M PREFACB> 



him, and which he is, perhaps on that account, invo- 

 luntarily disposed to think more natural and satisfac- 

 tory, he has extracted, from his own former publica- 

 tions^ such parts as he has felt himself compelled to 

 substitute for Mr. Laplace's introductory investiga- 

 tions, but without omitting, as collateral illustrations, 

 such of Mr. Laplace's demonstrations as appear to be 

 the most ingenious and satisfactoiy. In these earlier 

 parts, he has found it most convenient to adopt the 

 order and arrangement of his own elementary works, 

 inserting any of Mr. Laplace's remarks in the form 

 of Scholia or otherwise : but in the principal part of 

 the book he has followed the order of the original 

 sections, introducing any additions of his own in the 

 form of Lemmas or Scholia, besides the explanatory 

 remarks, and details of demonstration, which are dis- 

 tinguished by being included in crotchets. The text 

 is, however, throughout the whole, divided into dis- 

 tinct propositions, enunciated at the beginning of each 

 investigation, which is perhaps a departure from a 

 strict analytical order, but which affords the memory, 

 as well as the apprehension of the student, a very 

 material advantage. The steps required for each 

 demonstration are filled up by a recurrence to the 

 fundamental principles of mathematics and mecha- 

 nics, without reference to any other introductory work, 

 which indeed would have been insufficient for the 

 information of the mere English reader : but these 

 summary demonstrations must not be understood as 



