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BERNOULLI

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Originally appearing in Volume V03, Page 805 of the 1911 Encyclopedia Britannica.
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BERNOULLI , or BERNoUILLI, the name of an illustrious See also:

family in the See also:annals of See also:science, who came originally from See also:Antwerp. Driven from their See also:country during the oppressive See also:government of See also:Spain for their See also:attachment to the Reformed See also:religion, the Bernoullis sought first an See also:asylum at See also:Frankfort (1583), and afterwards at See also:Basel, where they ultimately obtained the highest distinctions. In the course of a See also:century eight of its members successfully cultivated various branches of See also:mathematics, and contributed powerfully to the advance of science. The most celebrated were Jacques (See also:James), See also:Jean (See also:John) and See also:Daniel, the first, second and See also:fourth as dealt with below; but, for the See also:sake of perspicuity they may be considered as nearly as possible in the See also:order of family See also:succession. A See also:complete See also:summary of the See also:great developments of mathematical learning, which the members of this family effected, lies outside the See also:scope of this See also:notice. More detailed accounts are to be found in the various mathematical articles. I. JACQUES BERNOULLI (1654-1705), mathematician, was See also:born at Basel on the 27th of See also:December 1654. Be was educated at the public school of Basel, and also received private instruction from the learned See also:Hoffmann, then See also:professor of See also:Greek. At the conclusion of his philosophical studies at the university, some geometrical figures, which See also:fell in his way, excited in him a See also:passion for mathematical pursuits, and in spite of the opposition of his See also:father, who wished him to be a clergyman, he applied himself in See also:secret to his favourite science. In 1676 he visited See also:Geneva on his way to See also:France, and subsequently travelled to See also:England and See also:Holland. While at Geneva he taught a See also:blind girl several branches of science, and also how to write; and this led him to publish A Method of Teaching Mathematics to the Blind.

At See also:

Bordeaux his Universal Tables on Dialling were constructed; and in See also:London he was admitted to the meetings of See also:Robert See also:Boyle, Robert See also:Hooke and other learned and scientific men. On his final return to Basel in 1682, he devoted himself to See also:physical and mathematical investigations, and opened a public See also:seminary for experimental physics. In the same See also:year he published his See also:essay on comets, Conamen Novi Systematis Cometarum, which was occasioned by the See also:appearance of the See also:comet of 1680. This essay, and his next publication, entitled De Gravitate Aetheris, were deeply tinged with the See also:philosophy of Rene See also:Descartes, but they contain truths not unworthy of the philosophy of See also:Sir See also:Isaac See also:Newton's Principia. Jacques Bernoulli cannot be strictly called an See also:independent discoverer; but, from his extensive and successful application of the calculus and other mathematical methods, he is deserving of a See also:place by the See also:side of Newton and See also:Leibnitz. As an additional claim to remembrance, he was the first to solve Leibnitz's problem of the isochronous See also:curve (Acta Eruditorum, 169o). He proposed the problem of the See also:catenary (q v.) or curve formed by a See also:chain suspended by its two extremities, accepted Leibnitz's construction of the curve and solved more complicated problems See also:relating to it. He determined the " elastic curve," which is formed by an elastic See also:plate or See also:rod fixed at one end and See also:bent by a See also:weight applied to the other, and which he showed to be the same as the curvature of an impervious See also:sail filled with a liquid (tintearia). In his investigations respecting cycloidal lines and various See also:spiral curves, his See also:attention was directed to the loxodromic and logarithmic spirals, in the last of which he took particular See also:interest from its remarkable See also:property of reproducing itself under a variety of conditions. In 1696 he proposed the famous problem of isoperimetrical figures, and offered a See also:reward for its See also:solution. This problem engaged the attention of See also:British as well as See also:continental mathematicians; and its proposal gave rise to a painful See also:quarrel with his See also:brother Jean. Jean offered a solution of the problem; his brother pronounced it to be wrong.

Jean then amended his solution, and again offered it, and claimed the reward. Jacques still declared it to be no solution, and soon after published his own. In 1701 he published also the demonstration of his solution, which was I accepted by the See also:

marquis de l'Hopital and Leibnitz. Jean, however, held his See also:peace for several years, and then dishonestly published, after the See also:death of Jacques, another incorrect solution; and not until 1718 did he admit that he had been in See also:error. Even then he set forth as his own his brother's solution purposely disguised. In 1687 the mathematical See also:chair of the university of Basel was conferred upon Jacques. He was once made See also:rector of his university, and had other distinctions bestowed on him. He and his brother Jean were the first two See also:foreign associates of the See also:Academy of Sciences of See also:Paris; and, at the See also:request of Leibnitz, they were both received as members of the academy of See also:Berlin. In 1684 he had been offered a professorship at See also:Heidelberg; but his See also:marriage with a See also:lady of his native See also:city led him to decline the invitation. Intense application brought on infirmities and a slow See also:fever, of which he died on the 16th of See also:August 1705. Like another See also:Archimedes, he requested that the logarithmic spiral should be engraven on his tombstone, with these words, Eadem mutata resurgo. Jacques Bernoulli wrote elegant verses in Latin, See also:German and See also:French; but although these were held in high estimation in his own See also:time, it is on his mathematical See also:works that his fame now rests.

These are:—Jacobi Bernoulli Basiliensis See also:

Opera (Genevae, 1744), 2 tom. 4to; Ars Conjectandi, See also:opus posthumum: accedunt tractatus de Seriebus Infinitis, et epistola (Gallice scripta) de Ludo Pilae Reticularis (Basiliae, 1713), I torn. 4to. II. JEAN BERNOULLI (1667-1748), brother of the preceding, was born at Basel on the 27th of See also:July 1667. After See also:finishing his See also:literary studies he was sent to See also:Neuchatel to learn See also:commerce and acquire the French See also:language. But at the end of a year he renounced the pursuits of commerce, returned to the university of Basel, and was admitted to the degree of See also:bachelor in philosophy; and a year later, at the See also:age of 18, to that of See also:master of arts. In his studies he was aided by his See also:elder brother Jacques. See also:Chemistry, as well as mathematics, seems to have been the See also:object of his See also:early attention; and in the year 1690 he published a dissertation on effervescence and See also:fermentation. The same year he went to Geneva, where he gave instruction in the See also:differential calculus to See also:Nicolas Fatio de Duillier, and afterwards proceeded to Paris, where he enjoyed the society of N. See also:Malebranche, J. D.

See also:

Cassini, See also:Philip de See also:Lahire and See also:Pierre Varignon. With the marquis de 1'Hbpital he spent four months studying higher See also:geometry and the resources of the new calculus. His independent discoveries in mathematics are numerous and important. Among these were the exponential calculus, and the curve called by him the linea brachistochrona, or See also:line of swiftest descent, which he was the first to determine, pointing out at the same time the relation which this curve bears to the path described by a See also:ray of See also:light passing through strata of variable See also:density. On his return to his native city he studied See also:medicine, and in 1694 took the degree of M.D. Although he had declined a professorship in See also:Germany, he now accepted an invitation to the chair of mathematics at See also:Groningen (Commercium Philosophicum, epist. xi. and xii.). There, in addition to the learned lectures by which he endeavoured to revive mathetriatical science in the university, he gave a public course of experimental physics. During a See also:residence of ten years in Groningen, his controversies were almost as numerous as his discoveries. His dissertation on the " barometric light," first observed by Jean See also:Picard, and discussed by Jean Bernoulli under the name of See also:mercurial See also:phosphorus, or See also:mercury shining in vacuo (See also:Diss. physica de mercurio lucenle in vacuo), procured him the notice of See also:royalty, and engaged him in controversy. Through the See also:influence of Leibnitz he received from the See also:king of See also:Prussia a See also:gold See also:medal for his supposed discoveries; but Nicolaus Hartsoekerand some of the French academicians disputed the fact. The family quarrel about the problem of isoperimetrical figures above mentioned began about this time. In his dispute with his brother, in his controversies with the See also:English and Scottish mathematicians, and in his harsh and jealous bearing to his son Daniel, he showed a mean, unfair and violent See also:temper.

He had declined, during his residence at Groningen, an invitation to See also:

Utrecht, but accepted in 1705 the mathematical chair in the university of his native city, vacant by the death of his brother Jacques; and here he remained till his death. His inaugural discourse was on the " new See also:analysis," which he so successfully applied in investigating various problems both in pure and applied mathematics. He was several times a successful competitor for the prizes given by the Academy of Sciences of Paris; the subjects of his essays being:—the See also:laws of See also:motion (Discours sur less lois de la communication du mouvement, 1727), the elliptical orbits of the See also:planets, and the inclinations of the planetary orbits (Essai d'une nouvelle physique See also:celeste, 1735). In the last See also:case his son Daniel divided the See also:prize with him. Some years after his return to Basel he published an essay, entitled Nouvelle Theorie de la manoeuvre See also:des vaisseaux. It is, however, his works in pure mathematics that are the permanent monuments of his fame. Jean le Rond d'See also:Alembert acknowledges with gratitude, that' " whatever he knew of mathematics he owed to the works of Jean Bernoulli." He was a member of almost every learned society in See also:Europe, and one of the first mathematicians of a mathematical age. He was as keen in his resentments as he was ardent in his friendships; fondly attached to his family, he yet disliked a deserving son; he gave full praise to Leibnitz and Leonhard See also:Euler, yet was blind to the excellence of Sir Isaac Newton. Such was the vigour of his constitution that he continued to pursue his usual mathematical studies till the age of eighty. He was then attacked by a complaint at first apparently trifling; but his strength daily and rapidly declined till the 1st of See also:January 1748, when he died peacefully in his See also:sleep. His writings were collected under his own See also:eye by See also:Gabriel See also:Cramer, professor of mathematics at Geneva, and published under the See also:title of Johannis Bernoulli Operi Omnia (Lausan. et Genev.), 4 tom. 4to; his interesting See also:correspondence with Leibnitz appeared under the title of Gut.

Leibnitii et Johannis Bernoulli Commercium Philosophicum et Mathematicum (Lausan. et Genev. 1745), 2 tom. 4to. Some of his papers are published in his father's works, and others in the Acta Erudilorum and the Comment. Acad. Petropol. IV. DANIEL BERNOULLI (1700-1782), the second son of Jean Bernoulli, was born on the 29th of January 1700, at Groningen. He studied medicine and became a physician, but his attention was early directed also to geometrical studies. The severity of his father's manner was See also:

ill-calculated to encourage the first efforts of one so sensitive; but fortunately, at the age of eleven, he became the See also:pupil of his brother Nicolas. He afterwards studied in See also:Italy under See also:Francesco Domenico Michelotti and Giambattista See also:Morgagni. After his return,though only twenty-four years of age, he was invited to become See also:president of an academy then projected at See also:Genoa; but, declining this See also:honour, he was, in the following year, appointed professor of mathematics at St See also:Petersburg.

In consequence of the See also:

state of his See also:health, however, he returned to Basel in 1733, where he was appointed professor of See also:anatomy and See also:botany, and afterwards of experimental and speculative philosophy. In the labours of this See also:office he spent the remaining years of his See also:life. He had previously published some medical and botanical See also:dissertations, besides his Exercitationes quaedam Mathematicae, containing a solution of the differential See also:equation proposed by See also:Riccati and now known by his name. In 1738 appeared his Hydrodynamica, in which the See also:equilibrium, the pressure, the reaction and varied velocities of fluids are considered both theoretically and practically. One of these problems, illustrated by experiment, deals with an ingenious mode of propelling vessels by the reaction of See also:water ejected from the stern. Some of his experiments on this subject were per-formed before Pierre See also:Louis M. de See also:Maupertuis and See also:Alexis See also:Claude Clairaut, whom the fame of the Bernoullis had attracted to Basel. With a success equalled only by Leonhard Euler, Daniel Bernoulli gained or shared no less than ten prizes of the Academy of Sciences of Paris. The first, for a memoir on the construction of a See also:clepsydra for measuring time exactly at See also:sea, he gained at the age of twenty-four; the second, for one on the physical cause of the inclination of the planetary orbits, he divided with his father; and the third, for a communication on the tides, he shared with Euler, See also:Colin See also:Maclaurin and another competitor. The problem of vibrating cords, which had been some time before resolved by See also:Brook See also:Taylor (1685–1731) and d'Alembert, became the subject of a See also:long discussion conducted in a generous spirit between Bernoulli and his friend Euler. In one of his early investigations he gave an ingenious though indirect demonstration of the problem of the parallelogram of forces. His labours in the decline of life were chiefly directed to the See also:doctrine of probabilities in reference to See also:practical purposes, and in particular to economical subjects, as, for example, to inoculation, and to the duration of married life in the two sexes, as well as to the relative proportion of male and See also:female births. He retained his usual vigour of understanding till near the age of eighty, when his See also:nephew Jacques relieved him of his public duties.

He was afflicted with See also:

asthma, and his retirement was relieved only by the society of a few chosen See also:friends. He died on the 17th of See also:March 1782 at Basel. Excluded by his professional See also:character from the See also:councils of the See also:republic, he nevertheless received all the deference and honour due to a first See also:magistrate. He was wont to mention the following as the two incidents in his life which had afforded him the greatest See also:pleasure,—that a stranger, whom he had met as a travelling See also:companion in his youth, made to his See also:declaration " I am Daniel Bernoulli " the incredulous and mocking reply, " And I am Isaac Newton "; and that, while entertaining See also:Konig and other guests, he solved without rising from table a problem which that mathematician had submitted as difficult and lengthy. Like his father, he was a member of almost every learned society of Europe, and he succeeded him as foreign See also:associate of the Academy of Paris. Several of his investigations are contained in the earlier volumes of the Comment. Acad. Petropol. ; and his separately published works are :—Dissertatio Inaugur. Phys. Med. de Respiratione (See also:Basil. 1721), 4to; Positiones Anatomico-Botanicae (Basil.

1721), 4to; Exercitationes quaedam Mathematicae (Venetiis, 1724), 4to; Hydrodynamica (Argentorati, 1738), 4to. V. JEAN BERNOULLI (1710-179o), the youngest of the three sons of Jean Bernoulli, was born at Basel on the 18th of May 1710. He studied See also:

law and mathematics, and, after travelling in France,was for five years professor of eloquence in the university of his native city. On the death of his father he succeeded him as professor of mathematics. He was thrice a successful competitor for the prizes of the Academy of Sciences of Paris. His prize subjects were, the See also:capstan, the See also:propagation of light, and the magnet. He enjoyed the friendship of P. L. M. de Maupertuis, who died under his roof while on his way to Berlin. He himself died in 1790. His two sons, Jean and Jacques, are the last noted mathematicians of the family.

VI. NICOLAS BERNOULLI (1687–1759), See also:

cousin of the three preceding, and son of Nicolas Bernoulli, one of the senators of Basel, was born in that city on the loth of See also:October 1687. He visited England, where he was kindly received by Sir Isaac Newton and See also:Edmund See also:Halley (See also:Corn. Phil. ep. 199), held for a time the mathematical chair at See also:Padua, and was successively professor of See also:logic and of law at Basel, where he died on the 29th of See also:November 1759. He was editor of the Ars Conjectandi of his See also:uncle Jacques. His own works are contained in the Ada Eruditorum, the Giornale de' letterati d' Italia, and the Commercium Philosophicum. He was tragically drowned while bathing in the See also:Neva in July 1789, a few months after his marriage with a daughter of See also:Albert Euler, son of Leonhard Euler. Several of his papers are contained in the first six volumes of Nova Acta Acad. Scien. Imper. Petropol., in the Acta Helvetica, in the See also:Memoirs of the See also:Academies of Berlin and See also:Turin, and in his brother John's publications.

He also published separately some juridical and physical theses, and a German See also:

translation of Mimoires du philosophe de See also:Merian. See generally M. Cantor, Geschichte der Mathemalik; J. C. See also:Poggendorff, Biographisch-literarisches Handworterbuch (1863–1904).

End of Article: BERNOULLI

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