Abacus manual calculator. Watch what is "Abak" in other dictionaries. Abak in various regions

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Abacus and scores

It is convenient to read on the fingers, it is impossible to store only the result. You will not be a whole day to walk with curved fingers. And a person guessed - for the account you can use everything that comes at hand. Pebbles, sticks, bones, ropes and so on. Graze shepherd flock sheep. He has a rope with a belt, and on the rope so many nodules, how many sheep in the herd. A lamb was born - the shepherd knit another nodule. The wolves of two sheep dragged - launched two nouts.

With the development of civilization, various receptions of the account appeared. They were needed and collectors of taxes, merchants, and craftsmen, and the usurists. The art of the account owned a few specially trained people - counters. They used counting tools - Abaki.

The simplest abacus is a board with gutters cut in it. To find the amount of two numbers (for example, 258 and 125), the counter first indicated the first term on Abacket. For this, he laid in the lower groove of 8 pebbles, in the next groove - 5 pebbles and 2 pebble - in the third groove. If in some category there was zero, then the corresponding chute remained empty. Further, the meter was added to the last chute to 8 more pebbles there 5 more, then removed from there (3) remained there) and 1 pebble was added to the second chute. Then added 2 pebble and 1 pebbles in the second gutter - in the third chute. After that, the pebbles on the board showed the number 383.

Abaki was already used in the V-IV centuries to our era. They were made of bronze, stone, ivory, stained glass. The word "Abak" has a Greek origin and literally means "dust", although its semantic meaning is the "counting board". What is the case? The answer is simple: Initially, the pebbles laid out on a completely flat board, and so that they do not roll from their original position, the board was covered with a thin layer of sand or dust. And from the words "pechers" (in Latin - "Calculus") the name of the modern counting device was the name - "Calculator".

Abacus was used in ancient Greece, and in ancient Rome, and then in Western Europe until the XVIII century. He looks like familiar scores - bones on the metal spokes inserted into the frame.

The scores used different peoples, and each people they had their own characteristics. So, in Russian accounts for ten bones in each row, and in Western European - nine. In Chinese accounts, San Pan on each wire for seven balls, and two are separated from the other five. Each of these two balls means five units of this discharge. Such an enhancement allows you to reduce the number of balls in the accounts.

In Japan, today there are competitions in the account speed between people, armed with Japanese accounts Sorobane, and operators of computing machines. And, as a rule, the calculators will defeat the accounts. After all, so that the car began to count, it is necessary to make a program for it.

Abacus

The development of European and Asian countries and the strengthening of trade relations between them led to the need to create a device that facilitates calculations when making trade transactions and tax collecting. As a result, an aback device was created, known from all nations. It was applied for the first time in Babylon (approximately VI century BC).

This device was a wooden plate, sprinkled with sand, on which the grooves were applied. In these grooves were placed pebbles or tokens that denoted numbers.

It is possible to restore the type of Babylonian Abaca by analyzing the principles of the Babylonian account. At that time, a sixteen positioning system was used, i.e. Each category of numbers contained 60 units, and, depending on its place, each category indicated either the number of units or tens and so on. Since to lay out in each groove for 60 pebbles was difficult, then the grooves were divided into two parts: in one pebbles, counting dozens (no more than five), and in the other - pebbles, counting units (no more than nine).

At the same time, the number of pebbles in the first groove marked the number of units, in the second - a dozen and so on. If in one groove the number counted with the pebbles exceeded 59, then the pebbles were removed and placed one pebbles into the next groove.

In ancient Rome, aback enhanced and besides stone plates used bronze, elephant bone and stained glass. Vertical grooves in Roman Abaca shared on 2 parts. The grooves of the lower field served for an account from unit to 5, if 5 balls were recruited in the lower groove, then one ball was added to the upper compartment, and from the bottom all the balls were filmed.

In the Neapolitan Museum of Antiquities, the Roman Abacus is kept, which is a blackboard with cutting slots, along which pebbles moved. On the blackboard there were eight long cracks and eight short, located over long. Above each long slit is the designation describing the appointment of the gap (left for the right):

This means that the slot is used to postpone the discharge of millions.

This means that the slot is used to postpone the discharge of hundreds of thousands.

This means that the slot is used to postpone the discharge of tens of thousands.

This means that the slot is used to postpone the discharge of thousands.

This means that the slot is used to postpone the discharge of hundreds.

This means that the slot is used to postpone the discharge of a dozen.

This means that the slot is used to postpone the discharge of units.

This means that this slit is used to deploy ounces (from zero to twelve).

At seven left long slots, up to four balls have placed, each of which was equated to a unit of the corresponding discharge of the number. On seven left short slots, there were up to one ball, which denoted five units of discharge. The eighth long strip (served to refer to ounces) contained up to five balls, each of which indicated the unit of discharge of the ounce. The eighth short contained to one ball, which denoted six units.

In addition, there were two more short gaps with one ball and one long gap with two balls on the right. There were labels about these slots:

Paul Oz

Quarter ounce

Sixth part of ounce

Abak was known in Greece. In 1846, a marble abacus was found in the Greek Island of Salamin in the form of a plate of 105x75 cm, dating from the III century to the new era. This abacus was named after the island, which was found - "Salaminskaya board".

Salamina board served for a five-day surgery, which confirm letter notation on it. Pebbles, symbolizing discharge numbers, laid only between lines. The columns located on the slab on the left were used to count the drachms and talents, on the right - for the fraction of drachma (shell and halki).

Approximately in the X-XI Aztec invented their kind of abaca. Through the wooden frame stretched the threads with nanous grains of corn. The frame was divided into two parts. In one part, three grains were rushed at the threads, in the other four. To work with Aztec Abacom used its own special account.

In European countries, Abak began spread from the X century. Up to our time, a number of works were preserved a number of works of Bernelini, Lansky and other authors dedicated to the calculation on Abaca and dated X-XII century. The most famous works of the French scientist and the clergyman of Herbert, in which the rules for working with Abacom are described in detail: multiplication, division, addition and subtraction.

Gerber suggested improving Abak with 12 columns to 27, which allowed to operate with huge numbers (up to ten in the twenty-seventh degree). Also, this abacus was introduced three additional columns for money and other measures. In the time of Herbert, many schools taught the art of working with Abacom, a lot of benefits were created to work with the device, so that it was widely used and used until the XVIII century.

abacus. - board) - a countable board applied to arithmetic computing from about the 5th century to n. e. In ancient Greece, ancient Rome.

The Abaca board was divided into strip lines, the score was carried out using stones placed on the stripes or other similar items. Pebble for Greek Abaca was called psyphos; From this word, a name was made for the account - psipophoria., "Folding Kameshkov" (title books on Indian arithmetic Maxim Planuda, who died in 1310, " Indian psyphoria») .

Abak in various regions

Ancient Babylon

For the first time appeared, probably in ancient Babylon OK. 3 thousand BC e. Initially, he was the board, separated on the strip or with the deposits made. Accurate labels (pebbles, bones) moved along lines or recesses. In 5 c. BC e. In Egypt, instead of lines and recesses, they began to use sticks and wire with nanous pebbles.

Ancient indium

Abacom used the peoples of India. Arabs got acquainted with Abaku in the subordinates of them nations. In the title of many Arab manuals on arithmetic appear words from the root " dust».

Western Europe, VIII-X century

Eastern Arabs, like the Indians, Abak was soon displaced by Indian numbering, but he held firmly from Western Arabs who captured in the late VIII century and Spain. In the 10th century, Herbert's Frenchman (-), who wrote about this book (-), who wrote about this book (-) was met here and promoting Abaca himself through his studies. Instead of pebbles, ties with the numerical signs, or Roman numbers, or special numeric signs, are used at the abacus. Herbert Apexes are close to the Gobar of Western Arabs. Apxas Herbert and his 27-Column Abacus, the subject of surprise of his contemporaries (reproduced in a restored form on various manuscripts by Professor N. M. Bubnov, professor of the history of Kiev University, beginning of the 20th century). The efforts of numerous students and followers of Herbert and thanks to its influence as a Pope (Sylvester II, -), Abak received widespread in Europe. Traces of this distribution were kept, by the way, in various languages. English verb. to Checker, or chequer.means graphite - in the word from the same root called cellular matter, the Chequee., or check. - Bank check, exchequer. - Treasury Department . The last term comes from the fact that in the bank the calculations were carried out on Abaca, the basis of which was the divorce board. The English State Treasury until recently was called Chamber of chessboard - on the checkered cloth, which was covered with a table of meetings. Checkered tablecloth served as abacus when calculating. Aroused in the XII century Chamber of chessboard It was the supreme financial management and the highest court on financial issues until 1873.

Far East

In the countries of the East, the Chinese analogue of Abaka is common - Suanban and Japanese - Soroban.

Russia, XVI century

Notes

Literature

Depima I. Ya. History of arithmetic. M.: Enlightenment, 1965, p. 79-88.

Links

// Encyclopedic Dictionary of Brockhaus and Efron: in 86 volumes (82 tons and 4 extra). - St. Petersburg. , 1890-1907.

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Watch what is "Abak" in other dictionaries:

- (arch.) Abacus (device for computing). (Greek. Abax, Abakion, Latin abacus board, counting board), 1) Counting board, used for arithmetic computing in ancient Greece, Rome, then in Western Europe to 18 V. The board was divided into ... ... Encyclopedia Color

- (from Greek. Abax board), upper plate Capitals columns, semi-column, pilasters. In classical architectural orders, Abak usually has square outlines with straight (in doric and ionic orders) or concave (in the Corinthian warrant) ... ... Artistic Encyclopedia.

abacus - A, m, Abaka and, g. abaque m., IT. Abaco Lat. Abacus c. ABAX, abakos. 1. Archite. In the art of the architectural top plate and the capitals of the column. Options 1789 Abaca is the highest part of the main pillar; Inacto, the boards are called .. the stove in the stone, ... ... Historical Dictionary of Gallicalism Russian Language

A. Mechanical wooden, bone or stone scores, which are a device, with moving along several guide plates, thanks to which calculations were made. It was used in Europe and Arab countries until the middle of XVLLL ... ... Business Terms Dictionary

- (from the Greek ABAX board), 1) The board for arithmetic calculations, divided into stripes where pebbles moved, bones (both in Russian accounts), in ancient Greece, Rome, then in Western Europe to 18 V. 2) in classic architectural orders ... ... Modern encyclopedia

- (from the Greek. Abax board) 1) The board, divided into stripes where pebbles moved, bones (both in Russian accounts) for arithmetic calculations in the DR. Greece, Rome, then in Zap. Europe to 18 B.2) In architectural orders, the top plate Capitals ... ... Big Encyclopedic Dictionary

Abacus, countable device used on the middle and Far East for addition and subtraction. The most common form of Abaca consists of beads, strung on the wire stretched and forming columns corresponding to the discharges of units, ... ... Scientific and Technical Encyclopedic Dictionary

In ancienturk language means the elder brother, uncle. Mongols: sculpture, which is worshiped, idol. Tatar, Turkic, Muslim male names. Dictionary of Terms ... Dictionary of personal names

Abacus (Dr.-Greek. ἄβαξ, ἀβάκιον, lat. Abacus - board) - accounting boardapplied to arithmetic calculations from approximately the V century BC. e. In ancient Greece, ancient Rome.

Antique period - This is a conditional segment of historical time, which covers a period of 1 thousand years BC, before the I millennium of our era. Historians celebrate this era like a breakdown of a slave-owned structure, which came to replace the primary.

The ideal location of Greece is a relatively Mediterranean, Aegean, Black and Marble Seas, as well as a mild climate, actively contributed to the successful development of not only different crafts, but also trade with neighboring states.

It should be noted unique at that time administrative device Countries - the bulk of the population with high levels Outcomes concentrated in large cities - polishes, which, in fact, was separate states. Policys submitted to themselves smaller settlements engaged in the delivery of agricultural products, household goods, materials for construction.

To exercise trade between cities, a special, unified unit was required, through which the value of all goods would be expressed. Barter could not always satisfy the interests of both sides, so money came to replace the type of plates from precious metals - Gold and silver. The disadvantage of the system was that each policy had its own money, which was often distinguished by the face value, weighing, shape. It was required to produce complex calculations to bring the result of trading for a general denominator, and it was almost impossible to do this without the use of the counting system.

The calculation of the money, and then and the usochemistry was engaged in a selected category of citizens of the policy, which enjoyed great authority and respect among other residents of the city. Over time, the number of operations conducted by them increased - the usurists not only were engaged in mediation in financial transactions, but also exchanged money, they were stored, gradually evolving in bankers. First, all the necessary entries and calculations were made on wooden planks or papyrus. Which at that time was inaccessible luxury, and spending it on the calculations even state importance was extremely wasteful. In order to speed up arithmetic operations, 2500 years ago an unknown inventor was invented uncomplicated in the manufacture of a device - abac.

History of the appearance of Abaka

Ancient Greece Gave the modern world many important and facilitating the life of inventions, one of which is rightfully considered to be aback. This simple device, designed to carry out simple mathematical calculations, appeared in approximately the V century BC, and was a wooden or stone plate with slots, which were freely moving along certain grooves of pebbles from wood or marble.

The most ancient, preserved aback, was discovered during excavations on the island of Cyprus, in the vicinity of the largest and fortified policy of Salamis. Nakhodka belongs to 300 BC, and it looks like a plate of white marble, and its size is rather impressive. The length of accounts is almost one and a half meters, the width is 75 cm. The thickness of the marble plate is 4.5 cm. Abacus has a complex system of slots, along which the balls from stone moved. The exact purpose of the device is not known, but judging by its size and weight, it served to count the taxes or expenses from the city budget, and was established near the Treasury of Salamiis.

Economy of ancient Greece

Researchers in the history of the ancient development of Greece often arises of such a domestic aspect as the economic relations of cities and their individual inhabitants with each other.

It is worth noting the pretty interesting views of the inhabitants of Eldlas for financial responsibility. Theft in ancient Greece Or the estate of the state budget was considered by them exclusively as an economic crime, the punishment for which was fully compensated for the shortage of a materially responsible person. Theft of money from the execution of the Polis was punished with a refund of a loss in tenfold, so that some earliest personalities were beneficial to put the banker of a rich resident of the city, after which to substitute him and blame him. Thus, the newly minted banker was forced to compensate for the damage, having lost its own property.

The system of banking records on different operations was carried out by applying marks for wooden tables in chronological order, no systematization was carried out. From time to time, to compile a report for the month or year it was required to do additional work - recapitulation, which was to reconcile records, and the establishment of their chronology. To facilitate the already difficult work of bankers, scores were used. Probably, at first they had the appearance of ordinary small pebbles - river or sea pebbles of the same size, with smooth, rounded outlines. By the way, the word " calculation", Happened from Latin" calculos."That marked small pebbles. Probably went from this and modern name River and marine sediments - pebbles.

It was very uncomfortable to use pebbles in a large number of monotonous calculations, since they constantly fell from the table, lost or rolled out of one armhole to another, which greatly reduced the accuracy of operations. In order to make accounting for monetary and material funds more perfect, unknown to date, the inventor took a marble plate, made a slot in it, and placed 10 pebbles in them, allowing them to move freely along the grooves. Such a tool could always be taken with you, and to control the consumption of materials on construction sites, count the number of taxes for merchants who came to the city, to record income into the state treasury.

Interesting was a system for storing public funds in the policies of ancient Greece. Each type of income received distributed in the following way: In a special reliable room there are several large jugs with letterproof indexes. In each jug, the means received from specific activities - taxes from merchants, income tax, fee received from ships in ports and other duties. The financing of these industries was out of the same jug, so the total balance of spending was not blown.

The keys to the room itself with money were kept by one banker, and to the room from all the documentation - the second. It was strictly prohibited to exchange keys, as a result of which the protection against deliberate embezzlement was high enough.

Taxation system of ancient Greece It was surprisingly arranged. When paying duties, not only arithmetic, but also a receipt of a linear or positional record. Bank records were also well organized. Each fee or issuance of funds could be carried out in cashlessly, and all finance movements were carefully recorded and could be made public in the business center of the Polis - Agore.

The maintenance of such detailed reports was impossible without aback. They were common everywhere - in banks, which then wearing the name "Madrons", in government agencies and ports.

Aback analogues in world history

Such an important invention like aback arose long before the appearance on the territory of GreeceAlthough it was in Eldead that it has gained modern features. The first well-known mention of Abaka has been preserved in the documents of the ancient Babylon, which relate to the III millennium to our era. Babylonian abacus had a view of a horizontal board with deepening, along which pebbles or other small items moved along which. Later, 500 years before our era, the Egyptians have improved and design, using not deepening, and sticks or copper wire, on which rosary of clay, wood or stone were rolled. Such a decision made it possible to use aback not only in the horizontal form, which was often uncomfortable, but also in the vertical.

After the appearance of Abaki in Greece, the Arabs and Hindus met the invention. They also brought scores to Western Europe, capturing Spain in the VIII century. Here Abaka somewhat modified - instead of Kameshkov, metal tokens began to use, for which Roman numbers were applied, or legend - Apks. State treasury calculations with the help of Abaki were conducted in Europe until the XVIII century, after which they were replaced by more productive methods of algorithmization.

Eastern countries, such as China and Japan also actively used abacus. The Chinese analogue was called Suanypan, and Japanese - Soroban. They practically did not differ from each other, which proves their overall origin. Suanatepan had 10 discharges - by the number of fingers on their hands, and two vertical columns - by the number of hands, and was intended for simple settlements of household, production about, construction and financial plan. Chinese and Japanese Abacus is not just a device to facilitate arithmetic action, but also a whole art. In Japan, the score on Sorobane is still officially included in the school curriculum, and work with it is not just a tribute to tradition or fashion, but also has a purely practical importance. Despite the large number of modern electronic devices, many small entrepreneurs, sellers in stores and markets prefer to use abacus in everyday life. Clearly developed algorithms of action make it possible to produce all major mathematical operations on Swanpan and the Surobane - addition, subtraction, multiplication and division, as well as raise the degree and extract square and cubic roots.

Russian scores make it possible not only to seen and deduct different numbers, but also work with the quarters, tenth and hundredths. The appearance of Abaca in Russia is referred to the XV-XVI century. The active distribution of accounts continued until the end of the twentieth century, when such devices were replaced by more accurate electronic calculators. Prior to the early 1980s, learning arithmetic actions in accounts was part of the school curriculum of Soviet schoolchildren.

Abaca in ancient Greece came to replace the old and demanding additional action Account on your fingers. The development of the technique made it possible to make calculations by fast, accurate and light. Each pebble on Abaca could mean both units and tens, hundreds, thousands, which significantly expanded the scope of the tool. On this occasion in Ellad, a joke was even widespread: "Court looks like pebbles for Abaka: the counter will want, the price will be whole talent, but he wants - only Chalk."

It is safe to say that the invention of Abaka gave a strong impetus not only about cash settlements and trade, but it made it possible to produce complex calculations in the construction of ancient temples, and other architecture facilities that we can enjoy to this day.

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Abacus manual calculator. Watch what is "Abak" in other dictionaries. Abak in various regions

Similar documents

Material For curious

Abacus and scores

Abacus

Abak in various regions

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Western Europe, VIII-X century

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Watch what is "Abak" in other dictionaries:

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It is necessary to know

Material
For curious