"The remarkable principle of James Bernoulli consists exactly of this... namely, that the mean given by a series of trials falls near the number sought within limits so much the more narrow as the trials are more multiplied. All the properties which result from his learned researches constitute one of the most honourable monuments to his memory. But Bernoulli established his calculations on the hypothesis that the number sought was fixed and determined. ... It may happen that this quantity will experience small variations... But the principle of Bernoulli is still applicable to this case and has been demonstrated by M. Poisson by means of analysis. ...In the case before us the experiments should generally be very numerous: it is for this reason that M. Poisson has designated the extension of Bernoulli's principle as the law of great numbers."
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Jacob Bernoulli
(January 6, 1655- August 16, 1705) also known as James or Jacques; was one of the many prominent mathematicians in the . He was an early proponent of Leibnizian calculus and had sided with Gottfried Wilhelm Leibniz during the . He is known for his numerous contributions to calculus, and along with his brother , was one of the founders of the . He also discovered the fundamental mathematical constant e. However, his most important contribution was in the field of probability, where he derived the
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