An Etymological Dictionary of the German Language/Gleißner
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Gleißner, m., ‘hypocrite,’ from the equiv. MidHG. gelîchesenœre, allied to older ModHG. gleißen, ‘to dissemble.’ The latter is from MidHG. glîhsen, gelîchesen, OHG. gilîhhisôn, ‘to dissemble’; lit. ‘to be equal to any one’ (from gleich), equiv. to the MidHG. parallel form gelîchsensen. Comp. further Lat. simulare, allied to similis.