392 D'ALEMBERT. 



tirely on himself; he is absolute master of his materials; 

 his whole investigations are conducted at his own good 

 pleasure, and under his own absolute and undivided con- 

 trol. 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 disproved, 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 

 supposed 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 discovered by others, with the demonstra- 

 tive evidence on which they rest, or carries the science 

 further, and himself adds to the number of the inter- 

 esting truths before known. He may be often stopped 

 in his researches by the difficulties that beset his 

 path; he may be frustrated in his attempts to discover 

 relations depending on complicated data which he cannot 

 unravel 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 mystery, 

 he possesses his mind in unruffled peace; bound by no 

 authority, regardless of all consequences as of all opposi- 



grand gcometre," is a phrase now universally understood and ap- 

 plied to mathematicians of every description. 



