613 



from which the property is inferred : 



III. I7i the proposition made in formulating II the projection of 

 a geodetic line by means of Q spaces on a P space^ or vice versa, 

 is, as far as existent, a geodetic one itself. 



If two points A and B are situated in a P space P^, the pro- 

 jections of these points on all spaces coincide. Hence the projections 

 on a Q space of the line AB geodetic in A„ passes twice through 

 the same point, being at the same time geodetic in Q, which is only 

 possible when that projection has degenerated into a point. But 

 then the geodetic line AB must be situated altogether in a P space, 

 e.g. in the present case in P■^. 



Hence any geodetic line, having two points in common with a 

 P-space, is entirely contained in that space. 



40* 



