Etymology
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brat (n.)
c. 1500, "beggar's child" ("... wyle beggar with thy brattis ...), originally slang, from a northern, Midlands and western England dialect word for "makeshift or ragged garment;" probably the same word as Old English bratt "cloak," which is from a Celtic source (compare Old Irish bratt "cloak, cloth"). The transferred meaning is perhaps from notion of "child's apron." Hollywood Brat Pack (modeled on 1950s Rat Pack) is from 1985. Brattery "nursery" is attested from 1788.
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bratty (adj.)
"spoiled and juvenile," 1929, from brat + -y (2).
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girl (n.)

c. 1300, gyrle "child, young person" (of either sex but most frequently of females), of unknown origin. One guess [OED] leans toward an unrecorded Old English *gyrele, from Proto-Germanic *gurwilon-, diminutive of *gurwjoz (apparently also represented by Low German gære "boy, girl," Norwegian dialectal gorre, Swedish dialectal gurre "small child," though the exact relationship, if any, between all these is obscure), from PIE *ghwrgh-, also found in Greek parthenos "virgin." But this involves some objectionable philology. Liberman (2008) writes:

Girl does not go back to any Old English or Old Germanic form. It is part of a large group of Germanic words whose root begins with a g or k and ends in r. The final consonant in girl is a diminutive suffix. The g-r words denote young animals, children, and all kinds of creatures considered immature, worthless, or past their prime.

Another candidate is Old English gierela "garment" (for possible sense evolution in this theory, compare brat). A former folk-etymology derivation from Latin garrulus "chattering, talkative" is now discarded. Like boy, lass, lad it is of more or less obscure origin. "Probably most of them arose as jocular transferred uses of words that had originally different meaning" [OED]. Specific meaning of "female child" is late 14c. Applied to "any young unmarried woman" since mid-15c. Meaning "sweetheart" is from 1640s. Old girl in reference to a woman of any age is recorded from 1826. Girl next door as a type of unflashy attractiveness is recorded by 1953 (the title of a 20th Century Fox film starring June Haver).

Doris [Day] was a big vocalist even before she hit the movies in 1948. There, as the latest movie colony "girl next door," sunny-faced Doris soon became a leading movie attraction as well as the world's top female recording star. "She's the girl next door, all right," said one Hollywood admirer. "Next door to the bank." [Life magazine, Dec. 22, 1958]

Girl Friday "resourceful young woman assistant" is from 1940, a reference to "Robinson Crusoe." Girl Scout is from 1909. For the usual Old English word, see maiden.

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bratwurst (n.)
type of sausage, 1904, from German Bratwurst, from wurst + Brät "lean meat, finely chipped calf or swine meat," from Old High German brato (12c.), from Proto-Germanic *bred-on- "roast flesh" (source also of Old English bræd "meat, flesh;" compare brawn), from PIE root *bhreu- "to boil, bubble, effervesce, burn." German folk etymology derives Brät from braten "to roast, bake, broil, grill;" more likely both are from the same ancient source.
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brain-child (n.)
"idea, creation of one's own mind," 1850, from brain (n.) + child. Earlier was the alliterative brain-brat (1630).
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love-child (n.)

"child born out of wedlock, child of illicit love," 1798, from love (n.) + child. Compare German Liebeskind. Earlier was love brat (17c.).

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git (n.)

"worthless person," 1946, British slang, a southern variant of Scottish get "illegitimate child, brat," which is attested by 1706 ("Gregor Burgess protested against the said Allane that called him a witch gyt or bratt"), according to "Dictionary of the Scots Language"); related to beget on the notion of "what is got." Scots get, gyt, geitt, etc. also can be an affectionate term for a child. 

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bastard (n.)
"illegitimate child," early 13c., from Old French bastard "acknowledged child of a nobleman by a woman other than his wife" (11c., Modern French bâtard), probably from fils de bast "packsaddle son," meaning a child conceived on an improvised bed (saddles often doubled as beds while traveling), with pejorative ending -art (see -ard). Alternative possibly is that the word is from Proto-Germanic *banstiz "barn," equally suggestive of low origin.

Compare German bänkling "bastard; child begotten on a bench" (and not in a marriage bed), the source of English bantling (1590s) "brat, small child." Bastard was not always regarded as a stigma; the Conqueror is referred to in state documents as "William the Bastard." Figurative sense of "something not pure or genuine" is late 14c. Use as a generic vulgar term of abuse for a man is attested from 1830. Among the "bastard" words in Halliwell-Phillipps' "Dictionary of Archaic and Provincial Words" are avetrol, chance-bairn, by-blow, harecoppe, horcop, and gimbo ("a bastard's bastard").

As an adjective from late 14c. It is used of things spurious or not genuine, having the appearance of being genuine, of abnormal or irregular shape or size, and of mongrels or mixed breeds.
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cognate (adj.)

1640s, "allied by blood, connected or related by birth, of the same parentage, descended from a common ancestor," from Latin cognatus "of common descent" (source also of Spanish cognado, Italian cognato), from assimilated form of com "together" (see co-) + gnatus, past participle of gnasci, older form of nasci "to be born" (from PIE root *gene- "give birth, beget").

Of things, "related in origin, traceable to the same source," by 1640s; specifically of words, "coming from the same root or original word but showing differences due to subsequent separate phonetic development," by 1782; of languages, "from the same original language," by 1799. French, Spanish, and Italian are cognate languages (all essentially descended from Latin) but are not cognate with Latin. English cognate, Spanish cognado and Italian cognato are cognate words from Latin cognatus. English brother, Sanskrit bhrtr-, Greek phratr, Latin frater, Russian brat are cognate words from the PIE root *bhrater. Words that are cognates are more like cousins than siblings; they develop in different languages.

Related: Cognatic; cognation (late 14c. in English as "blood-relationship, kinship"); cognateness. As a noun, "one connected to another by ties of kinship," from 1754.

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