288 Mr. T. S. Davies on Geometry and Geometers. 



deductions from previously established properties. What relations 

 these new truths have to any previously known, in respect of 

 systematic classification, they know not, and they care not ; the 

 mission of these geometers is fulfilled in making the deduction, 

 and upon this they rest their hopes of distinction as geometers. 

 Yet in reality they are hut " the hewers of wood and drawers of 

 water" for geometry. They are analogous to the ingenious, but 

 unreasoning, experimenters who abound in physical science; 

 they are, to use the language of Hartsoker, the manouvrieres of 

 the philosopher, whether geometrical or physical. At the same 

 time they are as necessary in all sciences as the " hod-man" is to 

 the builder, or the "bellows-boy" to the organist; and happily 

 they are found to exist in abundance, or unhappily in such super- 

 abundance as to create the desire for a large promotion of them 

 into the order of actual philosophers. The consequence is, that 

 there already exists such an immense mass of theorems and 

 problems relating to the ancient geometry, scattered in the most 

 sibylline confusion, and without the slightest indication of con- 

 nection, that they may be deemed as useless as the unreduced 

 accumulations of an observatory ; or, indeed, worse than these, 

 for observations are so kept together that they can be reduced, 

 whilst the labour of the whole life of a geometer would not suf- 

 fice to reduce into order (both as to subject and method) the 

 accumulations of English geometry within the last hundred years. 



The mathematician who looks at these accumulations in their 

 present unreduced state, and considers them to be the end at 

 which geometry proposes to terminate, may well be excused for 

 the opinion he forms unfavourable to this form of the science. 

 Yet this is not an inherent vice of geometry ; though it may and 

 does result from the inherent mental indolence of the geometer 

 himself. He satisfies himself with the deduction, and affects to 

 consider everything which relates to classification or method as 

 " too speculative" for so able a geometer as he is ! He " leaves 

 it to the talkers who call themselves philosophers, but who 

 cannot solve problems, to amuse themselves about such triviali- 

 ties." The truth however is, in the language of an eminent living 

 philosopher, the " contest of mind" which this requires is such as 

 to transcend the powers of the great majority of men, even 

 though their problem-solving powers may be altogether un- 

 questioned. 



Nor, if the inquirer apply directly for information on the sub- 

 ject from those geometers who are the most adroit in this class 

 of deductions and constructions, does he find much to enlighten 

 him. Such a geometer will at once sit down and analyse a 

 problem or a theorem proposed to him ; and in most cases obtain 

 a solution, sometimes of considerable elegance, however complex 



