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.

Summary:
The Yigu yanduan 益古演段 was written in 1259 by Li Ye 李冶 and published later in 1282. The Yigu yanduan presents itself as a list of 64 problems in three rolls. All the problems are related to the same topic which at first sight looks very pragmatic and simple: that is calculating the diameter or side of a field inside of which there is a pond. But the central topic of the Yigu yanduan is in fact the construction and formulation of quadratic equations derived from problems on squares, rectangles and circles.

The statute of this text was interpreted by historians as being an introduction to the Ceyuan haijing 測圓海鏡, the other mathematical masterpiece written by Li Ye in 1248, and published as the same time as the Yigu yanduan. The Yigu yanduan has long been regarded as a kind of text for popular purpose and remained in the shadow of the Ceyuan haijing. The book is still considered as a list of simplified examples in the procedure of the Celestial Source. The purpose of this study is to confront this point of view, to explain why there was such a misunderstanding and to put into light a peculiar field in Chinese mathematics. I show that this book is in fact masterpiece treatise whose practices can be related to the famous Han dynasty classic, the "Nine Chapters in Mathematical Art" 九章算術 and its commentary by Liu Hui (3rd century). The focus must be redirected on another procedure: the section of areas.

This study was done through careful comparison of all remaining available Qing dynasty editions of the Yigu yanduan, collection and reproduction of all the diagrams, and translation of the 64 problems. This study first shows how the Qing dynasty editors work with ancient sources and how their editorial choices mislead our modern interpretation. The systematic study of diagrams shows that one of the most important features of the Yigu yanduan is in fact a practice of manipulation of figures performed by the reader. The heart of the book relies on a non discursive practice: drawing and visualizing manipulations of figures.

Keywords: history of algebra, diagrams, transformation, tabular settings, analogy

Local access dig.pdf. [Bo-Yigu yanduan.pdf]

"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).

Shuli jingyun 數理精蘊.
T.p.: Yuzhi Shuli jingyun 御製數理精蘊
Dig. pdf (undated edition)
Cover collection title: Chizaotang Siku quanshu huiyao - Zibu - Shushulei 摛澡堂四庫全書薈要•子部•數術類
OCLC note for online edition: Originally published in 1723 (?) as part of the collection Lüli yuanyuan 律曆淵源, compiled ostensibly by He Guozong 何國宗, Mei Gucheng 梅榖成, and others, by direction of Qing Shengzu淸聖祖. Cf. Hummel. Eminent Chinese.
Local access dig.pdf [Folder-Shuli jingyun.pdf]

Volume 0735 nos. 05,18,25,27-30 (illustrated dance movements, foot placements, accompaniment, etc.) in pdf. See Dig. Archives folder Yuelü quanshu 樂律全書.

Zhoubi suanjing 周髀算經, see E. Wilkinson, Chinese history, a manual, pp. 470, 670, 789. For English translation and study, see C. Cullen, Astronomy and Mathematics in Ancient China, 1996.