738 

 Sections in planes through a will be dealt with later on. 



2. The restcurve in u is an oval which intersects a at A. In a 

 four branches depart from A: AB and AC on a and AE and AD 

 on the oval. Regarding the connection of these branches the Jordan 

 theorem for space leaves only two possibilities. 



Fig 12. 



First possibility: AC and AD are connected by \, AD and AB 

 bj II, AB and AE by III and lastly AE and ^6' by IV. If land 

 IV w^ere situated on the same side of a then a parallel linesegment 

 converging from that side towards E' D' would end up by having 

 two points in common with I and two with IV: a contiadiction. 



If I and II were situated on the same side of «, then a parallel 

 linesegment, converging from that side towards A' D" would end 

 up by having two points in common with I and also two with II: 

 a contradiction. 



In the same way it can be showen that III and IV cannot lie on 

 the same side of «. Combining these results it appears that the 

 connecting sets of points are situated alternately above and below «. 



Fig 13. 



Second yossihility. The following is a representative case: I con- 

 nects AB and AC above «and III connects AE with ADboiow a. 

 AC is connected with AD above or below a by II and lastly AB 

 with AE above or below « by IV. Let parallel linesegments con- 

 verge towards D' C' from that side on which II is situated. This 



