Etymology
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a- (1)

prefix or inseparable particle, a conglomerate of various Germanic and Latin elements.

In words derived from Old English, it commonly represents Old English an "on, in, into" (see on (prep.)), as in alive, above, asleep, aback, abroad, afoot, ashore, ahead, abed, aside, obsolete arank "in rank and file," etc., forming adjectives and adverbs from nouns, with the notion "in, at; engaged in." In this use it is identical to a (2).

It also can represent Middle English of (prep.) "off, from," as in anew, afresh, akin, abreast. Or it can be a reduced form of the Old English past participle prefix ge-, as in aware.

Or it can be the Old English intensive a-, originally ar- (cognate with German er- and probably implying originally "motion away from"), as in abide, arise, awake, ashamed, marking a verb as momentary, a single event. Such words sometimes were refashioned in early modern English as though the prefix were Latin (accursed, allay, affright are examples).

In words from Romanic languages, often it represents reduced forms of Latin ad "to, toward; for" (see ad-), or ab "from, away, off" (see ab-); both of which by about 7c. had been reduced to a in the ancestor of Old French. In a few cases it represents Latin ex.

[I]t naturally happened that all these a- prefixes were at length confusedly lumped together in idea, and the resultant a- looked upon as vaguely intensive, rhetorical, euphonic, or even archaic, and wholly otiose. [OED]
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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."
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ab- 
word-forming element meaning "away, from, from off, down," denoting disjunction, separation, departure; from Latin ab (prep.) "off, away from" in reference to space or distance, also of time, from PIE root *apo- "off, away" (also the source of Greek apo "off, away from, from," Sanskrit apa "away from," Gothic af, English of, off; see apo-).

The Latin word also denoted "agency by; source, origin; relation to, in consequence of." Since classical times usually reduced to a- before -m-, -p-, or -v-; typically abs- before -c-, -q-, or -t-.
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abs- 
the usual form of ab- before -c-, -q-, or -t-.
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aceto- 

before vowels acet-, word-forming element from acetic and generally indicating compounds from or related to acetic acid, thus ultimately from Latin acetum "vinegar."

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acro- 

word-forming element meaning "highest, topmost, at the extremities," before vowels acr-, from Latinized form of Greek akro- "pertaining to an end, extreme," from akros "at the end, at the top, outermost; consummate, excellent" (from PIE *akri-, from root *ak- "be sharp, rise (out) to a point, pierce").

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actino- 

before vowels actin-, word-forming element meaning "pertaining to rays," from Latinized form of Greek aktis (genitive aktinos) "ray of light, beam of light; spoke of a wheel;" a word of unknown etymology. It is perhaps cognate with Sanskrit aktuh "light, ray," Gothic uhtwo "dawn, daybreak," Lithuanian anksti "early" [Beekes].

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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 French refashioned its written forms on the Latin model 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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adeno- 

scientific word-forming element meaning "gland," from Greek adēn "gland," which is perhaps from a suffixed form of PIE root *engw- "groin; internal organ" (source also of Latin inguen "groin"), but Beekes rejects all cognates and calls it isolated.

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aero- 

word-forming element meaning "air, atmosphere; gases," in 20c. use with reference to aircraft or aviation, from Greek aēr (genitive aeros) "air, lower atmosphere" (see air (n.1)).

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