(774) 
there can be laid to p paths Dl, and EG, < 2, not cutting the 
line segment BC and for a >> im cutting each polygonal line }. only once, 
whilst the Sehnitt S, lies enclosed between these two paths. We 
may suppose ¢, so small that not only the are 7, D,L,G,, but also 
its image does not cut the path w. 
We now determine an approximating polygonal line ,, (v, > 7), 
possessing the following property : 
If a part of the circumference segment /,G, is separated from 
the infinite by the line segment BC, W, cuts the line segment BC 
between D,F, and EG; then the last point of intersection, which 
BC has there with W%,, we represent by P, ; 
1 : 
in the opposite case W, cuts a path <a s, leading to B, and not 
cutting DF, and EZG, ; then its last point of intersection with that 
path we represent by /,. 
Let S, be the last negatively directed circumference Schmitt not 
lving beyond C possessing the property that between A and S, all 
accessible points of y can be reached from the infinite along paths 
not meeting the straight line segment PC. 
We then choose on the polygonal line P, an are D,E, in which 
the distance of the endpoints is Se, and the distance of two arbitrary 
points is <16e,, in such a way that from D, and Z, there can 
be laid to p paths D,F, and #,G, < 2e, not cutting the line 
seement P,C and for a >> m cutting each polygonal line W, only 
once, whilst the Sehnitt S, lies enclosed between those two paths. 
We may suppose ¢, so small that not only the are F,D,£,G,, but 
also its image and its counterimage do not cut the path w. 
We now determine an approximating polygonal line },, (rn, > m) 
possessing the following property : 
If a part of the circumference segment /’,G, is separated from 
the infinite by the line segment P,C, 9, cuts the line segment P,C 
between D,/’, and Z,G,; we then represent the first point of inter- 
section, which P,C has there with },,, by Bis 
1 
in the opposite case ,, cuts a path a e, leading to C,and not 
cutting D,F, and £,G,; we then represent its first point of inter- 
section with that path by P,. 
Finally we impose on ®, as well as on 9, the condition that 
of their part contained between D,/', and #,G, the image as well 
as the counterimage lie inside 9, and inside the image of ‘,. 
In the linesegment BC, eventually completed with the paths 
leading to £ resp. to C' that have been added to it, now lies an 
