'non-homogeneous' originates from the negative prefix 'non-' (Latin 'non') meaning 'not', combined with 'homogeneous', which ultimately comes from Greek 'homogenēs' where 'homo-' meant 'same' and 'genēs' meant 'born, kind'.

'homogeneous' entered English via Latin/Medieval Latin and French from Greek 'homogenēs'; the modern English adjective 'homogeneous' developed from these forms, and the compound 'non-homogeneous' was formed by prefixing 'non-' to create the negated sense.

Initially, 'homogeneous' meant 'of the same kind or nature'; with the addition of 'non-' the phrase initially conveyed simple negation ('not of the same kind') and has come to be used particularly in scientific and technical contexts to mean 'not uniform in composition or structure'.