Under the cover of a beech tree; (also more generally) in the shade of a tree.
[1641 Wits Recreations(new ed.) sig. Y6v, This is the wine which in former time Each wise one of the Magi Was wont to carouse in a frolicke bouse, Recubans sub tegmine fagi.]
1713 W. Cecil Let. 15 Oct. in A. Hill Impartial Acct. Oil Beech Tree(1714) 17, I have taken all possible Care to be particularly inform'd in the Affair of Beech-Mast.., having liv'd Nine Years in a Part of France, where all the Inhabitants for many Miles round, are, as it were, Sub Tegmine Fagi.
1784 New Foundling Hosp. for Wit(new ed.) II. 56, I set you both down, not indeed sub tegmine fagi, but, for the sake of the costume, in a snug town coffee-house.
1859 T. C. Grattan Civilized Amer. I. xiv. 241, I have listened to him at great meetings in the open air; and sat beside him at public dinners under canvas, and literally sub tegmine fagi.
1864 T. Norris Amer. Angler's Bk. i. 36 When noon comes on, and the trout rise lazily or merely nip, he halts ‘sub tegmine fagi’, or under the shadow of the dark sugar-maple to build a fire and roast trout for his dinner.
1917 Nation (N.Y.) 19 July 65/1 The man..has no invincible repugnance to a glass of beer and a cheese sandwich on a hot summer's day, sub tegmine fagi.
2005 Internat. Labor & Working-class Hist. 67 107 The everyday rural world was naturally quite far away from peace and quiet necessary to lie down tranquilly and play the flageolet sub tegmine fagi.