Old English half, halb (Mercian), healf (W. Saxon) "side, part," not necessarily of equal division (original sense preserved in behalf), from Proto-Germanic *halbaz "something divided" (source also of Old Saxon halba, Old Norse halfr, Old Frisian, Middle Dutch half, German halb, Gothic halbs "half"), perhaps from PIE root *skel- (1) "to cut." 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."
half seas over
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