Etymology
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insinuate (v.)
1520s, "to covertly and subtly introduce into the mind or heart" (trans.), from Latin insinuatus, past participle of insinuare "to thrust in, push in, make a way; creep in, intrude, bring in by windings and curvings, wind one's way into," from in- "in" (from PIE root *en "in") + sinuare "to wind, bend, curve," from sinus "a curve, winding" (see sinus).

Intransitive meaning "hint obliquely" is from 1560s. Meaning "maneuver (someone or something) into some desired position or condition" is from 1570s. Physical or literal sense of "to introduce tortuously or indirectly" is from 1640s. Related: Insinuated; insinuating.
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insinuating (adj.)
"wheedling, ingratiating," 1590s, present-participle adjective from insinuate (v.). Related: Insinuatingly.
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sinuate (adj.)
1680s, from Latin sinuatus, past participle of sinuare (see insinuate).
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insinuation (n.)

1520s, "act of making an indirect suggestion;" 1530s, "that which is indirectly suggested," from French insinuation (16c.) or directly from Latin insinuationem (nominative insinuatio) "entrance through a narrow way; an ingratiating oneself," noun of action from past-participle stem of insinuare "creep in, intrude, wind one's way into" (see insinuate).

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