54 THE ANATOMY OF SCIENCE 



tries ; but there are a few characteristics of the 

 two flat geometries to which I shall find it neces- 

 sary to refer in subsequent chapters. Therefore, 

 without giving any proofs, I should like to de- 

 scribe a few more of the interesting features of 

 these geometries. 



X 



\ 



Figure 7 



Rotation of Perpendicular Lines in the 

 Three Geometries 



I have already shown the general characteris- 

 tics of rotation in the three geometries; let us 

 see what happens to a pair of perpendicular 

 lines in these three kinds of rotation. In Figure 

 7 we see on the left the Euclidean case, in which 

 OX and OY change into OX' and 0Y\ In the 

 middle is the shear rotation, in which only one 

 of the perpendiculars is changed in direction 

 by the rotation, but in accordance with our 

 rules we must still say that if OX is perpendicu- 

 lar to OY, OX' is also perpendicular to OY'. 



