Liber De Pascate Sive Cyclus Paschalis

Here begins the book of Dionysius Exiguus. Preface. To the most blessed and most beloved father, Petronius, bishop, Dionysius Exiguus. The reckoning of the Paschal feast, which the insistence of many has long and frequently demanded of us, we have now, aided by your prayers, taken care to explain. Following in all things the venerable three hundred and eighteen pontiffs who gathered at Nicaea, a city of Bithynia, against the madness of Arius, and their already absolute and true judgment on this matter; who fixed the fourteenth moons of the Paschal observance, through the nineteen-year cycle always returning into itself, as stable and immovable, which, in every age, by the same beginning by which they are repeated, glide without the variation of a divergent course. Moreover, they established this rule of the aforementioned cycle not so much by secular learning as by the illumination of the Holy Spirit, and are seen to have placed it as a firm and stable anchor for this reckoning of the lunar measure. This rule, afterwards, some either despising through arrogance, or transgressing through ignorance, led astray by the fables of the Jews, handed down a different and contrary form of the unique feast. And because without the solidity of a foundation no structure can stand, they chose to set forth the Lord's Pascha and the computation of the moon far otherwise in certain years, arranging disordered cycles; which not only have no stability of recurrence, but also exhibit a course marked by error.

But the archbishop of the city of Alexandria, the blessed Athanasius, who himself was present at the Council of Nicaea, then serving as deacon to the pontiff Saint Alexander, and was an assistant in all matters, and afterwards the venerable Theophilus and Cyril, have in no way departed from the venerable constitution of this synod. Rather, diligently retaining that same nineteen-year cycle, which is called enneacaidecaeteris in Greek, they are shown to have interpolated the Paschal course with no variations. Finally, Pope Theophilus, dedicating a course of one hundred years to the elder Emperor Theodosius, and Saint Cyril, composing a cycle of times of ninety-five years, have in all respects preserved this tradition of the holy council for observing the Paschal fourteenth moons. And because for those who are studious and seek to know what is true, the rule of this same cycle ought to adhere more firmly, we have believed it should be appended after our preface.

We have therefore endeavored to expedite this cycle of ninety-five years with all the diligence we could, presenting in this work the last of the same blessed Cyril, that is, his fifth cycle, since one hundred and six years still remained, and we profess that we have thereafter arranged five others according to the norm of the same pontiff, or rather of the oft-mentioned Council of Nicaea. But because Saint Cyril began his first cycle in the one hundred and fifty-third year of Diocletian and ended his last in the two hundred and forty-seventh, we, beginning from the two hundred and forty-eighth year of that tyrant rather than prince, have chosen not to bind our cycles to the memory of an impious man and persecutor, but have preferred to mark the times from the incarnation of our Lord Jesus Christ, so that the beginning of our hope might be more familiar to us, and the cause of human redemption, that is, the passion of our Redeemer, might shine forth more clearly.

We have further thought it right to warn the reader that this cycle of ninety-five years which we have made, when, after the completion of the period, it begins to return upon itself, does not in all respects maintain the proposed stability. For although the years of our Lord Jesus Christ preserve their order in an unbroken series, and the indictions run through fifteen years in their usual revolution, and the epacts also, which the Greeks call, that is, the annual lunar additions of eleven, which return upon themselves at the end of thirty days, you find noted down by fixed rules, and likewise the nineteen-year cycle and the paschal fourteenth moons you find the same in the revolution of all ages; nevertheless, the concurrent days of the weeks and the days of the Lord's Passover and the moon of that same Lord's day cannot maintain a similar constancy. Now the reckoning of the concurrents of the week, which arises from the course of the sun, is terminated by a seven-year continuous circuit. In this, for each single year you will count one; in that year only in which there is a bissextile, you will add two. This cause also makes it appear that this cycle of ninety-five years is not in all respects in agreement with its recurrence. For while in the other years it does not differ, in those years alone in which the bissextile interposes, the Lord's Passover with its moon occurs in a varying manner of reckoning. But those who run through all times in a fixed order can, by their stable circuit, direct the case of the movable elements without any difficulty.

And therefore, after the completion of the ninety-five years, when one diligently wishes to return to the beginning of these matters, let him not run back to the fifth cycle of St. Cyril, which we have necessarily set before us, but let him run attentively to our first; and, in the order we have stated, through those which maintain a fixed course, let him sustain the progress of those which seem to waver. We have also judged that the following should be noted with no less care, lest we be mistaken in the recognition of the first month. For nearly all error and discrepancy concerning Easter arises from this, when the beginning of the time is unknown. For when the almighty Lord commanded this most sacred solemnity to be celebrated by the children of Israel, who were being freed from Egyptian servitude, he says in the book of Exodus to Moses and Aaron in the land of Egypt: "This month is the beginning of months; it shall be the first of the months of the year." And likewise in the same place: "In the first month," he says, "on the fourteenth day of the month, at evening, you shall eat unleavened bread until the twenty-first of the same at evening." In Deuteronomy also, the same lawgiver Moses thus admonishes the people concerning this matter, saying: "Observe the month of new grain, and the first of springtime, that you may keep the Passover to the Lord your God, because in this month the Lord your God led you out of Egypt by night." By such great divine authority it has been made clear that the Paschal feast ought to be celebrated in the first month, on the fourteenth day, at evening, until the twenty-first.

But because it is not clearly read there where this month begins or where it ends, the aforementioned venerable three hundred and eighteen pontiffs, more diligently investigating the observance of the ancient custom handed down from holy Moses, as is related in the seventh book of the Ecclesiastical History, decreed that the new moon which makes the beginning of the first month occurs from the eighth day before the Ides of March up to the day of the Nones of April; and that the fourteenth moon is to be sought more diligently from the twelfth day before the Kalends of April up to the fourteenth day before the Kalends of May; which, because it does not revolve equally with the course of the sun, within such spans of days, follows the occurrence of the vernal equinox, which is especially noted on the twelfth day before the Kalends of April according to the opinions of all the Easterners, and especially of the Egyptians, who are more skilled than all in calculation. In which, even if the fourteenth moon should happen on a Sabbath, which is manifestly known to occur once in ninety-five years, the same holy synod without ambiguity established that Easter should be celebrated on the following Lord's day, that is, on the eleventh day before the Kalends of April, the fifteenth moon, admonishing in every way that no one should seek the fourteenth moon of the paschal feast before the twelfth day before the Kalends of April; which would be established as not of the first month, but of the last.

But we have thought this also not to be passed over, that those who, estimating that the moon completes the course of its cycle in a space of thirty days, count twelve lunar months as three hundred and sixty days, to which they also add five days, which antiquity called intercalary, so that they seem to fulfill the solar year, are greatly in error; since diligent inquiry into the truth has shown that in two lunar cycles not sixty days, but fifty-nine ought to be counted. And by this, in twelve lunar months a total of three hundred and fifty-four days is collected, to which the Egyptians add annual epacts, that is, eleven days, so that finally the lunar measure is made equal to the solar reckoning. That this is most true and most certain is confirmed by the opinion of the above-written Fathers, who, according to this calculation of the Egyptians, handed down the fourteenth moons of the paschal observance. But some, ignorant of such subtlety, or rather of such sanction, while they seek other arguments of computation, depart from the path of truth. Whence it often happens that what the often-mentioned Fathers set as the fourteenth moon, these suspect to be the fifteenth; and what is the twenty-first, they pronounce to be the twenty-second. But for us, who have love and care for the Christian religion, it is proper to depart in no way from the constitution of such great pontiffs; but it is fitting to keep the paschal rule fixed by them with the most sincere devotion.

How great indeed is the authority of these Fathers, which we strive to follow in the Churches spread throughout the whole world, it is not laborious to show, since the holy council convened at Antioch not long after those times decreed that the definition which they first set forth concerning the paschal reckoning was in no way to be violated. Finally, in the holy canons under the seventy-ninth title, which is the first of that Antiochene council, it is found expressed in these words: We decree that all who have dared to dissolve the definition of the holy and great council which was assembled at Nicaea, in the presence of the most pious and venerable Emperor Constantine, concerning the salutary paschal solemnity, are to be excommunicated and expelled from the Church, if, however, they persist more contentiously against those things which have been well decreed. And let these things be said concerning the laity. But if any of those who preside over the Church, whether bishop, or presbyter, or deacon, after this definition attempts, to the subversion of the peoples and the disturbance of the Churches, to assemble separately and to celebrate Easter with the Jews, the holy synod has judged this man already from this point alien from the Church: because he has been a cause of corruption and disturbance not only to himself but to very many. And not only does it remove such persons from ministry, but also those who after such condemnation have attempted to communicate with them are condemned, and are deprived of every external honor which the holy rule and the priesthood of God have merited.

Not dissimilar to these are the pronouncements of the venerable Pope Leo I, prelate of the apostolic see, who says: "Against the statutes of the canonical fathers, which many years ago in the city of Nicaea were established by spiritual decrees, nothing is permitted to anyone to dare; so that if anyone wishes to decree something different, he diminishes himself rather than corrupts them." And if these, as is fitting, are kept inviolate by all pontiffs, there will be peace and firm concord throughout all churches. And again: "In all ecclesiastical matters," he says, "we obey those laws which the Holy Spirit instituted through the three hundred and eighteen bishops for the peaceful observance of all priests; so that even if many more should decree something other than what they established, whatever is different from the constitution of the aforesaid is to be held in no reverence." Sufficiently, as we think, it is indicated to all that henceforth the most sacred Easter is not to be celebrated otherwise than as established by the holy Fathers. But if anyone, with an obstinate mind, should perhaps despise the testimonies of such great priests, he will also find similar things briefly set forth in ecclesiastical history; and through the account of many pontiffs, and especially of the blessed Athanasius, whom we mentioned above, he will come to know that these same things have been made public. Indeed, the very same thing is attested by the letter of the holy Proterius, bishop of the city of Alexandria, sent to the same Pope Leo concerning this same paschal question.

Which we, having translated from Greek before these years, have seen fit to be appended to this work. We have also subjoined the arguments sought by the sagacity of the Egyptians, by which, if perhaps they are unknown, the paschal titles can be easily discovered: that is, what year it is from the incarnation of the Lord, and what the indiction is, what also the lunar cycle or the nineteen-year cycle is, and the rest are sought by a similar compendium of calculation. May divine grace deign to preserve your blessedness praying for us. Here ends the preface. THE NINETEEN-YEAR CYCLE OF DIONYSIUS. Here begins the nineteen-year cycle, which the Greeks call the Enneacaidecaeteris, established by the holy Fathers, in which the paschal fourteenth moons are found at all times without any falsehood; only you must remember each year which cycle of the moon and which nineteen-year cycle exists. In the present, indeed, it is the third indiction, the consulship of the younger Probus, the thirteenth nineteen-year cycle, the tenth lunar cycle.

This year with its characters from the cycle of Dionysius, Bede in his work *On the Reckoning of Time*, chapter 45, mentions in these words: Because therefore the second year of the cycle, which Dionysius first wrote, the five hundred and twenty-third from the incarnation of the Lord, is completed, that year is indeed, according to the concurrence of the stars, that in which he deigned to be incarnate; for this second year of the nineteen-year cycle is the eighteenth of the lunar cycle, having eleven epacts and seven concurrent weekdays, the paschal moon the fourteenth on the eighth before the Kalends of April. Paschal Arguments. Here begin the arguments concerning the paschal titles, investigated by the sagacity of the Egyptians, so that they may indicate the present [years]. First Argument: On the years of Christ. If you wish to know what year it is from the incarnation of our Lord Jesus Christ, compute fifteen times thirty-four, they make five hundred and ten; to these always add twelve regulars, they make five hundred and twenty-two; also add the indiction of the year you wish, for example, the third, the consulship of Probus the younger, they make together five hundred and twenty-five. These are the years from the incarnation of the Lord.

ARG. II b. On the indiction. If you wish to know what the indiction is, for example, in the consulship of Probus the Younger, take the years from the incarnation of our Lord Jesus Christ, 525. Always add 3 to these, making 528. Divide these by 15, 3 remains. It is the third indiction. If nothing remains, it is the fifteenth indiction. ARG. III d. On the epacts. If you wish to know how many the epacts are, that is, the lunar additions, take the years from the incarnation of our Lord Jesus Christ, as many as there have been, 525. Divide these by 19, 3 remains. Multiply by 11, making 132. Divide these again by 30, 12 remains. There are twelve lunar additions. [Another computation. — Count from the first year up to whichever you wish, for example, to the year. Always subtract 1, 9 remains. Multiply by the 9 years the 11 annual epacts, and you will make nine times eleven, 99. Divide these by 30, that is, three times thirty, 90, 9 remains. The ninth is the epact of the nineteen-year cycle. Thus in year 11. Subtract one, 10 remains. Ten times eleven, 110. Divide these by 30, 20 remains. The twentieth lunar epact will be of the nineteen-year cycle in year 11. Thus you will compute through all nineteen years under this brevity.]

ARG. IV g. On the concurrents. If you wish to know the additions of the sun, that is, the concurrent weekdays, take the years from the incarnation of the Lord, how many there have been, for example 525; through the third indiction and always add a fourth part of the years that have been, that is, now 131, which together make 656. To these add 4, they make 660. Divide these by 7, 2 remain. These are the epacts of the sun, that is, the concurrent weekdays, for the aforementioned indiction, the consulship of Probus the Younger. [Likewise, a recently discovered method, I have indicated better, if it is briefly made clear. Compute in a similar way from the year which is after the consulship of our lord Tiberius the Younger Augustus, only so that at the end, where the above calculation has 4 added, you now add not 4 but 1 for the bissextile.] ARG. V b. On the nineteen-year cycle. If you wish to know what the year of the cycle of 19 years is, take the years of the Lord, for example, 525, and always add one, they make 526. Divide these by 19, 13 remain. The thirteenth is the year of the nineteen-year cycle. But if nothing remains, it is the nineteenth.

ARG. VI d. On the lunar cycle. If you wish to know what the lunar cycle is, which is contained in the nineteen-year cycle, take the years of the Lord, for example 525, and always subtract 2, and 523 remain. Divide these by 19, 10 remain. The tenth lunar cycle of the nineteen-year cycle. But whenever nothing remains, it is the nineteenth. ARG. VII. On the fourteenth moon in the month of March. If you wish to know in which years of the nineteen-year cycle the paschal fourteenth moon occurs in the month of March: in years II, V, VII, X, XIII, XVI, XVIII, you will find these above-written years in the month of March; the remaining twelve, according to the rule subjoined below, you will without doubt calculate in the month of April. ARG. VIII e. On the bissextile day. If you wish to know when the bissextile day is, take the years of the Lord, for example 525. Divide these by 4. If nothing remains, it is a bissextile year. If 1 or 2, or 3 remain, it is not a bissextile year. Lest perhaps some fog of error occur to you, throughout every computation through which you divide, if nothing is left over, recognize that computation to be that through which you divide, as for example, if you divide by 19, and nothing is left over, it is the nineteenth; if by 15, the fifteenth, and, if by 7, the seventh.

ARG. IX f. On the paschal moon in the month of March. If you wish to know what moon of the paschal feast occurs: if Easter is celebrated in the month of March, count the months from September to March; they are 6. To these always add the regulars 2, making 8; add the epacts, that is, the lunar additions of whatever year you wish, for example, of the third indiction I XII, making 20; and the day of the month on which Easter is celebrated, that is, March 30, making together 50. Subtract 30, 20 remain; the 20th is on the day of the Lord’s resurrection. In the month of April. — But if we celebrate Easter in the month of April, count the months from September to March, they are 7. To these always add 2, making 9. Add the epacts of the moon of whatever year you wish, for example, of the fourth indiction h, XXIII, which make 32, and the day of the month on which we celebrate Easter, that is, April 19, which likewise make 51; subtract 30, 21 remain. The 21st moon is on the day of the Lord’s resurrection.

If you seek from September up to December, you shall always add three regulars in these four months; but in a bissextile year only, you shall count two regulars for the aforementioned months, and for the 22nd day, in each single year you shall assume at the end of December the 12th. ARG. X. On the day of the holy week, the paschal ferial. If you wish to know what day of the week it is, take the days from January up to the month you wish, for example, to the 30th day of the month of March, they are 89. To these you shall always add one, making 90; and always add the solar epacts, that is, the concurrents of the week-days of whatever year you wish, for example, indiction 2, making together 92. Divide these by 7, one remains: that is the paschal Sunday of the feast. Thus, for any day from the 1st of January up to the 30th day of the month of December, you will find what ferial it is by computing, so that you assume together the one regular and the concurrents, which always begin in the month of January.

ARGUMENT XI. On the moon of the Paschal term. If you wish to know what moon it is on the eleventh day before the Kalends of April, take the years of the Incarnation of our Lord Jesus Christ, for example, 675. Divide these by 19, the result is 110. Divide by 30, the remainder is 20: the moon is the twentieth on the eleventh day before the Kalends of April. But if it were 7, it would be the seventh; if 1, the first. ARGUMENT XII. If you wish to know, for each year, what day of the week the Kalends of January fall on, take the years of the Incarnation of our Lord Jesus Christ, for example, the year 675. Subtract one, the remainder is 674. Divide these by a fourth part, and the fourth part which you have divided, you add to 674, making together 842. Divide these by 7, the remainder is 2. The second day of the week is the Kalends of January. If it were 5, it would be the fifth day of the week; if 1, the Lord's day; if 0, the Sabbath. ARGUMENT XIII. On the moon of the Kalends of January. If you wish to know what moon it is on the Kalends of January, know what the lunar cycle is, for example, cycle 15. Keep one for yourself, that is, the Kalends of January themselves, and multiply five times fifteen: they make 75; which you add to one, and they make 76. Likewise multiply six times fifteen, they make 90; which you add to 76, and thus the sum of the numbers is 166; divide these by 30, the remainder is 16. The sixteenth moon is on the Kalends of January, and 16 points. In this way, through the 19 lunar cycles, you will always compute, and on the Kalends of January, what moon it is, you will find without error.

When you have come to the 17th of the lunar cycle, and you have multiplied five times seventeen, over the Kalends of January, which make 85, if you divide by sixty, and add that same unit, they become 86. Then you multiply six times seventeen, they become 102. You add these to the 86, and they become 188. Divide there by thirty, 9 remain. The ninth moon is on the Kalends of January, and 26 points. Thus you will do also in the 18th and 19th cycle. But from the first lunar cycle up to the sixteenth, you shall not divide by sixty, lest you fall into error. ARGUMENT XIV. On what day of the week the 14th moon falls in the first year of the nineteen-year cycle. Here begins the calculation of how it may be found on what day of the week the 14th Paschal moon falls in each year, that is, of the first nineteen-year cycle. In the first year, because it has no lunar epacts, since from the 18th of the lower nineteenth year, and its 11 epacts, with also one day added by the Egyptians, they become 30, that is, a complete moon of one month, and nothing remains of the epacts, and because in the month of April in that year the 14th Paschal moon falls, keep the regulars in that month always as 35, subtract 30, that is, that same complete moon, and 5 remain. On the fifth day from the Kalends, that is, the Nones of April, the 14th Paschal moon occurs. Keep the above-written 5, add the concurrents of that same year, 4, they become 9. Add the regulars in that same month of April always, 7, they become 16. Divide these by 7, that is, twice seven is 14, 2 remain.

In the second year, the 14th paschal moon occurs on the second feria, and the Lord's day of the paschal feast on the 20th day of the moon. Second year. — Likewise, the second year of the aforementioned cycle, from which the epacts take their beginning, is 11. In that year, the 14th paschal moon falls in the month of March. Always take 36 regulars in it, always subtract the epacts 11, 25 remain. On the 25th day from the Kalends of March, which is the 8th before the Kalends of April, the 14th moon of the Passover occurs. Take the aforementioned 25, add the concurrents of the same year 5, they become 30. Always add at the end of this month the regulars 4, divide these by 7, that is, seven times four is 28, 2 remain. The 14th paschal moon occurs on the sixth feria, and the Lord's day of the paschal feast on the 16th day of the moon. Third year. — Likewise, in the month of April of the often-mentioned cycle, the first third year. Always take in that month, first of all, the regulars 35. Subtract the epacts of the same year 22, 13 remain. On the 13th day of the month, that is, the Ides of April, the 14th paschal moon occurs. Take these 13, add the concurrents 6, they become 19. Always add in April the lower regulars 7, they become 26. Divide these by 7, three times seven is 21, 5 remain. The 14th paschal moon will be on the fifth feria, and the Lord's day of the paschal feast on the 17th day of the moon. Thus you will calculate for each year from the first up to the ninety-fifth year.

If the 14th paschal moon occurs in the month of March, you should first hold 36 regulars, from which you subtract the epacts of whichever year you wish, and add the concurrents, and at the end: always increase by 4 regulars. In the month of April, however, always hold 35 at the beginning, from which, as above, subtract the epacts, and with the concurrents of the same year added to their regulars, increase by 7 at the end. For you will calculate all paschal arguments more easily and briefly. Yet let this also be known to the reader: whenever in both the aforementioned months it happens in the first rule that, after subtracting the epacts, more than 30 remain, discard the 30. If one or two, or more, remain over, that many days from the Kalends of January is the 14th paschal moon of that month. But when, after subtracting the epacts, less than 30 remain—for example, 20, or more or less—which is manifestly known to happen once in 19 years, the 14th paschal moon will be on the 30th day of April.

ARGUMENT 15. On the day of the equinox and solstice. On which day the Lord Jesus Christ was born according to the flesh from the Virgin Mary in Bethlehem, on which day the day begins to grow longer. The first equinox is on the 8th day before the Kalends of April, on which day the day is equal to the night. On the same day Gabriel announces to Saint Mary, saying: "The Holy Spirit will come upon you, and the power of the Most High will overshadow you." For this reason, he who will be born from you will be called the Son of God. On which day also Christ suffered according to the flesh. The second solstice is on the 8th day before the Kalends of July, on which day also Saint John the Baptist was born, and on which the day begins to grow shorter. The second equinox is on the 8th day before the Kalends of October, on which day John the Baptist was conceived. And from this point the day becomes shorter than the night, until the birthday of the Lord Savior. From the 8th day before the Kalends of April to the 8th day before the Kalends of January, 271 days are counted. Hence, according to the number of days, our Lord Christ was conceived on the Lord's day, the 8th day before the Kalends of April, and was born on the third feria, the 13th day before the Kalends of January, our Lord Christ. On the day on which he suffered, there are 133 years and 3 months, which are 11,414 days. Hence, according to the number of days, he was born on the third feria and suffered on the sixth feria: born on the 8th day before the Kalends of January, suffered on the 8th day before the Kalends of April. From the time when our Lord Jesus Christ was baptized, there are 2 years, and 90 days are counted, which make 820, with their bissextile days, and thus he is baptized on the 8th day before the Ides of January, the fifth feria, and suffered, as I said above, on the 8th day before the Kalends.

April, the sixth day of the week. With the bissextile days, they together make 12,415 days, and from the eighth day before the Ides of January to the eighth day before the Kalends of April, 90 days. ARGUMENT 16. On the reckoning of the bissextile day. The bissextile day is not made because of that day on which, as some think, Joshua prayed for the sun to stand still; for that day both was and has passed. But it is called bissextus because in each month one punctus increases. Now one punctus is a quarter of an hour. Four puncti make one hour; twelve puncti complete three hours. Therefore in four years, three hours, which are twelve, make one day, which is added to February, so that when it has had the sixth day before the Kalends of March, it also has it on the following day. For example, if today is the sixth day before the Kalends of March, that day is added in the completed fourth year; nevertheless, on the next day the sixth day before the Kalends of March is also observed. And therefore it is called bissextus, because February has twice the sixth day before the Kalends of March. In six days God made the world; on the seventh he rested. So that it may be more fully understood, compute how many hours one day has, and divide them into parts, and whatever remains, consider it the bissextile day. First, compute 300 days, how many hours they have: ten times three hundred is three thousand. Again you do: twice three hundred, six hundred: in 300 days there are 3,600 hours. Again you do: ten times sixty is 600, and twice sixty is 120. Therefore in 60 days there are 720 hours. Again you do: ten times five is 50, and twice five is 10. Behold, you have in five days 60 hours.

Together, in a whole year, there are 365 days, 4 hours, 380 [hours], and the same number in the night; together, the days and nights of the entire year make 8,760 hours. Divide those into 7 parts. First you do: seven times one thousand is 7,000; 760 remain. Next you do: seven times two hundred is 1,400; 360 remain. Next you do: seven times fifty is 350; 10 remain. Next you do: seven times one is 7; 3 remain. Those 3 hours make one day in 4 years.