A, as a prefix to English words, is derived from various sources. (1) It frequently signifies on or in (from an, a forms of AS. on), denoting a state, as in afoot, on foot, abed, amiss, asleep, aground, aloft, away (AS. onweg), and analogically, ablaze, atremble, etc. (2) AS. of off, from, as in adown (AS. ofd off the dun or hill). (3) AS. ā- (Goth. us-, ur-, Ger. er-), usually giving an intensive force, and sometimes the sense of away, on, back, as in arise, abide, ago. (4) Old English y- or i- (corrupted from the AS. inseparable particle ge-, cognate with OHG. ga-, gi-, Goth. ga-), which, as a prefix, made no essential addition to the meaning, as in aware. (5) French à (L. ad to), as in abase, achieve. (6) L. a, ab, abs, from, as in avert. (7) Greek insep. prefix abyss, atheist; akin to E. un-. [1913 Webster]
"Besides these, there are other sources from which the prefix a takes its origin." [1913 Webster]

a-, prefix not, without (amoral; agnostic; apetalous).

a-, prefix implying motion onward or away, adding intensity to verbs of motion (arise; awake).

a-, prefix to, at, or into a state (adroit; agree; amass; avenge).

a-, prefix.
1 from, away (abridge).
2 of (akin; anew).
3 out, utterly (abash; affray).
4 in, on, engaged in, etc. (see A(2)).

a-, prefix assim. form of AD- before sc, sp, st.