Etymology
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*ag- 

Proto-Indo-European root meaning "to drive, draw out or forth, move."

It forms all or part of: act; action; active; actor; actual; actuary; actuate; agency; agenda; agent; agile; agitation; agony; ambagious; ambassador; ambiguous; anagogical; antagonize; apagoge; assay; Auriga; auto-da-fe; axiom; cache; castigate; coagulate; cogent; cogitation; counteract; demagogue; embassy; epact; essay; exact; exacta; examine; exigency; exiguous; fumigation; glucagon; hypnagogic; interact; intransigent; isagoge; litigate; litigation; mitigate; mystagogue; navigate; objurgate; pedagogue; plutogogue; prodigal; protagonist; purge; react; redact; retroactive; squat; strategy; synagogue; transact; transaction; variegate.

It is the hypothetical source of/evidence for its existence is provided by: Greek agein "to lead, guide, drive, carry off," agon "assembly, contest in the games," agōgos "leader," axios "worth, worthy, weighing as much;" Sanskrit ajati "drives," ajirah "moving, active;" Latin actus "a doing; a driving, impulse, a setting in motion; a part in a play;" agere "to set in motion, drive, drive forward," hence "to do, perform," agilis "nimble, quick;" Old Norse aka "to drive;" Middle Irish ag "battle."

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-i- 
a "connective" element in many words formed with Latin or Greek suffixes, now often felt as part of them (as in -iac, -iacal, -ial, -ian, -ify, -ity, etc.). Properly it forms no proper part of the suffix but is often the stem-vowel of the initial word in the Latin compounds (genial from genius), or a modified form of it. As such forms were very common, -i- was used merely connectively or euphonically in some Latin compounds (uniformis) and in later words made from Latin components in English or French (centennial, editorial).

The Greek equivalent is -o-, which also became an active connective in English, but they now are used indifferently with elements from either language.
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*bheue- 

*bheuə-, also *bheu-, Proto-Indo-European root meaning "to be, exist, grow."

It forms all or part of: Bauhaus; be; beam; Boer; bondage; boodle; boom (n.1) "long pole;" boor; booth; bound (adj.2) "ready to go;" bower; bowery; build; bumpkin; busk; bustle (v.) "be active;" byre; bylaw; Eisteddfod; Euphues; fiat; forebear; future; husband; imp; Monophysite; neighbor; neophyte; phyletic; phylo-; phylum; phylogeny; physic; physico-; physics; physio-; physique; -phyte; phyto-; symphysis.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit bhavah "becoming," bhavati "becomes, happens," bhumih "earth, world;" Greek phyein "to bring forth, make grow," phytos, phyton "a plant," physis "growth, nature," phylon "tribe, class, race," phyle "tribe, clan;" Old English beon "be, exist, come to be, become, happen;" Old Church Slavonic byti "be," Greek phu- "become," Old Irish bi'u "I am," Lithuanian būti "to be," Russian byt' "to be."

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*teks- 

Proto-Indo-European root meaning "to weave," also "to fabricate," especially with an ax," also "to make wicker or wattle fabric for (mud-covered) house walls."

It forms all or part of: architect; context; dachshund; polytechnic; pretext; subtle; technical; techno-; technology; tectonic; tete; text; textile; tiller (n.1) ""bar to turn the rudder of a boat;" tissue; toil (n.2) "net, snare."

It is the hypothetical source of/evidence for its existence is provided by: *teks- "to weave, to fabricate, to make; make wicker or wattle framework" (source also of Sanskrit taksati "he fashions, constructs," taksan "carpenter;" Avestan taša "ax, hatchet," thwaxš- "be busy;" Old Persian taxš- "be active;" Latin texere "to weave, fabricate," tela "web, net, warp of a fabric;" Greek tekton "carpenter," tekhnē "art;" Old Church Slavonic tesla "ax, hatchet;" Lithuanian tašau, tašyti "to carve;" Old Irish tal "cooper's ax;" Old High German dahs, German Dachs "badger," literally "builder;" Hittite taksh- "to join, unite, build."

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