34 DYNAMICAL PRINCIPLE. 



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 de- 

 rives from his researches is of a pure and also of a lively 

 kind, whether he contemplates the truths discovered 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 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 independent of 

 accident ; his reliance is on his own powers ; doubt and con- 

 testation 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 con- 

 sequences as of all opposition, he is entire master of his con- 

 clusions as of his operations ; and feels even perfectly 

 indifferent to the acceptance or rejection of his doctrines, 

 because he confidently looks forward to their universal and 

 immediate admission the moment they are comprehended. 



It is to be further borne in mind, that from the labours of 

 the Geometrician are derived the most important assistance to 

 the researches of other philosophers, and to the perfection of the 

 most iiseful arts. This consideration resolves itself into two : 

 one is the pleasure of contemplation, and consequently is an 

 addition to the gratificatien of exactly the same kind, derived 

 immediately from the contemplation of pure mathematical 

 truth ; much, indeed, of the mixed mathematics is also purely 

 mathematical investigation, built upon premises derived from 

 induction. The other gratification is of a wholly different 

 description ; it is connected merely with the promotion of 

 arts subservient to the ordinary enjoyments of life. This is 

 nly a secondary and mixed use of science to the philosopher ; 



