Eminent Chinese of the Ch'ing Period/Ch'êng Ta-wei
CH'ÊNG Ta-wei 程大位 ( 汝思, 賓渠), ca. 1520–ca. 1600, Ming mathematician, was a native of Hsiu-ning, Anhwei. In early life he travelled as a teacher of mathematics to Wu 吳 (present Kiangsu) and to Ch'u 楚 (present Hupeh and Hunan), but retired to his home district when he became old. There he completed in 1593 his famous text-book on arithmetic, 算法統宗 Suan-fa t'ung-tsung in 13 chüan, which gave solutions to problems by means of the abacus, or suan-p'an 算盤. Early Chinese mathematicians had developed a method of calculation known as ch'ou-suan 籌算 (calculations by means of rods) which could be utilized to solve algebraic equations of higher degrees with as many as four unknowns. But ch'ou-suan was inconvenient for simple arithmetical calculations in daily commercial use. The introduction of the abacus into China about the latter half of the thirteenth century, and the omission of mathematics from the civil service examinations during the Yüan period (1280–1368), stopped abruptly the progress of Chinese mathematics by ch'ou-suan. Although in the ensuing Ming period (1368–1644) mathematical studies failed to revive, the abacus was nevertheless widely used, and by the time the Suan-fa t'ung-tsung was published (ca. 1593) the method of calculation by ch'ou-suan was virtually lost. Even in the early Ch'ing period the compilers of the massive encyclopedia, Ku-chin t'u-shu chi-ch'êng (see under Ch'ên Mêng-lei), which was completed in 1726, seem to have been unaware of the literature dealing with ch'ou-suan, since they copied the Suan-fa tung-tsung in its entirety as though it were representative of the whole field of Chinese mathematics. The recovery of older works on mathematics took place later (see under Tai Chên).
Judging from the numerous reprints of the Suan-fa t'ung-tsung in the past three centuries, one can say that it was the most widely used elementary book on the subject. Until recently it was regarded as the earliest work on the suan-p'an, but it is now known that the 數學通軌 Shu-hsüeh t'ung-kuei compiled by K'o Shang-ch'ien 柯尚遷 in 1578 antedated it by fifteen years. A revised edition of the Suan-fa t'ung-tsung, arranged by Mei Ku-ch'êng [q. v.] in 12 chüan, appeared in the eighteenth century. Another edition, in 17 chüan, was reprinted in 1716 by the author's great-grandsons. The book is noted for its study of magic squares. ts'ung-hêng t'u 縱橫圖, literally "criss-cross designs"—a phase of mathematics already treated by Yang Hui 楊輝 in the thirteenth century. It also contains the method of multiplication known as hsieh-suan 寫算—the 'gelosia' or 'grating' method employed by the Arabs and Indians several centuries earlier and possibly introduced to China by Arab traders. Most editions of the Suan-fa t'ung-tsung reproduce a portrait of the author depicting him in a class-room manipulating an abacus in the presence of two pupils. At the end of the book is a list of works on mathematics which existed prior to the author's time, but which are for the most part no longer extant.
[Li Yen 李儼, 中國算學小史 Chung-kuo suan-hsüeh hsiao shih (1931) pp. 61, 82–85; Ch'ien Pao-tsung 錢寶琮, 古算學考源 Ku-suan-hsüeh k'ao-yüan (1930) pp. 8–9; Ch'ou-jên chuan (see under Juan Yüan), (1799) 31/19b; 徽州府志 Hui-chou-fu chih (1827) 15/37b; Ssŭ-k'u (see under Chi Yün), 107/120; Smith, D. E., History of Mathematics (1923) I, p. 352; II, pp. 114–117; Mikami Yoshio, The Development of Mathematics in China and Japan (1913) p. 110, 111; T'oung Pao (1914) p.184; 科學 K'o-hsüeh, vol. XVIII, no. 11, Nov. 1934, p. 1549; Wylie, Notes p. 118.]