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."

early 14c., rekening, "a narration, account," verbal noun from reckon (v.). The meaning "a settling of accounts" is from mid-14c.; that of "act of counting or computing, a calculation" is from late 14c. as is the sense of "a bill of charges" (in an inn, tavern, etc.). Compare Dutch rekening "a bill, account, reckoning," Old High German rechenunga, German rechnung, Danish regning "a reckoning, computation."

The general sense is "a summing up," whether in words or numbers. In nautical use from 1660s: "Calculation of the position of a ship from the rate as determined by the log and the course as determined by the compass." Day of reckoning is attested from c. 1600; the notion is of rendering an account of one's life and conduct to God at death or judgment.

c. 1200, rekenere, "one who keeps accounts or computes," agent noun from reckon (v.). Later especially "an aid in reckoning, something that assists a person to reckon accounts;" especially "book of tables used in calculation," often known as a ready reckoner (1757).

quasi-proper name for a fox, c. 1300, Renard, from Old French Renart, Reynard, the name of the fox in Roman de Renart, from Old High German personal name Reginhart "strong in counsel," literally "counsel-brave." The first element is related to reckon, the second to hard.

The tales were enormously popular in medieval Western Europe; in them animals take the place of humans and each has a name: the lion is Noble, the cat Tibert, the bear Bruin, etc. The name of the fox thus became the word for "fox" in Old French (displacing golpil, gulpil, from a Vulgar Latin diminutive of Latin vulpes).

Old French also had renardie "craftiness." An old variant form of the name was Renald, and thus English had for a time renaldry "intrigue" (1610s). Old English had the first element of the name as regn-, an intensive prefix (as in regn-heard "very hard," regn-þeof "arch-thief," also in personal names).

masc. proper name, from Old French Reinald (Modern French Renaut, Latinized as Reginaldus), a popular name among the Normans, from Old High German Reginald, the first element related to reckon, the second to Old English wealdan "to rule," from Proto-Germanic *waldan "to rule," source of wield, from PIE root *wal- "to be strong." Related: Reynolds.