In order to put an end to this geometrical warfare, .whir.!} 'had now degenerated into personal abuse; Leibnitz, Newton, and the Marquis L'Hospital, were appointed arbiters ; but they do not seem to have come to any decision on the subject. In 1700, James Bernoulli published, in a letter to his brother, the formulas of the isoperimetrical problem without a demonstration, and invited him to make his own pub lic. John was still ignorant of the defect of his own method ; and so much was he' convinced of its accu racy, that he sent it under seal to the Academy of Sciences at Paris, in February 1701, on condition that it should not be opened till the appearance of his brother's demonstration. In consequence of this, James Bernoulli published his solution separately at Basle, and also in the acts of Leipsie for May 1701, under the title of Analysis magnt problematts hope rimetrici. The fame which was acquired by this ad Jnirable specimen of mathematical genius completely silenced the pretensions of John Bernoulli for five I years ; but after the death of his brother, in 1705, he published his solution in the memoirs of the academy' for 1706, as if he had thought his brother the only person who could detect the false principle upon which it was founded. After an interval of thirteen years, John Bernoulli discovered the source of his er ror. He ingenuously confessed his mistake ; and, published a new solution in the memoirs of the aca demy for 1718, which did not differ much from that of his brother.
In the year 1699, James Bernoulli was elected a foreign associate of the Academy of Sciences at Pa-, ris ; and, in 1701, the same honour was conferred up on him by the Royal Academy of Berlin. The se dentary life which he led, and his intense application to study, brought upon him a severe attack of the gout, accompanied with a slow fever, which put an. end to his life on the 16th of August 1705, in the 51st year of his age. He was married in the year 16S4, and left behind him one son and a daughter, neither of whom seem to have inherited any portion of their father's genius. The son was bred to the pro fession of a painter. James Bernoulli was engaged, at the time of his death, in a work entitled, Ars Con jectandi, or the art of forming conjectures concerning contingent events. It was printed at Basle in and contains a valuable treatise on infinite series, in which its author has given an admirable demonstration of the first case of the binomial theorem. This de monstration has been lately re-published in the third volume of the Scriptores Logarithmici, by Baron Ma seres.
Bernoulli was of a bilious and melancholy tempe rament, and possessed great perseverance in surmount ing difficulties. His genius, though of the first or der, was not of that quick and versatile character. which seizes a subject with instinctive penetration, and invents and discovers by a process almost intui tive. It was marked rather by an excess of caution.
He proceeded with slowness and suspicion, afraid of error, yet resolved to avoid it ; and even after success had taught him the extent of his own powers, and af ter the applause of all Europe had stamped immorta lity upon his name, he did not possess that confidence in his talents which is,.generally the most prominent qualities of flattered genius. When he challenged his brother John to the solution of tie isoperimetrical problem, on which for a long time laboured, he acted with more confidence than he usually•dis played ; but his excessive caution gave him ample security against the chance of error. His brother John, on the contrary, whose genius was more acute but less profound, obtained his solution of• the pro blem almost instantaneously. Without even revising his, investigations, he gave them to the world, careless about the mortification which he afterwards felt when they were be erroneous. In the keen•dis• pute which this circumstance occasioned, the charac ters of the two brothers appeared in their natural co lours. The cold defiance, the chastened severity, and the temperate sarcasms of the one, form a striking contrast with the thoughtless ostentation, the rude invectives, and the coarse raillery of the other., The writings of James Bernoulli are very numerous, and have been collected and published iu two volumes, 4to, at Geneva in 174•. The papers which lie pub ') lished in the memoirs of the academy, are, 1st, Sec tion itnie des Arcs Circulaires, en Celle le raison qu'on voudra, avec la maniere d'en declare les Sinus, &c. Mem. Acad. 170'2, p. 58. 2d, Demonstration Generale du centre de Balancement, on d'oscillation, tiree de la Nature du Levier, Id. 1703, p. 114. 3d, Application de sa rcgle du Centre de Balancement, a routes sortes de figures, Id. 4th, Demonstration du Principe de M. touchant le Centre de Balancement, et de l'Identite de ee Centre arec cclui de Percussion, Mem. Acad. 1701. 5th, Veritable Hypothese de la Resistance des la De monstration de la courbure des Corps, qui font res sort. Mem. .A cad. p. 130.
Besides these lie published no fewer than forty-seven papers in the Acta Eruditorum of Leipsic, mostly mathematical, though some of them related to pneu matics, and others to mechanics. He published also seven papers in the Journal des Scarans, some of which had appeared in the Acta Eruct:forum. See (Enures de Fontenelles, tom. v. p. 57. edit. 1767. General Diet. Lalande, Ribliarraphie Astranamique, p. 299. Montucla, Hist. des Mathemat. tom. ii, p. 355. 444. Bossut, Essai sur l'Hist. Gen. des Mathenzat. tom. ii. p. 30. Athence Rauriar. Adunzbratio erudito run: Basiliensium celebrium, Athenis Rauricis addi ta, Basil, 1780, 8vo. (g)