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juncture.9 l 2 ) Z (lying in u) and Z' (lying in u') form together a 
coherent set determining one rest region, or a point P of u, and its 
image P' in u' will find themselves on the same x n in such a way, 
that P lies outside K', and P' outside K. Then however in those 
points P and P' an enlargement of 0 and O' would be possible, 
which would clash with the property of a transformation domain. 
So we are sure, that both meetings take place in the first-mentioned way. 
Let us discern in a juncture Z, performing such a meeting, its 
right end Z r and its left end Zi . Let us represent by K r resp. Ki the 
branch of u approaching to Z r resp. Zr, by Sr resp. Si the part of 
the circumference *) of Z r resp. Zi, approximated by K, resp. Kr, 
and by S the complete circumference of Z. Let us further indicate 
^ {Z, Z') s by T, the circumference of T by r. [Z r , Z'i) by T r , 
ni {Zt,Z'r) by Ti, and the part of the circumference of Tr resp. j), 
approximated by K r and K'i resp. Ki and K' r , by r, resp. n. 
We at once see, that of the sets T r and Ti at least one is coherent. 
For in the opposite case we could choose on K r in the vicinity of Z, a 
point of u outside K', whose image on u' would lie outside K, and an 
enlargement of O and O' would be possible there .see the schematic 
fig. 4). 
Fig. 4. 
In the same way it is evident, that either S r and S'i or S r and Si 
must be identical to each other, or Z must be a part of Z' or Z' 
a part of Z. 
Otherwise namely either S r would have to lie partly outside Si 
and at the same time S' r partly outside Si or Si partly outside SV> 
and at the same time Si partly outside Sr, which free segments of 
circumference would partly correspond to each other, and would 
admit an enlargement of 0 and 0 ; in their vicinity. 
Of the two possibilities obtained we shall first discuss: 
1 ) Two arcs of curve cohere to a new arc of curve by means of a 11 juncture", 
which contains an end of each of them. In the following reasoning we suppose 
the considered juncture to be composed of two non-singular ends. For singular 
ends it needs a slight modification. 
2 ) 1 . e. the cyclically ordered set of its accessible points. 
