recovery of old works on mathematics. Ten such works, edited by officials of the Sung period for use as text-books, had been printed in 1084, under the collective title 算經十書 Suan-ching shih-shu. Early in the fifteenth century these works had been copied into the Yung-lo ta-tien, but subsequently became very rare. Mao I [q. v.] spent many years searching for them and in 1684 discovered seven, of which he published several copies traced in facsimile from Sung editions. Probably unaware of Mao I's labors, Tai Chên recovered (1774–76) six of the ten items from the Yung-lo ta-tien which, together with a seventh collated by him, were printed in the Wu-ying tien chü-chên pan ts'ung-shu. In the meantime Kung Chi-han (see under Shao Chin-han), who possessed a set of Mao I's traced copies, combined them with Tai's collated texts and thus gathered nine of the original ten works of 1084, which he printed under the original title Suan-ching shih-shu. To this K'ung added one ancient mathematical treatise not among the original ten; and two works by Tai—the aforementioned Ts'ê-suan; and a work on the measurement of the circle, entitled 勾股割圜記 Kou-ku ko-yüan chi, 3 chüan (first printed in 1755). In addition to these works Tai recovered several other rare items from the Yung-lo ta-tien, among them two Sung studies about the Decorum Ritual. While thus working on various phases of the Ssŭ-k'u project, he once again took the metropolitan examination (1775), and although he failed, he was, by a special decree, allowed to become a chin-shih and was appointed a bachelor in the Hanlin Academy. He continued to work on the Ssŭ-k'u project until his death, in Peking, two years later, in the home of a friend.
Tai Chên wrote or edited some fifty works of which thirty-five have been printed and are extant. About fifteen of these were printed during his lifetime, among them the two above-named local histories which he helped to edit, and ten works he edited for the Ssŭ-k'u ch'üan-shu. After his death, K'ung Chi-han printed (ca. 1777–79) a collection of fifteen items under the title 戴氏遺書 Tai-shih i-shu which included twelve items not previously printed. In the nineteenth century four more of his works were printed in various collectanea. In 1936 there appeared a more complete edition of Tai's collected works, entitled 戴東原先生全集 Tai Tung-yüan hsien-shêng ch'üan-chi. It constitutes the sixth series of the Anhwei ts'ung-shu, and contains, in addition to eighteen reprints, the following items: four works reproduced from hitherto unpublished manuscripts; some reproductions in facsimile of his handwriting; biographical sketches; a nien-p'u by Tuan Yü-ts'ai; and a bibliography of his writings.
Tai Chên made some contributions to the study of phonology, a subject which had been revived by Ku Yen-wu [q. v.] about a century earlier. He had studied the subject with Chiang Yung, discussed it with Tuan Yü-ts'ai, and left two works on it, entitled, 聲類表 Shêng lei piao, 9 chüan, printed in 1777 shortly before his death, and 聲韻考 Shêng yun k'ao, 4 chüan, printed by K'ung Chi-han. The former is his classification of ancient pronunciations; and the latter represents his views on various aspects of the subject, including a critical review of Ku Yen-wu's works. He also annotated the ancient dictionary of dialects, known as Fang-yen (see under Ch'ien Ta-chao), his edition of this work being entitled Fang-yen chu shu-chêng (注疏證), 13 chüan. A manuscript copy of his unfinished supplements to the Fang-yen, entitled Hsü (續) Fang-yen, was reproduced in 1936 in the Anhwei ts'ung-shu. Also reproduced in this collectanea are a manuscript copy of his notes on the study of the Classics, entitled 經考附錄 Ching-k'ao fu-lu, 7 chüan, and 3 chüan of the manuscript of the aforementioned Ch'ü Yüan fu chu. The main part of his notes on the Classics, Ching-k'ao, 5 chüan, had been previously published in the Hsü-chai ts'ung-shu (see under Chiao Hsün). A collection of his short articles in prose were printed by Kung Chi-han under the title Tai Tung-yüan chi (集), 10 chüan, being re-edited and supplemented by Tuan Yü-ts'ai in a second edition of 12 chüan, printed in 1792.
Tai Chên's most important contributions were, however, in the field of philosophy; he became, in fact, the greatest of the few philosophic thinkers whom China produced in the Ch'ing period. His philosophical views are embodied chiefly in two treatises: one, entitled 原善 Yüan-shan, 3 chüan, written in its present form in 1776; the other 孟子字義疏證 Mêng-tzŭ tzŭ-i shu-chêng, 3 chüan, first composed in 1769–72, under the title 緒言 Hsü-yen, but edited under its present title shortly before his death. The text, bearing the title Hsü-yen, appears in the Yüeh-ya t'ang ts'ung-shu (see under Wu Ch'ung-yüeh).
From Sung times onward the dominant philosophy of China had been a dualistic rationalism which was supposed by a long line of sponsors, official and private, to be firmly grounded on the Classics, but which the textual critics of the seventeenth century declared to be highly
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