Jiaohui guanjian 交會管見

Jiaohui guanjian 交會管見 "My humble view on eclipses" is a brief book on astronomy written during the early Qing period by Mei Wending 梅文鼎 (1633-1721). It is included in the series Mei Hu'an Xiansheng lisuan quanshu 梅勿庵先生曆算全書 and Meishi congshu jiyao 梅氏叢書輯要.

Mei Wending proposes a new method for determining the limits of eclipse obscuration. In this method, the occlusion on the upper, lower, left, and right portions of the Sun or Moon's disk is measured directly rather than relying on the conventional compass directions of east, west, south, and north.

The text consists of thirteen chapters, each detailing specific methods for calculating solar eclipses with a newly proposed system that replaces traditional directional references with a more direct geometric approach. The key sections include the determination of angular separation at the first and last contact, the points of first and last contact on the Sun's disk, the most extraordinary eclipse position on the Sun's disk, the geometry of the Sun's obscured periphery, the altitude of the three eclipse phases above the horizon, the longitude of the three eclipse phases on the horizon, the eclipse magnitude on the Sun's disk, and the eclipse geometry at the moments of entry and exit. These sections collectively introduce a new framework for measuring solar eclipses, moving away from conventional directional references and instead using a disk-based coordinate system, improving accuracy and consistency in eclipse predictions.

The section "Methods for drawing solar eclipse magnitude diagrams" (Zuo rishi fentu fa 作日食分圖法) explains calculations related to different phases of a solar eclipse, accompanied by detailed diagrams. These include the determination of the inclination of the eclipse path and present diagrams for the first contact, the maximum eclipse, and the last contact.

Additional topics covered include an explanation of the rationale behind the 90-degree ecliptic calculation, an alternative method for calculating the 90-degree distance from the zenith, a new method for calculating the 90-degree limit of the lunar path, and corrections to the lunar eclipse diagram.

In his book, Mei Wending made significant new contributions to the study of eclipses. Earlier scholars had overlooked specific critical issues, particularly regarding the orientation of first and last contact. Building on the work of Wang Xichan 王錫闡 (1628-1682), author of Xiao'an xinfa 曉庵新法, Mei devised an entirely new method for predicting the course of solar eclipses.