Etymology
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intercourse (n.)
mid-15c., "communication to and fro," ("In early use exclusively with reference to trade" [OED]), from Old French entrecors "exchange, commerce, communication" (12c., Modern French entrecours), from Late Latin intercursus "a running between, intervention," in Medieval Latin "intercommunication," from intercursus, past participle of intercurrere "to run between, intervene, mediate," from Latin inter "between" (see inter-) + currere "to run" (from PIE root *kers- "to run").

Sense of "frequent and habitual meeting and contact, social communication between persons" is from 1540s. Meaning "mental or spiritual exchange or intercommunication" is from 1560s. Meaning "sexual relations" (1798) probably is a shortening of euphemistic sexual intercourse (1771) with intercourse in its sense "social contact and relations."
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non-intercourse (n.)

"a refraining from intercourse," in any sense, 1809, from non- + intercourse.

Non-Intercourse Act, an act of the United States Congress of 1809 passed in retaliation for claims made by France and Great Britain affecting the commerce of the United States, and particularly the personal rights of United States seamen, continued 1809 and 1810, and against Great Britain 1811. It prohibited the entry of merchant vessels belonging to those countries into the ports of the United States, and the importation of goods grown or manufactured in those countries. [Century Dictionary]
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*kers- 

Proto-Indo-European root meaning "to run."

It forms all or part of: car; career; cargo; caricature; cark; carpenter; carriage; carrier; carry; charabanc; charette; charge; chariot; concourse; concur; concurrent; corral; corridor; corsair; courant; courier; course; currency; current; curriculum; cursive; cursor; cursory; discharge; discourse; encharge; excursion; hussar; incur; intercourse; kraal; miscarry; occur; precursor; recourse; recur; succor.

It is the hypothetical source of/evidence for its existence is provided by: Greek -khouros "running;" Latin currere "to run, move quickly;" Lithuanian karšiu, karšti "go quickly;"Old Irish and Middle Welsh carr "cart, wagon," Breton karr "chariot," Welsh carrog "torrent;" Old Norse horskr "swift."

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intercommunion (n.)
1749, "intimate intercourse, fellowship," from inter- "between" + communion (n.).
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shut-in (n.)
"person confined from normal social intercourse," 1904, from the verbal phrase, from shut (v.) + in (adv.).
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converse (n.2)

c. 1500, "acquaintance by frequent or customary intercourse," from converse (v.). From 1610s as "conversation, familiar discourse."

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shtup (v.)
"annoy," 1952; "have sexual intercourse with," 1967; from Yiddish, literally "push, shove," related to dialectal German stupfen "to nudge, jog."
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incest (n.)
"the crime of sexual intercourse between near kindred," c. 1200, from Old French inceste "incest; lechery, fornication," and directly from Latin incestum "unchastity, impious unchastity," also specifically "sexual intercourse between close relatives," noun use of neuter adjective incestus "unchaste, impure," from in- "not" (see in- (1)) + castus "pure" (see caste). Old English had sibleger "incest," literally "kin-lying."
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cohabitation (n.)

mid-15c., cohabitacioun, "action or state of living together," from Old French cohabitacion "cohabitation; sexual intercourse," or directly from Late Latin cohabitationem (nominative cohabitatio), noun of action from past participle stem of cohabitare "to dwell together," from co- "with, together" (see co-) + habitare "to live, inhabit, dwell," frequentative of habere "to have, to hold, possess" (from PIE root *ghabh- "to give or receive"). Specifically "state of living together as husband and wife without benefit of marriage," implying sexual intercourse, from 1540s.

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intimacy (n.)
1640s, from intimate (adj.) + abstract noun suffix -cy. Sense of "sexual intercourse" attested from 1670s but modern use is from newspaper euphemistic use (1882).
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