(?1?J 
such a way, that after having completed n x jJ^-arcs, but not yet 
rij-J-l /? Sl -arcs, we reach a point. A x , where for the first time we have 
approached the points zero as far as a distance t 1 . Then again there 
is a finite number n 2 in such a way that, having completed from 
A x n t , but not yet n % -f 1 /? % -ares, we reach a point A 2 , where for 
the first time we have approached the points zero as far as a distance 
e s . From there we pursue r with ft. 8 -arcs and continue this process 
indefinitely. 
If we understand by m(e„) the maximum distance from the points 
zero, which r reaches when being pursued after having for the first 
time approached the points zero as far as a distance s,„ then a first 
possibility is, that m(e„) converges with e n to zero. 
In that case the pursuing branch converges to one single point 
zero and it is an arc of simple curve, stopping at that point tero. 
We now suppose the second possibility, that m(e„) surpasses for each 
s n a certain finite quantity e. Then we can effect (by eventually 
omitting a finite number of terms of the series of €«'s), that each 
and each 
On the pursuing branch then certainly two points P x and Q x can 
be indicated both at a distance e from the points zero, and separated 
on r by at least one point at a distance s x from the points zero, 
whilst the distance between P x and Q x is < £ LetP X S and Q x U 
be pursuing £ fl -arcs, and P x R and Q x T recurring [Varcs. 
Let H x be a point of TV,, having from P, the smallest possible 
distance, tlien H x cannot coincide with T or U, so that the 
geodetic arc P X H X is in H x normal to the vector direction, and the 
vector directions in all points of that geodetic arc, forming with 
