Etymology
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lie (v.2)

"rest horizontally, be in a recumbent position," early 12c., from Old English licgan (class V strong verb; past tense læg, past participle legen) "be situated, have a specific position; remain; be at rest, lie down," from Proto-Germanic *legjan (source also of Old Norse liggja, Old Saxon liggian, Old Frisian lidzia, Middle Dutch ligghen, Dutch liggen, Old High German ligen, German liegen, Gothic ligan "to lie"), from PIE root *legh- "to lie down, lay."

Especially "to lie in bed," hence often with sexual implications, as in lie with "have sexual intercourse" (c. 1300), and compare Old English licgan mid "cohabit with." To lie in "be brought to childbed" is from mid-15c. To lie to at sea is to come to a standstill. To take (something) lying down "receive passively, receive with abject submission" is from 1854.

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with (prep.)

Old English wið "against, opposite, from, toward, by, near," a shortened form related to wiðer, from Proto-Germanic *withro- "against" (source also of Old Saxon withar "against," Old Norse viðr "against, with, toward, at," Middle Dutch, Dutch weder, Dutch weer "again," Gothic wiþra "against, opposite"), from PIE *wi-tero-, literally "more apart," suffixed form of *wi- "separation" (source also of Sanskrit vi "apart," Avestan vi- "asunder," Sanskrit vitaram "further, farther," Old Church Slavonic vutoru "other, second"). Compare widow (n.).

Sense shifted in Middle English to denote association, combination, and union, partly by influence of Old Norse vidh, and also perhaps by Latin cum "with" (as in pugnare cum "fight with"). In this sense, it replaced Old English mid "with," which survives only as a prefix (as in midwife). Original sense of "against, in opposition" is retained in compounds such as withhold, withdraw, withstand.

Often treated as a conjunction by ungrammatical writers and used where and would be correct. First record of with child "pregnant" is recorded from c. 1200. With it "cool" is African-American vernacular, recorded by 1931. French avec "with" was originally avoc, from Vulgar Latin *abhoc, from apud hoc, literally "with this."

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lie (v.1)

"speak falsely, tell an untruth for the purpose of misleading," late 12c., from Old English legan, ligan, earlier leogan "deceive, belie, betray" (class II strong verb; past tense leag, past participle logen), from Proto-Germanic *leuganan (source also of Old Norse ljuga, Danish lyve, Old Frisian liaga, Old Saxon and Old High German liogan, German lügen, Gothic liugan), a word of uncertain etymology, with possible cognates in Old Church Slavonic lugati, Russian luigatĭ; not found in Latin, Greek, or Sanskrit. Emphatic lie through (one's) teeth is from 1940s.

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lie (n.1)

"an untruth; conscious and intentional falsehood, false statement made with intent to deceive," Old English lyge, lige "lie, falsehood," from Proto-Germanic *lugiz (source also of Old Norse lygi, Danish løgn, Old Frisian leyne (fem.), Dutch leugen (fem.), Old High German lugi, German Lüge, Gothic liugn "a lie"), from the root of lie (v.1).

To give the lie to "accuse directly of lying" is attested from 1590s. Lie-detector is recorded by 1909.

In mod. use, the word is normally a violent expression of moral reprobation, which in polite conversation tends to be avoided, the synonyms falsehood and untruth being often substituted as relatively euphemistic. [OED]
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lie (n.2)
"manner of lying, relative position," 1690s, from lie (v.2). Sense in golf is from 1857.
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lie-down (n.)
period of rest reclining, 1840, from the verbal phrase (attested from c. 1200); see lie (v.2) + down (adv.).
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belie (v.)
Old English beleogan "to deceive by lies," from be- + lie (v.1) "to lie, tell lies." Current sense of "to contradict as a lie, give the lie to, show to be false" is first recorded 1640s.

The other verb lie once also had an identical variant form, from Old English belicgan, which meant "to encompass, beleaguer," and in Middle English was a euphemism for "to have sex with" (i.e. "to lie with carnally").
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fib (n.)
"a lie," especially a little one, "a white lie," 1610s, of uncertain origin, perhaps from fibble-fable "nonsense" (1580s), a reduplication of fable (n.).
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recumbent (adj.)

"leaning, reclining," 1705, from Latin recumbentem (nominative recumbens), present participle of recumbere "recline, lie down, lie down again;" of things, "to fall, sink down, settle down," from re- "back" (see re-) + -cumbere "to lie down" (related to cubare "lie down;" see cubicle). Related: Recumbency (1640s); recumbence (1670s). A verb, recumb, has been attempted in English occasionally since 1670s.

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*legh- 
Proto-Indo-European root meaning "to lie down, lay."

It forms all or part of: allay; anlage; belay; beleaguer; bylaw; coverlet; fellow; lager; lair; law; lawful; lawless; lawsuit; lawyer; lay (v.) "to cause to lie or rest;" ledge; ledger; lees; lie (v.2) "rest horizontally;" litter; lochia; low (adj.) "not high;" outlaw; scofflaw; stalag; vorlage.

It is the hypothetical source of/evidence for its existence is provided by: Hittite laggari "falls, lies;" Greek lekhesthai "to lie down," legos "bed," lokhos "lying in wait, ambush," alokhos "bedfellow, wife;" Latin lectus "bed;" Old Church Slavonic lego "to lie down;" Lithuanian at-lagai "fallow land;" Old Irish laigim "I lie down," Irish luighe "couch, grave;" Old English licgan "be situated, have a specific position; remain; be at rest, lie down."
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