Lifa Wenda (曆法問答, LFWD, Questions and Answers on Astronomy) was compiled by French Jesuit Jean-François Foucquet (1665-1741) in 1716 in Beijing. Compared with Chongzhen Lishu (崇禎曆書, CZLS, Chongzhen Reign-period Treatise on Astronomy and Calendrical Science, first form of the Jesuit astronomical encyclopedia, 103 vols, 1635) or Xiyang Xinfa Lishu (西洋新法曆書, XYXFLS, a slightly revised version of the former, 100 vols, 1645), LFWD introduces advanced theories of European astronomy. In the second volume of Wuwei Lizhi (五緯曆指, Treatise on Planetary Motions) of LFWD, Philippe de La Hire (1640-1718)’s theory of planetary motion, the related observation method and astronomical tables for the mean motion, the equation of the center of the planets were translated. Having analyzed the tables, investigated the original literature referenced by the Chinese version of LFWD, we realized that the planetary tables are based on new observation and model, the prograde, retrograde and station of the planets are described in detail, and the observational differences between geocentric and heliocentric models were explained. As the smaller error between theoretical calculations and actual astronomical observations in P. de La Hire’s model, being different from Johannes Kepler (1571-1630)’s, we have recovered P. de La Hire’s formulas, and the proportional relations of the elliptical orbit has been optimized for the improvement of the calculation and prediction accuracy.

The ancient Greek astronomers developed the uniform circular model to describe planetary motion. For explaining the irregularity of planetary apparent motion, Claudius Ptolemy (c. 100-170) introduced the equant which opposite to Earth from the enter of deferent in the Almagest. From the 11th to the 13th century, Islamic astronomers, Abū ‘Ubayd al-Jūzjānī (?-1070) and others, had improved and modified Ptolemy's planetary theory, formed two astronomical traditions in al-Andalūs and Marāgha. Muʾayyad al-Dīn al-ʿUrḍī (1200-1266) and Naṣīr al-Dīn al-Ṭūsī (1201-1274) have put forward new planetary theories with their own mechanisms. European astronomers inherited the traditions and established planetary theory based on new astronomical theories, instruments and observational data.
The chapters on planetary motion in De Revolutionibus Orbium Cælestium (1543) by Nicolaus Copernicus (1473-1543), Astronomia Danica (1622) by Christen Longomontanus (1562-1647), Astronomia nova (1609) and Tabulae Rudolphinae (1627) by Johannes Kepler (1571-1630) haved been analyzed and compared, and the calculating formulas and program for longitude and latitude of the five planets been restored by interpreting the astronomical models and tables in related works. The transform of the astronomy from mathematical astronomy to mathematical and physical astronomy, has been happened before Isaac Newton (1642-1727).

The compilation of chronological biographies has been an important form of recording the life stories of literati and scholars since the Song Dynasty, with differences in being compiled by the individuals themselves, by their disciples or by later generations. For the compilation of the chronological biographies of modern and contemporary scientists, first-hand materials can be obtained through interviews, oral histories and other means. References can also be made to their remaining manuscripts or by consulting archives. However, the compilation of the chronological biographies of ancient figures in science and technology is faced with the dilemma of a lack of materials. Based on the research framework of the group of Astronomers and Mathematicians in the Qing Dynasty, with the aid of the CBDB (China Biographical Database), the "Chou-Ren Zhuan（Biographies of Mathematicians and Astronomers）" and the historical materials scattered in various collections of works, diaries, notes and local chronicles, this study takes the editorial group of astronomical and mathematical works in the "Complete Library in the Four Branches of Literature" as the entry point to compile and supplement the chronological biographies of some of the key figures. Through horizontal references and vertical examinations, it draws the academic social network maps of the figures in science and technology in the Qing Dynasty, and further demonstrates the complexity of the social interactions within the group of Astronomers and Mathematicians in the Qing Dynasty.

During the period of late Ming and early Qing Dynasty, western missionaries came to China to preach their religion. With the increase of cultural exchange between west and east, several western scientific books were translated into Chinese, one of the most important branches is optics. Although Chinese academic exchanges were isolated from the western countries, some of Chinese intellectuals continued to study on optics, two of them are Zheng Fuguang (b.1780), known as his work Jingjing Lingchi(Treatise on Optics by an Untalented Scholar), and Zou Boqi(1819-1869), noted for his book Geshu Bu(Supplement to Geometric Optics).However, their research methods were quite different, despite they worked on the same field. This paper aims to analyze the similarities and differences between the work of Zheng and Zou, especially focus on how t he two optical books were written, which demonstrates how western scientific knowledge was accepted and developed in Qing Dynasty without more contact with western world.