Reich n.

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."

"next in order after the second; an ordinal numeral; being one of three equal parts into which a whole is regarded as divided;" late Old English metathesis of þridda, from Proto-Germanic *thridja- (source also of Old Frisian thredda, Old Saxon thriddio, Middle Low German drudde, Dutch derde, Old High German dritto, German dritte, Old Norse þriðe, Danish tredie, Swedish tredje, Gothic þridja), from PIE *tri-tyo- (source also of Sanskrit trtiyas, Avestan thritya, Greek tritos, Latin tertius (source of Italian terzo, Spanish tercio, French tiers), Old Church Slavonic tretiji, Lithuanian trečias, Old Irish triss, Welsh tryde), suffixed form of root *trei- (see three).

Metathesis of thrid into third is attested from c. 950 in Northumbrian (compare wright), but overall thrid was prevalent up to 16c. The noun meaning "third part of anything" is recorded from late 14c. Third rail in electric railway sense is recorded from 1890. Third World War as a possibility first recorded 1947. Third-rate "of poor quality" is from 1814, ultimately from classification of ships (1640s); third class in railway travel is from 1839. Third Reich (1930) is a partial translation of German drittes Reich (1923). Third party in law, insurance, etc., is from 1818.