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with a, domain which we shall cover entirely with tangent curves 
not crossing each other and we shall investigate the different ways in 
which that covering takes place in different cases. For the sake of 
more completeness and as an introduction we first do the same for 
a non-singular point. 
Let P be the point under consideration, RS an arc of tangent 
curve r containing P, JJV an arc containing P of an orthogonal 
curve of the vector distribution. We draw through V and V 
tangent curves « 0 and « 15 and through R and S orthogonal curves 
y and d, and we let the four points R, S t U, and V converge 
together to P. Before they have reached P, a moment comes when 
«#> «i> 7, and 6 form a curvilinear rectangle, inside which lies P, 
and inside which lies no point zero of the vector distribution, thus 
inside which on account of the first communication no closed 
tangent eurve can be drawn. 
We shall cover this curvilinear rectangle with tangent curves 
not crossing each other. 
We number «, with 0, r with ^ n, with 1. Let Qi be a point 
inside or on the rectangle A, B, S R (fig! 2) having from «. and r 
Fig. 2. Non-singular point. 
a distance as large as possible. We draw through Qi a tangent curve 
ab0U ‘ Which we as™- if « meets a. or r. we shall continue 
%hL P r U '” S ® recurrill g “• or r, until we come upon y or rf. 
en «_ is a tangent curve joining two points A± and B±_ of 
3- and a between «. and r. I„ the same way we construct inside 
