Etymology
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Words related to intricate

*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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extricate (v.)

"disentangle, disengage, set free," 1610s, from Latin extricatus, past participle of extricare "disentangle," figuratively "clear up, unravel," perhaps from ex "out of" (see ex-) + tricae (plural) "perplexities, hindrances," which is of unknown origin. Related: Extricated; extricating.

intricacy (n.)
c. 1600, "state of being complex;" 1610s, "an intricate situation or condition," from intricate (adj.) + -cy. Related: Intricacies.
intrigue (v.)

1610s, "to trick, deceive, cheat," from French intriguer (16c.), from Italian intrigare "to plot, meddle; perplex, puzzle," from Latin intricare "to entangle, perplex, embarrass" (see intricate).

Meaning "to plot or scheme" is recorded by 1714. That of "to excite curiosity" is from 1894 (OED calls this use "A modern gallicism"). It also could mean "carry on a clandestine or illicit sexual relationship" (1650s). The word appears earlier in English as entriken "entangle, ensnare; involve in perplexity, embarrass" (late 14c.), from Old French entrique or directly from the Latin verb. Related: Intrigued; intriguer; intriguing. Dutch intrigueren, German intriguiren are from French.