In the early period of the Qing Dynasty (1644-1911), The four calendars had been put into use, Xiyang Xinfa Lishu (Treatise on Mathematics (Astronomy and Calendrical Science) according to the Western method, issued in the Ming (1635) as Chongzhen reign-period Treatise on (Astronomy and) Calendrical Science, reissued and revised as the former by Johann Adam Schall von Bell (1591-1666) in 1645, 1628-1827, and the year of 1628 was selected as the epoch of the Calendar), Kangxi Yongnian Lifa (The Eternal Calendar of Kangxi Emperor, compiled by Ferdinand Verbiest (1623-1688) in 1669, 1828-3827), Yuzhi Lixiang Kaocheng (Complete Studies on Astronomy and Calendar, 1725, 1684-1983) and Yuzhi Lixiang Kaocheng Houbian (The Supplement to Complete Studies on Astronomy and Calendar, 1742, 1723-2022).

The Calendrical Book of Eclipses (Jiaoshi Lishu), compiled by Ferdinand Verbiest in 1683 and was of historic significance in the development of the Chinese Calendars in Qing Dynasty, has not been meticulously investigated upon to now, in which the obliquity of the Ecliptic of 23º32′, as the corresponding values of Profatius (c.1236-1305, Ibn Tibbon, Jacob ben Machir), was applied in Tables of Ninety Degrees of the Ecliptic and otherwise 23º30′ (Er shi san du ban) was permuted in Tables of the Solar Height. Furthermore, the methods of calculation and permutation in Tables of the Solar Height, of which the errors in 4′, developed and expanded asTables of the Solar Altitude in Yuzhi Lixiang Kaocheng, in which the obliquity of the Ecliptic is of 23º29′30″, is realized as a bridge for the continuity of the calendars in Qing Dynasty.

Introduction to, theories for and mathematical principles of calendrical science have been gradually interpreted in Xiyang Xinfa Lishu, Yuzhi Lixiang Kaocheng and Yuzhi Lixiang Kaocheng Houbian, and the Jesuit and Chinese astronomers had compiled the Calendars of Qing Dynasty in completeness and perfection.

The author gratefully acknowledges the support of

National Science Foundation of China (NSFC), K. C. Wong Education Foundation, CAS, and the China-Portugal Center for the History of Sciences (CPCHS)