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The English word reindeer n. is a combination of Old English hran followed by a tautological deer, with the compound itself first attested c.1440. This Anglo-Norman attestation would antedate the word to almost a century.
This passage in Livre de Regions translates Trevisa’s ‘þere ben eendeles many bestes of divers kynde, as beers, hertes, capriole, tragillaphi, bubali and bysontes’, with the word rainders representing Middle English bysontes, i.e. MED biso(u)nt n., ‘the European bison’.