In 1582, the Italian priest Matteo Ricci arrived in China with a copy of Euclid’s Elements in his luggage. In 1606, he and the Chinese scholar Xu Guangqi started to translate it into Chinese. Unfortunately, Ricci died in 1610 in Beijing. At that time they had only finished the first six Books. The remaining seven Books were not translated into Chinese until 250 years later, in 1857, by the British missionary Alexander Wylie and the Chinese mathematician Li Shanlan. This paper tells the dramatic story.
About 2,300 years ago, Euclid (330 BC–275 BC) completed his Στοιχεῖα, commonly known in English as Elements, one of the most important mathematical works to date. It contained thirteen Books : I. Foundations of plane geometry. II. The geometry of rectangles. III. The geometry of circles. IV. Regular polygons in circles. V. Magnitudes in proportion. VI. Geometry of similar figures. VII. Basic arithmetic. VIII. Numbers in continued proportion. IX. Prime numbers. X. Incommensurable line segments. XI. Foundations of solid geometry. XII. Areas and volumes. XIII. The Platonic solids. In particular, it established the mathematical system of definitions, axioms, and propositions, which has served as a model of rigorous mathematical reasoning for more than two thousand years, and perhaps will last forever.
In the following centuries, Euclid’s original copy was nowhere to be found. Instead, its contents were scattered in different manuscripts. At the end of the fourth century AD, Theon of Alexandria collected the manuscripts and edited a complete Greek copy. As one of the most important books in human civilization, Euclid’s Elements has a complicated and dramatic history. It has been translated into almost every language, in more than one thousand different editions.
In ancient times, China had few connections with other civilizations. More or less at the time of Euclid, the Chinese developed their own arithmetic and elementary geometry. Their earliest mathematical achievements were collected in Jiu Zhang Suan Shu (Nine Chapters on the Mathematical Art) which was compiled during the early Han Dynasty (202 BC–220 AD). No author or editor is known (Zhang Cang (256 BC–152 BC) and Geng Shouchang in Han Dynasty were the earliest recorded compilers). The book discussed 246 practical problems, such as how to do basic arithmetic, how to compute the area of a rectangle, an isosceles triangle, or a circle, how to calculate the volume of a pyramid, a cylinder, or a ball, and how to solve linear equations, in nine chapters. Of course, there were mistakes and inaccuracies in the early versions. In fact, many important later Chinese contributions to mathematics were achieved as commentaries to revisions of the Nine Chapters. Needless to say, it is the founding work of the Chinese mathematical tradition.
Bamboo strips of the Suanshu Shu.
In 1983–1984, Chinese archaeologists excavated an ancient tomb at Zhangjiashan in Hubei Province, which can be dated to around 186 BC in the Han Dynasty, and discovered a mathematics book, Suanshu Shu (Book of Numbers and Computations), written on some 200 bamboo strips. It dealt with 68 practical problems: 9 about multiplication and manipulating fractions, 44 on mercantile arithmetic such as collecting taxes and dividing coins, and 15 on geometric issues such as areas and volumes. For example, it presented a method to determine the volumes of a cone and a frustum*, under the assumption that π = 3. It is interesting to see that some problems of the Suanshu Shu are similar to those of the Nine Chapters, since the first is an original source and the second has been reedited many times.
In 221 BC, a little later than Euclid, the Qin Emperor (259 BC–210 BC) unified China. From 221 BC to 1912, China was ruled by more than four hundred emperors and Chinese society was rather closed. The earliest foreign influences to China were recorded in the Han Dynasty (202 BC–220 AD), Tang Dynasty (618–907), and Yuan Dynasty (1271–1368). Buddhism was introduced to China in the Han Dynasty from India. Islam was introduced to China in the Tang Dynasty from West Asia. Along with culture and religion, foreign knowledge such as astronomy and mathematics was also introduced to China. For example, the Persian astronomer Jamal ad-Din Bukhari worked in the Imperial Astronomical Bureau of the Yuan Dynasty and introduced Islamic astronomy into China. Marco Polo (1254–1324) also visited China in the Yuan Dynasty. However, at that time, there was no printed Elements yet.
In 1552, the first European missionary St. Francis Xavier (1506–1552) arrived in China. In fact, he did not set foot on the Chinese mainland, but rather an island off the south coast. He died there. The early missionaries mainly engaged in religion dissemination. The Chinese did not know the systematic work of the ancient Greeks until Matteo Ricci’s visit at the end of the 16th century.
* In geometry, a frustum is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting the solid. In the case of a pyramid, the base faces are polygonal and the side faces are trapezoidal. 
https://en.m.wikipedia.org/wiki/Frustum
In 1557, Macao became a Portuguese colony on the south coast of China. In 1571, a house of the Jesuits had been set up at Macao. In 1582, to extend the China mission, Matteo Ricci was called from Goa to Macao by Alessandro Valignano (1539–1606), the superior of all Jesuits in the Far East and a former teacher of Ricci when he studied at the Jesuit College in Rome.
When Ricci arrived at Macao, China was at the end of the Ming Dynasty (1368–1644). The dominant hierarchy was conservative and corrupt, and establishing the Jesuit mission was very difficult. In particular, obtaining residence permissions for foreign priests was very hard. Thus, Ricci quickly learned Chinese language and culture, dressed as a Chinese scholar, presented himself as a Buddhist monk rather than as an European priest, and tried to make friends with every Chinese person he met.
In 1583, priests Michele Ruggieri (1543–1607) and Ricci visited the governor of Zhaoqing, a Chinese state close to Macao. The governor was deeply impressed by their demonstrations: a mechanical clock which can ring the hours, a prism which can produce colorful lights in sunshine, and a harpsichord which can make music. In particular, the governor was suffering with some disease and the priests were able to cure him quickly. This made them good friends of the governor and they obtained permission to live in Zhaoqing. In twenty years, Ricci moved from Macao in the deep south to the Chinese capital Peking step by step, from Macao (1582–1583) to Zhaoqing (1583–1589), Shaozhou (1589–1595), Nanchang (1595–1598), Nanking (1598–1600), and finally, Peking (1601–1610). Of course, he traveled with his precious books, including Euclid’s Elements.
While Ricci was in Shaozhou, he met Qu Rukui (1548–1610), a bright young scholar and son of a top official of the Ming government. Ricci taught Qu mathematics and astronomy, and Qu introduced many important friends to Ricci. In fact, they once had the idea to translate the Elements into Chinese together and even finished part of the first Book. Unfortunately, the project was terminated at an early stage without known reason.
Having been prepared for almost twenty years, with the help of his important Chinese friends including princes, ministers, governors, and scholars, Ricci arrived in Peking in 1601 with his assistant Diego de Pantoja (1571–1618). Upon arriving in Peking, they presented the Emperor a set of well-prepared European gifts, including two magnificent mechanical clocks, a decorated harpsichord, a portrait of the Virgin Mary, and a beautiful world map in Chinese which was made by Ricci himself. They were invited to the Forbidden City, but were not received by the Emperor. Nevertheless, for his knowledge of science and technology, Ricci was appointed a royal position maintaining the clocks and other mechanisms in the Forbidden City. In this way, he obtained not only permission to reside in Peking, but also a royal salary.
The title page of the Chinese version of Euclid’s Elements, translated by Matteo Ricci and Xu Guangqi.
In 1604, Xu Guangqi (1562–1633) succeeded in the Imperial Examination and was assigned a position in the Hanlin Academy.Footnote4 From that point, he often visited Ricci and they became close friends. In fact, Xu first met Ricci in 1600 in Nanking, where he was baptized by Jean de Rocha (1566–1623) in 1603. Through this friendship Xu learned a lot from Ricci, not only in theology and religion, but also in astronomy and mathematics. In 1606, Ricci and Xu started to translate Euclid’s Elements from Clavius’s Latin version into Chinese: Ricci translated it from Latin to oral Chinese, after which Xu formulated it into classical Chinese. In 1607, they finished the first six Books and published them under the Chinese name Jihe Yuanben in Peking. Perhaps, they planned to translate the remaining Books of the Elements later. Unfortunately, Xu’s father died in 1607. In ancient China, a ranked official was expected to stay at home for three years if his father or mother died. Even more regrettably, when Xu returned to Peking three years later, Ricci had died.
The Chinese version of the Elements formally introduced “logical thinking” into Chinese mathematics. The traditional Chinese induction was mainly based on concrete examples, instead of logic and assumptions. Euclid’s mathematics is different from the ancient Chinese mathematics in nature. Unfortunately, at that time the Chinese education system paid no attention to mathematics and therefore only a handful of people knew Jihe Yuanben. Nevertheless, many Chinese mathematical terms (such as jihe for geometry, pingmian for plane, sanjiaoxing for triangle, lifangti for cube, and tiji for volume) created by Ricci and Xu are still in usage today.
Xu Guangqi was a very important politician and scholar in Chinese history. He made great contributions in agriculture, astronomy, and mathematics. At the end of the Ming Dynasty, the court was dominated by factions. Xu had a difficult political career in which he was dismissed or resigned several times. Nevertheless, he was appointed the minister of rites in 1630 and a grand secretary (more or less a vice prime minister) in 1632. He died at the height of his political career. There are many Chinese books about Xu. In China, few historical figures have museums. There is one in Shanghai devoted to Xu Guangqi, which has an original copy of Clavius’s Elements.
There was one emperor who was enthusiastic about Euclid’s Elements. Emperor Kangxi of the Qing Dynasty ascended the throne in 1661 when he was seven and reigned for 61 years. In 1689, he decided to learn mathematics and astronomy. For this purpose, two Frenchmen, Joachim Bouvet (1656–1730) and Jean-Francois Gerbillon (1654–1707), were appointed royal teachers. They were missionaries sent to China by King Louis XIV of France in 1687. Since the court language in the Qing Dynasty was Manchu rather than Chinese, the teachers had to learn Manchu first and then translate the selected Elements into Manchu. Of course, they taught the emperor in the Forbidden City.
The Manchu translation of the Elements used by Emperor Kangxi. The red notes were made by the emperor.
More in the full article
https://www.ams.org/journals/notices/202306/noti2719/noti2719.html