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Reconstructing Metonic 19-year Lunar Cycles

(on the basis of NASA's Six Millennium Catalog of Phases of the Moon)

Jan Zuidhoek • Boek • paperback

  • Samenvatting
    This book explains, by following the mainstream of the history of the computus (i.e. Paschal reckoning, developed from early in the third century for the purpose of determining Julian or Alexandrian calendar dates of Paschal Sunday) which rose shortly after AD 250 in Alexandria (Egypt) to ultimately in AD 1582 (turning point in the history of chronology) flow into a more realistic method for determining Gregorian calendar dates of Easter, how at the time calendar dates of Paschal Sunday depended on phases of the moon and how recently both lost Metonic (19 year) lunar cycles constructed in Alexandria before the first council of Nicaea in AD 325 (turning point in the history of Christianity) were reconstructed on the basis of Espenak’s Six Millennium Catalog of Phases of the Moon.
    The author of this groundbreaking book was born in 1938, studied mathematics, physics, and astronomy at the university of Utrecht from 1960 to 1969, and was a teacher of mathematics from 1970 to 2001 at the Gymnasium Celeanum in Zwolle. After having gone deeply into the history of mathematics, chronology, and early Christianity, ultimately resulting in his lucid webpage “Christian Era and Universal Time”, he became fascinated by the Alexandrian computus. In 2009 he succeeded, by using the Six Millennium Catalog, in determining the Metonic lunar cycle underlying the legendary 19 year Paschal cycle of the great third century Alexandrian computist Anatolius which is part of the fourth century Latin text De ratione paschali. The two presentations he gave at international conferences on the science of computus at the university of Galway resulted in 2017 in a pioneering article entitled “The initial year of De ratione paschali and the relevance of its paschal dates” and in 2019 in the first edition of this book reducing that article to a preparatory study.
  • Productinformatie
    Binding : Paperback
    Distributievorm : Boek (print, druk)
    Formaat : 170mm x 240mm
    Aantal pagina's : 130
    Uitgeverij : JZ
    ISBN : 9789090324678
    Datum publicatie : 08-2021
  • Inhoudsopgave
    Introduction 9
    A few ante-Nicene Metonic lunar cycles 12
    (1) Anatolius’ (19-year) lunar cycle 14
    Reconstructing Anatolius’ lunar cycle 19
    (0) The proto-Alexandrian (19-year) lunar cycle 31
    Searching for Anatolius’ lunar cycle 36
    Dating the spring equinox 40
    (2) The archetypal Alexandrian (19-year) lunar cycle 45
    Reconstructing the archetypal Alexandrian lunar cycle 48
    Three post-Nicene Metonic lunar cycles 58
    (3) The Festal Index (19-year) lunar cycle 60
    (4) Theophilus’ (19-year) lunar cycle 66
    (5) The classical Alexandrian (19-year) lunar cycle 67
    The ante Nicene Alexandrian 2-day gap 71
    More evidence 74
    Summary 92
    Epilogue 95
    Bibliography 97
    Index 100
    Appendix I (Dionysius Exiguus’ Paschal table) 106
    Appendix II (Beda Venerabilis’ Easter table) 109
    Appendix III (Christian Era and Universal Time) 124
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Summary
The development the Alexandrian method for determining Julian or Alexandrian calendar dates of Paschal Sunday underwent is nothing less than the mainstream of the history of the computus (i.e. Paschal reckoning) which rose in third century Alexandria (Egypt) to ultimately (in sixteenth century Rome) flow into an astronomically more realistic method for determining Gregorian calendar dates of Easter. In this mainstream there were only two real rapids:
1) first the solid construction (on the basis of at the time recent lunar tables) of the proto Alexandrian lunar cycle and Anatolius’ lunar cycle, being the (lost) Alexandrian Metonic lunar cycle(s) from which the great third century Alexandrian computist Anatolius started in order to construct his legendary 19 year Paschal cycle;
2) then the also solid construction (also on the basis of at the time recent lunar tables) of the archetypal Alexandrian lunar cycle, being the (also lost) ante Nicene common archetype of the three well known post Nicene Alexandrian Metonic lunar cycles.
The proto Alexandrian lunar cycle and Anatolius’ lunar cycle were constructed somewhere between AD 250 and 282 inclusive, the as well Metonically structured archetypal Alexandrian lunar cycle was constructed barely half a century later, not long before the first council of Nicaea in AD 325, turning point in the history of Christianity. And so it is not so much because of different moments of construction but because of different sets of computistical principles according to which they were constructed that the latter lunar cycle differs so much from the (mutually equal) former ones. After having reconstructed them, we establish (see Table 8) that:
1) there exists an unmistakably ante Nicene as well as just not quite perfect 2 day gap between Anatolius’ lunar cycle and the archetypal Alexandrian lunar cycle, the cause of which must be sought in the transition in Alexandria and beyond from the more Jewish Christian world of the third century to the more Gentile Christian world of the fourth (as a result of which Alexandrian computists went to use the Egyptian lunar calendar more familiar to them instead of the Alexandrian version of the Jewish lunar calendar);
2) Anatolius’ lunar cycle has de facto limit dates 23 March and 20 April, but the sequence of Paschal dates generated by this lunar cycle according to the old Alexandrian Paschal rule has de facto limit dates 23 March and 26 April;
3) the archetypal Alexandrian lunar cycle is the archetype from which after bishop Athanasius’ death in AD 373 one after another the three well known post Nicene Alexandrian Metonic lunar cycles would be obtained if not by simply adopting their archetype then by simply adapting their archetype by moving its saltus a few years afterward or forward;
4) the three well known post Nicene Alexandrian Metonic lunar cycles have, as well as the archetypal Alexandrian lunar cycle, de facto limit dates 21 March and 18 April, but each of the sequences of Paschal dates generated by them according to the new Alexandrian Paschal rule has de facto limit dates 22 March and 25 April.
We conclude that Anatolius can be regarded as the great founder, and the ante Nicene Alexandrian computists who constructed the archetypal Alexandrian lunar cycle and their great post Nicene follower Annianus as the most important developers, of the efficient Alexandrian Metonic lunar cycle method for determining Julian or Alexandrian calendar dates of Paschal Sunday from which, thirteen centuries after Anatolius’ death, because of the second great calendar reform in AD 1582, turning point in the history of chronology, an admittedly more complicated but astronomically more realistic method for determining Gregorian calendar dates of Easter would be developed. ×
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