Etymology
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rally (v.1)

"bring together or into order again by urgent effort," c. 1600, from French rallier, from Old French ralier "reassemble, unite again," from re- "again" (see re-) + alier "unite" (see ally (v.)).

In Old French (and Italian), re- often appeared as ra- by confusion with the true ra- (from Latin re- + ad-), and the following consonant often was doubled; compare rabbet (a doublet of rebate), rappel (a doublet of repeal). But as ra- was not recognized in English as a prefix, words with ra- in Old French usually returned to re- in English; Rally and rabbet never were because the accent had receded. In later borrowings (rappel, rapprochement, etc.) the words tend to keep their French forms. 

Intransitive meaning "pull together hastily, recover order, revive, rouse" is from 1660s. Related: Rallied; rallying. Rallying-point "place at or about which persons come together for action" is by 1798. Rally round the flag (1862) is a line from popular American Civil War song "Battle Cry of Freedom."

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rally (v.2)

"make fun of, tease in a good-natured way, attack with raillery," 1660s, from French railler "to rail, reproach" (see rail (v.1)).

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rally (n.)

1650s, in military language, "a rapid regrouping for renewed action after a repulse," from rally (v.1). Sense of "a mass meeting to stir enthusiasm" is attested by 1840, American English. Sense of "gathering of automobile enthusiasts" is from 1932, from French rallye, itself from the English noun. Sports sense of "long series of hits from one side to the other" in tennis, etc., is from 1881, earlier "series of back-and-forth blows in a boxing match" (1825).

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re-ally (v.)

"to form an alliance again, to connect or unite again," c. 1600, from re- + ally (v.). A doublet of rally (v.1), with hyphenated spelling and full pronunciation of the prefix to distinguish it from really. Related: Re-allied; re-alliance.

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rappel (n.)

mountaineering technique for descending steep faces, 1931, from French rappel, literally "recall" (Old French rapel), from rapeler "to recall, summon" (see repeal (v.), which is a doublet). The same word had been borrowed into English earlier to mean "a drum roll to summon soldiers" (1848). For spelling, see rally (v.1).

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rail (v.1)

"complain, speak vehemently and bitterly," late 15c., railen, from Old French raillier "to tease or joke" (15c.), which is perhaps from Old Provençal ralhar "scoff, to chat, to joke," from Vulgar Latin *ragulare "to bray" (source also of Italian ragghiare "to bray"), from Late Latin ragere "to roar," probably of imitative origin. See rally (v.2). Related: Railed; railing.

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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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re- 

word-forming element meaning "back, back from, back to the original place;" also "again, anew, once more," also conveying the notion of "undoing" or "backward," etc. (see sense evolution below), c. 1200, from Old French re- and directly from Latin re- an inseparable prefix meaning "again; back; anew, against."

Watkins (2000) describes this as a "Latin combining form conceivably from Indo-European *wret-, metathetical variant of *wert- "to turn." De Vaan says the "only acceptable etymology" for it is a 2004 explanation which reconstructs a root in PIE *ure "back."

In earliest Latin the prefix became red- before vowels and h-, a form preserved in redact, redeem, redolent, redundant, redintegrate, and, in disguise, render (v.). In some English words from French and Italian re- appears as ra- and the  following consonant is often doubled (see rally (v.1)).

The many meanings in the notion of "back" give re- its broad sense-range: "a turning back; opposition; restoration to a former state; "transition to an opposite state." From the extended senses in "again," re- becomes "repetition of an action," and in this sense it is extremely common as a formative element in English, applicable to any verb. OED writes that it is "impossible to attempt a complete record of all the forms resulting from its use," and adds that "The number of these is practically infinite ...."   

Often merely intensive, and in many of the older borrowings from French and Latin the precise sense of re- is forgotten, lost in secondary senses, or weakened beyond recognition, so that it has no apparent semantic content (receive, recommend, recover, reduce, recreate, refer, religion, remain, request, require). There seem to have been more such words in Middle English than after, e.g. recomfort (v.) "to comfort, console; encourage;" recourse (n.) "a process, way, course." Recover in Middle English also could mean "obtain, win" (happiness, a kingdom, etc.) with no notion of getting something back, also "gain the upper hand, overcome; arrive at;" also consider the legal sense of recovery as "obtain (property) by judgment or legal proceedings." 

And, due to sound changes and accent shifts, re- sometimes entirely loses its identity as a prefix (rebel, relic, remnant, restive, rest (n.2) "remainder," rally (v.1) "bring together"). In a few words it is reduced to r-, as in ransom (a doublet of redemption), rampart, etc.

It was used from Middle English in forming words from Germanic as well as Latin elements (rebuild, refill, reset, rewrite), and was used so even in Old French (regret, regard, reward, etc.).

Prefixed to a word beginning with e, re- is separated by a hyphen, as re-establish, re-estate, re-edify, etc. ; or else the second e has a dieresis over it: as, reëstablish, reëmbark, etc. The hyphen is also sometimes used to bring out emphatically the sense of repetition or iteration : as, sung and re-sung. The dieresis is not used over other vowels than e when re is prefixed : thus, reinforce, reunite, reabolish. [Century Dictionary, 1895]
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pep (n.)

"vigor, energy," 1912, shortened form of pepper (n.), which was used in the figurative sense of "spirit, energy" from at least 1847. Pep rally "meeting to inspire enthusiasm" is attested from 1915; pep talk is from 1926. To pep (something) up "fill or inspire with vigor or energy" is from 1925.

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populism (n.)

1893, "political doctrines or principles of the Populist Party," a left-wing agrarian faction in U.S. politics; see populist + -ism. After the movement faded the word was applied in other contexts (for example a French literary trend of the 1930s), and from the 1960s it was used for political movements that sought to rally ordinary people who see their concerns as being disregarded by established parties and elites, but it also is used pejoratively for irrational or simplistic demagoguery.

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