An Etymological Dictionary of the German Language/Schwelle
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Schwelle, f., ‘threshold, sill,’ from MidHG. swęlle, f. and n., ‘beam, threshold.’ OHG. swęlli, m., ‘threshold’; Goth. *swalli, ‘threshold,’ is wanting. Comp. AS. syll, f., E. sill, and the equiv. OIc. syll, svill, f.; allied to Goth. ga-suljan, ‘to establish,’ root swol, sū̆l, ‘to establish’; con Lat. solea (for *svolea)?. Akin also to OHG. sûl, ‘pillar’?.