This paper initially sorts out some groups of people who participated in the compilation of astronomy and mathematics categories in the "Complete Library in the Four Branches of Literature" through official archives, and subdivides the groups of people involved in such bibliographies according to their official positions and groups.

Based on the archives, this paper focuses on analyzing the relationship between the groups of people and the bibliographies of astronomy and mathematics, as well as the responsibilities shouldered by the people in the compilation process, and explores the ways they acquire relevant knowledge. Due to the dispersion and complexity of the materials, it is difficult to comprehensively and accurately determine the complete contribution context of each person. Through further excavation of relevant literature materials, the basic responsibilities and knowledge backgrounds of some people have been clarified, as well as their specific roles in the compilation process, which reflects the importance attached by the Qing court at that time to the fields of astronomy and mathematics and the characteristics of group cooperation behind cultural and academic inheritance.

French Jesuit Jean-François Foucquet (1665-1741) had compiled two astronomical works in 1710s for the court of the Qing Dynasty (1644-1911), one is Tianwen Wenda (Questions and Answers on Astronomy), in which the theory of gravitation of Isaac Newton (1642-1727) and new astronomical observation of “an unknown planet” were introduced. (问：啥人先晓得第个地末有力量，要吸引周围个物事，到本位个中心个道理？答：就是英吉利国一个人，姓末叫奴丹，名头叫以撒，第个人先得知。问：啥人先看见第个无没名头个星？答：也有一个极识天文个英吉利人，名头叫核屎借里者。) The other is Lifa Wenda (Questions and Answers on Calendrical Science), in which new astronomical theories and observations of Western astronomers, with the astronomical tables in Tabulæ astronomicæ Ludovici magni（1702）of Philippe de la Hire (1640-1718), were translated into Chinese with slightly revisions and corrections, especially of the calculating program for the solar eclipses.
Yuzhi Lixiang Kaocheng (YZLXKC, Compendium of Calendrical Science and Astronomy, 42 vols), compiled by Imperial Order of the Emperor Kangxi (1654-1722) and supervised by his third son Ying Zhi (1677-1732), who is one of the more importantly academic figures, and served as a key sponsor and scrutineer of J. F. Foucquet’s works as well. The logarithmic method for the solar eclipse method in de la Hire's work has not been introduced, but explicitly applied in the calculation of five planets's longitudes. The equivalence of the calculation programs for the solar eclipse in Lifa Wenda and YZLXKC has been revealed.
Key words: solar eclipse, Lifa Wenda, Yuzhi Lixiang Kaocheng, Tabulæ astronomicæ Ludovici magni

Sanjufīnī Zīj (1363), which follows the Ptolemaic and the Marāgha school’s traditions, was compiled by ‘Aṭā al-Samarqandī (c. 1310s-1380s) at the decreed of Zheng-xi Wu-jing-wang 鎮西武靖王 Bu-na-la卜納剌 (?-1373) for Yong-chang Fu 永昌府 (latitude 38°10′ in Gan-su甘肅, one of the provinces in Northwestern China) at the end of the Yuan Dynasty (1271-1368).
Sanjufīnī Zīj has been regarded as one of the most importantly original literature for the exchange of astronomy between the Chinese and the Islamic civilizations. Having based on the analysis of Sanjufīnī Zīj’s lunar tables, we have realized that Ptolemy’s second model for the lunar method be applied in the calcution of the first equation of the moon, ρ(2η) is substituted for R in the solar model; the inclination precisely defined as i = 5°02′30″. Forthermore, in the related Chinese versions of Huihui Lifa (回回曆法, 1477, compiled by Bei Lin貝琳 for Ming Court) and Chiljeongsan Oepyeon Jeongmyoyeon Gyeosik Garyeong (七政算外篇·丁卯年交食假令, 1442, compiled by Lee Soonji 李純之 for Joseon Court), there are not any contents about the lunar ecliptic longitude or any table for the third equation with max Δλ = 7′.

Labrang Lamasery (བླ་བྲང་བཀྲ་ཤིས་འཁྱིལ 拉卜楞寺) established in 1709, has been recognized as the most influential monastery in the Amdo region, for the comprehensive Tibetan Buddhist education system and the abundant collections of Tibetan manuscripts, documents and versions.
In 1763, Kalachakra College ( དུས་འཁོར་གྲྭ་ཚང་། 時輪金剛學院) was founded under the guidance of the Sixth Panchen Lama (1738-1780) and the Second Jamyang Jigme Wangpo (1728-1791), and Indian’s astronomy, astrology and mathematics have been introduced and revised.
Hevajra College (ཀྱཻ་རྡོར་གྲྭ་ཚང་། 喜金剛學院) was established in 1879, Kangxi Yuzhi Hanli Daquan Zang-yi-ben (རྒྱ་རྩིས་ཆེན་མོ། 康熙御製漢曆大全, 1715, mainly translated from ནུབ་ཕྱོགས་གསར་མའི་རྩིས་དཔེ། 西洋新法曆書 and ཁང་ཞི་རྟག་བརྟན་གྱི་རྩིས 康熙永年曆法) has been applied in the compilation of the yearly almanac for Tibetan regions.
Samdrup Gyatso (བསམ་འགྲུབ་རྒྱ་མཚོ།, 1923-2006) revitalized astronomical education system at Labrang Lamasery by integrating the traditions of both colleges with modern astronomy. Samdrup Gyatso, with his numerous students and followers, has inherited and developed the Tibetan astronomical education system and served for the prediction of eclipses, earthquakes, the production of Tibetan medication, which are of more important social and economical contribution for the Tibetan communities.