Editing Epact (section)

== History ==
The discovery of the epact for computing the date of Easter has been attributed to [[Patriarch of Alexandria|Patriarch]] [[Pope Demetrius I of Alexandria|Demetrius&nbsp;I of Alexandria]], who held office from 189–232&nbsp;{{sc|AD}}. In the year 214 he used the epact to produce an Easter calendar, which has not survived, which used an eight-year [[Lunisolar calendar|luni-solar cycle]].<ref name=Mosshammer-ch8year>
{{cite book
 | last = Mosshammer | first = Alden A.
 | year = 2008
 | chapter = The 8&nbsp;year cycle and the invention of the epacts
 | title = The Easter Computus and the Origins of the Christian Era
 | series = Oxford Early Christian Studies
 | place = Oxford, UK
 | publisher = Oxford University Press
 | isbn = 978-0-19-954312-0
 | pages = 109–125
}}
</ref>
A subsequent application of the epact to an Easter calendar, using a sixteen-year cycle, is found in the Paschal Table of Hippolytus, a 112&nbsp;year list of Easter dates beginning in the year 222 which is inscribed on the side of a statue found in Rome.<ref name=Mosshammer-ch8year/> Augustalis, whose dates had been disputed from the third to the fifth century,<ref name=Mosshammer-2008>
{{cite book
 | last = Mosshammer | first = Alden A.
 | year = 2008
 | title = The Easter Computus and the Origins of the Christian Era
 | series = Oxford Early Christian Studies
 | place = Oxford, UK
 | publisher = Oxford University Press
 | isbn = 978-0-19-954312-0
 |pages=39–40, 109–125, 224–228
}}
</ref>{{rp|style=ama|pp= 224–228}}
computed a {{lang|la|laterculus}} ("little tablet") of Easter dates. As reconstructed, it uses epacts (here the age of the moon on 1&nbsp;January) and an 84&nbsp;year luni-solar cycle to compute the dates of Easter using a base date of 213&nbsp;{{sc|AD}}. If we accept Augustalis's earlier dates, his ''laterculus'' extends from 213–312&nbsp;{{sc|AD}} and Augustalis originated the use of epacts to compute the date of Easter.<ref name=Pedersen-1983>
{{ cite conference
 | last = Pedersen | first = O. | author-link = Olaf Pedersen
 | date = c. 1982
 | title = The ecclesiastical calendar and the life of the Church
 | editor1-last = Coyne    | editor1-first = G.V. | editor1-link = George V. Coyne
 | editor2-last = Hoskin   | editor2-first = M.A.
 | editor3-last = Pedersen | editor3-first = O.   | editor3-link = Olaf Pedersen
 | publication-date = 1983
 | book-title = Gregorian Reform of the Calendar
 | conference = Vatican Conference to commemorate [the Gregorian Reform's] 400th&nbsp;Anniversary, 1582–1982
 | place = Vatican City, IT
 | publisher = [[Pontifical Academy of Sciences]], [[Vatican Observatory]]
 | pages = 39–59
 | conference-url = http://www.casinapioiv.va/content/dam/accademia/pdf/es3.pdf
 | url = http://www.casinapioiv.va/content/dam/accademia/pdf/es3.pdf  <!-- actually, URL for whole ''Proceedings of ...''. -->
 | access-date = 2023-05-13
 | archive-url = https://web.archive.org/web/20150525102109/http://www.casinapioiv.va/content/dam/accademia/pdf/es3.pdf
 | archive-date = 2015-05-25  |df = dmy-all
}}
</ref>{{rp|style=ama|pp= 40–45}}

As early as the fourth century we see Easter [[computus]] using the epact and the nineteen-year [[Metonic cycle]] in Alexandria, and subsequent computistical tables were influenced by the structure of the [[Alexandrian calendar]]. The epact was taken as the age of the Moon on 26&nbsp;Phamenoth (22&nbsp;March in the Julian calendar) but that value of the epact also corresponded to the age of the Moon on the last [[epagomenal day]] of the preceding year. Thus the epact can be seen as having been established at the beginning of the current year.<ref name=Mosshammer-2008/>{{rp|style=ama|pp=75–80}} Subsequent Easter tables, such as those of Bishop [[Theophilus I of Alexandria|Theophilus of Alexandria]], which covered 100&nbsp;years beginning in 380&nbsp;{{sc|AD}}, and of his successor Bishop [[Cyril of Alexandria|Cyril]], which covered 95&nbsp;years beginning in 437&nbsp;{{sc|AD}} discussed the computation of the epact in their introductory texts. Under the influence of [[Dionysius Exiguus]] and later, of [[Bede]], the ''Alexandrian Easter Tables'' were adopted throughout Europe where they established the convention that the epact was the age of the Moon on 22&nbsp;March.<ref name=Pedersen-1983/>{{rp|style=ama|p= 52}} This Dionysian epact fell into disuse after the introduction of a perpetual calendar based on the [[golden number (time)|golden number]], which made the calculation of epacts unnecessary for ordinary computistical calculations.<ref name = Dekker>
{{ Cite journal
 | last = Dekker | first = Elly | author-link = Elly Dekker
 | year = 1993
 | title = Epact Tables on Instruments: Their definition and use
 | journal = Annals of Science
 | volume = 50 | issue = 4 | pages = 303–324
 | doi=10.1080/00033799300200251
}}
</ref>

Two factors led to the creation of three new forms of the epact in the fifteenth and sixteenth centuries. The first was the increasing error of computistical techniques, which led to the introduction of a new Julian epact around 1478&nbsp;{{sc|AD}}, to be used for practical computations of the phase of the Moon for medical or astrological purposes. With the [[Gregorian reform of the calendar]] in 1582, two additional epacts came into use. The first was the Lilian epact, developed by [[Aloisius Lilius]] as an element of the ecclesiastical computations using the Gregorian calendar. The Lilian epact included corrections for the motions of the Sun and the Moon that broke the fixed relationship between the epact and the golden number. The second new epact was a simple adjustment of the practical Julian epact to account for the ten-day change produced by the Gregorian Calendar.<ref name = Dekker/>