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."
mast n.1
"long pole on a ship, secured as the lower end to the keel, to support the yards, sails, and rigging in general," Old English mæst, from Proto-Germanic *mastaz (source also of Old Norse mastr, Middle Dutch maste, Dutch, Danish mast, German Mast), from PIE *mazdo- "a pole, rod" (source also of Latin malus "mast," Old Irish matan "club," Irish maide "a stick," Old Church Slavonic mostu "bridge").
The single mast of an old ship was the boundary between the quarters of the officers and those of the crew, hence before the mast "serving as an ordinary seaman" in the title of Dana's book, etc.
In all large vessels the masts are composed of several lengths, called lower mast, topmast, and topgallantmast. The royalmast is now made in one piece with the topgallantmast. A mast consisting of a single length is called a pole-mast. In a full-rigged ship with three masts, each of three pieces, the masts are distinguished as the foremast, the mainmast, and the mizzenmast; and the pieces as the foremast (proper), foretopmast, foretopgallantmast, etc. In vessels with two masts, they are called the foremast and mainmast; in vessels with four masts, the aftermast is called the spanker-mast or jigger-mast. [Century Dictionary, 1895]