Geometrical and Statistical Methods of Analysis of Star Configurations

Cover\nTitle Page\nCopyright Page\nPREFACE\nCONTENTS\nINTRODUCTION\n	1. Brief description of the Almagest\n	2. A brief review of the history of the Almagest\n	3. Basic medieval star catalogs\n	4. Why dating star catalogs is interesting\nPART ONE: PRELIMINARY ANALYSIS\n	Chapter 1. Some Concepts of Astronomy and History of Astronomy\n		1. Ecliptic, equator and precession\n		2. Equatorial and ecliptic coordinates\n		3. Methods of measuring equatorial and ecliptic coordinates\n		4. Modern starry sky\n		5. Computation of the starry sky to the past. Catalogs K(t) Newcomb\'s theory\n		6. Astrometry. Some medieval astronomic instruments\n	Chapter 2. Star Catalog of the Almagest. Preliminary Analysis\n		1. Structure of the catalog\n		2. Distribution of well-identified and poorly identified stars of the Almagest\n		3. Seven domains in the star atlas of the Almagest and accuracy of measurements\n		4. On possible distortions of stellar positions due to atmospheric refraction\n		5. Analysis of distribution of informatas in the catalog of the Almagest\n		6. On reliability of measurement of latitudes and longitudes in the Almagest\n		7. Peters\' sine curve and the latitudes in the Almagest\n	Chapter 3. The Attempts to Date the Almagest With the Help of Simplest Procedures, and Why They Fail\n		1. An attempt to date the Almagest: comparison with computed catalogs in fast stars\n		2. An attempt to date the Almagest: comparison with computed catalogs in fast and named stars\n		3. An attempt to date the Almagest from comparison of stellar configurations\n		4. Conclusions and directions of further study. Description of the method. Plan of the following chapters\nPART TWO: DATING CATALOGS\n	Chapter 4. Who Is Who?\n		1. Preliminary remarks\n		2. The method for identification\n		3. The resulting identification of \"modern\" stars with the stars in the Almagest\n		4. Conclusions\n	Chapter 5. Analysis of Systematic Errors in Stellar Configurations\n		1. Classification of latitudinal errors\n		2. Parametrization of group and systematic errors\n		3. Method of least squares for the parameters γ and φ\n		4. Variation of γstat(t) and φstat(t) with the s a priori date\n		5. Statistical properties of the estimates γstat and φstat\n		6. Conclusions\n	Chapter 6. Statistical Properties and the Accuracy of the Catalog of the Almagest\n		1. Introductory remarks\n		2. Seven domains of the starry sky\n		3. Analysis of individual constellations\n		4. Brief conclusions\n	Chapter 7. Dating the Star Catalog of the Almagest\n		1. Informative kernel of the catalog\n		2. Preliminary considerations\n		3. Statistical dating procedure\n		4. Analysis of stability of the statistical dating procedure\n		5. Geometric dating procedure\n		6. Stability of the geometric dating procedure. Influence of possible instrumental errors on the results of dating\n		7. Behavior of longitudes\n		8. Behavior of angular deviations in the configuration formed by the informative kernel\n		9. Brief conclusions\n	Chapter 8. Inclination of the Ecliptic in the Almagest\n		1. Inclination of the ecliptic in the Almagest and the systematic error\n		2. Zodiac in the Almagest and the Peters\' sine curve\n	Chapter 9. Dating Other Medieval Catalogs\n		1. Introduction\n		2. Catalog of Tycho Brahe\n		3. Catalog of Ulugh Beg\n		4. Catalog of Hevelius\n		5. About Al Sufi\'s catalog\n	Chapter 10. A Date for the Almagest from Coverings of Stars and Lunar Eclipses\n		1. Introduction\n		2. A date from coverings of stars by planets\n		3. A date from lunar eclipses\n		4. Chronology of the Almagest\n			Appendix 1. Formulas for planetary positions\n			Appendix 2. Lunar eclipses in the Almagest\nPART THREE: ADDENDUM\n	Introduction. Problems and hypotheses connected with dating the Almagest\n		1. On dates for various manuscripts and printings of the Almagest, and how they agree with the date from astronomic analysis\n		2. About the R. Newton\'s book The Crime of Claudius Ptolemy\n		3. Why various versions of the Almagest differ\n		4. Does it follow from Ptolemy\'s text that he had carried out the observations himself?\n		5. Where did Ptolemy count longitudes from?\n		6. General review. The blossom of antique astronomy\n		7. The thousand years decline in the development of astronomy\n		8. The repeated blossom of astronomy in the Renaissance\n		9. Chronological table and the diagram of development of astronomy with time\n		10. Some other peculiarities in the Almagest\n		11. The Almagest and Halley\'s discovery of proper motions of stars\nAPPENDIX\nREFERENCES\nINDEX