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Reconstructing Alexandrian Lunar Cycles

(on the basis of Espenak'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
    computus (i.e. Paschal reckoning developed from early third century for
    determining Julian or Alexandrian calendar dates of Paschal Sunday) which
    shortly after AD 250 rose in Alexandria (Egypt) to ultimately in AD 1582
    (turning point in the history of chronology) flow into an astronomically 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 the three lost important 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 by the author of this book on the
    basis of the Six Millennium Catalog of Phases of the Moon compiled by NASA’s
    eclipse expert Fred Espenak.
    The author of this 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, of chronology, and of early
    Christianity, he became fascinated by the Alexandrian computus. In 2009 he
    succeeded, by using the Six Millennium Catalog, in reconstructing the lost
    predecessor of the lost Metonic lunar cycle underlying the famous 19-year
    Paschal cycle of the great third century Alexandrian computist Anatolius which
    had survived as a 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 in 2010 and in 2018 resulted in 2017 in a
    pioneering article and in 2019 in his first book, entitled “Reconstructing Metonic
    19-year Lunar Cycles”, reducing that article to a preparatory study. It is from
    the revised edition of that book that this new book was developed.
  • Productinformatie
    Binding : Paperback
    Distributievorm : Boek (print, druk)
    Formaat : 170mm x 240mm
    Aantal pagina's : 138
    Uitgeverij : JZ
    ISBN : 9789090370446
    Datum publicatie : 03-2023
  • Inhoudsopgave
    Introduction 9
    Three lost ante-Nicene Alexandrian lunar cycles 12
    (1) Anatolius’ lunar cycle 14
    Reconstructing Anatolius’ lunar cycle 19
    (0) The proto-Alexandrian lunar cycle 31
    Anatolian lunar cycles 32
    Searching for Anatolius’ lunar cycle 36
    Dating the spring equinox 40
    (2) The archetypal Alexandrian lunar cycle 45
    Reconstructing the archetypal Alexandrian lunar cycle 48
    Three well known post-Nicene Alexandrian lunar cycles 58
    (3) The Festal Index lunar cycle 60
    (4) Theophilus’ lunar cycle 66
    (5) The classical Alexandrian lunar cycle 67
    The ante Nicene Alexandrian 2-day gap 71
    More evidence 74
    Summary 92
    Epilogue 95
    Bibliography 103
    Index 105
    Appendix I (Dionysius Exiguus’ Paschal table) 111
    Appendix II (Beda Venerabilis’ Easter table) 114
    Appendix III (Christian Era and Universal Time) 129
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Fragment

Summary
The development the Alexandrian method for determining Alexandrian or Julian calendar dates of Paschal Sunday underwent is nothing less than the mainstream of the history of 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) the solid construction (on the basis of at the time relatively recent lunar tables) of the proto Alexandrian lunar cycle (around AD 260) and Anatolius’ lunar cycle (around AD 270), the former being the (lost) Metonic lunar cycle from which the great third century Alexandrian computist Anatolius originally started to determine his Paschal dates, the latter being the one from which he ultimately started in order to construct his famous 19 year Paschal cycle;
2) the solid construction (idem) of the archetypal Alexandrian lunar cycle (around AD 320), being the (lost) Metonically structured common archetype of the three (well-known) post Nicene Alexandrian Metonic lunar cycles.
The proto Alexandrian lunar cycle and Anatolius’ lunar cycle were constructed in the third quarter of the third century, the archetypal Alexandrian lunar cycle was constructed already half a century later, shortly before the first council of Nicaea in AD 325, turning point in the history of Christianity. And so it must have been not so much because of different moments of construction as because of different sets of computistical principles according to which they were constructed that the latter lunar cycle differs so much from both the former ones. After having reconstructed them, we establish that:
1) there exists a 2 day gap (in fact a systematic difference of on average just over 2 days) between Anatolius’ lunar cycle and the archetypal Alexandrian lunar cycle, the cause of which must be sought exclusively 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 much more familiar Egyptian lunar calendar instead of the Alexandrian version of the Jewish lunar calendar);
2) both the proto Alexandrian lunar cycle and Anatolius’ lunar cycle have de facto limit dates 23 March and 20 April, both sequences of Paschal dates generated by them have, according to the old Alexandrian Paschal rule, 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 each of the three (well-known) post Nicene Alexandrian Metonic lunar cycles would be obtained by accepting and whether or not adapting it by moving its saltus one or two years forward or afterward;
4) the three post Nicene Alexandrian Metonic lunar cycles have, as well as the archetypal Alexandrian lunar cycle, de facto limit dates 21 March and 18 April, the four sequences of Paschal dates generated by them all have, according to the new Alexandrian Paschal rule, de facto limit dates 22 March and 25 April.
We conclude that Anatolius can be regarded as the founder, and the ante Nicene Alexandrian computists who constructed the archetypal Alexandrian lunar cycle and their post Nicene follower Annianus as the most important developers, of the efficient Alexandrian Metonic lunar cycle method for determining Alexandrian or Julian 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, in the end an astronomically more realistic method for determining Gregorian calendar dates of Easter would be developed. ×
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