Etymology
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batten (v.2)

"to furnish with battens," 1775, from batten (n.) "strip of wood, bar nailed across parallel boards to hold them together." Nautical phrase batten down "cover (hatches) with tarpaulin and nail it down with battens to make it secure" is recorded from 1821. Related: Battened; battening.

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batten (n.)
"strip of wood, bar nailed across parallel boards to hold them together," 1650s, Englished variant of baton "a stick, a staff" (see baton). Nautical sense "strip of wood nailed down over a tarpaulin over a ship's hatches to prevent leakage in stormy weather" is attested from 1769.
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batten (v.1)
"to improve; to fatten," 1590s, probably representing an unrecorded Middle English dialectal survival of Old Norse batna "improve" (source also of Old English batian, Old Frisian batia, Old High German bazen, Gothic gabatnan "to become better, avail, benefit," Old English bet "better;" also see boot (n.2)). Related: Battened; battening.
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lattice (n.)
"work with open spaces formed by crossing or interlacing of laths, bars, etc.," c. 1300, from Old French latiz "lattice," from late "lath, board, plank, batten" (Modern French latte), from Frankish or some other Germanic source, such as Old High German latta "lath" (see lath). As a verb from early 15c. Related: Latticed.
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doornail (n.)

also door-nail, "large-headed nail used for studding batten doors for strength or ornament," late 14c.; see door (n.) + nail (n.). The figurative expression dead as a doornail is attested as early as the word itself.

But ich haue bote of mi bale bi a schort time, I am ded as dore-nail. ("William of Palerne," c. 1375).

Compare key-cold "lifeless, inanimate, devoid of heat, cold as a metal key" (1510s). Also in Middle English as a symbol of muteness (domb as a dor nail, c. 1400).  

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