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Old English steppan (Anglian), stæppan (West Saxon) "take a step," from West Germanic *stap- "tread" (cf. Old Frisian, Middle Dutch, Dutch stap, Old High German stapfo, German stapfe "footstep"), from PIE root *stebh- "to tread, step" (cf. Old Church Slavonic stopa "step, pace," stepeni "step, degree"). Originally strong (past tense stop, past participle bestapen); weak forms emerged 13c., universal from 16c. Stepping stone first recorded early 14c.; in the figurative sense 1650s. Step on it "hurry up" is 1923, from notion of gas pedal; step out (v.) is from 1907.
Old English steppa (Mercian), stæpe, stepe (West Saxon) "stair, act of stepping," from the source of step (v.). Meaning "action which leads toward a result" is recorded from 1540s. Warning phrase watch your step is attested from 1934. Step-dancing first recorded 1886.