Etymology
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Words related to step

staff (n.)

Old English stæf (plural stafas), "walking stick, strong pole used for carrying, rod used as a weapon, pastoral staff," probably originally *stæb, from Proto-Germanic *stab- (source also of Old Saxon staf, Old Norse stafr, Danish stav, Old Frisian stef, Middle Low German and Middle Dutch staf, Old High German stab, German Stab, Gothic *stafs "element;" Middle Dutch stapel "pillar, foundation").

This is reconstructed to be from PIE root *stebh- "post, stem, to support, place firmly on, fasten" (source also of Old Lithuanian stabas "idol," Lithuanian stiebas "staff, pillar;" Old Church Slavonic stoboru "pillar;" Sanskrit stabhnati "supports;" Greek stephein "to tie around, encircle, wreathe," staphyle "grapevine, bunch of grapes;" Old English stapol "post, pillar").

As "pole from which a flag is flown," 1610s. In musical notation from 1660s. Sense of "group of military officers that assists a commander" is attested from 1702, apparently from German, from the notion of the baton that is a badge of office or authority (a sense attested in English from 1530s); hence staff officer (1702), staff-sergeant (1811). The meaning "group of employees (as at an office or hospital)" is attested by 1837.

Staff of life "bread" is from the Biblical phrase break the staff of bread meaning "cut off the supply of food" (Leviticus xxvi.26), translating Hebrew matteh lekhem.

The Old English word, in plural, was the common one used for "letter of the alphabet, character," hence "writing, literature," and many compounds having to do with writing, such as stæfcræft "grammar," stæfcræftig "lettered," stæflic "literary," stæfleahtor "grammatical error," with leahtor "vice, sin, offense."

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stepping (n.)
early 14c., verbal noun from step (v.). Stepping stone first recorded early 14c.; in the figurative sense 1650s.
doorstep (n.)

also door-step, "threshold, step up from the ground to a door," 1810, from door + step (n.).

footstep (n.)
early 13c., "footprint," from foot (n.) + step (n.). Meaning "a tread or fall of the foot" is first attested 1530s. Figurative expression to follow in (someone's) footsteps is from 1540s.
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.

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.

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.

step-dance (n.)
one in which the steps are more important than the figure, especially one with difficult steps, 1857, from step (n.) + dance (n.). Related: Step-dancing (1872).
step-ladder (n.)
also stepladder, one with flat steps instead of rungs, 1728, from step (n.) + ladder.
stope (n.)
1747, a mining word, from Low German stope "a step," apparently cognate with step (n.). As a verb from 1778, "remove the contents of a vein," literally "to cut in stopes." Related: Stoped; stoping.