Etymology
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Words related to homo-

hetero- 
before vowels heter-, word-forming element meaning "other, different," from Greek heteros "the other (of two), another, different; second; other than usual." It is a compound; the first element means "one, at one, together," from PIE root *sem- (1) "one; as one, together with;" the second is cognate with the second element in Latin al-ter, Gothic an-þar, Old English o-ðer "other."

Compounds in classical Greek show the range of the word there: Heterokretes "true Cretan," (that is, of the old stock); heteroglossos "of foreign language;" heterozelos "zealous for one side;" heterotropos "of a different sort or fashion," literally "turning the other way;" heterophron "raving," literally "of other mind."
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*sem- (1)

Proto-Indo-European root meaning "one; as one, together with."

It forms all or part of: anomalous; anomaly; assemble; assimilate; ensemble; facsimile; fulsome; hamadryad; haplo-; haploid; hendeca-; hendiadys; henotheism; hetero-; heterodox; heterosexual; homeo-; homeopathy; homeostasis; homily; homo- (1) "same, the same, equal, like;" homogenous; homoiousian; homologous; homonym; homophone; homosexual; hyphen; resemble; same; samizdat; samovar; samsara; sangha; Sanskrit; seem; seemly; semper-; sempiternal; similar; simple; simplex; simplicity; simulacrum; simulate; simulation; simultaneous; single; singlet; singular; some; -some (1); -some (2); verisimilitude.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit sam "together," samah "even, level, similar, identical;" Avestan hama "similar, the same;" Greek hama "together with, at the same time," homos "one and the same," homios "like, resembling," homalos "even;" Latin similis "like;" Old Irish samail "likeness;" Old Church Slavonic samu "himself."

homosexual (adj.)

1892, in C.G. Chaddock's translation of Krafft-Ebing's "Psychopathia Sexualis," from German homosexual, homosexuale (by 1880, in Gustav Jäger), from Greek homos "same" (see homo- (1)) + Latin-based sexual.

'Homosexual' is a barbarously hybrid word, and I claim no responsibility for it. It is, however, convenient, and now widely used. 'Homogenic' has been suggested as a substitute. [H. Havelock Ellis, "Studies in Psychology," 1897]

Sexual inversion (1883, later simply inversion, by 1895) was an earlier clinical term for "homosexuality" in English, said by Ellis to have originated in Italian psychology writing. See also uranian. Unnatural love was used 18c.-19c. for homosexuality as well as pederasty and incest. In 17c.-18c., pathic was used as a noun and adjective in reference to a man that submits to sexual intercourse with another man. Related: Homosexually.

homoerotic (adj.)
also homo-erotic, 1916, from homo- (2) "homosexual" + erotic. Related: Homoeroticism.
homophile (n.)
1960, from homo- (2) "homosexual" + -phile. An attempt to coin a word for a homosexual person as part of a social group, rather than a sexual deviant.
homophobic (adj.)
by 1971, from homo- (2) "homosexual" + -phobia + -ic. Related: Homophobe; homophobia (which word is said to date from 1969 in this context; earlier "fear of men," by 1908).
homogamy (n.)
1805, "condition of bearing flowers that do not differ sexually," from homo- (1) "same" + -gamy.
homogeneous (adj.)
1640s, from Medieval Latin homogeneus, from Greek homogenes "of the same kind," from homos "same" (see homo- (1)) + genos "kind, gender, race, stock" (from PIE root *gene- "give birth, beget," with derivatives referring to procreation and familial and tribal groups). Earlier in this sense was homogeneal (c. 1600). Related: Homogeneously; homogeneousness.
homograph (n.)
1810 as a method of signalling, from homo- (1) "same" + -graph "something written." Meaning "a word of identical spelling with another, but of different origin and meaning," is from 1873. Related: Homographic; homography. Greek homographos meant "of the same letters."
homoioteleuton (n.)

 in general, "the repetition of endings in words, rhyme and near rhyme," but also, in palaeography, a form of scribal error which occurs "when two words/phrases/lines end with the same sequence of letters. The scribe, having finished copying the first, skips to the second, omitting all intervening words" [Robert B. Waltz, "The Encyclopedia of New Testament Textual Criticism," 2013]; Greek, literally "same ending;" see homo- (1) "the same" + telos.