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A Comparison of the Spread of the English Translation of Euclidean Geometry in 19Th Century China and Japan†

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A Comparison of the Spread of the English Translation of Euclidean Geometry in 19Th Century China and Japan† A Comparison of the Spread of the English Translation of Euclidean Geometry in 19th Century China and Japan† ∗ ∗∗ SARINA and Ying WANG Abstract In this paper, the authors compare the similarities and differences in the understanding and acceptance of Western geometry during the transformation of mathematics in China and Japan from the traditional mathematics model to the Western one. First, it starts with a detailed introduction to Euclidean geometry as it spread to the late Qing dynasty during the second half of the 19th century and early 20th century. Second, it compares the translations of Chinese and Japanese versions of Euclidian geometry and discusses the history of Western mathematics when it was introduced into the two countries. Third, we compare the relationship between the source books introduced into China and Japan, analyze their impact on the West, and offer reasons as to why the translators chose those particular source books in China and Japan. Finally, this paper ends with a discussion of the concrete influence of the Chinese and Japanese versions in spreading Western geometry and the transformation from the traditional mathematics model to the Western one. Key words: Euclidean geometry, Henry Billingsley, Robert Simson, late Qing dynasty, Meiji era 1. Introduction The famous ancient Greek geometer, Euclid, was the founder of Western mathemat- ics. In the 17th century, Euclidean geometry spread with the Jesuits to China, Japan, and other Asian countries. During the late Ming and early Qing dynasties, the Jesuit Matteo Ricci (1552–1610) and Xu Guangqi (1562–1633) jointly translated Jihe Yuanben, which comprised the first volumes of Euclidean geometry in the East. † The author, Sarina, gathered her data in the Institute for Research in Humanities of Kyoto University in Japan due to an invitation from Professor Tokimasa TAKEDA, who has also provided valuable advice on this paper. Professor Stephen Gaukroger from the Unit for the History and Philosophy of Science of the University of Sydney in Australia has offered his very generous help in improving this paper. Before contributing to this paper, Ms. Takane TAKAI from Kyoto University emailed the author papers on Yamamoto Masashi’s life. The authors would like to express their appreciation for all of this very kind assistance. This paper was funded by the 2014 Shanghai Liberal Arts Innovation Project 14ZS0292012, and the Studies on the Cultural History of the Chinese Translation of the Jihe Yuanben13AZS022, and the National Social Science Major Project 10&ZD063. ∗ Sarina, Shanghai Jiao Tong University, Shanghai, 200240, China. E-mail: [email protected] ∗∗ Ying Wang, Shanghai Jiao Tong University, Shanghai, 200240, China. E-mail: [email protected] HISTORIA SCIENTIARUM Vol. 24–2 (2015) A Comparison of the Spread of the English Translation of Euclidean Geometry 89 These first six volumes of Jihe Yuanben spread to Japan during its Edo period. The proof of Jihe Yuanben spreading to Japan can be found. The “Tian Xue Chu Han” version containing Jihe Yuanben had already been introduced to Japan by 1630. For example, the “Tian Xue Chu Han” (天学初函) version can be found in the “Royal Banned Book Catalog” (御禁書目錄) of the 1630 bibliography.1 In addition, the following sentence can be found in the preface by Hosoi Kotaku (細 井広沢, 1658–1736) for Mao Tokiharu’s Kikubuntoshu (万尾時春『規矩文等集』), which was published in 1722: “I smiled to myself when meeting by chance with such works from China as the Jihe Yuanben.” Thus, it is reasonable to presume that Hosoi Kotaku got the Jihe Yuanben into Japan before lifting the banned books in 1720.2 Japanese Jesuits who had been to Japan during its Edo period also brought Euclidean geometry and taught it in some church schools. It is said that in the Jesuit schools set up in the west of Japan in the 16th century, the contents of volumes 1–6 and volume 11 were taught, in addition to the Western arithmetic and algebra.3 In the “Rangaku” (蘭学) era, Euclidean geometry was directly introduced from the West to Japan. The geometry book entitled Grondbeginsels der meetkunst (Pibo Steenstra, Amsterdam, 1803) kept at Japanese Tokai Doh¯ o¯ University (東海同朋大学), was in the collection of translator (通詞) Yoshio Shunzo (吉雄俊蔵, 1787–1843) in Nagasaki. He was the grandson of Surgeon Yoshio Kogyu (吉雄耕牛, 1724–1800), and was a doctor at the Dutch business hall in Nagasaki. Shunzo acted as Rangaku’s professor and doctor, teaching Western medicine and astronomy. It was said that he died in an explosion during a chemical experiment.They are all written in Dutch, including what is quoted from volumes 1–6, volume 11, and volume 12 in Euclidean geometry. When Euclidean geometry spread to China and Japan, the two countries had their own traditional mathematics, “Zhong Suan (中算)” and “Wasan (和算)”, respectively. Eu- clidean geometry emphasized importance of logical deduction, but Chinese and Japanese traditional mathematics placed importance on numerical calculation. This is the greatest and fundamental difference between Euclidean geometry and traditional Eastern mathe- matics. When Euclidean geometry spread to China and Japan, it had a big impact on Chinese and Japanese mathematics. Scholars learning and studying Euclidean geometry appeared in China and Japan in the 17th and 18th centuries. Between the 17th and 19th centuries, both China and Japan successively went through historical periods in which the countries were closed to inter- national contact. In Japan, this was approximately between 1639 and the 1850s; and in China, this was approximately between 1757 and the 1840s. In the mid-19th century, advanced Western power opened the doors of China and Japan. The two Opium Wars and the arrival of the American Black Ships were shocks to 1 The Christian books were banned by the Tokugawa government (德川幕府) in 1630 (寬永 7 年), among which there are 32 kinds relating to Matteo Ricci. See Ohara Satoru, “Ways to Learn about the West during the Early Stage of Japan’s Seclusion「 ( 外なるもの」への意識―鎖国初期における日本人の海外知識の系譜),” Sophia, vol. 23, no. 2 (1974), p. 175. 2 The Editorial Committee of The Hundred Year History of Japanese Mathematics, The Hundred Year His- tory of Japanese Mathematics (Tokyo: Iwanami Shoten, 1983), vol. 1, p. 8. 3 Ibid., p. 4. 90 SARINA and Ying WANG the traditional civilization of the Japan. In the late 19th century, with the spread of Western science and technology, Euclidean geometry again spread to the late Qing China and to Japan as it was transitioning from the late Edo period into the Meiji era. In the late 19th century, some church and government translation agencies translated Western mathematics books into Chinese and Japanese. In China, this was done by the famous translation agency, the London Missionary Society Press (墨海書館), and workers at Translation Department of the Kiangnan Arsenal (江南 製造局翻訳処). The Western mathematics books in Chinese translation that emerged in the late 19th century are known as the late Qing translated Western mathematics books. The late Qing translated Western mathematics books were first published in China and then spread to Japan, which had a significant influence on Japanese learners’ understanding of Western mathematics through the late Edo to the early Meiji era. The set of the last nine volumes of the Jihe Yuanben translation is one of the late Qing translated Western mathematics books. In the late 19th century, when Euclidean geometry was spreading to Eastern coun- tries, the translated works by the two British scholars, Henry Billingsley (1538–1606) and Robert Simson (1687–1768), played a crucial role. Billingsley was a celebrity who once studied at the University of Cambridge and the University of Oxford and later traded in London. In 1596, he was elected Mayor of London. His translation, in 15 volumes, was the first English version of Euclidean geometry.4 The preface of the first edition was writ- ten by John Dee (1527–1608). In 1756, the most important English version of Euclidean geometry was published in Britain by Robert Simson. In this version, Simson corrected the errors by the ancient Greek mathematician, Theon of Alexandria (335–405), and added his own paraphrasing. Robert Simson’s version was printed many times. Volumes VII–X and volume XIII did not appear in some versions. Simson’s first version was entitled The Elements of Euclid and included the first six books together with the eleventh and twelfth. In this edition, the errors introduced by Theon or others were corrected and some of Euclid’s demonstrations were restored. It is these two English translations of Euclidean geometry that spread to China and Japan and other Eastern countries at the end of the 19th century and had a very important effect on the transformation of mathematical models in these countries. Alexander Wylie (1815–1887), a missionary from London, and American Edward Warren Clark (1849–1907), who had studied in Britain and worked in Japan, both con- tributed to the spreading of Euclid writings. In the following sections, the authors will present how Euclidean geometry was spread to China and Japan at the end of the 19th cen- tury and the important influences that followed. And in the subsequent section, the authors will offer a detailed comparison between historical China and Japan in their translations and study of Euclidean geometry. 4 J. Venn, “Billingsley, Henry,” in Alumni Cantabrigienses, ed. J. A. Venn (online ed.). (Cambridge: Cam- bridge University Press). A Comparison of the Spread of the English Translation of Euclidean Geometry 91 2. The Spread of Euclidean Geometry to Late 19th Century China In the postscript for the first six volumes, Xu Guangqi wrote, “More achievements should have been made. We have no idea when and by whom it will be accomplished. We will be awaited.”5 The scholar Li Shanlan and the missionary Alexander Wylie responded to his question 200 years later.
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