The designation of the numbers in Russian writing. Slavic numbers

The main prerequisite for all mathematical knowledge is the numbering that the different ancient peoples had a different look. Apparently, all the peoples initially denoted the numbers on chopsticks, which Russians were called tags. This method of debt or tax records was applied by a small population. different countries. A chopstick made cuts that correspond to the amount of debt, or tax. The wand was split in half: one half was left from the debtor or at the payer, the other was kept by the lender or in the Treasury. When we board, both halves checked folding.

With the advent of writing, the numbers appear to write numbers. At first, these numbers resembled scubons on sticks, then special signs appeared for some numbers, such as 5 and 10.

At that time, almost all numbering were not positional, but similar to Roman numbering. However, in a few centuries before new era invented new way The records of the numbers at which the letters of the usual alphabet served the numbers.

In one of the Russian manuscripts of the XVII century, we read the following: "... Know what is a hundred and what is a thousand, and that there is darkness, and that there is a legion, and that there is a leodr ...", "... There are ten hundred ten, and there are ten hundred ten hundred and thousands of ten thousands, and the Legion is ten topics, and Leodr has ten legions ... ".

While in countries Western Europe used Roman numbering, in ancient Russiawho was similar to others slavic countries In close cultural communion with Byzantium, the alphabetic numbering similar to Greek was distributed.

In the ancient Russian numbering of the number from 1 to 9, then dozens and hundreds depicted by consistent letters slavic alphabet (It was, the so-called Cyrillic, introduced in the IX century).

From this general rules There were some exceptions: 2 was not the second in the account of the letter "Buki", but the third "lead", since the letter 3 (ancient beta, the Byzantine Vita) was transmitted in an old worker with the sound of "B". "Fita", standing at the end of the Slavic alphabet, indicated as Greek 0 (ancient tat, the Byzantine Fita), the number 9, and 90 was marked with the letter "worm" (the Greeks were used for this purpose the letter "copy", which was absent in the living Greek alphabet ). Separate letters were not used. To indicate the fact that the sign is not a letter, and the special sign "~", called Titlo, was put on top above it. Here, for example, as the first nine numbers were recorded:

Tens of thousands were called "darkness", they were denoted by the signs of units with circles, for example, the number 10,000, 20,000, 50,000, respectively, were recorded as follows:

Hence the name "Darkness to the people", i.e., a lot of people. Hundreds of thousands were called "Legions", they were denoted by givingwalking signs, units with mugs from points. For example, the number 100,000, 200,000, respectively, had the designation

Millions were called "Leoders". They were denoted by jumping the signs of units with circles from rays or commas. Thus, the numbers 106 and 2 106 were designated respectively

Hundreds of millions were called "decks". The "deck" had a special designation: Square brackets were installed on the letter and under the letter.

The numbers from 11 to 19 were designated as:

The remaining numbers were recorded by letters from left to right, for example, the numbers 544 and 1135 had respectively designation

When recording large numbers than thousands, in practical activity (account, trade, etc.), instead of "circles", the sign "≠" was set in front of the letters, denoted dozens and hundreds, for example, recording

means the numbers respectively 500 044 and 540 004.

In the given system, the notation of the numbers did not go further than thousands of millions. Such an account was called a "Small Account". In some manuscripts, the authors were also considered "the Great Account", reaching the number 1050. Next it was said: "And more thangotten the human mind of understanding." Modern mathematics uses Indian numbering. In Russia, Indian numbers became known at the beginning of XVII.

Old Slavonic number system

In the Middle Ages on the lands, where Slavs lived, enjoyed the Cyrillic alphabet, the number of numbers based on this alphabet was distributed. Indian numbers appeared in 1611. By that time, the Slavic numbering consisted of 27 letters of the Cyrillic alphabet. Above letters, the figures denoted the mark - Title. IN early XVIII in. Due to the reform introduced by Peter I, Indian numbers and indian system Numbness outlined Slavic numbering from everybody, although in Russian orthodox church (in books) it is used until today. Cyrillic numbers lead their origin from Greek. In shape, this is the usual letters of the alphabet with special marks indicating their numerical reading. Greek and Old Slavic methods of recording numbers had a lot in common, but there were differences. The first Russian monument of mathematical content is still considered the handwritten work of the Novgorod monk Kirik, written by him in 1136. In this work, Kirik showed himself a very skillful meter and a great numerute. The main tasks that are considered Kirik, chronological order: Calculation of time, duct between any events. When calculating Kirik used the system of numbering, which was called a small list and was expressed by the following names:

10000 - Darkness

100000 - Legion

In addition to the small list, in Ancient Russia There was a big list that gave the opportunity to operate with very big numbers. In the large list system, the main discharge units had the same names as in small, but the relationship between these units was different, namely:

thousand Thousands - Darkness,

darkness darkness - Legion,

legion Legion - Leodr,

leodr Leeodriv - Raven,

10 rabrows - log.

About the last of these numbers, that is, about the log, it was said: "And more than this, to carry the human mind of the intelligence". Units, dozens and hundreds were depicted by Slavic letters with a sign of ~ called "Titlo", for the differences of numbers from the letters. Darkness, Legion and Leodr were depicted by the same letters, but for distinguishing from units, dozens, hundreds and tashchvones were circled with circles. With numerous fractions of one hour, Kirik introduced his system of fractional units, and he called the fifth part of the second hour, twenty-fifth - three hours, one hundred and twenty-fifth - four hours, etc., the smallest fraction he had seven hours, and he believed that There can no longer be less than any hours: "There is no longer it happens, there are not born from seventh fractional, which on days will be 987500." By making calculations, Kirik did the action of addition and multiplication, and the distribution, in all likelihood, he carried out with a hashindabe, considering consistently multiple for this divide and divider. The main chronological calculations of Kirik did from the date, was taken in ancient Russia for the date of creation of the world. Thus, thus, the moment of writing his work, Kirik (with a mistake of 24 months) argues that 79,728 months have passed since the creation of the world, or 200 of the unhealthy and 90 people and 1 in the union and 652 hours. The same kind of counting Kirik determines its age, and we learn that he was born in 1110 by operating with fractional hours, Kirik in essence dealt with geometric progress with denominator 5. In the work of Kirik, the place and the question of the calculus of Pellery, so important for the clergy And being one of the most difficult arithmetic issues, I had to solve the ministers of the church. If Kirik does not give general methods of this kind of calculations, then in any case he shows his ability to make them. The handwritten work of Kirika is the only mathematical document that has come down to us from those distant times. However, this does not mean that other mathematical works in that epoch did not exist in Russia. It must be assumed that many manuscripts are lost for us the reason that they were lost in the disturbing years of the princely interdiscructures, died in fires, always accompanied the raids of neighboring peoples on Russia.

We write numbers 23 and 444 in the Slavic number system.

We see that the recording turned out not longer than our decimal. This is explained by the fact that in alphabetic systems, at least 27 "digits" were used. But these systems were convenient only to record numbers up to 1000. True, Slavs, as well as the Greeks, were able to record numbers and more than 1000. For this, new designations added to the alphabetic system. For example, the numbers 1000, 2000, 3000 ... were recorded with the same "numbers" as 1, 2, 3 ..., only before the "digit" put a special sign on the left below. The number of 10,000 was indicated by the same letter as 1, only without a title, they were circle. It was called the number "Darkness". Hence, there was an expression "darkness to people".

Thus, to designate "Top" ( plural From the word Darkness) the first 9 "digits" were circled with circles.

10 Themes, or 100,000, was the unit of the highest discharge. She was called "Legion". 10 legions were "Leard". The largest of the values \u200b\u200bthat have its own designation was called the "deck", it was equal to 1050. It was believed that "Bolly to bear the human mind to be missed." This method of recording numbers, as in the alphabetic system, can be viewed as the root of the positional system, since in it, the same symbols that special signs were added to designate the units of different discharges to identify the discharge value were used. Alphabetic numbering systems were little suitable for operating with large numbers. In the course of development human society These systems gave way to positioning systems.

Before they were invented special symbolsTo denote the numbers, most of the peoples used for these purposes the letters of their alphabets. Ancient Slavs is no exception.
They have a separate letter corresponded to each digit (from 1 to 9), each ten (from 10 to 90) and each hundred (from 100 to 900). The numerals were written and uttered from left to right, with the exception of numerical from 11 to 19 (for example, 17 - sem-on-ten).
In order for the reading to understand that in front of him the numbers, a special sign was applied - Titlo. He was depicted in the form of a wavy line and placed above the letter. Example:

Such a sign is called "AZ under Title" and means one.
It is worth noting that not all the letters of the alphabet could be used as numbers. For example, "B" and "F" did not turn into numbers, because They were not in an ancient Greek alphabet, which was at the heart of the digital system. In addition, letters that are not in our modern alphabet - "KSI" and "PSI" appeared as numbers. For modern man It may seem unusual that in the counting row it was not usual to all zero.

If it was required to write a number more than 1000, a special sign of thousands was written in front of him in the form of a slant, crossed in two places. An example of writing numbers 2000 and 200,000:

To get even more values, other methods were used:

Az in a circle - darkness, or 10,000.
Az in a dot circle - legion, or 100,000.
Az in a mug of commas - Leodor, or 1,000,000.

Dates on Petrov coins

On the Golden Petrov coins, the date in the Slavic account appeared in 1701 and were affixed to 1707 inclusive.
On silver - from 1699 to 1722.
On copper - from 1700 P1721 year.
Even after the introduction of Peter I Arab numbers on the coins, the dates under Titlo were minted. Sometimes the engravers were mixed in the date Arabic and Slavic numbers. For example, on the coins of 1721, you can find the following options for dates: 17K and 17K1.

Designation of dates with letters on old Russian coins.

This numbering was created together with the Slavic alphabetic system for the transfer of sacred biblical books for Slavs by Greek monks by Brothers Kirill and Methodius in the 9th century. This form of the number of numbers was widely distributed due to the fact that there was a complete resemblance to the Greek records of numbers. Until the XVII century, this form of recording numbers was official in the territory modern Russia, Republic of Belarus, Ukraine, Bulgaria, Hungary, Serbia and Croatia. Until now, Orthodox church books use this numbering.

The numbers were recorded from numbers as to the left, to the right, from large to the smaller. The numbers from 11 to 19 were recorded by two digits, and the unit was in front of the top ten:

We read literally "Fourteen" - "Four and Ten". As hearing, and write: not 10 + 4, and 4 + 10, - four and ten (or for example, 17 - sem-on-time). The numbers from 21 and higher were recorded on the contrary, first wrote a sign of complete dozens.

The record of the number used by the Slavs additive, that is, it uses only addition:

= 800 + 60 + 3

In order not to confuse letters and numbers, the title was used - horizontal dashes over the numbers that we see in our illustration.

To refer to the numbers of large than 900, special icons were used, which were drawn around the letter. So the following large numbers were formed:

Slavic numbering existed to the end XVII centuryWhile the reforms of Peter I in Russia from Europe did not come a positional decimal number system - Arab numbers.

An interesting fact that almost the same system was also used in Greeks. This is what explains what for the letter b. There was no digital value. Although nothing particularly amazing here is not: Cyrillic numbering is completely copied with Greek. Close numbers were ready:

Year old Russian calendar

Here, too, there is a special calculation algorithm: if a month from January to August is inclusive (according to old style), then it is necessary to add 5508 to year ( new Year comes first of September by the old style). After the first of September it is necessary to add one more, that is, 5509. It is enough to remember three numbers: 5508, 5509 and September 1.

At the beginning of the XVIII century, a mixed system for recording numbers, consisting of Cyrillic, and from Arabic numbers was sometimes used. For example, on some copper kopecks, Date 17K1 (1721), and the like.

Converting Cyrillic numbers online

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Converting Cyrillic numbers