# Eminent Chinese of the Ch'ing Period/Lo Shih-lin

**LO** Shih-lin 羅士琳 (T. 次璆, H. 茗香), d. Apr., 1853, mathematician, was a native of Kan-ch'üan (Yangchow). He purchased the title of a student of the Imperial Academy and participated in several provincial examinations, but failed to pass. Thereupon he went to Peking where he became a student in the Astronomical College of the Imperial Board of Astronomy. In 1821, when he was in his thirties, he achieved notice for his knowledge of astronomy and mathematics and in particular for calculating that on May 2 of that year most of the planets could be seen together—a phenomenon which in Chinese astrology was regarded as a good omen for the throne and the country. His colleagues, however, became jealous of him, and because of their intrigues he failed to advance in his official career. He grew disgusted with official life in Peking, and after failing several times to pass the provincial examination, he left the city and travelled to various places, probably as secretary to magistrates or to local officials., At any rate we find him in 1828 in Hai-ch'êng near Mukden, and in 1832 in Yung-chia, Chekiang. He is said to have lived also in Honan and Hupeh—continuing during all his travels the study of mathematics. From the 1830's to 1853 he lived at home in Yangchow and there, from 1839 to 1849, associated intimately with his senior, Juan Yüan [*q. v.*], supervising the printing of the first seven of the eight *chüan* of Juan's *nien-p'u*, entitled 雷塘庵主弟子記 *Lei-t'ang an chu ti-tzŭ chi*—the eighth *chüan* being added after Juan's death. He also edited the mathematical works of Liu Hêng 劉衡 (T. 蘊聲, 訒堂, H. 簾舫, 1776–1841), entitled 六九軒算書
*Liu-chiu-hsüan suan-shu*, before their printing in 1850–51 at Yangchow. In 1851 he was recommended to the throne as *Hsiao Lien Fang Chêng* (see under Lo Tsê-nan; an honorary rank a little lower than a *chü-jên*) but did not go to the capital for formal confirmation. On April 2, 1853 Yangchow fell to the Taiping Rebels. Many inhabitants were killed or committed suicide, and Lo was one of those who perished at this time, being then in his sixties.

In his younger days Lo Shih-lin, like most of his contemporaries, studied only the mathematics which had been popularized by Western missionaries in the seventeenth and eighteenth centuries. But the Chinese, too, had earlier gone very far in some branches of mathematics, and some of the early textbooks gradually came to light (see under Tai Chên). Among them were the works of such Sung and Yüan mathematicians as Ch'in Chiu-shao 秦九韶 (T. 道古, 13th century), Yang Hui (see under Ch'êng Ta-wei), and Li Chih (see under Mei Ku-ch'êng). The first mentioned left a work entitled 數書九章
*Shu-shu chiu-chang*. Perhaps the greatest representative of the old school, however, was Chu Shih-chieh 朱世傑 (T. 漢卿, H. 松庭), a native of Chihli and a teacher of mathematics at Yangchow about the year 1300. He left an elementary textbook entitled 算學啟蒙 *Suan-hsüeh chi-mêng*, 3 *chüan*, printed in 1299 (and later recovered from a Korean exemplar); and an algebra, entitled 四元玉鑑 *Ssŭ-yüan yü-chien*, 3 *chüan*, with a preface dated 1303. This latter work, whose title is usually translated "The Precious Mirror of the Four Elements" (see bibliography below), had been almost wholly neglected for five centuries until Juan Yuan purchased an old manuscript copy at Hangchow shortly after 1800. Juan's disciple, Ho Yüan-hsi (see under Chang Hai-p'êng), had it printed. In 1822 Lo Shih-lin, then in Peking, saw it for the first time, and in the following year was given a copy of it by Kung Tzŭ-chên [*q. v.*]. Another friend lent Lo a manuscript copy, and with it he collated Ho's edition. After studying this algebra for twelve years (1823–35), making annotations, and explaining the old solutions with the calculating rods (*ch'ou-suan*, see under Ch'êng Ta-wei), he produced a work entitled *Ssŭ-yüan yü-chien hsi-ts'ao* (細草), 24 *chüan*, divided into three parts. It was printed in 1837 by a fellow-townsman, I Chih-han 易之瀚 (T. 浩川, H. 蓉湖), who added a supplement in 1 *chüan*, entitled *Ssŭ-yüan shih-li* (釋例), in which he gave examples of the use of calculating rods in solving algebraic equations. To I's work Lo added other examples early in 1839. By these examples, and by Lo's annotations, the *Ssŭ-yüan yü-chien* which represented the highest development of algebra in China, became intelligible to students. Other contemporary mathematicians who contributed to an understanding of the work were Shên Ch'in-p'ei 沈欽裴 (T. 俠侯, H. 狎鷗, *chü-jên* of 1807), Tai Hsü (see under Tai Hsi), and Hsü Yu-jên (see under Li Shan-lan). Hsü and Tai both died in consequence of the Taiping War, the former while serving as governor at Soochow, the latter committing suicide at Hangchow. Shen was the first collator of the *Shu-shu chiu-chang*, but his work, left unfinished, was carried on by his disciple, Sung Ching-ch'ang 宋景昌 (T. 勉之). These collation notes were edited into 4 *chüan* under the title, *Shu-shu chiu-chang cha-chi* (札記), and were printed in the *I-chia-t'ang ts'ung-shu* (see under Lu Hsin-yüan).

After editing the *Ssŭ-yüan yü-chien*, Lo Shih-lin studied the above-mentioned *Suan-hsüeh ch'i-mêng*, which included problems solved by simple algebraic equations, known as *t'ien-yüan* (天元), and his edition of this work was printed in 1839 with a preface by Juan Yüan. He also wrote the following works: 比例匯通 *Pi-li hui-t'ung*, 4 *chüan*, printed in 1818, on proportion; 演元九式 *Yen-yüan chiu-shih*, 1 *chüan*, printed in 1828, on algebra; 句股截積合較算術 *Kou-ku chieh-chi ho-chiao suan-shu*, 2 *chüan*, printed in 1848, on trigonometry; the first supplement to Juan Yüan's biographies of mathematicians (see under Juan Yüan); 春秋朔閏異同 *Ch'un-ch'iu shuo-jun i-t'ung*, 2 *chüan*, completed in 1828, on the calendar of the *Spring and Autumn Annals*; and 推求日食增廣新術 *T'ui-ch'iu jih-shih tsêng-kuang hsin-shu*, 2 *chüan*, printed in 1851, on the calculation of eclipses. These and others of his works are known collectively as 觀我生室彙稿 *Kuan-wo-shêng shih hui-kao*.

After Lo Shih-lin, Chinese mathematicians generally studied both Chinese and Western methods. One who specialized in Chinese mathematics was Lao Nai-hsüan (see under Tuan-fang) whose 古籌算考釋 *Ku ch'ou-suan k'ao-shih*, 6 *chüan* (1886), and a supplement, *Ku ch'ou-suan k'ao-shih hsü-pien* (續編), 8 *chüan* (1900), contain detailed explanations on the use of calculating rods. Most other mathematicians, however, became interested in Western mathematical works which they and others helped to translate into Chinese. Among the translators may be mentioned Li Shan-lan [*q. v.*] and Hua Hêng-fang 華衡芳 (T. 若汀, 1833–1902). Hua was attached to the Kiangnan Arsenal (see under Ting Jih-ch'ang) from its beginning and was one of the founders of its department for translating foreign books on science. He and Fryer (see under Wei Yüan) translated several works on mathematics, among them one on calculus, and Hua himself wrote six works on the subject which are known collectively as 行素軒算稿 *Hsing-su hsüan suan-kao*, printed in 1882. Among other translators in the Kiangnan Arsenal were Hsü Shou 徐壽 (T. 雪村, 1818–1884) and his son, Hsü Chien-yin 徐建寅 (T. 仲虎, 1845–1901). The latter was in Europe for five years (1879–84) visiting different factories, and at one time or another directed the arsenals at Tientsin, Tsinan, Nanking, Foochow and Hanyang.

Lo Shih-lin and Hua Hêng-fang were both interested in the history of Chinese mathematics, but the one who in recent years has written most in this field is Li Yen 李儼 (T. 樂知), author of the 中國算學史 *Chung-kuo suan-hsüeh shih* (1937); the *Chung suan shih lun-ts'ung* (論叢), a collection in 3 series (1933–35); the *Chin-tai* (近代) *Chung suan chu-shu chi* (著述記), a bibliography; and other works.

[1/512/13b; 2/69/48b; 6/31/16b; 6/42/6a; *Kan-ch'üan hsien-chih* (1885) 14/23b; Works by Li Yen; *Ch'ou-jên chuan san-pien* (see under Juan Yüan); Fryer, *An Account of the Department for the Translation of Foreign Books at the Kiangnan Arsenal*, Shanghai, 1880; Konantz, Emma L., "The Precious Mirror of the Four Elements," *The China Journal of Science and Arts*, II, no. 4 (July 1924), pp. 304–10; Vanhée, L., "Le précieux miroir des quatre eléments" in *Asia Major*, VII (1931–32), pp. 242–70.]

Fang Chao-ying