Etymology
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Cox 

surname, from early 16c., earlier Cocks (c. 1300), in many cases from cock (n.1), which apparently was used as a personal name in Old English, also a familiar term for a boy, later used of apprentices, servants, etc. Perhaps in some cases for the sign of an inn, and in some cases perhaps from cook (n.), or Welsh coch "red."

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hostess (n.)
late 13c., "woman who keeps an inn or public hotel," from host (n.1) + -ess, or from Old French ostesse, hostesse "hostess; servant; guest" (Modern French hôtesse). Old French also had ostelaine; the Latin word was hospita. Meaning "woman who presides at a dinner party, etc." recorded by 1822. Also used mid-20c. in sense "female who entertains customers in nightclubs," with overtones of prostitution.
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harbor (n.)

"lodging for ships; sheltered recess in a coastline," early 12c., a specialized sense of Middle English herberwe "temporary dwelling place, quarters, lodgings; an inn; the camp of an army in the field," probably from Old English here-beorg (West Saxon), *here-berg (Anglian) "lodgings, quarters," from Proto-Germanic compound *harja-bergaz "shelter, lodgings," from *heri "army, host" (see harry (v.)) + *burzjan- "protection, shelter" (from PIE root *bhergh- (1) "to hide, protect"). Perhaps modeled on Old Norse herbergi "room, lodgings, quarters."

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hospice (n.)
1818, "rest house for travelers," especially the houses of refuge and shelter kept by monks in the passes of the Alps, from French hospice "hospital, almshouse" (Old French ospice "hospice, shelter," also "hospitality," 13c.), from Latin hospitium "hospitable reception, entertainment; hospitality, bonds of hospitality, relationship of guest and host;" also "place of entertainment, lodging, inn, guest-house," from hospes (genitive hospitis) "guest; host," also "a stranger, foreigner" (see host (n.1)).

Sense of "home for the aged and terminally ill " is from 1879; hospice movement first attested 1978.
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harbinger (n.)
late 15c., herbengar "one sent ahead to arrange lodgings" (for a monarch, an army, etc.), alteration of Middle English herberger "provider of shelter, innkeeper" (late 12c.), from Old French herbergeor "one who offers lodging, innkeeper," agent noun from herbergier "provide lodging," from herber "lodging, shelter," from Frankish *heriberga "lodging, inn" (cognate with Old Saxon, Old High German heriberga "army shelter"), from Germanic compound *harja-bergaz "shelter, lodgings," which is also the source of harbor (n.). Sense of "forerunner, that which precedes and gives notice of the coming of another" is mid-16c. The unetymological -n- is from 15c. (see messenger). As a verb, from 1640s (harbinge "to lodge" is late 15c.).
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reckoning (n.)

early 14c., rekening, "a narration, account," verbal noun from reckon (v.). The meaning "a settling of accounts" is from mid-14c.; that of "act of counting or computing, a calculation" is from late 14c. as is the sense of "a bill of charges" (in an inn, tavern, etc.). Compare Dutch rekening "a bill, account, reckoning," Old High German rechenunga, German rechnung, Danish regning "a reckoning, computation."

The general sense is "a summing up," whether in words or numbers. In nautical use from 1660s: "Calculation of the position of a ship from the rate as determined by the log and the course as determined by the compass." Day of reckoning is attested from c. 1600; the notion is of rendering an account of one's life and conduct to God at death or judgment.

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innovator (n.)
"an introducer of changes," 1590s, from Late Latin innovator, agent noun from innovare "to change" (see innovate).
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innominable (adj.)

"unnameable," late 14c., from Old French innominable, from Late Latin innominabilis "that cannot be named," from in- "not, opposite of" (see in- (1)) + *nominabilis, from Latin nominalis "pertaining to a name or names," from nomen (genitive nominis) "name" (from PIE root *no-men- "name"). In jocular use, innominables = "trousers" (1827; see inexpressible).

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inner (adj.)

c. 1400, from Old English inra, comparative of inne (adv.) "inside" (see in (adv.)). Similar formation in Old High German innaro, German inner. The original order of comparison was in/inner/inmost; the evolution has been unusual for a comparative, and inner has not been used with than since Middle English.

Inner man "the soul" is from late Old English; as "the spiritual part of man" by late 14c. The Quaker inner light is attested by that name from 1833. Inner tube in the pneumatic tire sense is from 1894. Inner city is attested from 1690s; as a euphemism for "urban poverty and crime," from 1963.

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