Notices respecting Ne-do Books. 533 



or that the leading terms refer to the problem and the subsequent to 

 the theorem : — both being propositions. 'J'he first supj)osition is 

 too novel a mode of interpretation, we should suj)pose, even for 

 Mr. Bell in his rage for " improvements in conciseness and precision :" 

 and we will, for the sake of trying to make something out of it, se- 

 parate the definition into its two cases. 



" The rfa^a of a problem are the I "The premises of a theorem 



relations granted, from which nev/ I are the conditions given, from 



relations are to be deduced." which a construction is to be 



I effected." 



Was there ever such monstrous absurdity i)almed upon a govern- 

 ment, and that government call it geometry ? But this is not all : 

 though we must hasten forward. 



" Synthetic geonietrt/, or the ordinary didactic metliod, affords in the gra- 

 dual exposition of geometrical truth, excellent specimens cf the most clear 

 and satisfactory reasoning; and that branch (if it called geometrical analysis, 

 affords, in addition, examples of the resolution of truth into its simple elemen- 

 tary principles. But analytical geometry and the other analytical branches of 

 the science sup()ly the best examples of the resolution of comjjlex questions — ■ 

 a process which nuist be effected before the conditions can be comprised in 

 symbolical ex-jiressions ; they [who? or what .'J also accustom the mind to 

 comprehensive views, and afford excellent specimens of subtle reasoning j 

 and exercise the mind in the interpretations of the final result." — Preface, 

 p. 9. 



Geometrical analysis a " branch " of geometrical synthesis ! Why 

 not geometrical synthesis a " branch" of geometrical analysis ? Not 

 only the ancients, but the moderns without a single exception, till 

 Mr. Bell created one, have considered analysis and synthesis to be 

 co-ordinate with each other. This new " northern-light " has de- 

 creed that the ancients and moderns were alike wrong : that the term 

 synthesis shall no longer be considered to signify " composition," 

 nor analysis "resolution." D'Alembert, indeed, introduced the 

 general use of the term analysis to signify algebraic resolution, from 

 the fact, that the majority of algebraic processes was analytical ; 

 and in conformity with his view, the works in which geometry 

 was treated by means of algebra after the fashion of Des Cartes, 

 were called treatises on analytical geometry. Then Mr. Bell, who is 

 evidently as confined in his reading as he is confused in his thinking, 

 comes forward with a grand discrimination between synthetic geo- 

 metry and analytical geometry : which we venture to predict will by 

 some future Montucla eternalize his memory as a splendid instance of 

 ignorant temerity and impudent self-sufficiency. The entire para- 

 graph is one tissue of blunders and mis-statements, that would be 

 unpardonable in a mere boy who had received a respectable course 

 of elementary mathematical instruction. Nor does his description of 

 geometrical analysis in the body of the work itself at all redeem him 

 from the charge. 



"Def. o/" Geometrical Analysis. — In the method of Geometrical Ana- 

 lysis, the process of demonstration follows an order the reverse of that ob- 

 served in the ordinary Synthetic Metiiod. The latter method proceeds 



