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 mathematics. 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 mathematics. 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 countries, 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 written 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 contributed 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 century 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. Li Shanlan became familiar with ancient Chinese mathematics books and the late Ming to early Qing Western mathematics translations from very young. He exclaimed when he was reading the first six volumes of Jihe Yuanben, “I under- stand the meaning of the translation of the six volumes at the age of 15. In my opinion the last nine volumes must be more subtle, while they are not available. Such a pity that Xu and Ricci haven’t completed the translation.”6 In 1852, Li Shanlan arrived in Shanghai and met Missionary Alexander Wylie (偉烈亜力, 1815–1887) and Joseph Edkins (艾約瑟, 1823–1905). From 1852 to 1859, Li Shanlan and these missionaries jointly translated several Western science works in fields such as mathematics, mechanics, botany, and astronomy. In addition to being a missionary, Alexander Wylie was a sinologist. He was recommended by the British missionary James Legge (理雅各, 1815–1897) to China to do missionary work in 1847. During his time in China, he translated the Bible by himself and together with Chinese scholars, translated some Western science books as well. From August to November in 1852, Wylie wrote the paper Jottings on the Sciences of Chinese Mathematics for the North China Herald, which introduced traditional Chinese mathematics to the West. It was the major literature from which Western scholars learned about traditional Chinese mathematics before the publishing and circulation of The Devel- opment of Mathematics in China and Japan by Mikami Yoshio (三上義夫, 1875–1950).7 Shu Xue Qi Meng『数学啓蒙』( ) by Wylie was not only popular with Chinese scholars but also spread to Japan as an important book for Western mathematics education in early Meiji Japan. Hissan Kunmo 『筆算訓蒙』( ) was a textbook in the early Meiji era based on Shu Xue Qi Meng 『数学啓蒙』( ). When Wylie finished reading the first six volumes of Jihe Yuanben in China, he wrote “After I came to China, I met with the six volumes of Jihe Yuanben, translated by the Westerner Matteo Ricci in the Ming Dynasty. Chinese mathematicians all attached great importance to it. But after knowing it was not the translation of the whole volumes, I am not quite satisfied with it.”8 The last nine volumes of Jihe Yuanben were translated been 1852 and 1856. The completed merger of the last nine volumes and the first six volumes was published in

5 The original version in Chinese is “続成大業, 未知何日？未知何人？書以俟焉.” Xu Guangqi, Xu Guangqi Collection (徐光啓集), (Shanghai: Shanghai Ancient Books Publishing House, 1984) , p. 9. 6 The original version in Chinese is “年十五読旧訳六卷, 通其義．窃思後九卷必更精微, 欲見不可得, 輒恨徐, 利二翁之不尽訳全書也”, (Qing dynasty) Zhu Kebao (諸可宝). Chou Ren Biography (疇人伝), Volume 4 of Series 3, Li Shanlan (李善蘭), Collection of Qing Dynasty Tables (清碑伝合集), Series IV, p. 3625. 7 Mikami, Yoshio. The Development of Mathematics in China and Japan by Yoshio Mikami. (New York: Chelsea), 1974. 8 The original version in Chinese is “余来中国, 見有幾何六卷, 明泰西利氏翻, 算家多重之, 知其未為全書, 故亦不甚満志”, Alexander Wylie, the 7th year of Emperor Xianfeng (1857) the 10th of the ﬁrst lunar month, translated and edited Ji He Yuan Ben preface. 92 SARINA and Ying WANG

1865. The differences between the structure of the full version of Jihe Yuanben and the Ming-Qing version are:9 (1) The original preface was by Xu Guangqi and Matteo Ricci (徐光啓, 利瑪竇原序); (2) The original preface was by the successive translators Li Shanlan and Alexander Wylie (続訳原序); (3) The preface of Jihe Yuanben Xu was by Zeng Guofan (曾国藩序); (4) The preface Jihe Yuanben Za Yi was by Xu Guangqi (徐光啓幾何原本雑議); (5) The successive original postscript was by Han Yingbi (韓應陛続訳原跋); (6) The original postscript was by Xu Guangqi (徐光啓原跋); (7) The first six volumes were translated jointly by Xu Guangqi and Matteo Ricci (徐光啓, 利瑪竇合訳); (8) The last nine volumes were translated jointly by Li Shanlan and Wylie (李善蘭, 偉烈亜力合訳). The contents of the last nine volumes were as follows:10 volume 7 to volume 9 discussed the theory of numbers; volume 10 was devoted to commensurability and non- commensurable line and surface; volume 11 discussed lines in space and planes in all sorts of relations; volume 12 provided a “method of exhaustion” for a circular, pyramid, ball, and cone volumes; volume 13 focused on the five kinds of regular polyhedron; and volumes 14 and 15 were mainly concerned with comparing the composition of regular polyhedrons. According to Qian Baocong, the source book for the last nine volumes in the late Qing dynasty was Barrow’s version.11 However, in 2004, Xu Yibao suggested in his paper, The First Chinese Translation of the Last Nine Books of Euclid’s Elements and Its Source that the source book was actually the English translation by Henry Billingsley, which was published in 1570.12 The structure of the source book is composed of the following parts: the preface ti- tled as “The Translator to the Reader,” the 24-page-long introduction by mathematician John Dee (1527–1608), Euclid’s Vols. I–XIII, Vol. XIV and Vol. XV by the ancient Greek mathematician Hypsicles of Alexandria (about BC 180), and Vol. XVI added by Francis- cus Flussates Candalla, the researcher and editor for the Greek edition of Jihe Yuanben. Compared to the source book, the omitted contents were Vol. XVI, every preface in each volume, the explanations and definitions, as well as some additional content. The relationship of the late Qing dynasty version in the last nine volumes and the first six volumes follows the same form of translation (Chinese scholar-dictated by a western Missionary), with identical major terminologies. In addition, the structure of the content

9 Hai Shan Xian Kan Cong Shu『 ( 海山仙刊叢書』), 1874; Ren Jiyu, On China Science and Technology Books『 ( 中国科学技術典籍通匯』) (Vol. 5), Zhengzhou: Henan Education Press, pp. 1145–1500. 10 Ren Jiyu, On Chinese Science and Technology Books 《( 中国科学技術典籍通匯》) (Vol. V), Zhengzhou: Henan Education Press, pp. 1302–1500. 11 Qian Baocong, China’s History of Mathematics (Beijing: Science Press, 1964), p. 324. 12 Xu Yibao, “The First Chinese Translation of the Last Nine Books of Euclid’s Elements and Its Source,” Historia Mathematica , vol. 32 (2005), pp. 4–32. A Comparison of the Spread of the English Translation of Euclidean Geometry 93 is basically the same (figure). Li Shanlan created new terms (with reference to charts). It is a transformation of the mathematical terms in the first six volumes and the translator’s comments have been added (e.g., Shanlan note figure).

3. The Spread of Euclidean Geometry to Late 19th Century Japan

The spread of Euclidean geometry in modern Japan (the late Edo and early Meiji eras) is summarized as follows: In the late Edo era, the study of Western military and navigation technology at such institutions as the Nagasaki Kaigun Denshujo (長崎海軍伝習所) helped the spread of Eu- clidean geometry. In 1868, the Tokugawa family left Tokyo for Shizuoka, where they established Gakumonjo of Shizuoka (静岡学問所) and Heigakko of Numazu (沼津兵学校). Western-style physics and chemistry were taught at these two schools. During the early Meiji era, most graduates from the Nagasaki Kaigun Denshujo worked for schools such as Gakumonjo of Shizuoka and Heigakko of Numazu. The Gakumonjo and Heigakko could be regarded as an extension of the tradition of studying Euclidean geometry. Many students studied the contents of the Euclidean geometry in math class. The teacher who taught Euclidean geometry in the Gakumonjo of Shizuoka was the hired foreigner, Edward Warren Clark (1849–1907). A brief introduction to several translators starts with E. W. Clark. Katsu Awa (勝安房 or Katsu Kaishu¯ 勝海舟, 1823–1899) of Shizuoka-han (静岡藩) wanted an Amer- ican teacher who had university training in science and could teach Western sciences to Japanese students, and he consulted with W. E. Griffis (1843–1928), a Congregational minister, prolific author, and lecturer at Meishinkan, the official school of Fukui Domain. Griffis in turn recommended to Katsu E. W. Clark who had been his classmate at Rutgers University. Clark came to Japan and taught young sons of Tokugawa samurai mathematics, chemistry, and physics at the Gakumonjo of Shizuoka from 1871 to 1873.13 He was the first American science teacher at Shizuoka. The geometry that E. W. Clark taught in the classroom was translated into Japanese by his students and presented in the Kikagaku Genso (幾何学原礎) of Euclidean geometry, first translated and published by Japanese scholars. The Japanese scholars who translated Euclidean Geometry jointly with E. W. Clark were Kawakita Tomochika (川北朝鄰, 1840–1919) and Yamamoto Masashi (山本正至, 1834–1905).14 Kawakita Tomochika, born in Edo, began to study Wasan from his early age and studied it under noted Wasan mathematicians. He entered Gakumonjo of Shizuoka to study Western mathematics. He was one of the typical Japanese scholars who shifted spe- cialty from traditional mathematics to Western mathematics. He once was the leading member of the earliest mathematical society in Japan, the Tokyo Mathematical Society.

13 Edward R. Beauchamp, “An American Teacher in Early Meiji Japan,” Asian Studies at Hawaii, 17 (1976), pp. 58–60. 14 Suzuki Takeo, “Kikagaku Genso no Honyakusha Yamamoto Masashi ni tsuite,” Surikaiseki Kenkyujo Kokyuroku, 1739 (2011), pp. 138–148. 94 SARINA and Ying WANG

He also opened a private school teaching Western mathematics in Tokyo. He partici- pated in many Western mathematics translations, including the collaboration with Ueno Kiyoshi (上野清, 1854–1924) and Nagasawa Kamenosuke (長澤亀之助, 1860–1927) to translate a Western mathematics textbook,15 which contributed to the popularization of Meiji Japanese mathematics education, and which also had an impact on the popularization of Western mathematics education after it was introduced to China in the 20th century. Yamamoto Masayuki’s work, however, was rarely recorded, except for being briefly introduced in some library Meiji era literature, from which we see that he was a noble of Shizuoka domain (士族). Yamamoto once compiled Hissan Daiso 『筆算題叢』( ) with Tazawa Masanaga (田澤昌永), which used to be a popular mathematics textbook in the middle and primary schools in Shizuoka domain. The structure of Kikagaku Genso will be analyzed first in this section. Kikagaku Genso was composed of seven volumes and was published by Bunrindo (文林堂) in Shizuoka Prefecture. The front cover for volumes 1–6 was decorated with woodblock printing and the traditional Japanese binding. The volumes of Kikagaku Genso were published at different times: volumes 1–5 were published on December 5, 1875 (the 8th year of Meiji era), and volume 6 was published on October 6, 1878 (the 11th year of Meiji era). The front volume begins with Clark’s introduction in English, dated February 1873. He introduces the importance of mathematics in science as a whole, and the function of mathematics in training people’s logical thinking. He also introduces the history of Eu- clidean geometry and his experience teaching Western mathematics in Japan. The “Preface” is followed by “Explanatory Notes” (凡例). The Japanese of “Ex- planatory Notes” are presented below,16 the main contents were the history of Euclidean geometry. In the origin of the name Kikagaku Genso, the character “chu (basic 礎)”, namely because “ji chu (basic 基礎),” is different from Chinese names. It is likely to be translated by referring to ELEMENTA from its Greek origin, 6τoιχεια´ , which means α, β, that is “the alphabet of the language.” The explanatory notes also addressed the purpose of translating Kikagaku Genso and its application to geometry. “Explanatory Notes” is followed by “Translation Terms” (訳語), which are the mathematical terminologies used in this book. Each volume starts with “Translation Terms,” including the first one. It can be said that “Translation Terms” in Kikagaku Genso are the first group of mathematical terminology founded and defined by Japanese scholars. Some of these mathematical terminologies are borrowed from the Chinese version, Jihe Yuanben, others from Japanese traditional mathematics, and still others were created by the translator of this book. For example, “definition” is translated as “命名 (to name),” “postulate” as “確定 (to make certain),” “axiom” as “公論 (public opinion),” “proposition” as “考定 (to consider and set),” and “theorem” as “定理.” Of these, only the last term “定理” has survive as the

15 Ueno Kiyoshi et al., Shoto¯ Heimen Kikagaku (初等平面幾何学) (Tokyo: Yoshikawa Hanshichi, 1891). Nagasawa Kamenosuke, Euclid (宥克利) (Tokyo: Maruya Zenshichi, 1884). 16 E. W. Clark, Kawakita Tomochika, and Yamamoto Masashi, Kikagaku Genso (幾何学原礎) (Shizuoka: Bunrindo, 1875), vol. 1, p. 1. A Comparison of the Spread of the English Translation of Euclidean Geometry 95 formal technical term to mean the theorem. Nonetheless, the authors consider that these mathematical terms laid the foundation for modern Japanese mathematics education and thus have great significance in the history of Japanese mathematics. The first volume of the Kikagaku Genso with these Japanese translations of English mathematical terms was published in 1875, 5 years earlier than the time when the Com- mittee for Translation (訳語会) was established by the Tokyo Mathematical Society (東京数学会社). It is considered that the terminologies in the Kikagaku Genso would be the first mathematical terms created by modern Japanese scholars. Kawakita and his followers translated the mathematical terminologies and wrote down in the Kikagaku Genso so as to get rid of the influence from the Chinese terminologies. In fact, the last nine volumes of the Jihe Yuanben and other late Qing western mathematical works had been introduced to Japan by then. Many scholars adapted and referred to the terminologies in this book. Kawakita and his followers should be familiar with those mathematical terminologies, but in the book Kikagaku Genso the Chinese translation of mathematical terminologies were replaced by newly created terminologies. This replacement shows that these Japanese scholars started to break away from the influence from the Chinese translation of the West- ern mathematics. In addition, one aspect of the mutual influence of Sino-Japanese mathematics during their Westernization process is revealed through the impact of Japanese mathematical terminology on China. Here is the introduction from the source book for Kikagaku Genso. In order to find the source book for Kikagaku Genso, the authors of this paper compared several popular works on Euclidean geometry from 17th and 18th century Britain. When the authors compared The Elements of Euclid, published in Edinburgh in1787 by Robert Simson, they found that the contents from pages 1–195 were exactly the same as in Kikagaku Genso. Simson’s geometry book has 520 pages,17 and the geometrical drawings in Kikagaku Genso are completely the same as in Simson’s book. Thus, it can be concluded that Robert Simson’s The Elements of Euclid was the source book for Kikagaku Genso, the textbook used by Clark at Gakumonjo of Shizuoka. Words such as “卷七 (volume 7) and “卷八 (volume 8)” appear on the last page of the front part. It may be taken for granted that Kawakita Tomochika and some others may have attempted to translate the later parts.18 Next, we will compare the impacts of Jihe Yuanben and Kikagaku Genso on Chinese and Japanese mathematics education, respectively. Euclidean geometry had a significant impact on late Qing scholars’ mathematical study. For example, Li Shanlan not only translated the last nine volumes of Jihe Yuanben, but was also deeply affected by Euclidean geometry in his mathematical research. Western-style mathematics education was set up in the movement to Westernize schools during the late Qing dynasty. In these schools, Jihe Yuanben was used as a mathematics textbook. For example, it is recorded in the historical data of Jingshi Tongwenguan

17 Robert Simson, The Elements of Euclid (Edinburgh, 1787). 18 E. W. Clark, Kawakita Tomochika, and Yamamoto Masashi, Kikagaku Genso (幾何学原礎) (Shizuoka: Bunrindo, 1875), vol. 1, p. 1. 96 SARINA and Ying WANG

(京師同文館), founded in 1862, that Jihe Yuanben was used.19 In 1904, when the new education system—Zouding Xuetang Zhangcheng (奏定学堂章程) which meant the school charter—was promulgated in China, Jihe Yuanben was chosen as the geometry textbook.20 The contents of the first six volumes of Jihe Yuanben were used more often than the last nine volumes in the late Qing mathematics education. As for Kikagaku Genso, its published version was selected as the mathematics textbook for a number of key secondary and normal schools in early Meiji Japan. It was inscribed and published over and over again from 1872 to 1886. There are detailed records that show the use of Kikagaku Genso.21 In 1882 (明治 15), it was used in Aomori Prefec- ture Normal School (青森県師範学校), Fukui Prefecture Middle School (福井県中学校), Akita Prefecture Middle School (秋田県中学校), and Hiroshima Prefecture Middle School (廣島中学校). In 1883 (明治 16), it was used in Osaka Prefecture Normal School (大阪府師範学校), Yamaguchi Prefecture Normal School (山口県師範学校), Akita Prefecture Normal School (秋田県師範学校), Yamaguchi Prefecture Middle School (山口県中学校 ), and Osaka Prefecture Middle School (大阪府中学校). In 1884 (明治 17), it was used in Nagano Prefecture Normal School (長野県師範学校), Aomori Prefecture Middle School (青森県中学校), and Yamaguchi Prefecture Middle School (山口県中学校). In 1888 (明治 21), it was used in Shizuoka Prefecture Ordinary Middle School (静岡県尋常中学校). Thus, like Jihe Yuanben, Kikagaku Genso also played an important role in the popularity of Western-style mathematics education. The completion of Jihe Yuanben during the late Qing dynasty could be further analyzed according to the following aspects: The late Qing dynasty translation version inher- ited the tradition of the Ming dynasty. The completion of the last nine volumes was carried out to make up for and perfect the work of the predecessors. They had not been used in teaching until it was translated. Foreign missionaries played a leading role in the translating practice. This determined the selection of the source book in the translation process. The source books had been translated into both Chinese and Japanese. One translation was published in 1570, even earlier than the Latin version; another was influential with European geometry education from the 18th to 19th century. It was also clear that the Japanese source book was better than the Chinese one. Given this, why did Wylie use the English translation by H. Billingsley published in 1570? Wylie himself was aware of the insufficiency of this version, as he wrote in Preface, “The copy is an old version, but it was not well proofread and has mistakes.”22 When talking about the specific translation of Kikagaku Genso, we should recognize that while this was the first Japanese translation, it was based on the Chinese version, Jihe Yuanben. In the Japanese translation process, Japanese scholars played a leading role.

19 Tungwen College Rules (京師同文館規), Royal Xu Aiwen Collection《 ( 皇朝蓄艾文編》) Vol. XIV. 20 Zhu Youhuan, Historical Data on Modern China Educational System (朱有瓛《中国近代学制史料》) Vol. 1, Serious I, p. 532. 21 Neoi Makoto, “Report on the Mathematics Textbooks of Secondary Schools in the Meiji Era (3) Geometry (明治期中等学校の数学教科書について (3) 幾何編),” Journal of History of Mathematics (数学史研究), no. 152 (1997), pp. 45–47. 22 The original version in Chinese is “旧版, 校刊未精, 語訛字誤, 毫釐千里, 所失匪輕,” Wylie and Li, 1857/1865, Wylie’s preface, 3a. A Comparison of the Spread of the English Translation of Euclidean Geometry 97

At the beginning of the translation process, many preparations were made for teaching purposes. For example, one translator, Kawakita Tomochika, published a question and answer book to supply the need for exercises in this book. The Japanese translation came out when the Japanese mathematical community began to shrug off the effects of Chinese translation. Thus, Kikagaku Genso became used as a textbook at many key schools. This also reﬂects the embodiment of Japanese education policy, which popularized Western mathematics education.

4. Comparing the Countries’ Translators and Translations

Why, then, are there so many differences between the two translations? To answer this question, we will first compare the translators from the West, Wylie and Clark, who had many similarities but also great differences between them. What they had in common was they were both interested in Eastern countries and were living in the era when Western science and technology was spreading to the East. Both held religious beliefs. However, they were in entirely different missions. Wylie was sent by the London Missionary Society to do missionary work in China (funded by the Church of England). Clark was employed by the Japanese government, (and was awarded a local government salary). Wylie’s main purpose was to spread Western Christian doctrine (without much enthusiasm for education policy and no obligation to care about the education situation in China). Clark’s main mission was to teach Western-style science knowledge, with great enthusiasm for education policy—he proposed that the Meiji government follow the United States to set up well-known institutions of higher education in some places, though this recommendation was not adopted. For Wylie, translation was his major work, and he actively learned and mastered Chi- nese. As for Clark, lectures were his main business. He hired translators for his teaching assistants, for he could not speak Japanese. The missionary work was a life-long career for Wylie, so he did not leave China and return to the United Kingdom until he got blind in his old age. However, Clark left Japan just a few years after his employment. One of the reasons for his return was that his educational policy proposal was not adopted, which disappointed him very much. In comparing the Chinese scholar Li Shanlan and Japanese scholar Kawakita To- mochika, we should know that they had a similar educational background (the experience of both traditional and Western mathematics, which was a common characteristic of many Chinese and Japanese scholars in this era). The main contribution of Li Shanlan was in mathematical research. He was first and foremost a mathematician before a mathematics educator. Li Shanlan made very significant achievements in mathematical research, but he did not train successors. Li Shanlan got personal support from the bureaucrat Zeng Guofan for his mathematical achievements, but did not get very much recognition from the Chinese academic community. On the other hand, the main contribution by Kawakita Tomochika was in the field of mathematics education, and he was regarded as a mathematics educator. Although he made less significant mathematical achievements, he trained 98 SARINA and Ying WANG many successors. Kawakita Tomochika, as one of the founders of the Japanese Mathemat- ical Society, also founded a private school that taught Western mathematics. He led the Japanese mathematical community in the Meiji era and made a great contribution to the transition of the Japanese mathematical community from the traditional model to the West- ern mathematical model. The translation of mathematical works by Li Shanlan affected the mathematical community in modern China, while the mathematics textbook by Kawakita Tomochika affected the mathematical community in modern Japan. By comparison, we know that Li Shanlan and Kawakita Tomochika were not only important scholars in the spread of Western mathematics in China and Japan, but also important representatives of mutual exchange in the process of Westernization of modern Sino-Japanese mathematics.

5. Conclusion

This paper has discussed and compared the translation activities of Euclidean geometry in late Qing China and early Meiji Japan. From the above discussion, we may draw several conclusions. In the late 19th century, along with the spread of Western science and technology, Eu- clidean geometry, as a representative of Western mathematics, spread to China and Japan. The completion of the last nine volumes of Jihe Yuanben and of the Japanese translation have great signiﬁcance to East–West mathematical exchange and mathematical knowledge communication. The Japanese translation was completed by referring to the Chinese translation, and some Japanese terminology spread to China as well. It can be regarded as a typical representation of the Sino–Japanese exchanges in mathematics that these two translation works are related. The history of the creation of these works represents the common historical background that China and Japan shared at that time. The two Eastern Asian countries both translated representative works of Western mathematics, but as mentioned earlier, there were many differences between them. These differences were due to the differences between the Sino–Japanese traditional cultures and their different education policies at that time. The government of Meiji era Japan began very early to hire Westerners to teach Western mathematical knowledge, which laid the foundation for the popularization of Western mathematics education. Japan’s new education system was promulgated in 1872, but during the Westernization period of the Qing dynasty, China did not establish the relevant new education policy to support Western- style education. New education policies only began around 1904, nearly 30 years later than Japan.

(Received on 30 April 2014; Accepted on 24 September 2014)