Commentary

is diminished, in which xii hours and an *assis*—that is, the first part of twelve parts—are consumed. On this day, at evening, if the fourteenth moon had fallen, the lamb was sacrificed by the Jews. If, however, an exceeding number, the xv or xvi moon, should have been discovered, the Passover was celebrated at the evening of that same day on the xiv day of the second moon born in the same month; eating unleavened bread for seven days, until the xxi day in the evening. Therefore, if it happen to us similarly that both a Sunday and the xiv moon are found on the vi Kalends of April, the Passover must be celebrated on the fourteenth. But even if a xv or xvi, and up to the xx moon should be found, for the reverence of the Lord’s Resurrection which occurred on a Sunday, it must be celebrated by us in like manner; yet so that the beginning of the Passover does not exceed the end of their solemnity, that is, the twentieth moon. And for this reason, we have said that those who have dared to anticipate or exceed this number set into divine Scripture have not erred slightly. And from the v Kalends of April to the v Kalends of July, the day is diminished by days; by two moments and a half, and the sixth part of a moment, as the sun rises on each day. And from the vii Kalends of July to the v Kalends of October, it is similarly diminished by the hour over xv days, and four hours; with the sun descending on each day by the same number of moments; and the space that remains, until the viii Ka- ^B lends of January, is finished with a similar number of hours and moments. So that the viii Kalends of January should have an hour and a half of an hour. For the day and night are diminished to that extent. And the xii hours which were established in the spring equinox at the beginning by the Lord’s dispensation, are found, with the night diminished on the viii Kalends of July, as the sun rises through individual degrees—which we have mentioned above—to be added in the twelfth longer space of xviii. And again, the xii hours which are filled by the descent of the sun in the autumnal equinox, are found on the viii Kalends of January to be separated, divided into x, with the night holding xvi divided into x. Which, on the viii Kalends of July, similarly held vi divided into x.

XVII. Conclusion of the Work.

XVII. Furthermore, do not be ignorant of this: that these four limits of the seasons which we have mentioned, although they may approach the Kalends of the following months, nonetheless hold the middle of each season, that is, of spring and summer, autumn and winter. And the beginnings of the seasons do not start from there, where the Kalends of the months start. But each season is to be initiated such that it divides the season of the equinoxes from the first day of spring; and it is divided similarly for summer on the v Kalends of July, and for autumn on the v Kalends of October, and for winter on the viii Kalends of January.

ÆGIDII BUCHERII COMMENTARY ON THE PASCHAL CANON OF ST. ANATOLIUS OF ALEXANDRIA

CHAPTER FIRST.

Whether the Paschal Canon of Anatolius, written in Greek and rendered into Latin by Rufinus, is genuine. Reasons why such a Canon does not seem to be Anatolius’s. Eusebius, Bede, Colman, and Wilfrid attribute it to Anatolius. Bede quotes many things from this Canon verbatim.

Anatolius, an Alexandrian by race, no one doubts wrote his Canon in Greek. And Eusebius removes all doubt, as he quotes a good part of it in Greek. Everyone likewise attributes this Latin version to Rufinus, and for that reason, they judge it to be less than accurate and not sufficiently trustworthy. Indeed, the Greek texts, which Eusebius happily inserted into Book vii, chapter 26 (32) of his *Ecclesiastical History*, are both richer than the Rufinian [version], and are subsequently conceived in other and clearer ways; as is evident to anyone even on a first comparison. Therefore, I do not deny that some slight blemish could have crept into the text of this Canon. But the question is whether that text, setting aside the not-so-certain interpretation of Rufinus, is otherwise the genuine and true offspring of Anatolius, which Eusebius calls a *Canon on the Passover*, and Jerome calls a *Volume on the Passover*.

From the principles, indeed, that are certainly paradoxical, and set up contrary to the common opinion of those who have written about the Christian Passover, which this Canon bears, it might perhaps seem spurious and supposititious; and the work of another rather than that of Anatolius, a writer so highly praised and so Catholic. To select a few things here from many in the meantime: that it indicates the fourth moon for the Sunday Passover without any hesitation, which is in agreement with those who are "Quartodecimans," or "Tessareskaidekatitai," rejected by the Church: even if that is not perpetual for him; nor does it recur except three times in the whole nineteen-year cycle. Furthermore, he diffuses that same Sunday of the Passover from the xiii moon, at least at its end, only into the xx; although Scripture, and with it the Alexandrians among whom Anatolius studied, openly extend it from the xiv into the xxi; the Latins fear not to extend it also into the twenty-second. In addition to these things, he establishes the Sunday letters and the leap year, and many other things so confusedly, that he does not seem to be the work of any learned and holy Father, such as everyone supposes Anatolius to be, but rather a writer who is unlearned and ignorant, and perhaps strayed from Catholic truth. Concerning which, more in the third chapter shortly.

Nevertheless, there are things that more strongly evince the work of Anatolius. First, the authority of Eusebius of Caesarea, who could have seen it, and who brings forward no small fragment of this Canon in the name of Anatolius, which plainly conforms to this little work, except where the faith of the interpreter wavers. The same is done by Bede, in the beginning of his booklet *On the Equinox and the Calculation of Time*, chapter four. Then Colman, bishop of the Scots, cited by the same Bede in book iii of his *Ecclesiastical History of the English*, chapter 25, asserts that the man Anatolius, as he says, a holy man and most laudable in ecclesiastical history, taught that the Passover should be celebrated from the xiv moon to the xx. Which even the Catholic presbyter of the English, Wilfrid, while arguing against Colman for the Alexandrian Passover, not only admits, but adds further that the Scots begin the Passover from the xiii moon at evening.

223 EGIDII BUCHERII COMMENTARIUS 224

the intersection of the zodiac and equinoctial circles, on the twenty-first or twenty-second day of the Julian March (which coincide with the twenty-fifth and twenty-sixth of Phamenoth), no one will have denied it took place. How therefore could the sun, according to the sense of Anatolius so clearly expressed here, have traversed the fourth day in Aries at that time? But if instead of the twenty-sixth of Phamenoth, or the twenty-second of March, you substitute, as is fitting, the twenty-ninth of Phamenoth, the twenty-fifth of March, it will plainly be true that the sun, in the first segment of the zodiac which we call Aries, will have already traversed the fourth day completely, or is traversing the fifth. And the sense of Anatolius will be that the very intersection of the ^A circles occurs on the twenty-first of March rather than the twenty-second—a view which he had, as I believe, gleaned from the Alexandrians, who a few years later publicy reproached [it] for that which, from the reasoning of this Anatolian Canon, it is sometimes necessary to conclude. Finally, Bede himself frequently copies most things word for word from this Canon, and attributes them to Anatolius. For in his first little book on the equinox he discusses the opinion of Anatolius on fixing the equinox in such a way that anyone can easily see that he could not have drawn these things from anywhere other than this faulty and corrupted Latin Canon. On which [we shall speak] more fully in the following chapter. Again, the same Bede, in *The Reckoning of Time*, chapter 40, most explicitly writes that the lunar leap is placed by Anatolius, not at the end or the beginning of the nineteen-year cycle, but in its fourteenth year, which is the last of the ogdoad: "Making it," he says, "ascend (or leap) at the equinox, from the eighth to the twentieth." The diagram of this Canon clearly exhibits the same thing.

Finally, the same Bede, in that same book *The Reckoning of Time*, chapter 53, most clearly confirms this Anatolian Canon with these words: "But also the holy man of the Church, Anatolius, in his Paschal work, after he had discussed most subtly the equinoxes and solstices, and the increases of hours and moments, so ended his discussion and the little book itself: 'But do not ignore this, that these four limits of the seasons which we have mentioned, although they approach the Kalends of the following months, yet each one holds its middle period, that is, of spring and summer, autumn and winter; and the limits of the seasons do not begin ^B from where the Kalends of the months begin. But each season is to be so initiated that the spring season divides the equinox from the first day; and summer, on the eighth day before the Kalends of July; and autumn, on the eighth day before the Kalends of October; and winter, on the fifth day before the Kalends of January, likewise divides.' So he. These are plainly the same as the final words of our Canon, to which they therefore lend no small credit."

But the arguments brought forward here to the contrary will be more conveniently examined below in the third chapter.

CHAPTER II.

We understand well enough that this question was not raised today for the first time, but from ancient times, from Bede’s little book on the vernal equinox. "There are some," he says, "who contend that Anatolius, in this opinion (namely, regarding the day of the equinox), posited not the eleventh, but the eighth day before the Kalends of April." And yet, among modern writers, you would scarcely see one who does not assume as indubitable that the equinox, according to the mind of Anatolius, occurs on the eleventh day before the Kalends of April, or the twentieth of the Julian March. They prove it from his own words: "There is, therefore, in the first year the beginning of the first month (the Paschal month, namely), which is the beginning of the nineteen-year cycle, according to the Egyptians, the twenty-sixth day of the month of Phamenoth; but according to the Macedonians, the twenty-second day of the month of Dystrus; as the Romans however say, the eleventh day before the Kalends of April, etc." But I shall now show that these words are corrupt.

I say, therefore, that the opinion of Anatolius here is plainly that of Caesar or Sosigenes; namely, that the day of the equinox occurs on the twenty-ninth of Phamenoth, the twenty-fifth of Dystrus, the eighth day before the Kalends of April, or the twenty-fifth of March. This is established by three most clear and incorrupt passages of the text of Anatolius himself. First, he says: "On this day, the twenty-sixth of Phamenoth, the sun is found having not only entered the first segment of the Zodiac, but also to have already traversed the fourth day in it." Indeed, in the age of Anatolius, about the year 276 of the vulgar and modern era of Christ, in which I believe these things were worked out by him, the astronomical spring equinox ^C held [it]. Second, he adds in this same little work, § 3: "But what wonder if they erred on the twenty-first moon, who added three days before the equinox, in which they define that the Pasch can be sacrificed?" Which it is certain is even in every way considered absurd. By those who added the three days before the equinox, Anatolius here understands the Fathers of the council of Caesarea in Palestine. For although they themselves acknowledged the day of the civil equinox on the twenty-fifth of March, yet they did not wish to exclude from the paschal limit the three previous days in which Christ, after the venerable sacrament was instituted, was apprehended, suffered, and was buried. Nor do any others occur about whom this could be said. For the Jews and the first of the Christians, at least the Latins, who, as I said, had assigned the first entry of the sun into Aries to the eighteenth of March, had added not three, but seven days. Anatolius, therefore—if he thinks that the three previous days were added to the hitherto-usurped civil equinox, for so he hints—is necessarily stuck in the ancient equinox of Caesar, which was composed with the twenty-fifth of March, and does not choose that of the twenty-second of March. Which argument is certainly valid, and Bede also brings it forward in that little work of his on the day of the Equinox, and indeed from the objection and sense of those who even then were of our sentiment.

The third and most important passage of Anatolius is § 8, for there, through all the years of his nineteen-year cycle, determining also the day and weekday of his equinox, he always remains fixed and firm on the twenty-fifth of March, never on the twenty-second, as you can see in his table. And since he frequently repeats that the Pasch can never be duly celebrated except after the equinox has already passed, he himself observes it with such reverence and almost superstition, that he indicates the next Lord's Pasch not on the seventh, or the day after the Caesarean equinox, but first on the sixth day before the Kalends of April. I believe this was so that he might more certainly transmit the day of the equinox in his Paschal sanction, and that light might the more dominate the darkness. Thus, nothing is more certain than that the equinox was composed by Anatolius with the twenty-fifth of March.

The rationale of the adversaries, drawn from the words of Anatolius, has already long since been rejected by others, as Bede testifies, when they said that Eusebius (or whoever else) when he reported this work of Anatolius in his *Ecclesiastical History*, had changed one day for another; and because he saw that the rest were established well, wished to correct with one word what he had perceived was said less perfectly in it. Namely, that he did not expose the one he had intended to praise to open reproach, if he should put his pure words, and as he had written them, into his own Histories. I know that Bede cannot persuade himself of this regarding Eusebius. But we know that the dispositions of many of the Greeks were similar, especially those infected with heresy, of which kind Eusebius is clearly taught to have been by Baronius. Nor does it press any more, what the same Bede adds: "It is a wonder if such an imposture escaped Victor of Capua, who also himself reads in Anatolius the eleventh, not the sixth day before the Kalends of April." For this imposture deceived not only Victor, in the darkness of that age which still prevailed, but also most of the sharpest learned writers of that time. Eusebius wanted to praise Anatolius. He could not, unless he either said the equinox was badly fixed by the Nicene synod; or ^D [that he would restore Anatolius' text at least approximately to the judgment of the synod. Later pri...]

priority was believed to be more easy and acceptable. Nor are there wanting even now some traces of the corruption introduced. For the manuscript codex from which we have transcribed these things clearly shows VIII Kalends of April, from the true and first reading, not XI. Although it retains the twenty-second day of Dystrus from a faulty correction. Moreover, why Eusebius, or anyone else, having undertaken to correct Anatolius, should have substituted the twenty-second rather than the twenty-first of March for the twenty-fifth, I do not sufficiently perceive. For the Nicene synod fixed the equinox at March 21st, or 12th, not 11th Kalends of April, and the Church has retained it thus ever since. Indeed, Anatolius also appears to have thought so, when he openly writes that this very March 25th, on which he fixes his civil equinox, has already passed and exceeded the fourth day of the first dodecatemorion [segment], implying that the sun is then traversing the fifth. Nor will he be satisfied who says that Anatolius appears to have followed the opinion of Ptolemy. For why, if he were following the opinion of an ethnic writer 130 years older, would he have said that on March 25th the sun had already traversed the fourth part of the first dodecatemorion, and not rather that it was traversing it according to his sense? Would so great a man not have paid attention in such intense study to the motions of the heavens and of clocks? But whatever may be the basis for this (for it matters little), it is certain that Anatolius does not constitute the civil equinox in the first degree of the first segment; but either in the fifth, as we ourselves think more probable; or certainly, as others, in the fourth; just as we proved above in the third chapter of the treatise *On the Jewish Year* that Caesar and Meton constituted it in the eighth, and Eudoxus, according to the opinion of Gemini, in the sixth.

Before I finish this chapter, let the reader consider with me whether the doctors of the Alexandrian school have not up to this point retained the civil equinox on March 25th, since Anatolius, who was not the lowest among them, keeps to that day so tenaciously; even though he perceives that it corresponds to the fifth (at least the fourth) degree of the first dodecatemorion. And if this is so, then I must also say that the Alexandrian patriarch Dionysius, who died only eleven years before this work of Anatolius, adapted his own paschal octaeteris to this day of the Caesarean equinox, not the Nicene or Ptolemaic, since he also does not want Pascha to be celebrated before the equinox, as we have indicated above.

CHAPTER III.

Anatolius differs much from other computers, both Latin and Alexandrian, in the sun and moon. In the sun, indeed: 1° because he decides the civil equinox, not that of the Alexandrians and the Nicene synod, on March 21st, or, as the ancient Latins with the Jews, on the 16th, but on the 25th with Caesar, as we have already seen. Nor does he want Pascha to be celebrated before that, nor on that day, nor even the next day: so great is the concern in him for certainly skipping even the civil equinox. As long as (he says § 6) the equality between light and darkness persists, and it is shown that Pascha should not be sacrificed before the diminished light. Therefore, it is ordered that Pascha be sacrificed after the equinox, because the 14th day of the moon before the equinox, and on the equinox, does not fill the entire night. But after the equinox, the 14th day of the moon, with one day added (note ^A) which is the transgression of the equinox; although it does not reach the true light, that is, the rising of the sun, and the beginning of the day, yet it does not leave darkness behind it. Thus he; by which he constitutes his last paschal Sunday only on the second day after the equinox has been committed, or March 27th.

2° He dispenses the Dominical letters and leap years in a far different way. For of nineteen years he posits only two leap years, namely the 7th and 17th, as can be seen in his paschal table. And yet in nineteen years, four, at a minimum, and sometimes five, fall out. And since in seventy-six years nineteen leap years are entirely imputed, according to his teaching only eight would be appropriate. Thus he makes the solar year different from the Julian and so much shorter, and consequently he institutes paschal Sundays out of step with the spring, and which most often fall into simple weekdays. Certainly, he does not agree with the truth except in the first four years of his enneadecaeteris, and likewise in the seventh and eighth, unless perhaps he is aided by chance.

However, in the moon he differs even more: 1° Because the year which is the first of the enneadecaeteris for him is the eleventh for the Alexandrians, and for the Latins and our Victorius the second. Indeed, he begins his cycle from the 276th year of the common era of Christ, eight years before the Alexandrian, as we demonstrate subsequently, and especially in chapter 4. 2° He differs in the lunar leap. For the Alexandrians constitute this in the 19th year of their nineteen-year cycle, which is the first of our modern Romans; the Latins and Victorius in their 16th, and he himself in his 14th, as is clear from his table; which in that year makes the leap from 8 to 20. Concerning which Cyril also insinuates something in § 7 of his Prologue, although the name of Anatolius is suppressed; but Bede does so more expressly in *De Ratione Temporum*, chapter 40: "Finally," he says, "Anatolius, who very truly determines the beginning of the months and the head of the whole cycle and the term at the vernal equinox, did not place the change of the moon at the head, as the Romans do, or at the end, as the Egyptians, of his nineteen-year cycle, but in its 14th year, which is the last of the ogdoad, making it ascend from 8 to 20." Thus he. From this it happens that the Anatolian golden numbers are advanced upward by one day in the Julian Calendar from the 16th to the 19th.

3° He disagrees in the very placement of the golden numbers, and, what follows from that, in determining the age of the moon. For when he composes his first cycle for the 30th day of March twice expressly, once in § 11 of his text, and again in the first year of his table. Since this corresponds to the 11th cycle of the Alexandrians and the second of the Latins, it must necessarily precede the former by three days and the latter by two. The judgment of the other years is the same; whose position and age are gathered from the comparison with the first already mentioned, as well as from the fourth and last vertical row of Anatolius' paschal table; yet with the leap added for the last six years of the canon. Whence it happens that the moons of Anatolius for the most part precede the Alexandrian by two or three days, and the Latin ones by at least one day, sometimes two, very rarely three. Indeed, the 12th, 14th, and 15th cycles of Anatolius anticipate both the third, fifth, and sixth of the Alexandrians, and the 13th, 15th, and 16th of the Latins, by three days. But the 10th and 15th of Anatolius precede the Alexandrian 19th and 6th by four days, and the Latin 10th and 16th by only two days, as our table at the end of this chapter demonstrates. A great disparity, I confess; and of a more difficult faith regarding such a great man. But the age of the moon expressed twice for each year of the Anatolian table forces that belief even upon the unwilling.

Bede indeed, in *De Ratione Temporum*, c. 4, compares the 14th year of the Anatolian cycle with the last of the ogdoad, that is, as I think, the eighth of the Alexandrians, as we heard a little earlier, and consequently the first of that cycle with their 14th: and thus he institutes the moons of Anatolius as nearly contemporaneous with the Alexandrians and Latins. But three things prevent me from believing him less, although I would most wish to. 1° Bede himself, as I have already said, expressly places the lunar leap with Cyril in the 14th year of the cycle of Anatolius. For when ^B

priests arise: provided that the moon does not reach below the 14th nor above the 20th day (which, in his 17th year, concurs with the Alexandrian 14th day), whether the paschal limit, which is the 14th day of the moon, precedes the equinox, or follows it, or falls upon it. Behold his words, and his one and only rule: "This Pasch from the 6th day before the Kalends of April, up to the 9th day before the Kalends of May." Therefore, he expressly fixes his latest paschal Sunday on the 6th day before the Kalends of April, or March 27th, in the 19th or last year of his cycle, with its Dominical letter—and that erroneous 'B'—and likewise its moon 17. The most remote date, however, is the 9th day before the Kalends of May, or April 20th, with the erroneous Dominical letter 'A,' in the 14th year of his cycle, with its moon 20. Wherefore, he concludes the limits of paschal Sundays within only 28 days, from March 27th to April 23rd, and so he never admits Pasch in the Egyptian month of Pharmuthi alone, from its 1st day to the 28th, not in Phamenoth. Unless perhaps someone might think the day of March 26th, which is the last or 30th of Phamenoth—which we have already said is termed by him a transgression of the equinox—should for some reason be added to this limit as well. For thus 29 days would be completed, which I do not believe. But both the ancient Latins and the Alexandrians, by the nature of the matter, assign 35, and Victorius assigns 34, spread out over a whole week; which he therefore rejects. Indeed, he does not even wish to admit the limit of the Caesarean Fathers, although it is of only 31 days, since he speaks thus in § 15: "Certain African investigators approve these reasons in their calculation, composing a certain beginning and end of Pasch; that is, that Pasch is not to be sacrificed before the 11th day before the Kalends of April, nor after the 21st moon and the 11th day before the Kalends of May. We decree that these limits are not only not to be followed, but are to be detested and excised." Thus he says.

5° He differs in the age of the moon assigned to paschal Sunday. The Latins do not announce the latest Paschal Sunday before their 16th moon, the Alexandrians not before the 15th. He himself admits even the 14th moon, as is evident in the 2nd, 5th, and 17th years of his cycle, in which he agrees with the Quartodecimans. Hence it comes about that he never extends that same Paschal Sunday beyond the 20th moon, while the Alexandrians extend it to the 21st, and the Latins even to the 22nd. Why he does this, he attempts to give the reason for in § 8 of his treatise. And in this the ancient Scots agreed with him, if we trust Bede, Book III of the *Ecclesiastical History of the English*, ch. 25. In the final perpendicular column of Anatolius' table, where he designates the age of the moon on paschal Sunday, three years, namely the 8th, 11th, and 14th, show the 20th moon, and none show the 21st or 22nd.

6° Finally, Anatolius differs in the revolution of the paschal cycle itself; for while it is certain that it can only be completed in 532 years—namely with the lunar cycle led into the solar, or 19 years into 28—he concludes it in an interval of 19 years; thinking, I suppose, that the revolutions of the 14th moons and of the paschal Sundays are equal, which differ in their entire scope. Hence he says in § 12: "But this, he says, is defined by other wise and most acute men as impossible; that in that narrow and very brief space of the 19-year cycle, the truest Pasch, that is, on a Sunday, could be found after the equinox. But we, so that it may be made more manifest what induces incredulity in them, etc." Again, in § 13: "This 19-year cycle is not approved by certain African investigators who have written more ample (note) cycles, because it seems to be sufficiently contrary to their conjectures." But if he had followed those African investigators, he would not have been compelled to admit leap years less frequently, and to excise and confuse the series of Dominical letters thus; since indeed it cannot be concluded in such a short cycle. No one fails to see how paradoxical all these tenets of Anatolius are: from them, it is inevitable that great confusion must arise in the reader's intellect. So much so that we have not without cause questioned whether they could belong to such a great man as Anatolius. But so many testimonies of Bede, and indeed of Eusebius, which report the same words, and the manuscript...

manuscript codices forbid us to doubt, as we saw above. I indeed think it was hardly brought into use, unless perhaps for a few years at Laodicea, where Anatolius was bishop, or even in neighboring places. For the Sunday letters alone, placed with such error, sufficiently argue that it could not subsist for long. And the cycle of Eusebius, bishop of Caesarea, which began to be used not long after, as we said above, would easily have excluded it: so much so that this one, because it was more confused, was held in almost no place by posterity already imbued with clearer knowledge; and it immediately conceded the first place to Eusebius. I have tried here to make the mind of Anatolius understood, not unmindful of that saying, that nothing is invented and perfect at the same time. He was the first to attempt to adapt the lunar enneadecaeteris to the invention of the Christian Easter, none, as I think, having trodden it before. What wonder if he did not immediately reach the mark of truth?

But let us now exhibit two tables; of which the first compares the cycle of Anatolius with the golden numbers of the Alexandrians and Latins: the second arranges it methodically in the Julian Calendar, though from his erroneous opinion.

Cycle of Anatolius. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Cycle of the Alexandrians. 11 12 13 14 15 16 17 18 19 1 2 3 4 5 6 7 8 9 10 Cycle of Victorius and the Latins. 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 1

ARRANGEMENT OF THE ANATOLIAN CYCLE IN THE CALENDAR.

MARCH. Days of March. | Sunday Letters. | Months of the Egyptians. | Cycle of Anatolius. | Cycle of the Alexandrians. | Cycle of Victorius and the Latins. Kal. | 1 | d | 5 | | | VI | 2 | e | 6 | | | V | 3 | f | 7 | | 9 | 2 IV | 4 | g | 8 | 17 | XI | III | 5 | A | 9 | | | 10 Prid. | 6 | b | 10 | 6 | XIX | 18 Non. | 7 | c | 11 | 14 | VIII | VIII | 8 | d | 12 | 3 | XVI | VII | 9 | e | 13 | | V | 13 VI | 10 | f | 14 | 1 | | 4 V | 11 | g | 15 | 19 | XIII | IV | 12 | A | 16 | | II | 12 III | 13 | b | 17 | 8 | | 1 Prid. | 14 | c | 18 | 16 | X | Idib. | 15 | d | 19 | 5 | XVIII | 17 XVII | 16 | e | 20 | | VII | XVI | 17 | f | 21 | 13 | | 6 XV | 18 | g | 22 | 2 | XV | XIV | 19 | A | 23 | | IV | 14 XIII | 20 | b | 24 | 10 | | 3 XII | 21 | c | 25 | 18 | XII | XI | 22 | d | 26 | | 1 | 11 X | 23 | e | 27 | 7 | | 19 IX | 24 | f | 28 | 15 | IX | VIII | 25 | g | 29 | | | 8 VII | 26 | A | 30 | 4 | XVII | VI | 27 | b | 1 | | VI | 16 V | 28 | c | 2 | 12 | | 5 IV | 29 | d | 3 | 1 | XIV | III | 30 | e | 4 | 9 | III | 13 Prid. | 31 | f | 5 | | |

APRIL. Days of April. | Sunday Letters. | Months of the Egyptians. | Cycle of Anatolius. | Cycle of the Alexandrians. | Cycle of Victorius and the Latins. Kal. | 1 | g | 6 | 17 | | 2 IV | 2 | A | 7 | | XI | 10 III | 3 | b | 8 | 6 | | 18 Prid. | 4 | c | 9 | 14 | XIX | Non. | 5 | d | 10 | | VIII | 7 VIII | 6 | e | 11 | 3 | XVI | VII | 7 | f | 12 | 11 | V | 15 VI | 8 | g | 13 | 19 | | 4 V | 9 | A | 14 | | XIII | IV | 10 | b | 15 | 8 | II | 12 III | 11 | c | 16 | 16 | | 1 Prid. | 12 | d | 17 | | X | Idib. | 13 | e | 18 | | | XVIII | 14 | f | 19 | | | XVII | 15 | g | 20 | | | XVI | 16 | A | 21 | | | XV | 17 | b | 22 | | | XIV | 18 | c | 23 | | | XIII | 19 | d | 24 | | | XII | 20 | e | 25 | | | XI | 21 | f | 26 | | | X | 22 | g | 27 | | | IX | 23 | A | 28 | | | VIII | 24 | b | 29 | | | VII | 25 | c | 30 | | | VI | 26 | d | 1 | | | V | 27 | e | 2 | | | IV | 28 | f | 3 | | | III | 29 | g | 4 | | | Prid. | 30 | A | 5 | | |

CHAPTER IV.

I think there is hardly any cause to doubt that Anatolius published his nineteen-year cycle before the Alexandrians. For who could persuade himself that he would have been able to publish such a confused [cycle], if he had had before his eyes one so orderly as the Alexandrian one? Moreover, Eusebius, Timothy, Cyril, Victorinus, Bede, and others sufficiently intimate this in their writings: and it will shortly be made clear.

Georgius Hervart, in *Nova Chronologia*, chapter 236, deduces the beginning of this Anatolian Canon from the vulgar year of Christ 277, the second year of the emperor Probus, and he brings forward two reasons: First, because the years of so many different nations, so various, placed for that year in the Chronicle of Eusebius, are undoubtedly accommodated to the first year of the paschal cycle of Anatolius. For after the enumeration of these years, there soon follows in the Chronicle of Eusebius: "Anatolius, bishop of Laodicea, learned in the disciplines of the philosophers, is celebrated in the speech of many."

Second, Anatolius writes that in the first year of his cycle, the new moon of the first month, which is the beginning of the entire enneadecaeteris, falls on Phamenoth 26, Dystrus 22, and March 20. But this, according to astronomical truth, suits the year of Christ 277 better than eight years later—namely, the year of Christ 285. Thus Georgius Hervart.

But we, from what has been said, think that we must necessarily begin from the year preceding 276: 1° Because the Pascha of that year as Anatolius [defines it] demands it, whether you consider his lunar or solar cycle; for it is on the same day, indicated as April 16, which both the Alexandrians and the Latins indicate, even though they all differ as to the age of the moon. And it is not likely that Anatolius erred in the very first year. 2° The Dominical letters of the three immediately following years agree, as do those of the seventh and eighth years. But if the paschal Sundays are at times different, that arises from the various decisions of Anatolius: for example, because he ordains that the fourteenth moon constitutes the legitimate Pascha; because he does not recognize an equinox before March 25 and a Sunday Pascha before March 27; because he indicates new moons differently than others, and so on. And yet, in the fourth year of his cycle, he rightly determines Sunday Pascha on the Ides of April with both [parties].

^B Nor are the arguments of Hervart very pressing. For one who flourished in the year 277 could also have flourished in 276, or rather have begun then precisely. And as for one who brings a cycle to light in a year and marks the year of the edition with different characters, nothing prevents him from well deducing its beginning from a yet earlier year, if reasons perhaps require it. Finally, those diverse years of diverse peoples can be noted the more on account of the origin of the Manichaean heresy, which is rightly assigned to that year by the holy Fathers, insofar as it is better known than the more confused cycle of Anatolius. Scaliger also adverted to this in part before us. Nor is it true that Anatolius refers the beginning of his enneadecaeteris to the 20th of March, but rather to the 25th and 26th; as is clear from the second chapter of this Commentary, and more clearly still from the paschal table of Anatolius itself, and indeed from his own text, when he sets the new moon of the first month on March 30.

FRAGMENTS

From the Arithmetic books of Anatolius of Alexandria

What is mathematics?

From whom was mathematics so named?

able things, which are pure and simple, the Pythagoreans saw them circulating, for in these alone they thought that science consisted. ^A Recent philosophers, however, have extended this name further, so that they have wished the mathematician to be occupied not only with incorporeal and intelligible matter, but also with that which is close to corporeal and sensible substance. For he ought to be a theorist of the courses of the stars, [and] of their speeds, sizes, forms, and distances; he ought also to examine how the stars affect the eyes, investigating why, although the stars observed are such and so great, they are not seen as such and so great from every distance, even though these stars maintain their mutual relations, but produce deceptive appearances regarding their order and position. Such appearances of the stars are determined at times by the state of the sky and the air, at times by mirrors, or by any polished surface, or by translucent bodies, or by other things of this kind. Furthermore, they held that a man ought to be a master of machines, and a surveyor, and a logician. ^B Moreover, he must be occupied with the causes of the harmonious blending of sounds and of the composition of melody, which are bodies, or at least they make their final reference to sensible matter.

What is mathematics?

How many parts of mathematics are there?

That the circle has eight solids, six surfaces, and four angles...

Which parts of mathematics are closest to which?

That mathematics has its principles from a hypothesis and concerning a hypothesis. Hypothesis is spoken of in a threefold way, or