An Etymological Dictionary of the German Language/Steig
Steig, m., ‘path, footway,’ from the equiv. MidHG. and OHG. stîc (gen. stîges), m.; allied to steigen, ‘to mount,’ which is based on the equiv. MidHG. stîgen, OHG. stîgan, str. vb. The vb. is common to Teut. in the same sense; comp. OSax. stîgan, Du. stijgen, AS. stîgan (E. to sty), Goth. steigan. The Teut. root stī̆g (comp. also Steg, steil) corresponds to the widely-diffused Aryan root stī̆gh, ‘to step, stride,’ which appears in Sans. (rare) stigh, ‘to step, stride,’ Gr. στείχω, ‘to go,’ Lat. vestigium, ‘track, trace,’ OSlov. stignąti, ‘to hasten’; hence the meaning of the verbal root has been modified in Teut. — The vb. steigern, ‘to raise, increase, put up to auction,’ allied to MidHG. and OHG. steigen, ‘to cause something to ascend, to elevate or extol something,’ occurs in early ModHG. only; hence the vb. means lit. ‘to cause something to mount in price.’