Mv. T. S. Davies on Geometry and Geometers. 289 



the proposition may be ; but if be be asked why be employed some 

 particular method, or how he knew it would answer bis purpose, 

 he can give no other reason than tbat be "knew" (or be 

 "thought," or he "perceived") that it would be effective. It 

 thus gives to his processes the appearance of being the result of 

 mere tact or quickness of perception ; and tends to support the 

 view, that geometry, even in the hands of its best cultivators, is 

 only a system of expedients, that rather requires rapidity of 

 apprehension than profundity of intellect. The vanity too of 

 men who set a high value on present reputation, rather than on 

 great efforts, is gratified by this character for " quickness" and 

 "cleverness;" and instead of admitting that they are governed 

 by certain principles (though perhaps seldom or never enun- 

 ciated, even to themselves), they allow an erroneous opinion to 

 exist uncontradicted and unquestioned. In many cases, bow- 

 ever, these men have acquired the use of principles from long 

 habit in the imitative processes, without ever having attempted 

 to enunciate them in words, or to reflect further upon the pro- 

 cesses to which they apply than to the special case immediately 

 before them. I have known men eminently skilful in the use of 

 the geometrical analysis, who were yet unable to give the least 

 explanation of the principle on which it is based, or of the rules 

 that governed them in the employment of the method. All they 

 could tell me was, that it "answered the purpose admirably;" 

 and more than this they knew not, nor cared to know. When 

 I asked how I must proceed to acquire this knowledge and its 

 concomitant power, the answer was, "study good examples." 

 Upon this resource I was thrown, and it certainly was effective. 

 Tbe little tract of Lawson and the second volume of Leslie's 

 Geometry were of some use; but in looking back upon that 

 period when I did first study it, I have often regretted that some 

 work more adapted to the wants of the student, and in direct 

 illustration of the principles, has not been supplied. 



The student has within the last three years, however, been 

 placed in a considerably better position for tbe study of the geo- 

 metrical analysis, by Mr. Potts's Appendix to his 8vo Euclid, 

 1847. The attempt to comprise under one enunciation a de- 

 scription of the analysis of theorems and problems has been 

 abandoned, and the nature of the process is, in both cases, ren- 

 dered intelligible. They arc indeed so different in their cha- 

 racter and details, that when we sec the effect of their separation, 

 we can only wonder that they should have ever been united*. 



* In confirmation of the vagueness with which ordinary writers express 

 their \ i. us on this subject, I cony the following from a work of considerable 

 mathematical pretensions, published only about seven years ago :— " Ana- 

 Ijftit, or the Analytic Method, is that by which a remote truth is discovered 



Phil May. S. 1. Vol. 3. No. 18. April 1852. U 



