THE LETTER OF DIONYSIUS ON THE RECKONING OF EASTER, WRITTEN IN THE 526TH YEAR OF THE COMMON ERA OF CHRIST. To my lords most worthy of veneration, Boniface, chief of the notaries, and Bonus, second in rank, Dionysius Exiguus sends greeting. Having at length been compelled — by the long urging of the holy and venerable bishop Petronius — to commit to writing the rule of the Easter observance, I had believed that every ambiguity of divergence and all conflicting opposition was thereafter removed from the field:
especially because I had taken pains, with all my efforts, to instil the authority of the three hundred and eighteen holy bishops who had assembled at Nicaea, who in that venerable council, fixing the nineteen-year cycle by rule, noted down the fourteenth moons of the Easter observance as fixed and unchanging for all times by the law of their revolution. But since your holiness, when a question arose concerning this matter, has now brought forth from the archive of the Roman Church the writings of Paschasinus, the venerable bishop — who, as is established, presided over the holy Council of Chalcedon in the person of the most blessed Pope Leo — directed to that same Pope at that very time, which agree with the holy Fathers by evident reasoning, these I have inserted into the present work:
so that we might rely also on the testimony of this man, who by a manifest miracle confirms the Easter decrees of the venerable pontiffs. But since in his writings mention was made of common years and embolismic years, and this reckoning, which descends (so it is said) from the tradition of the Hebrews, is greatly inquired after by some, we have judged it necessary — for those wishing to know whether it seems to agree with the paternal rule — to set forth this account also, under forced brevity, lest it be proved to differ in any point. Let us know, therefore, that this same nineteen-year cycle always revolves within itself through an ogdoad and a hendecad. For that very number is unfolded into eight and eleven.
The ogdoad, then, which begins from the first year of the nineteen-year cycle (which is the seventeenth of the lunar cycle), is carried through in this manner: that it has the first and second years as common, that is, lesser; the third embolismic, that is, greater; the fourth and fifth years likewise common, the sixth embolismic, the seventh common, the eighth embolismic. And by this reckoning five common years and three embolismic are continuously assigned to the ogdoad. Now a common year gathers twelve lunar months, which make three hundred and fifty-four days. But an embolismic year is shown to have thirteen moons and three hundred and eighty-four days. Likewise the hendecad runs on by this law.
It begins from the ninth year of the nineteen-year cycle, which is the sixth of the lunar cycle; of which the first and second year is common, the third embolismic, the fourth and fifth common, the sixth embolismic, the seventh and eighth common, the ninth embolismic, the tenth common, the eleventh embolismic; and so the hendecad is terminated by seven common years and four embolismic. Now this reckoning of the embolismic years is shown to exist because it seems to make up the deficiencies of the common years, so that the lunar course may be equalised to the solar period. For although the moon goes round the circle of the solar year through each of its months, yet it cannot fill out its full completion in its twelve months.
Finally, in common years eleven days of the moon are seen to be lacking, by the reckoning of the solar year. But in embolismic years the moon is seen to exceed that same solar year by nineteen days. Wherefore let us bring forward into the open the years of the ogdoad and the hendecad, according to the order of the aforesaid cycle, and we shall clearly prove that through eight years and eleven the course of the moon keeps pace with the sun, since it gathers as many days as the sun has run. In the ogdoad we said there are five common years and three embolismic. Five times, then, three hundred and fifty-four make one thousand seven hundred and seventy; and three times three hundred and eighty-four make one thousand one hundred and fifty-two; and by this together they make one thousand nine hundred and twenty-two.
Likewise eight solar years, if reduced to a sum — that is, eight times three hundred and sixty-five, plus a quarter [for each] — make together two thousand nine hundred and twenty-two. In like manner too, the years of the hendecad, which are seven common and four embolismic, if you reckon them together in the sum by the computation we have stated, you will find them almost exactly as much as eleven solar years amount to, that is, four thousand and fourteen. This, then, is the reckoning of the embolismic years, as we said before: that by their increments they may compensate for the deficiencies of the common years. But now I will show you a most beautiful and excellent collation of the nineteen-year cycle itself, by which you may thereafter remove every ambiguity, if any should be stirred up:
and let no one be so struck with excessive astonishment as not to rejoice at the light of truth shown to him, and, leaving behind the darkness of ignorance, not at once to acquiesce in so great a reckoning. From the fifteenth moon of the Easter feast of the preceding year, for example, up to the fourteenth of the following Easter, if it is a common year, it will have three hundred and fifty-four days; if embolismic, three hundred and eighty-four. But if one day more or less should occur, it is a manifest error. Except, of course, in the first year of the oft-mentioned nineteen-year cycle, which we take care to count from the fourteenth moon of the Easter of the last, that is the nineteenth, year, up to the fourteenth of this same first year.
On this account, the same last year, then retaining eighteen epacts — that is, lunar additions — allots to the first year not eleven days, as is wont to happen in the other years, but twelve. And because they revolve in a span of thirty days, no epact is set at the beginning of this cycle, but the second year takes up eleven epacts. And therefore, as we said, there is no doubt that from the fifteenth moon of the Easter of the first cycle up to its end we find the prescribed days in the common and embolismic years. But if at any time it should perhaps have been set forth otherwise through the inexperience of those reckoning, by this observance the falsity of their computation will be exposed.
And that this may be understood more plainly, let us demonstrate it by the example of the present year. The indiction is indeed the fourth, and the lunar cycle the eleventh; the nineteen-year cycle is the fourteenth. And since it is the sixth year of the hendecad, it must needs be embolismic. Let us therefore inquire more diligently how many days there are from the fifteenth moon of the past feast up to the fourteenth of the present, and we shall find beyond doubt when we ought to celebrate Easter. The year being past, who would doubt — anyone who is known to take any care at all of this matter — that through the third indiction (at Easter) the fourteenth moon fell on the ninth day before the Kalends of April, that is, on the twenty-fourth of the month of March?
And therefore let us take the beginning of our counting from the eighth day before the Kalends of April: we have of March seven days, of April thirty, of May thirty-one, of June thirty, of July thirty-one, of August thirty-one, of September thirty, of October thirty-one, of November thirty, of December thirty-one, of January thirty-one, of February twenty-eight, of March thirty-one, of April twelve days, which is the day before the Ides of April. Together they make three hundred and eighty-four.
But if, according to the definition of those who reckon the moon otherwise than the truth holds, we should make the fourteenth fall not on the day before the Ides of April, but on the third before the Ides, three hundred and eighty-three days will be gathered with the number diminished; which can in no way be granted. And so always, as often as such a doubt arises, let us carefully compute, from the fifteenth moon of the past festival up to the fourteenth of Easter, the days that we seek. And if it is a common year, we shall find three hundred and fifty-four days; if it is embolismic, three hundred and eighty-four.
nor will any inequality occur at all, because the rule of this cycle subsists by this reckoning, whose precise formula we shall unfold in the description set out below. In the first year of the nineteen-year cycle, the seventeenth of the lunar cycle, from the fifteenth day before the Kalends of May up to the Nones of April, because it is common, there are three hundred and fifty-four days. In the second year of the nineteen-year cycle, the eighteenth of the lunar cycle, from the eighth before the Ides of April up to the eighth before the Kalends of April, because it is a common year, there are three hundred and fifty-four days. In the third year of the nineteen-year cycle, the nineteenth of the lunar cycle, from the seventh before the Kalends of April up to the Ides of April, because it is embolismic, there are three hundred and eighty-four days.
In the fourth year of the nineteen-year cycle, the first of the lunar cycle, from the eighteenth before the Kalends of May up to the fourth before the Nones of April, because it is common, there are three hundred and fifty-four days. In the fifth year of the nineteen-year cycle, the second of the lunar cycle, from the third before the Nones of April up to the eleventh before the Kalends of April, because it is common, there are three hundred and fifty-four days. In the sixth year of the nineteen-year cycle, the third of the lunar cycle, from the tenth before the Kalends of April up to the fourth before the Ides of April, because it is embolismic, there are three hundred and eighty-four days.
In the seventh year of the nineteen-year cycle, the fourth of the lunar cycle, from the third before the Ides of April up to the third before the Kalends of April, because it is common, there are three hundred and fifty-four days. In the eighth year of the nineteen-year cycle, the fifth of the lunar cycle, from the day before the Kalends of April up to the fourteenth before the Kalends of May, because it is embolismic, there are three hundred and eighty-four days. In the ninth year of the nineteen-year cycle, the sixth of the lunar cycle, from the thirteenth before the Kalends of May up to the seventh before the Ides of April, because it is common, there are three hundred and fifty-four days.
In the tenth year of the nineteen-year cycle, the seventh of the lunar cycle, from the sixth before the Ides of April up to the sixth before the Kalends of April, because it is common, there are three hundred and fifty-four days. In the eleventh year of the nineteen-year cycle, the eighth of the lunar cycle, from the fifth before the Kalends of April up to the seventeenth before the Kalends of May, because it is embolismic, there are three hundred and eighty-four days. In the twelfth year of the nineteen-year cycle, the ninth of the lunar cycle, from the sixteenth before the Kalends of May up to the day before the Nones of April, because it is common, there are three hundred and fifty-four days.
In the thirteenth year of the nineteen-year cycle, the tenth of the lunar cycle, from the Nones of April up to the ninth before the Kalends of April, because it is common, there are three hundred and fifty-four days. In the fourteenth year of the nineteen-year cycle, the eleventh of the lunar cycle, from the eighth before the Kalends of April up to the second before the Ides of April, because it is embolismic, there are three hundred and eighty-four days. In the fifteenth year of the nineteen-year cycle, the twelfth of the lunar cycle, from the Ides of April up to the Kalends of April, because it is common, there are three hundred and fifty-four days.
In the sixteenth year of the nineteen-year cycle, the thirteenth of the lunar cycle, from the fourth before the Nones of April up to the twelfth before the Kalends of April, because it is common, there are three hundred and fifty-four days. In the seventeenth year of the nineteen-year cycle, the fourteenth of the lunar cycle, from the eleventh before the Kalends of April up to the fifth before the Ides of April, because it is embolismic, there are three hundred and eighty-four days. In the eighteenth year of the nineteen-year cycle, the fifteenth of the lunar cycle, from the fourth before the Ides of April up to the fourth before the Kalends of April, because it is common, there are three hundred and fifty-four days.
In the nineteenth year of the nineteen-year cycle, the sixteenth of the lunar cycle, from the third before the Kalends of April up to the fifteenth before the Kalends of May, because it is embolismic, there are three hundred and eighty-four days.