Etymology
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negate (v.)

"deny, make negative or null," 1795 (with an isolated use from 1620s), a back-formation from negation, or else from Latin negatus, past participle of negare, from PIE root *ne- "not." Related: Negated; negates; negating.

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*ne- 
Proto-Indo-European root meaning "not."

It forms all or part of: a- (3) "not, without;" abnegate; ahimsa; an- (1) privative prefix; annihilate; annul; aught (n.2) "zero, nothing;" deny; hobnob; in- (1) "not, opposite of, without;" ixnay; naught; naughty; nay; nefarious; negate; neglect; negligee; negotiate; neither; nepenthe; nescience; nescient; neuter; never; nice; nihilism; nihility; nil; nill; nimiety; nix; no; non-; none; nonplus; nor; not; nothing; null; nullify; nulliparous; renegade; renege; un- (1) prefix of negation; willy-nilly.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit a-, an- "not;" Avestan na "not;" Greek a-, an-, ne- "not;" Latin in- "not," ne "that not;" Old Church Slavonic and Lithuanian ne "not;" Old Irish an-, ni, Cornish ny "not;" Gothic and Old English un- "not."
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not (adv.)

negative particle, a word expressing negation, denial, refusal, or prohibition, mid-13c., unstressed variant of noht, naht "in no way" (see naught). As an interjection to negate what was said before or reveal it as sarcasm, it is attested by 1900, popularized 1989 by "Wayne's World" sketches on "Saturday Night Live" TV show.

Not, spoken with emphasis, often stands for the negation of a whole sentence referred to: as, I hope not (that is, I hope that the state of things you describe does not exist). [Century Dictionary, 1895]

To not know X from Y (one's ass from one's elbow, shit from Shinola, etc.) was a construction attested from c. 1930 in modern use; but compare Middle English not know an A from a windmill (c. 1400). Double negative construction not un- was derided by Orwell, but is persistent and ancient in English, popular with Milton and the Anglo-Saxon poets.

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left (adj.)

c. 1200, "opposite of right," probably from Kentish and northern English forms of Old English *lyft "weak; foolish" (in lyft-adl "lameness, paralysis"). Compare East Frisian luf, Dutch dialectal loof "weak, worthless").

Sense of "opposite of right" is from the left being usually the weaker hand), a derived sense also found in cognate Middle Dutch and Low German luchter, luft. Compare Lithuanian kairys "left" and Lettish kreilis "left hand" both from a root that yields words for "twisted, crooked."

The usual Old English winstre/winestra "left" (adj.); "left hand," literally "friendlier," a euphemism used superstitiously to avoid invoking the unlucky forces connected with the left side (compare sinister). The Kentish word itself might have been originally a taboo replacement, if instead it represents PIE *laiwo- "considered conspicuous" (represented in Greek laios, Latin laevus, and Russian levyi). Greek also uses a euphemism for "left," aristeros "the better one" (compare also Avestan vairyastara- "to the left," from vairya- "desirable").

Meaning "being on the left-hand side" is from c. 1300. As an adverb from early 14c. For political senses, see left (n.). Used at least since c. 1600 in various senses of "irregular, illicit;" earlier proverbial sense was "opposite of what is expressed" (mid-15c.), for example over the left (shoulder) "not at all," added to a statement to negate or neglect what was just said (1705). To have two left feet "be clumsy" is attested by 1902.

Phrase out in left field "out of touch with pertinent realities" is attested from 1944, from the baseball fielding position that tends to be far removed from the play (left field in baseball attested by 1867; the fielding positions are from the point of view of the batter). The Parisian Left Bank (of the River Seine) has been associated with intellectual and artistic culture at least since 1893; Left Coast "Pacific Coast of the U.S." is by 1980s.

German link, Dutch linker "left" are said to be not directly related to these, being instead from Old High German slinc and Middle Dutch slink "left," related to Swedish linka "limp," slinka "dangle," and Old English slincan "crawl" (Modern English slink).

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