The Nine Chapters on the Mathematical Art
Basic arithmetic processes such as addition, subtraction, multiplication and division were present before the Han Dynasty. "The Nine Chapters on the Mathematical Art" take these basic operations for granted and simply instruct the reader to perform them. Han mathematicians calculated square and cubed roots in a similar manner as division, and problems on division and root extraction both occur in Chapter Four of "The Nine Chapters on the Mathematical Art". Calculating the squared and cubed roots of numbers is done through successive approximation, the same as division, and often uses similar terms such as dividend ("shi") and divisor ("fa") throughout the process. This process of successive approximation was then extended to solving quadratics of the second and third order, such as formula_1, using a method similar to Horner's method. The method was not extended to solve quadratics of the nth order during the Han Dynasty; however, this method was eventually used to solve these equations.