Ae. Bucherius, S.J., In S. Anatolii Canonem paschalem commentarius

is diminished, in which twelve hours and an as are used up, that is, the first part out of twelve small parts. On which day at evening, if the fourteenth moon had fallen on it, the lamb was sacrificed among the Jews. But if, the number running over, the fifteenth or sixteenth moon had been found, the Pasch was celebrated at evening on the evening of the same day, on the fourteenth day of the second moon born in the same month, eating unleavened bread for seven days, up to the twenty-first day at evening. For us, then, if it should likewise happen that on the seventh before the Kalends of April both the Lord's day and the fourteenth moon are found, Easter is to be celebrated on the fourteenth. But even if the fifteenth or sixteenth moon, and on up to the twentieth, should be found, out of reverence for the Lord's resurrection, which took place on the Lord's day, we must likewise celebrate it; yet so that the beginning of Easter does not go beyond the end of their solemnity, that is, the twentieth moon. And therefore we have said that those have erred not a little who have dared to anticipate or to exceed this number set in divine Scripture. And from the eighth before the Kalends of April to the eighth before the Kalends of July, an hour is diminished every fifteen days, by two moments and a half and the sixth part of a moment, as the sun ascends each day. And from the eighth before the Kalends of July to the eighth before the Kalends of October likewise, every fifteen days and four hours, an hour is diminished, the sun descending each day by the same number of moments; and the space that remains, up to the eighth before the Kalends of January, is completed with a like number of hours and moments. So that on the eighth before the Kalends of January the hour has an hour and half an hour. For up to that point the day and the night are diminished. And the twelve hours which at the vernal equinox were established in the beginning by the Lord's dispensation, being diminished in the night on the eighth before the Kalends of July, as the sun ascends through each of the eighteen degrees we spoke of above, are found joined, in the twelfth, to a longer space. And again the twelve hours which at the autumnal equinox are filled up by the sun's descent are found on the eighth before the Kalends of January to be six hours divided into twelve, disjoined, the night holding eighteen divided into twelve; which on the eighth before the Kalends of July likewise held six divided into twelve.

XVII. Conclusion of the work.

XVII. But you should not be unaware of this: that these four boundaries of the seasons of which we have spoken, although they draw near to the Kalends of the following months, each nevertheless holds the middle of its season, that is, of spring and of summer, of autumn and of winter. And the beginnings of the seasons do not start from the point where the Kalends of the months begin. But each season is to be begun in such a way that from the first day of spring the equinox divides the season; and summer is likewise divided on the eighth before the Kalends of July, and autumn on the eighth before the Kalends of October, and winter on the eighth before the Kalends of January.

GILES BOUCHER (AEGIDIUS BUCHERIUS)

Commentary on the Paschal Canon of St Anatolius of Alexandria.

CHAPTER I.

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 by Anatolius. Eusebius, Bede, Colman, and Wilfrid attribute it to Anatolius. Bede quotes several passages word for word from this Canon.

That Anatolius, an Alexandrian by race, wrote his Canon in Greek no one doubts. And Eusebius removes all doubt, who quotes a good part of it in Greek. All alike ascribe this Latin version to Rufinus, and on that account consider it not very accurate nor sufficiently faithful. Assuredly the Greek passages which Eusebius happily inserted in Book VII, chapter 26 (32) of his Ecclesiastical History are both fuller than Rufinus's and are repeatedly conceived otherwise and more clearly, as is evident to anyone even at first comparison. On this account I do not deny that some blemish may have crept into the text of this Canon. But the question is whether that text, setting aside the scarcely reliable translation of Rufinus, is in other respects the genuine and true offspring of Anatolius, which Eusebius calls the Canon on Easter and Jerome the Volume on Easter.

From principles indeed altogether paradoxical, and established contrary to the common opinion of those who have written on the Christian Easter, which this Canon displays, it might perhaps seem spurious and supposititious, and the work of another rather than of Anatolius, so praised and so Catholic a writer. To select here in the meantime a few points out of many: Easter Sunday he appoints without scruple on the fourteenth moon, wherein he sides with the Quartodecimans, or Tessareskaedecatites rejected by the Church, even though this is not perpetual with him, and recurs only three times in the whole nineteen-year cycle. Moreover, he extends the same Easter Sunday from the thirteenth moon, at least at its close, only to the twentieth; although Scripture, and with it the Alexandrians among whom Anatolius studied, openly extend it from the fourteenth to the twenty-first, and the Latins do not hesitate to extend it even to the twenty-second. In addition to this, he establishes the Dominical letters and the bissextile, and most other matters, so confusedly that it seems to be the work not of some learned and holy Father, such as all suppose Anatolius to have been, but rather of an unpolished and ignorant writer, and perhaps one straying from Catholic truth. Of which more presently in the third chapter.

Nevertheless, the following considerations more strongly prove it to be the genuine offspring of Anatolius. First, the authority of Eusebius of Caesarea, who could have seen him, and who brings forward in the name of Anatolius no slender fragment of this Canon, plainly conformable to this little work, save where the fidelity of the translator wavers. Bede also does the same at the beginning of his little book On the Equinox and on the Reckoning of Times, in the fourth chapter. Next, Colman, bishop of the Scots, in the same Bede, Book III of the Ecclesiastical History of the English, chapter 25, asserts that Anatolius, a man, as he says, holy and most praised in ecclesiastical history, handed down that Easter is to be celebrated from the fourteenth moon to the twentieth. Which also the Catholic presbyter of the English, Wilfrid, disputing against Colman for the Alexandrian Easter, not only admits, but moreover that the Scots repeatedly begin Easter from the thirteenth moon at evening

reproaches them with, which from the reckonings of this Anatolian Canon must sometimes necessarily come about. Finally, Bede himself quite often copies out very many things word for word from this Canon, and attributes them to Anatolius. For first, through almost the whole of his little book on the equinox, he disputes in such a way about the opinion of Anatolius in fixing the equinox that anyone may easily perceive that he could have drawn these things from no other source than from this very faulty and corrupt Latin Canon. Of which we shall speak more fully in the following chapter. Again, the same Bede, in On the Reckoning of Times, chapter 40, writes most expressly that the leap of the moon is placed by Anatolius not at the end or head 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. Which the diagram of this Canon plainly exhibits in the very same way.

Finally, most clearly the same Bede, in the same book On the Reckoning of Times, chapter 33, confirms this Anatolian Canon in these words: Moreover the holy man of the Church, Anatolius, in his Paschal work, when he had disputed most subtly concerning the equinoxes and solstices, and concerning the increments of hours and moments, ended his disputation and at the same time the little book itself thus: "Now you should not be ignorant of this, that although those four boundaries of the seasons which we have mentioned before approach the Kalends of the following months, nevertheless each one holds the middle of the seasons, that is, of spring and summer, of autumn and winter; and the boundaries of the seasons are not begun from where the Kalends of the months are initiated. Rather, each season is to be begun in such a way that the equinox divides the season from the first day of spring; and of summer, on the eighth day before the Kalends of July; and of autumn, on the eighth day before the Kalends of October; and of winter, on the eighth day before the Kalends of January it similarly divides it." Thus far Bede. Which are plainly the very same and final words of this Canon of ours, and accordingly lend no small credit to it.

The arguments, however, which are brought forward here to the contrary will be examined more conveniently below in the third chapter.

CHAPTER II.

On what day of the Julian March Anatolius fixes the equinox. Most think that he fixed it on the eleventh day before the Kalends of April. Yet it is demonstrated more truly that he fixed it with Caesar on the eighth day before the Kalends of April. The contrary argument is refuted. Whether Anatolius speaks according to the opinion of Ptolemy. The Alexandrians seem to have retained the civil equinox on the eighth day before the Kalends of April with Caesar until about the Synod of Nicaea.

That this question has been raised not today for the first time, but already from ancient times, we sufficiently understand from Bede's little book On the Vernal Equinox. There are some, he says, who contend that Anatolius in this opinion (namely concerning the day of the equinox) by no means set down the eleventh, but the eighth day before the Kalends of April. And yet among present-day writers you could scarcely see one who does not suppose as indubitable that the equinox according to the mind of Anatolius falls on the eleventh day before the Kalends of April, or the twenty-second of the Julian March. They prove it by his own words: There is therefore in the first year the beginning of the first month (namely the Paschal month), which is the beginning of the nineteen-year cycle, according to the Egyptians indeed on the twenty-sixth day of the month Phamenoth; according to the Macedonians on the twenty-second of the month Dystrus; and as the Romans speak, on the eleventh day before the Kalends of April, etc. But that these words are corrupt I shall now show.

I say therefore that the opinion of Anatolius here is most plainly that of Caesar or Sosigenes: namely, that the day of the equinox falls 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 especially clear and uncorrupted passages of the text of Anatolius himself. First he says: On that twenty-sixth day of Phamenoth the sun is found not only to have entered the first segment of the Zodiac, but also to have already traversed the fourth day within it. Assuredly in the age of Anatolius, about the common and present-day year of Christ 276, in which I judge these things to have been composed by him, the astronomical equinox of spring,

or the actual intersection of the zodiacal and equinoctial circles, no one would deny fell on the twenty-first or twenty-second day of the Julian March (which coincide with the twenty-fifth and twenty-sixth of Phamenoth). How therefore could the sun, according to the sense of Anatolius so clearly expressed here, have then traversed the fourth day in Aries? But if in place 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 be plainly true that the sun in the first segment of the zodiac, which we call Aries, had already altogether traversed the fourth day, or was traversing the fifth. And the sense of Anatolius will be that the actual intersection of the circles takes place on the twenty-first of March rather than the twenty-second, which he had drawn, as I suppose, from the Alexandrians, who a few years later publicly held this.

Secondly, he adds in this same little work, section 8: But what wonder if they have erred in the twenty-first moon, who have added three days before the equinox, in which they define that the Passover can be sacrificed? Which is altogether certain also to be deemed absurd. By those who added three days before the equinox, Anatolius here understands the Fathers of the council of Caesarea in Palestine. Who, although they too recognized the day of the civil equinox on the twenty-fifth of March, nevertheless had been unwilling that the three preceding days, on which Christ after instituting the venerable sacrament was arrested, suffered, and was buried, should be excluded outside the Paschal limit. For no others occur of whom this could be said. For the Jews and the first Christians, the Latins at least, who, as I have said, had affixed the first entrance of the sun into Aries to the eighteenth of March, had added not merely three, but seven days. Therefore, if Anatolius considers that three preceding days were absurdly—for so he hints—added to the civil equinox hitherto in use, he must necessarily cleave to the ancient equinox of Caesar, which was matched with the twenty-fifth of March, and not fix it on the twenty-second of March. Which truly valid argument Bede also brings 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 agreed with us.

The third and decisive passage of Anatolius is section 8; for there, through all the years of his nineteen-year cycle, determining also the day and weekday of his equinox, he always cleaves fixedly and firmly to the twenty-fifth of March, never to the twenty-second, as you may see in his table. And since he quite often repeats that Easter can never be duly celebrated except when the equinox is already past, he himself observes this with such scruple and almost superstition that he appoints the earliest Easter Sunday not on the seventh, or the day after the Caesarian equinox, but first on the sixth day before the Kalends of April. I believe, so that he might more certainly pass beyond the day of the equinox in the sanctioning of his Easter, and by so much the light might rule over the darkness. Thus nothing is more certain than that the equinox was matched by Anatolius with the twenty-fifth of March.

The argument of our adversaries, drawn from the words of Anatolius, was sufficiently rejected long ago by others, as Bede testifies, when they said that Eusebius (or someone else), when he reports this composition of Anatolius in his Ecclesiastical History, changed one day for another; and because he saw that the rest was well put, wished to correct with a single word what he had observed to be less perfectly stated in it: namely, lest he should openly show him whom he had proposed to praise to be blameworthy, if he inserted his pure words, just as he himself had written them, into his Histories. I know that Bede cannot persuade himself of this concerning Eusebius. But we know that many similar contrivances belonged to the wits of the Greeks, especially those infected with heresy, such as Baronius clearly teaches Eusebius to have been. Nor is there more force in what the same Bede subjoins: that it would be strange if such an imposture had escaped Victor of Capua, who himself also reads the eleventh, not the eighth day before the Kalends of April in Anatolius. For that same imposture deceived not only Victor, in that darkness of that age which still lingered, but also most of the sharpest writers of this most learned age. Eusebius wished to praise Anatolius. He could not do so unless he either said that the equinox had been badly fixed by the Synod of Nicaea, or

brought the text of Anatolius at least very close to the opinion of the synod. He believed the latter course easier and more acceptable than the former. Nor indeed are some traces of the introduced corruption wanting even now. For the manuscript codex from which we copied these things clearly exhibits the eighth day before the Kalends of April from the true and original reading, not the eleventh, even though it retains the twenty-second day of Dystrus from a faulty correction.

For the rest, why Eusebius, or whoever else undertook to correct Anatolius, substituted the twenty-second of March rather than the twenty-first for the twenty-fifth, I do not sufficiently perceive. For the Synod of Nicaea affixed the equinox to the twenty-first of March, or the twelfth, not the eleventh day before the Kalends of April, and so the Church thereafter retained it. Indeed Anatolius also seems to have thought thus, since on the twenty-fifth of March itself, on which he fixes his civil equinox, he openly writes that the sun in the first segment of the twelfth-part is already διαπορευόμενον, that is, having passed through and surmounted the fourth day, hinting that it is then traversing the fifth. Nor will he satisfy who says that Anatolius seems to have followed the opinion of Ptolemy. For why, if he were following the opinion of a pagan writer 130 years earlier, would he have said that on the twenty-fifth of March the sun had already traversed the fourth part of the first twelfth-part, and not rather, according to the same writer's sense, that it was traversing it? Would so great a man in so keen a study not have attended to the movements of the heavens and of the clocks? But whatever may underlie this (for it matters little), it is certain that Anatolius places the civil equinox not in the first degree of the first segment, but either in the fifth, as we indeed consider more probable, or certainly, as others hold, in the fourth; just as we declared above in the treatise On the Year of the Jews, chapter three, that Caesar and Meton placed it in the eighth, and Eudoxus according to the opinion of Geminus in the sixth.

Before I finish this chapter, let the reader consider here with me whether the teachers of the Alexandrian school did not retain the civil equinox on the twenty-fifth of March up to this point, seeing that Anatolius, who was not the lowest among them, retains it so tenaciously on that day, even though he perceives that it corresponds to the fifth (or at least the fourth) degree of the first twelfth-part. And if this is so, then it must also be said that the Alexandrian patriarch Dionysius, who died scarcely eleven years before this work of Anatolius, adapted his Paschal octaeteris to this day of the Caesarian equinox, not the Nicaean or Ptolemaic: inasmuch as he himself also does not allow Easter to be celebrated before the equinox, as we noted above.

CHAPTER III.

The Paschal limits and several paradoxes of Anatolius. Paradoxes in the sun; in the Dominical letters; in the moon. The different beginning of that cycle; likewise the leap of the moon. The different position of the golden numbers; the different age of the moon. What Bede seems to think here. The different beginning and end of the first or Paschal month. The Easter Sunday of Anatolius from the sixteenth moon to the twentieth. Anatolius thought that in nineteen years, just like the moon, so also Easter Sunday revolves upon itself. The cycle of Anatolius compared with the cycles or golden numbers of the Alexandrians and Latins. The arrangement of the Anatolian cycle in the Calendar.

From the other computists, both Latin and Alexandrian, Anatolius differs greatly as regards the sun and the moon.

As regards the sun indeed: 1st, because he decrees the civil equinox not, like the Alexandrians and the Synod of Nicaea, on the twenty-first of March, or, like the ancient Latins with the Jews, on the eighteenth, but on the twenty-fifth with Caesar, as we have already seen. And he wills that Easter be celebrated neither before it, nor on it, nor even on the day after it: so great is his solicitude certainly to pass beyond even the civil equinox. So long (he says in section 6) as equality between light and darkness endures, not diminished by the light, it is shown that the Passover is not to be sacrificed. On this account, therefore, the Passover is commanded to be sacrificed after the equinox, because the fourteenth moon before the equinox, and on the equinox, does not fill the whole night. After the equinox, however, the fourteenth moon, when one day has been added (note)

which is the passing of the equinox, although it has not reached to the true light, that is, the rising of the sun and the beginning of the day, nevertheless does not leave darkness behind it. So says he; by which words he establishes his earliest Easter Sunday only on the second day after the occurrence of the equinox, or the twenty-seventh of March.

2nd, he dispenses the Dominical letters and bissextiles by a far different reckoning. For out of nineteen years he sets down only two as bissextile, namely the seventh and the seventeenth, as may be seen in his Paschal table. Yet to nineteen years four at the least, and sometimes five, belong. And whereas in seventy-six years nineteen bissextiles in all are reckoned, according to his teaching only eight would belong. Thus he makes the solar year different from the Julian and by so much shorter, and accordingly establishes Easter Sundays out of conformity with the true ones, and which quite often fall on ordinary weekdays. Certainly he agrees with the truth only in the first four years of his nineteen-year cycle, and likewise in the seventh and eighth, unless perhaps he is helped by chance.

As regards the moon, however, he differs even more: 1st, because that which is for him the first year of the nineteen-year cycle is for the Alexandrians the eleventh, and for the Latins and our Victorius the second. For he begins his cycle from the year 276 of the common era of Christ, eight years before the Alexandrian, as we demonstrate hereafter, and especially in chapter 4.

2nd, he differs in the leap of the moon. For the Alexandrians place this in the nineteenth year of their nineteen-year cycle, which is the first of the present-day Romans; the Latins and Victorius in their sixteenth; and he himself in his fourteenth, as is clear from his table, which in that year makes the leap from the eighth to the twentieth. Concerning which Cyril also hints at something in sections 4 and 7 of his Prologue, although suppressing the name of Anatolius; and Bede more expressly in On the Reckoning of Times, chapter 40: Finally, he says, Anatolius, who most truly decrees the beginning of the months and the head and boundary of the whole cycle at the vernal equinox, himself placed this change of the moon not at the head, like the Romans, or at the end, like the Egyptians, of his nineteen-year cycle, but in its fourteenth year, which is the last of the ogdoad, making it ascend from the eighth to the twentieth. Thus far Bede. Hence it comes about that the Anatolian golden numbers from sixteen to nineteen are moved upward by one day in the Julian Calendar.

3rd, he disagrees in the very position of the golden numbers, and, what follows therefrom, in determining the age of the moon. For he twice expressly matches his first cycle with the thirtieth day of March, once in section 11 of his text, and again in the first year of his table. And since this corresponds to the eleventh cycle of the Alexandrians and the second of the Latins, it must necessarily precede the former by three days and the latter by two days. The judgement is the same concerning the remaining years, whose position and age are gathered alike both from comparison with the first already mentioned and from the fourth and last vertical column of the Paschal table of Anatolius, with the leap, however, added to the last six years of the canon. Whereby it comes about that the moons of Anatolius for the most part outrun the Alexandrian by two or three days, and the Latin by at least one day, sometimes by two days, and very rarely by three days. Indeed cycles twelve, fourteen, and fifteen of Anatolius anticipate both the third, fifth, and sixth of the Alexandrians and the thirteenth, fifteenth, and sixteenth of the Latins by three days. But the ninth and seventeenth of Anatolius precede the nineteenth and eighth of the Alexandrians by four days, and the tenth and eighteenth of the Latins by only two days, as our table at the end of this chapter demonstrates. A great disparity, I confess, and harder to believe of so great a man. But the age of the moon twice expressed in each year of the Anatolian table extorts that belief even from the unwilling.

Bede indeed in On the Reckoning of Times, chapter 4, matches the fourteenth year of the Anatolian cycle with the last of the ogdoad, that is, as I suppose, the eighth of the Alexandrians, as we heard a little before, and accordingly matches the first of that cycle with the fourteenth of theirs; and thus makes the moons of Anatolius almost coeval with the Alexandrian and Latin ones. But why I should less believe him, much as I would wish to, three things stand in the way. 1st, Bede himself with Cyril, as I have already said, expressly places the leap of the moon in the fourteenth year of the cycle of Anatolius. This with

the other cannot stand; for thus the leap of the moon, duly placed at the fourteenth year of the Anatolian table, would contrary to the supposition have to be transferred to the seventeenth of the same (which first coincides with the eighth of the Alexandrian). 2nd, there stands in the way the age of the moon, so explicitly noted by Anatolius, whether on the very day of the equinox, the twenty-fifth of March, or on the day of Easter; which can in no way square with this statement of Bede, as is evident of itself. 3rd, there stand in the way the Dominical letters, likewise twice marked here. For although I recognize them as true only in the earlier years of the table, and likewise in the seventh and eighth, and in the others as always erroneous, nevertheless the manuscript codex most plainly exhibits them as such: so that altogether either it or Bede must necessarily be mistaken. I assent more to the codex, both trustworthy and consistent in itself, and more conformable to the express words of Anatolius. For at the end of section 6 he ordains that both the equinox and the full moon are plainly to be passed beyond at Easter, so that light may overcome every power of darkness. Which Cyril also hints at in section 4 of his Prologue, when, treating of the leap both of the Latins and of Anatolius, he subjoins, plainly in accordance with the sense of our codex, that their computation is unsuitable and hastens too much.

Nevertheless I do not deny that the golden numbers of Anatolius, in March and the Paschal month, sometimes seemed to me to have been badly pushed upward by one day by a copyist; and it seemed that this could be sufficiently gathered from section 11 of his treatise, where the first golden number is matched with the first day of March. And although from the twenty-sixth age of the moon noted at the day of the Anatolian equinox it seems to be matched with the last day of February, namely one day earlier, yet that this rather is faulty is taught by the 59 days which Anatolius, like the rest, rightly counts from the first of January to the last of February; which is the just quantity of two lunar months. Hence also the golden number 1 seemed more rightly to have to be rolled down to the first and last day of March, so that this third moon of the year might be of thirty days no less than the first, according to the natural alternation, and not to be left at the thirtieth or penultimate day of March, although both in the Paschal table and in section 11 in part Anatolius ordains it so. There was added besides that, once these things were admitted, the moons of Anatolius now became in some way more coeval with the moons of the Latins and Alexandrians, and certainly outran them by one day less. Wherefore I was altogether inclined to do so. But I noticed that I then struck against a greater difficulty. Anatolius three times defined fourteenth Paschal moons in three years of his table, the second, fifth, and eighteenth. If we roll his golden numbers down by one day, those will now be not fourteenth, but thirteenth moons: which is contrary to his reckonings. The judgement is the same concerning his three twentieth Paschal moons as well. We must therefore rather adhere to the former opinion, and say that Anatolius, forgetting himself here in so intricate a matter (unless perhaps it was the copyist, which I do not think), confounds both himself and the reader.

4th, Anatolius differs in the beginning and end of the first month, which the Latins begin from the fifth day of March, and the Alexandrians from the eighth. He himself latest of all begins it from the tenth, because he also fixes the equinox latest of all. In the eleventh year of his cycle he appoints Easter Sunday on the fourth day before the Kalends of April, or the twenty-ninth of March, on his twentieth moon, and accordingly begins that moon from the tenth of March. In the nineteenth year of the cycle indeed he marks his earliest Easter Sunday on the sixth day before the Kalends of April, or the twenty-seventh of March. But since he counts that moon as only the seventeenth, he plainly deduces the first only from the eleventh of March, the day after the beginning of the moon already mentioned. Where it is to be noted that Anatolius cares nothing for that rule of the Alexandrians and of the present-day Church, that the Paschal fourteenth moon is that which falls either on the equinox itself or next after it. For he himself matches the equinox with the twenty-fifth of March. Nay more, he wills that one day besides, namely the twenty-sixth of March (which he calls the passing of the equinox), be passed beyond before the lawful performance of the earliest Easter, so that by so much the light may overcome the darkness. Thus he has no regard, or a very slender one, for the new moons and Paschal limits, but only for the Sundays which from the twenty-seventh of March to the twenty-third of April inclusive are found:

provided only that they fall neither below the fourteenth nor above the twentieth day of the moon; and that whether the Paschal limit, which is the fourteenth moon, precedes the equinox, or follows it, or falls upon it. Behold his words, and his sole and entire rule: This Easter is from the sixth day before the Kalends of April until the ninth day before the Kalends of May. Therefore he expressly affixes his earliest Easter Sunday to the sixth day before the Kalends of April, or the twenty-seventh of March, in the nineteenth or last year of his cycle, with his Dominical letter—and that an erroneous one—B, and likewise his seventeenth moon; and the latest, to the ninth day before the Kalends of May, or the twenty-third of April, with the erroneous Dominical letter A, in the fourteenth year of his cycle, on his twentieth moon. Wherefore he encloses the bounds of the Paschal Sundays within twenty-eight days only, from the twenty-seventh of March to the twenty-third of April, and consequently admits Easter only in the Egyptian month Pharmuthi, from its first day to the twenty-eighth, never in Phamenoth; unless perhaps someone should think that the twenty-sixth day of March besides, which is the last or thirtieth of Phamenoth, which we have already said is called by him the passing of the equinox, ought in some way to be added to this limit as well. For thus twenty-nine days will be made up, which I do not think. But both the ancient Latins and the Alexandrians, from the nature of the matter, assign thirty-five, and Victorius thirty-four, wider by a whole week; which he accordingly rejects. Nay, he is unwilling to admit even the limit of the Fathers of Caesarea, although of thirty-one days only, when in section 15 he speaks thus: Certain African calculators approve these reckonings in their computation, establishing a certain beginning and end of Easter, that is, that Easter is not to be sacrificed before the eleventh day before the Kalends of April, nor after the twenty-first moon and the eleventh day before the Kalends of May. Which limits we decree not only are not to be followed, but are even to be detested and cut away. Thus speaks he himself.

5th, he differs in the age of the moon to be assigned to Easter Sunday. The Latins appoint the earliest Easter Sunday not before their sixteenth moon, the Alexandrians not before the fifteenth. He himself admits it even on the fourteenth moon, as is clear in the second, fifth, and eighteenth years of his cycle, wherein he sides with the Quartodecimans. Hence it comes about that he never extends the same Easter Sunday beyond the twentieth moon, whereas the Alexandrians extend it to the twenty-first, and the Latins even to the twenty-second. Why he does this, he himself endeavours to give a reason in section 8 of his treatise. And in this the ancient Scots agreed with him, if credit is to be given to Bede, Book III of the Ecclesiastical History of the English, chapter 25. In the last vertical column of the table of Anatolius, which designates the age of the moon on Easter Sunday, three years, namely the eighth, eleventh, and fourteenth, exhibit the twentieth moon, and none the twenty-first or twenty-second.

6th, finally, Anatolius differs in the very revolution of the Paschal cycle; for whereas it is certain that this is completed only in 532 years, namely when the lunar cycle is multiplied into the solar, or nineteen years into twenty-eight, he himself nevertheless encloses it within the interval of nineteen years, supposing, I think, that the revolutions of the fourteenth moons and of the Paschal Sundays are equal, whereas they differ by the whole heaven. Hence he himself says in section 12: But this is defined by other wise and most acute men to be impossible, that within that narrow and briefest space of the nineteen-year cycle the truest Easter, that is, on the Lord's day, passing beyond the equinox, should be found. But that what brings unbelief to them may become more manifest, etc. Again in section 13: This cycle of nineteen years is not approved by certain African calculators who have drawn up larger (note) cycles, because it seems to be quite contrary to their conjectures. Yet if he had followed those African calculators, he would not have been forced to admit rarer bissextile years and thus to cut short and confound the series of Dominical letters, since in truth that series cannot be enclosed within so brief a cycle.

How paradoxical all these tenets of Anatolius are, everyone sees: from them indeed great confusion must necessarily arise in the mind of the reader; so that we have not without reason inquired whether they can belong to so great a man as Anatolius. But so many testimonies of Bede, and indeed of Eusebius, which report the same words, and the manuscript

codex forbid us to doubt, as we saw above. I indeed think that it was scarcely brought into use, unless perhaps for a few years at Laodicea, where Anatolius was bishop, or in neighbouring places also. For that it could not have subsisted for long, even the Dominical letters alone, placed with so great an error, sufficiently prove. And the cycle of Eusebius, bishop of Caesarea, which began to be used not so long afterwards, as we said above, would easily have excluded it: so much so that this one, because more confused, was held in almost no esteem by posterity, already imbued with clearer knowledge, and immediately yielded the first place to Eusebius. Here I have endeavoured to render the mind of Anatolius clear, not unmindful of that saying, Nothing is invented and perfected at the same time. He was the first to attempt to adapt the lunar nineteen-year cycle to the finding of the Christian Easter, a ground trodden, as I suppose, by no one before. What wonder if he did not immediately hit the mark of truth?

But let us now exhibit two tables, of which the first compares the cycle of Anatolius with the cycles or golden numbers of the Alexandrians and Latins, and the second arranges it methodically in the Julian Calendar as well, though according to 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 of the Latins. 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 1

THE CYCLE OF ANATOLIUS SET OUT IN THE CALENDAR.

MARCH.

Days of March. | Dominical Letters. | Months of the Egyptians. | Cycle of Anatolius. | Cycle of the Alexandrians. | Cycle of the Latins and of Victorius.

Kalends 1 d 5 Phamenoth. III 13

6th 2 e 6 9 2

5th 3 f 7 17 XI

4th 4 g 8 10

3rd 5 A 9 6 XIX 18

Day before 6 b 10 14 VIII

Nones 7 c 11

8th 8 d 12 3 XVI

7th 9 e 13 V 15

6th 10 f 14 1 4

5th 11 g 15 19 XIII

4th 12 A 16 II 12

3rd 13 b 17 8 1

Day before 14 c 18 16 X

Ides 15 d 19 9

17th 16 e 20 5 XVIII 17

16th 17 f 21 VII

15th 18 g 22 13 6

14th 19 A 23 2 XV

13th 20 b 24 IV 14

12th 21 c 25 10 3

11th 22 d 26 18 XII

10th 23 e 27 I 11

9th 24 f 28 7 19

8th 25 g 29 15 IX

7th 26 A 30 8

6th 27 b 1 Pharmuthi. 4 XVII

5th 28 c 2 VI 16

4th 29 d 3 12 5

3rd 30 e 4 1 XIV

Day before 31 f 5 9 III 13

APRIL.

Days of April. | Dominical Letters. | Months of the Egyptians. | Cycle of Anatolius. | Cycle of the Alexandrians. | Cycle of the Latins and of Victorius.

Kalends 1 g 6 Pharmuthi. 17 2

4th 2 A 7 XI 10

3rd 3 b 8 6 18

Day before 4 c 9 14 XIX

Nones 5 d 10 VIII 7

8th 6 e 11 3 XVI

7th 7 f 12 11 V 15

6th 8 g 13 19 4

5th 9 A 14 XIII

4th 10 b 15 8 II 12

3rd 11 c 16 16 1

Day before 12 d 17 X

Ides 13 e 18

18th 14 f 19

17th 15 g 20

16th 16 A 21

15th 17 b 22

14th 18 c 23

13th 19 d 24

12th 20 e 25

11th 21 f 26

10th 22 g 27

9th 23 A 28

8th 24 b 29

7th 25 c 30

6th 26 d 1 Pachon.

5th 27 e 2

4th 28 f 3

3rd 29 g

Day before 30 A