De Computo Paschali

ANONYMOUS LITTLE BOOK ON THE COMPUTUS OF EASTER. BOOK ONE. While a mind curious in so weighty a matter labored rather eagerly in a quite desirable way, and, panting, had long persisted in reading—that mind, namely, which purifies a man caught in mortal snares, cleansed by fasts from sins, and joins him to the chorus of the blessed; which exhibits the baptismal tunic, sprinkled with scarlet stains and a foreign blush, as white as snow; which also, in the wedding of the Lamb, swollen with old sins, raises up the temple of the Lord, fallen in ruin, restored by the prayers of priests, and shines with the flash of compassion's hatred; and the light of knowledge shone forth, so that those things which seemed obscured by certain mists to the seeker and desirer were laid open, all hidden things were revealed to him—by whom the lunar cycles were established in their entirety, and the paschal cycles, harmonious with each other, together with the lunar years and the titles of embolisms, were known without any error by the ignorant; in which the years of the octaeterides and endecads are so investigated and marked out, completed by divine will, that they seem in no respect to waver at all. By these, the providence of the Creator is known to be so fixed with such a title that in the tenth year of King Geiseric, four hundred and twenty years from the Lord's Passion were completed at the beginning of the first octaeteris, and such an Easter was found, both by Jews and Christians, as was then celebrated by the Lord with his disciples.

Meanwhile, for us, He suffered on the eighth day before the Kalends of April, the sixteenth day of the moon, the sixth day of the week, and rose from the dead on the sixth day before the same Kalends, the eighteenth day of the moon, the first day of the week, just as in the first year of the first octoëteris of the work undertaken, it is clearly shown to our eyes by truthful documents. For the present year is the four hundred and twenty-sixth from the Lord's Passion in the first octoëteris, the sixteenth year of the King, and the second cycle has its beginning in the year of the consulship of Theodosius for the seventeenth time and Festus, at the end of which, from the Israelites departing from Egypt, two thousand one hundred years were completed, and the Passover was found such as had first been sacrificed by the Fathers in Egypt; and in the sixteenth year of the King, two thousand one hundred and sixteen were noted in the twenty-sixth cycle, the seventeenth year of the same cycle, in which year the Lord's Passover is celebrated on the fifteenth day before the Kalends of May, the seventeenth day of the moon. But so that one additional unit may be found in this cycle and be turned back from the second day of the moon to the beginning, the lunar minutes have generated this, because among twelve years, so that we might be able to pronounce the paschal days as a whole, one unit from the accenting ounces will clearly be found besides that unit of weekdays, which is very often substituted among four years for the bissextile day.

Therefore, you have eighty-four years, which the most holy Augustine of memory noted with six of the seven asses in their own octoads and endecads, not in their proper places and seats; these eighty-four years the annual unciae found. For this reason, in his cycles an error is sometimes found, because the number of years and the courses of the elements are not attended to with sufficient clarity, although one assis out of seven is always deducted in eighty-four years, and is never at all conceded to the paschal computation; and that same assis, unless otherwise, he did not let it enter into the lunar course as its own, but rather avoided it as superfluous with whole assertions: it is this that is known to generate paschal errors, as is shown by the written series of years. But so that you may be able to find that assis which is excluded, you must use this computation. Eighty-four times the decusa uncia makes for you nine hundred thirty-one days; divide by thirty, you will find thirty-one: these are the thirty-one embolisms which every laterculus is known to have; one assis remains, that which is always deducted from the seven at the end of eighty-four years, which, as we have said, the lunar minutiae generated as superfluous.

He himself, along with Agriustia of his municipality of the royal Thimidenses, writing to Hilarianus concerning the reckoning of Easter, wished by a certain art to exclude the assis through scripula, relying not on eleven days and unciae for each year, but on eleven days, semiunciae, two selae, his own scripulum, a semissemiuncia, two selae, less by two scripula and a cincunsela to an uncia, which in eighty-four years makes two hundred four scripula and a sexta, which are eight hours, a semispuncla, and two habeo. They are divided and excluded outside. Therefore, there is less than a full day to be excluded from the septenary number by three hours, eleven scripula, and ten puncta; thus he was unable to determine some years in their entirety by his assertions. Therefore, foreseeing that the assis itself must be avoided in every way, if Augustalis had inserted six asses, as I have said, into the fixed numbers of the parts of the cycle, he would by no means have incurred error in the lunar course and the paschal years, from which the outcome of the error seemed to grant this assis superfluously and variably in his lunar course; but with the lesser element, in the third cycle of thirty years, the lunar course is concluded in the twenty-fourth year. It also suits these paschal cycles through eighty-four years, after which you return to the beginning, whether in the lunar tables or in the paschal years.

Therefore, their seventeenth year is in the sixteenth year of the King; but in the lunar course, as we have said, you insert one assis among twelve years into the first, second, and third compartment, above which the Kalends of January falls, and thus you support the truth through each individual year. When, therefore, you have reached the twenty-fourth year in the third compartment, you will return after eighty-four years, having excluded one day from the septenary number coming from the lunar increments, and you will find in the head of the compartments the second moon, in which ten letters are counted from A to K, which produce for themselves the days of the sinews, so that the monthly number is agitated. Moreover, through the twelve months, the letters fixed outside A are known, from which letters you look out for the cram on each individual day; and thus descending in the compartments through each individual year in a straight line, having followed the line of the era itself opposite, you will be able to find the true moon more truly, instructed by the sound knowledge of the heart. In the compartments of the weekdays, however, through the septenary number, an indication is given to the seeker; for from A to G seven letters are noted, in which the seventh year occurs, where in the bissextile you insert one assis every three four-year periods, that is, one year K, and in the order of the months, whichever you wish to seek, you will see the era noted on each individual day at the head, and opposite it in the same compartments you will find the fixed weekday. In the bissextile column, moreover, which is joined to the lunar compartments by a fixed limit, it is associated.

Therefore, the seventeenth year itself falls on the third feria; but where you find the day of the Kalends of March marked with minium, there you have the bissextile day designated by the inserted feria. When, however, you reach the twenty-eighth, you will return to the first year; and thus, until the end of the world, by recapitulating each of the paschal, bissextile, and also the lunar years, you will find the days of the feriae noted. But so that you may recognize the bissextile day itself in its entirety, you ought to follow this reasoning and know that this bissextile day is not to be worked. The Hebrews, first of all, taught by the wisdom not of their own but of God, could not err concerning the course of the moon; and therefore, when for the first time in Egypt on the day before the Ides of April, the fourth feria, the fourteenth moon, they sacrificed the Passover with a bessicilicus, two selae of a scripulum of trion, a semiuncia, and a sicilicus, they said "twelve of the waning and twelve of the waxing"; because they found that the moon, when it was made, began from the waning, not from the waxing; whence it is understood that the equinox was found to be the first day on the eighth Kalends of April, and on the fourth day, which is the fifth Kalends of the same, they said that Almighty God said, "Let there be two luminaries in the firmament of the sky, so that they shine upon the earth, and divide between day and night, and be in signs, and in seasons, and in days and in years, and be in splendor in the firmament of the sky so that they shine upon the earth"; and so it was done.

And God made two great lights: the greater light for the beginning of the day, and the lesser light for the beginning of the night; and so forth. Therefore, almighty God made the sun the beginning of the day, and it ran for eleven hours and a quarter of an hour before the moon was made; and immediately He ordered the moon to be made, and to follow it, with which such a great office in the heavens had been attained. The fifteenth day is therefore established as full, because the power of the Creator brought forth nothing that was not full and perfect. And for that reason it is certainly said, twelve waning and twelve waxing; for the moon wanes through twelve half-months, and waxes through twelve half-months, so that what the sun is known to have run short of a full day, this the moon is found by the wise to have diminished by divine instruction; and thus, when the Lord ordered it to increase by dodrantes and to wane by dodrantes, just as the calculated division is shown before it. For fifteen times dodrantes, decusas, quadran; but because it said twelve waning and twelve waxing, the twelfth in decusas quadran makes for you a deunsicilicus. But the lunar year has three hundred fifty-four days, in whose month of the year you will find twenty-nine and a half days, over which you add a deunsicilicus, and they become for you thirty days, cincunsicilicus.

Twelve times the trisciuncus sicilicus, therefore, make for you, according to the Roman reckoning, three hundred sixty-five days, and a quarter; and you will add up that quarter over a period of four years, and it makes for you one as bissextus, that is, four times the quarter of an as; this is one day of the week. Concerning the columns, however, which are painted with their lines at the head of the circles, this explanation is shown like a shield to the one who desires it. For whatever the moon was on the Kalends of January, you will find it by following the line drawn directly opposite it. In the second column, on whatever day of the first month you have the first moon fixed before your eyes; in the third, fourth, fifth, and sixth columns, however, on whatever day the tenth moon of the fourth, fifth, seventh, and tenth months will be, you, perceiving this line with your eye, see that it is arranged through four columns, being noted as serving for the lawful fasts, just as concerning the fast of the seventh month, the most holy Moses bears witness, the Lord commanding: This says the Lord: from the ninth of the month, he says, to the tenth of the month at evening you will keep your sabbaths; and everyone who has not humbled himself in that fast, I will destroy that soul from his people.

Thus also through Zacharias, the glory of all the prophets, concerning these sacred feasts and fasts which the Lord spoke after the time of the captivities, saying: "It came to pass," he says, "the word of the almighty Lord to me, saying: Say to the people of the land and to the priests: If you have fasted and mourned in the fifth or in the seventh fasts, and behold, for seventy years, have you fasted for me, O house of Israel? And if you have eaten and drunk, do you not eat and do you not drink, not these things? Are these the words which the Lord spoke through the hands of those prophets who were before us? When Jerusalem was inhabited and populous, and its cities round about, and the mountains and plains were inhabited. And the word of the Lord came to Zacharias, saying: Thus says the Lord Almighty: Judge a just judgment, show compassion and mercy each one to his brother, and to the widow and the orphan and the stranger, and let the poor be nobly ruled, and do not harbor the malice of your brother in your hearts. And a little later: Thus says the Lord Almighty: The fourth fast, and the fifth fast, the seventh fast, and the tenth fast will be for the house of Judah a joy, and a delight, and good solemnities, and you will be joyful and will love truth and peace. Behold, the legitimate fasts, how they ought to be observed, are announced by the Lord. But why they are designated in these months, we wish to show to those who are willing.

For the fourth fast is for the first fruits and months; and we fast the fifth fast for gathering the threshing-floors and offering the tithes; the seventh fast for gathering the vintage; and the tenth fast for the sowings, also for sowing, but for tasting the first fruits of the oil. In the four weeks of these fasts, without any error, you will observe the tenth moon, clearly. From the Lord's day of Easter and of each year you count eighty-four days, at the conclusion of which you will find the days of the Sabbath, which is the end of the week, which contains within itself the tenth moon of the fourth month, and you will break the fourth fast after the sacrifice. One hundred and twelve, the fifth fast; one hundred and seventy-five, the seventh fast; two hundred and sixty-six, the tenth fast; thus, by reviewing each in order, the master and teacher of this art will be able to discover them, if, however, the drowsiness of the heart, which is shunned by the wise, does not oppress the mind. To these aforementioned columns, seven others are joined, in which the moon of the Kalends of January and the Lord's days of Easter are noted; for the thirty-day number of the moon, divided by the sevenfold number of the week, separates the space into the number two hundred and ten.

You will find the day, the moon, and the weekday of each individual Easter by observing what was on the Kalends of January, so that, keeping the course of the moon in the same column, you may find the day of Easter, which seems to pertain to the aforementioned weekday; this same thing is also confirmed in the thirty following tables, in which you will find the moon and the weekday of the Kalends of March, through the sevenfold number of each, noted in the space of thirty days, two hundred and ten intervals, establishing most certainly the fixed dominical Easter of each individual year. For these tables are followed by three other columns as handmaidens, which are compelled to show more plainly, to the curious and well-diligent, the titles of the embolisms and the lunar years, drawn out in lines from the Kalends of January, whatever it was, so that the truth of these cycles may be displayed in all their adorned ornaments. BOOK TWO, WHICH CONTAINS IN ITSELF ALL THE ORNAMENTS OF THE CYCLES.

Another method concerning the twenty-fifth cycle, which contains within itself two thousand one hundred years from the most sacred day of Easter, namely the sacrifice in Egypt with the Lord’s consent, we have set forth clearly, so that you may note that on the Kalends of January the second moon, and the fourteenth day of the first month on the day before the Ides of April, and the fourth day of the week were fixed in their entirety at the beginning of the second cycle; and you, as a most diligent calculator, by reckoning, must find this in the following way. Four times eighty-three hundred fifty-four make for you twenty-nine thousand seven hundred thirty-six lunar days; and four times eighty decusas uncia make for you nine hundred thirty thousand six hundred one embolismic days, which you add to the sum above, and you have thirty thousand six hundred sixty-seven days. Then you subtract one day, which we teach is generated from the lunar defects in the following statements, and we demonstrate most clearly how it is removed. Therefore, one cycle has eighty-four years, which contain within themselves thirty thousand six hundred sixty-five nights.

And since the twenty-fifth cycle was completed in the consulship of Theodosius for the sixteenth time and Faustus from that same Easter, which, when you calculate by the elapsed time, you will find to have seven hundred sixty-six thousand six hundred twenty-five nights; when you have divided these into a sixtieth part, you will find twelve thousand seven hundred seventy-seven, one ounce; which sum you add to the previous sum, making seven hundred seventy-nine thousand four hundred two nights; in these, when you divide by thirty, you will have twenty-five thousand nine hundred eight, and a dipondius, one ounce remains; this, I say, was the second moon on the Kalends of January. Behold, thanks be to God, how worthily and reasonably the second moon was found on the Kalends of January. Which, generating the fourteenth of the first month with the title of the embolism, is found in all. From those same Kalends of January, so that you may find the fourteenth on the day before the Ides, calculating on the third Ides of April, you have one hundred and one days; to these days you add the second moon, which was found to be on those same Kalends of January, they make for you one hundred three days; you divide by sixty, you have a bes, two selae of a scruple, a triens, ounces, a siliqua; this you add to the one hundred three days, they make for you one hundred four days, a bes, two selae of a scruple, a triens, a semuncia, a siliqua; you divide by thirty, you find three in addition, and a decus, a quarter, a bes, two selae, of a scruple, a triens, a semuncia, a siliqua.

years. And you have the fourteenth of the first month, and it falls on the day before the Ides of April, which is the most sacred first day of Easter. But so that you may be able to find the fourth day of the week of that fourteenth moon of the departure of the sons of Israel from Egypt, pay attention; for the twenty-fifth cycle is found to be concluded at the end of the second little table concerning the sons of Israel departing from Egypt, just as the sixth twenty-five of the years of the history of the Law indicates. Therefore, if eighty-four make two thousand one hundred Easters, and in the twenty-sixth cycle at the beginning two thousand one hundred and two thousand years are completed; thus one hundred times three hundred and sixty-five quarters make for you six hundred and sixty-seven thousand and twenty-five days. In these you divide by seven and you have one hundred and nine thousand five hundred and seven, with four left over. Begin to count from the first day of the week which was on the Kalends of January in the first year of Easter sacrificed in Egypt from the first as in seven asses, and you will find the day before the Kalends of January to be the seventh day of the week; and on the Kalends of January itself the first day of the week; from whichever of these Kalends days you count to the day before the Ides of April, and you will find one hundred and two days. In these you divide by seven, and you have fourteen with four left over; this is the fourth day of the week of the fourteenth moon of the first month of the first year, as we have said, at the beginning of the second cycle, in which we find the most sacred Easter then sacrificed by the fathers in Egypt.

But when you have diligently followed these cycles in order, you will find the true days of Easter noted within the columns, and those which are outside, written with the most false error on the edge of the columns, are certainly fixed in error. You see, therefore, dearest ones, that Almighty God denies nothing to any of us: but how much does He bestow upon each who faithfully desires, as He wills, from Himself? For He has commanded these mysteries to be revealed in such a way that, in the four hundred and twentieth year of King Geiseric, on the tenth day, we might find the day on which the Lord ate the most sacred Passover with His disciples; in the same year, two thousand one hundred and ten years would also be completed, from that one-year-old lamb without blemish sacrificed in Egypt, as shown from the head of the second cycle, titled in order. Let us therefore begin, brothers, from the reading of Exodus concerning that lamb sacrificed in Egypt, to recall it to the minds of those who know, so that we may demonstrate the form of both lambs to those who wish. In which reading we recognize that God Himself and our Lord said to Moses and his brother Aaron in the land of Egypt: "This month," He says, "the beginning of months, shall be the first for you, in the months of the Passover," speaking to the whole Synagogue of the children of Israel.

on the tenth day of this month, each one in the houses of the tribes shall take for themselves a sheep per house; and if there are few in the house, so that they are not sufficient for a sheep, they shall take with them their nearest neighbor, each according to the number of souls they will reckon for themselves what suffices for the sheep. The sheep shall be without blemish, spotless, perfect, male, and a year old; it shall be taken for you from the lambs and from the goats; let it be observed by you until the fourteenth day of this month. And the whole multitude of the synagogue of the children of Israel shall kill it at evening; and they shall take of its blood, and place it on the two doorposts, and on the lintel in the houses in which they will eat it; in those same houses they shall eat the flesh itself, roasted by fire that night, and they shall eat unleavened bread with it. You shall not eat it raw, nor boiled in water, but only roasted by fire. The head with the feet, and the entrails, leaving nothing of them until morning, and you shall not break any bone from it. Whatever is left of it until morning shall be burned by fire. And you shall eat it thus: your loins girded, and shoes on your feet, and your staffs in your hands; and you shall eat it hastily, for it is the Passover of the Lord.

Therefore, Almighty God commanded through Moses the entire congregation of the sons of Israel, in the month of new [fruits], which is the beginning of months among the months of the year, in which they were to eat the Passover; to this end, certainly, that He might both manifest His divinity to us believing in Christ and demonstrate their brigandage, already then from the first Passover celebrated in Egypt; who in Egypt at evening, that is, in the last times of the world, girded and shod, would go out against the immaculate Lamb of God on the first day of Unleavened Bread at evening with swords and clubs, and would commit against Him all that had been foretold about Him by all the Prophets. And therefore we, who now celebrate Passover not according to the image, as they did, but according to the truth, in commemoration of the passion of the Son of God, ought in the first place to seek out nothing other than the very advent of our Lord with all the strength of our faith diligently, and then to revolve it in the series of cycles. For Gaius Julius Caesar first ruled Rome for ten years, four months, six days. After Gaius Julius Caesar, the Emperor Augustus succeeded, who ruled Rome for fifty-six years, four months, one day.

Under his rule came John, the son of the priest Zacharias, sent by God preaching the baptism of penance, who according to the preaching of the law and all the prophets showed Christ, that Christ the Son of God had come into this world, that is, into the region of Judea, saying: this is the Lamb of God, who takes away the sins of the world; and this is the Savior of the world; this is he of whom I said: a man made before me, whose sandal-strap I am not worthy to untie. Then Jesus began to teach the people and to perform great virtues and signs, which no other had done. Moreover, after the baptism he revealed himself to the whole human race as the Son of God, sent by God the Father to establish, reform, and reconcile the people composed for him. To these, twelve disciples were chosen, power was given in the Holy Spirit; and he sent them through all nations, teaching that they should teach. Then, after they were ordained to the office of preaching the grace of God made through his name, the remission of sins, the resurrection of the flesh, eternal life for the dead rising again, he foretold to them how much he would suffer from the Jews unto death, death by the cross, and that he would remain for three days in the heart of the earth, and that on the third day he would rise from the dead, and after the resurrection he would seek the heavens. Then Tiberius Caesar ruled for twenty-two years, seven months, twenty-two days. Under his rule, that is, the sixth.

In the fifteenth year of his reign, under the procurator of Judaea, Pontius Pilate, and the priests Annas and Caiaphas, on the eighth day before the Kalends of April, when the two Gemini were consuls, the sixteenth moon fell, a parasceve, when our Lord, the Saviour of the human race, Jesus Christ the Son of God, suffered. Therefore, having endured all that had been written about him, according to the preaching of the law and all the prophets and his Gospels, he suffered, as we have said, on the eighth day before the Kalends of April, a parasceve day. And on the third day he rose from the dead, on the Lord's day, the sixth day before the same Kalends, and after having conversed with the Apostles and Disciples for about forty days, he was received into heaven, surrounded by a cloud. From then on, therefore, with the grace of God reigning, men believing in his name began to be enlightened. And so in all these things let us give thanks to the one who disposes all these things for our salvation; and the Lord God Almighty, the Father of our Lord Jesus Christ, calls us to divine knowledge, to whom be honor and glory through the same Lord Christ in the Holy Spirit throughout all ages of ages. Amen.

Therefore, from the first-formed Adam to the sixteenth year of Tiberius Caesar, that is, to the day of the Lord's Passion, there are five thousand five hundred years; and from the Lord's Passion to the tenth year of the King, four hundred twenty years; in which year you will also find the most sacred day of Easter, on which our Lord, the Lamb of God, was sacrificed for us. That day is fixed at the head of the first cycle in the tenth year of the same King, inscribed with a complete number. In these Augustan years, therefore, the author of his own table, although endowed with knowledge of letters and skilled in the art of calculation, is known to have incurred an error, namely on account of the number of years in his lunar course, to which an extra unit from that same deceptive number of years is proved to have accrued. For he says that on the one hundred eighty-sixth year after the Lord's Passion, the day of the same Easter coincided with the day, whereas he ought to have found that day in the one hundred sixty-ninth year from the head of the third cycle, which he is known to have fixed in his cycles in the sixty-ninth year. But that day, without members, with a personal name, among us in the seventeenth year, he is shown to have inscribed at the head of his cycles with an uncertain number; therefore he seems to have fallen into error, as he himself professes in his own discourse. But that, in.

quit, not from that year in which the Lord suffered were the cycles of investigation ordained and discovered, but the usefulness of the compendium is that from the two Gemini consuls, in whose year the Lord suffered, up to the year of the consulate of Antoninus for the fourth time and Albinus, which is the first in this work, one hundred and eighty-six years are counted; and because it happened under this same consul that the day of Easter coincided entirely with the day of the Lord's Passion, the usefulness of the compendium, though washed away, ought not to be scorned. From this consul, therefore, from which the beginnings of the first octoad were started, up to that year in which the eighty-fourth year with its signs of embolisms is concluded, it is very easy for those inspecting the truth of Kosmutas's calculation to prove it also with the eyes as witnesses, how it promises to prove itself in this computation; since it has neither fixed the day of the Lord's Passion at the head of its first octoad in its entirety, nor truthfully determined the certain number of years; as the text of our following cycles indicates, in whose head, namely, one finds on the Kalends of January the twentieth moon, and the seventh second feria, the fourteenth of the first month; the tenth Kalends of April, feria IV; the Lord's Easter on the sixth Ides of April, the eighteenth moon; and in its cycles it is held at the head on the Kalends of January the twentieth moon, feria VI; the fourteenth of the first month on the eighth Kalends of April, feria V; the Lord's Easter on the fifth Kalends of April, the seventh moon.

On this day he thinks the Lord's Passion occurred, which in no way at all agrees with the truth. Thus also to our eyes the lunar cycle itself, radiant with gleaming light, indicates, and the number of years, rightly fixed in a certain place. But Agriustia, the first cultivator of perversity and lover of his own error, and the most unskilled teacher of his own assertion, and of himself, whom we said should be avoided, tries to scatter the years into individual scruples, so that his evident falsehood may be exposed and he may be seen to be revealed as alien from the truth. Then let him be agitated by more learned questions, as if he wished to extend the increase of the moon in his little tables by an argument of solace in the course of the year itself: eleven asses, a semuncia, two selae, one scruple, a semissis, an uncia, two selae, and not eleven asses and an uncia, which without doubt in that same annual separation the moon itself testifies to increase by increments. Through which uncia, indeed, in eighty-four years the calculator could have had seven asses, from which one ass, which runs after thirty-one at the time of Moses, he would have fully recognized the truth, had he declined it. Eighty-four times, therefore, as he says, a semuncia, two selae, one scruple, a semissis, an uncia, two selae; he himself thus answered: six, a quadrans, a scruple, eleven destun. (sic); which is what he asserts.

And he says: "There are six days, and a quarter of an hour, and eleven scruples, and they are proven to be less than two joined together, because in the remainder ten points are most clearly concluded." What in this question is more manifest, what in his response more probable, than that he should be defeated by his own fuel, the inept one, and that he, who had let loose eight hours of cabbage, attempted to exclude only two points according to the will of his own judgment, and was unable to avoid the full ass? For this reason he taught that all the heretics have fallen away from the rule of truth, and that, as if blind, they can no longer find the door of light. But how the captive and whole sense may be turned aside by prudent fixed numbers, and not delayed to avert: for eighty-four times three hundred and five fours are twenty-nine thousand seven hundred and thirty-six days; and again eighty-four times ten ounces make for you nine hundred and thirty-one days; which, added to the previous sum, will be thirty thousand six hundred and sixty-seven days: which days are known to be determined by ogdoads and endecads in such a way that they would exclude the very day which they contain superfluously in themselves, and would designate a fixed number enclosed in themselves.

For there are five ogdoads and four endecads, which five ogdoads contain within themselves fifteen embolismic and twenty-five lunar years, having four hundred ninety-five months, which in themselves contain fourteen thousand six hundred fourteen days; the endecads contain within themselves twenty-eight embolismic and lunar years, having five hundred forty-four months, which in themselves yield sixteen thousand fifty-six days; you add together the sum of these days, and they make for you thirty thousand six hundred sixty-six days. Behold, from thirty thousand six hundred sixty-seven days, one as has been briefly excluded in the ogdoads and endecads is truthfully proven by the division of days, and then is dissipated in contentions by the unskilled and the studious. Thus also in the following cycle, with the upper, a germinal concord has rested through embolisms and common years; you will find that very as, which the Curious one has as quickly as possible fully declined. For there are in the second cycle, just as in the first, thirty-one embolismic years and fifty-three common years. Three hundred ten times four responds to you eleven thousand nine hundred four, and fifty-three times three hundred fifty-four makes for you eighteen thousand seven hundred sixty-two days. These two sums joined together yield thirty thousand six hundred sixty-six days, and that aforesaid as is declined.

Let us therefore return to that sum mentioned above concerning that year, from which you learned that in the first year the Passover was celebrated in Egypt on the Kalends of January with the second moon. If you wish to attend to this very same as, you will most fully set it aside. For in the aforesaid sum are contained seven hundred sixty-six thousand six hundred twenty-five asses, from which you subtract three hundred sixty-five asses, namely of the last year of the cycles, so that the as itself appears, and by this sum it was excluded from the septenary number born from the increase of unciae. But also learn that the twenty-first moon without unciae is most fully bare of the eighty-fourth year. However, when you have recalled the aforesaid days of the higher sum, and have divided this same, you will find the second moon, which at the head of the second cycle on the Kalends of January you know was marked by hand. Therefore, subtracting these three hundred sixty-five asses, there remain seven hundred sixty-six thousand two hundred sixty asses, in which you divide the sixtieth, you will have twelve thousand seven hundred seventy-one; add this to the aforesaid sum, there will be seven hundred seventy-nine thousand three hundred one asses. In these you divide the thirtieth, you find twenty-five thousand nine hundred sixty-seven, and twenty-one asses remain. These are the twenty-first moon of the eighty-fourth year.

Having also recalled the aforementioned three hundred sixty-five asses to that higher sum, there will be seven hundred sixty-six thousand six hundred twenty-five asses, as above. In these, you divide by sixty, and you will find twelve thousand seven hundred seventy-seven, an uncia; you add to the aforementioned sum, and you have seven hundred nine thousand four hundred asses, a dipondius, an uncia. In these, you divide by thirty, and you will have twenty-five thousand nine hundred eighty, a dipondius, an uncia, as is the moon inscribed at the head of the second cycle, and you will turn aside to the half-itself, which we have very often said must be turned aside at the end of the cycles. Whoever you are, wounded by the deceit of folly, or ignorant of this reasoning, through which high and deep sum of division, to speak more truly, rather clearly demonstrated, recognize that this assis has been excluded from the number seven; since you have been unable to turn aside every such thing in your calculation, you are found to be neuter in either case. Desist, I beg you, desist now from leading wretched peoples into error through the deceit of your tricks; finally, at last, bend your stubborn neck to the truth, which through clouds and illusions from Egypt, from unknown spaces of provinces and a long interval of lands, as if coming to you, the most sacred day of the Pasch is frequently celebrated by you in vain without time. For you will glue the lunar course of these cycles into the feeling of your breast.

Then from the first year of the Passover in Egypt you will find the true foundation, which you recognize as sufficiently consistent with the lunar cycles and the paschal titles. For from the Kalends of January, on which, as stated above, the second moon was found and held at the head of the cycles, you will now calculate to the day before those same Kalends of January of the following year, and there will be three hundred sixty-five days, to which you add the second moon, which was on those same Kalends, as you may acknowledge the method of proceeding, and it becomes three hundred sixty-seven days, in which you divide by sixty, you find six unciae, which you add to the aforesaid sum, and you have three hundred seventy-three days, one uncia, two selae. In these, then, you divide by thirty, you find ten dipondii; the remainder is ten, three unciae, two selae. Similarly, also in the following year, which is called third in order, you must calculate. Thus three hundred sixty-five days become seven hundred thirty days. You add, as above, the second moon of the first year, and you have seven hundred thirty-two days, in which you divide by sixty, you find ten dipondii. Two selae remain; you add this to the aforesaid sum, and there will be seven hundred forty-four days; two selae remain, in which you divide by thirty, you find four days, and twenty-four, two selae remain.

Then you will calculate each individual year up to the eighty-third year; you recognize the eighty-fourth as marked at the end of the cycles, so that in each of these years you seem to insert eleven asses and an uncia, and you are known not to have erased any of the windings of the grid or the lunar titles at all. For our Lord Christ, obedient to his father’s command, brought forth this nourishing star of the moon in such a way that you will find from the night a light, which, solidified by the coverings of darkness, would diminish the shadows brought in by the clear chariot, having been emptied through errors, by secret operative causes; now it withdraws full to be fulfilled, and by revolving courses it is defined again. These, therefore, are the principles of the moon, and its duties divinely instituted in perpetual service; these have been made prescient in signs, and in times, and in days, and in years. For through this chaste and pure fabric, and by the presage of its majesty, the Lord designated for the church what is very often weakened by various mishaps and always diminished in the fallen; yet, supported by the luster of its splendor, it grows among the saints.

For thus I say specifically, the same Church speaks of herself: "I am dark and beautiful, O daughters of Jerusalem." And the Lord, through the Prophet, answered with a sonorous voice and says: "You are entirely beautiful as the sun, and perfect as the moon." And again: "I have once sworn by my holy one: if I should lie to David, his seed will remain forever, and his throne will be as the sun in my sight, and as the perfect moon forever." This entire mystery remains in the Church in Christ, and it is fitting; for we most diligently represent the most perfect course of the same moon, so that you may know it, as it were, bounded within its own grid on each individual day in its entirety. From the Kalends of January, I say, you will reckon to the day before that day on which you also ask what the moon's age is. But perhaps you say: why do you reckon to the day before and indicate what the moon's age is on the following day, because you collect the sum from the Kalends of January and you insert what the moon's age was on those Kalends? Can you not, in some way, count a single day as bipartite or doubled in number?

And so in these parts you divide the sixtieth, and what you have divided you place above the number of days, in which you similarly divide the thirtieth, and on whatever day, as I have said, the moon will be, which you will most expertly designate for the homeward journey through each day and year, although the birthdays of each Easter are not except the new general day of the first month; but that the first month itself is said by almost all to be from the third day before the Nones of March up to the fourth day before the Nones of April, it is shown by a certain and orderly reasoning, so that in these twenty-nine days the Paschal nativity is revealed, and through the first annual cycle it is shown more clearly by truthful proofs. For from the construction of the sun and moon, which began on the fifth day before the Kalends of April, we count three hundred and forty free days having occurred up to the future fifth day before the Nones of March, to which days we add the fifteenth moon, in which fullness of day, at the evening of that same fifth day before the Kalends of April, had been established by the Lord, and there are three hundred and fifty-five days, in which you divide the sixtieth, and you have five duounces; you add to the sum above, and there are three hundred and sixty days. Duounce. You divide the thirtieth and you find a decusdipondius over and a duounce.

And since the fifteenth moon, full, as we have said, had been made on the fifth day before the Kalends of April, on the day before the Ides of April it is diminished by its horns to fill its first month; for this reason the new moon was commanded to be observed by the Jews up to the present day. The second month, however, filled on the fourth day before the Ides of May, the third month on the fourth day before the Ides of June, the fourth month on the sixth day before the Ides of July, the fifth month on the sixth day before the Ides of August, the sixth month on the seventh day before the Ides of September, the seventh month on the day before the Nones of October, the eighth month on the Nones of November, the ninth month on the day before the Nones of December, the tenth month on the third day before the Nones of January, the eleventh month on the Kalends of February, the twelfth month on the fifth day before the Nones of March, and you have three hundred fifty-five days, which the first year contains, indeed therein with fifteen days of the moon, as much as the full moon had been made perfect. For from the fifth day before the Nones to the fourth day before the Nones of March, the calculation pronounces the moon, which is namely the day between the fifth and the third, in which the moon is waning and not full, which day is found to be one full day.

Therefore, the first month cannot begin from that day itself, but from the third day before the Nones of March to the fourth day before the Nones of April, on the fourth day before the Nones, the day before, that is, on the day of the Kalends of April, we reckon from the fifth day before the same Kalends of the past year, that is, the first year, on which day both luminaries in the signs, and in the seasons, and in the days, and in the years had been established by the Lord, and we find three hundred seventy days, to which we add the fifteenth moon, in which state it had meanwhile been made, and there become three hundred eighty-five days. From these days you subtract a sixtieth, and you have six; you add these to the aforesaid sum, and there become three hundred ninety-one; you subtract a thirtieth and you find thirteen, and one remains. Therefore, from the third day before the Nones of March to the fourth day before the Nones of April we ought to seek the first moon, because on whatever day the first moon exists for twenty-nine days, from there the first month begins, in which month Almighty God commanded the most sacred Passover to be celebrated, as He testifies and says in Exodus: "You shall observe the feast of Passover; for seven days you shall eat unleavened bread, as I commanded you, during the time of the month of new grain; for in it you came out of the land of Egypt." And in Leviticus the Lord commands and says: "In the first month, on the fourteenth day of the month, in the middle of the evening, the Passover of the Lord, and on the fifteenth day of this month the feast of unleavened bread to the Lord.

In Numbers: and the Lord spoke to Moses in the desert of Sinai in the second year as they were departing from Egypt, in the first month, saying: say, that the children of Israel should make the Passover in its proper time, on the fourteenth day of the first month at evening. According to the times, according to its law, and according to its comparison you shall do it. And Moses spoke to the children of Israel to make the Passover in the desert of Sinai according to what the Lord commanded Moses, and the children of Israel did so. And a little later, with a threat, the Lord commanded, and says: a man who is pure, and has not been on a long journey, and has failed to make the Passover, that soul shall be cut off from his people, because he did not offer the gift to the Lord in its proper time: and that man shall receive his sin. In Deuteronomy, Moses spoke to the people, saying: observe the month of new [grain], and you shall make the Passover to the Lord your God, because in the month of new [grain] you came out of the land of Egypt by night, and you shall sacrifice the Passover to the Lord your God. Likewise also in the first book of Ezra it is more clearly written: Josiah made the Passover in Jerusalem to God, and he sacrificed the phasec on the fourteenth day of the first month at evening.

Behold the fourteenth day of the moon, which extends from the fifteenth day before the Kalends of April up to the seventeenth day before the Kalends of May, so that it may be known to be legally established by true reasoning; and thus also from the third day before the Nones of March up to the tenth day before the Kalends of April there are nineteen days, in which, when the moon is born, it is undoubtedly assigned to lunar years; but from the ninth day before the Kalends of April up to the fourth day before the Nones of the same there are ten days, and when it is born in these, it is indeed marked as fixed for embolismic years, as is confirmed by the cycle in the ancient index. For six months divide the year; in an embolismic year, however, one month of thirty days is added as an extension; thus six times twenty-nine make for you one hundred seventy-four days; and seven times thirty you have two hundred ten; you add the sums together, they make for you three hundred eighty-four days. This is the embolismic year. A lunar year, equally, is divided into six months. Thus six times twenty-nine make for you one hundred seventy-four days, and six times thirty are one hundred eighty. The sums joined together make three hundred fifty-four days, not counted from the Lord's day to the Lord's day of Easter, but from the fourteenth to the fourteenth moon of the first month of the coming year; and thus you will find all the days collected in their order through eighty-four years in certain months without doubt, just as the aspect of the moon's birth shines forth through each month, witnessed by the eyes.

From the first moon of the Kalends of January up to the eighth, you will find embolismic years; from the ninth, however, up to the twenty-seventh, you will certainly find lunar years. Likewise, from the twenty-eighth up to the thirtieth, you will find embolismic years. You will observe all these things with the greatest care, and you will find the day of Easter in its entirety. Behold, you will not labor, for, with the Lord’s consent, each point is set forth clearly and perfectly, in which matters the faithlessness of the detractors is now refuted, so that the artless simplicity of the innocent may be recognized as subject to all; the errors of the hypocrites, however, are to be avoided, because boasting belongs to the ignorant, for the aforesaid virtues are full of modesty.