412:
equality cannot be assured in the way
Neugebauer tried to prove it, because the particular Metonic 19-year lunar cycle of the not-dated manuscript concerning AD 311-369 he staged, could have been obtained afterwards by simply extrapolating from the fifth century 7980-year framework. Moreover, Neugebauer not only ignored the difference between the classical Alexandrian and the Festal Index 19-year lunar cycle, but also kept us guessing about, at least refrained from showing, the (crucial) position of the saltus in the particular Metonic 19-year lunar cycle in question.
1123:
1063:
1215:
1191:
1203:
323:, and being strictly beleaguered by the Romans was in a state of starvation. Anatolius, who was living in Bruchium at the time, made arrangements with the besiegers to receive all the women and children, as well as the elderly, continuing at the same time to let as many as wished profit by the means of escaping. It broke up the defence and the rebels surrendered.
416:
theoretical lower limit date for all of his dates of
Paschal full moon. As a matter of fact, the corresponding de facto lower limit date (necessarily being either 22 or 23 March) is not 22 but 23 March, which easily can be derived from Anatolius’ Paschal table. In contrast, he used not only Ptolemy's but also the Roman equinox, March 25, in his Paschal table.
403:(1899-1990), according to himself, was in the dark about the date of compilation of the whole 7980-year framework (based on the classical Alexandrian 19-year lunar cycle) created by Alexandrian computists. Considering that only around AD 400 Annianus obtained his classical Alexandrian version of the Metonic 19-year lunar cycle by adapting
415:
Anatolius describes the vernal equinox as a section of the first zodiacal sign from March 22 to 25. Although he defines March 22 as the Sun's entry into the first sign, he never defines it as his equinox, but as
Ptolemy's equinox. This does not exclude that in reality he used Ptolemy's equinox as the
375:
The dates of the ultimately resulting classical
Alexandrian 19-year lunar cycle have recently appeared to be advanced by about two days over the dates of Anatolius’ 19-year lunar cycle. The former began somewhere in the 4th century, as evidenced by Ethiopic copies of Alexandrian tables covering three
308:
The character of its writing may be illustrated by the following quotation from it attributed to
Anatolius: " is called the "just number", due to the square being equal to its perimeter (i.e 4x4 = 4+4+4+4); of the numbers lesser than four, the perimeter of the square is greater than the area, while
411:
concludes that the compilation in question dates from the fifth century. Of course, this does not exclude that the (in principle tentative) version constructed in the first quarter of the fourth century could be, by chance, equal to
Annianus’ ultimately definitive one. In any case, this possible
304:
a
Neoplatonic treatise heavily influenced by Pythagoreanism, uncertainly attributed to Iamblichus ─ though not written in his style, it is a discussion of each of the first ten natural numerals that mixes accounts of formal arithmetical properties with mystical philosophical analysis.
347:
19-year lunar cycle (which 19-year periodic sequence of dates of the
Paschal full moon must not be confused with the Metonic cycle, of which it is an application in the Julian calendar). Therefore, Anatolius can be considered to be the founder of the new Alexandrian
436:
for
Diocletian years 44–50. These seven of the available 59 were transcribed because they are also the first seven in the festal letters of Athanasius, which also include the same epacts (they are years 6–12 of the Alexandrian lunar
1023:. The numbers on the pages of this edition are six less than the numbers of the corresponding pages of the original edition (1979), so six must be subtracted from page references in this edition's index and text.
330:
he was welcomed by the people and made bishop. Whether his friend
Eusebius had died, or whether they both occupied the see together, is a matter of much discussion. The question is treated at length in the
352:
which half a century after began with the active construction of the second version of the Metonic 19-year lunar cycle, which itself or a close variant of which ultimately would prevail throughout
312:
There is also a treatise on time of the Paschal celebration. His famous 19-year Paschal cycle has survived in seven different complete medieval manuscripts of the Latin text
376:
lunar cycles from 310/11 to 367/68. The dates are secured by the inclusion of an indiction column, and the included Easter dates are consistent with the later dates of
253:, during the early 3rd century. Prior to becoming one of the great lights of the Church, Anatolius enjoyed considerable prestige at Alexandria while working as a
319:
A story is told by Eusebius of the way in which Anatolius broke up a rebellion in a part of Alexandria known then as Bruchium. It was held by the forces of
1073:
399:
However, the Metonic 19-year lunar cycle which was added to Athanasius’ Festal Letters was a one which had 6 April instead of 5 April. Furthermore,
590:
392:
in his 532-year tables during the early 5th century, was fully enumerated in the subsequent 532-year Ethiopic tables, and was adopted by bishop
950:, A Library of Fathers of the Holy Catholic Church, anterior to the division of the East and West, translated by Burgess, Henry, Oxford, 1854
1270:
471:
1051:
1017:
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525:
234:
285:. Eusebius states that Anatolius was deemed worthy to maintain the school of the Aristotelian succession in Alexandria. The
515:
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1001:
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971:
929:
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1235:
384:. The classical Alexandrian 19-year lunar cycle itself or a close variant of it was added to the festal letters of
296:
There are fragments of ten books on arithmetic written by him; it's a mostly complete work known to us by the name
1127:
404:
1255:
1240:
202:
in AD 268. He was not only one of the foremost scholars of his day in the physical sciences, as well as in
134:
1250:
432:
Neugebauer transcribed seven of 58 years with 19 parameters each, including the lunar cycle, e (epact).
407:’ 19-year lunar cycle by moving its saltus 1 year forward by replacing its date 6 April by 5 April, the
1181:
364:). The seventeen-centuries-old enigma of his famous 19-year Paschal cycle (not to be confused with the
576:
385:
369:
203:
389:
199:
68:
1141:
1136:
1078:
656:
408:
226:
83:
1162:
658:
Dating the Passion: The Life of Jesus and the Emergence of Scientific Chronology (200–1600)
372:) was recently completely resolved by the Irish scholars Daniel Mc Carthy and Aidan Breen.
258:
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8:
1245:
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393:
719:
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501:"Lives of the Saints," Omer Englebert New York: Barnes & Noble Books, 1994, p. 256.
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300:. This work seems to have been copied by the author of the curious writing entitled
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1038:. Studia Traditionis Theologiae. Vol. 26. Brepols Publishers. pp. 71–93.
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52:
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Daniel P. Mc Carthy & Aidan Breen (2003), The ante-Nicene Christian Pasch
955:
Jones, Charles W. (1943), "Development of the Latin Ecclesiastical Calendar",
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1036:
Late Antique Calendrical Thought and its Reception in the Early Middle Ages
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1100:. Vol. 1. New York: Charles Scribner's Sons. pp. 148–149.
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Philip Schaff (1892) Athanasius (Select Works and Letters): New York
1066: This article incorporates text from a publication now in the
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981:(The Paschal tract of Anatolius, bishop of Laodicea): Dublin (
966:, Omer Englebert, New York: Barnes & Noble, 1994, pp 532,
1060:
The following concerns only the part "Life" of this article:
339:
Anatolius as the pioneer for the mainstream medieval computus
286:
187:
184:
181:
156:
148:
23:
881:
Institut de Mécanique Céleste et de Calcul des Éphémérides.
454:
140 although modern calculations reveal it occurred on March
381:
682:
McCarthy, Daniel (1995). "The Lunar and Paschal Tables of
309:
of those greater, the perimeter is lesser than the area."
994:
The Easter Computus and the Origins of the Christian Era
1179:
470:
20 at 15:52 UT. Modern calculations are according to
517:Greek Science of the Hellenistic Era: A Sourcebook
176:; early 3rd century – July 3, 283), also known as
1094:Kieffer, John (1970). "Anatolius of Alexandria".
1082:. Vol. 1. New York: Robert Appleton Company.
514:Irby-Massie, Georgia L.; Keyser, Paul T. (2013).
513:
1227:
356:for a long time (until the year 1582, when the
922:Anno Domini (the Origins of the Christian Era)
1169:Sur la Décade et Les Nombres Qu'elle Comprend
1155:Complete Dictionary of Scientific Biography:
959:, Medieval Academy of America, pp. 1–122
388:during the late 4th century; it was used by
1030:Zuidhoek, Jan (2017). "The initial year of
446:Ptolemy measured his equinox to be on March
396:(without any mention of a 532-year table).
343:Around AD 260 Anatolius invented the first
261:, he was credited with a rich knowledge of
1142:The Paschal Canon of Anatolius of Laodicea
1007:
225:Anatolius is recognised as a saint by the
1034:and the relevance of its paschal dates".
1012:(Red Sea Press ed.), Red Sea Press,
1071:
1029:
681:
1093:
944:"Index, A Chronological and Synoptical"
654:
588:
16:Bishop of Laodicea in the third century
1228:
686:Attributed to Anatolius of Laodicea".
577:Lives of the Philosophers and Sophists
954:
688:Archive for History of Exact Sciences
614:Michaud & Michaud (1811–1855) 94.
948:The Festal Epistles of S. Athanasius
745:Mc Carthy & Breen (2003) 15–143.
540:Acta Sanctorum I (5th century) July.
509:
507:
497:
495:
917:Acta Sanctorum I (5th century) July
763:Neugebauer (2016) 26–27, 37, 92–94.
623:Mc Carthy & Breen (2003) 25–43.
13:
1097:Dictionary of Scientific Biography
1087:
293:also studied among his disciples.
210:philosophies, but also a renowned
14:
1282:
1175:Five Metonic 19-year lunar cycles
1115:
1076:". In Herbermann, Charles (ed.).
1072:Campbell, Thomas Joseph (1907). "
504:
492:
245:Anatolius was born and raised in
235:Saint Anatolius of Constantinople
1213:
1201:
1189:
1121:
1061:
895:Mc Carthy & Breen (2003) 68.
549:Mc Carthy & Breen (2003) 18.
1010:Ethiopic Astronomy and Computus
904:Mc Carthy and Breen (2003) 101.
898:
889:
883:"Dates of Seasons for any Year"
874:
865:
856:
847:
838:
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820:
811:
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793:
784:
775:
766:
757:
748:
739:
730:
675:
655:Nothaft, C. Philipp E. (2011).
648:
639:
626:
440:
426:
1271:3rd-century Greek philosophers
617:
608:
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565:
552:
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534:
1:
485:
1165:Sur les Dix Premiers Nombres
992:Alden A. Mosshammer (2008),
7:
935:Michaud Frères (1811–1855)
237:, is celebrated on 3 July.
10:
1287:
1261:3rd-century Syrian bishops
1008:Neugebauer, Otto (2016) ,
911:
853:Mosshammer (2008) 202-203.
826:Mosshammer (2008) 202–203.
302:Theologoumena arithmetica,
298:Introduction to Arithmetic
1044:10.1484/M.STT-EB.5.114734
957:Bedae Opera de Temporibus
871:Neugebauer (1979) 98-100.
591:"Anatolius of Alexandria"
466:260, it occurred on March
173:
133:Teachers; Mathematicians;
127:
111:
101:
89:
79:
58:
42:
34:
21:
1163:Anatolius d'Alexandrie:
920:Georges Declercq (2000)
817:Neugebauer (2016) 50–57.
790:"Index" (1854) xv–xxvii.
781:Neugebauer (2016) 92–95.
589:Kieffer, John S (2019).
419:
1266:Saints from Roman Syria
1236:Syrian Christian saints
1157:Anatolius of Alexandria
1147:Catholic Encyclopedia:
520:(in Dutch). Routledge.
370:Eastern Orthodox Church
240:
178:Anatolius of Alexandria
937:Biographie universelle
835:Mosshammer (2008) 202.
808:Neugebauer (2016) 113.
772:Schaff (1892) 885-892.
754:Zuidhoek (2017) 87–93.
736:Declercq (2000) 65–66.
645:Declercq (2000) 65–66.
634:Historia Ecclesiastica
560:Historia Ecclesiastica
360:was replaced with the
1128:Anatolius of Laodicea
1079:Catholic Encyclopedia
862:Neugebauer (1979) 99.
844:Neugebauer (1979) 98.
661:. BRILL. p. 69.
434:e = 25 6 17 28 9 20 1
409:Catholic Encyclopedia
227:Roman Catholic Church
166:Anatolius of Laodicea
84:Roman Catholic Church
29:Anatolius of Laodicea
259:Eusebius of Caesarea
174:Ἀνατόλιος Λαοδικείας
1256:People from Latakia
1241:3rd-century writers
1032:De ratione paschali
979:De ratione paschali
964:Lives of the Saints
799:Jones (1943) 22–26.
684:De ratione paschali
394:Cyril of Alexandria
314:De ratione paschali
214:and teacher of the
1251:3rd-century Romans
1126:Works by or about
700:10.1007/BF00374701
362:Gregorian calendar
350:computus paschalis
1074:St. Anatolius (1)
1053:978-2-503-57709-8
1019:978-1-56902-440-9
668:978-90-04-21707-2
527:978-1-134-55639-7
476:Paris Observatory
378:Dionysius Exiguus
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80:Venerated in
46:Early 3rd century
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595:Encyclopedia
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974:(casebound)
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333:Bollandists
216:Neoplatonic
200:Roman Syria
69:Roman Syria
62:July 3, 283
35:Bishop and
1246:283 deaths
1230:Categories
1132:Wikisource
996:: Oxford (
636:7.32.6–13.
632:Eusebius,
558:Eusebius,
486:References
405:Theophilus
386:Athanasius
291:Iamblichus
263:arithmetic
247:Alexandria
220:Iamblichus
153:Alexandria
113:Attributes
49:Alexandria
1208:Biography
724:120081352
708:0003-9519
600:3 January
283:astronomy
279:dialectic
231:feast day
212:computist
198:coast of
129:Patronage
91:Canonized
37:Confessor
716:41134008
572:Eunapius
390:Annianus
328:Laodicea
275:rhetoric
267:geometry
208:Platonic
192:Laodicea
185:Egyptian
180:, was a
75:, Syria)
65:Laodicea
1182:Portals
1070::
939:: Paris
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