57. Formula based on the lunar cycle for ¢nding the age of the Moon on 1 January
TRANSLATION
In lunar year 16 (19-year cycle 19) running from the 16th kalends of January [17 December] up to the nones of December [5 December], there are 354 days, because it is common.
In lunar year 17 (19-year cycle 1) running from the nones of December [5 December] up to the 10th kalends of January [23 December], there are
384 days, because it is embolismic.
In lunar year 18 (19-year cycle 2) running from the 9th kalends of January [24 December] up to the 2nd ides of December [12 December], there are 354 days, because it is common.
In lunar year 19 (19-year cycle 3) running from the ides of December [13 December] up to the 2nd kalends of January [31 December], there are
384 days, because it is embolismic.50
The computation of the 17th lunar year begins on the same day on which the previous year ended, and not on the day following, as do the others, for this reason: so that one day will not seem to be lacking in that year, because of the so-called ''leap'' of the Moon. Dionysius, surveying the 19-year cycle in like fashion, taught the same thing: he brings the ¢nal year to a close on the same day on which the ¢rst year is to begin.51
57. FORMULA BASED ON THE LUNAR CYCLE FOR
FINDING THE AGE OF THE MOON ON 1 JANUARY52
Anyone who wants to can make a formula from the lunar cycle in order to ¢nd the age of the Moon on the kalends of January. Take any year of the lunar cycle, for instance, 5. Multiply by 11, and that makes 55.
Always add the regular [for January],53 and that makes 56. Divide by 30, and the remainder is 26. In the 5th year of the lunar cycle, the Moon is 26 days old on the kalends of January. Again, take 8. Multiply by 11, and it makes 88. Add one regular, and divide by /447/ 30, and 29 will be left over. In the 8th year of the lunar cycle, the Moon will be 29 days old
50 Bede's model here is the analogous list of years in the 19-year cycle in Dionysius
Exiguus, Epistola ad Bonifacium et Bonum (85^86).
51 Cf. ch. 42.
52 This chapter is based on (ps.-)Dionysius Exiguus, Argumenta 13 (78.9^15).
53 The lunar regular for January in this case is 1,because the lunar cycle begins in a year when the Moon is one dayold on 1 January.Compare the lunar regulars for the 19-year cycle, explained in ch. 20 and Commentary.