Etymology
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Words related to invitation

*en 
Proto-Indo-European root meaning "in."

It forms all or part of: and; atoll; dysentery; embargo; embarrass; embryo; empire; employ; en- (1) "in; into;" en- (2) "near, at, in, on, within;" enclave; endo-; enema; engine; enoptomancy; enter; enteric; enteritis; entero-; entice; ento-; entrails; envoy; envy; episode; esoteric; imbroglio; immolate; immure; impede; impend; impetus; important; impostor; impresario; impromptu; in; in- (2) "into, in, on, upon;" inchoate; incite; increase; inculcate; incumbent; industry; indigence; inflict; ingenuous; ingest; inly; inmost; inn; innate; inner; innuendo; inoculate; insignia; instant; intaglio; inter-; interim; interior; intern; internal; intestine; intimate (adj.) "closely acquainted, very familiar;" intra-; intricate; intrinsic; intro-; introduce; introduction; introit; introspect; invert; mesentery.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit antara- "interior;" Greek en "in," eis "into," endon "within;" Latin in "in, into," intro "inward," intra "inside, within;" Old Irish in, Welsh yn, Old Church Slavonic on-, Old English in "in, into," inne "within, inside."
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gain (v.)

1520s, "obtain as profit," from French gagner, from Old French gaaignier "to earn, gain; trade; capture, win," also "work in the fields, cultivate land," from Frankish *waidanjan "hunt, forage," also "graze, pasture," from Proto-Germanic *waithanjan "to hunt, plunder," from *waithjo- "pursuit, hunting" (source also of Old English waþ "hunting," German Weide "pasture, pasturage," Old Norse veiðr "hunting, fishing, catch of fish").

This is from PIE root *weie- "to go after, strive after, pursue vigorously, desire," with noun derivatives indicating "force, power" (related to *wi-ro- "man;" see virile). Cognates include Sanskrit padavi- "track, path, trail," veti- "follows, strives, leads, drives;" Avestan vateiti "follows, hunts;" Greek hiemai "move oneself forward, strive, desire;" Lithuanian vyti "to chase, pursue;" Old Norse veiðr "chase, hunting, fishing;" Old English OE wað "a chase, hunt."

Meaning "obtain by effort or striving" is from 1540s; intransitive sense of "profit, make gain" is from 1570s. Meaning "arrive at" is from c. 1600. Of timepieces by 1861. Related: Gained; gaining. To gain on "advance nearer" is from 1719. To gain ground (1620s) was originally military.

invita Minerva 
Latin adverbial phrase, used with reference to literary or artistic creation, "without inspiration," literally "Minerva unwilling;" i.e. "without inspiration from the goddess of wisdom;" ablative fem. of invitus "against the will, unwilling, reluctant," according to de Vaan from PIE compound *n-uih-to- "not turned to, not pursuing," related to the source of invitation. With Minervā, ablative absolute of Minerva.
invitational (adj.)
1894, from invitation + -al (1). The noun is by 1940, short for invitational tournament.
invitatory (adj.)

"using or containing invitation," 1640s, from Latin invitatorius "inviting," from invitat-, past-participle stem of invitare "to invite, treat, entertain" (see invitation).

invite (v.)

"solicit to come," 1530s, a back-formation from invitation, or else from French inviter (15c.), from Latin invitare "to invite," also "to summon, challenge; to feast, to entertain," a word of uncertain origin. Related: Invited; inviting.

vie (v.)
1560s, "to bet, make a bet," (literally "make a vie, the noun attested from 1530s in cards), especially in card-playing, "to wager the value of one's hand against an opponent's," shortened form of Middle English envie "make a challenge," from Old French envier "compete (against), provoke; invite, summon, subpoena;" in gambling, "put down a stake, up the bet;" from Latin invitare "to invite," also "to summon, challenge" (see invitation). Sense of "to contend (with) in rivalry" in English is from 1560s; that of "to contend, compete, strive for superiority" is from c. 1600.