Illustrated Commentary on Nine Chapters, Vol. 1

...read in many books and was especially skilled in mathematics, including astronomy and musical pitch systems, reaching a level of great subtlety. Regarding the ancient methods of "Setting the Heavenly Element" a method for solving polynomial equations, the "Great Extension" method for solving systems of linear congruences, and "Positive and Negative Root Extraction," he made many discoveries. He gained many new insights into the Nine Chapters and the Sea Island. He once said that simply setting out the numbers is the work of lower learning, while understanding the meaning is the achievement of higher understanding. For every number there is a form, and every form can be illustrated. The old commentaries mentioned that to understand these things, one must display them one by one through diagrams. Where Dai Dongyuan noted errors that could not be resolved, he clarified and solved them one by one. He explored the obscure, sought the hidden, and reached into the depths to bring forth clarity. By following the examples and headings of the ancients, he wrote the Illustrated Commentary on the Detailed Calculations of the Nine Chapters and the Sea Island in ten volumes. This follows the intention of Liu Hui, who used language to explain principles and diagrams to explain usage. Regrettably, he died before it was finalized. His nephew, the official Cheng Qingfeng, carefully guarded the legacy manuscript and invited Shen Tanhou, a licentiate from Suzhou, to his home to proofread and edit the work. They gathered workers to print it, in order to complete the coarse and simple draft of the original work.