﻿16 Dr. Norman Campbell on the 



The mathematicians who have recently taken over from 

 the philosophers the task of teaching experimenters their 

 business have decided that only the mathematical science 

 is properly termed geometry. In support of their claim 

 they appeal to the authority o£ the Greeks, and thereby 

 imply that Greek geometry is mathematical and not experi- 

 mental. This implication raises questions of scientific 

 interpretation and not of mere convenience in nomenclature. 

 For the matter cannot be decided by inquiring what Euclid 

 (for example) thought he was writing about : it is admitted 

 that, as an exponent of mathematical geometry, he was 

 guilty of errors ; and, if he was capable of error, he may 

 have been wrong as to the nature of his assumptions and of 

 his arguments. If we are justified today in confining the 

 term to one study rather than another, because that term 

 was used by Euclid, it can only be on the ground that 

 Euclid's propositions and his methods of proving them are 

 closely similar to those employed today in that study. 



If this test is applied, geometry is an experimental 

 science. For whereas the Elements is utterly different 

 from anything modern mathematical geometers produce, 

 it is, judged by modern standards, quite a creditable 

 attempt at an exposition of experimental geometry. It 

 can be regarded broadly as an attempt to deduce as many 

 important laws as possible from the single assumption 

 that length, area, angle, and (less definitely) volume are 

 magnitudes, universally measurable by the methods which 

 are actually employed in experimental physics, or to which 

 the methods that are actually employed would be referred 

 if doubt arose concerning their validity. Nothing is assumed 

 but that every straight line has a length, every pair of straight 

 lines an angle, and every plane surface an area. The 

 definitions, axioms, and postulates should then be state- 

 ments of the laws by virtue of which measurement is 

 possible. It is admitted that the attempt is not wholly 

 successful ; but its faults, or many of them, are readily 

 explicable : the author has not to be represented (as he 

 must be if he is an exponent of the mathematical science) 

 as constantly straining at gnats and swallowing camels. 



Such a view can be established only by a detailed and 

 tedious criticism which, in so far as it concerns Euclid's 

 intelligence, is not of scientific interest. In place of it 

 will be offered a very summary sketch of the fundamental 

 notions and laws of experimental geometry and sufficient 

 comparison of them with Euclid's assumptions to suggest 

 that on them might be founded a deduction, by methods 



