Etymology
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Words related to an-

ad- 

word-forming element expressing direction toward or in addition to, from Latin ad "to, toward" in space or time; "with regard to, in relation to," as a prefix, sometimes merely emphatic, from PIE root *ad- "to, near, at."

Simplified to a- before sc-, sp- and st-; modified to ac- before many consonants and then re-spelled af-, ag-, al-, etc., in conformity with the following consonant (as in affection, aggression). Also compare ap- (1).

In Old French, reduced to a- in all cases (an evolution already underway in Merovingian Latin), but written forms in French were refashioned after Latin in 14c. and English did likewise 15c. in words it had picked up from Old French. In many cases pronunciation followed the shift. Over-correction at the end of the Middle Ages in French and then English "restored" the -d- or a doubled consonant to some words that never had it (accursed, afford). The process went further in England than in France, where the vernacular sometimes resisted the pedantic, resulting in English adjourn, advance, address, advertisement (Modern French ajourner, avancer, adresser, avertissement). In modern word-formation sometimes ad- and ab- are regarded as opposites, but this was not in classical Latin.

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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."
a- (3)
prefix meaning "not, without," from Greek a-, an- "not" (the "alpha privative"), from PIE root *ne- "not" (source also of English un-).

In words from Greek, such as abysmal, adamant, amethyst; also partly nativized as a prefix of negation (asexual, amoral, agnostic). The ancient alpha privatum, denoting want or absence.

Greek also had an alpha copulativum, a- or ha-, expressing union or likeness, which is the a- expressing "together" in acolyte, acoustic, Adelphi, etc. It is from PIE root *sem- (1) "one; as one, together with."
abnormal (adj.)
Origin and meaning of abnormal

"not conformed or conforming to rule, deviating from a type or standard, contrary to system or law, irregular, unnatural," 1835, a refashioning of anormal (q.v.) under influence of Latin abnormalis "deviating from a fixed rule, irregular," from ab "off, away from" (see ab-) + norma "rule" (see norm).

The older form was from French anormal (13c.), from Medieval Latin anormalus, an altered (by association with norma) borrowing of Greek anomalos "uneven, irregular," from an- "not" (see an- (1)) + homalos "even," from homos "same" (from PIE root *sem- (1) "one; as one, together with"). Compare anomaly. "Few words show such a series of pseudo-etymological perversions." Another adjective was abnormous (1742) "irregular, misshapen," from Latin abnormis. Related: Abnormally.

anacoluthon (n.)

"want of grammatical sequence; changing constructions in mid-clause," whether arbitrary or intentional, 1706, from Latinized form of Greek anakoluthon, neuter of anakolouthos "inconsequent," from an- "not" (see an- (1)) + akolouthos "following," from copulative prefix a- expressing union or likeness (see a- (3)) + keleuthos "way, road, track, path, course, journey," which is of unknown etymology. "As a figure of speech it has propriety and force only so far as it suggests that the emotion of the speaker is so great as to make him forget how he began his sentence" [Century Dictionary]. Related: Anacoluthic.

Anacoluthon, though a grammatical defect, is a rhetorical beauty, if naturally produced or imitated; as, "If thou art he—but oh ! how fallen!" "He who hath seen life in all its shapes, and fully knows its good and evil—No ! there is nothing on earth which can make a wise man desire a greater length of days than heaven appoints." These are instances in which the break down is the effect of emotion. [James R. Boyd, "Elements of English Composition," 1874]
anaemia (n.)
"deficiency of blood in a living body," 1824, a medical term from French (1761), from Latinized form of Greek anaimia "lack of blood," from anaimos "bloodless," from an- "without" (see an- (1)) + haima "blood" (see -emia).
anaerobic (adj.)

"capable of living without oxygen," 1884 (earlier anaerobian, 1879), from French anaérobie, coined 1863 by French bacteriologist Louis Pasteur (1822-1895), from Greek an- "without" (see an- (1)) + aēr "air" (see air (n.1)) + bios "life," from PIE root *gwei- "to live."

analgesia (n.)
"absence of pain, incapacity of feeling pain in a part, though tactile sense is preserved," 1706, medical Latin, from Greek analgesia "want of feeling, insensibility," from analgetos "without pain, insensible to pain" (also "unfeeling, ruthless"), from an- "not" (see an- (1)) + algein "to feel pain" (see -algia). An alternative form is analgia.
anamniotic (adj.)
1880, "without an amnion" (of amphibians and fishes); from an- (1) "not, without" + amniotic.
anaphrodisiac (adj.)
"diminishing the sexual appetite," 1823, from Greek anaphroditos "without sexual desire," or from an- (1) "not, without" + aphrodisiac. Related: Anaphrodisia; anaphroditic; anaphroditous.