Hungai tongxian tushuo 渾蓋通憲圖說

Hungai tongxian tushuo 渾蓋通憲圖說 "Illustrated explanation on the use of an armillary sphere for calendrical astronomy" is a book on astronomy written during the late Ming period 明 (1368-1644) by Li Zhizao 李之藻 (1565-1630), courtesy name Zhenzhi 振之, from Renhe 仁和 (today part of Hangzhou 杭州, Zhejiang). He obtained the jinshi degree during the Wanli reign-period 萬曆 (1573-1619) and served as Assistant Director in the Ministry of Works (gongbu yuanwailang 工部員外郎) in Nanjing 南京 and Vice Minister of the Court of Imperial Sacrifices (taipusi shaoqing 太僕寺少卿).

A devoted follower of Matteo Ricci's (1552-1610; Ch. Li Madou 利瑪竇) teachings, he collaborated with Xu Guangqi 徐光啟 (1562-1633) in introducing Western scientific knowledge to China. His other works include Pan gong liyue shu 判宮禮樂疏, a memorial concerning rites and music and Yuarong jiaoyi 圓容較義, a comparative study of the circle and the sphere. In 1629, Li and Xu Guangqi were commissioned to revise the Chinese calendar, which led to his exposure to Western astronomical knowledge through Matteo Ricci. This book was a result of his studies on the astrolabe.

The Tushuo with a length of 2 juan provides an illustrated explanation of the construction, principles, and use of the astrolabe. The introduction discusses the structure of the celestial sphere (hungai 渾蓋). The first fascicle explains the divisions of degrees, time measurement, and the operational methods of the instrument. The second fascicle consists of detailed diagrams illustrating its design and functionality.

The book adopts the European system of measurement and, for the first time in China, introduces the ecliptic coordinate system (huangdao zuopiao xi 黃道坐標系). It also discusses concepts such as the definition of twilight (chenhun mengying 晨昏朦影), the size and distance of the Sun, Moon, and the five planets, the concept of stellar magnitudes (xingdeng 星等), and the method of determining longitude using lunar eclipses (liyong yueshi ding jingdu de yuanli 利用月食定經度的原理). However, the explanations contain several inaccuracies.

The text was printed during the late Ming period and is included in the series Tianxue chuhan 天學初函, Shoushange congshu 守山閣叢書, Siku quanshu 四庫全書, Congshu jicheng chubian 叢書集成初編 and Zhong-Xi suanxue congshu 中西算學叢書.