half-shirt (n.)

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."

Old English scyrte "skirt, tunic," from Proto-Germanic *skurtjon "a short garment" (source also of Old Norse skyrta, Swedish skjorta "skirt, kirtle;" Middle Dutch scorte, Dutch schort "apron;" Middle High German schurz, German Schurz "apron"), perhaps related to Old English scort, sceort "short," etc., from PIE root *sker- (1) "to cut," on the notion of "a cut piece." Lithuanian šarkas "shirt," Old Church Slavonic sraka "tunic," Russian soročka, Finnish sarkki "shirt" perhaps are from Germanic. 

Formerly of the chief garment worn by both sexes, but in modern use long only of that for men; in reference to women's tops, reintroduced 1896. Bloody shirt, exposed as a symbol of outrage, is attested from 1580s. To give (someone) the shirt off one's back is from 1771. To lose one's shirt "suffer total financial loss" is from 1935. To keep one's shirt on "be patient" (1904) is from the notion of (not) stripping down for a fight.