Gnaw

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Old English gnagen, of Germanic origin; related to German nagen, ultimately imitative.

wiktionary

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From Middle English gnawen, gnaȝen, from Old English gnagan, from Proto-Germanic *gnaganą. Cognate with Dutch knagen, German nagen, Norwegian Bokmål gnage, Norwegian Nynorsk gnaga, Swedish gnaga. Probably from Proto-Indo-European *gʰnēgʰ-(“to gnaw, scratch”)

etymonline

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gnaw (v.)

Old English gnagan "to gnaw, bite off little by little" (past tense *gnog, past participle gnagan), from Proto-Germanic *gh(e)n- "to gnaw" (source also of Old Saxon gnagan, Old Norse, Swedish gnaga, Middle Dutch, Dutch knagen, Old High German gnagan, German nagen "to gnaw"), probably imitative of gnawing. Figurative sense "wear away as if by continued biting" is from early 13c. Related: Gnawed; gnawing.