kiang. 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
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