344 PROCEEDINGS OF THE AMERICAN ACADEMY 



Michel Chasles was bom at Epernon ou the 5th of Novem- 

 ber, 1793. At the age of twenty he commenced a series of investi- 

 gations upon surfaces of the second degree, which almost immediately 

 gave him an European reputation ; and for sixty years he published 

 memoirs which placed him in the foremost rank of geometers. He 

 was the last and not the least of the constellation of French geniuses 

 who have given to transcendental geometry its finest precision and 

 most elegant expression. He was a master amid such names as 

 Carnot, Monge, Meusnier, Poinsot, Dupin, Poncelet, Fresnel, Olivier^ 

 and Liouville. In his discussion of the attraction of ellipsoids, and 

 his simple and ingenious development of the theory of the electrical 

 shell, he was original in his form and mode of inquiry, and was 

 scarcely anticipated by Greene and Gauss. The immense value of 

 such researches has been recently exhibited by Maxwell, who has 

 shown that the path of integration has coincided singularly with the 

 profound ideas upon the nature of electrical action developed by Faraday. 

 There is not in the history of physical science a more interesting cor- 

 relation of thought between observation and theory, nor one more 

 worthy of the attention of philosophers. 



The labors of almost every great mathematician have been per- 

 meated by some one leading idea, which, however small it may seem 

 in its general state, has grown in the fruitful soil of an original mind 

 into a comprehensive theory. It was so with Chasles. His attempts 

 to force geometrical demonstration from the variety of cases which em- 

 barrassed the ancient geometer, and to generalize them all into a single 

 argument in a purely geometrical form, and without resort to the alge- 

 braic symbol of negation, culminated finally in his " Superior Geom- 

 etry." This department of mathematics is now cultivated to such an 

 extent, that it is endowed with a distinct chair in the fully equipped 

 university. 



By a happy rebound of his elastic mind, Chasles was led in the 

 opposite direction to the curious problem of reproducing a lost work 

 of an eminent ancient geometer. The Porisms of Euclid were con- 

 sidered to be the most original and profound of his productions, and 

 its loss was greatly regretted. All that remained was a very indis- 

 tinct account by Pappus, and a loose description of the nature of a 

 porism given by Proclus. With the exception of a happy divination 

 of the definition of a porism by Simpson, and a nice example, Chasles 

 had nothing to guide liim but his own geometrical instinct, and the 

 almost unintelligible description of Proclus. But his effort was suc- 

 cessful beyond belief, and the words of Proclus apply to it with the 



