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	Daniel Bernoulli Summary
		Bernoulli's discovery was one of the great moments in the history of science, for his extraordinary insights laid the foundations for the kinetic theory of gases, which in the 19th century fully validated his profound understanding of the nature of gases.
		Bernoulli experimented by puncturing the wall of a pipe with a small, open-ended straw, and noted that as the fluid passed through the tube the height to which the fluid rose up the straw was related to fluid's pressure.
		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.
	www.bookrags.com /Daniel_Bernoulli (4786 words)

	Schiller Institute Pedagogical Studies-- "Justice for the Catenary"
		Bernoulli shows how the calculus was developed to solve certain physical-mechanical problems, such as determining the path of least-time and equal time, or the shape of the hanging chain.
		Bernoulli's treatment is found in a German translation of his 1691 "Lectures on the Integral calculus".
		Bernoulli shows that the shape of the hanging chain, which Huygens called the catenary curve, is that path that must be followed, so as to maintain an equal force on this lowest point.
	www.schillerinstitute.org /educ/pedagogy/bmd_catenary-1.html (1936 words)

	History of physics - Wikipedia
		In the 16th century Nicholas Copernicus rediscovered the heliocentric model of the solar system devised by Aristarchus (which had been preserved by Arab scholars).
		He published this model, though due to fears that he would be persecuted by the church, the idea was presented as only a mathematical convenience for calculating the positions of planets, and not as an account of the true nature of the planetary orbits.
		During World War II, research was conducted by each side into nuclear physics, for the purpose of creating a nuclear bomb.
	wikipedia.findthelinks.com /hi/History_of_Physics.html (4433 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.
		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.economyprofessor.com /theorists/danielbernoulli.php (2180 words)

	LTER II Proposal at Harvard Forest
		Consequently, in LTER II our research is integrated in the study of legacies of human land-use on modern forest processes and the extension of results from mechanistic and empirical studies to a regional scale.
		In LTER II we seek to determine whether the land-use/vegetation relationships observed at the site and landscape-scale are also evident at a subregional scale, where there are stronger environmental gradients.
		For LTER II we are initiating population studies that will focus on impacts of the physical disturbance of plowing on the distribution of understory plants.
	harvardforest.fas.harvard.edu /research/lterII/lter2.html (17558 words)

	BERNOULLI - Online Information article about BERNOULLI
		DANIEL BERNOULLI (1700-1782), the second son of Jean Bernoulli, was born on the 29th of January 1700, at Groningen.
		Claude Clairaut, whom the fame of the Bernoullis had attracted to Basel.
		JEAN BERNOULLI (1710-179o), the youngest of the three sons of Jean Bernoulli, was born at Basel on the 18th of May 1710.
	encyclopedia.jrank.org /BEC_BER/BERNOULLI.html (3330 words)

	Assignment 55
		Nicholas I (1695-1726) developed properties of curves, differential equations, and calculus.
		Johann II (1710-1790) wrote about the mathematical theory of heat and light.
		The Bernoullis were prolific writers, and their ideas filled the pages of many books.
	www.herkimershideaway.org /algebra2/doc_page63.html (311 words)

	Clan Stirling Online! Bios Article (Site not responding. Last check: 2007-11-02)
		The Jacobite cause was that of the Stuart king, James II (of Britain -- James VII of Scotland: Jacobus in Latin), exiled after the Revolution of 1688, and his descendants.
		There are results on the curve of quickest descent, results on the catenary (in particular relating this problems to that of placing spheres in an arch), and results on orthogonal trajectories.
		There is a story told by Tweedie in [5] that Stirling learned the secrets of the glass industry while in Italy and had to flee for fear of his life since the glass-makers may have tried to assassinate him to prevent their secrets becoming known.
	www.clanstirling.org /Main/bios/EpEkFukEAZUExmQRLm.html (2447 words)

	Jacob Bernoulli Deciphered
		Presumably, Jakob Bernoulli wanted to indicate that his proposal represented a new scientific discipline to be applied to all levels of human society, in politics, morals and economics (in civilibus, moralibus and oeconomicis) for gaining new knowledge and solving problems.
		In other words, Jakob Bernoulli had realized that the wrong decisions which are made everywhere at every time are in their majority due to the fact that man tends to assume to have truth, although this is impossible.
		Nicholas Bernoully: I heartily thank that Gentleman for the good opinion he has of me; but I willingly resign my share of that task into better Hands, wishing that either he himself would prosecute that Design, he having formerly published some successful Essays of that Kind, or that his Uncle, Mr.
	isi.cbs.nl /bnews/06b/bn_1.html (4975 words)

	Schiller Institute-- On the Subject of Metaphor, by Lyndon H. LaRouche
		By the close of the seventeenth century, the successive work of Huygens, Leibniz, and the Bernoullis on the tautochrone/brachistochrone problem for isochronism and for light, had shown implicitly that all possible action in our universe must conform to multiply interacting circular action upon circular action, not straight line interaction between points considered pairwise.
		The geometrical construction employed as proofs, together with the Bernoulli experiment itself, are, combined into one, the experiment X; the Bernoulli experiment itself, is the relevant physical experiment.
		This higher quality of thought-object is therefore of a distinct Cantorian Type: that array of thought-objects, considered as they might have been generated in that selection and assigned order, generated by a constant principle of difference, forms a manifold, or sub-manifold of this description.
	www.schillerinstitute.org /fid_91-96/fid_923_lhl_metaphor.html (9599 words)

	Bernoulli at AllExperts (via CobWeb/3.1 planetlab2.isi.jhu.edu) (Site not responding. Last check: 2007-11-02)
		The Bernoullis are a family of traders and scholars from Basel, Switzerland.
		The founder of the family, Leon Bernoulli, immigrated to Basel from Antwerp, Belgium in the 16th century.
		* Nicolaus I Bernoulli (1687–1759), nephew of Jakob and Johann.
	experts.about.com.cob-web.org:8888 /e/b/be/Bernoulli.htm (131 words)

	The Expected Utility Hypothesis - Introduction
		The expected utility hypothesis stems from Daniel Bernoulli's (1738) solution to the famous St. Petersburg Paradox posed in 1713 by his cousin Nicholas Bernoulli (it is common to note that Gabriel Cramer, another Swiss mathematician, also provided effectively the same solution ten years before Bernoulli).
		Daniel Bernoulli's solution involved two ideas that have since revolutionized economics: firstly, that people's utility from wealth, u(w), is not linearly related to wealth (w) but rather increases at a decreasing rate - the famous idea of diminishing marginal utility, u
		Channelled by Gossen (1854), Bernoulli's idea of diminishing marginal utility of wealth became a centerpiece in the Marginalist Revolution of 1871-4 in the work of Jevons (1871), Menger (1871) and Walras (1874).
	cepa.newschool.edu /het/essays/uncert/bernoulhyp.htm (457 words)

	Saint Petersburg (Site not responding. Last check: 2007-11-02)
		It is followed by the Naval Cathedral of St Nicholas (1753–1762), a lofty structure dedicated to the Russian Navy, the outside being covered with plaques to sailors lost at sea.
		St Isaac's Square is graced by a monument to Nicholas I, which was spared by Bolshevik authorities from destruction as the only equestrian statue in the world with merely two support points (the rear feet of the horse).
		The public monuments of St Petersburg also include the circular statue of Catherine II on the Nevsky Prospect, fine horse statues on the Anichkov bridge, a Rodin-like equestrian statue of Alexander III, and the Tercentenary monument presented by France in 2003 and installed on the Sennaya Square.
	saint-petersburg.kiwiki.homeip.net (3641 words)

	Algebraic Number Theory Archive (Site not responding. Last check: 2007-11-02)
		ANT-0174: 5 Nov 2001, Euler characteristics and elliptic curves II, by John H. Coates and Susan Howson.
		ANT-0157: 4 Dec 1998, On the arithmetic of the curves y^2 = x^ell + A, II, by Michael Stoll.
		ANT-0130: 31 Aug 1998, Counterexamples to a conjecture of Lemmermeyer, by Nigel Boston and Charles Leedham-Green.
	front.math.ucdavis.edu /ANT (12251 words)

	Sir Isaac Newton (1642 - 1727)
		II, part 4] and observations on the inflexion of light [bk.
		He also used the series to determine the areas of the circle and the hyperbola in infinite series, and he found that the results were the same as those he had arrived at by other means.
		Of these Newton enumerated one seventy-two; four of the remainder were mentioned by Stirling in 1717, one by Nicole in 1731, and one by Nicholas Bernoulli about the same time.
	www.cwu.edu /~lewiss/newton.htm (8697 words)

	ipedia.com: Saint Petersburg Article (Site not responding. Last check: 2007-11-02)
		Alexander II's emancipation of the serfs (1861) caused the influx of large numbers of poor into the city.
		Socialist organizations were responsible for the assassinations of many royal officials, including that of Alexander II in 1881.
		During World War II, Leningrad was surrounded and besieged by the German Wehrmacht in the Siege of Leningrad from September 8, 1941, until January 27, 1944, a total of twenty-nine months.
	www.ipedia.com /saint_petersburg.html (1643 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).
		Adding to the confusion is the fact that this Nikolaus, a professor of mathematics at Padua and later of law and logic at Basel, contributed to the study of probability and infinite series—as did "Nikolaus III," eldest son of Johann.
	www.bookrags.com /Nicolaus_II_Bernoulli (559 words)

	6 February in History
		Nicholas, his wife Alexandra, and their four girls and one son were held at Czarskoye Selo palace and then taken to Ekaterinburg in the Urals after the Bolsheviks seized power in the October Revolution.
		Fearing that Nicholas and his family would be rescued, the local authorities passed a death sentence on the Romanovs.
		Just after midnight on 17 July 1918, Nicholas, Alexandra, their five children, and four family retainers, among them Dr. Botkin, were ordered to dress quickly and go down to the cellar of the house in which they were being held.
	www.safran-arts.com /42day/history/h4feb/h4feb06.html (11841 words)

	Continuity and Infinitesimals (Stanford Encyclopedia of Philosophy)
		We have noted their reappearance as indivisibles in the sixteenth and seventeenth centuries: in this form they were systematically employed by Kepler, Galileo's student Cavalieri, the Bernoulli clan, and a number of other mathematicians.
		A letter of his to Leibniz written in 1698 contains the forthright assertion that “inasmuch as the number of terms in nature is infinite, the infinitesimal exists ipso facto.” One of his arguments for the existence of actual infinitesimals begins with the positing of the infinite sequence 1/2, 1/3, 1/4,….
		Possibilities (ii) and (iii) may be ruled out because f is continuous.
	plato.stanford.edu /entries/continuity (16769 words)

	Attorney Client Confidentiality in the Criminal Environmental Law Context:
		Part II discusses how environmental problems are different from other regulatory issues by examining the following threshold questions: (1) what environmental laws are implicated by the client's actions, and (2) whether those actions reach criminal proportion.
		Nicholas Targ is an attorney with the United States Department of the Interior.
		Similarly, if it were not reasonably clear that the material transported was dangerous and, thus likely to be regulated, the Court noted that the public welfare doctrine would not apply.
	www.pace.edu /LawSchool/pelr/vol14no1f1996/targ.html (11803 words)

	Physics > History (Site not responding. Last check: 2007-11-02)
		In the 16th century Nicholas Copernicus revived the heliocentric model of the solar system devised by Aristarchus (which survives primarily in a passing mention in the Sand Reckoner of Archimedes).
		When this model was published at the end of his life, it was with a preface by Osiander that piously represented it as only a mathematical convenience for calculating the positions of planets, and not an account of the true nature of the planetary orbits.
		Unfortunately the theory was never published, but Tesla may have been developing a theory about gravity waves.
	www.physics.teleactivities.net /history (2725 words)

	The Mathematical Realm of Nature
		Nonetheless, the accompanying discussion suggested that the equality of volumes followed from the one-one correspondence of cross-sections, and Galileo went on to speculate about how one might conceive of finite quantities as composed of an infinite number of indivisibles; in this case of the bowl and the cone consisting respectively of all the corresponding cross-sections.
		As Book II of the Géométrie shows, Descartes could apply the laws of optics mathematically to derive the reflective and refractive properties of curved lenses, and in that sense his theory of optics was fully mathematical.
		The velocity of each depends on the center of oscillation of the bar, which is located by setting the heights of the centers of gravity of the constrained and the unconstrained systems equal to one another.
	www.princeton.edu /~mike/articles/mathnat/mathnat.htm (16417 words)

	The Discovery of the Deep Sky Objects
		Abbe Nicholas Louis de la Caille (Lacaille, 1713-1762) observed stars and Deep Sky objects in the Southern sky from South Africa during his 1751-52 journey, invented several southern constellations (many of which are still in use), and compiled a catalog of Southern Deep-Sky objects with 42 entries, 32 of which are real.
		His other findings were listed in a letter to Bernoulli of Berlin dated May 6, 1783.
		Abbe Nicholas Louis de la Caille (Lacaille) published his catalog of Southern Deep-Sky objects of 42 entries, 9 of which are errata and asterisms, but 33 are real objects, in the Memoirs of the French Royal Academy.
	www.seds.org /messier/xtra/history/deepskyd.html (4406 words)

	Utility Theory
		Well, then your personal bias is consistent with what Bernoulli said, in the 18th century.
		It was posed by Nicholas Bernoulli and solved by his cousin Daniel Bernoulli who introduced this logarithmic
		Indeed, Daniel wanted a diminishing marginal utility, a function which increased less and less rapidly (the graph is concave DOWN, like the graph in Figure 2) such that the infinite series would converge to a finite value.
	www.gummy-stuff.org /utility-theory.htm (1292 words)

	Science & Infrastructure (Site not responding. Last check: 2007-11-02)
		All three were in accord with the gnostic, ivory-tower dogma of Aristotle, insisting that man could not know the efficient causes of action, but must accept the appearances judged in terms of presumably unchanging principles expressed by what was assumed to be "perfect" uniform motion.
		It is by uncovering the fallacies of sense-certainty, by discovering the principles required by encounter with ontological paradoxes, that mankind overcomes a childish faith in the shadow world of sense-certainty, to discover those universal principles, by means of which we act to increase man's power in and over the real universe.
		This was more than two and a half centuries before Leibniz and Bernoulli had settled the role the catenary in defining both the proof of the infinitesimal principle of the calculus and the principle of universal least action.
	larouchein2004.net /pages/writings/2002/020823scienceinf.htm (16782 words)

	17 Jul History: This Date (Site not responding. Last check: 2007-11-02)
		1328 David II [05 Mar 1324 – 22 Feb 1371], in accordance with the Anglo-Scottish peace treaty of Northampton, is married to Joanna, sister of King Edward III [13 Nov 1312 – 21 Jun 1377] of England.
		David II would succeeded as king of Scots at the death of his father, Robert I the Bruce [11 Jul 1274 – 07 June 1329].
		1790 Johann II Bernoulli, Basel Swiss lawyer, physicist, and mathematician, born on 28 May 1710, the best known of the three sons of Johann Bernoulli [27 Jul 1667 – 01 Jan 1748] and father of Johann III Bernoulli [04 Nov 1744 – 13 Jul 1809].
	www.jcanu.hpg.ig.com.br /history/h4jul/h4jul17.html (9990 words)

	Earliest Known Uses of Some of the Words of Mathematics (M) (Site not responding. Last check: 2007-11-02)
		II: "It follows that f(s) is a monotonic function that actually decreases in parts of the interval..." (OED2).
		May 1728 written by Gabriel Cramer; see letter 8 in Correspondence of Nicholas Bernoulli concerning the St Petersburg game with Montmort, Daniel Bernoulli and Cramer (translation by Richard J. Pulskamp.) Daniel Bernoulli published an extract from this letter in his "Specimen Theoriae Novae de Mensara Sortis," Commentarii Academiae Scientiarum Imperialis Petropolitana, 5, 175-192 (1738).
		That is morally certain whose probability nearly equals the whole certainty, so that a morally certain event cannot be perceived not to happen: on the other hand, that is morally impossible which has merely as much probability as renders the certainty of failure moral certainty.
	members.aol.com /jeff570/m.html (9381 words)

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