Old English half, halb (Mercian), healf (W. Saxon) "side, part," not necessarily of equal division (original sense preserved in behalf), from Proto-Germanic *halba- "something divided" (source also of Old Saxon halba, Old Norse halfr, Old Frisian, Middle Dutch half, German halb, Gothic halbs "half"), a word of no certain etymology. Perhaps from PIE root *skel- (1) "to cut," or perhaps a substratum word. Noun, adjective, and adverb all were in Old English.

Used also in Old English phrases, as in modern German, to mean "one half unit less than," for example þridda healf "two and a half," literally "half third." The construction in two and a half, etc., is first recorded c. 1200. Of time, in half past ten, etc., first attested 1750; in Scottish, the half often is prefixed to the following hour (as in German, halb elf = "ten thirty").

To go off half-cocked in the figurative sense "speak or act too hastily" (1833) is in allusion to firearms going off prematurely; half-cocked in a literal sense "with the cock lifted to the first catch, at which position the trigger does not act" is recorded by 1750. In 1770 it was noted as a synonym for "drunk." Bartlett ("Dictionary of Americanisms," 1848) writes that it was "a metaphorical expression borrowed from the language of sportsmen, and is applied to a person who attempts a thing in a hurry without due preparation, and consequently fails."

Definitions of half
half (adj.)
consisting of one of two equivalent parts in value or quantity;
lasted a half hour
a half chicken
half (adj.)
he did only a half job
gave me a half smile
half (adj.)
(of siblings) related through one parent only;
a half brother
half sister
half (n.)
one of two equal parts of a divisible whole;
half an hour
half a loaf
a century and one half
Synonyms: one-half
half (n.)
one of two divisions into which some games or performances are divided: the two divisions are separated by an interval;
half (adv.)
partially or to the extent of a half;
he was half hidden by the bushes