in anatomy, "the terminal section of the intestine, ending in the anus," early 15c., from Latin intestinum rectum "straight intestine" (in contrast to the convolution of the rest of the bowels), from neuter past participle of regere "to keep straight" (from PIE root *reg- "move in a straight line"). A loan-translation of Greek apeuthysmeon enteron, "the name given to the lowest part of the large intestine by Galen, who so called it because he dissected only animals whose rectum (in contradistinction to that of man) is really straight" [Klein].

word-forming element in anatomy meaning "rectal, pertaining to or involving the rectum," before vowels rect-, from combining form of rectum.

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."

"pain in the anus or rectum," 1811, from medical Latin proct-, Latinized form of Greek combining form of prōktos "anus" (see proctology) + algos "pain" (see -algia).

"branch of medicine concerned with the anus or rectum," 1896, from Latinized form of Greek prōktos "anus" (from PIE *prokto-, source also of  Armenian erastan-k' "buttocks") + -logy "study of." Related: Proctologist (1897).

"right-hand page in an open book" (opposed to verso or reverso), 1824, from Latin recto (in recto folio), ablative of rectum "right" (see right (adj.2)).

"pertaining to or connected with the rectum," 1822, from stem of rectum + -al (1). Related: Rectally.

"pertaining to the colon and the rectum," by 1918, from combining form of colon (n.2) + rectal.

Middle English shit "diarrhea," from Old English scitte "purging, diarrhea," from source of shit (v.). The general sense of "excrement" dates from 1580s (Old English had scytel, Middle English shitel for "dung, excrement;" the usual 14c. noun for natural discharges of the bodies of men or beasts seems to have been turd or filth). As an exclamation attested in print by 1920 but certainly older. Use for "obnoxious person" is by 1508; meaning "misfortune, trouble" is attested from 1937.

Shit-faced "drunk" is 1960s student slang; shit list is from 1942. Shit-hole is by 1937 as "rectum," by 1969 in reference to undesirable locations. Shitload (also shit-load) for "a great many" is by 1970. Shitticism is Robert Frost's word for scatological writing.  

Up shit creek "in trouble" is by 1868 in a South Carolina context (compare the metaphoric salt river, of which it perhaps a coarse variant). Slang not give a shit "not care" is by 1922. Pessimistic expression same shit different day is attested by 1989. To get (one's) shit together "manage ones affairs" is by 1969. Emphatic shit out of luck is by 1942.

The expression when the shit hits the fan "alluding to a moment of crisis or its disastrous consequences" [OED] is attested by 1967.

The expression is related to, and may well derive from, an old joke. A man in a crowded bar needed to defecate but couldn't find a bathroom, so he went upstairs and used a hole in the floor. Returning, he found everyone had gone except the bartender, who was cowering behind the bar. When the man asked what had happened, the bartender replied, 'Where were you when the shit hit the fan?' [Hugh Rawson, "Wicked Words," 1989]