Etymology
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quality (n.)

c. 1300, qualite, "temperament, character, disposition," from Old French calite, qualite "quality, nature, characteristic" (12c., Modern French qualité), from Latin qualitatem (nominative qualitas) "a quality, property; nature, state, condition" (said [Tucker, etc.] to have been coined by Cicero to translate Greek poiotēs), from qualis "what kind of a" (from PIE root *kwo-, stem of relative and interrogative pronouns).

In early use, and for long thereafter, with awareness of the word's use in Aristotelian philosophy. From late 14c. as "an inherent attribute," also "degree of goodness or excellence." Meaning "social rank, position" is c. 1400, hence "nobility, gentry." From 1580s as "a distinguished and characteristic excellence." 

Noun phrase quality time "time spent giving undivided attention to another person to build a relationship" is recorded by 1977. Quality of life "degree to which a person is healthy and able to participate in or enjoy life events" is from 1943. Quality control "maintenance of desired quality in a manufactured product" is attested from 1935.

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qualitative (adj.)

early 15c., qualitatif, "that produces a (physical) quality," from Medieval Latin qualitativus "relating to quality," from stem of Latin qualitas "a quality, property, nature" (see quality). Meaning "concerned with quality, relating to the possession of qualities without reference to quantities" is from c. 1600 in English, from French qualitatif or Medieval Latin qualitativus. Related: Qualitatively.

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qualify (v.)

mid-15c., qualifien, transitive, "to invest with (a quality), impart a certain quality to," from French qualifier (15c.) and directly from Medieval Latin qualificare "attribute a quality to; make of a certain quality," from Latin qualis "of what sort?," correlative pronominal adjective (see quality) + combining form of facere "to make" (from PIE root *dhe- "to set, put").

Meaning "to limit, modify by a limitation or reservation, restrict" is from 1530s, as is the sense of "to have or have taken the necessary steps for rendering oneself capable of holding an office, etc." The sense of "to be or become fit for an employment, office, etc." is by 1580s. Related: Qualified; qualifying.

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*kwo- 

also *kwi-, Proto-Indo-European root, stem of relative and interrogative pronouns.

It forms all or part of: cheese (n.2) "a big thing;" cue (n.1) "stage direction;" either; hidalgo; how; kickshaw; neither; neuter; qua; quality; quandary; quantity; quasar; quasi; quasi-; query; quib; quibble; quiddity; quidnunc; quip; quodlibet; quondam; quorum; quote; quotidian; quotient; ubi; ubiquity; what; when; whence; where; whether; which; whither; who; whoever; whom; whose; why.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit kah "who, which;" Avestan ko, Hittite kuish "who;" Latin quis/quid "in what respect, to what extent; how, why," qua "where, which way," qui/quae/quod "who, which;" Lithuanian kas "who;" Old Church Slavonic kuto, Russian kto "who;" Old Irish ce, Welsh pwy "who;" Old English hwa, hwæt, hwær, etc.

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salience (n.)

1836, "quality of leaping;" 1849, "quality of standing out, state of projecting or being projected;" see salient (adj.) + -ence. The psychological sense of "quality of being more prominent in the mind or memory" is by 1938.

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modernity (n.)

1620s, "quality or state of being modern," from Medieval Latin modernitatem, noun of quality from modernus (see modern (adj.)). Meaning "something that is modern" is from 1733.

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dearness (n.)

early 14c., "quality of being held in esteem or affection," from dear (adj.) + -ness. From 1520s as "quality of being costly."

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acidity (n.)

"quality of being acid or sour; tartness," 1610s, from French acidité (16c.) or directly from Latin aciditatem (nominative aciditas) "sourness," noun of quality from Latin acidus "sour, tart" (see acid (adj.)).

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brotherliness (n.)

Old English broðorlichnes, in a literal sense, "state or quality of being brothers;" see brotherly + -ness. The meaning "quality of being fraternally kind or affectionate" is from 1530s.

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memorability (n.)

"memorableness, quality of being memorable," 1660s, from memorable + -ity.

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