Page:Proceedings of the Royal Society of London Vol 4.djvu/377

Rh geometrice consideratd ; seu de Maximis et Minimis pars prior ele- mentaris, and in which he treats geometrically, and with singular elegance and vigour of demonstration, all the elementary problems relating to isoperimetric figures and solids. About the same time he presented to the Academy of Berlin a memoir, which was after- wards published in its Transactions, on the minima relating to the figure of the cells of bees, a subject which he appears, in that paper, to have exhausted.

The prize proposed by the same Academy in 1786, was adjudi- cated to him for a memoir, which was since published under the title of Exposition elementaire des principes des calculs superieurs. In this masterly essay the differential 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, I'Huillier published an opus- cle, M^hich acquired great celebrity, entitled La Polygonometrie ; ou de la mesure des figures rectilignes, et abrege dHsoperimetrie ele- mentaire, ou de la dependance 7nutuelle des grandeurs et des limites des figures ; at the conclusion of which he gives a masterly sum- mary of his former researches on elementary isoperimetry. In this work are given several formulee of great genei-ality, and which, at that time, were entirely new, and were calculated to facilitate the study of numerous relations arising from the perimeters 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 had 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, which appeared at Tubin- gen, in 1795, under the title Principiorum calculi differentialis et integralis expositio elementaris.

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 offer: 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 problems belonging to this department of mathematics, are yet re- solved by methods remarkable for their perspicuity and elegance. L'Huillier published, in 1804, his Elemens raisonnes d'Algebi-e, pu- blics a Vusage des etudians ; in 2 vols. 8vo, a work of considerable