PREFACE. XI 



erudition of his contemporaries would be sufficient to prevent 

 them from ascribing to himself more than was justly due. 



It will be seen that I have ventured to survey a very extensive 

 field of mathematical research. It has been mv aim to estimate 

 carefully and impartially the character and the merit of tlie 

 numerous memoirs and works which I have examined; my criti- 

 cism has been intentionally close and searching, but I trust never 

 irreverent nor unjust. I have sometimes explained fully the 

 errors which I detected; sometimes, when the detailed exposition 

 of the error would have recpiired more space than the matter 

 deserved, I have given only a brief indication which may be 

 serviceable to a student of the original production itself I have 

 not hesitated to introduce remarks and developments of my 

 own whenever the subject seemed to require them. In an 

 elaborate German review of my former puljlication on mathe- 

 matical history it was suggested that my own contributions were 

 too prominent, and that the purely historical character of the 

 work was thereby impaired; but I have not been induced to 

 change my plan, for I continue to think that such additions as I 

 have been able to make tend to render the subject more in- 

 telligible and more complete, without disturbing in any serious 

 degree the continuity of the history. I cannot venture to expect 

 that in such a difficult subject I shall be quite free from error 

 either in my exposition of the labours of others, or in my own 

 contributions; but I hope that such failures will not be numerous 

 nor important. I shall receive most gratefully intimations of any 

 errors or omissions whicli may be detected in the work. 



I have been careful to corroborate mv statements bv exact 

 quotations from the originals, and these I have given in the lan- 

 guages in which they were published, instead of translating them ; 

 the course which I have here adopted is I understand more agree- 

 able to foreign students into whose hands the book may fall. I 

 have been careful to preserve the historical notices and references 

 which occurred in the works I studied ; and by the aid of the 

 Table of Contents, the Chronological List, and the Index, which 

 accompany the present volume, it will be easy to ascertain with 

 regard to any proposed mathematician down to the close of the 

 eighteenth century, whether he has written au}'thing upon the 

 Theory of Probability. 



I have carried the history down to the close of the eighteenth 

 century ; in the case of Laplace, however, I have passed beyond this 

 limit: but by far the larger part of his labours on the Theory of 

 Probability were accomplished during tlie eighteenth century, 

 though collected and republished by him in his celebrated work in 

 the early part of the present century, and it was therefore conve- 



