46 



Fine Arts, and also appointed the members of the restored Acade- 

 mies. In the Academy of Sciences, two celebrated names, those of 

 Carnot and Monge, were replaced by two new names, Breguet and 

 Cauchy. The opinion of men of science was indulgent towards 

 Breguet, but severe towards Cauchy. 



Towards the end of 1815 he was appointed Assistant-Professor of 

 Analysis at the Ecole Polytechnique ; he became titular Professor 

 in 1816. It was impossible for any man to be more zealous than 

 Cauchy in discharging the duties imposed upon him. Appointed to 

 teach, he turned all his thoughts to the art of teaching. Between 

 1816 and 1826 he published his Course of Algebraic Analysis, of 

 Differential Calculus, of the application of Infinitesimal Analysis to 

 the Theory of Curves ; three excellent works, well arranged, pro- 

 ceeding by vigorous demonstrations and rich in new details, leaving 

 nothing to be desired except perhaps a little condescension in ex- 

 plaining the abstractions of analysis by geometrical considerations. 

 In the same interval he published a memoir on integrals taken 

 between imaginary limits, which has been the foundation of import- 

 ant investigations for many of our young geometers. But even 

 this was not sufficient for his indefatigable ardour; he undertook 

 and commenced publishing, in 1826, a kind of periodical review of 

 his own, entitled ' Exercices Mathematiques,' in which every depart- 

 ment of mathematics, the most elementary as well as the highest, 

 was handled with so much generality, fertility and inventive power, 

 that on reading this publication, Abel, one of the most profound 

 analysts of our times, wrote to one of his friends, " Cauchy is, of all 

 others, the geometer who best understands how mathematics ought 

 to be studied." In fact, the discoveries of methods and the 

 sketches of new views, scattered through these 'Exercises,' have 

 been not only to the author, but also to many other geometers, 

 the fertile initiative of brilliant researches. Cauchy continued the 

 nurture and publication of this mathematical treasury up to the time 

 of his death. 



The calm flow of his existence was unexpectedly disturbed by the 

 Revolution of 1830. At this epoch he was married and the father 

 of two daughters. He had allied himself with an honourable family, 

 whose social position, tastes and sentiments were in harmony with 

 his own. Besides his Professorship at the Ecole Polytechnique, he 



