JapSin II, 62
Biaodu shuo 表度說.
Transmitted orally by Xiong Sanba 熊三拔 (Sabatino de Ursis) and written down by Zhou Ziyu 周子愚 and Zhuo Erkang 卓爾康.
One juan. Bamboo paper in one ce with a paper case. No date or place of publication.

The cover bears a label with the title and a Latin inscription: “De Gnomonica | a p. Sabbathinus | de Ursis S.J.”

Cf. Pfister, p. 105, no. 3; Feng 1938, p. 125; Hsü 1949, pp. 281–284; SKTY 3:2180–2181; Courant 4903; Couplet, p. 13; DMB 2:1332.

Source: Albert Chan, S.J., Chinese Books and Documents in the Jesuit Archives in Rome, p. 368.

Jap-Sin II, 32
Chousuan 籌算.
By Luo Yagu 羅雅谷 (Giacomo Rho).
One juan. Bound in one volume, European style. No date or place of publication.

The first folio mentions the collection (Xiyang xinfa lishu and the section to which the text belongs: 西洋新法曆書，法數部，籌算, the chief compiler (Xu Guangqi): 明禮部尚書兼翰林院學士協理詹事府事加一級俸徐光啟督修，the author and reviser (Giacomo Rho and Adam Schall): 修政曆法極西耶穌會士羅雅谷撰，湯若望訂，and the proofreaders (Zhu Guoshou, Zhu Guangda, Chen Suoxing, Huang Hongxian, Sun Silie and Jiao Yingxu): 門人朱國壽，朱光大， 陳所性， 黃宏憲， 孫嗣烈，焦應旭受法.

There is a preface, dated 20.III 1628 (Chongzhen 1) by Rho himself, followed by the table of contents of the book. The whole book consists of thirty-nine folios. There are nine columns in each half folio with twenty-one or twenty-two characters to each column. The title of the book and the number of the folio are given in the middle of each folio.

Rho states in his preface that the science of calculation is so widely employed in scientific studies as well as in people’s daily life that it can be called universal. He then goes on to say that though the study of arithmetic was common among his countrymen, those who were poor in memory found it hard to learn. The Napier’s rods method was invented to facilitate the study of arithmetic. It was for this purpose that this book was written in Chinese as a new method to help Chinese students.

Cf. Pfister, p. 191, no. 16 (Arithmétique népérienne, 1 vol.); Couplet, p. 23 (De Arithmetica); Wylie, p. 112 (On the Principle of Napier’s Rods).

Source: Albert Chan, Chinese Books and Documents in the Jesuit Archives in Rome (2002), p. 314-315.

Full bibliographic information see Ad Dudink & Nicolas Standaert, Chinese Christian Texts Database (CCT-Database)
Local access dig. archives, see folder ARSI Jap-Sin I-IV (II, 32)

Du Shiran 杜石然 et Han Qi 韓琦.
Extract from: Impact: science et société, no. 167, p. 275-285.
Includes bibliographical references.
Also published in English: The contribution of French Jesuits to Chinese science in the seventeenth and eighteenth centuries.

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.

Local access dig.pdf. [Jami-Emperors-New-Mathematics.pdf]

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]

Preface / Luís Saraiva -- Les sciences mathématiques en Chine vers 1600 / Jean-Claude Martzloff --The Portuguese assistancy of the Society of Jesus and scientific activities in its Asian missions until 1640 / Ugo Baldini -- L'Exploration d'une mathématique: l'École de Jésuite Grégoire de Saint-Vincent dans les Pays Ibériques et Au-Delà / Jean Dhombres -- O problema da longitude posto pelas Navegações, o Tratado de Tordesilhas e as Negociações de Elas-Badajoz / José Joaquim Dionísio -- Os Jesuítas e o Intercâmbio Científico entre a Europa e o Oriente do século XVI ao século XVIII / Alfredo Dinis -- F. Furtado (1587-1653) S.J. and his Chinese translation of Aristotle’s Cosmology / Han Qi -- The Pleasure-Garden of Myriad Forms: some reflections on the Chinese translation of Euclid (1607) / Peter Engelfreit -- P. Andreas Pereira and his contribution to mathematics and astronomy in China / Wang Yusheng -- D. Frei Alexandre de Gouveia, Bispo de Pequim, Astrónomo e matemático na Corte Chinesa / Antonio Graça de Abreu -- Nagasáqui e a primeira Abertura do Japão ao Ocidente / João Paulo Oliveira e Costa -- The navigational instruments in Duarte de Sande's Dialogus de Missione Legatorum Iaponensium ad Romanum Curiam (1590) / Charles Burnett -- Notes on the contents and fate of the Western scientific influence in Japan in the sixteenth and seventeenth centuries / Henrique Leitão -- Les activités scientifiques (mathématiques, astronomie) des Missions Catholiques au Japon et en Chine du milieu du XVI^e Siècle au milieu di XIX^e Siècle / Jean-Claude Martzloff -- Two Jesuit contributions to geometry in China / Joseph MacDonnell -- Image and patronage: the role of Portugal in the transmission of scientific knowledge from Europe to China / Catherine Jami.

"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.

"Accounts of the seventeenth-century Jesuit Mission to China have often celebrated it as the great encounter of two civilizations. The Jesuits portrayed themselves as wise men from the West who used mathematics and science in service of their mission. Chinese literati-official Xu Guangqi (1562-1633), who collaborated with the Italian Jesuit Matteo Ricci (1552-1610) to translate Euclid's Elements into Chinese, reportedly recognized the superiority of Western mathematics and science and converted to Christianity. Most narratives relegate Xu and the Chinese to subsidiary roles as the Jesuits' translators, followers, and converts. Imagined Civilizations tells the story from the Chinese point of view. Using Chinese primary sources, Roger Hart focuses in particular on Xu, who was in a position of considerable power over Ricci. The result is a perspective startlingly different from that found in previous studies. Hart analyzes Chinese mathematical treatises of the period, revealing that Xu and his collaborators could not have believed their declaration of the superiority of Western mathematics. Imagined Civilizations explains how Xu's West served as a crucial resource. While the Jesuits claimed Xu as a convert, he presented the Jesuits as men from afar who had traveled from the West to China to serve the emperor."--Publisher's website.

Science as the measure of civilizations -- From Copula to incommensurable worlds -- Mathematical texts in historical context -- Tracing practices purloined by the three pillars -- Xu Guangqi, Grand Guardian -- Conclusions -- Acknowledgments -- Appendix A: Zhu Zaiyu's New theory of calculation -- Appendix B: Xu Guangqi's Right triangles, meanings -- Appendix C: Xu Guangqi's writings.

In English; some text in Chinese with accompanying English translation.
Text also online at EBSCO host (USF community only).

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.”

" ... compilation of Shuli jingyun (Essential principles of mathematics, 1722) can be traced back to 1689 when two French Jesuits, Jean-François Gerbillon (1654-1707) and Joachim Bouvet (1656-1730), and a Belgian, Antoine Thomas (1644-1707) took up the task of tutoring the Kangxi Emperor in mathematics....this article focuses on the contribution of Antoine Thomas. It provides evidence that the Chinese treatise Suanfa zuanyao zonggang (Outline of the essentials of calculation) was to a large extent based on Thomas' Latin treatise, the Synopsis Mathematica (1685). The source for significant portions of Shuli jingyun is thus identified...”—English abstract, p. 22.

The Contribution of French Jesuits to Chinese science in the seventeenth and eighteenth centuries / Du Shiran 杜石然 and Han Qi 韓琦.
Extract from: Impact of science on society, no. 167, p. 265-275.
Library has offprint & pdf electronic document.
Also available in French.
Includes bibliographical references.

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.

Agradecimientos -- Introducción : la llegada de los jesuitas a China. El nacimiento de la Compañía de Jesús. La llegada de los jesuitas a China : Matteo Ricci. La acomodación de los jesuitas en China -- 1. Introducción de la astronomía europea en China. El contexto astronómico europeo. La llegada de los jesuitas astrónomos a la corte de Beijing -- 2. Vida de Giacomo Rho. Nacimiento y procedencia. Formación y viaje de Rho. Papel de Rho en la defensa de Macao contra los holandeses. Ultimos años y muerte de Giacomo Rho -- 3. Un nuevo catálogo de las obras de Rho. Obras religiosas. Obras científicas. Cartas. Conclusión : las obras de Rho rectalogadas -- 4. Matemáticas en China y en Europa en el tiempo de Rho. Las matemáticas en China. Las matemáticas para la Compañía de Jesús. Las matemáticas introducidas por los jesuitas en China. John Napier y su búsqueda de métodos rápidos para calcular -- 5. El Chou Suan de Giacomo Rho. Generalidades y fechas. Aspectos generales del Chou Suan. Fontispicio, prefacio e índice. Primera parte : construcción de las varillas. Segunda parte : las operaciones más simples. Multiplicación y división. Raíz cuadrada. Raíz cúbica. Anexo sobre economía -- 6. Recepción y significado del Chou Suan de Rho. El Chou Suan de Mei Wending. La inculturación en China mediante las matemáticas -- Un breve sobre el trabajo astronómico de Rho -- Conclusión : Rho como matemático y astrónomo en Beijing -- Bibliografía -- Anexos. Anexo A. Documentos procedentes del Archivo Histórico de Macao. A.1. Informaçoěs Comuăs dos Padres que vieram para a China, Com o Padre Nicolao Trigao, no anno de 1620. A2. Morte do Doutor Leam, e do Padre Joaŏ Terencio ambos na Corte, saŏ chamados a ella por ordem Real os Padres Jacome Rho, e Joaŏ Adaŏ. A.3. Carta do Padre Alberto à o Padre Jacome Rho.

A.4. Carta do Pe. Jacome Rho ao Pe. Geronimo Roiz Vizitador da Companhia de Jesus na China, e Japaŏ A.4. Carta do Pe. Jacome Rho ao Pe. Geronimo Roiz Vizitador da Companhia de Jesus na China, Japaŏ. A.5. Cristiandades soguitas à Corte de Pekim e Morte do Padre Jacome Rho. Capitulo 8°. A.6. La morte do Padre Jacome Rho. A.7. Do estado em que estado estaŏ as couzas do Calendario. A.8. Do Estado do Calendario -- Anexo B. Información sobre Giacomo Rho (Luo Yagu) en el Chou Ren Zhuan -- Anexo C. Situación de las obras científicas de Rho en el Si Ku Quan Shu -- Anexo D. Fotografías de la estela conmemorativa de Giacomo Rho -- Anexo E. El Chou Suan.

Dig.pdf. local access [Cervera-Rho Napier en China.pdf]

Xiangshu lun 象數論 / wumingshi 無名氏.
In: Yesuhui Luoma dang'anguan Ming-Qing Tianzhujiao wenxian 耶穌會羅馬檔案館明清天主教文獻 / Edited by Nicolas Standaert [鐘鳴旦] [and] Adrian Dudink [杜鼎克]. Reproduction of original text in vol. 6 of this collection. 

Jap-Sin II, 166.
Xiangshu lun 象數論.
By Xiong Sanba 熊三拔 (Sabbatino de Ursis, 1575–1620).
Manuscript (incomplete), one juan, one ce; written on Chinese paper with red squares. 25 x 15.5 cm.

The cover bears an inscription in Portuguese: “Do P. Sabbatino de Ursis sobre o Ye kim.”

There are nine columns in each half folio with twenty characters to each column. The text, which is incomplete, consists of twenty-one unnumbered folios (including the covers) and contains illustrations.
The author of the manuscript is not given. However, in folio 1, column 4, there is a remark : Yougangzi yue 有綱子曰. Now Yougang is the zi of Sabbatino de Ursis, which clearly indicates that he is the author. This title does not appear in Pfister or elsewhere.
The book, written in dialogue form, begins with the objection that in China the teaching of the savants is based on moral problems and not on God or on mathematical signs. To this the reply is that the Golden Mean [i.e. Zhongyong 中庸] (one of the Four Books in the Chinese classics) begins with the service of God. The savants observed the heavenly law and expressed it in writing and by diagrams. Thus, one practices virtues according to the dictate of the heavenly [Lord] and one governs by divine law without intervention of the impetuous human self.
The treatise then goes on to discuss the philosophy of mathematics, beginning from the point which is the centre of the Taiji 太極 (the Absolute), as was indicated by the Song philosophers. It then goes on to discuss the line, the surface and tries to refute the theory of Wuji 無極 and Taiji.
Source: Albert Chan, S.J., Chinese Books and Documents in the Jesuit Archives in Rome, p. 454.