39. Measuring the leap-year increment
TRANSLATION
heavens,347 it has been our care to gratify him with commonplace and perhaps rather concise and straightforward reasoning, so that he who did not learn to recognize the constellations in his elementary schooling
/401/ can at least discover what he needs to know by the lines of the sundial on the ground. He should know, then, that the Sun supplies this quarter-day to the year by brief delays and daily retardation, according to the ordering work of the Creator. Closer inspection shows that the Sun cannot be completely carried back to the same line on the sundial in 365 days. But if this year, for instance, at the [time of the] spring equinox (which according to the Egyptians, who bear the palm as computists, ordinarily comes on the 12th kalends of April [21
March]),348 the Sun rises in the mid-point of the east,349 on the same day a year later it will rise a little lower down.350 In the third, fourth and ¢fth years, it will augment this diminution, according to the natural measure of its course, to such a degree that unless the bissextile day is inserted beforehand according to custom, [the Sun] will then rise at the mid-point of the east to make the equinox on the 11th kalends of April [22 March], while at the same time continuing a regular pattern of retardation in its other risings and settings throughout the whole year regardless.
39. MEASURING THE LEAP-YEAR INCREMENT
But in case you ¢nd what we said concerning the measure of the leap-year increment obscure, we say that one quarter of that same day ^ that is, six hours ^ accumulates each year: one hour every two months, /402/ half an hour in every natural solar month, and indeed the fourth part of an hour (that is, a punctus) in half a month. For we know that the Sun goes around the zodiacal circle, that is, the twelve signs of the horoscope, in 347 Jones (BOT 372) thinks that Bede must be referring here, not to The ReckoningofTime, but to another tract composed by himself. He suggests that this is the text beginning Primo igitur anno praeparationis bissexti. . . (''In the ¢rst year leading up to the leap year . . .'') printed in PL 90.357^361A, and edited by Jones in BOD 649^653. This tract matches Bede's description, in that it discusses the leap-year increment in terms of the timing of the Sun's entrance into the various zodiac signs. To students unfamiliar with the zodiac, it would have been very challenging.
348 Bede, HE 5.21 (524); cf. On Times 10 (593.14^15); Dionysius Exiguus, Ep. ad Petronium (65.20^22).
349 I.e. on the celestial equator.
350 I.e. towards the south.
THE RECKONING OF TIME
365 days and 6 hours,351 and covers each sign of the same zodiac, according to its natural course, in 30 days and 10ˆ~˜ hours, and traverses half a sign in 15 days and 5ˆ~˘ hours. As for those who say that only three hours accrue to the bissextus every year, as if ascribing nothing to the night, we do not think that their judgement is to be accepted at all. If this were so, the whole day which accumulates would not be complete before the passage of seven years. For even the base herd [uulgus ignobile] know that a whole day, that is, [a day] together with its night, has 24 hours. If they do not deny that the whole [day] is ¢lled up in four years, why do they deny that one-fourth is ¢lled up by each of the four years?
In fact, should anyone think our position on this issue ought to be rejected, let him read the fourth book On the Trinity of the blessed Aurelius Augustine. In his discussion of the perfection of the number six in which the world is made, he does not neglect to mention this quarterday ^ nay rather, he teaches that it was made and ordained by the Creator's omnipotent wisdom for the sake of a certain hidden meaning. He says: For one and two and three make six, which /403/ number is said to be perfect because it is made up of its parts. For it has three [parts]: a sixth, a third, and a half. Nor is any other part found in it whose number can be expressed. One sixth of it is one, one third, two, and one half, three; and one and two and three total six. Holy Scripture commends its perfection to us, particularly because God ¢nished his work in six days, and on the sixth day, man was made in the image of God. And in the sixth age of the human race, the Son of God came and was made the Son of Man, that he might reshape us into the image of God. Now one year, if one considers 12 whole months of 30 days, which manifests the orbit of the Moon (for the ancients observed a month of this length), operates according to the number six. Six produces six in the ¢rst rank of numbers, which we know arrives at ten by units; it produces 60 in the second rank, which we know arrives at 100 by tens. Therefore 60 is the number of days in a sixth part of a year. And shortly thereafter he says:
Likewise the sixth of the second rank is multiplied by the sixth of the ¢rst rank, and six times 60 makes 360 days, which are 12 whole months. But as the orbit of the Moon marks the month for men, /404/ so the year is indicated by the circuit of the Sun. So there remain ¢ve and a quarter days until the Sun can complete its course and the year come to an end.
For four quarter-days make one day that must be intercalated in the 351 See above, ch. 16.