GEOMETRICAL AXIOMS. 35 



would be generated by a solid moving out of the space 

 we know. By the much-abused expression ' to re- 

 present 'or ' to be able to think how something 

 happens ' I understand and I do not see how any- 

 thing else can be understood by it without loss of all 

 meaning the power of imagining the whole series of 

 sensible impressions that would be had in such a case. 

 Now as no sensible impression is known relating to 

 such an unheard-of event, as the movement to a fourth 

 dimension would be to us, or as a movement to our 

 third dimension would be to the inhabitants of a 

 surface, such a ' representation ' is as impossible as 

 the ' representation ' of colours would be to one born 

 blind, if a description of them in general terms could 

 be given to him. 



Our surface-beings would also be able to draw 

 shortest lines in their superficial space. These would 

 not necessarily be straight lines in our sense, but what 

 are technically called geodetic lines of the surface on 

 which they live ; lines such as are described by a tense 

 thread laid along the surface, and which can slide upon 

 it freely. I will henceforth speak of such lines as the 

 straightest lines of any particular surface or given 

 space, so as to bring out their analogy with the 

 straight line in a plane. I hope by this expression to 

 make the conception more easy for the apprehension 



D 2 



