( 71 & ) 
and the geodetic arc K q H q , belonging to u q , has either no point 
in common with VW, or none with CD. 
In the first case we determine on VW a point M, having from 
B a distance as small as possible. The geodetic arc BM is then in 
M normal to VW, and has a last point of intersection N with CD, 
so that the geodetic arc NM forms with one of the arcs NM of 
u q , not containing e.g. the point C, a closed curve; u q , taken with 
a certain sense of circuit, would at M enter one of the two domains 
determined by this closed curve, to leave it no more; further C 
would lie outside that domain; thus u q would never be able to 
reach C, with which the absurdity of our assumption has been proved. 
In the second case we determine on CD a point M having from 
S a distance as small as possible, and on the geodetic arc SM the 
last point of intersection N with VW. The further reasoning remains 
analogous to the one just followed : the parts of the arcs VW and 
CD are only interchanged. 
Let now B « be the only limit- point of a certain fundamental 
Series of points B lt B z , B 9 , ..., lying respectively on u x , u„ u t ,... 
We assume that 24 is not a point zero; it has then for a suitably 
selected p a distance 4 and }> 4 ;4 from the points zero. 
Let further each m* be ]>p and let B Wl > D,„ 2 , B m% ,... be a fun¬ 
damental series contained in the series just mentioned, whose points 
have all from 24 a distance <^— and <[ — 
If then further on the different u mjc B,„ k D mk are pursuing, 
recurring -i /Scares, we prove by the reasoning followed in the 
first communication p. 854, that there exists a series- C nx D ni , 
C„,D ni , C n% D„ t , _ converging uniformly to an arc 6424 of a 
tangent curve iu> in such a way, that all arcs C» k D„ k lie on the 
same side of C«2)». ^ 
If we describe round 24 a geodetic circle with radius — /J, 
then it cuts from 24 an arc FI containing 24; this arc divides 
its inner domain into two regions, into one of which, to be called 
neither the arcs C„ k D„ k , nor any other parts of the curves u„ k can 
penetrate, as they would get there a distance ^ ^ from 24 fc . 
As further the region g cannot lie outside all curves it must 
lie inside all curves u„ k . 
