"having a sharp slope," Old English steap "high, lofty; deep; prominent, projecting," from Proto-Germanic *staupa- (source also of Old Frisian stap "high, lofty," Middle High German *stouf), from PIE *steup-, extended form of root *(s)teu- (1) "to push, stick, knock, beat," with derivations referring to projecting objects (source also of Greek typtein "to strike," typos "a blow, mold, die;" Sanskrit tup- "harm," tundate "pushes, stabs;" Gothic stautan "push;" Old Norse stuttr "short"). The sense of "precipitous" is from c. 1200. The slang sense "at a high price" is a U.S. coinage first attested 1856. Related: Steeply; steepness. The noun meaning "steep place" is from 1550s.
word-forming element denoting action, quality, or state, attached to an adjective or past participle to form an abstract noun, from Old English -nes(s), from Proto-Germanic *in-assu- (cognates: Old Saxon -nissi, Middle Dutch -nisse, Dutch -nis, Old High German -nissa, German -nis, Gothic -inassus), from *-in-, originally belonging to the noun stem, + *-assu-, abstract noun suffix, probably from the same root as Latin -tudo (see -tude).
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Definitions of steepness from WordNet
the property possessed by a slope that is very steep;