An Etymological Dictionary of the German Language/Annotated/Gruß
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Gruß, masculine, ‘greeting, salute,’ from the equivalent Middle High German and Old High German gruoȥ, masculine; corresponding to Dutch groet. ‘To this is allied grüßen, from Middle High German grüeȥen (grüetzen), Old High German gruoȥȥen (gruozzen), weak verb, ‘to address, accost’ (also with hostile intent ‘to attack’); corresponding to Anglo-Saxon grêtan, English to greet, Dutch groeten, Old Saxon grôtian, ‘to address,’ Old Icelandic grœta. The latter is probably the primary meaning of the cognates, which are merely West Teutonic. Origin obscure.