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Year 13 (XIII) was a common year starting on Sunday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Silius and Plancus (or, less frequently, year 766 Ab urbe condita). The denomination 13 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.
During 248 AD, Philip the Arab celebrated Rome's first millennium, together with Ludi saeculares for Rome's alleged tenth saeculum. Coins from his reign commemorate the celebrations. A coin by a contender for the imperial throne, Pacatianus, explicitly states "Year one thousand and first", which is an indication that the citizens of the Empire had a sense of the beginning of a new era, a Saeculum Novum.
Also Pacatianus, usurper against Philip, celebrated the Saeculum Novum. This antoninianus bears the legend ROMAE AETER AN MIL ET PRIMO, "To eternal Rome, in its one thousand and first year".
1 ab urbe condita = 753 Before Christ
2 AUC = 752 BC
749 AUC = 5 BC
750 AUC = 4 BC (Death of Herod the Great)
753 AUC = 1 BC
754 AUC = 1 Anno Domini
755 AUC = 2 AD
759 AUC = 6 AD (Quirinius becomes governor of Syria)
2753 AUC = 2000 AD
2765 AUC = 2012 AD
According to Velleius Paterculus the foundation of Rome occurred 437 years after the capture of Troy by the Achaeans (1182 BC). It occurred soon before an eclipse of the Sun that was observed at Rome on 25 June 745 BC and had a magnitude of 50.3%. Its beginning occurred at 16:38, its middle at 17:28, and its end at 18:16
However, according to Lucius Tarrutius of Firmum, Romulus and Remus were conceived in the womb on the 23rd day of the Egyptian month Choiac, at the time of a total eclipse of the Sun. (This eclipse occurred on 15 June 763 BC, with a magnitude of 62.5% at Rome. Its beginning occurred at 6:49, its middle at 7:47 and its end at 8:51.) They were born on the 21st day of the month Thoth. The first day of Thoth fell on 2 March in that year. Rome was founded on the ninth day of the month Pharmuthi, which was 21 April, as universally agreed. The Romans add that about the time Romulus started to build the city, an eclipse of the Sun was observed by Antimachus, the Teian poet, on the 30th day of the lunar month. This eclipse on 25 June 745 BC (see above) had a magnitude of 54.6% at Teos, Asia Minor. It started at 17:49; it was still eclipsed at sunset, at 19:20. Romulus vanished in the 54th year of his life, on the Nones of Quintilis (July), on a day when the Sun was darkened. The day became like night, which sudden darkness was believed to be an eclipse of the Sun. It occurred on 17 July 709 BC, with a magnitude of 93.7%, beginning at 5:04 and ending at 6:57. (All these eclipse data have been calculated by Prof. Aurél Ponori-Thewrewk, retired director of the Planetarium of Budapest.) Plutarch placed it in the 37th year from the foundation of Rome, on the fifth of our July, then called Quintilis, also states that Romulus ruled for 37 years. He was either slain by the senate or disappeared during the 38th year of his reign. Most of these data have been recorded by Plutarch, Florus, Cicero, Dio (Dion) Cassius and Dionysius of Halicarnassus (L. 2). Dio in his Roman History (Book I) confirms this data by telling that Romulus was in his 18th year of age when he had initiated Rome. Thus, three eclipse calculations may be evidence for the suggestion that Romulus reigned from 746 BC to 709 BC, and Rome was founded during 745 BC.
Q. Fabius Pictor (c. 250 BC) tells that Roman consuls started for the first time 239 years after Rome's foundation. Livy gives almost the same, 240 years for that interval. Polybius tells that 28 years after the expulsion of the last Persian king Xerxes crossed over to Greece, and that event is fixed to 478 BC by two solar eclipses.