教會法與復活節計算 第 10 章

HERE BEGINS THE BOOK OF DIONYSIUS EXIGUUS. PREFACE. To the most blessed and greatly longed-for lord and father, Petronius the bishop, Dionysius Exiguus. The reckoning of the Paschal feast, which the urgent insistence of many has long and frequently demanded of us, we have now, aided by your prayers, taken care to set forth — following in all things the venerable three hundred and eighteen pontiffs who assembled at Nicaea, a city of Bithynia, against the madness of Arius, and arrived at a complete and true judgment in this matter. They fixed the fourteenth moons of Paschal observance as stable and unmoved, returning ever upon themselves through a cycle of nineteen years, which in all ages glide on from the same beginning at which they are repeated, without any divergence of variation.

This rule of the aforesaid cycle they sanctioned not so much by worldly skill as by the illumination of the Holy Spirit, and they are seen to have set it, as it were, as a firm and stable anchor to this reckoning of the lunar measure. Yet afterward certain men — some despising it through arrogance, others transgressing it through ignorance, led by Jewish fables — handed down a form for the single festival that was diverse and contrary. And because no structure can stand without the firmness of a foundation, in certain years they preferred to set the Lord's Pascha and the lunar computation far otherwise, arranging disordered cycles; these not only present no stability of recurrence, but even display a course notable for its error.

But the archbishop of the city of Alexandria, the blessed Athanasius — who himself also took part in the Council of Nicaea, then being deacon of the holy pontiff Alexander and his helper in all things — and afterward the venerable Theophilus and Cyril, in no way departed from this venerable ordinance of the synod. Rather, carefully retaining that same nineteen-year cycle, which by a Greek term is called the 'enneacaidecaeteris,' they are shown to have interpolated the Paschal course with no discrepancies. Finally Pope Theophilus, dedicating a course of a hundred years to the elder emperor Theodosius, and St. [Cyril...]

Cyril, composing a cycle of times of ninety-five years, preserved in all things this tradition of the holy council for the observing of the Paschal fourteenth moons. And because the rule of that same cycle ought to cling more firmly to those who are diligent and who seek to know what is true, we have thought it should be appended after our preface. We have therefore striven to set forth this cycle of ninety-five years with what diligence we could — placing in this our work the last cycle of the same blessed Cyril, that is, the fifth cycle (since six years of it still remained over), and thereafter we declare that we have arranged five others according to the norm of the same pontiff, or rather of the often-mentioned Council of Nicaea. But because St. [Cyril...]

Cyril began his first cycle from the one hundred and fifty-third year of Diocletian and ended the last in the two hundred and forty-seventh, we, beginning from the two hundred and forty-eighth year of that tyrant — rather than emperor — were unwilling to weave the memory of an impious man and persecutor into our cycles, but chose rather to mark out the spans of years from the Incarnation of our Lord Jesus Christ, so that the beginning of our hope might be more clearly known to us, and the cause of human restoration — that is, the Passion of our Redeemer — might shine forth more evidently.

Moreover, we have thought the reader ought to be warned of this: that this cycle of ninety-five years which we have made, when, the period being completed, it begins to return upon itself, does not in all respects keep the firmness proposed. For although the years of our Lord Jesus Christ keep their order in a continuous series, and the indictions run their course through fifteen years by their accustomed revolution, and you may find the epacts (as the Greeks call them) — that is, the eleven annual lunar additions which return upon themselves at the end of thirty days — noted down by fixed rules, and you may find the nineteen-year recurrence too, and the Paschal fourteenth moons the same throughout the revolution of all ages;

nevertheless the concurrent days of the weeks, and the days of the Lord's Pascha, and the moon of that same Lord's day, cannot keep a like tenor of constancy. Now the reckoning of the concurrents of the weeks, which arises from the course of the sun, is bounded by a continuous circuit of seven years. In this you must take care to count one for each single year; only in that year in which there is a bissextile (leap year) you shall add two. This is also the reason why this cycle of ninety-five years does not in all things appear to agree with its own recurrence. For though in the other years it does not disagree, in those alone in which the bissextile inserts itself, the Lord's Pascha with its moon meets the reckoning in a varying manner.

But those things which run their course through all times in a fixed order can, by their stable circuit, without any difficulty direct the fall of the movable elements. And therefore, after the completion of the ninety-five years, when one diligently desires to return to the beginning of these matters, let him not run to the fifth cycle of St. Cyril, which we proposed of necessity, but let him watchfully run forward to our first; and in the order we have stated, by means of those things which retain a firm course, let him support the progress of those things which seem to totter. This too we have judged ought to be noted with no less care, lest we be deceived in the recognition of the first month. For from this arises almost the whole error of the Paschal discrepancy, while the beginning of the time is unknown.

For when the almighty Lord appointed this most sacred solemnity to be celebrated by the children of Israel, who were being freed from Egyptian bondage, He says in the book of Exodus to Moses and Aaron in the land of Egypt: 'This month shall be the beginning of months; it shall be the first in the months of the year.' And likewise in the same place: 'In the first month,' He says, 'on the fourteenth day of the month, toward evening, you shall eat unleavened bread, until the twenty-first of the same, toward evening.' In Deuteronomy too the same lawgiver Moses thus admonishes the people concerning this matter, saying: 'Observe the month of the new produce, and the first of the spring season, that you may keep the Pascha to the Lord your God; for in this month the Lord your God brought you out of Egypt by night.'

By so great a divine authority it became clear that in the first month, on the fourteenth day, toward evening, until the twenty-first, the Paschal festivity ought to be celebrated. But because it is not clearly read there whence this month takes its beginning or where it ends, the aforesaid venerable three hundred and eighteen ancient pontiffs, more diligently investigating the observance of ancient custom handed down thereafter from holy Moses — as is reported in the seventh book of the Ecclesiastical History — declared that the moon born from the eighth of the Ides of March until the day of the Nones of April makes the beginning of the first month; and that the fourteenth moon is more diligently to be sought from the twelfth day before the Kalends of April until the fourteenth before the Kalends of May;

which, because it does not revolve equally with the course of the sun, follows the meeting of the vernal equinox by the spaces of so many days — which equinox, by the judgments of all the Easterns, and especially of the Egyptians, who are skilled in calculation above all others, is specially noted on the twelfth day before the Kalends of April. In which, even if the fourteenth moon should fall on a Saturday — which is manifest to happen once in ninety-five years — the same holy synod established without ambiguity that the Pascha is to be celebrated on the following Lord's day, that is, on the eleventh before the Kalends of April, the moon being the fifteenth — admonishing in every way that no one should seek the fourteenth moon of the Paschal feast before the twelfth before the Kalends of April;

for it would be established to be not of the first month, but of the last. But neither did we think this should be passed over: that those err exceedingly who, estimating the moon to complete the course of its cycle in spaces of thirty days, count twelve lunar months in three hundred and sixty days, to which they also add five days, which antiquity called intercalary, so that they may seem to fill out the solar year; whereas a diligent inquiry into the truth has shown that in two cycles of the moon there ought to be counted not sixty days, but fifty-nine.

And by this, in twelve lunar months there is gathered the sum of three hundred and fifty-four days, to which the Egyptians add the annual epacts, that is, eleven days, so that at last the lunar measurement may be made equal to the reckoning of the sun. That this is most true and most certain is proved by the judgment of the Fathers written above, who, according to this calculation of the Egyptians, handed down the fourteenth moons of the Paschal observance. But some, ignorant of so great a subtlety, or rather of the sanction, while they seek out other arguments of computation, recede from the path of truth. Whence it most often happens that the moon which the often-mentioned Fathers set as the fourteenth, these men suspect to be the fifteenth;

and what is the twenty-first they pronounce to be the twenty-second. But for us, who have love and care for the Christian religion, it is by no means fitting to depart by any reasoning from the ordinance of so many pontiffs; but it is fitting to keep with most sincere devotion the Paschal rule fixed by them. How greatly we rely upon the authority of these Fathers in the Churches spread throughout the whole world, it is no labor to show, since the holy council assembling at Antioch not so long afterward judged that the definition which they first set forth concerning the Paschal reckoning was in no way to be violated.

Finally, in the holy canons under the seventy-ninth title, which is the first of that same Council of Antioch, it is found expressed in these words: 'All who shall have dared to dissolve the definition of the holy and great council which was gathered at Nicaea, in the presence of the most pious and venerable prince Constantine, concerning the saving solemnity of Pascha, we judge are to be excommunicated and expelled from the Church, if indeed they shall contentiously persist against those things which have been well decreed.' And let these things indeed be said concerning the laity.

But if any of those who preside over the Church — whether bishop, or presbyter, or deacon — shall after this definition attempt, to the subversion of peoples and the perturbation of the Churches, to gather separately and to celebrate Pascha with the Jews, the holy synod has judged such a one already henceforth an alien from the Church: because he has become a cause of corruption and perturbation not only to himself but to very many. And it not only removes such men from the ministry, but those also who after the condemnation of such a one shall attempt to communicate with him are condemned, being deprived also of every outward honor which the holy rule and the priesthood of God has merited. Things not unlike these the venerable Pope Leo, prelate of the Apostolic See, pronounces, saying:

'Against the statutes of the canons of the Fathers, which were founded so many years ago, in the age of greatest antiquity, in the city of Nicaea by spiritual decrees, it is granted to no one to dare anything; so that if anyone should wish to decree something different, let him rather diminish himself than corrupt those decrees. And if, as is fitting, they are kept inviolate by all the pontiffs, throughout all the Churches there will be peace and firm concord.' And again: 'In all ecclesiastical causes,' he says, 'we obey those laws which the Holy Spirit instituted, through the three hundred and eighteen bishops, for the peaceful observance of all the priests;'

'so that even if many more should decree something other than what those decreed, whatever shall be different from the ordinance of the aforesaid is to be held in no reverence.' Sufficiently, as we think, it is enjoined upon all that henceforth the most sacred Pascha should not be celebrated otherwise than was established by the holy Fathers. But if perhaps anyone with an obstinate mind should despise the testimonies of so many priests, he will find like things briefly indicated also in the ecclesiastical history; and by the report of many pontiffs, and especially of the blessed Athanasius, whom we mentioned above, he will learn that these same things have been made public.

And this same thing the Epistle of Saint Proterius, bishop of the city of Alexandria, to that same Pope Leo, directed concerning this very Paschal question, attests. Translating it from the Greek some years ago, we have judged that it should be attached to this work. We have also subjoined the arguments sought out by the sagacity of the Egyptians, by which, if perchance they be unknown, the Paschal headings may easily be found: that is, what is the year from the Incarnation of the Lord, and what the indiction, what too the lunar cycle, or what the nineteen-year cycle may be, and the rest are to be sought by a like brief compendium of computation. May the divine grace deign to guard your blessedness as it prays for us. Here ends the preface. THE NINETEEN-YEAR CYCLE OF DIONYSIUS.

Here begins the nineteen-year cycle, which the Greeks call the Enneacaidecaeteris, established by the holy Fathers, in which you may find the Paschal fourteenths at all times without any falsity; only remember, for each single year, which lunar cycle and which nineteen-year cycle it may be. For in the present there is the third indiction, in the consulship of Probus the younger, the thirteenth circle of the nineteen-year cycle, and it is the tenth lunar. Bede recalls this year with its characters from the cycle of Dionysius in his book On the Reckoning of Times, chapter 45, in these words:

'Since therefore in the second year of the cycle which Dionysius wrote first, the five hundred and twenty-third year from the Incarnation of the Lord was completed, that is indeed the very year — according to the concurrence of the stars — in which He deigned to be incarnate; for this second year of the nineteen-year cycle is the eighteenth of the lunar cycle, having eleven epacts, the concurrent days of the week, the Paschal moon the fourteenth on the eighth before the Kalends of April.' HERE BEGIN THE ARGUMENTS CONCERNING THE PASCHAL HEADINGS, INVESTIGATED BY THE SKILL OF THE EGYPTIANS, THAT THEY MAY INDICATE THE PRESENT [DATES]. THE FIRST ARGUMENT, On the years of Christ. If you wish to know what is the year from the Incarnation of our Lord Jesus Christ, compute fifteen times thirty-four, they make five hundred and ten; to these always add twelve regulars, they make five hundred and twenty-two;

add also the indiction of the year of whatever you wish — for example, the third, in the consulship of Probus the younger — they make together five hundred and twenty-five years. These are the years from the Incarnation of the Lord. ARGUMENT II. On the indiction. If you wish to know what is the indiction — for example, in the consulship of Probus the younger — take the years from the Incarnation of our Lord Jesus Christ, five hundred and twenty-five. To these always add three, they make five hundred and twenty-eight. Divide these by fifteen; there remain three. It is the third indiction. But if nothing remains, it is the fifteenth indiction. ARGUMENT III. On the epacts. If you wish to know how many are the epacts, that is, the lunar additions, take the years from the Incarnation of our Lord Jesus Christ, however many they be, five hundred and twenty-five. Divide these by nineteen; there remain three. Multiply by eleven, they make one hundred and thirty-two.

Divide these again by thirty; there remain twelve. Twelve are the lunar additions. [Likewise another computation. Compute from the first year up to whatever you wish — for example, to the tenth year. Always dismiss one; there remain nine. Multiply the eleven annual epacts by nine years, and you will make nine times eleven, ninety-nine. Divide these by thirty, that is, three times thirty, ninety; there remain nine. The ninth is the epact of the nineteen-year cycle, thus in the eleventh year. Dismiss one; there remain ten. Ten times eleven, one hundred and ten. Divide these by thirty; there remain twenty. The twentieth will be the lunar epact of the nineteen-year cycle in the eleventh year. Thus through all nineteen years you will compute under this brevity.] ARGUMENT IV. On the concurrents.

If you wish to know the additions of the sun, that is, the concurrent days of the week, take the years from the Incarnation of the Lord, however many they be — for example, five hundred and twenty-five; through the third indiction and the fourth part of the years that there have been, always add — that is, now one hundred and thirty-one, which together make six hundred and fifty-six. To these add four, they make six hundred and sixty. Divide these by seven; there remain two. These are the epacts of the sun, that is, the concurrent days of the week, through the above-written indiction, in the consulship of Probus the younger. [Likewise, a recently discovered method I have indicated better, that it may be briefly made plain. In a like manner compute from the year which is after the consulship of our lord Tiberius the younger Augustus, only that at the end, where the above calculation has four added, you should now add not four but one for the two.] ARGUMENT V.

On the nineteen-year cycle. If you wish to know what is the year of the cycle of nineteen years, take the years of the Lord — for example, five hundred and twenty-five — and always add one; they make five hundred and twenty-six. Divide these by nineteen; there remain thirteen. The thirteenth is the year of the nineteen-year cycle. But if nothing remains, it is the nineteenth. ARGUMENT VI. On the lunar cycle. If you wish to know what is the cycle of the moon which is contained in the nineteen-year cycle, take the years of the Lord — for example, five hundred and twenty-five — and always subtract two, and there remain five hundred and twenty-three. Divide these by nineteen; there remain ten. The tenth is the lunar cycle of the nineteen-year cycle. But as often as nothing remains, it is the nineteenth. ARGUMENT VII. On the fourteenth moon in the month of March.

If you wish to know in which years of the nineteen-year cycle the Paschal fourteenth moon falls in the month of March: in years two, five, seven, ten, thirteen, sixteen, eighteen — these above-written years you will find in the month of March; but the remaining twelve, according to the rule annexed below, you will without doubt calculate in the month of April. ARGUMENT VIII. On the bissextile. If you wish to know when the bissextile day is, take the years of the Lord, for example five hundred and twenty-five. Divide these by four. If nothing remains, it is bissextile. If one, or two, or three remain, it is not bissextile. Lest perhaps some fog of error befall you, in every computation by which you proceed, if nothing be left over, know that it is the same number by which you proceed — for example, if you proceed by nineteen and nothing is left over, that it is nineteen;

if by fifteen, the fifteenth; and, if by seven, the seventh. ARGUMENT IX. On the Paschal moon in the month of March. If you wish to know what Paschal moon of the feast occurs: if Pascha is celebrated in the month of March, compute the months from September to March; they make six. To these always add the two regulars; they make eight. Add the epacts, that is, the lunar additions of whatever year you wish — for example, of the third indiction, twelve — they make twenty; and the day of the month on which Pascha is celebrated, that is, the thirtieth of March, they make together fifty. Subtract thirty; there remain twenty: the twentieth is on the day of the Lord's resurrection. In the month of April. — But if we celebrate Pascha in the month of April, compute the months from September to March; they make seven. To these always add two; they make nine.

Add the epacts of the moon of whatever year you wish — for example, of the fourth indiction, twenty-three — which make thirty-two; and the day of the month on which we celebrate Pascha, that is, the nineteenth of April, which together make fifty-one; subtract thirty, there remain twenty-one. The twenty-first moon is on the day of the Lord's resurrection. If you inquire from September up to December, you should always add three regulars in these four months; but in a bissextile year only you shall number two regulars to the above-written months, and for the twenty-second day, you shall take twenty-two for each single year in the month of December at the end. ARGUMENT X. On the day of holy week, the Paschal feria. If you wish to know what day of the week it is, take the days from January up to whatever month you wish — for example, to the thirtieth day of the month of March — they make eighty-nine.

To these you shall always add one; they make ninety; and always add the epacts of the sun, that is, the concurrent days of the week of whatever year you wish — for example, of the second indiction — they make together ninety-two. Divide these by seven; there remains one: that itself is the Paschal Lord's day of the feast. Thus, whatever day from the Kalends of January up to the thirtieth day of the month of December, you will find by computing what feria it is, provided that you take equally the one regular and the concurrents, which always begin from the month of January. ARGUMENT XI. On the moon of the last [day before] Pascha. If you wish to know what moon it is on the eleventh before the Kalends of April, take the years of the Incarnation of our Lord Jesus Christ — for example, six hundred and seventy-five. Divide these by eleven; they make six hundred and ten. Divide by thirty; there remain twenty: the twentieth moon is on the eleventh before the Kalends of April.

But if seven, the seventh; if a unit, the first. ARGUMENT XII. If you wish to know the day of the Kalends of January, what feria it is for each single year, take the years of the Incarnation of our Lord Jesus Christ — for example, the years six hundred and seventy-five. Subtract a unit; there remain six hundred and seventy-four. Divide these by the fourth part, and the fourth part which you have divided, you shall add upon six hundred and seventy-four; they make together eight hundred and forty-two. Divide these by seven; there remain two. The second is the day of the Kalends of January. If five, the fifth feria; if a unit, the first; if nothing, the Sabbath. ARGUMENT XIII. On the moon of the Kalends of January. If you wish to know what moon it is on the Kalends of January, know what the lunar cycle is — for instance, the fifteenth cycle.

Hold for yourself one, that is, the Kalends of January themselves, and you shall lead five times five times ten: they make seventy-five; which you shall add upon the one, and they make seventy-six. Likewise you shall lead six times ten five times, they make ninety; which you shall add upon seventy-six, and thus the sum of the numbers is one hundred and sixty-six; in which divide by thirty, there remain sixteen. The sixteenth moon is on the Kalends of January, and of points sixteen. In this manner you will compute always through the nineteen lunar cycles, and you will find on the Kalends of January, what moon it is, without error. But when you come to the seventeenth lunar cycle, and you shall have led five times ten seven times, upon the Kalends of January, which make eighty-five, if you divide by sixty, and you shall add the unit itself, they make eighty-six.

Then you lead six times ten seven times, they make one hundred and two. These you shall add upon eighty-six, and they make one hundred and eighty-eight. Divide there by thirty; there remain nine. The ninth moon is on the Kalends of January, and of points twenty-six. So too in the eighteenth and nineteenth cycle you shall do. But from the first lunar cycle up to the sixteenth, do not divide by sixty, lest you fall into error. ARGUMENT XIV. What feria the fourteenth moon falls on, in the first year of the nineteen-year cycle. Here begins the calculation of how it may be found what feria of each single year [there is] from the fourteenth Paschal moon, that is, of the first circle of the nineteen-year cycle.

In the first year, because it has no lunar epacts — for the reason that, with the eighteenth [year] of the lower nineteenth year and its eleven epacts, with one day added also by the Egyptians, they make thirty, that is, the complete moon of one month, and nothing remains of the epacts — and because in that year the Paschal fourteenth moon falls in the month of April, hold the regulars always in it as thirty-five, subtract thirty, that is, the complete moon itself, and there remain five. On the fifth day from the Kalends, that is, the Nones of April, the Paschal fourteenth moon occurs. Hold the above-written five, add also the concurrents of that same year, four, they make nine. Add also the regulars in it always for the month of April, seven, they make sixteen. Divide these by seven, that is, twice seven, fourteen; there remain two.

On the second feria occurs the Paschal fourteenth moon, and the Lord's day of the Paschal feast is the twentieth moon. In the second year. — Likewise the second year of the aforesaid cycle, from which the eleven epacts take their beginning. In that year the Paschal fourteenth moon falls in the month of March. Hold the thirty-six regulars always in it, subtract always the eleven epacts, there remain twenty-five. On the twenty-fifth day from the Kalends of March, which is the eighth before the Kalends of April, occurs the Paschal fourteenth moon. Hold the above-written twenty-five, add the concurrents of that same year, five, they make thirty. Add always at the end of this month the regulars four, divide these by seven, that is, seven times four, twenty-eight; there remain six. On the sixth feria occurs the fourteenth Paschal moon, and the Lord's day of the Paschal feast is the sixteenth moon. In the third year.

— Likewise in the month of April, in the third year of the often-mentioned first cycle. Hold always in that month first of all the thirty-five regulars. Subtract the epacts of that same year, twenty-two; there remain thirteen. On the thirteenth day of the month, that is, the Ides of April, occurs the Paschal fourteenth moon. Hold these thirteen, add the concurrents six, they make nineteen. Add in April always below the regulars seven, they make twenty-six. Divide these by seven, three times seven, twenty-one; there remain five. On the fifth feria will be the fourteenth Paschal moon, and the Lord's day of the Paschal feast is the seventeenth moon. Thus for each single year, from the first up to the ninety-fifth year, you will calculate.

Whenever the Paschal fourteenth moon falls in the month of March, you should hold first the thirty-six regulars, from which you may deduct the epacts of whatever year you wish, and add the concurrents, and at the end always increase by four regulars. But in the month of April hold always thirty-five at the head, from which, as for the above-said epacts, and for the concurrents of that same year added to them, increase at the end by seven regulars. For more easily and more briefly you will calculate all the Paschal arguments. Yet let this besides be known to the reader: that whenever it happens in either of the above-written months, in the first rule, that after the deducted epacts more should remain than thirty, dismiss thirty.

But if one or two, or more, be left over, on so many days of that month from the Kalends of January let the Paschal fourteenth moon be. But when, after the deducted epacts, less than thirty — for example twenty, or more or less — should remain (which is manifest to happen once in nineteen years), on the thirtieth day of April will be the Paschal fourteenth moon. ARGUMENT XV. On the day of the equinox and solstice. On what day the Lord Jesus Christ was born according to the flesh from the Virgin Mary in Bethlehem — on which the day begins to grow. The first equinox is on the eighth before the Kalends of April, on which the day is made equal with the night. On the same day Gabriel announces to St. Mary, saying: 'The Holy Spirit shall come upon you, and the power of the Most High shall overshadow you.'

'Therefore that which shall be born of you shall be called the Son of God.' On which day also Christ suffered according to the flesh. The second solstice is on the eighth before the Kalends of July, when also St. John the Baptist was born, from which the day begins to decrease. The second equinox is on the eighth before the Kalends of October, on which day John the Baptist was conceived. And from this now the day becomes shorter than the night, until the Nativity of the Lord and Savior. From the eighth before the Kalends of April to the eighth before the Kalends of January, the days are counted as two hundred and seventy-one. Whence, according to the number of days, Christ our Lord was conceived on the Lord's day, the eighth before the Kalends of April, and Christ our Lord was born on the third feria, the thirteenth before the Kalends of January.

On the day on which he suffered there are completed 133 years and 3 months, which amount to 12,414 days. Hence, according to the number of his days, it stands that he was born on the fourth day of the week and suffered on the sixth: born on the eighth day before the Kalends of January, and suffered on the eighth day before the Kalends of April. From the time when Jesus Christ our Lord was baptized there are completed years, and the days are reckoned as ninety, which make 820, together with their leap-day additions; and thus he was baptized on the eighth before the Ides of January, on the fifth day of the week, and suffered, as I said above, on the eighth before the Kalends of April, on the sixth day of the week. With the leap-day additions they amount altogether to 12,415 days, and from the eighth before the Ides of January to the eighth before the Kalends of April there are ninety days. ARGUMENT 16. On the reckoning of the bissextile (leap-day). It must be believed that the bissextile is not made on account of that day on which, as some suppose, Joshua prayed for the sun to stand still;

for that day both existed and passed away. Rather it is called bissextile from this, that in each single month one 'point' accrues. Now one point is a quarter of an hour; four points make one hour, and twelve points complete three hours. Therefore in four years the threefold hours, which are twelve, make one day, which is added to February, since it then has the sixth day before the Kalends of March, so that on the following day it has it likewise. For example, if today is the sixth before the Kalends of March, that day is added in the completed fourth year; nonetheless on the morrow also let it be reckoned as the sixth before the Kalends of March. And it is therefore called bissextile (twice-sixth), because February twice has the sixth before the Kalends of March. In six days God made the world; on the seventh he rested.

Therefore, that it may be more fully understood, compute how many hours one day has, and divide them into seven parts, and however much remains, from that comes the bissextile. First compute the days, three hundred, how many hours they have: ten times three hundred is three thousand. Again you make: twice three hundred is six hundred; so in three hundred days there are 3,600 hours. Again you make: ten times sixty is six hundred, and twice sixty is one hundred and twenty. Therefore in sixty days there are 720 hours. Again you make: ten times five is fifty, and twice five is ten. Behold, in five days you have sixty hours. Together, in the whole year of 365 days there are 4,380 hours, and as many again in the night; together for the days and nights of the whole year there are 8,760 hours. Divide these into seven parts. First you make:

seven times one thousand is seven thousand, with 760 remaining. Likewise you make: seven times two hundred is fourteen hundred, with 360 remaining. Likewise you make: seven times fifty is three hundred and fifty, with ten remaining. Likewise you make: seven times one is seven, with three remaining. These three hours make, in four years, one day.