The numeral system of ancient Russia. Cyrillic numeral system

Darkness: Darkness is darkness, absence of light. Darkness (number) is a number in the old Russian account, equal to ten thousand or a million. Darkness (river) is a river in the Tver region, a left tributary of the Volga. Darkness on microcalculators numbers from ± 1 × 10500 to ... ... Wikipedia

See a lot, darkness is Egyptian darkness ... Dictionary of Russian synonyms and similar expressions. under. ed. N. Abramova, M .: Russian dictionaries, 1999. darkness is a lot, darkness; ignorance, ignorance, illiteracy, underdevelopment; cart, cloud, herd, chorus ... Synonym dictionary

See many Dictionary of synonyms of the Russian language. Practical guide. M .: Russian language. Z.E. Aleksandrova. 2011. darkness, many darkness, a mass of shelters ... Synonym dictionary

- [darkness] n., f., uptr. cf. often Morphology: (no) what? darkness, what? darkness, (see) what? darkness than? darkness, about what? about darkness and in darkness 1. Darkness is the absence of light, for example, when it is night or there is no illumination. Night, impenetrable, dense darkness. ... ... Dmitriev's Explanatory Dictionary

NUMBER, numbers, pl. numbers, numbers, numbers, cf. 1. The concept that serves as an expression of quantity, that, with the help of which objects and phenomena are counted (mat.). Integer. Fractional number. Named number. Prime number. (see simple1 in 1 value). ... ... Ushakov's Explanatory Dictionary

DARK- In the Old Russian account: ten thousand. The word darkness is borrowed from the Turkic languages, in which the word tumen denoted the number of 10,000, and also called the highest organizational and tactical unit of the Mongol Tatar army in the XII-XIV centuries. number of ... ... Linguistic and Cultural Dictionary

See also: Number (linguistics) Number is an abstraction used to quantify objects. Having arisen back in primitive society from the needs of counting, the concept of number changed and enriched and turned into the most important mathematical ... Wikipedia

The number, although it is an important characteristic of spatial dimensions, quantity and time, in Holy Scripture very often has a relative, symbolic or allegorical meaning (see seven, seven nations, three, thirty, darkness, ... ... Bible. Old and New Testaments. Synodal translation. Bible encyclopedia of arch. Nicephorus.

dark- (Lev. 26: 8; Num. 10:36; Deut. 32:30; Deut. 33: 2, 17; Jud. 20:10; Ps. 3: 7; Ps. 67:18; Ps. 143: 13; Dan. 7:10; Jude 1:14; 1 Cor. 14:19; Heb. 12:22; Revelation 5:11; Rev. 9:16) a very large number, or a number equal to 10,000 (see. Judgment 20:10) ... Complete and detailed Bible Dictionary to the Russian canonical Bible

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Before special symbols were invented to denote numbers, most peoples used the letters of their alphabets for this purpose. The ancient Slavs were no exception.
They had a separate letter corresponding to each digit (from 1 to 9), each ten (from 10 to 90) and each hundred (from 100 to 900). Numbers were written and pronounced from left to right, with the exception of numbers from 11 to 19 (for example, 17 is seventeen).
In order for the reader to understand that there are numbers in front of him, a special sign was used - titlo. It was depicted as a wavy line and placed above the letter. Example:

This sign is called "az under titlo" and means one.
It should be noted that not all letters of the alphabet could be used as numbers. For example, "B" and "F" did not turn into numbers, since they were not in the ancient Greek alphabet, which was the basis of the digital system. In addition, the numbers were letters that are not in our modern alphabet - "xi" and "psi". For a modern person, it may also seem unusual that there was no zero familiar to everyone in the counting row.

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

To get even larger values, other methods were used:

Az in the circle is darkness, or 10,000.
Az in a dotted circle is a legion, or 100,000.
Az in a circle of commas is leodor, or 1,000,000.

Dates on Peter's coins

On Peter's gold coins, dates in the Slavic account appeared in 1701 and were affixed until 1707 inclusive.
On silver coins - from 1699 to 1722.
On copper - from 1700 to 1721.
Even after the introduction of Arabic numerals by Peter I on coins, dates were minted under the title for a long time. Sometimes engravers mixed Arabic and Slavic numbers in the date. For example, on coins of 1721, you can find the following date options: 17KA and 17K1.

Date designation with letters on old Russian coins.

Hello. In this episode of TranslatorsCafe.com, we're going to talk about numbers. We will look at various number systems and classifications of numbers, as well as discuss interesting facts about numbers. Number is an abstract mathematical concept for quantity. Numbers have been used by humans for counting since ancient times. At first, numbers were denoted with counting sticks, or notches, or dashes on wood or bone. Later, numbers began to be used in more abstract systems. There are many ways to express and work with numbers; we will look at some of them a little later in this video. Number systems have evolved over the centuries. Some ancient systems have been replaced by others that are more convenient to use. Some systems, which we will discuss below, are no longer used. Scientists believe that the concept of number arose independently in different cultures. Symbols to denote numbers in writing also originated in each culture separately. Gradually, with the development of commerce, people began to exchange ideas and borrow from each other the principles of calculating or writing numbers. Therefore, the number systems that we now use were created by many peoples. The Arabic numeral system is one of the most widely used systems. It was borrowed from India and refined by Persian and Arab mathematicians. During the Middle Ages, this system spread to Europe as a result of trade and replaced Roman numerals. Influenced the spread of Arabic numerals and European colonization. In Europe, Arabic numerals were first used in monasteries, and later in secular society. The Arabic system is decimal, that is, base 10. It uses ten characters to express all possible numbers. Ten is one of the most widely used numbers in counting systems and the decimal system is common in many countries. This is due to the fact that for a long time people used ten fingers on their hands for counting. Until now, people who are learning to count or want to illustrate an example related to counting use their fingers. There are even expressions such as “counting on your fingers”. In some cultures, the toes, knuckles, and even the space between the toes were also used for counting. Interestingly, in many languages ​​the word for fingers and numbers are the same. For example, in English, this word is "digit". Roman numerals were used in ancient Rome and Europe until about the 14th century. They are still used in some cases, such as on watch dials. You can also meet them in the names of the Pope. Roman numerals are also often used in the names of recurring events, such as the Olympic Games. The Roman numeral system uses seven letters of the Latin alphabet to represent all possible combinations of numbers: The order of the numerals in the Roman numeral system matters. A larger number to the left of a smaller one means that both numbers must be added. On the other hand, the smaller number to the left of the larger number should be subtracted from the larger number. For example, this number equals eleven, and this is 9. This rule is not universal and only applies to numbers like: IV (4), IX (9), XL (40), XC (90), CD (400) and CM (900). In some cases, these rules are not followed, and numbers are written in a row, such as this number, which means 50. The inscription in Latin using Roman numbers on the Admiralty Arch in London reads: In the tenth year of the reign of King Edward VII to Queen Victoria, from grateful citizens, 1910 Numeral systems similar to Roman and Arabic were used in many cultures. For example, in the Cyrillic numeral system, numbers from one to nine, ten, and multiples of one hundred were written in Cyrillic letters. There were also signs for larger numbers. There was also a special sign, similar to a tilde, which was written over such numbers to show that they were not letters. There was a similar system using the Glagolitic alphabet. In the Hebrew numbering system, the letters of the Hebrew alphabet were used to write numbers from one to ten, multiples of ten, as well as one hundred, two hundred, three hundred, and four hundred. The rest of the numbers were written as the sum or product of these numbers. The Greek number system is also similar to the systems above. In some cultures, the number systems were simpler. For example, Babylonian numbers could be written with just two cuneiform signs, representing one and ten. The sign for one looks like a big T, and ten looks like a C. So, for example, 32 can be written like this, using the appropriate cuneiform signs. The Egyptian number system is similar, only there were also symbols for zero, hundreds, thousand, ten thousand, one hundred thousand and a million, and there were also special signs for writing fractions. Maya numbers were written using the signs denoting zero, one and five. Numbers above nineteen also had a peculiar spelling. They used the signs for one and five, but with a different arrangement to indicate that the meaning of these numbers is different. In the unit or unary number system, only one sign is used to represent the unit. Each number is written using such characters, the number of which is equal to this number. For example, if such a sign is the letter "A", then the number five can be written as five letters A in a row. The unary system is often used by teachers teaching children to count because it helps children understand the relationship between the number of objects, such as counting sticks or pencils, and the more abstract concept of number. The unary system is often used during games to record the points scored by teams or to count days or items. In addition to simple counting and accounting, the unary system is also used in computer technology and electronics. Moreover, the recording method differs in different cultures. For example, in many countries of Europe and America, they usually write four vertical dashes one after the other, which they cross out on the count of five with a horizontal or diagonal line, and continue the count with a new group of dashes. Here the count reaches four, after which these lines are crossed out by the fifth. Then they add five more lines, and again a new row begins. In countries where Chinese characters are used or used in the language, for example, in China, Japan and Korea, people usually draw not four lines crossed out by the fifth, but a special character, but also of five strokes. The sequence of these strokes is not arbitrary, but is established by the rules of the spelling of hieroglyphs. In our example, the count comes to five and the person writes the first two strokes of the next hieroglyph, ending the count at seven. We will now look at positional number systems. In positional numeral systems, the meaning of each sign denoting a digit depends on its position in the number. The position is usually referred to as a discharge. This value also depends on the radix. For example, the number 101 in binary is not equal to one hundred and one in decimal. Consider the positional number system using the decimal as an example: The first digit is for ones, that is, numbers from zero to nine. The first digit is multiplied by ten to the zero power, that is, by one. The second digit is for tens and the digit in the second digit is multiplied by ten to the first power, that is, 10. The third digit is for hundreds and the digit in the third digit is multiplied by ten to the second power, and so on until the digits run out. To get the value of a number, add up all the numbers obtained above, that is, the values ​​of the numbers in each digit. This way of writing numbers allows you to work with large numbers. Numbers do not take up as much space in the text, compared to the numbers of non-positional number systems. The binary system is widely used in mathematics and computing. All possible numbers are represented in it using only two digits, "0" and "1", although in some cases other signs are used, for example "+", "-". Binary numbers are represented as binary zero and one. Addition rules are used to represent numbers greater than one. Binary addition is based on the same principle as decimal. To add one to a number, use the following rule: For numbers ending in zero, this last zero is replaced by one. For example, add 1-0-0, which is 4 in decimal, and 1, which is 1 in decimal. We get 1-0-1, that is 5. Hereinafter, for comparison, examples with the same numbers in the decimal system are given. In a number ending in one, but not consisting only of ones, replace the first zero on the right with one. All ones that follow it, that is, to the right of it, are replaced with zeros. Add 1-0-1-1, which is 11 and 1, which is 1 in decimal. We get 1-1-0-0. In a number consisting of only ones, replace all ones with zeros, and at the beginning, that is, on the left, add one. For example, add 1-1-1, that is, 7 and 1. We get 1-0-0-0, that is 8. It should be noted that arithmetic operations in the binary system are done in exactly the same way as the usual operations in a column in the decimal system, with the only the difference is that instead of 10 they use 2. When adding, they write both numbers one below the other, as in decimal addition. The rules are as follows: 0 + 0 = 0 1 + 0 = 1 1 + 1 = 10. In this case, 0 is written in the right bit and 1 is transferred to the next bit. Now let's try to add 1-1-1-1-1 and 1-0-1-1. When adding in a column from right to left, we get: 1 + 1 = 0, and we transfer one to the next bit 1 + 1 + 1 = 1, and we transfer one to the next bit 1 + 1 = 0, we transfer one to the next bit 1 + 1 + 1 = 1, and again the unit is transferred to the next category 1 + 1 = 10 That is, we get 1-0-1-0-1-0. Subtraction is similar to addition, only instead of transferring, on the contrary, "occupy" a unit from the higher digits. Multiplication is similar to decimal too. The result of multiplying two units is one, and multiplying by zero gives zero. If you look closely, you can see that all operations are reduced to addition and shifts. This feature of the binary system is widely used in computer systems. Division and square root is also not very different from working with decimal numbers. Numbers are grouped into classes, and some numbers can be included in several classes at the same time. Negative numbers indicate negative values. A minus sign is placed in front of them to distinguish them from positive ones. For example, if a person owes the bank that issued the credit card fifty thousand rubles, then he has -50,000 rubles. Here –50,000 is a negative number. Natural numbers are zero and positive integers. For example, 7 and 86 766 are natural numbers. Integers are zero, negative and positive numbers that are not fractions. For example, −65 and 11,223 are integers. Rational numbers are those numbers that can be represented as a fraction, where the denominator is a positive natural number and the numerator is an integer. For example, 3/4 or −10/5, that is, −2 are rational numbers. Complex numbers are obtained by adding a real, that is, non-complex number and another real number multiplied by an imaginary unit i, for which the equality i ^ 2 = –1 is satisfied. That is, a complex number is a number of the form a + bi, Here a is the real part of a complex number and b is its imaginary part. It is worth noting here that in electrical engineering, the letter j is used instead of i, since the letter I denotes current - so that there is no confusion. Prime numbers are natural numbers, more than one, which are divisible without remainder only by one and by themselves. Examples of primes are: 3, 5, and 11. 2 ^ 57 885 161−1 is the largest prime number known as of February 2013. It contains 17,425,170 digits. Prime numbers are used in public key cryptosystems. This type of coding is used in the encryption of electronic information in cases where it is necessary to ensure information security, for example, on the websites of online stores, electronic wallets and banks. Now let's talk about some interesting features of numbers. In China, they use a separate notation for numbers for business and financial transactions. The usual hieroglyphs used for the names of numbers are too simple. They can be easily counterfeited or altered by changing their denomination with just a few touches. Therefore, special, more complex hieroglyphs are usually used on bank checks and other financial documents. In the languages ​​of countries where the decimal number system is adopted, words have still survived, indicating that a system with a different basis was previously used there. For example, in English, the word “dozen” is still used, meaning twelve. In many English-speaking countries, eggs, flour products, wine and flowers are counted and sold in dozens. And the Khmer language has words for fruit counting, based on the decimal system. In the West, as well as in many Christian countries, 13 is considered an unlucky number. Historians believe this is related to Christianity and Judaism. According to the Bible, exactly thirteen of Jesus' disciples were present at the Last Supper, and the thirteenth, Judas, later betrayed Christ. The Vikings also had a belief that when thirteen people got together, one of them would surely die in the next year. In countries where Russian is spoken, even numbers are considered unsuccessful. This is probably due to the beliefs of the ancient Slavs, who believed that even numbers are static, motionless, and therefore dead. The odd ones, on the contrary, are mobile, looking for additions, changing, which means they are alive. Therefore, an even number of flowers are brought only to funerals, but not given to living people. In the Western world, on the other hand, giving an even number is quite normal, and flowers are often counted in dozens. China, Korea and Japan do not like the number 4 because it is consonant with the word "death". Often not only the number four itself is avoided, but also the numbers containing it. For example, 4, 14, 24, and other similar numbers are often skipped in the numbering of floors and apartments. In China, they also do not like the number 7, due to the fact that the seventh month in the Chinese calendar is the month of spirits. It is believed that in this month the border between the world of people and the world of spirits disappears, and spirits come to visit people. The number 9 is considered unfortunate in Japan, as it is consonant with the word "suffering". An unlucky number in Italy is 17, because its spelling in Roman numerals can be rewritten as "VIXI" by changing the order of the letters. Often this phrase was written on the graves of the ancient Romans and meant "I lived", therefore it is associated with the end of life and death. 666 is an unlucky number known to many, also called "the number of the beast" in the Bible. Some believe that in fact the "number of the beast" is 616, but the mention of 666 is more common. Many believe that this number will designate the Antichrist, that is, the viceroy of the devil. Therefore, sometimes this number is associated with the devil himself. The origin of this number is unknown, but some are convinced that 666 and 616 are the encrypted name of the Roman emperor Nero in Hebrew and Latin, respectively, expressed in numbers. Such a possibility does exist, since Nero is known for persecuting Christians and for his bloody rule. Some historians even believe that it was Nero who was the initiator of the great fire of Rome, although many historians do not agree with this interpretation of events. Thank you for your attention! If you enjoyed this video, please don't forget to subscribe to our channel!

Old Church Slavonic number system

In the Middle Ages, in the lands where the Slavs lived, they used the Cyrillic alphabet, and a system for writing numbers based on this alphabet was widespread. Indian numerals appeared in 1611. By that time, the Slavic numbering was used, which consisted of 27 letters of the Cyrillic alphabet. Above the letters denoting the numbers they put a mark - titlo. At the beginning of the 18th century. As a result of the reform introduced by Peter I, Indian numerals and the Indian numbering system supplanted Slavic numbering from everyday life, although in the Russian Orthodox Church (in books) it is still used today. Cyrillic numbers are derived from the Greek ones. In shape, these are ordinary letters of the alphabet with special marks indicating their numerical readings. The Greek and Old Church Slavonic ways of writing numbers had a lot in common, but there were also differences. The first Russian monument of mathematical content is still considered a handwritten work of the Novgorod monk Kirik, written by him in 1136. In this work, Kirik proved himself to be a very skillful counter and a great number lover. The main tasks considered by Kirik are of chronological order: calculating time, flow between any events. In his calculations, Kirik used the numbering system, which was called the small list and was expressed by the following names:

10000 - darkness

100,000 - legion

In addition to the small list, in Ancient Russia there was an even larger list that made it possible to operate with very large numbers. In the system of the large list, the main bit units had the same names as in the small one, but the relationship between these units was different, namely:

a thousand thousand - darkness,

darkness to darkness - legion,

legion of legions - leodr,

leodr leodriv - raven,

10 ravens - a log.

About the last of these numbers, that is, about the log, it was said: "And more than this, the human mind will be able to bear it." Units, tens and hundreds were depicted in Slavic letters with a sign ~, called "titlo", placed above them, to distinguish numbers from letters. Darkness, legion and leodr were depicted with the same letters, but to distinguish them from units, tens, hundreds and tysyachvons were circled. With numerous fractions of one hour, Kirik introduced his own system of fractional units, and he called the fifth part the second hour, the twenty-fifth - three hours, one hundred twenty-fifth - four hours, etc. there can no longer be less fractions of hours: "This does not happen anymore, there are no births from the seventh fractional hours, of which there will be 987500 in days." When doing the calculations, Kirik did the operations of addition and multiplication, and, in all likelihood, he carried out the distribution by considering the successive multiples for a given dividend and divisor. Kirik made the main chronological calculations from the date taken in Ancient Rus as the date of the creation of the world. Calculating in this way the moment of writing his work, Kirik (with an error of 24 months) claims that 79,728 months have passed since the creation of the world, or 200 unknown and 90 unknown and 1 unknown and 652 hours. By the same kind of counting, Kirik determines his age, and we learn that he was born in 1110. Operating with fractional hours, Kirik, in essence, dealt with a geometric progression with a denominator 5. In the work of Kirik, a place is also given to the issue of calculating the Paschal, which is so important for churchmen and being one of the most difficult arithmetic questions, the ministers of the church had to decide. If Kirik does not give general methods of this kind of calculations, then in any case he shows his ability to do them. Kirik's handwritten work is the only mathematical document that has come down to us since those distant times. However, this does not mean at all that other mathematical products did not exist in Russia at that time. We must assume that many manuscripts have been lost for us because they were lost in the troubled years of princely strife, perished in fires, and always accompanied the raids of neighboring peoples to Russia.

Let's write the numbers 23 and 444 in the Slavic number system.

We see that the record is no longer than our decimal. This is because alphabetic systems used at least 27 "numbers". But these systems were convenient only for writing numbers up to 1000. True, the Slavs, like the Greeks, knew how to write numbers and more than 1000. For this, new designations were added to the alphabetical system. So, for example, numbers 1000, 2000, 3000 ... were written with the same "numbers" as 1, 2, 3 ..., only a special sign was put in front of the "number" from the bottom left. The number 10,000 was designated by the same letter as 1, only without the title, it was encircled. This number was called "darkness". Hence the expression "darkness to the people" came from.

Thus, to designate "themes" (plural from the word darkness), the first 9 "numbers" were circled.

10 topics, or 100,000, was a unit of the highest category. They called her "legion". 10 legions made up the "leord". The largest of the quantities that have their own designation was called the "deck", it was equal to 1050. It was believed that "more than this can not be understood by the human mind." This way of writing numbers, as in the alphabetical system, can be considered as the beginnings of a positional system, since in it the same symbols were used to designate units of different digits, to which only special signs were added to determine the value of the digit. Alphabetic number systems were of little use for dealing with large numbers. In the course of the development of human society, these systems gave way to positional systems.