Qizheng tuibu 七政推步

Qizheng tuibu 七政推步 is a book on calculations of the empheremides (tuibu 推步) of the "seven celestial bodies" (qizheng 七政) sun, moon, Mercury, Venus, Mars, Jupiter, and Saturn. The book of 7 juan length was published in 1477 by Bei Lin 貝琳 (d. 1490), courtesy name Zongqi 宗器, style Zhuxi 竹溪, from Jinling 金陵 (today's Nanjing, Jiangsu).

His traditional Confucian education included instruction in astronomical matters, for which Bei showed great interest, and was in 1470 appointed to the post of Vice Director of Astronomy (qintianjian jianfu 欽天監監副). During the 1440s and 1450, Bei also served in the military.

The book was based on the Islamic Hijri calendar (huihui lifa 回回曆法) with its "soil calculation method" (tupan lifa 土盤曆法). It had been translated in 1385 into Chinese by Wu Zongbo 吳宗伯, Li Chong 李翀, "Mashayihei" 馬沙亦黑 and Yuan Tong 元統. The Ming dynasty 明 (1368-1644) established a special Bureau for the Islamic Calendar (huihui like 回回曆科) subordinated to the Directorate of Astronomy. During the whole Ming period, the Islamic calendar was used along with the Chinese calendar.

Bei's book is important because it preserves methods of the Islamic "Calendar of Ten Thousand Years" (wannian li 萬年曆) of Jamāl ud-Dīn Bukhārī (Ch. Zhamaluding 札馬魯丁) and "Alimading" 阿里馬丁 that was written in Arab language. This Arab original is long lost. The other two calendars of the Yuan period 元 (1279-1368), Yelu Chucai's 耶律楚材 (1190–1244) Gengyu yuanli 庚午元曆, and Guo Shoujing's 郭守敬 (1231–1316) Shoushi Calendar 授時曆 have survived.

Bei Lin's translated version of the Islamic Calendar adds some information not included in the Arab original and its first translation. Such are, for example the original Farsi names of the seven days (qiyao 七曜) and the twelve months (shi'er gong 十二宮 "palaces"), like fa'erhan'erding 法而斡而丁 (from farvardīn) for the first month, a'erdibixishi 阿而的必喜世 (from urdbihisht) for the second month, hu'erda 虎而达 (from khurdād) for the third month, or dushanbie 都閃別 (from dūshanbah) for Monday, xieshanbie 寫閃別 (from sahshanbah) for Tuesday, and cha'ershanbie 察兒閃別 (from chihār shanbah) for Wednesday.

References to the problems of conversion into the Chinese calendar can be found in Bei's discussions about determining intercalary months (runyue 閏月). Bei also presented the 29 calculation tables (licheng 立成) of the Islamic calendar, as well as 10 additional tables produced under the Ming dynasty. The tables are important because they represent an early stage of knowledge than the tables presented in the treatise on the calendar (31-39 Lizhi 曆志) in the official dynastic history of the Ming, Mingshi 明史. The Qizheng tuibu also introduced names, designations and classifications of stars and constellations not known in Chinese astronomy until that date. Such are, for example, the constellations Cancer (juxie 巨蟹), Leo (shizi 獅子), Gemini (shuangnü 雙女 "two girls"), Libra (tiancheng 天秤) or Scorpio (tianxie 天蝎). The 13 star maps are also different from traditional Chinese maps, as they are centered on the solar ecliptic (huangdao 黄道), like in Arab maps (Chen 1991; the Siku version does not include star maps).

The Chinese version of the book only circulated as a manuscript owned by the Tianyige Library 天一閣. It found entry into the imperial series Siku quanshu 四庫全書.