An Etymological Dictionary of the German Language/Annotated/Steig
Steig, masculine, ‘path, footway,’ from the equivalent Middle High German and Old High German stîc (genitive stîges), masculine; allied to steigen, ‘to mount,’ which is based on the equivalent Middle High German stîgen, Old High German stîgan, strong verb. The verb is common to Teutonic in the same sense; compare Old Saxon stîgan, Dutch stijgen, Anglo-Saxon stîgan (English to sty), Gothic steigan. The Teutonic root stī̆g (compare also Steg, steil) corresponds to the widely-diffused Aryan root stī̆gh, ‘to step, stride,’ which appears in Sanscrit (rare) stigh, ‘to step, stride,’ Greek στείχω, ‘to go,’ Latin vestigium, ‘track, trace,’ Old Slovenian stignąti, ‘to hasten’; hence the meaning of the verbal root has been modified in Teutonic — The verb steigern, ‘to raise, increase, put up to auction,’ allied to Middle High German and Old High German steigen, ‘to cause something to ascend, to elevate or extol something,’ occurs in early Modern High German only; hence the verb means literally ‘to cause something to mount in price.’