An Etymological Dictionary of the German Language/Annotated/Wüste
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Wüste, feminine, ‘desert, wilderness,’ from the equivalent Middle High German wüeste, Old High German wuostî (wuostinna), feminine; compare Old Saxon wôstinnia, Anglo-Saxon wêsten, ‘wilderness.’ To these West Teutonic cognates, which point to a pre-Teutonic adjective wâstu, Old Irish fás, and Latin vâstus, ‘waste,’ are primitively allied. The West Teutonic adjective cannot be borrowed from Latin (only Middle High German waste, ‘desert,’ is probably thus obtained).