Datong lizhi 大統曆志

Datong lizhi 大統曆志, with a length of 8 juan and an appendix of 1 fascicle, is a book on calendrical calculations written by Mei Wending 梅文鼎 (1633-1721), who wrote, among others, the collection Lisuan quanshu 曆算全書.

During the Yuan period 元 (1279-1368), Guo Shoujing 郭守敬 (1231-1316) and others devised the Shoushi Calendar 授時歷, which applied the method of arc and chord segmentation (hushi geyuan shu 弧矢割圓術) to handle conversions between ecliptic longitude, right ascension, and declination (huangjing 黃經, chijing 赤經, chiwei 赤緯). The method also used the interpolation technique (zhaochafa 招差法) to calculate the movements of the Sun, Moon, and planets, relying entirely on empirical observations with remarkable accuracy. The Ming dynasty 明 (1368-1644) adopted this calendar without modification and renamed it the Datong Calendar 大統歷, which was in use for 364 years. During the Chongzhen reign-era 崇禎 (1628-1644), Xu Guangqi 徐光啟 (1562-1633) introduced Western astronomical methods, leading to a distinction between the new and old systems and sparking disputes (see Chongzhen lishu 崇禎曆書).

Mei's book focuses on explaining the origins, strengths and weaknesses of the Datong Calendar. It divides the content into three parts: Fundamentals of methods (Fayuan 法原), Establishment of data (Licheng 立成), and Computational steps (Tuibu 推步).

The chapter on methods explains the Pythagorean measurement (gougu celiang 勾股測量), arc and chord segmentation (hushi geyuan 弧矢割圓), ecliptic-equatorial differences (huang-chidao cha 黃赤道差), internal and external ecliptic and equatorial paths (huang-chidao nei-wai 黃赤道內外), lunar nodal cycles (baidao jiaozhou 白道交周), the three inequalities in the movements of the Sun, Moon, and Five Planets (ping-li-ding sancha 平立定三差), and corrections for the Earth's rotation and timekeeping (licha louke 里差漏刻). The establishment of data elucidates the solar expansion and contraction (taiyang yingsuo 太陽盈縮), solar speed variations (taiyang chiji 太陽遲疾), day and night time division (zhouye kefen 晝夜刻分), and the expansion and contraction of the Five Planets' orbits (wuxing yingsuo 五星盈縮). It records the data obtained through empirical observation. The computational steps refer to solar terms (qishuo 氣朔), solar motion (richan 日躔), lunar position (yueli 月離), central eclipse (zhongshi 中食), eclipse calculation (jiaoshi 交食), and planetary motions. This book systematically explains the principles behind Guo Shoujing's calendar system and the step-by-step computational methods.

The text is included in the series Siku quanshu 四庫全書.