Hun gai tong xian tu shuo (Illustrated explanation of the sphere and the astrolabe) is a translation of selections taken from Xing pan (Astrolabium), a work of Christoph Clavius (1538−1612), a German Jesuit and teacher of Jesuit missionary Li Madou (Matteo Ricci, 1552−1610), which was included in Si ku quan shu (Complete library of the four treasures). The work was written in 1605 by Li Zhizao (1565−1630) and is based on the lectures given by Ricci and on the author’s own knowledge. Li Zhizao, courtesy names Zhenzhi and Wocun, and style name Chunanjushi, was a native of Renhe (present-day Hangzhou, Zhejiang). In 1598 he received his jin shi degree and took various posts, among them vice director of the Bureau of Works, director of the Bureau of Waterways, and vice director of the Court of the Imperial Stud. He was one of the participants in compiling the almanac. In 1601 he made the acquaintance of Ricci, under whose tutelage he began to study Western science. Ricci, courtesy name Xitai, was an Italian who joined the Jesuits in 1571 and arrived in Macao in 1582. Together with Luo Mingjian (Michele Ruggieri, 1543−1607), Ricci reached Zhaoqing, Guangdong, in 1583, the beginning of the Jesuit mission to the interior of China. While in Zhaoqing, Ricci created his famous world map, which was greatly welcomed by Chinese scholars. He continued his mission in Shaozhou in 1595 and in 1596 became the head of the mission. In 1601 he was called to Beijing, where he presented gifts to the court. Highly appreciated by the Ming emperor Shenzong (reigned 1572−1620), he was permitted to remain in Beijing. Among Ricci’s works were Tian zhu shi yi (The true notion of the Lord of Heaven), Jiao you lun (Treatise on friendship), Ji ren shi pian (Ten paradoxes), Ji he yuan ben (Euclid’s Elements), Tong wen suan zhi (Treatise on arithmetic), Ce liang fa yi (Work on trigonometry), Gou gu yi (Principle of right-angle triangles), Yuan rong jiao yi (Treatise on geometry), Wan guo yu tu (Map of ten thousand countries), and Qian kun ti yi (Structure and meanings of heaven and earth). This work has an introductory juan on the celestial globe. Preceding the text is a preface by Li Zhizao. The work has two juan of 21 parts, with the main content focusing on the structural principles and methods of the Western astrolabe. Juan 1 discusses the methods of mapping various coordinate nets on the surface of the astrolabe, including the equatorial, the ecliptic and the horizontal coordinate systems and stereographic projections for the astrolabe. Juan 2 introduces the structure of the astrolabe, methods of mapping stars with it, and use of the astrolabe, and applying European measurements. The work introduced to China the system of ecliptic coordinates, the strict definition of twilight, the sizes and distances of the sun, the moon, and the five constellations, and the principle of defining the longitude of the lunar eclipse. It was the first work in China that described Western astronomical instruments, with early drawings based on knowledge of geometry. It thus made a great contribution to Chinese scientific research. The complete work is shown here.