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      Chinese painters, The Study of Vision was the only treatise on Western-style painting produced until the very end of the Qing dynasty, when progressive changes to art education began to incorporate foreign methods.

      Although it is impossible to conclusively attribute the development of scenic illusion paintings at the Yongzheng court to Giuseppe Castiglione, it is significant that Nian specifically credits Castiglione as the teacher from whom he learned Western painting. Castiglione was the only European painter present at the Yongzheng court after Matteo Ripa returned to Italy in 1723, and Nian’s two investigations into illusionistic painting were both published during the following years, when scenic illusions were developed. Nian takes pains to point out that the differences between Western and Chinese painting lay not in some inherent biological or even cultural difference in human vision, but rather in the practical techniques of pictorial representation, which led to different results. He argues that the production, rather than the perception, of pictorial illusions was culturally conditioned because of the differences between Chinese literati antimimetic and antitechnical ink painting as a means of self-expression on the one hand and, on the other, Western perspectival illusionistic painting, which was grounded in mathematics, taught techniques, and technical drawing using tools as a means of achieving mimesis. Nian therefore equated linear perspective with illusionistic painting, just as the term “perspectival painting” was interchangeable with “scenic illusion painting” at the Qing court. The Study of Vision is therefore the key to understanding how linear perspective was transformed from a novel aspect of technical knowledge for Kangxi into the familiar basis of scenic illusions for Qianlong.

      The Study of Vision has been difficult to categorize. The Jesuit introduction of linear perspective alongside mathematics and astronomy, along with Nian’s identity as an amateur mathematician and his otherwise exclusively scientific publication history, are perhaps responsible for its only full facsimile publication being within a compendium of scientific and technical texts.¹ Most scholars consider it an art treatise; however, it has been omitted from discussions both of Chinese mathematics and of huapu, the broad category that comprises Chinese painting manuals, painting catalogues, and art treatises. Huapu peaked in the late Ming dynasty between 1570 and 1620, roughly concurrent with the apex of the late imperial printed book industry and Dong Qichang’s codification of literati painting.² These manuals emphasized literati painting aesthetics, subjects, and pictorial treatments, and recent research suggests that they were published as much for artists as for a broad readership interested in developing the social and cultural markers of the intellectual elite.³ Other than being a woodblock-printed publication that combines instructions and illustrations, The Study of Vision bears little resemblance to the standard definition of Chinese painting manuals. Neither a mathematical treatise nor a manual on literati painting, The Study of Vision is sui generis, dissolving the barriers often raised between art and mathematics in the study of High Qing art that engages Western ideas. Like much of Nian Xiyao’s life and work, it should instead be placed at the intersection of these two areas.

      After the first five pages, which contain two prose prefaces, the remainder of The Study of Vision consists of diagrams inconsistently paired with brief, no-nonsense instructions. Although illustrations therefore make up more than 95 percent of the treatise, previous scholarly attention has focused almost exclusively on translating and interpreting the prefaces. Studies of eighteenth-century Sino-European contact often hint at the connection between The Study of Vision and illusionistic painting, but none engage the entire treatise primarily through its illustrations.⁴ Most scholarship dedicated to The Study of Vision includes fewer than two illustrations from the treatise, while some include none at all.⁵ Only three studies in Western languages present more than one or two diagrams, but only one author (and only in the case of two particular illustrations) provides any visual analysis other than the most basic description.⁶ One Chinese scholar has focused on the illustrations, but is predominantly concerned with architectural drawing and replicating Nian’s diagrams from his textual instructions, actually using the treatise as it was intended.⁷ Assessments of The Study of Vision are therefore largely grounded in the prefaces, where Nian mentions Giuseppe Castiglione, and the first few diagrams, which are derived from Andrea Pozzo’s Perspectiva, although their accompanying texts are not. Consequently, The Study of Vision is generally seen as a demonstration of “Jesuit perspective,” a reflection of Jesuit influence at the Qing court and therefore of the Jesuit mission itself.⁸

      However, this characterization contradicts the shared conclusion that Nian contextualized linear perspective and Western painting using established Chinese references, and more importantly, ignores the information conveyed in the illustrations. The illustrations do not support a Jesuit reading of the treatise, but rather reflect both Nian’s interest in mathematics, a critical aspect of his identity that is inseparable from The Study of Vision, and the Yongzheng emperor’s own fascination with Western things, which has been overshadowed by his negative treatment of the Jesuits. Without neglecting the prefaces, recentering a discussion of the treatise on its illustrations returns attention to the core of The Study of Vision and to the images that establish its art-historical significance relative to scenic illusion painting.

      Nian Xiyao, Practical Mathematician and Expert in Western Things

      Nian Xiyao was the oldest son of Huguang (present-day Hubei and Hunan) governor Nian Xialing (1643–1727), younger brother of General Nian Gengyao (1665?–1726), and brother-in-law to the Yongzheng emperor.⁹ Born in Guangning, Liaoning, within the historic Manchu homeland of northeast China, Nian was a Han-martial (Hanjun) bannerman (baoyi, originally Manchu booi) under the Bordered Yellow Banner, that closest to the emperor.¹⁰ This sociocultural identity as a bannerman and imperial bondservant automatically positioned Nian for a career in the Qing bureaucracy. Although the precise dates of his first two official posts are still unknown, Nian began his bureaucratic career under Kangxi as a clerk (bitieshi), a modest term for a common post that was nevertheless

      only available to bannermen, before progressing to deputy prefect (tongzhi) of Jingdong prefecture in the southwestern province of Yunnan. In 1706 he returned to north China as prefect (zhifu) of Guangping County in Zhili, and in 1711 he became circuit intendant (daotai) of Daming County in the Metropolitan Circuit of Zhili, both positions in southern Hebei approximately 280 miles from Beijing. In 1713 he moved to south China as surveillance commissioner (anchashi) of Guangdong; in 1716 he became provincial administration commissioner (buzhengshi) for Anhui; and in 1722 he rose to acting provincial governor (shuli xunfu) of Guangdong.

      These increasingly important positions demonstrate Nian’s progressively rising political star and increasing responsibility, which gave him the experience necessary to assume even more influential posts upon Yongzheng’s ascension to the throne in 1723. This was a watershed event in Nian’s career, the family connection resulting in his promotion to full provincial governor (xunfu) of Guangdong, a very powerful and influential position given the significance of the port of Guangzhou.¹¹ Moving to Beijing in 1725, Nian spent a year in the Ministry of Works (Gongbu) as vice minister of the right (youshilang), and in 1726 Yongzheng promoted him to grand minister supervisor (zongguan neiwufu dachen) in the Imperial Household Department.¹² Subsequently he was dispatched south as superintendent of the Imperial Ceramic Factories at Jingdezhen (duli Jingdezhen yuyao) to oversee the famous kilns that since the seventeenth century had served the court as well as export markets in Japan, Southeast Asia, and Europe.¹³ Beginning in 1727, he held the Jingdezhen superintendency simultaneously with the superintendency (jiandu) of the Huai’an and Suqian customs barriers in Jiangsu, both major stops on the internal water transport route of the Grand Canal, which linked Beijing with Hangzhou. Nian’s customs responsibilities required him to reside primarily at Huai’an, and he only occasionally

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