Notices respeclmg Nexo Books. 529 



bring number into the domain of mathematics. Its " precision " con- 

 sists in suggesting an erroneous idea of the essential character of 

 one-half of mathematical science, and never at all refemng to the 

 other half. The idea of " measure " is never brought under any 

 aspect into theoretical geometry, such as that of Euclid ; all idea of 

 number (and hence of algebra) is excluded from mathematics in this 

 definition ; and it is not true that we actually measure all the quan- 

 tities that become the subjects of mathematical investigation — as 

 forces, heat, &c. 



Def. 2. "Geometry is a branch of mathematics which treats of 

 that species of quantity called magnitude." 



Here again the "precision" depends upon the definition oi mag- 

 nitude : whilst its conciseness consists of the needless interpolations 

 of the "branch" and the " si)ecies of quantity;" and of the total 

 omission of two out of three of the essential characters of geometrical 

 magnitude, species and position. 



Def. 3 . "Magnitudes are of one, two, or three dimensions ; as lines, 

 surfaces and solids. They have no material existence, but they may 

 be represented by diagrams." 



The first part of this is " concise " enough certainly ; of its " pre- 

 cision " we must leave our readers to judge, keeping in mind that 

 the term " dimension " has not been defined. 



Respecting the latter part, we scarcely see how the statement of 

 " mathematics treating of measurable quantities," and this branch 

 of mathematics treating of things which have " no material exist- 

 ence," are to be considered as " tending to precision of geometrical 

 language," or even to precision of idea. Neither do we understand 

 the precision of the language which tells us that immaterial exist- 

 ences may be " represented by diagrams." It seems not altogether 

 unlike a ghost upon canvass. 



Def. 4. "That branch of geometry which refers to magnitudes 

 described upon a plane, is called Plane Geometry." 



Indeed ! What, then, did the ancients call a " a solid problem ? " 

 In our own simplicity, we have always believed that plane geometry 

 was the geometry which involved only the straight line and circle ; 

 and that every problem which involved any other curve than the 

 circle was called a solid problem. AVe have never till now heard 

 that the conic sections (to say nothing of the higher classes of curves, 

 transcendental and all) were comprised by geometers in plane geo- 

 metry. Were we to admit that Mr. Bell had any right to change 

 the signification of a term so universally employed in one sense to 

 suit his penchant for " improvement," we should still consider his re- 

 jiresentation of his own being the usual meaning, as a discreditable 

 imposition upon his readers. 



Mr. Bell's definition of a point is that of Professor Jardine, first 

 published by Playfair. It has been much eulogised : but we are not 

 disposed to discuss it here. We may, however, state that we con- 

 sider the definition of Euclid to be more in keeping with Euclid's 

 general idea of his own system than the amended one. We would 

 onlv suggest that this definition harmonizes but strangely witii Mr. 



Phil. Mag. S. 3. No. 2 18. Suppl. Vol. '.VI. 2 M 



