Date Easter
And where the dating of Sundays was made with the words of holiday hymns, the entire calendar in the literal sense of the word was associated with Easter. Rather, even with the "Pentecost"( "trinity"), because from here the church counts the days( weeks) of the year: "1st week after Pentecost", "2nd week. ..", etc. up to"The Week of the Publican and the Pharisee," which, however, as it were, begins a new Easter cycle. In Western Europe, with Easter, even the beginning of the new year has been tied up for several centuries.
Here are examples of dating documents for Easter and related "mobile holidays".
Prince Andrey Vladimirovich of Radonezh was given a letter of commendation to the abbot of the Trinity-St. Sergius Monastery Nikon, the date is defined as follows: "A letter was given to the prince when the Grand Duchess gave it to the Tsar for that winter for a pickaxe"( "Verbnitsa", "Palm Week" - the second weekbefore Easter).The chronicle points out that the Grand Duke Vasily Dmitrievich gave his daughter for the Greek Tsarevich Ivan in 1411, Easter this year was on April 12, the same Sunday for April 5.Consequently, the letter was given "on the Palm Sunday" - between March 30 and April 5.
And here's the message that the great artist "Rafael died on the night of Friday 1520".Easter in 1520 fell on April 8, the "great", or "holy" Friday - on April 6.Consequently, Rafael died on the night of April 5 to April 6, 1520.
We add the text of the donation inscription made by VA Zhukovsky in the portrait donated to Alexander Pushkin: "The winner-pupil from the defeated teacher on that high-day day, in thewhich he finished his poem "Ruslan and Lyudmila."1820, March 26, Great Friday. "Using the tables and formulas given below, the reader will establish that the date here is correct, since Easter in 1820 was indeed on March 28.
"Border keys". According to the established in the IV.rules Christian Easter should be celebrated on the first Sunday after the first spring full moon. But instead of exact calculations of the astronomical phases of the moon, the "Moon phase schedule" is used for each year by the months of the 19-year Metonic cycle, and the date of the vernal equinox was assumed on March 21.The result of such a "bundle" of two calendars - the solar and lunar calendars, each of which had its own internal flaws, is known - the forced reform of 1582, and this is yet to be discussed. Here we confine ourselves to a brief exposition of the main principles underlying the calculation of the Easter dates.
1. If the full moon comes on March 21 and this day is Saturday, the Easter date will be March 22.This is her earliest time. When the full moon is due on March 19( the "moon phase" is such that it does not happen on March 20), the following spring is considered to be spring( 19 + 30 - 31 =) on April 18.And in the case when this day is Sunday, Easter is postponed to the next Sunday - on April 25.This is her latest date. Thus, Easter can fall on one of 35 days - from March 22 to April 25.
2. The days from March 22 to April 25 are designated by 35 letters of the Slavic alphabet from "aza" to "yusa small", they are called key or Easter letters, they are also the keys of borders( from Latin granes - "leaf edge", sincedescriptions of Easter eggs printed in large print on the edges of the pages).The key values of the boundaries can also be given numerical values of z, denoting them from z = 1( "as") to z = 35( "small").Thus, the Easter date is defined as( 21 + z) March or at z & gt;10( z-10) of April Art. Art. This also simplifies the calculation of other Easter-related dates.
For example, the date of the already mentioned week of the "publican and the Pharisee" is defined as January 10 + z( in the leap year-January 11 + z), "trinity" - May 9 + z, etc. Knowledge of the number z allowed to establish and control daysweeks, falling on separate church holidays, and thus also on other calendar numbers. For example, the day of the week, which happened in some year with the famous z "Annunciation"( March 25) is defined as
and the day of "George the Victorious"( April 23), kaki, etc. The numerical order of days in the week is as follows: Monday-1, Tuesday - 2, etc.
3. Already in the V century.n.e.a new moon schedule was compiled for the 19-year lunar cycle, which is used invariably so far to determine the Easter phases of the moon. On this basis, it was already easy to calculate the dates of the spring full moons for each lunar circle. The easter date was set up in two simple steps:
a) First, the place that took a given year in the 19-year lunar cycle, that is, its circle of the Moon L, was determined, and thus by table.- the date of the spring full moon for this year.
b) the circle of the Sun Q was calculated and was handed over to W this year, as a result of which it was established on what day of the week this full moon had to be. After that there was the date of the nearest Sunday - Easter.
This has made it possible to compare the dates of Easter( and the corresponding border keys) with the circles of the Moon and the return flights, as shown in Table.
Table. Correspondence of Easter dates to key letters, lits and lunar circles( m - March, a - April)
From it we find that at the Paschke chronicle mentioned in the Pskov chronicle the border of P Passover falls on the 8th of April, which corresponds to the third and the lunar circle., all these dating elements in this example are completely consistent with each other.we find that both the circle of the Moon L and the circle of the Sun Q correspond to the year "from Adam" 6496.
Now we can establish the meaning of the data in Table.serviceable letters. These are the keys of the borders that fall on the numbers of months that follow this year immediately after the full moon( the next day!).They indicate the date of the "damage"( the phase of the moon "full moon plus one day") and give in accordance with Table.the earliest date on which( if "damage" falls on a Sunday), Easter may fall this year. The definition of a working letter of the year is one of the main tasks of calendar calculations that have been conducted in Russia for many centuries. Needless to emphasize that her calculation had an independent meaning, because it determines the date of the spring full moon!
Note that after 19 X 28 = 532 years, the phases of the moon( calculated!) And the days of the week fall on the same numbers of the month. Therefore, every 532 years, the dates of Easter are completely repeated. This time interval was called a great indiction. Indians were counted from the beginning of the Byzantine era. In particular, the 12th Great Indiction began in 345, the 13th in 877, the 14th in 1409, the 15th Great Indiction began in 1941
of the Gauss Formula. The possibilities of comparing and verifying many documents and annalistic dates have increased significantly after the outstanding German mathematician Karl Friedrich Gauss( 1777-1855) derived formulas for the direct determination of the dates of Christian and Jewish Passover. In particular, according to the formulas for the Jewish Passover, the date of the true( astronomical) spring full moon is set with high accuracy, which allows us to verify - there could be either a ket in the time specified by the chronicler, say, a solar or lunar eclipse, etc. These formulas will be discussed later.
The scheme for calculating the date of Catholic Easter is as follows. Dividing the first year of R by 19, 4 and 7, we obtain the remainders a, b and c respectively. Next we find the value 19ax, divide it by 30 and denote the remainder by d. After this we compose the sum 2b + 4c + 6d + y and divide it by 7, the remainder is denoted by e. Easter will be 22 +( d + e) March n. Art.or,
if d + e is greater than 10,( d + e) - April 9 n. Art. The values of x and y are respectively
from 1582 to 1699. 22 and 2,
from 1700 to 1799 years. 23 and 3,
from 1800 to 1899 years. 23 and 4,
from 1900 to 2099 24 and 5.
The limits here are the same as in Orthodox Easter - from March 22 to April 25( however - a new style!).The formulas provide for two exceptions: 1) if( d + e) - 9 = April 26, Easter is postponed to April 19( this applies to the years 1609, 1981, 2076 and 2133), and 2) if d = 28 and e= 6, so that( d + e) - 9 = 25, Easter is transferred to April 18( this happened in 1954 and will be in 2049 and 2106).
The Orthodox Easter date is calculated according to the same scheme, but with constant values of x and y.x = 15 and y = 6. The result is obtained in the dates of Art. Art.
Note that the remainder of d specifies the number of days in which the Easter full moon left its limit on March 21 in the Rth year, the value( e + 1) is the number of days from the Easter full moon to the first Sunday after it. The remainder of dividing the value of 5b + 3c + 4 by 7 determines the next year.
Let's calculate the date of Easter for 1411, when "the verbitsa" was given the above mentioned letter of commendation. Dividing 1411 by 19, 4 and 7, we find the residuals a = 5, b = 3 and c = 4. We form the quantity 19a + 15 = 110 and divide it by 30, in the remainder we obtain d = 20. Next we find the value 26 + 4c +6d + 6 = 2X 3 + 4 X 4 + 6 X 20 + 6 = 148 and dividing it by 7, we find e-1 in the remainder. Hence, in 1411, Easter was in( d + e) - 9 =( 20 + 1) - 9 = April 12, Art. Art.
The derivation and explanation of the individual stages of the Gauss formulas are given in the article of G. Kinkelin.