Summa of Chinese Mathematical Knowledge

CHENG Dawei 程大位.

Zeng shan suan fa tong zong 增刪算法統宗 [Comprehensive Collection of Computational Methods, Revised and Expanded] (title page) [or] Yuan ben zhi zhi suan fa tong zong 原本直指筭法統宗 [Comprehensive Collection of Computational Methods, Pointing Directly at the Origin] (at beginning of text).

1897. Many woodcut illus. & diagrams, including a full-page woodcut port. of the author with an abacus. Introductory juan & 12 numbered juan bound in six vols. 8vo, orig. wrappers (a bit rubbed & frayed), stitched. [Shanghai]: Jiang nan zhi zao ju 江南製造局, 1897.

An excellent and rare edition, richly illustrated, of “a summa of mathematical knowledge assembled by the author after 20 years of bibliographic research. Re-edited several times through the 19th century, the Comprehensive Collection of Computational Methods was the main source — and still is an important source — available to scholars in China, and more generally in East Asia, concerning mathematics as it developed in China’s tradition” (Encyclopædia Britannica, “East Asian Mathematics”).

The 16th and 17th centuries constituted a peculiar, transitional moment in the history of Chinese mathematics. The great achievements such as the Jiu zhang suan shu 九章算數 [Nine Chapters of Computation] of the first century B.C.E. and the impressive advancements in the study of polynomials and modular arithmetic during the 11th to 13th centuries, belonged to a distant, nearly forgotten past, their texts no longer remembered or comprehensible. This “falling into oblivion” of traditional mathematics in China coincided with an era of commercialization that saw the “rapid diffusion of the abacus, for which many books were written” (“East Asian Mathematics”); and in the realm of theoretical mathematics per se, it was followed by the Jesuit translations of Western mathematical works into Chinese, including Euclid’s Elements in 1607.

The historical significance of the Comprehensive Collection of Computational Methods, first published in 1592, therefore lies not in the new mathematical discoveries it presents but in its comprehensive survey of what was known of practical mathematics in late Ming China. From basic arithmetic formulae and names of metrical units to instructions for using the abacus, from practical problems of geometry (related to agriculture and hydraulics) to dedicated discussions of cubic roots and musical ratios, the work contained all that someone in 16th-century China would need to know about numbers — and then some. For those who needed a handbook for day-to-day calculations in business transactions, the work offers plenty of mnemonic ditties set to the tunes of popular songs of its day. For those who delighted instead in difficult mathematical problems, the work left behind obscure and challenging problems laboriously collected by the author, Cheng Dawei (1533–1606), sometimes without even offering a solution. Notably, the book also contains one of the earliest Chinese demonstrations of the “lattice” or “Gelosia” method of multiplication, a technique likely of South or West Asian origin that spread across Eurasia under the Mongol empire.

The popularity and influence of the Comprehensive Collection of Computational Methods cannot be overstated. It was reprinted many times in the Ming and Qing periods. Like many popular books in late Ming China, the work also traveled to Japan, Korea, and Vietnam. It was especially pivotal for the development of the Japanese mathematical tradition (wasan 和算), as Yoshida Mitsuyoshi 吉田光由 (1598–1673) took it as a model for his own work Jinkōki 塵劫記 (1627), widely acknowledged as one of the most important and influential mathematical texts in Japanese history.

We should also note that the Comprehensive Collection of Computational Methods was one of Europe’s first windows into the Chinese mathematical tradition.

The title page is dated “winter of Guangxu 23” (1897). The book was carved for the famous Jiangnan Arsenal in Shanghai, established in 1865 during the Self-Strengthening Movement as a center for scientific and technological collaborations between the Qing empire and the West.

Fine set and rare. According to WorldCat, there is no copy in North America.

Price: $11,500.00

Item ID: 10811