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To the all-glorious patrician Mr. Peter - Maxim, a humble monk. 1. Since I know that you, the all-valid and God-protected ruler, have made the highest wisdom as your teacher and companion of life, by which you are always generous to divine zeal and virtue, as well as the God-given ability and power to think and do good, the basis of which is pious and Orthodox faith, which through hope gives confidence in the invisible as in something that by grace has already become almost visible and reveals it even before its appearance - for those who, as you, constantly awaiting and awaiting the Coming of the Word in a steady pursuit of Him, as well as for your others, I decided - solely trusting and at the same time counting on a condescension that exceeds all - to write out and send to your all-gloriousness and glory the sacred canon 53, including both the beginning of the holy days of [Great] Lent and the feast of the Holy Resurrection, and in addition the tenth day of the seventh Jewish month 54, anciently important, but now insignificant for us - after all, nothing ever gets into it by us, although in general it is celebrated - when once a year, according to the Law, the bishop entered into the Holy of Holies: on this very day the gospel to Zechariah about John, the great Forerunner and herald of the Truth 55 took place - why it was I, without hesitation, but on the contrary, with care, who took the trouble to indicate it for the sake of the curiosity of lovers learning, seeing that from here it will be easy for you to find out any of the sought-after [dates]: the plot 56, the Resurrection, and this very tenth day of the seventh month. Following the mentioned schedule of the canon, I also made a brief explanation of it, containing the following. What is a canon and what is the significance of its contents 58. 2. The proposed canon reads as follows. It consists of three parts, including the [day] of the prayer for the sacred Fast, the fourteenth day of the first Jewish month, that is, Nisan, on which their Passover is celebrated, and the tenth day of the seventh month, that is, Fersi 59, on which in ancient times the bishop entered the Holy of Holies. At the same time, the indication of the fasting spell in this canon is written on the left, the fourteenth day of the Jewish first month is on the right near the “wheel” painted in the middle 60, and behind it even more to the right is the mentioned tenth day of the seventh month; Thus, one schedule on the left refers to the fasting fast, and on the right - to the other two, that is, the fourteenth day of the first and the seventh day of the tenth month. This is the meaning of what is written as a whole. 3. On the left side of the canon, in its first column, 7 embolimic months 61 are located vertically. In the second column there are 19 lunar years, starting with the 19th, followed by the first, second and so on, stopping at the 18th. The third column contains epacts of lunar years. In the fourth column are the Roman months of January and February. In the fifth column are the numbers of these months in which the Meat Empty Festival falls. In the sixth column are additional days written in red lead. This is the one on the left. 4. On the right in the first column are the mentioned 19 lunar years, starting from the first in order through the second, third and so on and ending with the 19th. The second column shows the Roman months of September and October. In the third column are the numbers of these months in which the tenth day of the seventh Jewish month falls in each year. The fourth column contains additional numbers written in red lead. The fifth column shows the Roman months of March and April. In the sixth column are the numbers of these months, in which the fourteenth day of the first Jewish month occurs each year. In the seventh column there are additional numbers again, written in red lead. This is the one on the right. What is written in the “wheel”. 5. In the middle between them there is a solar “wheel” containing within itself: seven leap years, spaced four years apart; after the leap years, in the nearest first row, that is, the circle, there are 28 solar years, written in order from the first and second to the 28th; in the second circular row are the epacts of these 28 years, recorded for each current year. This is about the middle “wheel”. Why does the left diagram count from the 19th lunar year, and not from the first? 6. The reason why the record of lunar years on the left is located not from the first year, but from the 19th, first, second, and so on, is this. The spell is always in the penultimate, that is, the eleventh month of the year, just as the Easter holiday is in the first [month] of the coming year. In this regard, the holy days of Lent cross two years, or more precisely, they consist of [days] of both: they begin in the current lunar year, and end in the next one. By necessity, the beginning of Lent is always recorded in the table from the 19th year, when the saving Easter is celebrated in the first year of the moon. In the same way, further from the 1st year, when the Feast of the Resurrection is in the 2nd; from the 2nd - when in the third; from the third - when in the 4th and so on until the end. This is the count in the schedule of lunar years on the left. What are embolimic [months] and what are epacts of the moon. 7. The seven embolimic (intercalary) months are made up of the so-called lunar epacts in the second or third year, accumulating a number of 30 days. Epacts are given due to the insufficiency of the lunar year in relation to the solar one, since the solar year consists of 365 days, and the year of the moon - of 354, which is why its month contains 29 and a half days. Any lunar year that includes one embolic month is always thirteen months, getting it literally “attached” to twelve, so that in the end after adding the embolic month there are not 354 days, as in other lunar years, but 384. About the Jewish months located in the canon on the left and their numbers, what they are and why they differ. 8. So, therefore, the penultimate month from the end of such a lunar year is not the eleventh, but the twelfth. As a result of this, the order for the holy Lent is recorded in the table taking into account this redundancy of the month, violating the rule of its onset from the eleventh month, so that the number of days [of Lent] is not counted more than the actual one and so that those who count do not make a mistake in them. At the same time, in the left part of the canon, the same number of each month, the eleventh or twelfth, corresponding to the Roman account is not preserved - as we see fulfilled for the 14th of the month indicated on the right side of the table, the same for any year - but different each time. It is either the seventeenth day of the 11th Jewish month of Shavat 62 - in those years that do not have an embolic month, or the eighteenth day of the 12th month, called Adar 63 - in years that have an embolic month 64. And this is completely justified. After all, since we count each of the twelve lunar months alternately into 29 and 30 days, so as not to divide the days in order to get 29.5 days (for in this way the number of 354 days of every lunar year comes out completely counted, so that not a single day has to be divided), as a result of this sequence starting from the first month, the 11th month turns out to be of 29 days, and the 12th of 30 65. So, accordingly, in years that do not have embolimic months, we placed [this day] in the 11th month of the 17th day: after all, from this day to the 14th [day] of the first Jewish month of the coming year, there is an exact number of days of Holy Lent, that is, 57 - that is, obviously, 8 weeks 66. Of these, the 13 remaining days are from the 11th month, since, as I said, it has 29 days; 30 days – from the 12th month; and 14 days - from the first. It is clear that 13 and 30 and 14 make 57 days. And in years that have an intercalary month, we look at the twelfth month, its eighteenth day. For from it to the 14th day of the first month there are again 57 days. Of these, 13 are the remaining days of the 12th month, since it counts 30 days; and 30, which contains embolimic, that is, the thirteenth; and 14 days of the first month. Moreover, in the last, that is, the 19th year, we even indicated the 16th day of the 11th month, due to the fact that we consider its twelfth month to only have 29 days, like this 11th (we will explain the reason for this further). So, because of this, we faithfully observe an equal distance from these above-mentioned months, that is, their numbers [indicated] for the day of the ritual on the left in the canon, to the 14th first month, which we have on the right side of the same canon for [indicating] the Resurrection, which occurs on the holy Sunday day following Sunday, Monday and other days of the week. Having said this, we must devote our speech to an accurate description of the lunar years. About the course of lunar years and the totality of days. 9 . So, the total number of lunar years, as was said, is 19. Of these, 7 have equal embolimic months, that is, they consist of 384 days, and 12 are so-called ordinary ones, that is, of 354 days. Nevertheless, the days of these 19 lunar years, precisely taking into account the embolimic months, turn out to be equal to the days of 19 solar years, that is, out of 365 days. For this is why 7 embolimic months are inserted into lunar years, in order to make them completely equal; and they are not only 6726 67, but 6935 68 days. For so many days make up 19 solar years, and only one extra day is in the cycle of the entire nineteen years. How one extra day of embolimic months is truncated and in what year. 10. For although we insert into it [the nineteenth year] 7 months, that is, 210 days, despite the fact that due to the annual excess of eleven days only 209 are accumulated in it, but the last, 19th year for this reason is less by one day, being 383 days, in order to truncate one extra day in the embolimic months. For it begins on April 4, and ends on March 22, 69. Thus, the correspondence of embolimic supplements to the equality of days is observed, and the entire nineteen-year cycle turns out not to exceed by a single day the sum of nineteen solar years. The fact that quintupling and quintupling lunar years also truncates the excess, although in a different year. 11. Therefore, those who multiply the years of the moon by five and six and thus count its days, for their part, receive one excess day of the embolimic months gone into the remainder of the fraction in the eleventh year of their count, which we consider to be the fourteenth 70 . For this 11th year is 353 days long and, beginning on December 31st, ends on the 18th of the same month 71 . This is clear from the fact that the twelfth [year], according to their calculation, has the fourteenth [lunar] day on the first of January, so that its new moon turns out to be December 19. Why do they multiply the years of the moon and why do they make mistakes in calculating it, and how does their year differ from the one we calculate? 12. They took care to insert this remainder in the following way. Since they take the lunar month into 30 days by adding and accumulating one sixtieth on each day 72 , it was decided for the sake of this day - I mean the remainder for the eleventh year - to annually add 5 sixtieths so that, having accumulated it (i.e., the day) for the 12th year, transfer the last day of that year to the first day of this year: that is, to the mentioned December 19 73 . And this day is the end of one year and the beginning of another according to this far-fetched counting and method - but not so in truth and in reality. For how can one day be made into two, or instead of two? Establishing this is not only impossible, but also completely stupid 74 . So here they are also mistaken regarding the calculation of the moon, since the exact definition is increased due to the unjustified involvement of 5 sixties. As for making her months 30 days, here, thanks to the addition to each day, as was said, one sixtieth, there is no excess, although her month does not consist of so many days. For its decomposition into 30, and not into 29 and a half component parts, compensating for the addition of half a day with the help of sixtieth [shares], does not allow us to obtain more than 29 and a half days. But adding 5 sixtieths for each year in order to make up for the truncated part for the eleventh, in any case, leads those calculating to an error. This is clear from the fact that after this one day, out of the 7 lunar years remaining until the end of the nineteenth year, 35 sixties are discarded as unnecessary 75. And everything that is discarded without reasoning in the calculation demonstrates the inconsistency of the entire cycle [compiled] according to their method and exposes the error of those who use it. For their intention, as I said, is to bring together this one day, but not at all the accuracy of the whole. And the year they calculate differs, as I said, from what we calculate according to church tradition: since they add 16 to the years from Adam. But, having said this about them along the way, we return to the previous one, clarifying the reason for adding embolimic months to lunar years. What and why the embolimic months are added to lunar years. And where the first one always begins and where the last one ends. 13. So, we believe that [these months] are inserted into them so that they can be counted in the table from the same month, which is possible only after this procedure - due to the annual lack of 11 days before, so that the solar year, which has no deficiency (ellipsis), is considered to always begin in the same month, namely the same one in which spring and the equinox are located: that is, among the Romans it is April, among the Macedonians Xanthic, among the Egyptians is Farmuti, among the Jews Nisan, and according to the zodiac called by the outer [sages] Aries. For since in each year the moon, due to the missing 11 days mentioned, descends by the same amount below the day from which it began, and does not retain its beginning in any one month, special from the others, but in all of them in turn, since in the indicated manner it moves back after each [month], - because of this, in the end, it is impossible to indicate the beginning of the years of its new moon 76 . This artificial calculation and method consists of adding seven embolimic months to it so that it, in the same way as the sun, can be listed in a table and calculated from the same day. And not only for this, but also so that, just as one solar year always turns out to be equal to itself, so every nineteen-year cycle would be the same, starting on the same day and ending on the same day, namely, always beginning in its first year on the twenty-third of March and in the last, that is, the nineteenth, year having an end on the twenty-second day of the same month. So, this is what can be said about the epacts of the moon and the embolimic months. 14. It is further necessary to indicate the month within which the new moons of all lunar years are contained - which is why some call it Easter - where it begins and where it ends 77. So, we say that it starts on March 8th and ends on April 5th. For from this day to that is a whole month of the moon, that is, 29 days. It is on so many days that her years pass up and down in their new moons, on the one hand, due to the 11-day deficiency, and on the other, due to the 30-day insertion and addition. Likewise, the fourteenth days, counted directly from the new moons, on which the Jews celebrate Passover, ascending and descending in the same way, have their beginning on the twenty-first of March and their end on the 18th of April. For from this to that there are again 29 days. The lowest (earliest) of all new moons [and] fourteenth days forms the sixteenth lunar year, and the highest (latest) - the 8th. About the deviation 78 from Easter of the Law and about the feast of Christ, from which and until which day it is signed in the canon. 15. That is why we, who are privileged by grace to celebrate the Passover of Christ our God in the “unleavened bread of truth” (1 Cor. 5:8), retreat just one day - when we see the twenty-first of March, which corresponds to the 14th day of the moon, falling on Saturday, or 7 days - when we find April 18, on which the Jews equally celebrate the 14th day of the first month, which happens to be Sunday, and we describe in the canon the celebration of the saving Passover during 35 days (for so many of them are accumulated from the twenty-second of March to the twenty-fifth of April), not descending below the first [date], but also not rising above the last, due to the fact that for these days and within these boundaries church law and tradition are commanded to us. So here we have the new moons and the fourteenth days of the moon calculated in this way. From what Roman month do they write Paschal and all the years of the moon “multiplied by five and six” and why, how and in what years they consider the 14th day of the first Jewish month to be the fifteenth and sixteenth. 16. But those who multiply this by five and six [count] from another Roman month, namely from December: after all, they, taking its fourth number as the beginning, so that all the new moons are contained within this very month, place its end on the first of January 79. For from that date to this one there are 29 days [inclusive]. That is why it is precisely from this date, that is, from the first of January, that they write down every lunar year in the canon; then, to calculate the day of Easter, they evenly add sixtieths of 90 days (from here to the end of March), and after dividing these three months by 30 they are left with half a day, that is, 30 sixtieths. So, to these 30 sixties they also add annual additions consisting of 5 sixties, getting one day 80. And it happens that, due to the retreat of Easter, they extend the calculation further than it should be, to certain days of April. After all, we have to add the sixties to this [Easter interval]. It always turns out that due to an increase of one or two days, the fourteenth day of the first Jewish month turns out to be either the fifteenth or even the sixteenth. 15th - in the following years: in the fifth, sixth, 7th, 8th, 9th, 10th, 11th, 12th, 13th, 14th, 15th, 17th and 19th. Sixteenth - in the year of the same number, that is, in the sixteenth. They agree, considering the 14th day to be the fourteenth, only in 5 years, that is, in the one that they consider the first, but with us it turns out to be the fourth, as well as in the second, 3rd, 4th and 18th. So, obtaining such results, when the 14th day of the first Jewish month coincides with Sunday, the Passover of Christ occurs, of necessity, on the twenty-first day of the moon, and according to their erroneous calculation, for the reason stated above, on the twenty-third. This is what should have been said here about the month of Easter and about the error regarding the fourteenth day of those who count in this way. About the years of Adam, how many there are and how to find the current year of the sun and moon and leap year from them. 17. After this, it is necessary to know the number of years from Adam. So, according to church accounts and tradition, until the present 14th indiction, the 31st year of the reign of Heraclius, our most pious king 81, is 6133 years 82. How many years should be counted and divided in order to find out the current year of the sun, moon and leap year: if it is a solar year, divide by 28, because that is how many solar years are established, that is, 28; if, in turn, it is lunar, it is 19, since, as I said, there are exactly that many. In the same way for a leap year - through [division] by four. For each of these years is clearly recognized by the division of the years from Adam, making up a whole part of the years from the remainder: that is, if one remains from division by 28, 19 or 4, then it is clear that this year is the first year of the sun, moon or leap year respectively; if there are two, then the second, and if there are 3, then the 3rd, and so on until the 28th, 19th or 4th year. And in this way the current and proper year is known in each case. How else are the years of the sun, moon and leap year calculated? 18. On the other hand, this can be calculated in another way. For if someone divides these 6133 years into 532 years, he will find 11 completed 532-year periods and the twelfth, which has 281 years. So, these 281, divided in this way by 28 for the solar year, by 19 for the lunar year and by four for the leap year, will always give the current year of each of these [cycles]. 532 years are formed by combining the years of the moon with the years of the sun and his years with hers. For if 19 is multiplied by 28, or 28 is multiplied by 19, the number obtained is 532 years. So, the current year of the sun, moon and leap year is recognized in the indicated way both through the years from Adam, that is, 6133, and through the twelfth period that has come, that is, 281. Now we have to explain the method by which the most important day of the ritual and the Resurrection is quickly learned from this canon. An explanation of the way in which Easter can be calculated for each year from this canon. 19. So, after, according to the calculation clearly described above, the coming year of the moon is found (say, the coming fifteenth, in which those who celebrate it spiritually will celebrate the saving Easter), and then the coming year [of the sun] 83 is also known (that is, the first, because it just begins 84), one should turn in order to the column on the right side of the canon, in which this year is written as the fifteenth. And if we want to know the Feast of the Resurrection itself, we look for the Roman month opposite the fifteenth year of the moon; and having found that it is April, we take its number next to it, namely the first - since on this first day of the month of April, always in this 15th lunar year, the 14th day of the moon comes, namely the first Jewish month (I mean Nisan). And to this first of April we add the epacts of the coming solar year, that is, the first, number 7, recorded for this first year of the sun. Thus, we divide 8 by 7, and from the resulting remainder of one day we learn that the day of the week on the first of April is the first, that is, Holy Sunday. Finally, from him we move the Feast of the Resurrection to the next Holy Sunday, which, obviously, is April 8th. Since we must necessarily depart from the Jewish Passover - I mean the 14th day of the moon of the first Jewish month - moving, if it falls on Sunday, to another holy Sunday, if on Monday or Tuesday [and so on], - similarly to this same Sunday, if on Saturday - then to tomorrow, that is, the day of the moon will then be the fifteenth; when we, on the other hand, make a transfer from Sunday to the next Holy Sunday, [the day of the moon] is the twenty-first. As has already been said, we implement a retreat from the Jewish Passover, that is, the 14th day of the moon, only up to 7 days, and never more. That's the thing about Easter. About the 10th day of the seventh month, how it is also recognized. 20. If someone wants to know the 10th day of the Jewish seventh month, let him look in the right, that is, written after Easter, canon, the Roman month adjacent to this 15th year of the moon, I mean September; and, taking his number lying nearby, which is the 21st, he learns that this day in the 15th lunar year always falls on the 10th day of this Jewish month. If you want to find out the day of the week on this day of September, I mean the twenty-first, you need to add up the 85 additional days indicated next to the red lead [6] with the epacts of the present year of the sun, of which there are 7 days in the first year, and thus 34 in total, divide by 7 - and the resulting six will certainly be equal to the desired day of the week, that is, Friday 86. In the same way, let everyone use the instructions in the right column of the canon for each year, wanting to know either the 14th day of the first Jewish month, or the tenth of the seventh. We wrote this 10th day of the seventh month not so much for the sake of the holiday that takes place on it (for nothing is celebrated on it at all), but for the sake of those who wish not to experience ignorance of anything out of love for learning. This applies to the canon located on the right side. About the plan for Holy Lent, how to recognize this day for every year. 21. Если же кто захочет узнать день заговенья на святой Пост, пусть посмотрит в расписании слева год луны, находящегося напротив указанного справа 15-го года, точно записанный слева как 14-й год луны: ведь мы сказали, что заговенье на святой Пост совершается в конце установленного года. Итак, найдя этот 14-й год луны, пусть посмотрит лежащий рядом римский месяц, то есть февраль, и, взяв стоящее рядом число его, а именно 4-е, и прибавив к нему указанные рядом суриком 4 добавочных дня и 7 дней, то есть эпакты наступающего солнечного года, а именно первого 87 , разделит сумму, – составившую число 15, – на 7. И поскольку в остатке получился один день, искомый день недели указанного четвертого февраля будет первым, то есть святым воскресеньем. От него перейдя к другому святому воскресенью, попадающему на одиннадцатое февраля, он непременно найдет для 14-го года луны праздник мясопуста 88 . For we should observe the same transfer for the day of fasting in the left canon, as in the right for the 14th day of the first Jewish month, transferring it from Sunday, Monday, Tuesday and so on until Saturday on the next holy Sunday. In the same way, in every other year of the moon, one should calculate the day of the spell, namely, to explain briefly again: find the year, then the Roman month and its number, add to it the additional days and epacts of the real solar year indicated by the minium. Indeed, for all the months placed in this canon, one should use the epacts of the same solar year - for example, the present one - adding them to their numbers along with the additional days highlighted by minium. And thus divide by 7, and from the resulting remainder find out the day of the week. And from there, finally, move on to the next Holy Sunday. What must be observed on the left side of the “canon” on every leap year. 22. However, in the left canon the following should be observed: when a leap year occurs, the additional days adjacent to the numbers of months, highlighted by minium, must be reduced by one when calculating for this year. For example, if there is only one additional day, do not add anything at all instead, but take only the number of the Roman month and the epacts of the sun, and thus divide by 7; if there are 4 additional days indicated by the minium, add 3, but not 4. This happens in order to eliminate the extra one day in this leap year, so that because of it we do not make a mistake when finding the day of the week in two Roman months, January and February. After all, a leap year is taken into account after it has passed, but in no case before that. In those years when there is no leap year, finding the day of the week from this canon turns out to be accurate, giving the same result in the canon of the day of the order - I mean the one on the left - and for Easter: that is, Sunday and Sunday, Monday and Monday, and so on for other days. Когда же настает високосный год, в левой части получается не тот же самый день, но на один позже. Например, слева, скажем, воскресенье, справа же всегда будет находиться понедельник; again, here it’s Monday, then there it’s obviously Tuesday; таким же образом и если окажется суббота, ясно, что в правой части канония получается воскресенье. After all, an additional day in a leap year makes a decrease of one day on the left. Итак, когда мы видим, что в високосный год число января и февраля попадает на субботу, а в правой части [число] марта и апреля – на воскресенье, то в последнем случае нам следует переходить на 7 дней (считая с понедельника до воскресенья), а в первом – всегда перемещаться на 8 (идя от воскресенья до воскресенья): чтобы через 8 [дней] был точно вычислен праздник заговенья, определяемый от того воскресенья. This is something that will need to be observed during a leap year. About the epacts of the sun, what they are and why we use them. 23. Lest what we have said regarding the sun be insufficient, let us say that the epacts of the years of the sun represent a cyclic remainder from the day of the week from which the solar year begins to the first day of the same week, namely Holy Sunday. Let's give an example for the present 28th year 89. After all, it began on the first day of April, on the seventh, that is, Saturday 90. So, the epacts form the past days of this week from Sunday: that is, Friday, Thursday, Wednesday, Tuesday, Monday and Holy Sunday itself, so that from here in the 28th year there are six epacts. Hence, since the coming, that is, the first year [of the cycle] begins on the first day, on Holy Sunday, the epacts form 7 days, namely, counting from Saturday to the last Holy Sunday. Likewise, the second year, which begins on the second day of the week, forms only one epacta, that is, Holy Sunday, since it has no other day passed during this week except this Holy Sunday. We take these days into account in order to write down each solar year in a table in a weekly sense, that is, from the beginning of the week, in order to find the day of the week when we want to know it on [some] date of each month. After all, if every solar year were not listed in the table in this way, that is, from the first day of the week, namely Holy Sunday, it would be impossible for those who wish to calculate the day of the week on which this or that day of the month falls. Let us take as an example the present year, as stated, the 28th year, beginning on Saturday 91. If we had not added the 6 days preceding Saturday to the first of April, we would not have known that this day is Saturday. After all, since the last 27th year ended on Friday, the 92 days equivalent to Friday, as it turns out, on the one hand, indicate that that year ended on this day of the week, and on the other hand, they represent epacts, since they are added to the first day of April and thereby indicate the day of the week on which this 28th year began. Indeed, in this way, on the one hand, consistency in relation to weekly harmony is always maintained, and on the other hand, the movement of solar years from the beginning of the week, that is, the first day, is tabulated. And thanks to this, there is not a single mistake for those wishing to calculate the day of the week on any day of the month. How to find what day of the week is what day of each month. 24. After all, when figuring out what day of the week a particular day of the month is, you should use exactly the same method that we used for the first of April. Something like this: add epacts of the present solar year to the days that have passed from this very first of April to the day of this or that month we are looking for; and divide the amount by seven; and from the resulting remainder we find out the day of the week equal to it in number. Or in another way, [adding] only these epacts and days of months exceeding 28, which are 2 in April, 3 in May, and so on in the same way until we count to the desired month; and then, adding to this the number we are looking for, we again divide by seven, and from the resulting remainder we always find the day of the week. It is for this reason that it is said that the years of the sun have epacts, and for this we have used them appropriately. Which sunny years are without epact. 25. Therefore, we call years starting from Sunday (such as the first, seventh, twelfth, 18th) non-effective due to the fact that they do not have a single preceding day: after all, there is no other before the first [day of the week]. In addition, the epacts of the solar year are not introduced in the same way as those of the lunar year (after all, the first is not delayed in relation to 365 days, like the second, by 11 days, due to which the 19-year cycle receives the addition of seven intercalary months), but only in order to calculate the day of the week for 12 months by preserving and observing the weekly harmony that lies at the beginning of solar years. This is about the epacts of the sun. About additional days, what they are and where they come from. 26. The additional days 93, which are written in red lead, about which we have already said that they are added to the epacts of the solar year in each Roman month and thus divide by 7, have the following meaning. As indicated, the day of the week is calculated in two ways: as the totality of all days, namely from the first of April to one or another day of the month in question; so also when counting days exceeding 28. These excess days turn out to be 13 by September, 15 by October; dividing 13 by 7 [and obtaining a remainder of 6], we indicated them with red lead in September; and since 2 weeks are subtracted from 15, that is, 14 days, in October we wrote down a unit in red lead. For it makes no difference what to take into account in order to find the day of the week in these two months: 13 and 15 or only 6 and 1 - of course, after taking the epact of the real solar year, which is the calculated one: the first, second and in order until the 28th year. The same explanation applies to the 4 and one days indicated by minium, located in March and February and in January, although after additional days the rule for their weekly calculation turns out to be the opposite of the months recorded in descending order, such as September and October, since the latter are both counted and refer to the current solar year. After all, the calculation must be carried out only from the present [year], that is, its epact, which will clearly represent the day of the week to those who wish. After all, it is always advisable to make the transition from Sunday, Monday, Tuesday, and so on to another holy Sunday [simultaneously] in both the right and left canons: in one, as was said, for entering into holy Lent, namely the feast of meat, and in the other - for the saving Easter. This applies to the additional days indicated by the minium, so that after the explanation of this canon presented in all respects, understanding its contents becomes easy for the hardworking. About the epacts of the moon, how they are calculated. 27. After all this has been said, we should again turn to the epacts of the moon located in the left canon and explain how they are counted. So, you need to multiply the established lunar year by 11, - for example, the current 14th, - and reduce the 154 days obtained after multiplication by two days, since the first lunar year has only 9 epact; and this, I mean 152, divided by 30, since that is how long the embolimic months last; and the remainder will let you know how much epact a lunar year has, that is, 2 days. So much is recorded for this 14th year in this very canon. So, for every other lunar year you should do the same. It turns out that these epacts always represent the days that the lunar year has on the thirty-first day of the month of March. Therefore, you should always know how many there are: after all, it is advisable to count and find on which day of the moon each of the twelve months falls. How do we find the number in each lunar month. 28. For example, let's count the days from the first of April to any desired date of the Roman month and add to them the mentioned lunar epacts, which, as I said, turn out to be the days [of the moon] on the thirty-first of March; and divide the amount by 29 and a half. And what is received in the remainder will let us know the day of the moon. This concerns the method of finding lunar epacts. About the epacts of the sun, how they are counted. 29. You should also find out about solar epacts and how you should take them. So, it is necessary in the established solar year, say, in the current 28th year, to take an equal number of days, except for one day, that is, 27 days, and add a quarter of the equal number without subtracting a quarter, that is, 28x1/4, which will obviously be seven days; and divide this entire amount, that is, 34, by 7 by week. And what is received in the remainder, that is, 6 days, lets us know how much epact this 28th year has - this is how much it has been recorded by us in this very canon, like the rest of its kind. They do the same with every other [year], finding its epacts. Why do solar years have either equal or excess epacts? 30. Each year of the sun forms one and a quarter epacta, which is nothing more than an excess of 365 days over 52 complete weeks. Because of the transition and growth of one and a quarter that occurs from year to year, they say that there are 2, 3, 4, and so on up to 7. After all, as soon as a week is completed, that is, 7 days, the increase continuously begins again over the years. In this way, a leap year occurs, when one day accumulates from the quarters of a four-year period, and its formation gives a certain excess to the increase in the impact of the next year, adding two days instead of one - which can be seen in this 28th year. Indeed, while the previous year, that is, the 27th year, had four [epacts], this one, due to the accumulated quarters of the day, forms six [epacts]. Therefore, the mentioned 27th year did not end on the same day on which it began. Since with 365 days [the year] always ends on the same day from which it began, for example, from Sunday - on Sunday or from Monday - on Monday; but with 366 days - one day after the one on which it began: that is, from Sunday - to Monday, and from there - to Tuesday, and so on in a similar way. Because of this, it is necessary to observe the epacts of the sun and consider them in the described way. Namely, let us say again: (1) take the number of days equal to the established solar year, which is calculated, except for one day; (2) and a quarter of an equal number without subtracting one quarter; (3) and divide by 7. And the remainder will always be the epacts of this year given to us for calculation. And we said to take the number of days one less than the number of the year because the first year is written as having a quarter epact, since it begins in the canon from the first day, that is, Holy Sunday. After all, every year starting from Sunday, as was said above, does not form any epacts at all, except perhaps some fractions: a quarter, half or half and a quarter (3/4), which are not taken into account when finding the day of the week until they form one day after four years. How can you determine the epacts of the sun and moon differently? 31. And if we talk briefly about the epacts of the sun and the moon and about their easy definition, then the moon, that is, its current year, always certainly has as many epacts as the number of days it has on the thirty-first of March; the sun, that is, its current year, always certainly has the number of its epacts equal to the day of the week on which the end of the previous year falls on the mentioned thirty-first day of the same month of March. This is about the epacts of the sun and their location. About the Nativity of the Lord according to the flesh, Baptism and Passion, in which year of the sun and moon they occurred and on what day of the week. 32. After all this has been said, one of the most necessary things is to indicate the year of peace in which our Lord and God Jesus Christ performed the super-peaceful Incarnation in the world from the Holy Theotokos and Ever-Virgin Mary. So, at that time the year was 5501, according to the record on the sacred tablets of years counted from Adam 94. This year saw both the Annunciation of the Virgin and the incorruptible and most holy Nativity from her. It was the 13th year of the sun, the 10th moon, the day of the week of the Annunciation - 2nd (Monday) 95, Christmas - 4th (Wednesday) 96. Likewise, His blessed Baptism took place in 5530. It was the 14th year of the sun and the 1st moon, the day of the week was the 3rd (Tuesday) 97. In turn, His saving Passion, that is, the Crucifixion, was in 5534. It was the 18th year of the sun and the 5th moon, and the day, as is obvious, was Friday 98. So from His incarnation to the current indiction, the 31st year of the reign of Heraclius, our most pious king, 633 years. And from saving Baptism and Suffering, as it obviously follows from this, 604 and 601 years, respectively 99. Because of what, the year of the Nativity of the Lord is recorded in another year of indiction, and why and where the indiction is calculated from. 33. For each of these [dates] we find that the distribution, which the Romans call indiction, is different, since it is differently calculated from the years from Adam and from the [year] from which it itself originated. It originated, according to historical writers, from Augustus Caesar, in the second year of his reign. It was then 5460 from the birth of the world 100, which, divided by 15, represents the end of the indiction, that is, the 15th year itself; He (August), having laid the beginning of his (indiction) in this year according to the command, made the last [year] the first 101. So because of this, the result is that the indiction calculated from the second year of the reign of Augustus moves forward one year relative to that calculated from the creation of the world by dividing it into 15 years from Adam. Hence, according to this account, the year in which the Nativity of the Savior according to the flesh took place was the 11th year of the indiction, but therefore the 12th, since one year should be added. Likewise the sacred Baptism - 10 and 11, and the saving Passion - 14 and 15. For in the 43rd year of the reign of Augustus, He celebrated the Nativity for us as a man, who before the ages was born of the Father as the Son. So, dividing 42 by 15 represents, as I said, the Nativity of the Lord in the 12th year of the indiction. Likewise, on the other hand, dividing 5501 by the same number is in the 11th. From both of these calculations, one can similarly find the current year of the indiction: that is, by adding, for the reason indicated, one year to the years from Adam, which will be 6134, and dividing by 15; or from the 2nd year of the reign of Augustus, of which there are only 674,102, dividing them by the same number; for from both we learn the current 14th [indiction]. The same can always be done in another case by those who wish to consider the number of each year of the indiction. About the prediction to Zechariah and the years of John and the Savior. 34. It should be recalled in order and with precision about the prediction about John the Baptist who came to Zechariah, which we previously mentioned, in what year of the sun and moon it occurred. For those who are attentive, it is already clear that both years precede the Nativity of the Savior, that is, the 12th sun and 9th moon; was the Roman month of September, the 27th, day of the week 5th (Thursday) 103. After all, the year of birth of John himself was the same year of the sun and moon in which the Nativity of the Lord took place, in an obviously different month, June, the 24th, on the second day of the week (Monday). The year of his death, that is, beheading, was the 17th year of the sun, the 4th moon, the month of August, the 29th, the 3rd day of the week (Tuesday). So the Savior according to the flesh was 33 years 89 days, and John the Baptist was 33 years 67 days, 22 days less than the Savior. So, God-protected ruler, possessing the knowledge briefly explained here, adhere to the sacred triumph of the sacred feasts of our Savior, in order to find yourself permanently received into heavenly glory and triumph with the angels, through the prayers and intercession of our all-glorious and immaculate Lady Theotokos and Ever-Virgin Mary and all the saints. Amen. 10 Tishri - Day of Atonement, or Day of Judgment (see Lev. 23, 26–32). The tradition relating the news of the angel Zechariah about the birth of John the Baptist (Luke 1:5-25) to the 10th day of the 7th month, when the high priest entered the Holy of Holies of the Jerusalem Temple only once a year, is attested in the 5th century. at St. John Chrysostom (Joannis Chrysostomi In diem natalem // PG. 49. Col. 356–357); however, for some reason he considers this day the Feast of Tabernacles (ἐν τῷ καιρῷ τῆς Σκηνοπηγίας). Here and further in the original, the term “παρείσβασις” is used to designate the week of meat-eating (Sunday before cheese week), which is regularly translated as a conspiracy. The subheadings, judging by their style, were not in the original text and were inserted by the editors. Θερσί is a distorted name for the Jewish month of Tishri. A “wheel” is a pie chart that is convenient for recording cycles. That is, 30-day additional “thirteenth” months inserted to align the lunar months with the solar year. There are only 7 of them in a 19-year cycle. Shevat (shevat) is a month of the Jewish calendar (11th, starting with Nisan). Adar is the month of the Jewish calendar preceding Nisan. In the Jewish calendar, the embolic month of Ve-Adar is inserted before Adar, so that it is considered the 12th. However, the lunar calendar of St. The maxim is not the same as the Hebrew (see also next note). Thus, Nisan is considered to be 29 days by Maximus the Confessor; in Jewish tradition it is always 30 days. From Sunday to Sunday inclusive. 19x365=19x354+7x30–1=6935. In the Alexandrian Easter, the 1st year of the lunar cycle begins on March 23 (full moon on Nisan 14 - April 5). In the “adding five mites” system, it is assumed that in 365 solar days the moon travels 12 full months of 30 days and another 11 1/12 days (365x(1+1/60) = 371 1/12 = 30x12+ 1/12); these 11 1/12 days are, strictly speaking, annual epacts. Increasing by 5 lepta (1/12 = 5/60) per year, the fractional part of the epact by the 11th year gives a whole unit, which compensates for the extra day of the 19-year cycle. It follows that the embolimic month, required in the 11th year of the cycle, was inserted before the 1st month, that is, at the end of the 10th year. Thus, the conditional “lunar day” (1/30 of the month) is introduced, which is 1/60 shorter than the solar day; a lunar month of 30 such “days” is equal to 29.5 solar days; a year of 365 days includes 371 1/12 “lunar days”, that is, 12 months and 11 5/60 “days”; a period of 19 years, that is, 6935 solar days, consists of 7050 7/12 “lunar days,” that is, 235 lunar months and a remainder of 35 lepta (7/12 = 35/60). The phase of the moon is calculated as the serial number N of the day in the years starting from January 1, subtracting 30-day months and adding 1/60ths of the shares accumulated to this day. Adopting a regular lunar month of 30 “lunar days”, each of which is 1/60 shorter than solar days, makes it possible to determine the fractional (accurate to mite) lunar phase. The lengthening of each year by 5/60 (with zero epact at midnight from December 31 to January 1) and, accordingly, the accumulation of fractional shares of epact to a whole number at the beginning of the 12th year (analogous to the “moon jump”: 5/60x12 = 1) are not the goal, but an inevitable consequence of the calculation method using the “lunar day”. Mathematically, the method of "adding five and six mites" results in a shift similar to the "moon leap" at the end of the 11th year of the lunar cycle. It is designed as a “combination” of the 29th day of the 12th and the 1st day of the 1st month, which causes criticism from Maximus the Confessor. In a 19-year lunar cycle of 6935 days, there are not exactly 235 months of 30 “lunar days”, but 35 lepta more: 6935x(1+1/60) = 7050 7/12 = (235x30)+ 35/60. These additional increments of epact of 5 lepta for the next 7 years were not taken into account (“discarded”), which, as St. points out. Maxim questions the validity of the methodology used. That is, those years that begin on the new moon (from such a year the 19-year cycle begins). We are talking about a 29-day range, containing the new moons of all Easter months - and therefore the beginning of lunar years - in a 19-year cycle: from March 8 (the earliest Easter new moon, in the 16th year of the cycle) to April 5 (at the latest, in the 8th year of the cycle). We are talking about the interval separating the Old Testament (“legal”) Easter from the Christian, Sunday. Inaccurate. January 1 is indeed the beginning of the 19th lunar year of the “multiplying” cycle, however, the range of new moons, similar to the Alexandrian “month of Paschal” described above, should be counted not from December 4 to January 1, but from December 8 to January 6 inclusive. The same day that is similar to the “leap” at the end of the Alexandrian cycle (see above). Let us note that St. Maximus respectfully titles Emperor Heraclius, despite his disagreement with the Monothelite Exposition of the Faith (Ektesis) published by him in 638. The 14th indiction began on September 1, 640, the 31st year of the reign of Heraclius began on October 5, 640, and the year 6133 from Adam according to the Alexandrian era began on March 25, 641 (below, St. Maximus says that this year is “just beginning,” and considers April 1 to be the beginning of the year). Since Heraclius died in February 641, the treatise should be dated to March 641, when Africa had not yet received news from Constantinople about the death of the emperor. We are talking about 641 AD. e. Easter this year is April 8th. There is a gap in the text, but the table shows the number 6. Friday 21 September 641 Solar epacts are taken from the coming year, since the plot is tied to the day of Easter, which already belongs to the next year of the cycle. Sunday 11 February 641 28th year of the solar cycle - from April 1, 640 to March 31, 641. April 1, 640, Saturday. It follows from this that the beginning of the solar year of St. Maximus the Confessor counts April 1, not March 25 (the day of the week of these dates always coincides). That is 6, because Friday is the 6th day of the week. The term προσθεταὶ ἡμέραι corresponds to the “butts” of Russian Easter eggs and “regulares” of Western ones. This solemn phrase probably refers to the tradition of recording the current year from the creation of the world on special tablets installed in churches. In Rome in the 7th–8th centuries. in a similar way, the year from the Resurrection of Christ was recorded on the so-called ceras (see: Beda Venerabilis. De temporum ratione // PL. 90. Col. 484). March 25, 9 AD e., Monday. December 25, 9 AD e., Wednesday. January 6, 39 AD e., Tuesday. 23 March 42 AD uh, Friday. The calculation is incorrect: until March 641 AD. e. (14 ind., 31 Heraclius) dated March 25, 9 AD. e. (Incarnation) turned 632 years old, from January 6, 39 AD. e. (Epiphany) - 602 years old, from March 23, 42 AD. e. (Crucifixion) – 599 years. The error seems to be due to the fact that it was 6133 from Adam, the 633rd year from the Incarnation (that is, the number of years that have passed is confused with the serial number of the year). For some reason, the years of Baptism and Passion are taken to be the 30th and 33rd years of Christ, whereas according to tradition, the Savior at the time of these events had already turned 30 and 33 years old, respectively (they were 31st and 34th years, respectively). 5460 of the world - 2 August according to the chronology of Julius Africanus (= 43 BC). 5460 Alexandrian era corresponds to 33 BC. e., 1 year of indictment. This legend is intended to explain why the Alexandrian chronology (unlike the Byzantine one) begins not with the 1st, but with the 2nd year of indiction. 8 AD e. (Alexandrian Annian system; cf. Georgii Syncelli Ecloga chronographica / Ed. A. A. Mosshammer. Lpz., 1984. P. 380).