Etymology
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Words related to on

a- (1)

prefix or inseparable particle, a relic 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 (2)
as in twice a day, etc., a reduced form of Old English an "on" (see on (prep.)), in this case "on each." The sense was extended from time to measure, price, place, etc. The habit of tacking a onto a gerund (as in a-hunting we will go) was archaic after 18c.
about (adv., prep.)
Origin and meaning of about

Middle English aboute, from Old English abutan (adv., prep.), earlier onbutan "on the outside of; around the circumference of, enveloping; in the vicinity of, near; hither and thither, from place to place," also "with a rotating or spinning motion," in late Old English "near in time, number, degree, etc., approximately;" a compound or contraction of on (see on; also see a- (1)) + be "by" (see by) + utan "outside," from ut (see out (adv.)).

By c. 1300 it had developed senses of "around, in a circular course, round and round; on every side, so as to surround; in every direction;" also "engaged in" (Wist ye not that I must be about my Father's business?), and gradually it forced out Old English ymbe, ymbutan (from PIE root *ambhi- "around") in the sense "round about, in the neighborhood of."

From mid-13c. as "in the matter, in connection with." From early 14c. as "in partial rotation, so as to face in a different direction." From late 14c. as "near at hand, about one's person." "In a circuitous course," hence "on the move" (late 13c.), and in Middle English "be about to do, be busy in preparation for," hence its use as a future participle in (to be) about to "in readiness, intending." Abouts (late 14c.), with adverbial genitive, still found in hereabouts, etc., probably is a northern dialectal form.

To bring about "cause or affect" and to come about "happen" are from late 14c. About face as a military command (short for right about face) is first attested 1861, American English.

above (adv., prep.)
Origin and meaning of above

Middle English above, aboven (also aboun in northern dialects, abow in southwestern dialects), from Old English abufan (adv., prep.), earlier onbufan "above, in or to a higher place, on the upper side; directly over, in or to a higher place than," a contraction or compound of on (also see a- (1)) + bufan "over."

The second element is itself a compound of be "by" (see by) + ufan "over/high" (from Proto-Germanic *ufan-, source also of Old Saxon, Old High German oban, German oben; from PIE root *upo "under," also "up from under," hence also "over").

From c. 1200 as "of higher rank or position, superior in authority or power; of higher rank than, superior to." This sense in Middle English perhaps was reinforced by a literal use of above in the sense "higher at the table than," thus "in a place of greater honor than, taking precedence over" (mid-14c.) From mid-14c. as "in addition to;" also "superior to, out of reach of, not condescending to." From late 14c. as "more" (in number, linear measurement, weight, value); "older; better than, more desirable than, superior to."

Phrase above all "before other considerations" is from late 14c. To be above (someone's) head in the figurative sense "out of range of his or her intellect" is from 1914 (above in the sense "not to be grasped or understood by" is from mid-14c.). In Middle English to be above erthe was "above ground, unburied," hence "living, among the living."

acknowledge (v.)
late 15c., "admit or show one's knowledge," a blend of Middle English aknow "admit or show one's knowledge" (from Old English oncnawan "understand, come to recognize," from on (see on (prep.)) + cnawan "recognize;" see know) and Middle English knowlechen "admit, acknowledge" (c. 1200; see knowledge). "By 16th c. the earlier vbs. knowledge and a(c)know ... were obs., and acknowledge took their place" [OED].

In the merger, an unetymological -c- slipped in; perhaps the explanation is that when English kn- became a simple "n" sound, the -c- stepped up to preserve, in this word, the ancient "kn-" sound. Related: Acknowledged; acknowledging.
add-on (n.)
"additional component," 1941, from verbal phrase add on; see add (v.) + on (adv.).
afar (adv.)
contraction of Middle English of feor (late 12c.), on ferr (c. 1300), from Old English feor "far" (see far); the a- (1) in compounds representing both of and on (which in this use meant the same thing). Spelled afer in 14c.
again (adv.)

late Old English agan, from earlier ongean (prep.) "toward; opposite, against, contrary to; in exchange for," as an adverb "in the opposite direction, back, to or toward a former place or position," from on "on" (see on (prep.) and compare a- (1)) + -gegn "against, toward," from Germanic root *gagina (source also of Old Norse gegn "straight, direct;" Danish igen "against;" Old Frisian jen, Old High German gegin, German gegen "against, toward," entgegen "against, in opposition to")

In Old English, eft (see eftsoons) was the main word for "again," but this often was strengthened by ongean, which became the principal word by 13c. Norse influence is responsible for the hard -g-. Differentiated from against (q.v.) 16c. in southern writers, again becoming an adverb only, and against taking over as preposition and conjunction, but again clung to all senses in northern and Scottish dialect (where against was not adopted). Of action, "in return," early 13c.; of action or fact, "once more," late 14c.

aloft (adv.)
"on high, in the air," c. 1200, from a Scandinavian source such as Old Norse a lopt "up above," literally "up in the air," from a "in, on" (see on) + lopt "sky, air, atmosphere; loft, upper room," from the general Germanic word for "air" (cognate with Gothic luftus, Old High German luft, Old English lyft "air;" see loft (n.)). Scandinavian -pt- pronounced like -ft-. The Old English equivalent was on þa lyft.
ana- 

before vowels an-, word-forming element meaning: 1. "upward, up in place or time," 2. "back, backward, against," 3. "again, anew," from Greek ana (prep.) "up, on, upon; up to, toward; throughout; back, backwards; again, anew," from an extended form of PIE root *an- (1) "on, upon, above" (see on, which is the English cognate). In old medical prescriptions, ana by itself meant "an equal quantity of each."