SPACE AND GEOMETRY 



47 



A'B'. In other words, we may compare a length 

 along any one line with a length along any 

 other parallel line, but our rules so far give us 

 no information whatever as to the relative 



Figure 2 

 The Parallel Shift 



length of AB and AD. Certainly AD looks 

 longer, but our eye is trained only in Euclidean 

 methods of measurement, and we must now 

 agree to form no such judgment until we have 

 set up definite rules for the comparison of non- 

 parallel lines. 



