Etymology
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league (v.)
"to form a league," 1610s, from league (n.1). Related: Leagued; leaguing.
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league (n.1)

"alliance," mid-15c., ligg, from French ligue "confederacy, league" (15c.), from Italian lega, from legare "to tie, to bind," from Latin ligare "to bind" (from PIE root *leig- "to tie, bind"). Originally among nations, subsequently extended to political associations (1846) and sports associations (1879). League of Nations is attested from 1917 (created 1919).

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league (n.2)
itinerary unit in medieval England, distance of about three statute miles, late 14c., ultimately from Late Latin leuga (source also of French lieue, Spanish legua, Italian lega), which is said by Roman writers to be from Gaulish. A vague measure (perhaps originally an hour's hike), in England it was a conventional, not a legal measure, and in English it is found more often in poetic than in practical writing.
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big-league (adj.)
"prominent, important, first-rate," by 1925, a figurative use from baseball, where big league was used for "a major league" by 1891. See league (n.1).
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interleague (adj.)
also inter-league, by 1917 in a U.S. baseball sense, from inter- "between" + league (n.). Earlier (1580s) as a verb, "to combine in a league."
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bush league (adj.)
"mean, petty, unprofessional," 1906, from baseball slang for the small-town baseball clubs below the minor league where talent was developed (by 1903), from bush (n.) in the adjectival slang sense of "rural, provincial," which originally was simple description, not a value judgment.
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banlieue (n.)
French word for "suburbs, outskirts, outlying precincts of a town or city," 13c., from Vulgar Latin *banleuca, from Germanic *ban (see ban (n.1)) + leuca "a league" (of distance, in Medieval Latin, "indefinite extent of territory;" see league (n.2)). So, originally, "area around a town within which the bans -- rules and proclamations of that place -- were in force; territory outside the walls but within the legal jurisdiction." German had a similar formation, bann-meile (see mile (n.)), in the same sense; and compare Middle English bane cruces "crosses marking the boundary of territory subject to the edicts or laws of a certain ruler."
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*leig- 

Proto-Indo-European root meaning "to tie, bind." 

It forms all or part of: alloy; ally; colligate; deligate; furl; league (n.1) "alliance;" legato; liable; liaison; lien; lictor; ligand; ligament; ligate; ligation; ligature; oblige; rally (v.1) "bring together;" religion; rely.

It is the hypothetical source of/evidence for its existence is provided by: Latin ligare "to bind;" Albanian lidh "I bind," and possibly Middle Low German lik "band," Middle High German geleich "joint, limb."

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confederate (v.)
Origin and meaning of confederate

1530s, "to unite in a league or alliance," from Late Latin confoederatus, past participle of confoederare "to unite by a league," from assimilated form of com "with, together" (see con-) + foederare, from foedus (genitive foederis) "a league," from suffixed form of PIE root *bheidh- "to trust, confide, persuade."

The older verb was confeder (late 14c.), from Old French confederer, Medieval Latin confederare. Related: Confederated; confederating.

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federation (n.)

1721, "union by agreement," from French fédération, from Late Latin foederationem (nominative foederatio), noun of action from past-participle stem of Latin foederare "league together," from foedus "covenant, league" (from PIE root *bheidh- "to trust, confide, persuade").

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