528 Notices respecting New Books. 



the essential principles of geometrical logic. We may indeed say of 

 it, " whatever is good is not new, and whatever is new is not good." 

 Even when he appropriates an idea, he mangles it in the expression ; 

 as for instance in his remarks upon " mathematical taste " (Pref. xi.), 

 taken from Lawson, or his description of " Analysis" (p. 205), imi- 

 tated from Leslie. Nor are his appropriations of particular processes 

 of demonstration materially different in their characteristic features. 



Supposing, iiowever, that we divest this edition of all its super- 

 fluities, and view it as a hare treatise on Geometry, we do not deem 

 it a safe one to follow, inasmuch as the author having adventured 

 upon changes in the text, and finding in his addenda the most un- 

 questionable evidences of his heterodoxy in respect to the principles 

 of geometry, we should feel no confidence (without an entire collation 

 and careful examination of all the steps) that some of the " improve- 

 ments" which would invalidate the argument had not been made 

 even here. The price we know is a temptation to schoolmasters ; 

 but he who adopts this edition without complete assurance of its 

 not being vitiated, is false to the trust reposed in him. We express 

 no decided opinion as to the extent to which Mr. Bell has carried his 

 " improvements " of the general text, though we could quote a few 

 instances of such that we think ought to open the eyes of even offi- 

 cial personages. We will rather turn, then, to the parts which are 

 professedly Mr. Bell's own contributions to Geometiy ; and we do 

 it in confidence of showing that this gentleman and his employers 

 were alike incompetent to presume upon any " imjirovements" upon 

 the Elements of Euclid — at least if the most complete ignorance of 

 the ordinary terms of geometrical science be any proof. 



First, then, his definitions. There grew up with the renovated 

 science of the mediaeval period, a practice of seeming to be systematic; 

 and this was especially evinced by an attem])t to define every term. 

 Thus, mathematics, geometry, algebra, mechanics, and every other 

 branch of science was described by some circumlocutory phrases ; 

 and this was called " definition ! " Such definitions are vicious : they^ 

 are always either defective from their involving terms that have them- 

 selves not been defined, or insignificant from their not expressing 

 the defined subject at all. The usual definition of mechanics falls 

 under the first head, from its involving the word "force;" and that 

 of geometry under the second, from its conveying no descriptive idea 

 whatever. Archimedes, we believe, attempted no definition of me- 

 chanics ; and Euclid, we are sure, attempted none of geometry. 

 Mr. Bell's " improvements," however, do not go to the exclusion of 

 such inane practices from our books, but to the "addition of many 

 useful definitions." Let us see how far a few of these fulfill his pro- 

 mise — that they " tend to improve the language of geometry in re- 

 spect to conciseness and precision." 



Def. 1. "Mathematics is that branch of science which treats of 

 Measurable Quantity." 



Now the " conciseness " of this passage consists of two counter- 

 parts : — the interpolation of the metaphorical term '• branch," which 

 is altogether superfluous, and the elision of the term that would 



