九章算术
Double false position arose in late antiquity as a purely arithmetical algorithm. In the ancient Chinese mathematical text called "The Nine Chapters on the Mathematical Art" (九章算術), dated from 200 BC to AD 100, most of Chapter 7 was devoted to the algorithm. There, the procedure was justified by concrete arithmetical arguments, then applied creatively to a wide variety of story problems, including one involving what we would call secant lines on a conic section. A more typical example is this "joint purchase" problem: