Etymology
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appointment (n.)
early 15c., "an agreement," also "a fixing of a date for official business," from Old French apointement, from apointer "arrange, settle, place" (see appoint). Meaning "act of placing in office" is attested from 1650s.
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*peuk- 
also *peug-, Proto-Indo-European root meaning "to prick."

It forms all or part of: appoint; appointment; bung; compunction; contrapuntal; expugn; expunge; impugn; interpunction; oppugn; pink; poignant; point; pointe; pointillism; poniard; pounce; pugilism; pugilist; pugnacious; pugnacity; punch (n.1) "pointed tool for making holes or embossing;" punch (n.3) "a quick blow with the fist;" punch (v.) "to hit with the fist;" puncheon (n.2) "pointed tool for punching or piercing;" punctilio; punctilious; punctual; punctuate; punctuation; puncture; pungent; punty; Pygmy; repugn; repugnance; repugnant.

It is the hypothetical source of/evidence for its existence is provided by: Greek pyx "with clenched fist," pygme "fist, boxing," pyktes "boxer;" Latin pugnare "to fight," especially with the fists, pungere "to pierce, prick."
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cronyism (n.)

1840, "friendship," from crony + -ism. Meaning "appointment of friends to important positions, regardless of ability" is originally American English, by 1952.

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walk-in (adj.)
1928, "without appointment," from the verbal phrase, from walk (v.) + in (adv.). As a noun, meaning "walk-in closet," by 1946.
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disappoint (v.)

mid-15c., disappointen, "dispossess of appointed office," from dis- "reverse, opposite of" + appoint, or else from Old French desapointer "undo the appointment, remove from office" (14c., Modern French from désappointer). Modern sense of "to frustrate the expectations or desires of" is from late 15c. of persons; of plans, etc., "defeat the realization or fulfillment of," from 1570s, perhaps via a secondary meaning of "fail to keep an appointment."

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deputation (n.)

late 14c., deputacioun, "appointment or authority to represent or act for another or others," noun of action from depute (v.). From 1732 as "person or persons authorized to represent or act for others."

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date (n.3)

"liaison at a particular time, by prearrangement," 1885, gradually evolving from date (n.1) in its general sense of "appointment." The romantic sense is by 1890s. Meaning "person one has a date with" is by 1900. Date-rape is attested by 1973.

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Samarra 

city in north-central Iraq; phrase an appointment in Samarra indicating the inevitability of death is from an old Arabic tale (first told in English apparently in W. Somerset Maugham's play "Sheppey," 1933): One day in the marketplace in Baghdad a man encounters Death (with a surprised look on his bony face); the man flees in terror and by dusk has reached Samarra. Death casually takes him there, and, when questioned, says, "I was astonished to see him in Baghdad, for I had an appointment with him tonight in Samarra."

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engagement (n.)

1620s, "formal promise," from engage + -ment. Meaning "a battle or fight between armies or fleets" is from 1660s; sense of "state of having entered into a promise of marriage" is from 1742; meaning "appointment" is from 1806. Engagement ring attested by 1840.

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nepotism (n.)
"favoritism shown to relatives, especially in appointment to high office," 1660s, from French népotisme (1650s), from Italian nepotismo, from nepote "nephew," from Latin nepotem (nominative nepos) "grandson, nephew" (see nephew). Originally, practice of granting privileges to a pope's "nephew" which was a euphemism for his natural son.
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