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Polish word niemiecki comes from Proto-Slavic *němъ, and later Proto-Slavic *němьčьskъ (German.)
*němъ (Proto-Slavic)
Dumb, mute (not able to speak). Unclear or incomprehensible speaker, muttering, mammering.
*němьcь (Proto-Slavic)
Foreigner, non-Slav. Specifically, a German (someone who speaks a Germanic language).
*němьčьskъ (Proto-Slavic)
German.
niemiecki (Polish)
German (language) German.