"formed by subtraction of one quantity from another, of or like a residuum," 1560s, from residue + -al (1), or from French résiduel, from Latin residuum "that which is left behind." By c. 1600 as "remaining, left over."
1550s, in mathematics, "a residual quantity," from residual (adj.) or from residue + -al (2). Residuals "royalties for repeated performance or broadcast" is attested by 1960.