Definition of "complementary"

Using the terminology we introduced earlier, we might then say that black and white squares are in complementary distribution on a chessboard. By this we mean two things: firstly, black squares and white squares occupy different positions on the board: and secondly, the black and white squares complement each other in the sense that the black squares together with the white squares comprise the total set of 64 squares found on the board (i.e. there is no square on the board which is not either black or white).

1988, Andrew Radford, Transformational grammar: a first course, Cambridge, UK: Cambridge University Press, page 140

the hands of the most skilful and cunning complementaries alive

1600 (first performance), Benjamin Jonson [i.e., Ben Jonson], “Cynthias Revels, or The Fountayne of Selfe-Loue. […]”, in The Workes of Ben Jonson (First Folio), London: […] Will[iam] Stansby, published 1616