Chapter I: JACQUES BERNOULLI (1654-1705), mathematician, was born at Basel on

the 27th of December 1654. He was educated at the public school of Basel, and also received private instruction from the learned Hoffmann, then professor of Greek. At the conclusion of his philosophical studies at the university, some geometrical figures, which fell in his way, excited in him a passion for mathematical pursuits, and in spite of the opposition of his father, who wished him to be a clergyman, he applied himself in secret to his favourite science. In 1676 he visited Geneva on his way to France, and subsequently travelled to England and Holland. While at Geneva he taught a 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 Bordeaux his _Universal Tables on Dialling_ were constructed; and in London he was admitted to the meetings of Robert Boyle, Robert Hooke and other learned and scientific men. On his final return to Basel in 1682, he devoted himself to physical and mathematical investigations, and opened a public seminary for experimental physics. In the same year he published his essay on comets, _Conamen Novi Systematis Cometarum_, which was occasioned by the appearance of the comet of 1680. This essay, and his next publication, entitled _De Gravitate Aetheris_, were deeply tinged with the philosophy of Rene Descartes, but they contain truths not unworthy of the philosophy of Sir Isaac Newton's _Principia_.

Jacques Bernoulli cannot be strictly called an independent discoverer; but, from his extensive and successful application of the calculus and other mathematical methods, he is deserving of a place by the side of Newton and Leibnitz. As an additional claim to remembrance, he was the first to solve Leibnitz's problem of the isochronous curve (_Acta Eruditorum_, 1690). He proposed the problem of the catenary (q.v.) or curve formed by a chain suspended by its two extremities, accepted Leibnitz's construction of the curve and solved more complicated problems relating to it. He determined the "elastic curve," which is formed by an elastic plate or rod fixed at one end and bent by a weight applied to the other, and which he showed to be the same as the curvature of an impervious sail filled with a liquid (_lintearia_). In his investigations respecting cycloidal lines and various spiral curves, his attention was directed to the loxodromic and logarithmic spirals, in the last of which he took particular interest from its remarkable property of reproducing itself under a variety of conditions.

In 1696 he proposed the famous problem of isoperimetrical figures, and offered a reward for its solution. This problem engaged the attention of British as well as continental mathematicians; and its proposal gave rise to a painful quarrel with his 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 accepted by the marquis de l'Hopital and Leibnitz. Jean, however, held his peace for several years, and then dishonestly published, after the death of Jacques, another incorrect solution; and not until 1718 did he admit that he had been in error. Even then he set forth as his own his brother's solution purposely disguised.

In 1687 the mathematical chair of the university of Basel was conferred upon Jacques. He was once made rector of his university, and had other distinctions bestowed on him. He and his brother Jean were the first two foreign associates of the Academy of Sciences of Paris; and, at the request of Leibnitz, they were both received as members of the academy of Berlin. In 1684 he had been offered a professorship at Heidelberg; but his marriage with a lady of his native city led him to decline the invitation. Intense application brought on infirmities and a slow fever, of which he died on the 16th of August 1705. Like another 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, German and French;
but although these were held in high estimation in his own time, it is
on his mathematical works that his fame now rests. These are:--_Jacobi
Bernoulli Basiliensis Opera_ (Genevae, 1744), 2 tom. 4to; _Ars
Conjectandi, opus posthumum: accedunt tractatus de Seriebus Infinitis,
et epistola (Gallice scripta) de Ludo Pilae Reticularis_ (Basiliae,
1713), 1 tom. 4to.