he astronomical systems used at the time, but they only provide formulae that performed various almanac calculations. The theory behind the formulae and how they were derived were kept secret. In the Ming dynasty (1368-1644), the officials in the Imperial Astronomical Bureau (欽天監) were hereditary. The Ming dynasty kept using the almanac developed in 1280, which abandoned the superior epoch, without trying to improve it. In the late 15th century, the almanac failed to predict a number of eclipses. The 