Work on Trigonometry


This work is a treatise on trigonometry by Li Madou, the Chinese name of the Italian Jesuit Matteo Ricci (1552–1610). Ricci left for China in 1581 and arrived in Macao in 1582. Together with Luo Mingjian (Michele Ruggieri, 1543–1607), he began his mission in Zhaoqing, Guangdong Province, where he published his Wan guo yu tu (Map of 10,000 countries), which was well received by Chinese scholars. He was expelled from Zhaoqing and went to Jiangxi, where in 1596 he became the superior of the mission. He lived in Beijing from 1600 until his death. In recognition of his scientific abilities, and in particular of his accurate predictions of solar eclipses, Ricci was invited by the emperor to become an advisor. He established the first Catholic church in China, had free access to the court, and met important officials and influential scholars. Among his numerous works are Tian zhu shi yi (The true notion of the Lord of Heaven), in two juan; Jiao you lun (Treatise on friendship); Ji ren shi pian, also known as Tian zhu shi jie (Ten paradoxes), in two juan; Bian xue yi du (Debates on criticisms of Christian doctrines); Tong wen suan zhi (Treatise on arithmetic), in 11 juan; Gou gu yi (Principle of right-angle triangles); and this treatise, Ce liang fa yi (Work on trigonometry). It was written down by Xu Guangqi (1562–1633) from oral dictation by Ricci. Xu Guangqi was the scholar and official who received instruction in various subjects from Ricci and worked with him continuously from 1604 to 1607. Xu translated Western works on mathematics, hydraulics, astronomy, and geography, among which the most influential was Euclid’s Elements, entitled Ji he yuan ben, published in 1611. The translation of this work was done in 1606–8. Ricci also cooperated with translator Li Zhizao on several works including Yuan rong jiao yi (Treatise on geometry). The National Central Library has in its collection a series entitled Hai shan xian guan cong shu (Collection of the celestial mansion of sea and mountain), which contains, among other titles, this work, together with Yuan rong jiao yi, Ce liang yi tong, and Gou gu yi. This work focuses on the principle of right-angle triangles. It discusses tools for measuring length and angle, and then focuses on images, such as direct image, inverted image, and calculation. Questions and answers follow, for example on how to measure the height of a mountain and a balcony, the depth of a well and a valley, and distances on land and roads. At the end, examples are given comparing the mathematical system described in Jiu zhang (Nine chapters of the mathematical art), an anonymous work and one of the earliest surviving Chinese mathematical texts, with the Western method of multiplication and division.

Last updated: January 3, 2018