Etymology
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*aus- (1)

Proto-Indo-European root meaning "to shine," especially of the dawn. It forms all or part of: austral; Australia; Austria; Austro-; Aurora; east; Easter; eastern; eo-; Ostrogoth.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit usah "dawn;" Greek ēōs "dawn;" Latin Aurora "goddess of dawn," auster "south wind;" Lithuanian aušra "dawn;" Old English east "east."

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*deks- 

Proto-Indo-European root meaning "right, opposite left," hence "south" (from the viewpoint of one facing east).

It forms all or part of: ambidexterity; ambidextrous; deasil; destrier; Dexter; dexterity; dexterous; dextro-.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit daksinah "on the right hand, southern, skillful;" Avestan dashina- "on the right hand;" Greek dexios "on the right hand," also "fortunate, clever;" Latin dexter "skillful," also "right (hand);" Old Irish dess "on the right hand, southern;" Welsh deheu; Gaulish Dexsiva, name of a goddess of fortune; Gothic taihswa; Lithuanian dešinas; Old Church Slavonic desnu, Russian desnoj

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*sawel- 

*sāwel-, Proto-Indo-European root meaning "the sun." According to Watkins, the *-el- in it originally was a suffix, and there was an alternative form *s(u)wen-, with suffix *-en-, hence the two forms represented by Latin sol, English sun.

It forms all or part of: anthelion; aphelion; girasole; heliacal; helio-; heliotrope; helium; insolate; insolation; parasol; parhelion; perihelion; Sol; solar; solarium; solstice; south; southern; sun; Sunday.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit suryah, Avestan hvar "sun, light, heavens;" Greek hēlios; Latin sol "the sun, sunlight;" Lithuanian saulė, Old Church Slavonic slunice; Gothic sauil, Old English sol "sun;" Old English swegl "sky, heavens, the sun;" Welsh haul, Old Cornish heuul, Breton heol "sun;" Old Irish suil "eye;" Avestan xueng "sun;" Old Irish fur-sunnud "lighting up;" Old English sunne German Sonne, Gothic sunno "the sun."

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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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