This work is devoted to describing new statistical and geometrical procedures for dating ancient star catalogues considering numerical data contained in these catalogues and the known real configurations of stars on the celestial sphere. The method was tested on several star catalogues whose dates are well known (Tycho Brahe, etc.) and on several artificially generated star catalogues. Then the same method was applied to the Almagest. The results obtained do not confirm the traditional dating of the Almagest (2nd century AD or 2nd century BC) but shift its dating to the Arabian epoch: 600-1300 AD. O. Preliminary Remarks on the Mathematical Aspects of the ProblemThis paper involves at least three aspects: historical (Section 1), astronomical (Sections 2 and 3) and mathematical (Sections 4-8).Its main problem is: 'Is it possible to date an ancient star catalogue by mathematical tools?' Our answer is: 'Yes'.The initial data are star coordinates contained in the star catalogue. In order to determine the date of its compilation, we need to know the correct star coordinates for any point of time in the past. For this purpose, we use the well-known equations describing the trajectories of stars starting from their present positions. Every star from the catalogue has two coordinates -longitude and latitude. We consider in our work only latitudes. The reason for this is that it is possible to obtain all the necessary information for dating using latitudes only. Longitudes are not reliable for this purpose (see details in Section 1). They lead to additional errors, and eliminating them provides additional accuracy.

The book presents an unusual application of statistical and geometrical methods to dating ancient astronomical documents. An exciting result of the book consists of placing the date of Ptolemy's principal work "Almagest" in the Middle Ages instead of its traditional date (second century A.D.). The main body of the book contains statistical analysis of Ptolemy's star catalogue (systematic errors, accuracy, inclination of the ecliptic, dating the star cata

This paper is a natural extension and continuation of the authors' studies of the astronomical dating problem of Ptolemy's famous Almagest. In previous papers, the authors suggested and developed a new geometrical-statistical method for dating ancient star catalogues. This method was then applied to Ptolemy's Almagest. The results obtained do not confirm the traditional dating of the Almagest (2nd century AD or 2nd century BC) but shift it to the epoch AD 600-1300. In this paper, we extend our analysis to other parts of the Almagest and study the dating problem for series of lunar eclipses described in the Almagest and for the covering of stars by planets. The results obtained completely agree with our previous results and give the same time interval, AD 600-1300. (1991). 01A35, 51 F99, 62J99. Mathematics Subject Classifications