Etymology
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regulate (v.)

early 15c., regulaten, "adjust by rule, method, or control," from Late Latin regulatus, past participle of regulare "to control by rule, direct," from Latin regula "rule, straight piece of wood" (from PIE root *reg- "move in a straight line," with derivatives meaning "to direct in a straight line," thus "to lead, rule").

Meaning "to govern by restriction" is from 1620s. Sense of "adjust (a clock, etc.) with reference to a standard of accuracy" is by 1660s. Related: Regulated; regulating.

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self-regulating (adj.)
1837, from self- + present participle of regulate (v.).
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well-regulated (adj.)
1709 (Shaftsbury), from well (adv.) + past participle of regulate (v.).
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deregulate (v.)

"remove regulatory restrictions from," 1950, American English, in reference to railroads, from de- + regulate. Deregulation is attested from 1955. Related: Deregulated; deregulating; deregulatory.

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regulation (n.)

1670s, "act of regulating; state of being reduced to order," noun of action from regulate. Meaning "a rule for management prescribed by a superior or competent authority" is from 1715. As an adjective, "having a fixed pattern; in accord with a rule or standard," by 1836. Related: Regulations.

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regulator (n.)

1650s, "one who regulates" in any sense, agent noun in Latin form from regulate. In English history from 1680s; in American history from 1767, applied to local posses that kept order (or disturbed it) in rural regions. From 1702 as "device for controlling machinery in motion;" the specific sense of "mechanical device or clock used to set the time of other pieces" is from 1758.

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roil (v.)

1580s, "render (liquid) turbid or muddy by stirring up dregs or sediment," also figurative, "excite to some degree of anger, perturb," a word of uncertain origin. Perhaps it is from French rouiller "to rust, make muddy," from Old French roil "mud, muck, rust" (12c.), from Vulgar Latin *robicula, from Latin robigo "rust" (see robust). Or perhaps from Old French ruiler "to mix mortar," from late Latin regulare "to regulate" (see regulate). Or perhaps somehow imitative. An earlier borrowing of the French verb is Middle English roil "to roam or rove about" (early 14c.); also compare rile (v.), formerly the common colloquial form in the U.S. Related: Roiled; roiling.

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*reg- 

Proto-Indo-European root meaning "move in a straight line," with derivatives meaning "to direct in a straight line," thus "to lead, rule."

It forms all or part of: abrogate; address; adroit; Alaric; alert; anorectic; anorexia; arrogant; arrogate; bishopric; correct; corvee; derecho; derogate; derogatory; Dietrich; direct; dress; eldritch; erect; ergo; Eric; Frederick; Henry; incorrigible; interregnum; interrogate; maharajah; Maratha; prerogative; prorogue; rack (n.1) "frame with bars;" rail (n.1) "horizontal bar passing from one post or support to another;" Raj; rajah; rake (n.1) "toothed tool for drawing or scraping things together;" rake (n.2) "debauchee; idle, dissolute person;" rakish; rank (adj.) "corrupt, loathsome, foul;" real (n.) "small Spanish silver coin;" realm; reck; reckless; reckon; rectangle; rectify; rectilinear; rectitude; recto; recto-; rector; rectum; regal; regent; regicide; regime; regimen; regiment; region; regular; regulate; Regulus; Reich; reign; resurgent; rex; rich; right; Risorgimento; rogation; royal; rule; sord; source; subrogate; subrogation; surge; surrogate; viceroy.

It is the hypothetical source of/evidence for its existence is provided by:

Sanskrit raj- "a king, a leader," rjyati "he stretches himself," riag "torture" (by racking); Avestan razeyeiti "directs," raštva- "directed, arranged, straight;" Persian rahst "right, correct;" Latin regere "to rule, direct, lead, govern," rex (genitive regis) "king," rectus "right, correct;" Greek oregein "to reach, extend;" Old Irish ri, Gaelic righ "a king," Gaulish -rix "a king" (in personal names, such as Vircingetorix), Old Irish rigim "to stretch out;" Gothic reiks "a leader," raihts "straight, right;" Lithuanian raižytis "to stretch oneself;" Old English rice "kingdom," -ric "king," rice "rich, powerful," riht "correct;" Gothic raihts, Old High German recht, Old Swedish reht, Old Norse rettr "correct."

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cadence (v.)
"to regulate by musical measure," 1749, from cadence (n.). Related: Cadenced; cadencing.
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flywheel (n.)
also fly-wheel, "heavy-rimmed revolving wheel to regulate motion," 1784, from fly (n.) "speed-regulating device" (1590s, from fly (v.1)) + wheel (n.).
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