Etymology
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*sekw- (1)

Proto-Indo-European root meaning "to follow."

It forms all or part of: associate; association; consequence; consequent; dissociate; ensue; execute; extrinsic; intrinsic; obsequious; persecute; persecution; prosecute; pursue; second (adj.) "next after first;" second (n.) "one-sixtieth of a minute;" sect; secundine; segue; sequacious; sequel; sequence; sequester; sociable; social; society; socio-; subsequent; sue; suit; suite; suitor; tocsin.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit sacate "accompanies, follows;" Avestan hacaiti, Greek hepesthai "to follow;" Latin sequi "to follow, come after," secundus "second, the following;" Lithuanian seku, sekti "to follow;" Old Irish sechim "I follow."

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*ghos-ti- 

Proto-Indo-European root meaning "stranger, guest, host," properly "someone with whom one has reciprocal duties of hospitality," representing "a mutual exchange relationship highly important to ancient Indo-European society" [Watkins]. But as strangers are potential enemies as well as guests, the word has a forked path.

The word ghos-ti- was thus the central expression of the guest-host relationship, a mutual exchange relationship highly important to ancient Indo-European society. A guest-friendship was a bond of trust between two people that was accompanied by ritualized gift-giving and created an obligation of mutual hospitality and friendship that, once established, could continue in perpetuity and be renewed years later by the same parties or their descendants. [Calvert Watkins, "American Heritage Dictionary of Indo-European Roots"]

It forms all or part of: Euxine; guest; hospice; hospitable; hospital; hospitality; hospodar; host (n.1) "person who receives guests;" host (n.2) "multitude;" hostage; hostel; hostile; hostility; hostler; hotel; Xenia; xeno-; xenon.

It is the hypothetical source of/evidence for its existence is provided by: Greek xenos "guest, host, stranger;" Latin hostis, in earlier use "a stranger," in classical use "an enemy," hospes "host;" Old Church Slavonic gosti "guest, friend," gospodi "lord, master;" Old English gæst, "chance comer, a stranger."

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*da- 

*dā-, Proto-Indo-European root meaning "to divide."

It forms all or part of: betide; daimon; Damocles; deal (v.); deal (n.1) "part, portion;" demagogue; demiurge; democracy; demography; demon; demotic; dole; endemic; epidemic; eudaemonic; geodesic; geodesy; ordeal; pandemic; pandemonium; tidal; tide (n.) "rise and fall of the sea;" tidings; tidy; time; zeitgeist.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit dati "cuts, divides;" Greek dēmos "people, land," perhaps literally "division of society," daiesthai "to divide;" Old Irish dam "troop, company;" Old English tid "point or portion of time," German Zeit "time."

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*mei- (1)
Proto-Indo-European root meaning "to change, go, move," "with derivatives referring to the exchange of goods and services within a society as regulated by custom or law" [Watkins].

It forms all or part of: amiss; amoeba; azimuth; common; commune; communicate; communication; communism; commute; congee; demean; emigrate; emigration; excommunicate; excommunication; immune; immutable; incommunicado; mad; mean (adj.1) "low-quality;" mew (n.2) "cage;" mews; migrate; migration; mis- (1) "bad, wrong;" mistake; Mithras; molt; Mstislav; municipal; munificent; mutable; mutant; mutate; mutation; mutatis mutandis; mutual; permeable; permeate; permutation; permute; remunerate; remuneration; transmutation; transmute; zenith.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit methati "changes, alternates, joins, meets;" Avestan mitho "perverted, false;" Hittite mutai- "be changed into;" Latin mutare "to change," meare "to go, pass," migrare "to move from one place to another," mutuus "done in exchange;" Old Church Slavonic mite "alternately;" Czech mijim "to go by, pass by," Polish mijać "avoid;" Gothic maidjan "to change."
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