|TXCH, vol. 5, pp. 2771-3032; vol. 6, pp. 3033-3426
Tongwen suanzhi 同文算指 (Rules of Arithmetic Common to Cultures, 1614). Cf. Standaert, Handbook of Christianity in China, p. 693, 739, 741, 744, 746.
Full bibliographic citation see: Ad Dudink & Nicolas Standaert, Chinese Christian Texts Database (CCT-Database).
JapSin II, 11
Tongwen suanzhi 同文算指.
Dictated by Li Madou 利瑪竇 (Matteo Ricci) and recorded by Li Zhizao 李之藻.
One juan; one ce in Chinese bamboo paper. No date or place of publication.
On the cover there is a label with the title in Chinese and a Latin inscription: “Arithmetica | a p. Math. Ricci, S.I.”Passages in this copy are marked with circles and dots in both red and black ink. On the recto of folio 1 of juan A there is an inscription in red that reads: 甲子冬十一月二十九日月閱起 ([I] started to read this book in the winter of the jiazi year on the twenty-ninth day of the eleventh month).
There is a preface (four folios), dated Wanli 42 (1614) by Xu Guangqi 徐光啟 and another preface (four folios), dated Wanli 41 (1613), by Li Zhizao. The second part (通編) has a preface by Yang Tingyun 楊廷筠.
Each half folio consists of ten columns with twenty-two characters in each column. A table of contents in one folio is given after the prefaces. In the middle of each folio the title of the book is given with the number of the bian (section); the number of the juan and of the folio are given below the fish tail. The recto of folio 1 has: 同文算指前編卷下 (juan B of the first section of the Tongwen suanzhi) 西海利瑪竇授 (dictated by Li Madou of the Western Sea) 浙西李之藻演 (recorded by Li Zhizao of western Zhejiang).
In his preface Li Zhizao tells us that when Ricci showed him this book he found it useful for daily use, because one needs no help from mathematical instruments; work could be done with the brush only. Above all, it was particularly handy for geometry and algebra in contrast with the old Chinese method, which is by no means easy to understand.
The first section of the book gives all the fundamentals with examples designed to make it easy for the public to understand. Sometimes old Chinese mathematical methods are given, when they coincide with the Western method. The second section deals with special methods of calculation.
Pfister (p. 38, no. 12): “Cette arithmétique se trouve dans le grand catalogue impérial [Siku quanshu zongmu tiyao 四庫全書總目提要]. Elle est divisée en deux parties: la première traite de la numération, des 4 règles et des opérations sur les fractions; la seconde comprend les règles de trois, sous toutes les faces, l’extraction des racines et quelques calcus trigonométriques. Elle est reproduite dans le recueil précédent 天學初函 T’ien hio tch’ou han [Tianxue chuhan]).”
Wylie (p. 118): “The 同文算指 T’ûng wan swán chè, in ten books, is a treatise on arithmetic, by Lè Che tsaou, published in 1614, being a digest of the science as then known in Europe, which had been communicated to him by Ricci. It is divided into two parts; the first preliminary portion merely containing the rules for Notation, Addition, Subtraction, Multiplication, Division, and the various operations of Fractional computation. The second part which comprises four fifths of the whole, treats at great length on the Rule of Three in all its phases, Extraction of Roots, and Trigonometrical Calculations 10. . . .”
Li Yan 1976, pp. 217–221, 230–236: This book consists of eleven juan. The translation is based on the Epitome Arithmeticae Practicae (Rome, 1595) of Cristoforo Clavius (Verhaeren, no. 1296) and on the work of a contemporary Chinese mathematician, Cheng Dawei 程大位 (zi 汝思, hao 賓渠), a native of Xiuning 休寧 (Anhui). The work he wrote and published in 1592, when he was sixty sui, had the title Zhizhi suanfa tongzong 直指算法統宗 (seventeen juan), which is after the style of the ancient Chinese book Jiuzhang suanshu 九章算書. The general section (前編) of the Tongwen suanzhi follows the same order as the original text of Clavius. The second part (通編) also follows the same order, except that Li Zhizao added some old traditional Chinese methods to it. The third part (別編) remained in manuscript form and has never been published. The book is the first on arithmetic introduced into China from Europe. It had a great influence in China in a later period.
The Tongwen suanzhi can be found in the following congshu (collection of books): Tianxue chuhan 天學初函, Haishan xian’guan congshu 海山仙館叢書, Zhong-Xi suanxue congshu 中西算學叢書, and Congshu jicheng chubian 叢書集成初編.
Cf. Li Yan 李儼, Zhongguo suanxueshi luncong 中國算學史論叢 (Taipei, 1954), p. 164; SHS, pp. 236–238; Fang Hao 1966, pp. 97–100; FR, vol. I, p. 297; Hsü 1949, pp. 265–267; SKTY 3:2209–2210; Couplet, p. 6 (Universa arithmetica practica, 11 vol.). Courant 4861–4863: “Traité de mathématique. I (4861), 前編 Section préliminaire. Eléments d’arithmétique. 2 livres. II (4862), 通編 Section général. Arithmétique et géometrie. 8 livres. III (4863) 別編, Section spéciale. Logarithmes, calcul astronomiques. 1 volume.”
Source: Albert Chan, S.J., Chinese Books and Documents in the Jesuit Archives in Rome, pp. 288-290.