An Etymological Dictionary of the German Language/Annotated/genau
genau, ‘accurate, precise, strict, parsimonious,’ from late Middle High German (Middle German) nouwe, ‘careful, exact,’ akin to nouwe, genouwe, adverb, ‘scarcely’; compare Dutch naauw, ‘narrow, exact, punctual.’ Probably these cognates, in their Gothic form *ga-nêws, are to be connected with Gothic nêhws, High German nahe. Others refer them to a root nau, ‘to narrow,’ in Not and its cognates.