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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 paschalis developed from early in the third century for the purpose of determining (Alexandrian or Julian calendar) dates of Paschal Sunday which rised 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 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 council of Nicaea in AD 325 (turning point in the history of Christianity) were reconstructed on the basis of NASA’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 19-year lunar cycle underlying the legendary 19-year Paschal cycle of the famous third century Alexandrian computist Anatolius contained in the fourth or fifth century Latin text De ratione paschali. The presentations he gave at the international conferences on the science of computus at the university of Galway in 2010 and 2018 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 : 128
    Uitgeverij : JZ
    ISBN : 9789090324678
    Datum publicatie : 08-2021
  • Inhoudsopgave
    Table of Contents
    Introduction
    Two ante-Nicene Metonic 19 year lunar cycles
    (1) Anatolius’ 19-year lunar cycle
    Reconstructing Anatolius’ 19-year lunar cycle
    (0) The proto-Alexandrian cycle
    Searching for Anatolius’ 19 year lunar cycle
    Dating the spring equinox
    (2) The archetypal Alexandrian (19 year lunar) cycle
    Reconstructing the archetypal Alexandrian cycle
    Three post-Nicene Metonic 19-year lunar cycles
    (3) The Festal Index (19-year lunar) cycle
    (4) Theophilus’ 19-year lunar cycle
    (5) The classical Alexandrian (19-year lunar) cycle
    The ante-Nicene Alexandrian 2-day gap
    More evidence
    Summary
    Epilogue
    Bibliography
    Index
    Appendix I (Dionysius Exiguus’ Paschal table)
    Appendix II (Beda Venerabilis’ Easter table)
    Appendix III (Christian Era and Universal Time)
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Summary
It is the development the Alexandrian method for determining (Alexandrian calendar or Julian calendar) dates of Paschal Sunday underwent which forms the mainstream of the history of the computus paschalis 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 construction of the proto-Alexandrian cycle, being the lost Metonic 19-year lunar cycle from which the famous Alexandrian computist Anatolius originally (around AD 260) started to construct his legendary 19-year Pachal cycle;
2) the construction of the archetypal Alexandrian cycle, being the also lost and also ante Nicene common archetype of the three well-known post-Nicene Alexandrian Metonic 19-year lunar cycles.
The proto-Alexandrian cycle appears to be equal to Anatolius’ 19-year lunar cycle, being the also lost Metonic 19-year lunar cycle from which Anatolius ultimately (around AD 270) started to construct his 19-year Paschal cycle. The cognate but completely different archetypal Alexandrian cycle was constructed by Alexandrian computists shortly before the council of Nicaea in AD 325, turning point in the history of Christianity.
Of course the archetypal Alexandrian cycle as well as both its predecessors was constructed essentially on the basis of at the time recent lunar tables, but the set of computistical principles according to which the former was constructed was rather different from the set of computistical principles according to which each of the latter was constructed. After having reconstructed them, we establish (see Table 8) that:
1) there exists an almost perfect 2-day gap (referred to as ‘the ante-Nicene Alexandrian 2-day gap’) between Anatolius’ 19-year lunar cycle and the archetypal Alexandrian 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) both Anatolius’ 19-year lunar cycle and the sequence of Paschal dates generated by it according to the old Alexandrian Paschal rule have de facto lower limit date 23 March;
3) the archetypal Alexandrian 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 19-year lunar cycles could simply be obtained either by simply adopting the archetypal Alexandrian cycle or by adapting the archetypal Alexandrian cycle by only moving its saltus 1 year afterward or 2 years forward;
4) the archetypal Alexandrian cycle has de facto lower limit date 21 March (like the well-known three post-Nicene Alexandrian Metonic 19-year lunar cycles) but the sequence of Paschal dates generated by it according to the new Alexandrian Paschal rule has de facto lower limit date 22 March (idem).
We conclude that Anatolius can be considered to be the founder of the efficient Alexandrian Metonic 19-year lunar cycle method for determining Alexandrian calendar or Julian calendar dates of Paschal Sunday from which after the great calendar reform in AD 1582, turning point in the history of chronology, an astronomically more realistic (but necessarily also much more complicated) method for determining Gregorian calendar dates of Easter would be developed.

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