48 THE ANATOMY OF SCIENCE 



In the meantime, if we had the time, we might 

 develop the full geometry of the parallel postu- 

 late and the associated parallel transformation, 

 and thus obtain a large number of theorems 

 regarding triangles and parallelograms which 

 are to be found in the geometry of Euclid, but 

 which are also contained in the other flat geome- 

 tries which I am going to describe. 



Figure 3 

 Parallel Ruler and Compass 



The theorems of which I have just spoken 

 are only a part, however, of the geometry of 

 Euclid; the rest depend upon the circular pos- 

 tulate and the associated transformation, which 

 is called a rotation. The two transformations of 

 Euclidean geometry may be carried out by 

 means of the two instruments sho\^Ti in Figure 

 3. The one on the left is the parallel ruler made 

 of four rods hinged together; the one on the 



