for the Emperor out of the English ships,” suggesting that Nian had personal contact with the European objects arriving in China.16 In contrast to Yongzheng’s generally anti-Jesuit policies, he was personally fascinated by Western things, and increased both Western imports and the domestic production of occidentalizing goods during his reign. Among the approximately five hundred Guangzhou tribute lists detailing objects sent to the Yongzheng court, there is an unprecedented specific category just for Western imports (yanghuo, literally “ocean goods”).17 Building on the imperial workshops that Kangxi had founded to produce some of the most prized Western and Western-style goods in China, Yongzheng expanded the imperial glassworks, clockmaking workshop, and enamel painting workshop, and established a new imperial workshop to produce spectacles, a category of foreign object that particularly fascinated him.18 Even Giuseppe Castiglione’s earliest extant painting (Auspicious Objects [Juruitu], 1723, National Palace Museum, Taipei) dates from early in the first official year of the Yongzheng reign, demonstrating how Yongzheng made use of Western painting from the very start of his time as emperor. Despite his general rejection of the Jesuits, Yongzheng was clearly able to separate his distaste for the missionaries from his love of Western things, and while in Guangdong Nian Xiyao seems to have played an important role in fulfilling the emperor’s desires for such things that cannot be unrelated to the development of his own interests.
Nian carried these interests in Western things with him to Jingdezhen, where certain porcelains were decorated with “foreign colors” (yangcai, as the imported famille rose palette was known), while those incorporating Western designs, shading, and pictorial realism in their painted decoration became known as “Nian wares” (Nian yao). Nian himself seems to have been a reasonably gifted painter of traditional landscapes and of birds and flowers, but claimed that he could paint in Western styles as well.19 He published on a diverse range of technical subjects, including chronology and medicine, but Western mathematics was his most persistent interest and the one that came to define him.20 Letters written by Gaubil and Dominique Parrenin, S.J. (Ba Duoming, 1665–1741), consistently mention Nian in the context of mathematical and scientific discussions.21 Although his formal education is still only speculative, Nian was not a literati scholar-official who had studied the Confucian classics to pass the government examinations for a civil bureaucratic post; instead, he seems to have been a self-taught mathematician.22 In Biographies of Astronomers and Mathematicians (Chouren zhuan), which Ruan Yuan
(1764–1849) compiled circa 1797 to 1799, Nian is described as “one who took Western calculation to be of vital importance” (yi Xiren cesuan zhi qieyao zhe).23 Biographies lists him as the author of The Measure of Calculation (Cesuan daogui, 1718) on trigonometry;24 Table of the Myriad Square Roots and Cube Roots (Wanshu pingli fangbiao); Logarithmic Tables (Duishu biao) and Extensive Use of Logarithms (Duishu guang yun) on logarithmic calculus; and Brief Guide to Polyhedron Proportions (Mianti bili bianlan, 1735) on calculating the area of polygons and the volume of polyhedrons, also using logarithmic calculus.
Nian was most active during the Yongzheng reign, but most of his life and his formative years were spent under the Kangxi reign; consequently, the Kangxi intellectual and cultural environments profoundly affected his work.25 In late imperial China, approaches to knowledge and understanding the natural world emphasized investigating things and extending knowledge (gewu zhizhi) in order to understand the myriad things (wanwu), which encompassed visible, tangible objects as well as immaterial mental and physical phenomena, historical and natural events, unknown or inexplicable occurrences, and otherworldly anomalies. Investigating things (gewu) revealed universal principles (li) for the real world, and fathoming these principles (qiongli) using the Confucian classics was termed “Learning of the Way” (Daoxue).26 Kangxi was particularly interested in fathoming the principles and the investigation of things as part of “practical learning” (shixue): a new interest in military training, strategy, archery, boxing, mechanics, mathematics, astronomy, history, and chronology that he promoted in the early Qing.27 Such areas of practical learning were the subjects on which a bannerman such as Nian would have focused, providing fertile soil in which Western mathematics could take root. All of the mathematical subjects on which Nian published were included in Kangxi’s Imperially Composed Essence of Numbers and Their Principles (Yuzhi shuli jingyun, 1722, hereafter Essence of Numbers). This vast mathematical compendium was based on the Jesuits’ lecture notes produced for Kangxi’s mathematics tutoring in the 1690s, but published by Kangxi’s Office of Mathematics (Suanxueguan) without Jesuit editorial contributions.28 Historically, mathematics was one of the Confucian Six Arts (liuyi, along with rites, music, archery, charioteering, and calligraphy) mentioned in the ancient classic The Book of Rites (Liji), but this implied amateur accomplishment rather than well-developed ability.29 Mathematics was practiced throughout Chinese history, but the increased seventeenth-and eighteenth-century interest in it was unprecedented, and is often attributed to the Jesuit introduction of Western mathematics and astronomy alongside court sponsorship.
Only three months after Nian published The Study of Vision, he also published the Brief Guide to Polyhedron Proportions, an unstudied text that not only exemplifies Nian’s predominantly mathematical leanings but also is very closely related to The Study of Vision in its presentation of how to understand specifically three-dimensional things.30 The Brief Guide therefore offers a glimpse into the mathematics of how Nian conceptualized the representation of objects, as well as his deep understanding of the complex mathematics that supported illusionistic painting and his commitment to spreading that knowledge. Nian begins
the preface to the Brief Guide (the full text and a translation of which can be found in the Chinese text appendix) by distinguishing two types of numbers: those used for the precise measurements and calculations surrounding tangible and visible things in the phenomenal world, and those used for intangible and invisible phenomena such as yin and yang and the flow of time. Citing several of the earliest Chinese mathematical texts, and sagely ancient rulers such as the Yellow Emperor and the Duke of Zhou who used them,31 Nian offers irrefutable precedents for an emperor’s use of mathematics. He then explicitly blames the scholar-official class (xueshidaifu) for the demise of mathematics in China, implicitly distinguishing himself from this group, and praises Kangxi’s restoration of it by comparing it to sight being restored to the blind. Naming the two translated Western mathematical treatises that most affected Kangxi,32 Elements of Geometry (Jihe yuanben, a translation of Euclid’s Elements) and Elements of Calculation (Suanfa yuanben), both produced by the Jesuits, Nian singles out their practical calculations: for example, the areas of farm fields and the volume of spheres in Elements of Geometry, and logarithms (jiashu; literally “false numbers”) in Elements of Calculation.33 Praising Yongzheng for completing Kangxi’s Essence of Numbers and predicting that it would encourage scholar-official use of mathematics as one of the Confucian Six Arts, Nian concludes the Brief Guide by specifying that he studies measurable things in the phenomenal world. Ultimately, he defines the treatise as an accessible beginner’s introduction to topics presented in more advanced and abstract forms thirteen years earlier in Essence of Numbers.
The body of the treatise progresses sequentially through the equations required to calculate the circumference, perimeter, diameter, side length, and area for circles, squares, inscribed circles, or circumscribed polygons (2r–15v). These basic calculations reveal a fixed ratio, and therefore a logarithm can be used to facilitate those calculations, which Nian applies to polygons of up to ten sides. Moving from two-dimensional polygons to three-dimensional polyhedrons, he then presents the same calculations and logarithms for spheres, cubes, and polyhedrons of four, eight, twelve, and twenty faces,34 in addition to cylinders, cones, truncated cones, circumspheres, and inspheres (15v–29v). The remainder of the text consists of illustrated logarithmic tables for each of those calculations (30r–40v), as well as logarithmic tables for calculating the weights and volumes of various substances such as precious and semiprecious
