Etymology
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Words related to homeo-

*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."

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homeomorphism (n.)
1854, from homeomorphous (1832), from homeo- + morphous (see morphic); originally of crystals. Homeomorphic is from 1902.
homeopathy (n.)
1830, from German Homöopathie, coined 1824 by German physician Samuel Friedrich Hahnemann (1755-1843) from Greek homoios "like, similar, of the same kind" (see homeo-) + -patheia "disease," also "feeling, emotion" (see -pathy). Greek homoiopathes meant "having like feelings or affections, sympathetic."
homeostasis (n.)
"tendency toward stability among interdependent elements," 1926, from homeo- "similar to" + stasis "a standing still." Related: Homeostatic.