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.
c. 1200, pece, "fixed amount, measure, portion;" c. 1300, "fragment of an object, bit of a whole, slice of meat; separate fragment, section, or part," from Old French piece "piece, bit portion; item; coin" (12c.), from Vulgar Latin *pettia, probably from Gaulish *pettsi (compare Welsh peth "thing," Breton pez "piece, a little"), perhaps from an Old Celtic base *kwezd-i-, from PIE root *kwezd- "a part, piece" (source also of Russian chast' "part"). Related: Pieces.
Meaning "separate article forming part of a class or group" is from c. 1400; that of "specimen, instance, example" is from 1560s. Sense of "portable firearm" is from 1580s, earlier "artillery weapon" (1540s). The meaning "chessman" is from 1560s. Meaning "a period of time" is from early 14c.; that of "a portion of a distance" is from 1610s; that of "literary composition" dates from 1530s.
Piece of (one's) mind "one's opinion expressed bluntly" is from 1570s. Piece of work "remarkable person" echoes Hamlet. Piece as "a coin" is attested in English from c. 1400, hence piece of eight, old name for the Spanish dollar (c. 1600) of the value of 8 reals and bearing a numeral 8. Adverbial phrase in one piece "whole, undivided, without loss or injury" is by 1580s; of a piece "as of the same piece or whole" is from 1610s.
Others are reading
Definitions of apiece from WordNet
to or from every one of two or more (considered individually);
Synonyms: each / to each one / for each one / from each one