JapSin II, 51
Dace 大測.
By Deng Yuhan 鄧玉函 (Johann Terrenz [Schreck]).
Two juan. Bamboo paper in a paper case. No date or place of publication.

The cover bears a label with the title and a Latin inscription: “Liber Primus | De Resolutione triangulorum | recti, lineorum et sphaericorum Liber secundus | de arte construendi tabellas | sinuum tangentium Sectantium | a p. Joanne Terrentio S.J.”

Cf. Pfister, p. 157, no. 4; Feng 1938, p. 185, no. 4; Hsü 1949, p. 369; Couplet, p. 18; Courant 4876.
Source: Albert Chan, S.J., Chinese Books and Documents in the Jesuit Archives in Rome, pp. 354-355.

JapSin II, 51 D
Dace 大測.
By Deng Yuhan 鄧玉函 (Johann Terrenz [Schreck]).
Two juan. Bamboo paper in a paper case. No date or place of publication.

This book is a duplicate of Jap-Sin II, 51, except that the title page does not give the four characters 新法曆書, as does the latter.
Source: Albert Chan, S.J., Chinese Books and Documents in the Jesuit Archives in Rome, p. 355.

Euclid in China : the genesis of the first Chinese translation of Euclid's Elements, books I-VI (Jihe yuanben, Beijing, 1607) and its reception up to 1723 / by Peter M. Engelfriet.
Includes bibliographical references (p. [467]-482) and index.

Ch. 1. Introduction. Pt. I From Rome to Beijing.
Ch. 2. Mathematics in Jesuit Context: A. The educational mission. Ricci’s pre-mathematical education. B. Clavius’ promotion of the mathematical sciences. Introduction of the Elements. Opposition against mathematics. C. Mathematics in Aristotelian context. Quantity. The Syllogism. D. The "School of Clavius": Ricci’s mathematical training. Limitations of Jesuit mathematics.
Ch. 3. Matteo Ricci and Xu Guangqi in Late Ming Society. A. Matteo Ricci: from Macao to Beijing. B. Calendar reform and a possible earlier translation of Euclid. C. Xu Guangqi’s background. D. Some aspects of intellectual life during the Ming: the cultural environment – Neo-Confucian concepts relevant to science – Diagrams and charts. E. Mathematics during the Ming.
Pt. II The Translation.
Ch. 4. Clavius' 1574 Edition. Preliminary remarks. B. Transmission of the Elements. Arabic translations and Latin middle ages – Renaissance. C. Clavius’ edition. D. Theory of proportions. Clavius versus Commandino: a point of divergence. E. Postulates, axioms and constructions.
Ch. 5. The Jihe yuanben. Editions. Terminology and language. Definitions, axioms and postulates. (Book I-VI).
Appendix to Ch. 5. The Enunciations of all Propositions.
Pt. III Reception and Influence: Ch. 6 Mathematics in the Service of the Dynasty. Xu Guangqi’s preface, Researches into traditional mathematics, books on "forms and numbers". Yuanrongjiao yi : Tongwen suanzhi : The year 1616. The period 1620-1635. Qiqi tushuo ; Jihe yaofa : Calendar reform : Celiang quanyi.
Ch. 7 The Ming-Qing Transition. A. Brief historical survey. B. Chinese cosmology and Western science - Xiong Mingyu - The Fang family. C. "Expansion of Numbers and magnitudes" : the Jihe yue. D. Between Ming and Qing: Huang Zongxi - Lu Shiyi - Wang Xichan.
Ch. 8 Three Scholar-Mathematicians of the Late Seventeenth Century: A. Li Zijin. B. Du Zhigeng: the Jihe lunyue. C. Mei Wending: life till 1700 - Euclidean geometry explained by Gougu - extension to three dimensional space - Views on Mathematics.
Ch. 9 The Royal Road: A. Kangxi Emperor. B. New "Elements". C. Shuli jingyun and beyond.
Ch. 10 Conclusion. App. 1: Preface by Matteo Ricci. App. 2: Preface by Wu Xuehao . Abbreviations – Bibliography – Index.

Local access dig.pdf. [Euclid in China.pdf]

"This book explores the interaction between Europe and East Asia between the 16th and 18th centuries in the field of mathematical sciences, bringing to the fore the role of Portugal as an agent of transmission of European science to East Asia. It is an important contribution to understanding this fundamental period of scientific history, beginning with the arrival of Vasco da Gama in India in 1498 and ending with the expulsion of the Society of Jesus from Portugal in 1759."

Macau: an intercultural frontier in the Ming period / Luís Filipe Barreto -- Survey and study of pre-1900 Chinese maps seen in Europe / Li Xiaocong -- Western knowledge of geography reflected in Juan Cobo's Shilu (1593) / Liu Dun -- The continuing influence of the Portuguese: "A new interpretation of world geography" / Wang Qianjin -- Teachers of mathematics in China: the Jesuits and their textbooks (1580-1723) / Catherine Jami -- News from China in sixteenth century Europe: the Portuguese connection / Rui Loureiro -- The Indianization of Spain in the 16th century / Juan Gil -- Jesuit observations and star-mappings in Beijing as the transmission of scientific knowledge / Keizo Hashimoto -- The compilation of the Lixiang Kaocheng houbian, its origin, sources, and social context / Han Qi -- A Japanese reaction to Aristotelian cosmology / Tadashi Yoshida -- Portugal and Korea: obscure connections in the pre-modern sciences before 1900 / Park Seong-Rae -- Translations of Portuguese texts into Konkani and Konkani compositions into Portuguese, with educational influence on literature and art and the transfer of technology / Joseph Velinkar.

Local access dig.pdf & djvu [Saraiva-Mathematical-Sciences.pdf & .djvu]
Also available online via Gleeson Library.

The Jesuit mathematicians of the Portuguese Assistancy and the Portuguese historians of mathematics (1819-1940) / Luis Manuel Ribeiro Saraiva -- The Jesuit College in Macao as a meeting point of the European, Chinese and Japanese mathematical traditions. Some remarks on the present state of research, mainly concerning sources (16th-17th centuries) / Ugo Baldini -- The transmission of Western cosmology to 16th century Japan / Hiraoka Ryuji -- The contents and context of Manuel Dias' Tianwenlüe / Henrique Leitao -- The textual tradition of Manuel Dias' Tianwenlüe / Rui Magone -- Restoring the unity of the world: Fang Yizhi and Jie Xuan's responses to Aristotelian natural philosophy / Lim Jongtae -- Traditional Vietnamese astronomy in accounts of Jesuit missionaries / Alexei Volkov -- Tomé Pereira (1645-1708), clockmaker, musician and interpreter at the Kangxi Court: Portuguese interests and the transmission of science / Catherine Jami -- The Yuzhi lixiang kaocheng houbian in Korea / Shi Yunli.

At the end of the 15th century, Portugal was given the oversight (Padroado) of all Catholic missions in Asia. The Society of Jesus played a major role in this enterprise of evangelization, which in Jesuit hands led to the transmission of major elements of European mathematical sciences to East Asia. The essays in this volume present important new data and analysis on the extent to and ways in which Jesuit scientific culture and Portuguese policies regarding education, trade and mission shaped the reception of "Western learning" in China, Japan, Korea and Vietnam in the early modern period.

Includes bibliographical references.

Local access dig.pdf. [Saraiva-Jami-Jesuits Padroado Asian science.pdf]
Online edition via Gleeson Library (ebsco).

JapSin II, 17
Jihe yaofa 幾何要法.
Dictated by Ai Rulue 艾儒略 (Giulio Aleni) and transcribed by Qu Shigu 瞿式榖.
Four juan. Bamboo paper, two ce bound in one volume, European style. Published by the Catholic church of Fuzhou 閩中景教堂 (Fujian). No date of publication.

The middle of the title page bears the title in four large characters; on the right the author’s name is given 艾思及先生述 and on the left that of the publisher: 閩中景教堂藏板. On the verso of this folio the title of the book and the author’s name are given again, with the names of the censors: Gao Yizhi 高一志 (Alfonso Vagnone) and Deng Yuhan 鄧玉函 (Johann Schreck [Terrenz]). The imprimatur was given by Yang Manuo 陽瑪諾 (Manuel Dias Jr.), then Vice-Provincial.
There is a preface in four folios by Zheng Hongyou 鄭洪猷 of Liu’an 六安 (Anhui), dated Chongzhen 4 (1631).
The first folio of each juan gives the title of the book, the number of the juan, the names of the authors: 泰西艾儒略口述 | 海虞瞿式榖筆受 and of the proofreader, Ye Yifan 葉益蕃 of Fujian.
Each of the four juan has a table of contents (two, three, two and two folios). The main text of juan 1 consists of nineteen folios, juan 2 of nineteen folios, juan 3 of eight folios and juan 4 of ten folios.
In the middle of each folio the title of the book is given and the number of juan is given below the fish tail. Each half folio has nine columns, with nineteen characters in each column.
Pfister describes this book as: “Principes de géométrie” (p. 135, no. 22) and Couplet’s Catalogus as: “Praxes necessariae Geometricae” (p. 17). It deals with the line and the plane in geometry.
Qu Shigu was the eldest son of Qu Taisu 瞿太素, one of the first converts of Ricci. He was born in 1593 (Wanli 21) and baptized in 1607. In homage to Ricci he took the Christian name Matteo. In 1623 (Tianqi 3) he invited the missioners to Changshu 常熟, his native place, to start a mission there. We are told that through his efforts over 200 of his countrymen became Christians within a short period (cf. JWC 1:276–277; ECCP 1:199).

Cf. CJC, juan 44, ce 5, p. 576.
Source: Albert Chan, S.J., Chinese Books and Documents in the Jesuit Archives in Rome, pp. 297-298.

JapSin II, 18
Jihe yaofa 幾何要法.
Dictated by Ai Rulue 艾儒略 (Giulio Aleni) and transcribed by Qu Shigu 瞿式榖.
Four juan. Bamboo paper, two ce bound in one volume, European style. No date or place of publication.

The cover bears a label with the title and a Latin inscription: “Liber Primus | Geometricus | de lineis. | Liber Secundus de lineis | inscriptis et circumscriptis | circulo. Liber Tertius de Angulis | et Triangulis. | Liber Quartus de Potentia linearum. | a p. Julio Aleni, S.J.”

JapSin II, 18a
Jihe yaofa 幾何要法.
Dictated by Ai Rulue 艾儒略 (Giulio Aleni) and transcribed by Qu Shigu 瞿式榖.
Four juan. Bamboo paper, two ce bound in one volume, European style. No date or place of publication.

The cover bears a label with the title of the book and a Latin inscription: “Compendium geo | metriae | a p. Julio Aleni | S.J.”

Tianxue chuhan 天學初函 / Li Zhizao deng bianji 李之藻等編輯.

"... Tianxue chuhan (1626)...writings concerning Heavenly Studies divided into those pertaining to principles li 理 (nine works) and to concrete things (objects) qi 器 (ten works)...a sample of the topics discussed and of their status in the Jesuits presentation of Christian learning and religion...described the curriculum of European universities, philosophy, rhetoric, medicine, law, canon law, theology...philosophy divided into five fields: logic, physics, metaphysics, mathematics, ethics; Physics, six topics: nature, incorruptible things, corruptible things, the four elements, their changes, living things; geography ..." Cf. Handbook of Christianity in China, vol. 1, p. 602-603; 698.

V. 1. Xixue fan 西學凡 / Giulio Aleni 艾儒略 -- (Tang) Jingjiao liuxing Zhongguo beisong 唐景教流行中國碑頌 -- Jiren shipian fu Xiqin quyi 畸人十篇附西琴曲意 -- Jiaoyou lun 交友論 -- Ershiwu yan 二十五言 -- Tianzhu shiyi 天主實義 / Matteo Ricci 利瑪竇.
V. 2. Bianxue yidu 辯學遺牘 -- Qike 七克 / Diego de Pantoja 龐迪我 (Seven Capital sins and seven opposing virtues)-- Lingyan lishao 靈言蠡勺 / Francesco Sambiasi 畢方濟, Xu Guangqi 徐光啟 (question of the soul, Aristotle's De Anima)
V. 3. Zhifang waiji 職方外紀 -- Qibian zongmu 器編總目-- Taixi shuifa 泰西水法 / Sabatino De Ursis (Xiong Sanba 熊三拔) -- Hun'gai tongxian tushuo 渾蓋通憲圖說 / Li Zhizao 李之藻.
V. 4. Jihe yuanben 幾何原本 / Matteo Ricci (Li Madou 利瑪竇) and Xu Guangqi 徐光啟 (1607)
V. 5. Biaodu shuo 表度說 / Sabatino De Ursis (Xiong Sanba 熊三拔) -- Tianwen lue 天文略 / Manuel Dias Jr. (Yang Manuo 陽瑪諾)(1615) -- Jianpingyi shuo 簡平義說 / Sabatino De Ursis (Xiong Sanba 熊三拔)(1611) -- Tongwen suanzhi 同文算指 / Matteo Ricci (Li Madou 利瑪竇) and Li Zhizao 李之藻 (1614)
V. 6. Yuanrong jiaoyi 圓容較義 / Matteo Ricci (Li Madou 利瑪竇) and Li Zhizao 李之藻 (1614) -- Celiang fayi 測量法義 -- Celiang yitong 測量異同 -- Gougu yi 勾股義 / Xu Guangqi 徐光啟 (1608)

Yingyin Jinling daxue jicun Luoma cangben 影印金陵大學寄存羅馬藏本.
Foreward to the yinyinben 影印本 by Luo Guang 羅光.
Preface by Fang Hao 方豪 entitled: Li Zhizao jike Tianxue chuhan kao: Li Zhizao dansheng sibainian jinian lunwen 李之藻輯刻天學初函考 : 李之藻誕生四百年紀念論文.
For detailed citatation see: Ad Dudink & Nicolas Standaert, Chinese Christian Texts Database (CCT-Database)

Dig.ed. local access only. [Tianxue Chuhan.pdf]

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.”

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.