590 



extension of the limits within which the geometrical division of the 

 circle had hitherto been confined ; a discovery sufficiently memorable 

 to form a great epoch in the history of the progress of geometry and 

 analysis, and to place its author, in the estimation of the few persons 

 who would appreciate its value, in the highest rank of the mathe- 

 maticians of his age. 



In dedicating his ' Disquisitiones Arithmetics ' to the Duke of 

 Brunswick, he acknowledges in very touching terms the wise and 

 liberal patronage which had not only provided for the expenses of 

 publishing his work, but also enabled him to exchange permanently 

 the humble pursuits of trade for those of science. The work itself, 

 as its author assures us, assumed many changes of form in its pro- 

 gress to maturity, as new views presented themselves from time to 

 time to his mind ; but, as is well known, the course which is fol- 

 lowed in the invention of new truths is rarely that which is most 

 favourable to clearness in their exposition, more especially when it 

 has been pursued in solitude, with little communication with other 

 minds ; whilst the peculiar terminology which he has employed in 

 the classification of numbers and their relations, and which is so 

 completely embodied in the enunciation and demonstration of nearly 

 every proposition that it can never be absent from the mind of the 

 reader, renders the study of this work so laborious and embarrassing, 

 that few persons have ever mastered its contents. Even Legendre, 

 who had written so much and so successfully on the same subject, 

 and who, in the second edition of his ' Throne des Nombres,' makes 

 the great discovery which this work contains the occasion not merely 

 of special investigation but of the most emphatic praise, complains of 

 the great difficulty of adapting its forms of exposition to his own ; 

 whilst the writers of the ' Biographic des Contemporains,' in a 

 notice of the author at a much later period, when he had established 

 many other and almost equally unquestionable claims to immortality, 

 quote an extract from a Report of a Commission of the Institute of 

 France, to whom it was referred in 1810, in which it is said, " that 

 it was impossible for them to give an idea of this work, inasmuch as 

 everything in it is new, and surpasses our comprehension even in its 

 language." The biographers then proceed to stigmatize the book 

 as full of puerilities, and refer to the success which it had obtained, 

 including its translation into two languages, as affording grounds 



