Etymology
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step (n.)
Old English steppa (Mercian), stæpe, stepe (West Saxon) "stair, act of stepping," from the source of step (v.). Compare Old Frisian, Middle Dutch, Dutch stap, Old High German stapfo, German Stapfe "footstep"). From late Old English as "degree on a scale." Figurative meaning "action which leads toward a result" is recorded from 1540s. In dancing, from 1670s. Meaning "type of military pace" is from 1798. Warning phrase watch your step is attested from 1911 (Wyclif (late 14c.) has keep thy foot in essentially the same sense). Step by step indicating steady progression is from 1580s. To follow in (someone's) steps is from mid-13c.
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step (v.)
Old English steppan (Anglian), stæppan (West Saxon) "take a step," from West Germanic *stap- "tread" (source also of Old Frisian stapa, Middle Dutch, Dutch stappen, Old High German stapfon, German stapfen "step"), from PIE root *stebh- "post, stem; to support, place firmly on" (see staff (n.); source also of Old Church Slavonic stopa "step, pace," stepeni "step, degree"). The notion is perhaps "a treading firmly on; a foothold."

Transitive sense (as in step foot in) attested from 1530s. Related: Stepped; stepping. Originally strong (past tense stop, past participle bestapen); weak forms emerged 13c., universal from 16c. To step out "leave for a short time" is from 1530s; meaning "to go out in public in style" is from 1907. Step on it "hurry up" is 1923, from notion of gas pedal.
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step- 
Old English steop-, with connotations of "loss," in combinations like steopcild "orphan," related to astiepan, bestiepan "to bereave, to deprive of parents or children," from Proto-Germanic *steupa- "bereft" (source also of Old Frisian stiap-, Old Norse stjup-, Swedish styv-, Middle Low German stef-, Dutch stief-, Old High German stiof-, German stief-), literally "pushed out," from PIE *steup-, from root *(s)teu- (1) "to push, stick, knock," with derivatives referring to fragments (see steep (adj.)). Barnhart suggests the forms in -f- are by assimilation of the first sound in following words for "father."

Etymologically, a stepfather or stepmother is one who becomes father or mother to an orphan, but the notion of orphanage faded in 20c. and came to denote simply relation through marriage. For sense evolution, compare Latin privignus "stepson," related to privus "deprived." Compare orphan (n.).
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step-ladder (n.)
also stepladder, one with flat steps instead of rungs, 1728, from step (n.) + ladder.
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step-daughter (n.)
Old English stepdohtor; see step- + daughter (n.). Similar formation in German Stieftochter.
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goose-step (n.)
1806, originally a military drill to teach balance; "to stand on each leg alternately and swing the other back and forth." This, presumably, reminded someone of a goose's way of walking. In reference to "marching without bending the knees" (as in Nazi military reviews) it apparently is first recorded 1916. As a verb by 1854.
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quick-step (n.)

1802, "step used in marching in quick-time" (110 steps per minute); by 1811 as "a march in quick-time," from quick (adj.) + step (n.). Also of music adapted to such a march. By 1880 as "a fast dance." From 1906 as a verb. Related: quick-stepped; quick-stepping.

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step-son (n.)
also stepson, Old English steopsunu; see step- + son.
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lock-step (n.)

1802, in military writing, to describe a very tight style of mass marching, from lock (n.1) + step (n.).

Lock-step. A mode of marching by a body of men going one after another as closely as possible, in which the leg of each moves at the same time with and closely follows the corresponding leg of the person directly before him. [Thomas Wilhelm, "Military Dictionary and Gazetteer," Philadelphia, 1881]

Figurative use by 1836.

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side-step (n.)

also sidestep, 1757, "a stepping to the side" (originally in military drill), from side (adj.) + step (n.). The verb is recorded from 1895, "step to one side;" the figurative sense of "evade (an issue), prevaricate" is attested from 1900.

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