482 



BERNOULLI. 



Bernoulli, 

 John. 



and have been collected and published in two volumes, 

 4to, at Geneva in 1744. The papers which he pub- 

 lished in the memoirs of the academy, are, 1st, Sec- 

 tion indefmie des Arcs Ciradaires, en telle raison 

 nu'on voudra, avec la mnniere d'en dedidre les Sinus, 

 &c. Mem. Acad. 1702, p. 58. 2d, Demonstration 

 Generate du centre de Balancement, on d'oscillation, 

 tirie de la Nature du Lcvier, Id. 1703, p. 1 14-. 3d, 

 Application de sa regie du Centre de lialancement, 

 atoutes sortes de figures, Id. 4th, Demonstration 

 du Principe de M. "Huygens, touchant le Centre de 

 Balancement, et de I'ldentite de ce Centre avec eclui 

 de Percussion, Mem. Acad. 1704. 5th, Veritable 

 Hypolhese de la Resistance des Solides, avec la De- 

 monstration de la courbure des Corps, qui font res- 

 sort. Mem. Acad. p. 130. 



Besides these he 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 Scavans, some of which 

 had appeared in the Acta Eruditorum. See CEuvres 

 de Fontenelks, torn. v. p. 57. edit. 1767. General 

 Diet. Lalande, Bibliographie Astronomique, p. 299. 

 Montucla, Hist, des Mathemat. torn. ii. p. 355. 444. 

 Bossut, Essai sur I' Hist. Gen. des Mathemat. torn. 

 ii. p. 30. Athenae Rauricce. Adumbratio erudito- 

 rum Basiliensium celebrium, Athenis Rauricis addi- 

 ta, Basil, 1780, 8vo. (/3) 



BERNOULLI, John, the tenth son of Nicholas 

 Bernoulli, and the brother of James Bernoulli, was 

 born at Basle, in Switzerland, on the 27th of July, 

 O. S. 1667. In the year 1682 he began his acade- 

 mical studies, and was soon afterwards sent to Neuf- 

 chatel, to prepare himself for those commercial pur- 

 suits for which he was intended by his father. The 

 early developement of his brilliant talents, seconded 

 by an ardent thirst for knowledge, gave a new direc- 

 tion to his father's plans, who henceforth determined 

 to form the mind of his son for those noble pursuits 

 in which nature had destined him to engage. He 

 was received master of arts at the age of eighteen ; 

 and on this occasion he defended a Latin thesis, De 

 igni lambente, and likewise a thesis in Greek verse. 

 The study of medicine now occupied his attention ; 

 but though he prosecuted this subject to such a 

 length as to compose and defend in public a thesis De 

 effetvescentia et fermentatione, in 1690, his mind was 

 gradually turning to that sublime science, in which 

 hia brother had already acquired such distinguished 

 fame. Under the guidance of that illustrious mathe- 

 matician, he made rapid advances in the higher geome- 

 try, and was soon enabled to illustrate the new calcu- 

 lus which Newton and Leibnitz had discovered. 

 About the end of the year 1690, John Bernoulli set 

 out for Geneva ; and, in the course of his journey, 

 he nearly lost his life by a dangerous fall from his 

 horse. In that seat of learning, he formed an inti- 

 macy with many of its most distinguished citizens, 

 and particularly with Messrs Fatio, who were then 

 celebrated for their mathematical acquirements. From 

 Geneva he went to France ; and having reached Pa- 

 ris about the year 1691, he was introduced to the 

 Marquis de L'Hospital, Malebranche, De la Hire, 

 Yarignon, and the two Cassmis. He spent some 



time at the country house of the Marquis de L'Ho3. Bernoulli, 

 pital near Blois, and such was the friendship which 

 subsisted between them, that he instructed his host in 

 the differential calculus, ainl composed for ha 

 Lecons de Calcul differential et integral, which is 

 published in the third volume of his works. Varig- 

 non was likewise initiated into the new geometry by 

 the Swiss mathematician ; who soon enjoyed the sa- 

 tisfaction of seeing these distinguished pupils ranked 

 among the first analysts of the age. In the year 

 1692, he returned to his native country, where the 

 loss of the brilliant society of Paris was compen- 

 sated by a constant correspondence with Leibnitz, 

 which continued till the death of the latter in 1716. 

 Being about to enter into a matrimonial connection, he 

 was prevented by this and other causes from accepting 

 the professorship of mathematics at Wolfenbuttle, 

 which was offered him in 1693. The decree of doctor 

 of medicine was about thjs time conferred upon him, 

 after having defended a thesis on muscular motion. 

 His marriage took place on the 6th March, 1694 ; 

 and, in obedience to the solicitations of the university 

 of Groningen, in 1695, he accepted the professorship 

 of experimental philosophy, in which he was installed 

 on the 28th of November. In this new situation his 

 fame began to extend itself with unusual rapidity. 

 The learned societies of Europe were proud to adorn 

 their lists with his name, and sovereigns themselves 

 felt an accession to their greatness by honouring him 

 with marks of royal favour. He was elected a fo- 

 reign associate of the Academy of Sciences at Paris 

 in 1699, along with his brother. The Academy at 

 Berlin chose him a member in 1701. He was intro- 

 duced into the Royal Society of London in 1712; 

 into the Institute of Bologna in 1724 ; and into the 

 Imperial Academy of Sciences at St Petersburgh in 

 1725. His invention of the luminous barometer, or 

 of the mercurial phosphorus, arising from the friction 

 of mercury upon glass in a partial vacuum, was shewn 

 by Leibnitz to Frederick I. of Prussia, who present- 

 ed Bernoulli with a golden medal of the weight of 

 forty ducats. 



In 1691, John Bernoulli solved the problem of the 

 catenary curve along with Leibnitz and Huygens, 

 though it is generally supposed, that this solutioi; 

 was partly the work of his brother. In 1697, he 

 published his first essays on a new branch of analysis, 

 to which he gave the name of the Exponential Calcu- 

 lus, which consists in differencing and integrating ex- 

 ponential quantities, or powers, with variable expo- 

 nents. Leibnitz and John Bernoulli made this import- 

 ant discovery, without any communication, in 1694; 

 but wet' are indebted to Bernoulli for a complete ex- 

 planation of the rules of the calculus, and the pur. 

 poses to which it might be applied. About the 

 same time, he directed the attention of mathemati- 

 cians to the celebrated problem of the brachystochro- 

 7i07i, which consisted in finding the curve, along the 

 concave side of which a heavy body would descend 

 from one point to another in the least time possible, 

 the line joining the two points being inclined to the 

 direction of gravity. This difficult problem, which 

 Bernoulli himself had solved, was also resolved by 

 Leibnitz on the very day on which he received it. 

 These two mathematicians determined to conceal their 



