BERNOULLI, JAKOB, JACQ CES, or JAMES ( 1654-1705). A celebrated mathematician. He was born at Basel. Destined by his father for a chair of theology, he early showed his prefer ence for science, and, after visiting France. Hol land. and England, he was made professor of mathematics in the University of Basel (1087). He and his younger brother, Johann (q.v.), were among the first to understand and use the new method of Leibnitz. He solved the latter's prob lem 0687) of the isochronous curve, proposed and solved the problem of the catenary, solved that of the brachistochrone proposed by Johann, contributed to the theory of isoperimetry, and, in general, was one of a famous group of prob lem solvers, including his brother, Leibnitz, and Huygens. The result of the dis putes over these problems was a serious estrange ment between his brother and himself. He was a voluminous writer, his principal works in cluding: Conamen Novi Systematis Cometarum (Amsterdam. 1682), suggested by the appearance of the comet of 1680; Dissertatio de gravitate .Etheris (Amsterdam, 1683) : and his contribu tions to the Acta Erudito•um, in one of which (May, 1690) the word 'integral.' as applied to a differential equation, is used for the first time, although Leibnitz had already used the symbol The best known of his works, Ars Conjec /and/ (1713), published posthumously (by Nicolas Bernoulli), extended the doctrine of probabilities to moral, political, and economical subjects.
In connection with the effort to prove that the number of times an event can happen in e trials lies between definite limits, Bernoulli proved the celebrated proposition, according to which "it is always possible to increase the num ber of trials till it becomes a certainty that the proportion of occurrences of the event will differ from p, its probability on a single trial, by a quantity less than any assignable." His works were published under the title Jacobi Bernoulli Basilcensis Opera, in two vol umes (Geneva, 1744). At his request, recalling the example of Archimedes (q.v.). a logarithmic spiral was engraved on his tomb, with the motto, Eadcm Mutata llesurgo: and this is still to he seen in the cloisters of the cathedral at Basel. Consult: Saalseliiitz, Forlesungen fiber die noulliqchen Zablen (Berlin, 1893) ; and Cantor, Gesehiehte der Alathenzatik (2d ed., Leipzig, 1898).