A third party which shall be nameless. The expression originated with Pythagoras, who, defining bipeds, said -
“Sunt bipes homo, et avis, et tertium quid.”
“A man is a biped, so is a bird, and a third thing (which shall be nameless).”
Iamblichus says this third thing was Pythagoras himself. (Vita Pyth., cxxvii.) In chemistry, when two substances chemically unite, the new substance is called a tertium quid, as a neutral salt produced by the mixture of an acid and alkali.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894