On Easter, or the Paschal Cycle

Dionysius Exiguus · the golden age of the Fathers

On Easter, or the Paschal Cycle

On Easter, or the Paschal Cycle Dionysius Exiguus to the most blessed and very dear father, Petronius, bishop. The reasoning of the feast of Easter, which many have frequently and urgently asked us, with the help of your prayers, we have now proceeded to set forth. Following in all things the venerable 318 pontiffs, who came together at Nicaea, a city of Bithynia, against the madness of Arius, and besides [gave] a perfect and true opinion on this matter; who having observed 14 months of Easter through 19 years always returning in a cycle to the same position, fixed it stable and immoveable, which in all ages is repeated in the same way, as a beginning, without going off into an excursion of various things. However they sanctioned this rule of the aforementioned cycle, not so much from secular knowledge as by the illumination of the Holy Spirit, and as if determined to have assigned a firm and stable anchor to this reasoning of the lunar calculation. As after a while some, whether despising from arrogance or crossing over from ignorance, were influenced by Jewish fables, they handed down a different and contrary form of the only festival. And because without solidity of foundation no structure can stand, for a long time they were inclined to work out differently the Lord's Easter and the computation of the moon, ordaining unordained cycles; which not only has no stability, indeed also they prefer a notable direction in error.

But at the city of Alexandria the archbishop, blessed Athanasius, who also was involved in the Nicene Council, at that time as deacon of the holy pontiff Alexander and [his] helper in all things, and then the venerable Theophilus and Cyril, departed very little from the worshipful decision of the synod. Indeed rather sollicitously retaining the same 19-year cycle, which in a Greek word is called enneacaidecaeteris, they are shown to have not interpolated the paschal cycle with any changes. Then Pope Theophilus, dedicating the 100th course of the years to the emperor Theodosius the Elder, and St. Cyril, compiling a cycle of time of 95 years, preserved through everything this tradition of the holy council of the importance of observing 14 paschal months. And because -- the students also having been seeking to know what is true -- we must hold fast to the rule of his cycle more firmly, we believe that we must give it after our preface. Therefore we hurried to set out this cycle of 95 years, in which study we have succeeded, preferring in our work this [cycle], the last one of the same blessed Cyril, that is the 5th cycle, because 6 years of it remain; and thereafter we profess that we laid out 5 others according to the pattern of the same pontiff, or rather of the often mentioned Nicene Council. But because St.

Cyril began his first cycle from the 153rd year of Diocletian, and besides ended in the 247th, we, starting from the 248th [year] of the same tyrant -- a better [word] than prince -do not wish to bind to our circles the memory of this impious man and persecutor, but choose rather to count the time of the years from the incarnation of our Lord Jesus Christ, so that the beginning of our hope will appear better known to us, and the cause of the restoration of mankind, i.e. the passion of our Redeemer, may shine forth more clearly. In addition we think that this reader should be reminded that that cycle of 95 years, which we make, when, its time being up, begins to repeat, not through everything may he support firmness. For it is allowed ... the years of our Lord Jesus Christ ... his/its order ... for the continued series .... that they may preserve ... , and they might run through the accustomed indictions through 15 years, also the epacts, as the Greeks call them, i.e the additions ... 11 annual months ... which 30 of days up to in itself they return, .... ...however they are unable to protect a similar movement of constancy concurrent days of the week, and the day(s) of the Lord's Pasch and the month of the dominical day itself. However the reason of the concurrency of the week, which comes from the course of the sun, it is concluded in a continual circuit of seven years.

In which you will take care to enumerate through the years each one; only in that year in which it will have been a leap year, you will add two. Which cause also makes that not through the whole 95 years does that circle seem to harmonize with its recursion. For when in other years it does not deviate, in this alone, in which the leap year is inserted, the Pasch of the churches with its month occurs in various ways of reason (rationis). .... ... (To be completed) NINETEEN YEAR CYCLE OF DIONYSIUS (CYCLUS DECEMNOVENNALIS DIONYSII) The nineteen year cycle begins, which the Greek call Enneakaidekaeterida (nineteen yearly), established by the holy Church Fathers, in which you shall find fourteen paschal moons each time without error; you shall just bear in mind, in each of the years, which cycle of the moon and which nineteen year cycle prevails. In the present year, in the consulship of Probus Junior, it is the thirteenth of the nineteen year cycle, and the tenth lunar one. ANNI epactae, id quota sit luna quae sint concurrentes quotus sit quae sit luna dies Dominicae DIOCLE est adjectiones ipsius diei indictiones dies lunae circsulus XIIII paschalis festivitatis TIANI lunae dominici epacts, ie What are which is the which is the day of YARS OF increments of concurrent date of day 14 of day of the the circle of the the moon on this DIOCLETIAN the days the paschal moon Sunday festival indictions moon Sunday moon CCXXVIIII non.Apr.

vii id.Apr. vi nulla i xvii xvi 229 (513) Apr 05 Apr 07 CCXXX viii k.Apr. iii k.Apr. vii xi ii xviii xviiii 230 (514) Mar 25 Mar 30 CCXXXI id. Apr. xiii k.Maii viii xxii iii xviiii xx 231 (515) Apr 13 Apr 19 CCXXXII non.Apr. iii non.Apr. viiii iii v i xv 232 (516) Apr 02 Apr 03 CCXXXIII xi k.Apr. vii k.Apr. x xiiii vi ii xviii 233 (517) Mar 22 Mar 26 CCXXXIIII iiii id.Apr. xvii k.Maii xi xxv vi iii xviiii 234 (518) Apr 10 Apr 15 CCXXXVI xiiii k.Maii xiii k.Maii xv ogd. xiii xvii iii v 236 (520) Apr 18* Apr 19 * CCXXXVII vii id.Apr. iii id.Apr. xiiii xxviii iiii vi xviii 237 (521) Apr 07 Apr 11 CCXXXVIII vi k.Apr. iii non.Apr. xxi xv viiii v vii 238 (522) Mar 27 Apr 03 * CCXXXVIIII xvii k.Maii xvi k.Maii xv i xx vi viii 239 (523) Apr 15 Apr 16 * CCXLII ii id.Apr. xiii k.Maii xxi iiii xxiii iii xi 242 (526) Apr 12 Apr 19 * CCXLIII k.Apr. ii non.Apr. v iiii iiii xii xvii 243 (527) Apr 01 Apr 04 CCXLIIII xii k.Apr. vii k.Apr. vi xv vi xiii xviiii 244 (528) Mar 21* Mar 26 CCXLV v id.Apr. xvii k.Maii vii xxvi vii xiiii xx 245 (529) Apr 09 Apr 15 CCXLVII xv k.Maii xii k.Maii viiii xviii ii xvi xvii hend.

247 (531) Apr 17 Apr 20 ANNI DOMINI epactae, id quotus sit quota sit luna quae sint concurrentes quae sit luna dies Dominicae NOSTRI JESU est adjectiones lunae ipsius diei indictiones dies XIIII paschalis festivitatis CHRISTI lunae circsulus dominici epacts, ie YARS OF OUR What are which is the which is the day of increments of concurrent date of day 14 of day of the LORD the circle of the the moon on this the days the paschal moon Sunday festival JESUS CHRIST indictions moon Sunday moon B DXXXII non.Apr. iii id.Apr. x nulla iiii xvii xx 0532 Apr 05 Apr 11 DXXXIII viii k.Apr. vi k.Apr. xi xi v xviii xvi 0533 Mar 25 Mar 27 DXXXIIII id.Apr. xvi k.Maii xii xxii vi xviiii xvii 0534 Apr 13 Apr 16 DXXXV iiii non.Apr. vi id.Apr. xiii iii vii i xx 0535 Apr 02 Apr 08 B DXXXVI xi k.Apr. x k.Apr. xv xiiii xiiii ii ii 0536 Mar 22 Mar 23 * DXXXVII iiii id.Apr. ii id.Apr. xv xxv iii iii xvi 0537 Apr 10 Apr 12 DXXXVIII iii k.Apr. ii non.Apr. i vi iiii iiii xviiii 0538 Mar 30 Apr 04 DXXXVIIII xiiii k.Maii viii k.Maii ii xvii v v xx ogd. 0539 Apr 18* Apr 24 B DXL vii id.Apr. vi id.Apr. xv iii xxviii vii vi 0540 Apr 07 Apr 08 * DXLI vi k.Apr. ii k.Apr.

iiii viiii i vii xviii 0541 Mar 27 Mar 31 DXLII xvii k.Maii xii k.Maii v xx ii viii xviiii 0542 Apr 15 Apr 20 DXLIII ii non.Apr. non.Apr. xv vi i iii viiii 0543 Apr 04 Apr 05 * B DXLIIII viiii k.Apr. vi k.Apr. vii xii v x xvii 0544 Mar 24 Mar 27 DXLV ii id.Apr. xvi k.Maii viii xxiii vi xi xviii 0545 Apr 12 Apr 16 DXLVI k.Apr. vi id.Apr. xxi viiii iiii vii xii 0546 Apr 01 Apr 08 * DXLVII xii k.Apr. viiii k.Apr. x xv i xiii xvii 0547 Mar 21* Mar 24 B DXLVIII v id.Apr. ii id.Apr. xi xxvi iii xiiii xvii 0548 Apr 09 Apr 12 DXLVIIII iiii k.Apr. ii non.Apr. xii vii iiii xv xx 0549 Mar 29 Apr 04 DL xv k.Maii viii k.Maii xxi hend. xiii xviii v xvi 0550 Apr 17 Apr 24 * DLI non.Apr. v id.Apr. xiiii nulla vi xvii xviii 0551 Apr 05 Apr 09 B DLII viii k.Apr. ii k.Apr. xv xi i xviii xx 0552 Mar 25 Mar 31 DLIII id.Apr. xii k.Maii xxi i xxii ii xviiii 0553 Apr 13 Apr 20 * DLIIII iiii non.Apr. non.Apr. ii iii iii i xvii 0554 Apr 02 Apr 05 DLV xi k.Apr. v k.Apr. iii xiiii iiii ii xx 0555 Mar 22 Mar 28 B DLVI iiii id.Apr. xvi k.Maii iiii xxv vi iii xx 0556 Apr 10 Apr 16 DLVII iii k.Apr.

k.Apr. v vi vii iiii xvi 0557 Mar 30 Apr 01 DLVIII xiiii k.Maii xi k.Maii vi xvii i v xvii ogd. 0558 Apr 18* Apr 21 DLVIIII vii id.Apr. id.Apr. vii xxviii ii vi xx 0559 Apr 07 Apr 13 B DLX vi k.Apr. v k.Apr. xv viii viiii iiii vii 0560 Mar 27 Mar 28 * DLXI xvii k.Maii xv k.Maii viiii xx v viii xvi 0561 Apr 15 Apr 17 DLXII ii non.Apr. v id.Apr. x i vi viiii xviiii 0562 Apr 04 Apr 09 DLXIII viiii k.Apr. viii k.Apr. xv xi xii vii x 0563 Mar 24 Mar 25 * B DLXIIII ii id.Apr. id.Apr. xv xii xxiii ii xi 0564 Apr 12 Apr 13 * DLXV k.Apr. non.Apr. xiii iiii iii xii xviii 0565 Apr 01 Apr 05 DLXVI xii k.Apr. v k.Apr. xxi xiiii xv iiii xiii 0566 Mar 21* Mar 28 * DLXVII v id.Apr. iiii id.Apr. xv xv xxvi v xiiii 0567 Apr 09 Apr 10 * B DLXVIII iiii k.Apr. k.Apr. i vii vii xv xii 0568 Mar 29 Apr 01 DLXVIIII xv k.Maii xi k.Maii ii xviii i xvi xviii hend. 0569 Apr 17 Apr 21 DLXX non.Apr. viii id.Apr. xv iii nulla ii xvii 0570 Apr 05 Apr 06 * DLXXI viii k.Apr. iiii k.Apr. iiii xi iii xviii xviii 0571 Mar 25 Mar 29 B DLXXII id.Apr. xv k.Maii v xxii v xviiii xviii 0572 Apr 13 Apr 17 DLXXIII iiii non.Apr.

v id.Apr. xxi vi iii vi i 0573 Apr 02 Apr 09 * DLXXIIII xi k.Apr. viii k.Apr. vii xiiii vii ii xvii 0574 Mar 22 Mar 25 DLXXV iiii id.Apr. xviii k.Maii viii xxv i iii xviii 0575 Apr 10 Apr 14 B DLXXVI iii k.Apr. non.Apr. viiii vi iii iiii xx 0576 Mar 30 Apr 05 DLXXVII xiiii k.Maii vii k.Maii xxi ogd. x xvii iiii v 0577 Apr 18* Apr 25* * DLXXVIII vii id.Apr. iiii id.Apr xi xxviii v vi xvii 0578 Apr 07 Apr 10 DLXXVIIII vi k.Apr. iiii non.Apr. xii viiii vi vii xx 0579 Mar 27 Apr 02 B DLXXX xvii k.Maii xi k.Maii xiii xx i viii xx 0580 Apr 15 Apr 21 DLXXXI ii non.Apr. viii id.Apr. xiiii i ii viiii xvi 0581 Apr 04 Apr 06 DLXXXII viiii k.Apr. iiii k.Apr. xv xii iii x xviiii 0582 Mar 24 Mar 29 DLXXXIII ii id.Apr. xiiii k.Maii i xxiii iiii xi xx 0583 Apr 12 Apr 18 B DLXXXIIII k.Apr. iiii non.Apr. xv ii iiii vi xii 0584 Apr 01 Apr 02 * DLXXXV xii k.Apr. viii k.Apr. iii xv vii xiii xviii 0585 Mar 21* Mar 25 DLXXXVI v id.Apr. xviii k.Maii iiii xxvi i xiiii xviiii 0586 Apr 09 Apr 14 DLXXXVII iiii k.Apr. iii k.Apr. xv v vii ii xv 0587 Mar 29 Mar 30 * B xv k.Maii xiiii k.Maii xv hend.

DLXXXVIII vi xviii iiii xvi DLXXXVIIII non.Apr. iiii id.Apr. vii nulla v xvii xviiii 0589 Apr 05 Apr 10 DXC viii k.Apr. vii k.Apr. xv viii xi vi xviii 0590 Mar 25 Mar 26 * DXCI id.Apr. xvii k.Maii viiii xxii vii xviiii xvi 0591 Apr 13 Apr 15 B DXCII iiii non.Apr. viii id.Apr. x iii ii i xviii 0592 Apr 02 Apr 06 DXCIII xi k.Apr. iiii k.Apr. xxi xi xiiii iii ii 0593 Mar 22 Mar 29 * DXCIIII iiii id.Apr. iii id.Apr. xv xii xxv iiii iii 0594 Apr 10 Apr 11 * DXCV iii k.Apr. iii non.Apr. xiii vi v iiii xviii 0595 Mar 30 Apr 03 B DXCVI xiiii k.Maii x k.Maii xiiii xvii vii v xviii ogd. 0596 Apr 18* Apr 22 DXCVII vii id.Apr. xviii k.Maii xxi xv xxviii i vi 0597 Apr 07 Apr 14 * DXCVIII vi k.Apr. iii k.Apr. i viiii ii vii xvii 0598 Mar 27 Mar 30 DXCVIIII xvii k.Maii xiii k.Maii ii xx iii viii xviii 0599 Apr 15 Apr 19 B DC ii non.Apr. iiii id.Apr. iii i v viiii xx 0600 Apr 04 Apr 10 DCI viiii k.Apr. vii k.Apr. iiii xii vi x xvi 0601 Mar 24 Mar 26 DCII ii id.Apr. xvii k.Maii v xxiii vii xi xvii 0602 Apr 12 Apr 15 DCIII k.Apr. vii id.Apr. vi iiii i xii xx 0603 Apr 01 Apr 07 B DCIIII xii k.Apr.

xi k.Apr. xv vii xv iii xiii 0604 Mar 21* Mar 22* * DCV v id.Apr. iii id.Apr. viii xxvi iiii xiiii xvi 0605 Apr 09 Apr 11 DCVI iiii k.Apr. iii non.Apr. viiii vii v xv xviiii 0606 Mar 29 Apr 03 DCVII xv k.Maii viiii k.Maii x xviii vi xvi xx hend. 0607 Apr 17 Apr 23 B DCVIII non.Apr. vii id.Apr. xi nulla i xvii xvi 0608 Apr 05 Apr 07 DCVIIII viii k.Apr. iii k.Apr. xii xi ii xviii xviiii 0609 Mar 25 Mar 30 DCX id.Apr. xiii k.Maii xiii xxii iii xviiii xx 0610 Apr 13 Apr 19 DCXI iiii non.Apr. ii non.Apr. xiiii iii iiii i xvi 0611 Apr 02 Apr 04 B DCXII xi k.Apr. vii k.Apr. xv xiiii vi ii xviii 0612 Mar 22 Mar 26 DCXIII iiii id.Apr. xvii k.Maii i xxv vii iii xviiii 0613 Apr 10 Apr 15 DCXIIII iii k.Apr. ii k.Apr. xv ii vi i iiii 0614 Mar 30 Mar 31 * DCXV xiiii k.Maii xii k.Maii iii xvii ii v xvi ogd. 0615 Apr 18* Apr 20 B DCXVI vii id.Apr. iii id.Apr. iiii xxviii iiii vi xviii 0616 Apr 07 Apr 11 DCXVII vi k.Apr. iii non.Apr. xxi v viiii v vii 0617 Mar 27 Apr 03 * DCXVIII xvii k.Maii xvi k.Maii xv vi xx vi viii 0618 Apr 15 Apr 16 * DCXVIIII ii non.Apr.

vi id.Apr. vii i vii viiii xviii 0619 Apr 04 Apr 08 B DCXX viiii k.Apr. iii k.Apr. viii xii ii x xx 0620 Mar 24 Mar 30 DCXXI ii id.Apr. xiii k.Maii xxi viiii xxiii iii xi 0621 Apr 12 Apr 19 * DCXXII k.Apr. ii non.Apr. x iiii iiii xii xvii 0622 Apr 01 Apr 04 DCXXIII xii k.Apr. vi k.Apr. xi xv v xiii xx 0623 Mar 21* Mar 27 B DCXXIIII v id.Apr. xvii k.Maii xii xxvi vii xiiii xx 0624 Apr 09 Apr 15 DCXXV iiii k.Apr. ii k.Apr. xiii vii i xv xvi 0625 Mar 29 Mar 31 DCXXVI xv k.Maii xii k.Maii xiiii xviii ii xvi xvii hend. 0626 Apr 17 Apr 20 This begins the argumenta on the determination of Easter by the Egyptians, carefully investigated as shown in the following. First Argumentum. On the years of Christ. If you want to find out which year it is since the incarnation of our Lord Jesus Christ, compute fifteen times 34, yielding 510; to these always add the correction 12, yielding 522; also add the indiction of the year you want, say, in the consulship of Probus Junior, the third, yielding 525 years altogether. These are the years since the incarnation of the Lord. Argumentum 2. On the indiction. If you want to know which indiction it is, say in the consulship of Probus Junior, then add the years since the incarnation of our Lord Jesus Christ, 525.

To this always add 3, yielding 528. Divide these by 15, 3 are left over. It is the third indiction. But if nothing would be left over then it is the fifteenth indiction. Argumentum 3. On the epacts. If you want to learn the number of epacts, that is, of the lunar increments, then add the years since the incarnation of our Lord Jesus Christ, of which 525 have passed. Divide those by 19, 12 are left over. Multiply by 11, yielding 132. And then divide those by 30, 12 are left over. Twelve is the lunar increment. Argumentum 4. On the concurrents. If you want to know the solar increments, that is the concurrent days of the week, add the years since the incarnation of the Lord that have passed, say 525; for the third indiction and the years that have passed until then always add the fourth part, which is now 131, these yield 656 altogether. To these add 4, yielding 660. Divide those by 7, 2 are left over. Two are the epacts of the sun, that is, the concurrent days of the week, for the indiction described above, in the consulship of Probus Junior. Argumentum 5. On the cycle of nineteen years. If you want to know which year it is in the circle of 10 plus 9 years, add the years of the Lord, say 525, and always add one, yielding 526.

Divide those by 10 plus 9, 13 are left over. The year is the thirteenth in the nineteen year cycle. If nothing would be left over, it is the nineteenth. Argumentum 6. On the lunar cycle. If you want to know which cycle of the moon it is, that is contained in the nineteen year circle, add the years of the Lord, say 525, and always subtract 2, and 523 are left over. Divide those by 10 plus 9, 10 are left over. It is the tenth lunar cycle in the nineteen year circle. And whenever nothing is left over, it is the nineteenth. Argumentum 7. On the fourteenth moon in the month of March. If you want to find out in which years of the nineteen year circle the 14th paschal moon occurs in the month of March: in the year 2, 5, 7, 10, 13, 16, 18, in these 7 years above you shall see it in the month of March; but in the remaining 12 you will calculate it without doubt in the month of April, according to the rule appended below. Argumentum 8. On the leap day. If you want to know when the leap day is, add the years of the Lord, say 525. Divide those by 4. If nothing should be left over, there is a leap day. If 1 or 2 or 3 are left over, there is no leap day.

So that any unclarity does not possibly lead you into error, for all divisions you do, if nothing is left over, you should consider this computation to yield that by which you divide, thus for instance, if you divide by 10 plus 9, and nothing would remain, you should consider it to be 19; if by 15, then fifteen, and if by 7, then seven. Argumentum 9. On the Easter moon in the month of March. If you want to learn which moon it is on which the feast of Easter occurs; if Easter is celebrated in the month of March, compute the months from September to February, yielding 6. To this always add the correction 2, yielding 8; add the epacts, that is, the lunar increments of the year you want, say 12 for the third indiction, yielding 20; and the day of the month on which Easter is celebrated, that is March 30, yielding together 50. Deduct 30, 20 are left over; the twentieth moon is on the day of the resurrection of the Lord. In the month of April. If however we celebrate Easter in the month of April, compute the months from September to March, yielding 7. To this always add 2, yielding 9. Add the lunar epacts of the year you want, say 23 for indiction 4, yielding 32, and the day of the month in which we celebrate Easter, that is April 19, which together yield 51; deduct 30, 21 are left over.

The age of the moon is 21 on the day of the resurrection of the Lord. If you need it from September to December, you should always add the correction three in these 4 months: only in a leap year you also shall add the correction two for these months described above, and finally in non-leap years, for day 31 in the month of December you should assume 32. Argumentum 10. On the day of the holy week of the feast of Easter. If you want to learn which day of the week it is, add the days since January until the month you want, say until March 30, there are 89. To this always add one, yielding 90; and always add the solar epacts, that is, the concurrents of the seven day week for the year you want, say 2 for the indiction 3, yielding 92 altogether. Divide those by 7, one is left over: this is the Sunday of the feast of Easter. In this way, if you venture to compute which day of the week it is for any day from the first of January until the 31st of the month of December, you should equally assume the correction one and the concurrents which always begin in the month of January. Argumentum 11. On the moon closest to Easter. If you want to know which moon it is on March 22, add the years since the incarnation of our Lord Jesus Christ, say 675.

Divide those by 19, 10 are left over; and multiply ten by 11, yielding 110. Divide by 30, 20 are left over: it is the twentieth day of the moon on March 22. And if 7 is left over, then the seventh, if one, the first. If you want to find out which day of the week it is on the first day of January, for non-leap years, then add the years since the incarnation of our Lord Jesus Christ, say 675 years. Subtract one, 674 are left over. Divide those into the fourth part, and add the fourth part obtained by the division to 674, yielding 842 altogether. Divide those by 7, 2 are left over. It is Monday on the first of January. If 5 are left over then it is Thursday, if one, then Sunday; if nothing, Saturday. Argumentum 13. On the age of the moon on the first of January. If you want to know which moon it is on January 01, knowing which lunar cycle it is, for instance cycle 15. Retain one, which is for the same January 01, and take five fifteen times: yielding 75; to which you always add one, thus yielding 76. Now take six fifteen times, making 90, which you add to 76, thus the sum of the numbers is 166; divide these into the thirtieth part, 16 are left over.

It is the sixteenth moon on January 01, and 16 puncti. In this way you can always compute for the 19 cycles of the moon, and you will obtain without error the age of the moon on January 01. As soon as you shall come to lunar cycle 17, then take five times seventeen, after January 01, which makes 85, if you divide into the sixtieth part, and add the resulting one to it, this yields 86. Meanwhile take six times seventeen, yielding 102. Those add to 86, and it yields 188. Add one, yielding 189. Divide this by thirty, 9 are left over. It is the ninth moon on January 01, and 26 puncti. In this way you also compute in cycles 18 and 19. From the first lunar cycle until the sixteenth you do not divide by 60 so as not to make an error. Argumentum 14. On which day of the week the fourteenth moon falls in the first year of the nineteen year cycle. The calculation begins whereby one can find out on which day of the week the fourteenth paschal moon falls in a single year, this one being for the first circle of nineteen. In the first year, which does not have lunar epacts, because to those 18 from the previous nineteenth year, and its 11 epacts, one day is added by the Egyptians, yielding 30, that is one full lunar month, so that nothing remains from the epacts, and so that in this year the 14th paschal moon falls in the month of April, in this year always take the correction 35, subtract 30, that is this full month, and 5 remains.

The 14th paschal moon occurs five days from the Kalends, which is April 05. Take the 5 from above, and add the concurrents 4 of this year, yielding 9. And always add to this the correction 7 in the month of April, yielding 16. Divide those by 7, that is, two times seven is 14, 2 are left over. On Monday occurs the 14th paschal moon, and the Sunday of the Easter holiday on the day of the 20th moon. In the second year. Now to the second year of the above mentioned circle, for which the epacts add up to 11 to begin with. In this year, the 14th paschal moon occurs in the month of March. In this month, always take the correction 36, always subtract the epacts 11, 25 are left over. The 14th paschal moon occurs twenty five days from the beginning of March, that is, on March 25. Take the 25 from above, add the concurrents 5 for this year, yielding 30. Finally always add the correction 4 for this month, divide those by 7, that is four times seven or 28, 6 remain. The 14th paschal moon occurs on Friday, and the Sunday of the feast of Easter is the day of the 16th moon. In the third year. In the third year of said first cycle, the 14th moon occurs also always in the month of April.

For this month, always take first the correction 35. Subtract the epacts 22 of this year, 13 are left over. The 14th paschal moon occurs on the thirteenth day of the month, that is on April 13. Take those 13, add the concurrents 6, yielding 19. Then always add in April the correction 7, yielding 26. Divide those by 7, three times 7 are 21, five are left over. On Thursday was the fourteenth paschal moon, and the Sunday of the feast of Easter on the 17th moon. These are the same rules as for the first year. In this way you calculate for each year from the first to the nineteenth year. When the 14th moon occurs in the month of March, then you first take the correction 36, from which you deduct the epacts of the year you want, and add the concurrents, and finally you always add the correction 4. But in April you keep 35 in mind, from which you take the epacts mentioned above, and finally add the correction 7 increased by the concurrents of the same year. Thus you will calculate all the argumenta for Easter more easily and faster. Above all, let the reader know that, whenever it happens that more than 30 are left over when the epacts are deducted for any of the months described above to which the first rule applies, then dismiss 30.

When one or two or more are left over, then so many days from January 01 (or April 01) is the 14th paschal moon. And if less than 30 (or 21) should be left over (after) the epacts have been deducted, say 20, or more or less, which is bound to happen once in 19 years then the 14th paschal moon will be on the 30th day of April. Argumentum 15. On the day of the equinox and the solstice. The day on which the Lord Jesus Christ was born into flesh from the Virgin Mary in Bethlehem is the one on which the day begins to increase. The first equinox is on March 25, when day is equal with night. On this very day Gabriel annunciates to Holy Mary, saying: The Holy Ghost shall come upon thee, and the power of the Highest shall overshadow thee. Therefore also that which shall be born of thee shall be called the Son of God. Also on this day Christ has suffered in the flesh. The second solstice is on June 24, from which the day starts to decrease, and also when Saint John the Baptist was born. The second equinox is on September 24, on which day John the Baptist was conceived. And right from then on until the birth of the Lord and Saviour, the day becomes shorter than the night.

From March 25 and until December 25, the days number 271. And that number of days after our Lord Christ was conceived on Sunday March 25, our Lord Christ was born on Tuesday December 20. On the day on which he has suffered death, 133 (or 33) years and 3 months have elapsed, which are 12,414 days. And that number of days after his birth took place on a Tuesday, he suffered death on a Friday: he was born on December 25 and suffered death on March 25. From when our Lord Jesus Christ was baptized, there were 2 years and the days numbered 90, yielding 820, with its leap days, and so he was baptized on the day January 06, a Thursday, and suffered death, as I said above, on March 25, a Friday. With its leap days this yields 12,415 days altogether, and 90 days from January 06 to March 25. Argumentum 16. On the rationale of the leap day. One must not believe what some people maintain, that the leap day has arisen from that day on which Joshua commanded the sun to stand still: that day has been and is long gone. But it is called leap day because it gains one punctus in each month. The punctus is indeed the fourth part of an hour. And 4 puncti make one hour; and 12 puncti explain 3 hours.

Hence in 4 years three hours each, which are 12, making 1 day which is added to February, so that when it is February 24, it is the same the next day. For instance, if today is February 24 and that day is added if 4 years are complete; then it will nevertheless be February 24 tomorrow. And it is called bisextile because February has two times the 6th of the calends of March. In six days God created the world, on the seventh he rested. So that this can be more fully understood, compute the number of hours one day (or year) has, and divide those into 7 parts, and the leap day shall come from what is left over. First compute how many hours 300 days have, ten times three hundred are three thousand. Then do: two times three hundred, six hundred: yielding 3600 hours in three hundred days. Then do: ten times six is 60, and two times sixty is 120. Thus, this yields 720 hours in sixty days. Then do: ten five times is 50, and two times five is 10. Thus you have 60 hours in five days. Together, a whole year in 365 days yields 4,380 hours, and as many also in the night, yielding with day and night together 8760 hours. Divide those into 7 parts. First do: seven times thousand is 7,000, 1,760 are left over.

Then do: seven times two hundred yield 1400, 360 are left over. Then do: seven times fifty yield 350, 10 are left over. Then do: seven times one is 7, 3 are left over. These three hours make a day in 4 years.