The Planetary Longitude Theory of Qizheng Tuibu (1477)

The models with eccentricities and radius, and the calculation formula underlying in the 10 planetary longitude tables in the Qizheng Tuibu (1477), have been completely outlined. Ptolemaic planetary theory has been applied in the compilation of these tables with slightly revision of the parameters and variables. The first equation (aequatio centri) for the superior planets in the relative tables in the Qizheng Tuibu is the same as q(cm) in Almagest. The values for the first equation for Venus are the same as the solar equation of the center in the Qizheng Tuibu. The model of the first equation for Mercury has the same as Ptolemaic eccentricity but with different radius. The variable for proportion of Saturn is the mean argument of center, of Jupiter, Mars and Venus is the true argument of center, of Mercury is a particular one. The variable for the second equation (aequatio argumenti) p is the true argument of anomaly, different from Ptolemaic selection of the mean argument of anomaly p(am). The same 10 tables from 47^v to 52^r of the Sanjufīnī Zīj (1366), without the columns for q(n+1)-q(n), p(n+1)-p(n) in the Qizheng Tuibu, have been explained.