One of the mysteries of the English language finally explained.
Under the cover of a beech tree; (also more generally) in the shade of a tree.
Early 18th century. From classical Latin sub tegmine fāgī under the cover of a spreading beech tree (Virgil Eclogues 1. 1) from sub + tegmine, ablative of tegmen + fāgī, genitive of fāgus beech.
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