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word-forming element with a wide range of meaning: "thoroughly, completely; to make, cause seem; to provide with; at, on, to, for," from Old English be- "on all sides" (also used to make transitive verbs and as a privative or intensive prefix), from weak form of Old English bi "by," probably cognate with second syllable of Greek amphi, Latin ambi and originally meaning "about" (see ambi-).
This sense naturally drifted into intensive (cf. bespatter "spatter about," therefore "spatter very much"). Be- can also be privative (cf. behead), causative, or have just about any sense required. The prefix was productive 16c.-17c. in forming useful words, many of which have not survived, e.g. bethwack "to thrash soundly" (1550s), betongue "to assail in speech, to scold" (1630s).