Epistola 'De Ratione Paschae'

The Letter of Dionysius on the Reckoning of Easter, Written in the Common Year of Christ 76. To my most revered lords, Boniface, the chief notary, and Bonus, the second notary, Dionysius the Small sends greetings. Having been long urged by the holy and venerable bishop Petronius to commit to writing the rule for the observance of Easter, I was at last compelled to do so, and I believed that thereafter all ambiguity of diversity and all opposition had been removed, especially because I had taken care to set forth with all my might the authority of the three hundred and eighteen holy bishops who had assembled at Nicaea, who in that venerable council, by regularly fixing the nineteen-year cycle, noted down the fourteenth moons of the paschal observance as immovable for all times by the law of their own revolution. But since your holiness, when a question on this matter arose, has now brought forth from the archives of the Roman Church the writings of the venerable bishop Paschasinus, who is known to have presided over the holy Council of Chalcedon in the place of the most blessed Pope Leo, writings sent to that same pope at that time, which agree with the holy Fathers by evident reason, I have inserted these into the present work, so that we might also rely on the testimony of this man, who by a manifest miracle confirms the paschal decrees of the venerable pontiffs.

Now because in his writings mention is made of common years and embolismic years, and this reckoning, which is said to descend from Hebrew tradition, is greatly sought after by some who wish to know whether it appears to be in harmony with the ancestral rule, we have deemed it necessary to set forth this knowledge as well, in compressed brevity, lest it be found to disagree in any respect. Let us therefore know that this same nineteen-year cycle always revolves within itself through the ogdoas and the hendecas. For the number itself is made up of eight and eleven. The ogdoas, therefore, which begins from the first nineteen-year cycle, which is the seventeenth lunar year, is completed in this manner: that it has the first and second years common, that is, shorter; the third embolismic, that is, longer; the fourth and fifth years likewise common; the sixth embolismic; the seventh common; the eighth embolismic. And by this means, five common years and three embolismic years are constantly assigned to the ogdoas. A common year, moreover, gathers twelve lunar months, which make three hundred fifty-four days. An embolismic year, however, is shown to have thirteen moons and three hundred eighty-four days. Likewise, the hendecas runs its course under this rule.

It begins with the ninth cycle of nineteen years, which is the sixth lunar cycle; its first and second years are common, the third is embolismic, the fourth and fifth are common, the sixth is embolismic, the seventh and eighth are common, the ninth is embolismic, the tenth is common, the eleventh is embolismic, and thus the hendecad ends with seven common years and four embolisms. Moreover, this system of embolisms is proven to exist because it seems to supply the deficiencies of common years, so that the lunar course may be equalized to the solar time. For although the moon traverses the circle of the solar year through each month, it is unable to complete its perfection in its own twelve months. Indeed, in common years, eleven days of the moon are seen to be lacking relative to the reckoning of the solar year. In embolismic years, however, the moon appears to exceed the same solar year by nineteen days. Therefore, let us set forth the years of the ogdoad and the hendecad according to the order of the aforementioned cycle, and we will clearly prove that over eight years and eleven the moon’s course contends with the sun, when it gathers as many days as the sun has run.

In the ogdoad we said that five years are common, three embolismic. Therefore five times 354 makes 1,770; and three times 384 makes 1,152; and thus together they become 2,922. Similarly, eight solar years, if reduced to a sum, that is eight times 365 and a quarter, together make 2,922. In like manner, the years of the hendecad, which are seven common and four embolismic, if you gather them into a sum by the calculation we have described, you will find almost the same amount as eleven solar years produce, that is four times 1,014. This, therefore, is the rationale of the embolisms, as we have said before, so that by their increments they compensate for the deficiencies of the common years. But now I will show you a most beautiful and clear collection of the nineteen-year cycle itself, by which you may remove all subsequent ambiguity, if any should arise; nor should anyone be so struck by excessive stupor that he does not rejoice in the light of truth shown to him, and, having abandoned the darkness of ignorance, does not immediately acquiesce to such great reasoning. From the fifteenth moon of the paschal feast of, for example, the preceding year, up to the fourteenth of the following Easter, if the year is common, it will have 354 days; if embolismic, 384. But if one day more or less should occur, the error is evident.

except for the first year of the often-mentioned nineteen-year cycle, which we take care to count from the fourteenth moon of the last Easter, that is, of the nineteenth year, up to the fourteenth of that same first year. For this reason, that same last year, then retaining eighteen lunar epacts, that is, additions, supplies twelve days to the first year, not eleven, as is usually done in the other years. And because the cycles are completed at the end of thirty days, no epact is placed at the beginning of the cycle itself, but the second year receives eleven epacts: and therefore, as we have said, from the fifteenth moon of the Easter of the first cycle up to its end, there is no doubt that we find the prescribed days in common and embolismic years. But if this has perhaps been otherwise set forth by the inexperience of some calculators, the falsity of their reasoning will be refuted by this method of calculation. And so that this may be more clearly understood, let us demonstrate it by the example of the present year. For the indiction is 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 necessarily be an embolismic year. Therefore, from the fifteenth moon of the past feast up to the fourteenth of the present, let us diligently inquire how many days there are, and we will undoubtedly find when we ought to celebrate Easter.

After the third indiction year has passed, who, having even the slightest care for this matter, would doubt that the fourteenth moon of Easter was on the ninth day before the Kalends of April, that is, the twenty-fourth day of March? And therefore let us take the beginning of our counting from the eighth day before the Kalends of April: we have seven days of March, thirty of April, thirty-one of May, thirty of June, thirty-one of July, thirty of August, thirty of September, thirty-one of October, thirty of November, thirty-one of December, thirty-one of January, twenty-eight of February, thirty-one of March, and twelve days of April, which is the day before the Ides of April. Together they make three hundred eighty-four. But if, according to the definition of those who compute the moon otherwise than the truth holds, the fourteenth moon should occur not on the day before the Ides of April, but on the third day before the Ides, then a reduced number of three hundred eighty-three days would be collected, which is allowed by no means. And thus always, whenever such a doubt occurs, let us diligently count the days from the fifteenth moon of the past feast up to the fourteenth moon of the Easter we seek. And if it is a common year, we will find three hundred fifty-four days; if it is an embolismic year, we will find three hundred eighty-four: nor will any inequality arise, because the rule of this cycle stands by this reasoning, whose clear formula we will set forth in the appended description.

In the first year of the nineteen-year cycle, the lunar year being the seventeenth, from the fifteenth day before the Kalends of May to the Nones of April, because it is a common year, there are three hundred fifty-four days. In the second year of the nineteen-year cycle, the lunar year being the eighteenth, from the eighth day before the Ides of April to the eighth day before the Kalends of April, because it is a common year, there are three hundred fifty-four days. In the third year of the nineteen-year cycle, the lunar year being the nineteenth, from the seventh day before the Kalends of April to the Ides of April, because it is an embolismic year, there are three hundred eighty-four days. In the fourth year of the nineteen-year cycle, the lunar year being the first, from the eighteenth day before the Kalends of May to the fourth day before the Nones of April, because it is a common year, there are three hundred fifty-four days. In the fifth year of the nineteen-year cycle, the lunar year being the second, from the third day before the Nones of April to the eleventh day before the Kalends of April, because it is a common year, there are three hundred fifty-four days.

In the sixth year of the nineteen-year cycle, the lunar year being the third, from the tenth day before the Kalends of April to the fourth day before the Ides of April, because it is an embolismic year, there are three hundred eighty-four days. In the seventh year of the nineteen-year cycle, the lunar year being the fourth, from the third day before the Ides of April to the third day before the Kalends of April, because it is a common year, there are three hundred fifty-four days. In the eighth year of the nineteen-year cycle, the lunar year being the fifth, from the day before the Kalends of April to the fourteenth day before the Kalends of May, because it is an embolismic year, there are three hundred eighty-four days. In the ninth year of the nineteen-year cycle, the lunar year being the sixth, from the thirteenth day before the Kalends of May to the seventh day before the Ides of April, because it is a common year, there are three hundred fifty-four days. In the tenth year of the nineteen-year cycle, the lunar year being the seventh, from the sixth day before the Ides of April to the sixth day before the Kalends of April, because it is a common year, there are three hundred fifty-four days.

In the eleventh year of the nineteen-year cycle, the lunar year being the eighth, from the fifth day before the Kalends of April to the seventeenth day before the Kalends of May, because it is an embolismic year, there are three hundred eighty-four days. In the twelfth year of the nineteen-year cycle, the lunar year being the ninth, from the sixteenth day before the Kalends of May to the day before the Nones of April, because it is a common year, there are three hundred fifty-four days. In the thirteenth year of the nineteen-year cycle, the lunar year being the tenth, from the Nones of April to the ninth day before the Kalends of April, because it is a common year, there are three hundred fifty-four days. In the fourteenth year of the nineteen-year cycle, the lunar year being the eleventh, from the eighth day before the Kalends of April to the second day before the Ides of April, because it is an embolismic year, there are three hundred eighty-four days. In the fifteenth year of the nineteen-year cycle, the lunar year being the twelfth, from the Ides of April to the Kalends of April, because it is a common year, there are three hundred fifty-four days.

In the sixteenth year of the nineteen-year cycle, the lunar year being the thirteenth, from the fourth day before the Nones of April to the twelfth day before the Kalends of April, because it is common, there are 354 days. In the seventeenth year of the nineteen-year cycle, the lunar year being the fourteenth, from the eleventh day before the Kalends of April to the fifth day before the Ides of April, because it is an embolismic year, there are 384 days. In the eighteenth year of the nineteen-year cycle, the lunar year being the fifteenth, from the fourth day before the Ides of April to the fourth day before the Kalends of April, because it is common, there are 354 days. In the nineteenth year of the nineteen-year cycle, the lunar year being the sixteenth, from the third day before the Kalends of April to the fifteenth day before the Kalends of May, because it is an embolismic year, there are 384 days.