Etymology
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common (adj.)
Origin and meaning of common

c. 1300, "belonging to all, owned or used jointly, general, of a public nature or character," from Old French comun "common, general, free, open, public" (9c., Modern French commun), from Latin communis "in common, public, shared by all or many; general, not specific; familiar, not pretentious." This is from a reconstructed PIE compound *ko-moin-i- "held in common," compound adjective formed from *ko- "together" + *moi-n-, suffixed form of root *mei- (1) "to change, go, move," hence literally "shared by all."

The second element of the compound also is the source of Latin munia "duties, public duties, functions," those related to munia "office." Perhaps reinforced in Old French by the Germanic form of PIE *ko-moin-i- (compare German gemein, Old English gemne "common, public, general, universal;" see mean (adj.)), which came to French via Frankish.

Used disparagingly of women and criminals since c. 1300. Meaning "pertaining equally to or proceeding equally from two or more" is from c. 1400. Meaning "usual, not exceptional, of frequent occurrence" is from late 14c. Sense of "not distinguished, belonging to the general mass" is from c. 1400; of things, "ordinary, not excellent," late 14c.

Common pleas is 13c., from Anglo-French communs plets, hearing civil actions by one subject against another as opposed to pleas of the crown. Common prayer is that done in public in unity with other worshipers; contrasted with private prayer. Common stock is attested from 1888. Common speech (late 14c.) is the vernacular, as opposed to Latin. Common good (late 14c.) translates Latin bonum publicum "the common weal." The college common room (1660s) is one to which all members have common access. 

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divisor (n.)

"a number by which another number is divided," mid-15c., divisour, from Latin divisor, agent noun from dividere "to divide" (see divide (v.)).

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common (n.)
Origin and meaning of common

c. 1300, "a fellowship or brotherhood; early 14c., "people of a community or town, freemen, citizenry;" late 15c., "land held in common," from Old French commune and Medieval Latin communia, and partly from common (adj.). Also compare commons. Latin communis "common, general" (adj.) also served as a noun meaning "common property; state, commonwealth."

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common law (n.)

mid-14c., "the customary and unwritten laws of England as embodied in commentaries and old cases" (see common (adj.)), as opposed to statute law. Phrase common-law marriage is attested from 1909.

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common-sensical (adj.)

1839, from common sense, with ending as in nonsensical, etc. Common-sensible is attested from 1848.

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common sense (n.)

late 14c., originally an internal mental power supposed to unite (reduce to a common perception) the impressions conveyed by the five physical senses (Latin sensus communis, Greek koine aisthesis). Thus "ordinary understanding, without which one is foolish or insane" (1530s); the meaning "good sense" is from 1726. Also, as an adjective, common-sense "characterized by common sense" (1854).

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utilitarianism (n.)

1827, from utilitarian + -ism. The doctrine that the end of all action should be the greatest happiness of the greatest number.

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maximum (adj.)

"greatest, at the maximum," 1834, from maximum (n.).

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happiness (n.)

1520s, "good fortune," from happy + -ness. Meaning "pleasant and contented mental state" is from 1590s. Phrase greatest happiness for the greatest number was in Francis Hutcheson (1725) but later was associated with Bentham.

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