Etymology
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Words related to *kes-

caret (n.)
"mark in correcting printers' proofs to show where something is to be inserted," 1680s, from Latin caret "there is lacking," 3rd person singular indicative of carere "to lack, to want" (from suffixed form of PIE root *kes- "to cut").
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cashier (v.)
"dismiss from an office or place of trust," 1590s, from Middle Dutch casseren, kaseeren "to cast off, discharge," from French casser "to discharge, annul," from Late Latin cassare "annul," from Latin cassus "void, empty" (from extended form of PIE root *kes- "to cut"). Related: Cashiered; cashiering.
cassation (n.)
"anullment, act of cancelling," early 15c., from Old French cassation, from casser, from Late Latin cassare, from Latin quassare "annul, quash" (see quash).
caste (n.)

"one of the hereditary social groups of India," 1610s from Portuguese casta "breed, race, caste," earlier casta raça, "unmixed race," from Latin castus "cut off, separated" (also "pure," via notion of "cut off" from faults), past participle of carere "to be cut off from," from PIE *kas-to-, from root *kes- "to cut." Caste system is first recorded 1840. An earlier, now-obsolete sense of caste in English is "a race of men" (1550s), from Latin castus "chaste."

Of the castes, the first three are the natural and gradually established divisions of the Aryan invaders and conquerors of India; the fourth was made up of the subjugated aborigines. The Sanskrit name for caste is varna, color, the different castes having been at first marked by differences of complexion, according to race, and in some degree according to occupation and consequent exposure. [Century Dictionary, 1895]
castellan (n.)

also castellain, "a governor of a castle," late 14c., from Old North French castelain,Old French chastelain "owner and lord of a castle, nobleman; keeper of a castle" (Modern French châtelaine),from chastel"castle," from Latin castellum "castle" (see castle (n.)). Related: Castellany"jurisdiction of a castellan."

castellated (adj.)

"furnished with turrets and battlements," 1670s, from Medieval Latin castellatus "built like a castle," past participle of castellare "to fortify as a castle, build as a castle, furnish with turrets and battlements," from Latin castellum "castle, fort, citadel, stronghold" (see castle (n.)). Related: Castellation.

Castile 

medieval Spanish county and later kingdom, from Vulgar Latin *castilla, from Latin castella, plural of castellum "castle, fort, citadel, stronghold" (see castle (n.)); so called in reference to the many fortified places there during the Moorish wars. The name in Spanish is said to date back to c.800. Related: Castilian. As a fine kind of soap, in English from 1610s.

castle (n.)

late Old English castel "village" (this sense from a biblical usage in Vulgar Latin); later "large building or series of connected buildings fortified for defense, fortress, stronghold" (late Old English), in this sense from Old North French castel (Old French chastel, 12c.; Modern French château), from Latin castellum "a castle, fort, citadel, stronghold; fortified village," diminutive of castrum "fort," from Proto-Italic *kastro- "part, share;" cognate with Old Irish cather, Welsh caer "town" (probably related to castrare via notion of "cut off," from PIE root *kes- "to cut"). In early bibles, castle was used to translate Greek kome "village."

Latin castrum in its plural castra was used for "military encampment, military post" and thus it came into Old English as ceaster and formed the -caster and -chester in place names. Spanish alcazar "castle" is from Arabic al-qasr, from Latin castrum. Castles in Spain "visionary project, vague imagination of possible wealth" translates 14c. French chastel en Espaigne (the imaginary castles sometimes stood in Brie, Asia, or Albania) and probably reflects the hopes of landless knights to establish themselves abroad. The statement that an (English) man's home is his castle is from 16c.

THAT the house of every man is to him as his castle and fortress, as well for his defence against injuries and violence, as for his repose .... [Edward Coke, "Semaynes Case," 1604]
castigate (v.)

"to chastise, punish," c. 1600, from Latin castigatus, past participle of castigare "to correct, set right; purify; chastise, punish," from castus "pure" (see caste) + agere "to do" (from PIE root *ag- "to drive, draw out or forth, move"). The notion behind the word is "make someone pure by correction or reproof." Compare purge (v.), from purus + agere. Related: Castigated; castigating; castigator; castigatory.

If thou didst put this soure cold habit on To castigate thy pride, 'twere well. [Shakespeare, "Timon" IV.iii (1607)]
castrate (v.)

"to deprive of the testicles, emasculate," 1610s (implied in castrated), back-formation from castration (q.v.), or from Latin castratus, past participle of castrare "to castrate, emasculate; to prune," supposedly from a noun *castrum "knife, instrument that cuts," from PIE root *kes- "to cut." The figurative sense "destroy the strength or vitality of" is attested earlier (1550s). Related: Castrating.