older brother of Johann II, Daniel Bernoulli was by far the ablest of the younger Bernoullis.
		Daniel Bernoulli also was the author in 1738 of the "Exposition of a New Theory on the Measurement of Risk", (Econometrica vol 22 (1954), pp23-36; Stanford Encyclopaedia of Philosophy) which St. Petersburg paradox was the base of the economic theory of risk aversion, risk premium and utility.
	www.speedace.info /pitot_tube.htm (1803 words)

	Daniel Bernoulli (Site not responding. Last check: 2007-10-11)
		Daniel Bernoulli was born on January 20,1700 in Groningen, Netherlands.
		He was the son of Johann Bernoulli, brother of Nicolaus (II) Bernoulli and nephew of Jacob Bernoulli.
		By this time, Johann Bernoulli was prepared to teach his son more mathematics while he studied medicine and he studied his father’s theories of kinetic energy.
	www.qerhs.k12.nf.ca /projects/physics/bernoulli-2.html (1119 words)

	Bernoulli_Nicolaus(I)
		Jacob Bernoulli who supervised Nicolaus's Master's degree at the University of Basel which he was awarded in 1704.
		Montmort's work we can see that Nicolaus formulated certain problems in the theory of probability, in particular the problem which today is known as the St Petersburg problem.
		Jacob Bernoulli's complete works and supplemented it with results taken from Jacob's diary.
	www.educ.fc.ul.pt /icm/icm2003/icm14/Bernoulli_Nicolaus(I).htm (400 words)

	Bernoulli_Johann
		Bernoulli's course is virtually identical with de l'Hôpital's book but it is worth pointing out that de l'Hôpital had corrected a number of errors such as Bernoulli's mistaken belief that the integral of 1/x is finite.
		Neither Bernoulli's wife nor his father-in-law had been happy about the move to Groningen especially since the journey was such a difficult one with a young baby.
		Although Bernoulli was essentially correct in his support of the superior calculus methods of Leibniz, he also supported Descartes' vortex theory over Newton's theory of gravitation and here he was certainly incorrect.
	homepages.compuserve.de /thweidenfeller/mathematiker/bernoullijo.html (2457 words)

	Highbeam Encyclopedia - Search Results for Bernoulli (Site not responding. Last check: 2007-10-11)
		Bernoulli's principle physical principle formulated by Daniel Bernoulli that states that as the speed of a moving fluid (liquid or gas) increases, the pressure within the fluid decreases.
		The phenomenon described by Bernoulli's principle has many practical applications; it is employed in the carburetor and the atomizer,
		Born and educated at Basel, where he knew the Bernoullis, he went to St. Petersburg (1727) at the invitation of Catherine I, becoming professor of mathematics there on the departure of Daniel Bernoulli (1733).
	www.encyclopedia.com /SearchResults.aspx?Q=Bernoulli (614 words)

	bernoulli (Site not responding. Last check: 2007-10-11)
		His father Johann Bernoulli held the chair of mathematics at Groningen University in the Netherlands and his uncle Jakob Bernoulli was also an accomplished mathematician, as was his oldest brother Nicolaus (II) Bernoulli.
		The young Bernoulli found a kindred spirit in the English physician William Harvey who wrote in his book On the Movement of Heat and Blood in Animals that the heart was like a pump which forced blood to flow like a fluid through our arteries.
		However, Bernoulli's method of measuring pressure is still used today in modern aircraft to measure the speed of the air passing the plane; that is its air speed.
	www.qerhs.k12.nf.ca /projects/physics/bernoulli.html (2069 words)

	Nicolaus Bernoulli (Site not responding. Last check: 2007-10-11)
		Nicolaus Bernoulli was a nephew of Jacob Bernoulli and Johann Bernoulli, two other famous mathematicians.
		Bernoulli was appointed to Galileo's chair at Padua in 1716.
		From Montmort's work we can see that Bernoulli formulated certain problems in the theory of probability, in particular the problem which today is known as the St. Petersburg problem.
	www.stetson.edu /~efriedma/periodictable/html/Bi.html (354 words)

	Nicolaus Bernoulli (Site not responding. Last check: 2007-10-11)
		Nicolaus Bernoulli was the father of the mathematical geniuses that came from within the Bernoulli clan.
		He headed the Bernoulli genetic table and was the father to at least 10 children, the 5th child being Jakob(I) Bernoulli and the 10th child being Johann(I) Bernoulli.
		Nicolaus did all that he could to prevent his sons from taking up mathematics as full time careers, but this did not last for long.
	www.unisanet.unisa.edu.au /07305/Nicolaus.htm (148 words)

	Nicolaus II Bernoulli Summary
		The first and favorite son of Johann Bernoulli (1667-1748), Nikolaus Bernoulli was destined to be overshadowed by his younger brother Daniel (1700-1782).
		The Bernoullis were a distinguished family of Swiss mathematicians and scientists dating back to Nikolaus's grandfather, Nikolas (1623-1708).
		Nicolaus II Bernoulli at the MacTutor History of Mathematics archive.
	www.bookrags.com /Nicolaus_II_Bernoulli (559 words)

	The Saint Petersburg paradox
		Actually, his cousin, Nicholas Bernoulli, proposed it in 1713 in a letter to Pierre Rémond de Montmort who put it in his book Essay d'analyse sur les jeux de hazard that same year (see Montmort and the Grand Jan).
		In a letter to me written in 1732 he declared that he was in no way dissatisfied with my proposition on the evaluation of risky propositions when applied to the case of a man who is to evaluate his own prosepcts.
		See also the link "Bernoulli family tree" near the end of the page Johann Bernoulli, which has no pictures but is a little more complete and easier to understand.
	www.math.fau.edu /Richman/Ideas/petersburg.htm (676 words)

	Bernoulli. The Columbia Encyclopedia, Sixth Edition. 2001-05
		Jacob, Jacques, or James Bernoulli, 1654–1705, became professor at Basel in 1687.
		He was succeeded at Basel by his brother, Johann, Jean, or John Bernoulli, 1667–1748, who earlier had been professor at Gröningen and who was famous for his work in the field of integral and exponential calculus and was also a founder of the calculus of variations.
		His son, Daniel Bernoulli, 1700–1782, was a mathematician, physicist, and physician and has often been called the first mathematical physicist.
	www.bartleby.com /65/be/BernoulFam.html (343 words)

	Bryson Burke Diamond Corporation: Diamond Exploration and Mining in Canada
		Nicolaus(II) Bernoulli died in St Petersburg in July 1726 creating a vacancy there, Euler was offered the post which would involve him in teaching applications of mathematics and mechanics to physiology.
		Daniel Bernoulli who, already unhappy in Russia, had requested that Euler bring him tea, coffee, brandy and other delicacies from Switzerland.
		Daniel Bernoulli held the senior chair in mathematics at the Academy but when he left St Petersburg to return to Basel in 1733 it was Euler who was appointed to this senior chair of mathematics.
	brysonburke.com /latest_euler.html (3991 words)

	Euler
		Through the requests of Daniel Bernoulli and Jakob Hermann, Euler was appointed to the mathematical-physical division of the Academy rather than to the physiology post he had originally been offered.
		Now Daniel Bernoulli held the senior chair in mathematics at the Academy but when he left St Petersburg to return to Basel in 1733 it was Euler who was appointed to this senior chair of mathematics.
		However sublime are the researches on fluids which we owe to Messrs Bernoulli, Clairaut and d'Alembert, they flow so naturally from my two general formulae that one cannot sufficiently admire this accord of their profound meditations with the simplicity of the principles from which I have drawn my two equations...
	www.weizmann.ac.il /lvov/Lecture-Online/Bib/Euler.html (3720 words)

	boys
		Nicolaus Bernoulli was a merchant in Basel, Switzerland.
		Jacob was the first of the numerous Bernoullis to study mathematics.
		The tenth child of Nicolaus Bernoulli, Johann was born on July 27th, 1667, twelve years after his brother Jacob.
	jwilson.coe.uga.edu /EMT668/EMAT6680.Folders/Dickerson/Bernoulli/boys.html (778 words)

	Pascal's Wager and Bernoulli Trials
		Nicolaus was a magistrate, and important member of the town.
		Bernoulli studied theology due to his father’s will, but later studied mathematics and astronomy.
		Although Bernoulli and his brother, Johann, often disputed over who was superior in discovery and mathematics, both worked diligently and published works on probability and geometry, from 1685 to 1687.
	members.tripod.com /math2005uts/id5.html (936 words)

	A short history of probability and statistics: 18th century
		Nicolaus Bernoulli's dissertation De Usu Artis Conjectandi in Jure dated june 1709, is published.
		He meets with Nicolaus Bernoulli (1687-1759), who is visiting the Hague on his way to England, and discusses Arbuthnots paper with him.
		It is based on an unpublished memoir from 1772 and the publication seems largely motivated by the knowledge that others (Joseph-Louis Lagrange and Johan III Bernoulli) are working on the same problem.
	www.leidenuniv.nl /fsw/verduin/stathist/sh_18.htm (999 words)

	Bernoulli_Nicolaus(II)
		Nicolaus(II) Bernoulli was the favourite of three sons of
		He entered the University of Basel when only 13 years of age and, like many other members of his family, studied both mathematics and law.
		Nicolaus worked as his father's assistant helping him with correspondence.
	www.educ.fc.ul.pt /icm/icm2003/icm14/Bernoulli_Nicolaus(II).htm (148 words)

	Portal de matematica (Site not responding. Last check: 2007-10-11)
		It must be understood that Leibniz 's publications on the calculus were very obscure to mathematicians of that time and the Bernoullis were the first to try to understand and apply Leibniz 's theories.
		Johann Bernoulli 's boasts were the first cause of Jacob's attacks on him and Jacob wrote that Johann was his pupil whose only achievements were to repeat what his teacher had taught him.
		Jacob Bernoulli's first important contributions were a pamphlet on the parallels of logic and algebra published in 1685, work on
	www.learn-math.info /historyDetail.do?id=Bernoulli_Jacob (1824 words)

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