A Study On Almagest Of Ptolemy

The Greek astronomer Ptolemy, who dealt with mathematical astronomy in Almagest, is systematically studied in this doctoral dissertation. From the viewpoint of the research on mathematical history in China, some new results are reached. This paper contains six parts.Based on the original works of Ptolemy and modern mathematics, the paper discusses how geometrical models could be constructed by means of empirical data stemming from careful observations. It illustrates and analyzes the theories of the Sun and the Moon, the parallax of the Moon, the eclipses, the fixed stars, the planets, the retrograde and maximum elongations and the latitudes of planets.Based on the original works, it solves two questions: the understanding of the works of Hipparchus and the distinguishing of Ptolemy's work from Hipparchus's.The procedure of constructing tables and various numerical calculations, which was concealed in Almagest, is analyzed and discussed. This paper holds the view that the use of a standard procedure of this kind presupposes the existence of a functional relationship between two sets of variables. The standard procedure reduced a function of two variables to an algebraic expression in functions of one variables, through analyzing it is strong or weak variable or not .The formulae of the middle values of tables characterize a specific method which we shall call Ptolemaic interpolation.It explains some terms and concepts in Almagest and cleared up their clue of historical development. The agencies of a few observation data and the quantity of physics are compared with the modern theory. It points out the weaknesses of Ptolemy's astronomy and the influences of them.It makes up and proofreads some contents of transformation of sphere coordinates in the Yuanshi and Mingshi. Some important rules and methods are further analyzed. It also compares the agency of transformation of ecliptic and equator coordinates in Almagest and Shoushili with the modern theory. It concludes that there was nearly no discrepancy and probes the reasons.It distinguishes the astronomy concepts stemming from Almagest in Congzhen Lishu and gives exploration of their meanings after translating into Chinese. It also distinguishes the contents of Ptolemy's astronomy in Congzhen Lishu. Not only does it study and analyze the research of Ming and Qing Dynasty's scholars after Congzhen Lishu in China, but also concludes that the level of accepting western methods was rather low.