Etymology
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tertium quid (n.)
something indeterminate between two other things, 1724, Latin, literally "third something," from tertius "third, a third," from the root of tres "three" (see three). A loan-translation of Greek triton ti (Plato), used in alchemy for "unidentified element present in a combination of two known ones." The Latin word also figures in phrases tertium non datur "no third possibility exists," and tertius gaudens "a third party that benefits from conflict between the other two."
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quid pro quo 

"one thing in place of another," 1560s, from Latin, literally "something for something, one thing for another," from nominative (quid) and ablative (quo) neuter singulars of relative pronoun qui "who" (from PIE root *kwo-, stem of relative and interrogative pronouns) + pro "for" (see pro-).

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