purpose of discipline, has not so much occasion for the con- ^ 



chision as the premises; in this intellectual chace, it is not 

 the possession of the prey, but the invigoration of our own 

 powers, that should be the primary object. It is evident to 

 every one that this end is not so happily attained by the 

 analytic metliods so much; in use at present, as by the an- 

 cient geometry. For the youth who is destined to be a mere 

 mathematician, algebra offers, in general, an eas}' and com- 

 pendious mode of advancing in knowledge, but his know- 

 ledge is not philosophy, it is not (to borrow a logical defini- 

 tion) ** acquired by the sole force of reason." Were it ne- 

 cessary to insist on this, it would be easy to illustrate it by 

 a comparison of^ the truths contained in the 2d book of 

 Euclid, as treated by that geometer, and as they would be 

 by an analyst, or b}' remarking the dift'erence between a de- 

 monstration, as it is handled by Hamilton, and by Emerson 

 or L'Hospital ; and perhaps still more strongly by observing, 

 that mere characters, of whose meaning no one has or ever 

 can have any conception, (they being supposed the marks of 

 inconsistent notions, as the very name, "impossible quan- 

 tity," denotes,) are as proper objects of analytical compu- 

 tation, except in the mechanical difficulty of managing them, 

 as real and adequate ideas. 



Again it may be prejudicial to the imagination to enter 

 with minute accuracy into any scientific enquiry. He Avho 

 has been too long habituated to the consideration of abstruse 

 metaphysical enquiries, the patient investigation of mathe- 



