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Abacus manual calculator. Material for curious. Western Europe, VIII-X 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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Synonyms:

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 and scores

A truly revolutionary event in the history of the account was the appearance of devices,

united by a common name - aback. Abak could have the shape of a wooden board,

clay tile or just outlined piece of earth. It is important that on Abaca

places (speakers or lines) were marked for individual discharge numbers.

For the first time, Abaka mentions the historian of the ancient world Herodotus. Abacus was wide

distributed in the ancient world. Its options were used in ancient Rome and

Babylon, China, Japan and many other countries. Mathematical task

considered solved if its decision could be reproduced on

abaca. Abak (Greek Abax, Abakion, Latin Abacus - board, counting board), counting board, used for arithmetic computing in ancient Greece, Rome, then in Western Europe until the 18th century. In ancient Greece, the joke told:

"Court looks like pebbles for Abaka: the counter will want, the price will be a whole talent, but he wants - only Chalch."

The board was divided into stripes, the score was carried out by moving in the bands of countable brands (bones, stones, etc.). In the countries of the Far East, the Chinese analogue of Abaka is common - Suan Pan, in Russia - accounts.

In Russia, Abak penetrated not

later XVI century, but most likely it happened much earlier. Russian

abaka variants were a "bone account" and "dumping account".

The most primitive abacus, indeed, represented such a skid. They conducted a sharp stick on it, and pebbles were placed in the resulting columns. This means that there were columns of units, dozens, hundreds and so on. Exactly unknown, where exactly the first aback appeared. Perhaps in Phenicia. Greeks moving pebbles from left to right. Unlike them, the Egyptians did it to the right left. In ancient Rome, Abak was called "Calculi" or "Abaculi" and was made of bronze, stone, ivory or stained glass. From the word "Calculus", meaning "pebbles", "naked", the Latin word "Calculatore" (calculate) and a modern "calculator" occurred. The bronze roman abacus has been preserved, on which pebbles moved in vertical grooves. In the lower part there were pebbles for an account to five, and in the top - pebbles corresponding to the top five.

Chinese abacus - suanypan - appeared in the VI century AD, and its modern look - in about the XII century. Suanindan is a rectangular frame in which 9 or more parallel wires or ropes are stretched. Perpendicular to this on the Board of Suanypan is overclosed by a ruler into two unequal parts: "Earth", in which 5 balls, strung on each wire, and "heaven" - here 2 balls. The balls in the "Earth" is like five fingers, and the balls in the "sky" are two hands. Wires are decimal discharges: units, dozens, and so on.

With the help of Suan Pan, it was possible not only to fold, but also multiply, divide, operate with fractions, extract square and cubic roots. In all likelihood, it was the first position-known positional decimal system. Sucan-pan helped make fundamental discoveries in mathematics. Actions with numerals and denominers led to the concept of fraction as a number.

About Russian Abaca - accounts, appeared at the turn of the XVI - XVII centuries, the scores have a horizontal arrangement of the knitting spokes and are based on a decimal, and not a five-packed system of numbering Russian scores were widely used not only for computing, but also as a training manual for initial learning arithmetic.

To distinguish positive numbers from negative, various sticks were used in Suan Pan. The positive numbers were designated red chopsticks or with a square cross section, and the negative was black or triangular.

Russian Abak appeared at the turn of the 16-17 centuries. The most common account tool in Dopurerovskaya Rus was a "account account", which represents a special board or table. Before carrying out computations, they needed to demolish horizontal lines. Four arithmetic actions were carried out with the help of a pebble, fruit bone or a special tokens.

The scores began to lose the value of the universal counting device, gradually turning into auxiliary. With the help of a new system in writing, on paper, it turned out to be much more convenient to perform mathematical calculations than using Abaca. This process was accompanied by a sharp struggle, as two sciences thought: Mathematics on Abak and Mathematics without Abaka - on paper. This struggle is known as opposition to abakists and algorithmics. The countable device of the Major General of the Russian Army F.M. Freedom, invented by him in 1828. He developed a simple rules for the information of arithmetic action to the sequence of addition and subtraction, which, together with the memorization of several simple auxiliary tables (such as the multiplication table), the time of calculations was noticeably reduced. In the basis of this device - for multiple addition and subtraction - the principle of action is the principle of action of the same Russian account.

Abacus - Counting Board Used by many nations. The Greeks and Egyptians used abacus with drawn lines or extended grooves. Along the lines or in the grooves stacked pebbles. Each pebble meant a single computing, and the line itself is the discharge of this unit.

Calculations with the help of Greek and Egyptian abacks, as well as with the help of the Suan Pan and Sorobana, were made as follows. In each groove (on each line or on every twist) there were five pebbles (or balls). Pebbles in the first groove meant a unit. Pebble in the second groove - five units. Pebbles in the third groove - twenty-five units. Pebbles in the fourth groove - one hundred and twenty-five units.

Thus, a five-way calculus system was used in Abaka and its early analogues. The main advantage of Abaca was the claritude of the calculations and the so-called positional representation system of numbers. The result of the calculations did not require any decryption - it was enough to look at the location of the pebbles on the abacus to instantly determine which number it turned out. The disadvantage of the ancient Abaka was precisely a five targeting system, which was not suitable invented invented later than a weekly system and did not allow to operate with fractions.

Elderly Abac , or russian accounts A year is used and the ability to operate with tenth and hundredth fractional shares, appearedat the turn of the XVI and XVII centuries .

From the classic Abaka, the scores are distinguished by an increase in the discharge of each numeric row and design. The scores are a frame within which thin rods are located. Round bones are attached to the rods - ten pieces on each rod. Two lower rows mean hundredths and tenths. Then there is an intermediate series (it is usually highlighted by four bones, which are not involved in calculations). Then there is a first row of knuckles, each of which means one, the second row, in which each knuckle corresponds to the top ten, then, respectively, there are hundreds, thousands, tens of thousands and so on. Later there were extended modifications of accounts - the fractional part could reach four rows, and a part of the integers - seven rows.

For the clarity of the calculations of the knuckles of Russian bills had a two-color color. The fifth and sixth knuckles on each axis were stained in a darker (black) color, the rest - in bright (brown or yellow). The two-color staining of knuckles allowed to very quickly determine which number is typed on accounts, since four light bones and two dark ones on the left side are faster defined as the number 6 than six single-color knuckles.

It should be noted that from the moment of the emergence of Russian Abaka, the scores have changed little over time. The rods on which the knuckles were located, acquired a convex profile - so that the knuckles spontaneously were mixed from one side to another. The rods themselves began to make from thick metal wire, and the knuckles and the frame of the accounts were made of oak wood.

The scores lived safely to our time and went off the scene only in recent decades, giving way to electronic calculators. However, Russian Abacus was and remains the most efficient tool for learning the account. A person who can quickly believe in accounts, faster thinks in mind.

Despite the fact that the scores simplify monotonous bulky calculations, they do not allow simplifying the operations of multiplication and division. Multiply and share with Abaca - this in any case can be repeatedly folded and deducted.

Complexes of measuring and computing flow and amounts of aback + liquids and gases (hereinafter - IVK) are intended for: measurement, transformations, registration, processing, control, storage, and indication of the process parameters in real time, by measuring signals from voluminous and Mass meter-flow meters, moisture meters and measuring transducers of density, viscosity, pressure, pressure differences, temperature, level and any other parameters of fluids and gases, as well as signals from thermoelectric converters according to GOST 6616-94 and resistance thermal converters according to GOST 6651-2009 ; performing signaling functions on the established limits; transmissions of the values \u200b\u200bof the process parameters by playing output analog signal signals and DC voltage and output digital signals; reception, processing and formation of output discrete signals; performing the functions of the analytical controller for chromatograph; calculating the heat of combustion, relative density, the number of Vobbe and the energy content of natural gas according to GOST 31369-2008, etc. 50.2.019-2006; Definitions of the temperature point of the dew of natural gas on water according to GOST R 53763-2009; bringing the volume flow (volume) of natural and associated (free) oil gases (in accordance with GOST R 8.615-2005 and GOST R 8.733-2011) (hereinafter - PNG) under work conditions to standard conditions in accordance with GOST 2939-63; Calculations of volumetric flow (volume) of natural gas and a PNG given to the standard conditions on the suspending devices installed in pipelines in accordance with GOST 8.586.1-2005, GOST 8.586.2-2005, GOST 8.586.4-2005, GOST 8.586.5 -2005 and aulent pressure tubes "Annubar Diamond II +", "Annubar 285", "Annubar 485" and "Annubar 585" in accordance with Mi 2667-2011; Calculations of mass flow rate (mass) of oil and petroleum products, liquid hydrocarbon environments in accordance with GOST R 8.595-2004 and GOST R 8.615-2005 according to the measurements of Coriolis (massive) measuring flow transducers, as well as turbine or ultrasound measuring flow converters complete with measuring density, pressure and temperature converters; Bringing to standard conditions for the volume and density of oil, petroleum products, liquid hydrocarbon environments in accordance with GOST R 8.595-2004; Calculations of mass flow rate (mass) of single-phase and homogeneous on the physical properties of liquids and gases according to the results of measuring measurements by corino-fox (massive) flow transducers.

Description

The IVC is produced in three versions: on TU INX.425210.001, Inks.425210.002 and Inks.425210.003. The IRC consists of embedded in the processor body with built-in coprocessors, display and keyboard.

Depending on the IVC configuration selected, RS232 / RS485, USB communication ports, Ethernet communication interface (10 / 100Baset), pulse inputs, analog and frequency-output modules with support for the hot-swap mechanism are supported.

In IVK, TU INX.425210.003 provides for the possibility of implementing the technological process management algorithms.

The principle of operation of the IRC is to measure and convert input signals from measuring flow transducers (vortex, turbine, rotary, ultrasonic, coriolis (mass)), pressure, pressure differences, temperature, input signals of thermoelectric converters according to GOST 6616-94 and resistance thermometers According to GOST 6651-2009 (for IVK on TU INX.425210.002), frequency measurement signals from the measuring density transducers.

Thus, the IRC provides the measurement of the following flow parameters:

Natural gas and APG: Volumetric flow rate (volume) at operating conditions, pressure, temperature, pressure drop on standard tape devices (aperture for GOST 8.586.2-2005 and Venturi pipe according to GOST 8.586.4-2005) or on auxiliary pressure tubes " Annubar "Alive 2667-2011;

Oil and petroleum products, liquid hydrocarbon environments: mass flow (weight), volume flow (volume) at operating conditions, density at operating conditions, pressure, temperature;

Single-phase and homogeneous on the physical properties of liquids: mass flow (weight), density at operating conditions, pressure, temperature.

The IRC calculates the calculation of the volume flow (volume) of natural gas and the PNG given to the standard conditions, and the mass flow rate (mass) of the fluid according to the method of variable pressure drop in accordance with the calculation algorithms given in GOST 8.586.2-2005, GOST 8.586.4- 2005, GOST 8.586.5-2005 and MI 2667-2011.

The IRC drives the surround flow rate (volume) of natural gas and APG under working conditions to standard conditions in accordance with GOST 2939-63, by automatically electronically correction of indications of measuring flow transducers: vortex, turbine, rotational, ultrasonic temperature and pressure of the measured medium (natural Gas and PNG), the compressibility coefficient of the measured medium (natural gas) in accordance with GOST R 8.740-2011 and PR 50.2.019-2006 for volumetric flow transducers.

The calculation of the physical properties of natural gas is carried out by an IRU according to GOST 30319.096, GOST 30319.1-96, GOST 30319.2-96 and GOST 30319.3-96. The natural gas compressibility coefficient is calculated by any of the four methods presented in GOST 30319.2-96: the modified method NX19 mod., Modified equation of the state of GERG-91 mod., Equation of the state of the CMV, the AGA8-92 DC status equation.

The calculation of the PHG physical properties is carried out by an IRC according to the GSSD MR 113-03. Calculation of the heat of combustion, relative density, the number of Vobbe and the Energy-Building of Natural Gas is conducted by an IRC according to GOST 31369-2008, and PR 50.2.019-2006; Determination of the temperature of the point of the dew of natural gas on the water is carried out by an IRC according to GOST R 53763-2009.

The IRC calculates the mass flow rate (mass), bringing to standard conditions for the volume and density of oil, petroleum products, liquid hydrocarbon environments in accordance with GOST R 8.595-2004.

IVK allows you to keep track of the volumetric flow (volume) of natural gas and the PNG, which reduced to standard conditions, mass flow (mass) of oil, petroleum products, liquid hydrocarbon media, single-phase and homogeneous on the physical properties of liquids not more than three measuring lines for the IVC for INCS.425210.001, no more than six - for IRK on TU INX.425210.002 and no more than twelve - for IVK on TU INX.425210.003.

IVK Abak + on that

INKS.425210.001 and IVK Abak + on TU INX.425210.003

Inx.425210.002.

Software (software) ensures the implementation of IVK functions. The IRC is divided into a metrologically significant and metrologically insignificant part. The first stores all the procedures, functions and subprograms, carrying out registration, processing, storage, control, indication and transmission of measurement results and IVC calculations; as well as protection and identification of software. The second stores all libraries, procedures and routines of interaction with the operating system and peripheral devices (not related to measurements and calculations of the IVC).

Protection on the IRC from unintentional and deliberate changes and ensuring its compliance with the approved type is carried out by separation, identification and protection against unauthorized access to software.

Table 1

IVC identification is carried out by displaying the identification data structure on the display. Some of this structure relating to the identification of the metrologically significant part of the IRC is a hash sum (checksum) at significant parts.

The IRC is protected from unauthorized access, changes in algorithms and set parameters by entering a login and password, which is read only to read event log. Access to the metrologically significant part on the IRC for the user is closed. When changing the set parameters (source data) in the IVC, confirmation of changes is provided, checking changes for compliance with the requirements of implemented algorithms, and the events' messages (changes) are written to the event log, read-only. Data containing measurement results are protected from any distortion by coding. IVC has protection level C.

Name
Name	INCS.425210.	INCS.425210.	INCS.425210.
Ranges of input signals
voltage, B.	from 0 to 5 from 1 to 5	from 0 to 5 from 1 to 5 from 0 to 10
dC forces, ma		from 0 to 5 from 0 to 20 from 4 to 20
pulsed, Hz	from 0 to 12000
frequency, Hz	from 0 to 12000
thermoelectric converters according to GOST 6616-94 with a nominal static characteristic (NCH): With output signal, mv		from minus 200 to 760 from minus 230 to 1370 from minus 240 to 1000 from minus 240 to 400 ± 80
resistance thermometers according to GOST 66512009 (type PT100): Temperature, ° С Resistance, Oh.		from minus 200 to 800 from 0 to 500
Output ranges
voltage, B.		from 0 to 10 from 0 to 5 from 1 to 5 from 2 to 10
dC forces, ma		from 0 to 5 from 4 to 20 from 0 to 20
The limits of the allowable IRK error when converting the input analog signal to the value of the measured physical value
voltage: Main,% Additional,% / ° C In operating conditions,%
dC forces: Main,% Additional,% / ° C In operating conditions,%

Name
Name	INCS.425210.	INCS.425210.	INCS.425210.
the thermoelectric converter according to GOST 6616 with a nominal static characteristic (NCX): With output signal ± 80 mV,%
resistance thermometer according to GOST R 8.625 (type PT100): Temperature, % Resistance,%
The limits of the allowed IRK error when converting the input frequency signal to the value of the measured physical quantity
absolute, Mc absolute, units. Right. relative: Main,% Additional,% / ° C
The limits of the allowable IVC error when converting the physical value to the output analog signal
voltage: Main,% Additional,% / ° C In operating conditions,%
dC forces Main,% Additional,% / ° C In operating conditions,%
The limits of the allowed absolute error of the IVC when converting the input pulse signal to the value of the measured physical quantity, the number of pulses per 10,000 pulses
Limits of permissible relative error of the IRC when measuring time interval,%
The limits of the permissible relative error of the IVK:
when calculating the volume flow (volume) of natural gas and a PNG given to standard conditions,%
when bringing a volume flow (volume) of natural gas and a PNG under working conditions to standard conditions,%
in calculating the mass flow rate (mass) of oil and petroleum products, liquid hydrocarbon media, single-phase and homogeneous on the physical properties of fluids,%

Name
	INCS.425210.	INCS.425210.	INCS.425210.
Operating conditions
ambient temperature, ° С		from minus 40 to 60	from minus 40 to 70
normal ambient temperature, ° С
relative humidity,%	from 5 to 95 without condensation
atmospheric pressure, kPa	from 84 to 106.7
Supply voltage (DC source), in
Power consumption, W, no more
Overall dimensions, mm, no more
Mass, kg, no more
Average work on failure, h, not less
Average service life, years, not less

Notes:

* - error at normal ambient temperature;

** - an additional error caused by a change in the ambient temperature for each 1 ° C from normal (for IVC on TU INX.425210.001 and INCS.425210.003);

*** - Error at ambient temperature other than normal (for IVK on TU INX.425210.002).

Type approval sign

it is applied to the IRU body by the method of silk screen and on the title sheet of passport by a typographical way.

Completeness

Table 3.

Name	number
Complexes of measuring and computing flow and amounts of liquids and gases "Abak +".
Complexes of measuring and computing flow and amounts of liquids and gases "Abak +". Manual.
Complexes of measuring and computing flow and amounts of liquids and gases "Abak +". Passport.
Instruction. GS Complexes of measuring and computing flow and amounts of liquids and gases "Abak +". Verification technique.
Configuration Software "Interface of a set of measuring and computing consumption and the amount of liquids and gases" Abac + ".

Verification

under the document MP 17-30138-2012 "Instruction. GS Complexes of measuring and computing flow and amounts of liquids and gases "Abak +". The technique of calibration ", approved by the GTCI" STP "on September 18, 2012

List of fixed assets of calibration (standards):

Calibrator Multifunctional MC5-R.

Information about measurement methods

The measurement method is set out in the instruction manual.

Regulatory documents establishing the requirements for the IVC

1. GOST 2939-63 "GAZ. Conditions for determining the volume. "

2. GOST 30319.0-96 "Natural gas. Methods for calculating physical properties. General. "

3. GOST 30319.1-96 "Natural gas. Methods for calculating physical properties. Determination of the physical properties of natural gas, its components and products of its processing. "

4. GOST 30319.2-96 "Natural gas. Methods for calculating physical properties. Determination of the compressibility coefficient. "

5. GOST 30319.3-96 "Natural gas. Methods for calculating physical properties. Determining the physical properties by the status equation.

6. GOST 31369-2008 "Natural gas. Calculating the heat of combustion, density, relative density and number Vobbe based on component composition. "

7. GOST 6616-94 "Thermoelectric converters. General specifications. "

8. GOST 6651-2009 "GSI. Thermal converters resistance from platinum, copper and nickel. General technical requirements and test methods".

9. GOST 8.586.1-2005 "GSI. Measurement of the flow and amount of liquids and gases using standard tousing devices. The principle of the measurement method and general requirements. "

10. GOST 8.586.2-2005 "GSI. Measurement of the flow and amount of liquids and gases using standard tousing devices. Diaphragms. Technical requirements".

11. GOST 8.586.4-2005 "GSI. Measurement of the flow and amount of liquids and gases using standard tousing devices. Venturi pipes. Technical requirements".

12. GOST 8.586.5-2005 "GSI. Measurement of the flow and amount of liquids and gases using standard tousing devices. Methods for performing measurements. "

13. GOST R 8.585-2001 "GSI. Thermocouples. Nominal static conversion characteristics. "

14. GOST R 8.615-2005 "GSI. Measurement of the amount of oil and oil gas extracted from the bowels. General metrological and technical requirements. "

15. GOST R 8.733-2011 "GSI. Systems for measuring the number and parameters of free oil gas. General metrological and technical requirements. "

16. GOST R 8.740-2011 "GSI. Consumption and amount of gas. Measuring methods using turbine, rotational and vortex flow meters and counters. "

17. GOST R 8.595-2004 "GSI. Mass of oil and petroleum products. General requirements for measurement methods. "

18. GOST R 53763-2009 "Gases combustible natural. Determination of the temperature of the point of dew on water. "

19. GSSD MR 113-03 "GSSD Methodology. Determination of density, compressibility factor, indicator of adiabat and coefficient of dynamic viscosity of wet oil gas in the temperature range 263 .. .500 to pressures up to 15 MPa. "

20. PR 50.2.019-2006 "GOOSI. Methods of performing measurements with the help of turbine, rotary and vortex meters. "

22. Inx.425210.001 TU "Complexes of measuring and computing consumption and the number of liquids and gases" Abak + ". Technical conditions. "

23. INCS.425210.002 TU "Complexes of measuring and computing flow and amounts of liquids and gases" Abak + ". Technical conditions »

24. INCS.425210.003 TU "Complexes of measuring and computational flows and amounts of liquids and gases" Abak + ". Technical conditions. "

The implementation of government accounting operations, trade and commodity exchange operations.

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 the 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.

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