258 Royal Society: Anniversary 1841: Obituary Notices. 



The prize proposed by the same Academy in 1786, was adjudi- 

 cated to liim for a memoir, which was since published under the 

 title of Exposition elementnire cles principes des catculs superieurs. 

 In this masterly essay the dift'erential calculus is derived from a prin- 

 ciple which D'Alembert had, in the first edition of the Encyclo- 

 pedie, so happily illustrated, and which is now so generally recog- 

 nised as the basis of that calculus; namely, the doctrine of limits. 



On his return to Geneva in 1789, fHuillier published an opus- 

 cle, which acquired great celebrity, entitled Lm Polygonometrie ; 

 ou de la mesiirc des Jigures rectilignes, et abrege d'isoperimetrie ele- 

 mentuire, ou de la depeiidance imituelle des grandeurs et des limites 

 des figures; at the conclusion of which he gives a masterly sum- 

 mary of his former researches on elementary isoperimotry. In this 

 work are given several formula? of great generality, and which, at 

 that time, were entirely new, and were calculated to facilitate the 

 study of numerous relations arising from the nerimeters and areas of 

 polygons. About the same period, indeed, Mascheroni published 

 formulae very analogous to those of I'Huillier ; but the latter after- 

 wards succeeded in showing that he liad arrived at the same results 

 by original processes. 



During the tempestuous years of the revolution, I'Huillier sought 

 in Germany the retirement so necessary to his pursuits ; and chose 

 Tubingen as his residence. The fruit of his labours during this 

 seclusion was a work almost wholly new, Avhich appeared at Tubin- 

 gen, in 1795, under the title Principiorum calculi dijferentialis et 

 integralis expositio eleinentaris. 



He was invited, about this time, to the chair of the Higher Ma- 

 thematics in the University of Leyden ; but his attachment to his 

 native country was too deeply rooted to admit of his accepting this 

 flattering ofler: and eventually, in June of the same year (1795), 

 he attained the object of his highest ambition, by receiving, after 

 a successful public competition, the appointment of Professor of 

 Mathematics in the Academy of Geneva. 



At a subsequent period he was associated with his friend and col- 

 league Professor Prevost in the composition of several memoirs on 

 the calculation of probabilities, which appeared under their joint 

 names in the memoirs of the Berlin Academy. The questions 

 treated of in these memoirs, although they do not reach the higher 

 pi'oblems belonging to this department of mathematics, are yet re- 

 solved by methods remarkable for their perspicuity and elegance. 

 L'Huillier published, in 1 8G 1, \\\sEleme7ts raisounes d'Algebre, publics 

 d Vusage des etudians ; in 2 vols. 8vo, a work of considerable merit, 

 as developing with clearness the true principles by which the under- 

 standing advances from that which is known to thatwhich is unknown. 



His last work, the Elhnens d' Analyse Geometrique et Algebrique, 

 appliquees a la recherche des lietix geometriqtics, in 4to, appeared in 

 the year 1 809. It was dedicated to his former pupil, Prince Czar- 

 torynski, who was, at that time, minister of public instruction in the 

 vast empire of Russia, but who has since become better known to 

 Europe as the most illustrious of the exiled Poles. 



