Etymology
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trench (n.)

late 14c., "track cut through a wood," later "long, narrow ditch" (late 15c.), from Old French trenche "a slice, cut, gash, slash; defensive ditch" (13c., Modern French tranche), from trenchier "to cut, carve, slice," possibly from Vulgar Latin *trincare, from Latin truncare "to maim, mutilate, cut off," from truncus "maimed, mutilated," also "trunk of a tree, trunk of the body," of uncertain origin, probably originally "mutilated, cut off," and perhaps from PIE root *tere- (2) "cross over, pass through, overcome."

Trenches for military protection are first so called c. 1500. Trench warfare first attested 1918. Trench-coat first recorded 1916, a type of coat worn by British officers in the trenches during World War I.

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trenchant (adj.)
early 14c., "cutting, sharp," from Old French trenchant "cutting, sharp" (literal and figurative), present participle of trenchier "to cut" (see trench). Figurative sense in English is from c. 1600.
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tranche (n.)
c. 1500, from French tranche "a cutting," from trancher, trencher "to cut," Old French trenchier "to cut, carve, slice" (see trench). Economic sense is from 1930.
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entrench (v.)
also intrench, 1550s, implied in intrenched, from en- (1) "make, put in" + trench (n.). Figurative use is from 1590s. Related: Entrenched; entrenching.
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trencher (n.)
"wooden platter on which to cut meat," c. 1300, from Anglo-French trenchour, Old North French trencheor "a trencher," literally "a cutting place," from Old French trenchier "to cut, carve, slice" (see trench).
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retrench (v.2)

"cut off, cut down, pare away" (expenses, etc.), 1620s, from obsolete French retrencher "to cut off, lessen, shorten" (Modern French retrancher, Old French retrenchier), from re- "back" (see re-) + Old French trenchier "to cut" (see trench). Especially "reduce (expenses) by economy" (1709). Related: Retrenched; retrenching.

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*tere- (2)

*terə- Proto-Indo-European root meaning "cross over, pass through, overcome."

It forms all or part of: avatar; caravanserai; nectar; nectarine; nostril; seraglio; thrill; thorough; through; tranche; trans-; transient; transom; trench; truculent; truncate; trunk.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit tirah, Avestan taro "through, beyond;" Latin trans "beyond;" Old Irish tre, Welsh tra "through;" Old English þurh "through."

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retrench (v.1)
1590s, "dig a new trench as a second line of defense," 1590s, probably a back-formation from retrenchment in the military sense. Related: Retrenched; retrenching.
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sulcate (adj.)
"furrowed, grooved," 1760, from Latin sulcatus, past participle of sulcare "to make furrowed," from sulcus "furrow, trench, ditch" (see sulcus).
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sike (n.)
also syke, "small stream," a Scottish and Northern word, from Old English sic or cognate Old Norse sik "a ditch, trench."
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