Jieviewofthe Cambridge Course of Mathematics. 309 



ry proposition in Geometry, and every principle in Alge- 

 bra ; still he may be indebted to these sciences learned in 

 early life, for no small part of his skill in separating error 

 from truth, for his power of fixed attention, for his caution 

 in admitting proof and in drawing conclusions, for the £,ene- 

 ral discipline of his mental faculties, and his capacity for ar- 

 ranging all the parts of a long argument, so that it may re- 

 sult in the clear establishment of the desired truth. Such 

 a habit of mind constitutes tnie leamimx, a rare acquire- 

 ment; and ought to be the ultimate object of ^very system 

 of education It is capable of application to every subject, 

 at all times, and in every situation. VVithoLit the accomplish- 

 ment of this object, no education can be in a considera'ile 

 degree complete, much less can the mind be highly cultiva- 

 ted. 



It may be interesting to know the views of Lacroix in 

 composing his course, and the principles by which be was 

 guided. " Having been from early life," says he,* (Essais 

 sur I'enseignement, p, 171,) " engaged in the labours of in- 

 struction, I always turned my attention upon the means of 

 presenting the I'esults of science by the most simple meth- 

 ods, (par lesfaces les plus simples,) and in themost natural or- 

 der. With this view, I originally conceived the design of 

 embodying in a series of volumes, all the materials of Ge- 

 ometry and of the transcendant analysis. Called to the 

 functions of a professorship, which before I had perform- 

 ed only in schools, in v.'hich the form and matter of the in- 

 struction were rigorously fixed, and that of the Central 

 Schools being left entirely at the disposition of the master, 

 I was led by this Hberty to reflect upon the means of per- 

 fecting the course which had been entrusted to me. I 

 tried experimentally, upon a numerous class, (auditoire) the 

 principles and the methods which I hid conceived ; their 

 application served to confirm them, or sometimes n odified 

 them for the belter." 



Again, " teaching the sciences," says he,* (idem p. 173) 

 '^ is subject to the same rules as that of the arts; the choice 

 of examples is much more important than their numbers, a 

 few truths thoroughly investigated, throw mu. h more i ght 

 upon the true method o^ procedure, than a great number 

 of theories discussed in an incomplete manner. The first 

 cast their roots deep, which cannot fail to spread themselves, 



40. 



