According to CDB, the German and English words originally meant 'field' in the most general sense (OHG, MHG, OE), before becoming more specialised to mean 'tract of land for cultivation' in Middle and Modern English and in German.
Guus Kroonen. Etymological Dictionary of Proto-Germanic. Indo-European Etymological Dictionaries Online. Edited by Alexander Lubotsky. Brill. Brill Online.
Svensk Ordbok, Allén, Sture, Abelin, Åsa (1986). Svensk ordbok: [ordens betydelse och användning] : [mer än 100.000 ord och fraser]. Solna: Esselte studium.
Robert Farren, PIE culture words collection, 2017
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