An Etymological Dictionary of the German Language/dehnen
dehnen, vb., ‘to stretch, extend, lengthen,’ from MidHG. and OHG. denen, dennen, wk. vb., ‘to stretch, draw, strain’; comp. Goth. ufþanjan, ‘to extend’; AS. þenian, þennan, ‘to stretch.’ The Goth. þanjan is a deriv. of a str. vb. *þënan, like þakjan, ‘to cover,’ from a str. vb. *þëkan (Lat. tego); þanja and þëna are primit. cognate with Gr. τείνω. The root ten is widely diffused in the Aryan group. Sans. root tan, ‘to strain, widen, extend (of time), endure’; tántu-s, m., ‘thread,’ tánti-s, f., ‘line, rope’; Gr. τείνω, τάνυμαι, τάσις, τένων, ‘sinew,’ ταινία, ‘strip’; OSlov. teneto, tonoto, ‘cord,’ Lat. tenus, ‘cord,’ Lith. tìnklas, ‘net.’ The idea of extension is shown also by the root ten (Lat. teneo, tendo) in an old Aryan adj.; see dünn and Dohne. A figurative sense of the same root is seen in donnern; the evolution of meaning may be ‘extension—sound—noise.’