52 



THE ANATOMY OF SCIENCE 



of two non-parallel lines. Since in our trans- 

 formation OA goes into OB and OB into OC, we 

 must say that A, B and C are equidistant from 

 O. Thus we lay down the rules of a geometry 

 which is as simple and beautiful as the geometry 



Figure 6 

 The Three Types of Rotation 



of Euclid, and which has such important appli- 

 cations that we may before long see this geome- 

 tr}^ taught by the side of Euclid in our schools. 

 Finally, we may set up rules for a third flat 

 geometry in which the curve of rotation is 

 neither circular nor asymptotic, but merely a 

 straight line. The three types of curves of rota- 

 tion are showTi in Figure 6. The new kind of 

 rotation corresponds to what physicists call a 



