Etymology
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Words related to *tkei-

Amphictyonic (adj.)
in reference to one of several ancient Greek confederations of neighboring states, 1753, probably via French, from Greek amphiktionikos, from amphiktiones "neighbors," literally "they that dwell round about," from amphi "on both sides, all around" (from PIE root *ambhi- "around") + second element related to ktizein "to create, found," ktoina "habitation, township," from PIE *kti-, metathesized form of root *tkei- "to settle, dwell, be home."

The most famous was that of Delphi. Madison and other U.S. Founders devoted close study to it. Shaftesbury has amphictyonian (1711).
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hamlet (n.)
early 14c., from Old French hamelet "small village," diminutive of hamel "village," itself a diminutive of ham "village," from Frankish *haim or some other Germanic source, from Proto-Germanic *haimaz "home" (from PIE root *tkei- "to settle, dwell, be home"); for ending, see -let. Especially a village without a church.
hangar (n.)

1852, "shed for carriages," from French hangar "shed," which is of uncertain origin. Probably from hanghart (14c.), which is perhaps an alteration of Middle Dutch *ham-gaerd "enclosure near a house" [Barnhart, Watkins], from a Proto-Germanic compound *haimgardaz of the elements that make home (n.) and yard (n.1). Or French hanghart might be from Medieval Latin angarium "shed in which horses are shod" [Gamillscheg, Klein]. Sense of "covered shed for airplanes" first recorded in English 1902, from French use in that sense.

haunt (v.)
early 13c., "to practice habitually, busy oneself with, take part in," from Old French hanter "to frequent, visit regularly; have to do with, be familiar with; indulge in, cultivate" (12c.), of uncertain origin, perhaps from Old Norse heimta "bring home," from Proto-Germanic *haimatjanan "to go or bring home," from *haimaz- "home" (from PIE root *tkei- "to settle, dwell, be home").

Meaning "to frequent (a place)" is from c. 1300 in English. In Middle English to haunte scole was "attend school," and in Middle English as in Old French the verb had a secondary sense of "have sexual intercourse with." Use in reference to a spirit or ghost returning to the house where it had lived perhaps was in Proto-Germanic, but if so it was lost or buried; revived by Shakespeare's plays, it is first recorded 1590 in "A Midsummer Night's Dream." Old French had a noun derivative, hantise "obsession, obsessive fear" (14c.).
home (n.)

Old English ham "dwelling place, house, abode, fixed residence; estate; village; region, country," from Proto-Germanic *haimaz "home" (source also of Old Frisian hem "home, village," Old Norse heimr "residence, world," heima "home," Danish hjem, Middle Dutch heem, German heim "home," Gothic haims "village"), from PIE *(t)koimo-, suffixed form of root *tkei- "to settle, dwell, be home." As an adjective from 1550s. The old Germanic sense of "village" is preserved in place names and in hamlet.

'Home' in the full range and feeling of [Modern English] home is a conception that belongs distinctively to the word home and some of its Gmc. cognates and is not covered by any single word in most of the IE languages. [Buck]

Slang phrase make (oneself) at home "become comfortable in a place one does not live" dates from 1892 (at home "at one's ease" is from 1510s). To keep the home fires burning is a song title from 1914. To be nothing to write home about "unremarkable" is from 1907. Home movie is from 1919; home computer is from 1967. Home stretch (1841) is from horse racing (see stretch (n.)). Home economics as a school course first attested 1899; the phrase itself by 1879 (as "household management" is the original literal sense of economy, the phrase is etymologically redundant).

Home as the goal in a sport or game is from 1778. Home base in baseball attested by 1856; home plate by 1867. Home team in sports is from 1869; home field "grounds belonging to the local team" is from 1802 (the 1800 citation in OED 2nd ed. print is a date typo, as it refers to baseball in Spokane Falls). Home-field advantage attested from 1955.

site (n.)
"place or position occupied by something," especially with reference to environment, late 14c., from Anglo-French site, Old French site "place, site; position," and directly from Latin situs "a place, position, situation, location, station; idleness, sloth, inactivity; forgetfulness; the effects of neglect," from past participle of sinere "let, leave alone, permit," from PIE *si-tu-, from root *tkei- "to settle, dwell, be home."
situate (v.)
early 15c., "to place in a particular state or condition," from Medieval Latin situatus, past participle of situare "to place, locate," from Latin situs "a place, position" (from PIE root *tkei- "to settle, dwell, be home"). Related: Situated; situating.
situation (n.)
Origin and meaning of situation

early 15c., situacioun, "place, position, or location," from Old French situacion or directly from Medieval Latin situationem (nominative situatio) "a position, situation," noun of action from past-participle stem of situare "to place, locate," from Latin situs "a place, position" (from PIE root *tkei- "to settle, dwell, be home"). Meaning "state of affairs" is from 1710; meaning "employment post" is from 1803.

situs (n.)
Latin, "situation, position" (see site). In technical uses in English, "proper or original position and location of something" (as in in situ).
Niflheim 
realm of the dead in Norse mythology, from Old Norse nifl- "mist; dark" (from Proto-Germanic *nibila-, from PIE root *nebh- "cloud") + heimr "residence, world" (from Proto-Germanic *haimaz, from PIE root *tkei- "to settle, dwell, be home").