Etymology
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Words related to eu-

*es- 

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

It forms all or part of: absence; absent; am; Bodhisattva; entity; essence; essential; essive; eu-; eucalyptus; Eucharist; Euclidean; Eudora; Eugene; eugenics; eulogy; Eunice; euphemism; euphoria; euthanasia; homoiousian; improve; interest; is; onto-; Parousia; present (adj.) "existing at the time;" present (n.2) "what is offered or given as a gift;" proud; quintessence; represent; satyagraha; sin; sooth; soothe; suttee; swastika; yes.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit asmi, Hittite eimi, Greek esti-, Latin est, Old Church Slavonic jesmi, Lithuanian esmi, Gothic imi, Old English eom, German ist.

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aneuploidy (n.)

abnormal number of chromosomes, 1934, from adjective aneuploid (1931), Modern Latin, coined 1922 by G. Täckholm from Greek an- "not, without" (see an- (1)) + euploid, from Greek eu "well, good" (see eu-) + -ploid, from -ploos "fold" (from PIE root *pel- (2) "to fold").

eubacteria (n.)
singular eubacterium, 1939, coined in German 1930; see eu-, here meaning "good," + bacteria. Classically, as an adverb, eu should form compounds only with verbs.
Euboea 
large island of Greece north of Attica and Boeotia, literally "rich in cattle," from eu- "good, well" (see eu-) + bous "ox, cow" (from PIE root *gwou- "ox, bull, cow"). Related: Euboean.
eucalyptus (n.)

evergreen genus of Australia, 1789, from Modern Latin, coined 1788 by French botanist Charles Louis L'héritier de Brutelle (1746-1800) from Greek eu "well" (see eu-) + kalyptos "covered" (from PIE root *kel- (1) "to cover, conceal, save"); so called for the covering on the bud.

Eucharist (n.)

"sacrament of the Lord's Supper, the Communion," mid-14c., from Old French eucariste, from Late Latin eucharistia, from Greek eukharistia "thanksgiving, gratitude," later "the Lord's Supper," from eukharistos "grateful," from eu "well" (see eu-) + stem of kharizesthai "show favor," from kharis "favor, grace," from PIE root *gher- (2) "to like, want." Eukharisteo is the usual verb for "to thank, to be thankful" in Septuagint and Greek New Testament. Related: Eucharistic.

Euclidean (adj.)
1650s, "of or pertaining to Euclid" (Greek Eukleides), c. 300 B.C.E. geometer of Alexandria. Now often used in contrast to alternative models based on rejection of some of his axioms. His name in Greek means "renowned, glorious," from eu "well" (see eu-) + kleos "fame" (see Clio).
eudaemonic (adj.)

also eudemonic, "producing happiness," 1856, from Greek eudaimonikos "conducive to happiness," from eudaimonia "happiness," from eu "good" (see eu-) + daimōn "guardian, genius" (see daimon). Related: Eudaimonia; eudemonia; eudaemonical.

Eudora 

fem. proper name, Greek, literally "generous," fem. of eudoros, from eu "well, good" (see eu-) + dōron "gift" (from PIE root *do- "to give").

eugenics (n.)

"doctrine of progress in evolution of the human race, race-culture," 1883, coined (along with adjective eugenic) by English scientist Francis Galton (1822-1911) on analogy of ethics, physics, etc. from Greek eugenes "well-born, of good stock, of noble race," from eu- "good" (see eu-) + genos "birth" (from PIE root *gene- "give birth, beget").

The investigation of human eugenics, that is, of the conditions under which men of a high type are produced. [Galton, "Human Faculty," 1883]