Etymology
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cheat (n.)

late 14c., "forfeited property, reversion of property to a lord," from cheat (v.) or from escheat (n.). Meaning "a fraud committed by deception, a deceptive act" is from 1640s; earlier, in thieves' jargon, it meant "a stolen thing" (late 16c.), and earlier still "dice" (1530s). It also was used in canting slang generally, as an affix, for any "thing" (e.g. cackling-chete "a fowl," crashing-chetes "the teeth"). Meaning "a swindler, a person who cheats" is from 1660s; from 1680s as "anything which deceives or is intended to deceive."

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cheat (v.)

mid-15c., "to escheat, to seize as an escheat," a shortening of Old French escheat, legal term for revision of property to the state when the owner dies without heirs, literally "that which falls to one," past participle of escheoir "happen, befall, occur, take place; fall due; lapse (legally)," from Late Latin *excadere "fall away, fall out," from Latin ex- "out" (see ex-) + cadere "to fall" (from PIE root *kad- "to fall").

Also compare escheat. The royal officers who had charge of  escheats evidently had a reputation for unscrupulousness, and the meaning of the verb evolved through "confiscate" (mid-15c.) to "deprive unfairly" (1580s), to "deceive, impose upon, trick" (1630s). Intransitive sense "act dishonestly, practice fraud or trickery" is from 1630s. To cheat on (someone) "be sexually unfaithful" is attested by 1934. Related: Cheated; cheating.

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on- 

the preposition and adverb on used as a prefix; Old English on-, an-.

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-on 
subatomic particle suffix, from ion.
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on (prep., adv.)

"in a position above and in contact with; in such a position as to be supported by;" also noting the goal to which some action is or has been directed; "about, concerning, regarding; in a position to cover;" as an adverb, "in or into a position in contact with and supported by the top or upper part of something; in or into place; in place for use or action; into movement or action; in operation," Old English on, unstressed variant of an "in, on, into," from Proto-Germanic *ana "on" (source also of Dutch aan, German an, Gothic ana "on, upon"), from PIE root *an- (1) "on" (source also of Avestan ana "on," Greek ana "on, upon," Latin an-, Old Church Slavonic na, Lithuanian nuo "down from").

Also used in Old English in many places where we now would use in. From 16c.-18c. (and still in northern England dialect) often reduced to o'. Phrase on to "aware" is from 1877.

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clip-on (adj.)

"held on by means of a clip," 1909, from the verbal phrase; see clip (v.2) + on (adv.).

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hang on (v.)
1860, "to remain clinging," 1860, especially "cling fondly to" (1871); see hang (v.) + on (adv.). As a command to be patient, wait a minute, from 1936, originally in telephone conversations.
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hard-on (n.)
"penile erection," 1922, earlier as an adjective (1893), from hard + on.
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add-on (n.)
"additional component," 1941, from verbal phrase add on; see add (v.) + on (adv.).
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