# À.Ò.Fomenko, V.V.Kalashnikov, G.V.Nosovskiy STARS TESTIFY

Dating of the star catalogue of "Almagest".

Volume 3, Book 1
Publishing house AST, 2012.

ABSTRACT

## CONTENTS

FOREWORD.

INTRODUCTION.

1. Short characteristics of Almagest.

2. Short history of Almagest.

3. Main medieval star catalogues.

4. Why a question of dating of old star catalogues is interesting.

5. Hipparch.

6. Ptolemy.

7. Copernicus

8. Tycho Brahe.

9. An important investigation of Almagest by astronomer Robert Newton and his book "Crime of Claudius Ptolemy".

Chapter 1. SOME NECESSARY DATA FROM THE ASTRONOMY AND THE HISTORY OF ASTRONOMY.

1. Ecliptics, equator, precession.

2. Equatorial and ecliptic coordinates.

3. Means of measurement of equatorial and ecliptic coordinates.

4. Modern star sky.

5. Calculation of the star sky "to the past". Estimated catalogues $K(t)$. Formulas of Newcomb-Kinoshita.

6. Astrometry. Old astronomical measuring instruments of the XV--XVII centuries.

7. Measurement of the time and clock in the old astronomical observations of the Middle Ages.

Chapter 2. PRELIMINARY ANALYSIS OF THE STAR CATALOGUE OF ALMAGEST.

1. Description of the structure of the catalogue.

2. Analysis of distribution of well and badly identified stars in Almagest.

3. Seven areas, noticeably differing from each other in the quantity of reliably identified star, are discovered on the star atlas of Almagest.

4. About possible distortion of the coordinates of stars due to atmospheric refraction.

5. Analysis of distribution of informat in the catalogue of Almagest.

6. Analysis of the variants of coordinates in different manuscripts of the catalogue of Almagest. Comparison of 26 main manuscripts with a canonical version of the catalogue.

7. Density of variants as density of independent observations of stars. Again seven areas on the star atlas of Almagest. Adjustment with the previous results.

8. About the reliability of measurement of latitudes and longitudes in Almagest.

9. Doubtfulness of the traditional opinion, like it follows from the text of Ptolemy, that he "personally observed" the stars and "personally made" the described in Almagest measurements and observations.

10. From which point on ecliptics Ptolemy counted off longitudes?

11. Sinusoid of Peters in longitudes of Almagest.

Chapter 3. UNSUCCESSFUL ATTEMPTS OF DATING Of ALMAGEST. REASONS OF FAILS. OUR NEW APPROACH AND SHORT STATEMENT OF THE RESULTS.

1. An attempt to date Almagest with a comparison with calculated catalogues by the movement of the fastest stars.

2. An attempt to date the catalogue of Almagest by the total of fast and named stars by means of comparison with calculated catalogues.

3. An attempt to date the catalogue of Almagest by movement of separate stars on the background of their nearest environment.

4. Analysis of some mistaken works, devoted to the dating of Almagest based on proper motions of the stars.

5. Conclusions and the ways of further research. Our approach and short description of the received by us main results.

Chapter 4. WHO IS WHO?

1. Preliminary notes.

2. Formal search of the fastest stars in the catalogue of Almagest.

3. Search of all fast stars, reliably identified in the catalogue of Almagest.

Chapter 5. ANALYSIS OF SYSTEMATICAL MISTAKES OF THE STAR CATALOGUE.

0. Main idea.

1. Main designations.

2. Parameterization of group and systematical mistakes.

3. Determination of the parameters $\gamma(t)$ and $\varphi(t)$ by the method of lower squares.

4. Change of parameters $\gamma_{stat}(t)$ and $\varphi_{stat}(t)$ through time.

5. Statistical characteristics of estimations of $\gamma_{stat}$ and $\varphi_{stat}$.

6. Conclusions.

Chapter 6. STATISTICAL AND ACCURACY CHARACTERISTICS OF THE CATALOGUE OF ALMAGEST.

1. Introduction notes.

2. Seven areas of the star sky.

3. Analysis of separate constellations of Almagest.

4. Conclusions.

Chapter 7. DATING OF THE STAR CATALOGUE OF ALMAGEST. STATISTICAL AND GEOMETRICAL METHODS.

1. Informative core of the catalogue – these are well measured named stars.

2. Preliminary considerations about dating of the catalogue of Almagest by measurement of the coordinates of named stars.

3. Statistical procedure of dating.

4. Dating of the catalogue of Almagest by widened informative core.

5. Dating of the catalogue of Almagest by the plenty of 8-star configurations, consisting of bright stars.

6. Analysis of the steadiness of statistical procedure of dating of the catalogue of Almagest.

7. Geometrical dating of the catalogue of Almagest.

8. Steadiness of geometrical method of dating of the catalogue of Almagest. Influence of possible errors of astronomical device on the result of dating.

9. Behavior of the longitudes of named stars of Almagest.

10. Behavior of arch closing errors in a configuration, made by the informative core of Almagest.

11. Conclusions.

Chapter 8. A DECLINE ANGLE OF THE ECLIPTICS TO THE EQUATOR IN ALMAGEST.

1. Imaginations of Ptolemy about the value of the decline angle of ecliptics and systematical mistake of $\gamma$.

2. Zodiac of Almagest and sinusoids of Peters.

Chapter 9. DATING OF OTHER MEDIEVAL CATALOGUES WITH OUR METHOD.

1. Introduction.

2. The catalogue of Tycho Brahe.

3. The catalogue of Ulugbek.

4. The catalogue of Hevel.

5. The catalogue of al Sufi.

Chapter 10. ADDITIONAL CONSIDERATIONS ABOUT THE DATING OF ALMAGEST. COVERS OF THE STARS AND MOON ECLIPSES. - À.Ò.Fomenko, G.V.Nosovskiy.

1. Introduction.

2. Dating of covers of the stars with planets. Calculation by medium elements.

3. Dating of described in Almagest covers of the stars with planets. Specified calculation.

4. What is the era of Nabu-nasir according to the late-medieval solution.

5. When Almagest of Ptolemy was written and how this book got its modern form. Ptolemy and Copernicus.

6. "Antique" Hipparch – it is, in a big measure, a phantom reflection of a famous astronomer Tycho Brahe.

7. Most likely Almagest of Ptolemy was finally finished already after Tycho Brahe = "antique" Hipparch.

8. According to the statement of Robert Newton, most moon eclipses, provided in Almagest, are later fakes.

Chapter 11. OTHER PROBLEMS, CONNECTED WITH DATING OF THE CATALOGUE OF ALMAGEST. - À.Ò.Fomenko, G.V.Nosovskiy.

1. Some additional oddities of Almagest.

2. Almagest and opening of proper motions of the stars by Halley.

3. Who is "antique" imperator Pius, at the time of whom many astronomical observations of Ptolemy took place. When and where he lived.

4. The Scaligerian datings of the manuscripts and printed editions of Almagest.

5. What is Almagest?

6. A strange development of astronomy, and how it is described in "the textbook of Scaliger".

7. Copernicus, Tycho Brahe and Kepler. What was the relation of Johannes Kepler to the edition of the final version of the book of Copernicus?

8. Anna Komnina considers that Hipparch or Ptolemy was her coeval. It again appears that Hipparch and Ptolemy lived not earlier than at the epoch of the XI-XII centuries.

9. Clear dating of the epoch of Ptolemy on his portrait in the ancient German "Global Chronic" of Shadel.

10. What meant the word Pelusiensis or Pheludiensis in the name of Ptolemy.

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Appendix 1. TABLES OF FAST, NAMED AND RELIABLY IDENTIFIED STARS OF ALMAGEST.

Appendix 2. COMPUTER PROGRAM OF GEOMETRICAL METHOD OF DATING OF THE STAR CONFIGURATIONS BY MEANS OF PROPER MOTIONS WITH THE ACCOUNT OF SYSTEMATICAL MISTAKE OF THE CATALOGUE.

LITERATURE.