Etymology
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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]
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Eugene 
masc. proper name, from French Eugène, from Latin Eugenius, from Greek Eugenios, literally "nobility of birth," from eugenes "well-born" (see eugenics).
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dysgenics (n.)

 "study of the factors producing genetic deterioration, also loosely, "the carrying on of the species by the worst members," 1906, from dys- + ending from eugenics. Hence dysgenic "having or causing a detrimental effect on the race" (1909).

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Owen 

Celtic masc. proper name, ultimately from Greek eugenes "well-born" (see eugenics) via Gaelic Eòghann, Old Irish Eogán, Old Welsh Eugein, Ougein. In Medieval records, frequently Latinized as Eugenius; the form Eugene emerged in Scotland by late 12c. The Breton form Even led to modern French Ivain. Owenite in reference to the communistic system of social reformer Robert Owen (1771-1858) is attested from 1829.

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*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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*gene- 

*genə-, also *gen-, Proto-Indo-European root meaning "give birth, beget," with derivatives referring to procreation and familial and tribal groups.

It forms all or part of: Antigone; autogenous; benign; cognate; congener; congenial; congenital; connate; cosmogony; cryogenic; degenerate; engender; engine; epigone; eugenics; -gen; gendarme; gender; gene; genealogy; general; generate; generation; generic; generous; genesis; -genesis; genial; -genic; genital; genitive; genius; genocide; genotype; genre; gens; gent; genteel; gentile; gentle; gentry; genuine; genus; -geny; germ; german (adj.) "of the same parents or grandparents;" germane; germinal; germinate; germination; gingerly; gonad; gono-; gonorrhea; heterogeneous; homogeneous; homogenize; homogenous; impregnate; indigenous; ingenious; ingenuous; innate; jaunty; kermes; kin; kindergarten; kindred; king; kind (n.) "class, sort, variety;" kind (adj.) "friendly, deliberately doing good to others;" Kriss Kringle; malign; miscegenation; nada; naive; nascent; natal; Natalie; nation; native; nature; nee; neonate; Noel; oncogene; ontogeny; photogenic; phylogeny; pregnant (adj.1) "with child;" primogenitor; primogeniture; progenitor; progeny; puisne; puny; renaissance; theogony; wunderkind.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit janati "begets, bears," janah "offspring, child, person," janman- "birth, origin," jatah "born;" Avestan zizanenti "they bear;" Greek gignesthai "to become, happen," genos "race, kind," gonos "birth, offspring, stock;" Latin gignere "to beget," gnasci "to be born," genus (genitive generis) "race, stock, kind; family, birth, descent, origin," genius "procreative divinity, inborn tutelary spirit, innate quality," ingenium "inborn character," possibly germen "shoot, bud, embryo, germ;" Lithuanian gentis "kinsmen;" Gothic kuni "race;" Old English cennan "beget, create," gecynd "kind, nature, race;" Old High German kind "child;" Old Irish ro-genar "I was born;" Welsh geni "to be born;" Armenian cnanim "I bear, I am born."

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