53. Solar epacts
THE RECKONING OF TIME
725. Divide by 19:19 times 30 is 570 and 19 times 8 is 152, with 3 left over.
Multiply these by 11, which makes 33. Subtract 30, and the remainder is 3. The epact, that is, the lunar increment, is 3.46 /442/
53. SOLAR EPACTS
In the fourth column [tramite] of the 19-year cycle the solar epacts are designated, that is, the concurrent days of the week, which for three years always increase by the addition of one, but during leap year by the addition of two, up to the number seven. Their cycle runs for four times seven, or 28 years, because assuredly it cannot be completed until the leap-year day, which recurs in the fourth year, has fallen on every day of the week, that is, Sunday, Friday, Wednesday, Monday, Saturday,
Thursday, Tuesday; it runs through them in this order.
Although every day of the year has its concurrents, those concurrents which are particularly attached to the [19-year] cycle are those which designate the weekday of the 9th kalends of April [24 March]. This is so that, being placed quite close to the beginning of the Paschal festivity, they may very readily display the day of the epacts, or what day of the week the fourteenth Moon [falls on], and thereby smooth the way to the discovery of Easter Sunday. For every year, the same day of the concurrents will fall on the 2nd kalends of April [31 March], the 7th ides of April [7 April], the 18th kalends of May [14 April] and the 11th kalends of May [21 April]: it is helpful to the computist to memorize these.
The course of their cycle is such that whatever the concurrents are in leap year, they are the same ¢ve years earlier and six years later. Whatever they are in the ¢rst year after the leap year, they will be the same as those which occurred eleven years before, and those which will recur in six years. Those for the second year after the leap year are the same as those which occurred six years previously, and which will recur after eleven years. Those in the third year after leap year are the same as those which took place six years before, and which will revert after ¢ve years. And the regular pattern of this division applies to all the days of the revolving year.
Take careful note of the fact that because of this solar cycle, which runs for 28 years, it is necessary that 28 19-year cycles be completed before the identical sequence for the observation of Easter is repeated in 46 Cf. Dionysius Exiguus, Argumenta titulorum paschalium 3 (75).