Preface to Liu Hui's Commentary on the Nine Chapters on the Mathematical Art

In the past, the divine Pao-hsi A legendary figure, also known as Fuxi, credited with the invention of the Eight Trigrams. first drew the Eight Trigrams to comprehend the virtues of the divine and categorize the nature of all things. He created the method of "nine-nines" An ancient term for the multiplication table. to harmonize with the changes of the six lines. By the time of the Yellow Emperor, these methods became miraculous and transformative; they were expanded and extended. Thereupon, the calendar was established and the musical pitches were harmonized, employing the original principles of the Way, and only then could the subtle energies of the Two Modes The Yin and Yang. and the Four Symbols be manifested. Records mention that Li Shou A legendary official credited with the invention of arithmetic. created mathematics, though the details are unknown. According to the Rites of the Duke of Zhou, the Nine Numbers were established. The Nine Chapters are the descendants of these Nine Numbers. In the past, the cruel Qin dynasty burned the books, and the classic techniques were scattered and lost. After that time, Zhang Cang, the Marquis of Beiping, and Geng Shouchang, the Vice-Minister of the Grand Granary, both famous for their mathematical skill during the Han dynasty, used the remnants of old texts. Each performed deletions and additions. Thus, when comparing their chapters to ancient versions, they are different, and much of what they discuss reflects the colloquial language of that time. From a young age, I, Hui Refers to Liu Hui, the author of the commentary., studied the Nine Chapters, and as an adult, I examined them repeatedly, observing how the Yin and Yang are split and separated, totaling...