S'20 Review of the Cambridge Course of Mathematics. 



stract character, and that it is infinitely more concise, 

 which properties enable tlie calculator by a glance of the 

 eye, to comprehend all the conditions, relations and corjse- 

 (jueiices of the most complicated and bewildering enuncia- 

 tion. The learner is here, likewise, instructed in transla- 

 ting an enunciation from common to algebraic language, 

 and vice versa ; and in the nature and use of general for- 

 mulas as independent of particular problems, and as mere- 

 ly indicating operations to be performed upon numbers in 

 order to find the numerical results belonging to any prob- 

 lem whose solution is required. This, if the student has 

 vigour of mind sufficient to grasp the idea in all its extent, 

 will forever remove the difliculties arising from the general 

 and abstract nature of algebraic expressions, a difficulty 

 which must be fully overcome by him, before his path in 

 this science will be luminous, or even in a considerable 

 degree free from embarrassment. 



Our author next introduces the resolution of equations 

 of the first degree with oue in known quantity. We have 

 heard him complained of for this early introduction of equa- 

 tions, but when we reflect, that equations are involved in 

 one shape or another, even in the most simple arithmeti- 

 cal calculations, and that his early discussion of them gives 

 rise to some remaiks which throw much light upon the 

 succeeding parts, we, cannot consider his arrangement er- 

 roneous. Considering addition, subtraction, multiplica- 

 tion and division only as operations analogom to the like 

 arithmetical operations, and presenting them in a point of 

 view highly interesting, he has removed all the difficulty 

 relative to the doctrine of plus and minus quantities, which 

 is generally to beginners, so much a source of embarrass- 

 ment and discouragement. In the investiga<^ion of the 

 greatest common divisor of two expressions, his method 

 will be found far more complete than those in common 

 treatises, as must be evident to every one who will take 

 the trouble of a comparison. In particular, the artifice of 

 expunging from one of the expressions, any factor or fac- 

 tors not entering into all the terms of the other expression ; 

 and on the other hand, of introducing into one of the ex- 

 pressions, a factor not contained in all the terms of the oth- 

 er, is illustrated from the theory of multiplication in a very 

 elementary manner. These improvements in the investi- 

 gation of the greatest common divisor are the more valua- 



