384 D'ALEMBEET. 



control. He seeks the aid of no assistant, requires the 

 use of no apparatus, hardly wants any books ; and with 

 the fullest reliance on the perfect instruments of his 

 operations, and on the altogether certain nature of his 

 results, he is quite assured that the truths which he 

 has found out, though they may lay the foundation of 

 further discovery, can never by possibility be dis- 

 proved, nor his reasonings upon them shaken, by all 

 the progress that the science can make to the very end 

 of time. 



The life of the geometrician, then, may well be sup- 

 posed an uninterrupted calm; and the gratification which 

 he derives from his researches is of a pure and also of 

 a lively kind, whether he contemplates the truths dis- 

 covered by others, with the demonstrative evidence on 

 which they rest, or carries the science further, and 

 himself adds to the number of the interesting truths 

 before known. He may be often stopped in his re- 

 searches by the difficulties that beset his path ; he 

 may be frustrated in his attempts to discover relations 

 depending on complicated data which he cannot un- 

 ravel or reconcile ; but his study is wholly indepen- 

 dent of accident ; his reliance is on his own powers ; 

 doubt and contestation and uncertainty he never can 

 know ; a stranger to all controversy, above all mys- 

 tery, he possesses his mind in unruffled peace ; bound 

 by no authority, regardless of all consequences as of 

 all opposition, he is entire master of his conclusions 

 as of his operations ; and feels even perfectly indif- 

 ferent to the acceptance or rejection of his doctrines, 

 because he confidently looks forward to their univer- 

 sal and immediate admission the moment they are 

 comprehended. 



It is to be further borne in mind, that from the la- 

 bours of the geometrician are derived the most impor- 

 tant assistance to the researches of other philosophers, 

 and to the perfection of the most useful arts. This 

 consideration resolves itself into two : one is the plea- 



