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Topic: Jacob Bernoulli

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	Bernoulli_Jacob biography
		Jacob Bernoulli was the brother of Johann Bernoulli and the uncle of Daniel Bernoulli.
		Jacob probably felt that Johann was the more powerful mathematician of the two and, this hurt since Jacob's nature meant that he always had to feel that he was winning praise from all sides.
		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-groups.dcs.st-and.ac.uk /~history/Biographies/Bernoulli_Jacob.html (1894 words)

	Jakob 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...
		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 had always found the properties of the logarithmic spiral to be almost magical and he had requested that it be carved on his tombstone with the Latin inscription "Eadem Mutata Resurgo" meaning "I shall arise the same though changed".
	www.mathematik.ch /mathematiker/jakob_bernoulli.php (1815 words)

	The Bernoulli Family
		The eldest son, Jacob (James or Jacques), was born 1654 and died 1705 in Bale, Switzerland.
		Jacob and Johann went back and forth with comments in the academic community which developed a notorious reputation of their family togetherness.
		In 1695, Jacob was the chair of mathematics in Bale.
	www.math.wichita.edu /history/men/bernoulli.html (786 words)

	Jacob Bernoulli
		During the time that Jacob Bernoulli was taking his university degree in theology he was studying mathematics and astronomy against the wishes of his parents.
		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 had always found the properties of the logarithmic spiral to be almost magical and he had requested that it be carved on his tombstone.
	www.stetson.edu /~efriedma/periodictable/html/Br.html (785 words)

	Johann Bernoulli
		He was the brother of Jacob Bernoulli but Johann was twelve years younger than his brother Jacob which meant that Jacob was already a young man while Johann was still a child.
		Jacob was lecturing on experimental physics at the University of Basel when Johann entered the university and it soon became clear that Johann's time was mostly devoted to studying Leibniz's papers on the calculus with his brother Jacob.
		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.
	www.mathematik.ch /mathematiker/johann_bernoulli.php (2449 words)

	Bernoulli Equation: History of Daniel Bernoulli and his Equation (Site not responding. Last check: 2007-09-02)
		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.
		Johannes, Jacob, and, to a lesser extent, Nicolaus led the development of calculus and the calculus of variations in those early years of the field.
		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.
	www.fluidmech.net /tutorials/bernoulli/bernoulli-history.htm (1254 words)

	Bernoulli
		Jacob began publishing in the journal Acta Eruditorum which was established in Leipzig in 1682.
		Bernoulli greatly advanced algebra, the infinitesimal calculus, the calculus of variations, mechanics, the theory of series, and the theory of probability.
		Bernoulli was one of the most significant promoters of the formal methods of higher analysis.
	www.thocp.net /biographies/bernoulli.html (1926 words)

	Bernoulli. The Columbia Encyclopedia, Sixth Edition. 2001-05
		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.bartleby.com /65/be/BernoulFam.html (343 words)

	AllRefer.com - Bernoulli (Mathematics, Biography) - Encyclopedia (Site not responding. Last check: 2007-09-02)
		Bernoulli or Bernouilli[both: bernOOyE´] Pronunciation Key, name of a family distinguished in scientific and mathematical history.
		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 GrOningen 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.
	reference.allrefer.com /encyclopedia/B/BernoulFam.html (387 words)

	Page Title
		Bernoulli's Principle states that a fluid in motion has a lower pressure than the same fluid not in motion.
		Daniel Bernoulli was born on the eighth of February in 1700 in Groningen, The Netherlands to a prestigious family of mathematicians.
		His father was Johann Bernoulli, his brothers were Nicolaus and Jacob (II) Bernoulli, and his uncle was Jacob Bernoulli, all of which were well-known European mathematicians of the 18th century (Quinney, 2001).
	physicsprinciples.tripod.com /Bernoulli.htm (372 words)

	Daniel Bernoulli (Site not responding. Last check: 2007-09-02)
		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.
		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.
		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.engineering.com /content/ContentDisplay?contentId=41003009 (2115 words)

	Jacob (Site not responding. Last check: 2007-09-02)
		By the time Jacob began his duties at the University he had already mastered Descartes' Geometry and had begun his work on Probability that would not be published in its entirety until after his death, in the book entitled Ars Conjectandi (Basel, 1713).
		In his analysis of the problem (1689–90) Jacob showed himself a master of the differential and integral calculus and formulated the problem of the catenary as a related problem.
		Jacob was also the first of the Bernoulli family to earn his living as a professional mathematician.
	www.fyma.ucl.ac.be /~gaino/Bernoulli/Jacob.html (1419 words)

	Department of Statistics - Bernoulli logo
		A society needs a logo, and if the society is called the Bernoulli Society it seems natural to look for the logo in the works of our namesake, the Swiss mathematician Jacob Bernoulli (1654-1705).
		Though we may value Bernoulli's contributions to probability theory (where would we be without Bernoulli trials?) Jacob Bernoulli had a special attachment to his work on the logarithmic spiral.
		Bernoulli found this the most remarkable property of all and described the spiral as `spiralis miribabilis', the miraculous spiral.
	www2.warwick.ac.uk /fac/sci/statistics/bernoulli/logo (489 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.
		Bernoulli was obviously enraged by the theft and ceased helping his freeloading friend.
		He and his brother Jacob are credited with the beginnings of the calculus of variations, which was inspired over an argument on a geometric figure known as the brachistochrone.
	web01.shu.edu /projects/reals/history/bernoull.html (833 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.
		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.
	www.economyprofessor.com /theorists/danielbernoulli.php (2180 words)

	Fermat's Last Theorem
		Jacob Bernoulli was the oldest of the famous Bernoulli mathematicians.
		Jacob was born on December 27, 1654 to a prominent and wealthy family of merchants in Basel, Switzerland.
		Jacob Bernoulli became the chair of mathematics and the University of Basel and held this post until his death in 1705.
	fermatslasttheorem.blogspot.com (3883 words)

	Hilldale Lectures in the Physical Sciences - University of Wisconsin-Madison - 2004-2005
		Jacob Bernoulli's treatise (Ars Conjectandi) posthumously published in 1713 introduced the numbers that bear his name.
		This Table has clearly admirable and extraordinary properties, for beyond what I have already shown of the mystery of combinations hiding within it, it is known to those skilled in the more hidden parts of geometry that the most important secrets of all the rest of mathematics lie concealed within it.
		The lecture will show how Bernoulli numbers themselves are connected with much of the rest of mathematics, pure and applied, and how they unify branches of mathematics as disparate as differential topology and modular forms.
	www.secfac.wisc.edu /lectures/hilldale/physical/20042005Mazur.htm (280 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)

	James Bernoulli - Wikipedia, the free encyclopedia
		James Bernoulli (also known as Jacob I) was born in Basel, Switzerland on December 27, 1654 and lived until August 16, 1705.
		He is one of the eight prominent mathematicians in the Bernoulli family.
		Bernoulli crater, on the Moon, is also named after him jointly with his brother Johann.
	en.wikipedia.org /wiki/Jacob_Bernoulli (310 words)

	Bernoulli, Jakob (1654-1705) -- from Eric Weisstein's World of Scientific Biography
		Swiss mathematician (also known as Jacque I or James I) who was the brother of Johann Bernoulli.
		In his Ars conjectandi (1713), which was published posthumously, he developed the properties of Bernoulli numbers.
		In a paper of sums, he remarks how useless Bullialdus's voluminous work Opus novum ad arithmeticum infinitorum (1682) was, which "did nothing more that compute with immense labor the sums of the first six powers, which is only a part of what we have accomplished in the space of a single page" (Smith 1994, p.
	scienceworld.wolfram.com /biography/BernoulliJakob.html (200 words)

	lemniscate of Bernoulli
		Bernoulli named the curve "lemniscate" after the Greek lemniskus for a pendant ribbon (the type fastened to a victor's garland).
		At the time he wrote his article, Bernoulli wasn't aware that the curve he was describing was a special case of a Cassinian oval, which had been described by Cassini in 1680.
		The general properties of the lemniscate were discovered by Giovanni Fagnano (1715-1797) in 1750; Leonhard Euler's investigations of the length of arc of the curve (1751) led to later work on elliptic functions.
	www.daviddarling.info /encyclopedia/L/lemniscate.html (231 words)

	Daniel Bernoulli
		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 numbers and the Pascal triangle
		The Bernoulli numbers plays an important role in mathematics.They first appeard in Ars Conjectandi, a famous (and posthumous) published treatise in 1713, by Jakob Bernoulli.
		Bernoulli`s numbers appears in analysis, number theory and differential topology.
		Thus, the Bernoulli numbers may be determined step by step from the last symbolic formula; note that after the binomial expansion the powers of the B numbers must be replaced by Bernoulli numbers with the appropriate indices.
	milan.milanovic.org /math/english/bernoulli/bernoulli.html (235 words)

	Memories (via CobWeb/3.1 planetlab2.isi.jhu.edu) (Site not responding. Last check: 2007-09-02)
		we celebrated 300 years anniversary of passing away of Jacob Bernoulli, a Swiss mathematician considered to be one of the most important founders of calculus of variations and probability theory.
		Jacob Bernoulli graduated in philosophy (1671, masters degree) and theology (1676, Licencié), but his true passion was mathematics and theoretical physics.
		Jacob Bernoulli had always been impressed by the properties of the logarithmic spiral.
	isi.cbs.nl.cob-web.org:8888 /bnews/05b/bn_3.html (243 words)

	Nicolaus Bernoulli (Site not responding. Last check: 2007-09-02)
		Nicolaus Bernoulli was a nephew of Jacob Bernoulli and Johann Bernoulli, two other famous mathematicians.
		In fact it was Jacob Bernoulli who supervised Nicolaus's Master's degree at the University of Basel, which he was awarded in 1704.
		Bernoulli was appointed to Galileo's chair at Padua in 1716.
	www.stetson.edu /~efriedma/periodictable/html/Bi.html (354 words)

	A short history of probability and statistics: 18th century
		This might have been stimulated by 'whispers' and writings about that elusive piece Ars Conjectandi, on which Jacob Bernoulli had been brooding for 20 years, and which was still not finished when he died.
		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)

	Iztok Hozo Genealogy
		In 1748 in Introductio in analysin infinitorum Euler made ideas of Johann Bernoulli more precise in defining a function, and he stated that mathematical analysis was the study of functions.
		In Introductio in analysin infinitorum Euler dealt with logarithms.
		However it did assure de l'Hôpital of a place in the history of mathematics since he published the first calculus book Analyse des infiniment petits pour l'intelligence des lignes courbes (1696) which was based on the lessons that Johann Bernoulli sent to him (without acknowledging that fact).
	www.iun.edu /~mathiho/genealogy/IztokHozoGenealogy.htm (1260 words)

	Bernoulli — Infoplease.com
		Bernoulli's principle - Bernoulli's principle, physical principle formulated by Daniel Bernoulli that states that as the...
		Bernoulli, Jacques - Bernoulli, Jacques scientist Birthplace: Basel, Switzerland Born: 1654 Died: 1705 Information...
		Small-sample interval estimation of Bernoulli and Poisson parameters.
	www.infoplease.com /ce6/people/A0807243.html (442 words)

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