Little is known of Jia Xian's life except that he served as a minor functionary during the reign of Emperor Renzong of Northern Song dynasty in the first half of the eleventh century. He learnt mathematics from Chu Yan, a famous astronomer and mathematician (fl. AD 1022–1054). Jia Xian was said to have written two books, Huangdi Jiuzhang Suanjing Xicao (Detailed Workings of the Nine Chapters on Mathematical Art), and Suanfa Xuegu Ji (A Collection of Ancient Mathematical Rules). While the latter was irretrievably lost, the former was largely found in Yang Hui's Xiangjie Jiuzhang Suanfa (A Detailed Analysis of the Mathematical Rules in the Nine Chapters) of AD 1261 preserved in Ms. form in chapter 16,344 of the Yonglo Dadian encyclopedia compiled by Xie Jin in 1407 during the Ming dynasty. In his preface, Yang Hui explicitly stated that his text was an attempt to expound and preserve the works of his predecessors, notably those of Jia Xian.
Jia Xian's main contribution to mathematics...
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