Etymology
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*bhergh- (1)

Proto-Indo-European root meaning "to hide, protect." It forms all or part of: bargain; borrow; burial; bury; harbor; hauberk; scabbard.

It is the hypothetical source of/evidence for its existence is provided by: Old English Old English borgian "to lend, be surety for;" Old Church Slavonic brěgo "I preserve, guard," Lithuanian bìrginti "be parsimonious." But, absent other possible cognates, Boutkan writes that it is not certainly Indo-European and "probably a substratum word."

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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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*dhwer- 

Proto-Indo-European root meaning "door, doorway." The base form is frequently in dual or plural, leading to speculation that houses of the original Indo-Europeans had doors with two swinging halves.

It forms all or part of: afforest; deforest; door; faubourg; foreclose; foreign; forensic; forest; forfeit; forum; hors d'oeuvre; thyroid.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit duárah "door, gate;" Old Persian duvara- "door;" Lithuanian dùrys (plural); Greek thyra "door;" Latin foris "out-of-doors, outside;" Gaulish doro "mouth;" Old Prussian dwaris "gate;" Russian dver' "a door;" Old English dor, German Tür "door," Gothic dauro "gate."

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*g(a)lag- 
also *g(a)lakt-, Proto-Indo-European root meaning "milk."

It forms all or part of: ablactation; cafe au lait; galactic; galaxy; lactate (v.); lactate (n.); lactation; lacteal; lactescence; lactic; lactivorous; lacto-; lactose; latte; lettuce.

It is the hypothetical source of/evidence for its existence is provided by: Latin lac (genitive lactis) "milk;" Greek gala (genitive galaktos), "milk;" Armenian dialectal kaxc' "milk." The initial "g" probably was lost in Latin by dissimilation. This and the separate root *melg-, account for words for "milk" in most of the Indo-European languages. The absence of a common word for it is considered a mystery.
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*awi- 

Proto-Indo-European root meaning "bird." It also might be the source of *wyo, *yyo, Proto-Indo-European words for "egg."

It forms all or part of: auspex; auspices; auspicious; avian; aviary; aviation; aviator; avicide; aviculture; aviform; caviar; cockney; egg (n.); ocarina; oo-; oocyte; oolite; oology; osprey; ostrich; oval; ovary; ovate (adj.); oviform; oviparous; ovoviviparous; ovoid; ovulate; ovulation; ovule; ovum.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit vih, Avestan vish, Latin avis "bird;" Greek aietos "eagle;" Old Church Slavonic aja, Russian jajco, Breton ui, Welsh wy, Greek ōon, Latin ovum, Old Norse egg, Old High German ei, Gothic ada all meaning "egg."

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*mel- (2)

Proto-Indo-European root meaning "strong, great." It forms all or part of: ameliorate; amelioration; meliorate; melioration; meliorism; multi-; multiform; multiple; multiply; multitude. It is the hypothetical source of/evidence for its existence is provided by: Greek mala "very, very much;" Latin multus "much, many," melior "better."  

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*ghes- 

Proto-Indo-European root meaning "the hand." 

It forms all or part of: chiral; chiro-; chirognomy; chirography; chirology; chiromancy; chiropodist; chiropractic; chiropractor; chirosophy; chirurgeon; enchiridion; surgeon; surgery; surgical.

It is the hypothetical source of/evidence for its existence is provided by: Greek kheir, Hittite keshshar, Armenian jern "the hand" 

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*neu- 
Proto-Indo-European root meaning "to shout." It forms all or part of: announce; denounce; enunciate; nuncio; pronounce; renounce.

It is the hypothetical source of/evidence for its existence is provided by: Greek neuo "to nod, beckon," Latin nuntius "messenger," Old Irish noid "make known."
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*ghwer- 

Proto-Indo-European root meaning "wild beast."

It forms all or part of: baluchitherium; feral; ferine; ferocious; ferocity; fierce; ther-; Theropoda; treacle.

It is the hypothetical source of/evidence for its existence is provided by: Latin ferus "wild, untamed;" Greek thēr, Old Church Slavonic zveri, Lithuanian žvėris "wild beast."

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*ater- 
*āter-, Proto-Indo-European root meaning "fire." It forms all or part of: atrabiliary; atrabilious; atrium; atrocious.

It is the hypothetical source of/evidence for its existence is provided by: Old Persian atar "fire;" Latin ater "black" ("blackened by fire"), atrox "frightful" ("of fiery or threatening appearance").
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