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:''For other family members named Jacob, see Bernoulli family.'' Jacob Bernoulli (also known as James or Jacques; – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family. He was an early proponent of Leibnizian calculus and had sided with Leibniz during the Leibniz–Newton calculus controversy. He is known for his numerous contributions to calculus, and along with his brother Johann, was one of the founders of the calculus of variations. However, his most important contribution was in the field of probability, where he derived the first version of the law of large numbers in his work ''Ars Conjectandi''.〔(Jacob (Jacques) Bernoulli ), (The MacTutor History of Mathematics archive ), School of Mathematics and Statistics, University of St Andrews, UK.〕 ==Biography== Jacob Bernoulli was born in Basel, Switzerland. Following his father's wish, he studied theology and entered the ministry. But contrary to the desires of his parents , he also studied mathematics and astronomy. He traveled throughout Europe from 1676 to 1682, learning about the latest discoveries in mathematics and the sciences under leading figures of the time. This included the work of Hudde, Robert Boyle, and Robert Hooke. During this time he also produced an incorrect theory of comets. Bernoulli returned to Switzerland and began teaching mechanics at the University in Basel from 1683. In 1684 he married Judith Stupanus; and they had two children. During this decade, he also began a fertile research career. His travels allowed him to establish correspondence with many leading mathematicians and scientists of his era, which he maintained throughout his life. During this time, he studied the new discoveries in mathematics, including Christiaan Huygens's ''De ratiociniis in aleae ludo'', Descartes' ''Geometrie'' and Frans van Schooten's supplements of it. He also studied Isaac Barrow and John Wallis, leading to his interest in infinitesimal geometry. Apart from these, it was between 1684 and 1689 that many of the results that were to make up ''Ars Conjectandi'' were discovered. He was appointed professor of mathematics at the University of Basel in 1687, remaining in this position for the rest of his life. By that time, he had begun tutoring his brother Johann Bernoulli on mathematical topics. 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...'' published in ''Acta Eruditorum''. They also studied the publications of von Tschirnhaus. 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. Jacob collaborated with his brother on various applications of calculus. However the atmosphere of collaboration between the two brothers turned into rivalry as Johann's own mathematical genius began to mature, with both of them attacking each other in print, and posing difficult mathematical challenges to test each other's skills. By 1697 the relationship had completely broken down. Jacob Bernoulli died in 1705. Bernoulli chose a figure of a logarithmic spiral and the motto ''Eadem mutata resurgo'' ''("Changed and yet the same, I rise again")'' for his gravestone; the spiral executed by the stonemasons was, however, an Archimedean spiral, “(Bernoulli ) wrote that the logarithmic spiral ‘may be used as a symbol, either of fortitude and constancy in adversity, or of the human body, which after all its changes, even after death, will be restored to its exact and perfect self’.” (Livio 2002: 116). His grave is in Basel Munster or Cathedral where the gravestone shown below is located. The lunar crater Bernoulli is also named after him jointly with his brother Johann. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Jacob Bernoulli」の詳細全文を読む スポンサード リンク
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