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Explanation of the underlying wheel. 1. I consider it prudent, having explained to the hardworking how to find and recognize the day of the week with the help of painted canons and outlined methods, to paint for this purpose a special independent wheel; in it you can correctly and easily determine each desired day in any of the twelve Roman months for every solar year. It is reversible in different directions, that is, when using a progressive account and going from the month of April, May, June and so on, or, on the other hand, when returning from the month of March, February and January and so on to the previous ones. 2. The schedule of the wheel is as follows. It contains 3 belts and inside them is a square canon. So, the first belt contains epacts of 28 years of the sun. The second is these 28 years of the sun, recorded in order from the first to the last. The third is four-year leap years. 3. The canon has 7 lines in which the days of the week are located. But in the first line - in order, that is, 1st, 2nd, third to 7th; and in those after the first row - as required by the score. On both sides of it, these days of the week are again written in red lead, arranged vertically; and behind them are the twelve Roman months written down. Only the month of March turns out to be written in two ways due to the leap year. This is about the structure of the canon. Demonstration of progressive counting. 4. So, when we want to find out from this wheel the day of the week on which such and such a day of the Roman month falls, we first look, using the method outlined above, for the real year of the sun, say, the current 28th. Then we take its epacts, numbering 6, and if we are talking about two Roman months located in the first line, that is, April and July (after all, they are written in the same line), we add them to the number we are looking for in them and divide by 7. And from the result we find the day of the week equal to the value of the remainder. This is what we do with the months located in the first line. If we are looking for the same twenty-eighth year for the day of the week in two other months in the 2nd line, that is, May and January, we take the number written in the same column in the 2nd line and lying under the indicated 6 epacts, that is, one. And in a similar way we add to the number we are looking for in them, and divide the sum by 7. So, we look at this column, that is, what is written in it, in other lines to find the day of the week in the Roman months written on the sides for the 28th year. In the same way in every other year of the sun: first we determine the epacts themselves according to the canon; then those [days] that lie under them and are written in the same column, in no case deviating to the right or left, remaining for a given year in the same column: but for the 2 months located in the first line, epacts [are taken], and for the months in the other 6 lines - the days written in the same column. 5. It should be noted that March, unless there is a leap year, is counted according to the days of February; when the year is a leap year - according to the days of December (where “leap year” is written). After all, it is for this reason that we put March under these two months. Thus we find the day of the week from this wheel when we count progressively, as was said: through April, May, June and so on. 6. When we want to find the day of the week from the epact of the present year, namely the 28th, in reverse order, that is, through March, February, January and previous months, we do not need the epacts of the previous 27th year for this determination. If we are looking for this day in the months located in the first line, we add the indicated six epacts with the number of April or July of the month after the days indicated by the lead opposite April, that is, 6, when there is no leap year, and divide the sum by 7. When there is a leap year, we [take] the days opposite July, that is, 5, followed by 6 epact, and divide the sum by the indicated number. After all, according to this backward counting, you should use the days indicated by the red lead on the left without a leap; when is a leap - written in red lead on the right. This is in two months of the first line; and in the 2nd line, in May and January, in the same 28th year, we add these six epacts with the desired number after the days indicated by the red lead opposite January, that is, 7 days, and divide by the same number. That’s why I said “opposite January,” since last year, that is, the 27th, had a leap year. And for the leap year, as I said, the red lead entry is made on the right. 7. By the same counting back, it should be noted that March is always, both after a leap year and without it, counted according to the days of December, that is, according to the four recorded by red lead. And neither for September nor for February, as we said, should one make calculations using the described method, but only according to these four days recorded in red lead, lying opposite the month of December. Simply put, if we briefly define both calculations: in 7 lines of the canon for the twelve Roman months indicated on the sides in every year we use the described calculation; in two vertically arranged rows written in red lead, we use the reverse method, in combination, as I said, with the epacts of the real solar year, for which 7 lines are written in the canon. Having explained this regarding this wheel, we have made it as convenient as possible for those who wish to find it on any day of the week. How to calculate the day of the moon 114. 8. 1. We take the epacts of the moon and the number of a given Egyptian month, and half the months from that, and one catholic 115. And if we find 30 of them or up to 30, we know that the moon has that many [days]. If it is over 30, the same thing after subtracting thirty from them. 2. Otherwise. Subtracting one from the years from Diocletian, we divide by 19 and take the remainder; we add: to one year, if only it remains in the remainder after division - 10 days; by 2 years – 20; at 3 - nothing, also nothing at 6, 9, 12 and then every three years; by the age of 4 - again 10, by 5 - 20 and so on in order, starting from 7, from 10, from 13 and further, counting after three years. So, we take, as has been said, the remaining years and the days to them in the manner indicated, and the number of a given Egyptian month, and half the months from that and one catholic; and divide the amount by 30. 3. Otherwise. We take the epacts of the moon and one day for each Roman month, starting from September 116 to the calculated one, and the number of the given Roman month, and two catholics; and divide the amount by 30,117. 4. Otherwise. We take the epacts of the moon with unit 118 and the days from [1] January to what we are looking for; and their 60th [part]; and divide the amount by 30. 5. Otherwise. We take the epacts of the moon and half of the months from April to the calculated one, and thirty-one, and the day of the given month; and divide the amount by 30,119. 6. Otherwise. We multiply the year of the moon by eleven and take the days from the first of January to the desired day and their 60th part; and, discarding 3 catholics, we thus divide the sum by 30,120. 7. Otherwise. We take epacts of the moon and use them entirely in January and February; in March without one day; in April and subsequent [months] – entirely; adding with them one day for each next month before the calculated month (and only in August - two) and the day of the month; and divide the amount by 30,121. 8. Otherwise. We take the epacts of the moon and the days from the first of April to the desired one, and the number of the month; and divide the amount by 29 and a half 122. About the years from Diocletian, how they are counted and how to use them to find the year of the moon. 9 . The years of Diocletian until the present fourteenth indiction, the 31st year of our most pious Basileus Heraclius, are 357. They are counted in this way. We multiply 15 years of indiction by 22 and add to this 13 “catholics” and years of real indiction 123. If this fifteen year period ends, the multiplication should be done by twenty-three. In the same way, after its completion - by twenty-four, and so on, one should multiply at the end of each fifteen years, adding the remaining year, and at the end, obviously, adding 13 “catholics”. Thus, it will be easy for those who wish to learn the calculation of years from Diocletian to the present day. And having already divided these 357 years by 19, we recognize in the remainder the real year of the moon. About moon epacts and how to use them. 10. Epacts of the moon are recorded in two ways, namely on the eve of the thirty-first of March and the twenty-eighth of August. So, if we are looking for the eve of the twenty-eighth [August], we subtract one from the number of years from Diocletian and divide this [difference] by 19; the remainder, multiplied by 11, divided by 30 and we recognize them [epacts] by the remainder. If we determine the epacts of the moon on the eve of the thirty-first of March, we multiply its given year by eleven and, subtracting 2 days from this, divide by 30. Since there is a twofold method in relation to epact, this should be taken into account in the calculations described above regarding the day of the moon. And where we indicate March 31st, use epacts on the eve of this day, and where we indicate the 28th [August] - on the eve of this. After all, in this case, there will be no error for those who count. About the first Egyptian month, which the Romans have and when it begins. 11. It should be pointed out that the Egyptian [month] Thoth among the Romans is September, always having its beginning, that is, the new moon, on August 29. Calculus and sum of years 124 About six thousand years, when and under whom each of them ended. About 11 periods of 532 years, when and under whom each of them ended. Explanation of the subject chapters, when and under whom each ended. In the 81st year of Moses, the exodus from Egypt and the first Passover of the children of Israel took place during their first month, namely Nisan. From Adam the year was 3822. 133 In the 12th [2nd] 134 year of Joshua [the people] entered the promised land, and the high priest entered the Holy of Holies, on the 10th day of the 7th month, that is, Tersi. The year from Adam was 3863. In the 25th year of the same Jesus, the Jews began to count Jubilees (Ἰεβουλαῖοι), that is, fifty years. 135 From Adam the year was 3886. In the 4th year of Solomon's reign, construction of the temple in Jerusalem began. From Adam the year was 4474. 136 In the 3rd year of the reign of Joachim, the countdown began for the first year of the eviction of the children of Israel to Babylon. From Adam the year was 4900. In the 11th [1st] 137 year of Cyrus the Persian, the last year, that is, the 70th year of captivity, ended. From Adam the year was 4970. In the 3rd year of the reign of Darius the Mede, the temple in Jerusalem was built again by Jesus the son of Jozedek and Zerubbabel the son of Shealtiel. From Adam the year was 5011. In the 2nd year of the reign of Augustus Caesar, the countdown of indicts began, and the Roman months were invented by them no earlier than this time. From Adam the year was 5460 138. In his 43rd year, the only begotten Son of the Father, Jesus Christ, who is above us, is born for us and becomes by nature a perfect man for our sake, being by nature a perfect God for His own sake. The year from Adam was 5501. In the 15th year of the reign of Tiberius, He accepts Baptism in the Jordan and grants the believers adoption as sons in the Holy Spirit. The year from Adam was 5530. In the 19th year of his reign, He goes to the saving passion, thereby granting dispassion to our nature. The year from Adam was 5534. In the 20th year of the reign of Constantine, the Council took place in Nicaea. From Adam the year was 5816, from Christ 316. In the 2nd year of the reign of Theodosius, a Council was held in Constantinople. From Adam the year was 5872, from Christ 372. In the 13th year of the reign of Theodosius the Younger, the first Council took place in Ephesus. From Adam the year was 5913, from Christ 413 139. In the 1st year of Marcian's reign, the Council took place in Calchidon. From Adam the year was 5943, from Christ 443. In the 26th year of Justinian's reign, the 5th Council took place. From Adam the year was 6045, from Christ 545. Center wheel: 28 year sun circle 140 The top row is the years of the Alexandrian cycle. Middle row – epacts. The bottom one is leapfrogs. Tables: 19-year lunar circle Columns: I. Embolimic days. II. Years of the lunar cycle. III. Epacts [moons]. IV–V. Roman month number [for meat empty]. VI. Additional (αἱ προσθηταὶ ἡμέραι) [for meat empty]. VII. Additional [for the Easter full moon]. VIII–IX. Roman month number [for the Easter full moon]. X. Additional [for 10 Tishri]. XI–XII. Number of the Roman month [for 10 Tishri]. XIII. Years of the lunar cycle. The 1st and 4th zones indicate the years of the solar circle according to the Alexandrian and Byzantine systems, and the two zones located between them indicate the epacts of the sun 141 and leap years, which is important for determining the phase taking into account the leap addition. In addition, they also indicate the number of 19-year lunar cycles, from 1 to 28, which make up the complete 532-year Easter cycle. Each number corresponds to a sector of two columns: on the right - the years of a given lunar cycle are indicated, in which there are cases of unacceptable, from the point of view of Maximus the Confessor, deviation of calculations “multiplying by 5 and 6” from the Paschalistic tradition; on the left are the years of their corresponding solar cycles (as well as the serial numbers of solar cycles in the 532nd anniversary, from 1 to 19). There can be up to five segments in a sector (that is, there can be up to 5 cases of deviation in one 19-year cycle). In the original, each of them was marked with dots (from 0 to 3), indicating the type of deviation. These icons were not preserved in the Vatican manuscript, but they can be restored based on the instructions of St. Maxima. In contrast to the reconstruction of Schwartz 142, the system of marks proposed below is more accurately consistent with both the text of the treatise (which has a small gap in this place) and with the logic of the author’s reasoning. In particular, from his words it is clear that for many years there are no litters at all - which is left unnoticed by Schwartz. The years of deviations “multiplying by 5 and 6” from the Alexandrian Paschal, included in the table of Maximus the Confessor, are divided into 3 groups, separated according to the degree of violation of the Paschal tradition: 1) Easter turns out to be the 22nd day of the moon instead of the 21st (without litter); this happens when “Nisan 14” is considered the 15th day for them and falls on a Sunday of a simple year; 2) Passover not only happens to be the 22nd day, but also precedes the Alexandrian “14th Nisan” (“Jewish Passover”); this happens: a) in a leap year - when “Nisan 14” falls on Monday and is considered the 15th (taking into account the 16th leap year) day or on Tuesday and is considered the 16th (17th) day (sign *); b) in a normal year - when “Nisan 14” falls on Monday and is considered the 16th day (sign **); 3) Easter turns out to be the 23rd or more day of the moon (sign ***); this occurs when "Nisan 14" is considered the 15th day of a leap year on Sunday, or the 16th day of a common year on Sunday, and the 16th day of a leap year on Sunday and Monday; in the latter case, the phase will reach 24 and at the same time Easter will be before “Nisan 14”. 143 For clarity, here is a table:56 On the sides of the “wheel” in the manuscript there are 2 tables: The left table has 5 columns containing: I) indication of embolimic years; II–ΙΙΙ) years of the 19-year cycle according to the Alexandrian and Byzantine accounts; IV) integer epacts for January 1, calculated using the method of “multiplying by 5 and 6” (with a jump between the 11th and 12th years); V) lunar phases, calculated using the same method for the Alexandrian Easter full moon (Nisan 14) and in all years except 1–4 and 18 exceeding the number 14 (hence the name - περιτταί “excess days”). On the right there are also 5 columns, counting from right to left: I) years of the Alexandrian 146 19-year cycle; II) Alexandrian epacts on March 31; 147 III–IV) day and month of the Alexandrian Easter full moon (Nisan 14); 148 V) “additional numbers” to find the day of the week of the Easter full moon (for March 4, for April 0). For ease of perception, the data from the “wheel” and tables are summarized in a general table with the following columns: I – years of the 532-year cycle (according to the Alexandrian and Byzantine accounts), in which unacceptable deviations of the “quintuple” system from the traditional Paschal occur, leading to a violation of tradition. II – years of the Alexandrian 28-year cycle; III – “leap increment” of solar epacts; IV – leap years. V – years of the Byzantine 28-year cycles, with the number of cycles in the 532nd anniversary. VI – years of the Byzantine 19-year cycles, with the number of cycles in the 532nd anniversary. VII is the traditional date and day of the week of the Easter full moon (Nisan 14). VIII–IX – lunar phases of the dates of the Easter full moon and Easter Sunday, respectively, calculated using the method of “multiplying by 5 and 6” (the phase taking into account the leap year is indicated in brackets). X – type of unacceptable deviation of the calculated phase from the Easter tradition (when Easter goes beyond the 21st day of the moon), based on the method of St. Maxima. The outer zones of the table depict the 28-year cycle of the Alexandrian type. I zone – numbers of the years of the cycle; II belt – solar epacts; III belt – leapfrogs. The internal table indicates the “monthly numbers”→ordinal numbers of the day of the week before the beginning of the month. The series corresponding to April and July coincides with the solar epacts of a given year→in the 1st year of the cycle, epacts = 7 = 0, April 1 and July 1 are Sunday. The extreme columns on the left and right→in italics show how to use the table in the case of a leap year, as well as when counting back from March to September→using the example of the 28th year of a cycle with 6 epics. This chapter is distinguished by its concise presentation. An additional day, called “katholica” (καθολική, analogous to the Latin regularis), appears as a result of a shift in the order of 30- and 29-day months: in St. The Maxima lunar month, which begins the 19-year cycle, has 29 days, while in the classical Easter - 30; therefore, the epacts correspond to the age of the moon not on August 28, but on August 27. To obtain the initial calculated phase at the beginning of the Egyptian year (eve of August 29), you need to add one. Petavius’s Latin translation gives “ab Aprili”, but in this case 2 “catholics” are not needed. This method is accurate only when calculating from September to January, and only if Nissan counts 30 days (and not 29, like Maxim). Since February it has been malfunctioning. For example, in the 1st year of the cycle (epact 11), he gives the following values ​​for the first numbers of the months: September 1 – 11+1+2+1=15 (according to Easter 15); October 1 – 16 (16); November 1 – 17 (17); December 1 – 18 (18); January 1 – 19 (19); February 1 – 20 (Easter 21); March 1 – 21 (19); April 1 – 22 (21); May 1 – 23 (21); June 1 – 24 (23); July 1 – 25 (23); August 1 – 26 (25); September 1 – 22+1+2+1=26 (25). We are talking about epacts of the “Byzantine” type. The unit should be added, not subtracted (the Latin translation gives “unitateminus”), since on January 1 of the 1st year of the Byzantine cycle the age of the moon should be 11 + 1 + 1 / 60 = 12 1 / 60. This technique corresponds to the Byzantine cycle with the 29-day Nisan. The method is similar to that described in paragraph 4, but the years in the cycle are counted according to the Alexandrian system (for which 3 “catholics” are subtracted). This method works for the Constantinople system if in March you subtract 1 day and do not add 1 day (for March 1, 1: 11+1+1–1=12); starting from April, 1 day should again be added to whole epacts in each subsequent month (in August 2, in September 0, in October 2, in November 0). Epacts should be taken according to the Constantinople system. At the same time, in 1–5 years the age of the moon will be less than usual by 1, from the 6th year (due to the deduction of 59 days instead of 60) it will be equal, from the 12th it will exceed by 1, from the 18th it will be 2. By 641, from the beginning of the era of Diocletian, 22 complete indicts, 13 years of incomplete first indict (1 year of Diocletian = 3 years of indict) and 14 years of the current indict had passed. The chronological table attached to the treatise is brought up to 920. However, the dates contained in it exactly correspond to the system followed by Maximus the Confessor, which allows us to consider it a continuation of the list compiled by St. himself. Maxim. The world chronology here is based on the Alexandrian era, but is somewhat different from the chronology of George Sincellus, a historian of the early 9th century. (Georgii Syncelli Ecloga chronographica / Ed. A. Mosshammer. Lpz., 1984). Here, in the year of the Flood, the counting of years from Adam is temporarily interrupted. The 50 years of the reign of the elders should be corrected from 50 (νʹ) to 9 (θʹ), if, in accordance with the year of entry into the Promised Land indicated below (3863), we consider the beginning of the reign of Joshua to be 3862. George Sincellus has 4455. George Sinkella has 5181. Above in the treatise (I 33) the 2nd year of Augustus is designated as the year 5460 of the world, which exactly corresponds to this table, where the reign of Augustus is counted from 5459. The cessation of the final summation of years at the accession of Michael III and Theodora, from 6334 AD (842 AD) indicates one of the intermediate milestones in the editing of the list. Thus, the compilation of the final version of the table can be dated back to 920 AD. e., when Constantine VII Porphyrogenitus crowned his father-in-law Roman I Lecapin as co-ruler; from 921, after the coronation of Roman's son Christopher, the emperors were listed in a different order: Roman, Constantine, Christopher. The 11th 532-year Alexandrian period ended in 360 AD. e. In the edition this number (consistent with the following date: 3822+40+1=3863) is given in the apparatus; in the main text and translation "3827". Should be corrected to "Year 2". The account of the “anniversary” periods of St. Maximus the Confessor differs from all known versions. George Sincellus has 4459. Above, the beginning of the reign of Cyrus is attributed to 4969/70. Correct date: 5923 (423) = 431 AD e. In the original - a circular table E. Schwartz, who had photocopies of the tables, reports that this series has the form of fractions (leap increments): ., ó, ó+., 1, etc. (Schwartz. Ostertafeln. S. 84). Min's edition contains integer epacts. Schwartz. Ostertafeln. S. 85–87. Schwartz, restores the marks differently: * – 22nd day due to a leap year; ** – 22nd day without leap year; *** – 23 day; **** (a sign not used by St. Maximus) – day 24 (in 396 of the cycle, phase 23, taking into account the leap year – 24). However, it is not always consistent. It is not clear, for example, why the sign ** marks the 508th year of the cycle, the same type as the 484th year, where there is a * (22nd day due to the leap year). There are no years without marks in the Schwartz table at all, which contradicts the words of St. Maxima. According to the Alexandrian Easter. That is, Christian Easter, falling on the first Sunday after the estimated 14th day of the moon. And not “Constantinople,” as Schwartz erroneously writes (Ostertafeln. S. 85). St. speaks directly about this. Maxim, although Schwartz writes “on January 1” (Ibidem). However, in this Easter, the lunar epacts of these dates coincide. In the 17th year, April 5 was mistakenly recorded instead of April 9. In the 10th year there is no error, contrary to the opinion of Schwartz (Ibidem. S. 85. Anm. 1). The dates of full moons for years 1 and 2 of the cycle are not “errors” (as Schwartz thinks), but relics of the so-called. The Constantinople cycle of Andrew, also depicted on the IV “wheel” in the “Easter Chronicle”: April 6 and March 26 (see: Grumel V. La Chronologie. Paris, 1958. P. 54 (N IV), 78). The phases are compared, however, with the dates of the Alexandrian Easter (April 5 and March 25).