An Etymological Dictionary of the German Language/fügen
fügen, vb., ‘to fit together, connect’; (refl.) ‘to accommodate oneself,’ from MidHG. vüegen, OHG. fuogen, ‘to shape or unite suitably’; comp. Du. voegen, AS. gefêgan, E. to fay (‘to suit, unite’); Goth. *fôgjan, ‘to make suitable,’ is a factitive of the Teut. root fag, in Goth. fagrs, ‘suitable, fitted,’ whose nearer cognates are to be found under fegen; E. to fadge (‘to suit, join’), may also be mentioned here.