An Etymological Dictionary of the German Language/Stiege
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Stiege (1.), f., ‘stair, staircase,’ from the equiv. MidHG. stiege, OHG. stiega, f.; the same as Steg; the broken MidHG. ie is similar to MidHG. wiege, ‘cradle,’ and schiec, ‘awry’ (see schief).
Stiege (2.), f. (dial. Steig), in the sense of ‘score,’ has been derived from the allied MidHG. stîge, f., ‘stall for small cattle’ (Swe. stia, ‘piasty’), it being assumed that a stall contained twenty sheep. Yet it is remarkable that the Crim. Goth. stega was used in the 16th cent. in the sense of ‘score’ (comp. Shock; E. score, lit. ‘notch’; Du. snees, ‘score,’ lît, ‘row, series’).