Who defined the word addition. The history of the emergence of arithmetic operations. Examples of the use of the word addition in the literature

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The history of the origin of mathematical signs Prepared by: Cherepanov Ivan, student 5th grade Mathematics teacher: Mosunova O.A. As there is no table in the world without table legs, As there is no goat horns in the world, Cats without mustaches and without crayfish shells, So there are no actions in arithmetic without signs!

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Tasks Consider where mathematical signs came to us from and what they originally meant. Compare mathematical signs of different peoples. Consider the similarities of modern mathematical signs with the signs of our ancestors

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Object: mathematical signs of different nations. Main research methods: literature analysis, comparison, student survey, analysis and generalization of the data obtained during the study.

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Why in our time do we use just such mathematical signs: + “plus”, - “minus”, ∙ “multiplication” and: “division”, and not some others? Problem

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Hypothesis I think that mathematical signs arose simultaneously with the appearance of numbers and numbers

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The origin of mathematical signs The origin of these signs cannot always be precisely established. The symbols for the arithmetic operations of addition (plus "+'') and subtraction (minus "-'') are so common that we almost never think that they did not always exist. Indeed, someone had to invent these symbols (or at least others that later developed into the ones we use today). Certainly also some time passed before these symbols became generally accepted. There is an opinion that the signs "+" and "-" originated in trading practice. The vintner marked with dashes how many measures of wine he sold from the barrel. Pouring new reserves into the barrel, he crossed out as many expendable lines as he restored the measures. So, supposedly, there were signs of addition and subtraction in the 15th century. There is another explanation regarding the origin of the “+” sign. Instead of "a + b" they wrote "a and b", in Latin "a et b". Since the word “et” (“and”) had to be written very often, they began to abbreviate it: first they wrote one letter t, which, in the end, turned into a “+” sign

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The algebraic sign “-” The first use of the modern algebraic sign “+” refers to a German manuscript on algebra from 1481, which was found in the Dresden library. In a Latin manuscript from the same time (also from the Dresden library), there are both symbols: + and - . Johann Widmann is known to have reviewed and commented on both of these manuscripts. In 1489, in Leipzig, he published the first printed book (Mercantile Arithmetic - “Commercial Arithmetic”), in which both + and - signs were present (see figure). The fact that Widman used these symbols as if they were common knowledge points to the possibility of their origin in trade. An anonymous manuscript, apparently written around the same time, also contains the same characters, and this provided two additional books published in 1518 and 1525.

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Some mathematicians such as Record, Harriot and Descartes used the same sign. Others (eg Hume, Huygens, and Fermat) used the Latin cross “†” sometimes placed horizontally, with a crossbar at one end or the other. Finally, some (like Halley) used more decorative look Widman

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The first occurrence of "+" and "-" on English language discovered in the 1551 algebra book "The Whetstone of Witte" by the Oxford mathematician Robert Record, who also introduced the equals sign, which was much longer than the current sign. In describing the plus and minus signs, Record wrote: “Other two signs are often used, the first of which is written “+” and means more, and the second “-” and means less.

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Subtraction sign The subtraction notation was somewhat less fancy, but perhaps more confusing (for us, at least), as instead of the simple "-" sign, German, Swiss, and Dutch books sometimes used the symbol "÷'', which we now denote division. Several books of the seventeenth century (for example, those of Halley and Mersenne) use two dots "∙ ∙" or three dots "∙ ∙ ∙" to indicate subtraction.

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In ancient Egypt In the famous Egyptian papyrus of Ahmes, a pair of legs going forward indicates addition, and leaving - subtraction

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The ancient Greeks denoted addition by writing side by side, but occasionally used the slash symbol “/'' and the semi-elliptic curve for subtraction. The Hindus, like the Greeks, usually did not denote addition in any way, except that the symbols used in Bakhshali's Arithmetic manuscript (probably third or fourth century).

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At the end of the fifteenth century, the French mathematician Chuquet (1484) and the Italian Pacioli (1494) used “p” (denoting “plus”) for addition and “m” (denoting “minus”) for subtraction. Shuke

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In Italy In Italy, the symbols "+" and "-" were adopted by the astronomer Christopher Clavius ​​(a German living in Rome), the mathematicians Gloriosi and Cavalieri in the early seventeenth century Christopher Clavius

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Multiplication sign To denote the action of multiplication, some of the European mathematicians of the 16th century used the letter M, which was the initial in the Latin word for increase, multiplication, - animation (the name "cartoon" comes from this word). In the 17th century, some mathematicians began to denote multiplication with a slash "×", while others used a period for this. In Europe, for a long time, the product was called the sum of multiplication. The name "multiplier" is mentioned in the works of the XI century. For thousands of years, the action of division was not indicated by signs. The Arabs introduced the line "/" to indicate division. It was adopted from the Arabs in the 13th century by the Italian mathematician Fibonacci. He was the first to use the term "private". The colon sign ":" to indicate division came into use at the end of the 17th century. In Russia, the names “divisible”, “divisor”, “private” were first introduced by L.F. Magnitsky at the beginning of the 18th century. The multiplication sign was introduced in 1631 by William Ootred (England) in the form of an oblique cross. Before him, the letter M was used. Later, Leibniz replaced the cross with a dot (late 17th century) so as not to confuse it with the letter x; before him, such symbolism was found in Regiomontanus (XV century) and the English scientist Thomas Harriot (1560-1621).

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Division marks Oughtred preferred the slash "/". Colon division began to denote Leibniz. Before them, the letter D was also often used. In England and the United States, the ÷ (obelus) symbol, which was proposed by Johann Rahn and John Pell in the middle of the 17th century, became widespread.

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Equality and Inequality Signs The equal sign was designated at different times in different ways: both by words and by various symbols. The “=” sign, so convenient and understandable now, came into general use only in the 18th century. And this sign was proposed to denote the equality of two expressions by the English author of the algebra textbook Robert Ricord in 1557. He explained that there is nothing more equal in the world than two parallel segments of the same length. In continental Europe, the equal sign was introduced by Leibniz. The "not equal" sign is first encountered by Euler. Comparison marks were introduced by Thomas Harriot in his work, published posthumously in 1631. Before him, they wrote in words: more, less.

Explanatory Dictionary of the Living Great Russian Language by Vladimir Dahl

Addition, add up, complex, etc., see add up.

Explanatory dictionary of Ozhegov

Addition, -i, cf.

see fold.

A mathematical operation, by means of which a new one is obtained from two or more numbers (or values), containing as many units (or values) as there were in all the given numbers (values) together. Task on p.

A word formed according to the method of conditional addition (special). , -i, cf. Same as physique. Bogatyrskoye s.

Explanatory dictionary of the Russian language Ushakov

ADDITION, additions, cf.

Only ed. action on verb. add up to 2, 5 and 7 digits. - fold - fold. Addition of forces (replacement of several forces by one that produces an equivalent action; physical). Addition of values. Addition of responsibilities.

Only ed. One of the four arithmetic operations, by means of which a new (sum) is obtained from two or more numbers (summands), containing as many units as there were in all these numbers together. Addition rule. Addition task. Perform addition.

Same as physique; general physical condition of the body. A heroic addition, hefty was a kid. Nekrasov. I do not brag about my constitution, but I am cheerful and fresh, and lived to gray hair. Griboyedov. || The structure of matter (spec.). Nasal fold.

There is an action by which the set of given numbers is reduced to the form a010n + a110n-1+ a210n-2 +.. . + an+an+110-1 + an+210-2 +.. . where all coefficients are less than ten. Everyone knows how to perform this transformation, and therefore we do not consider it necessary to go into details. D.S. Encyclopedic Dictionary of Brockhaus and Efron

Tsygankov Alexander, student of the 4th grade, secondary school No. 7, Mirny

In mathematics lessons, we constantly work with one of the mathematical operations - addition, and we thought about when people first began to add, who and when gave the names to the components of this action, and what else can be learned about the addition action.

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HISTORY OF THE ACTION OF ADDITION FROM ANCIENT TIMES TO THE PRESENT DAYS.

In mathematics lessons, we constantly work with one of the mathematical operations - addition, and we thought about when people first began to add, who and when gave the names to the components of this action, and what else can be learned about the addition action.

Gradually, we learned that everyone needs mathematics in everyday life. Everyone has to count in life, we often use (without noticing it) knowledge about the quantities of length, time, mass. We realized that mathematics is an important part of human culture.

This paper considers a number interesting questions about the operation of addition, as one of the basic arithmetic operations.

Since ancient times, people have counted objects. People have been learning how to do arithmetic for over a thousand years.

Human fingers were not only the first counting instrument, but also the first calculating machine. Nature itself provided man with this universal counting tool. For many peoples, fingers (or their joints) played the role of the first counting device in any trading operations. For most of the everyday needs of people, their help was enough.

However, counting results were recorded in various ways.: notching, counting sticks, knots, etc. For example, the peoples of pre-Columbian America had a highly developed knot count. Moreover, the system of nodules also served as a storage and chronicle, having a rather complex structure. However, its use required a good memory training.

Many number systems go back to counting on the fingers, for example, five-fold (one hand), decimal (two hands), vigesimal (fingers and toes), forty-fold (the total number of fingers and toes of the buyer and seller). For many peoples, the fingers of the hands remained for a long time a counting tool even at the highest levels of development.

Well-known medieval mathematicians recommended finger counting as an auxiliary tool, which allows quite effective counting systems.

However, in different countries and at different times considered differently.

Despite the fact that for many peoples the hand is a synonym and the actual basis of the numeral "five", for different peoples with a finger count from one to five, the index and thumb can have different meanings.

The Italians when counting on the fingers thumb indicates the number 1, and the index - the number 2; when the Americans and the British count, the index finger means the number 1, and the middle finger means 2, in this case the thumb represents the number 5. And the Russians start counting on the fingers, bending the little finger first, and end with the thumb indicating the number 5, while the index the finger was compared with the number 4. But when they show the number, they put up the index finger, then the middle and ring fingers.

Each nation had its own arithmetic operations. And they were all used to perform operations on numbers. For a long time, people performed addition of numbers only verbally with the help of any objects - fingers, pebbles, shells, beans, sticks.

In ancient India, they found a way to add numbers in writing. When calculating, they wrote down the numbers with a stick on the sand, poured on a special board.

Indian sages suggested writing numbers in a column - one under the other; the answer is written below.

In ancient China, addition was done on the board with the help of special sticks. They were made from bamboo or ivory.

V Ancient Egypt for addition, a hieroglyph in the form of walking legs was used. The direction of the legs coincided with the direction of the letter, which means that addition must be performed.

V Ancient Russia Russian people in their calculations used only two arithmetic operations - addition and subtraction, and called them doubling and bifurcation.

Some signs for addition appeared in antiquity, but until the 15th century there was almost no generally accepted sign. There are several points of view on how the sign for addition appeared.

In the 15th - 16th centuries, the Latin letter "P" was used for the addition sign, initial letter plus words. Gradually, this letter began to be written with two lines. For addition, the Latin word " et" (floor) , denoting "And", which means "greater than". Since the word “et” had to be written very often, they began to shorten it: first they wrote one letter “t”, which gradually turned into the sign “+ ». There is a third opinion: the “+” sign originated in trading practice.

For the first time, the “+” sign appears in print in the book “A Quick and Beautiful Account for Merchants”. It was written by the Czech mathematician Jan Widman in 1489.

Man has always sought to simplify and speed up the solution of expressions, and this has led to the creation of computing devices. The ancient peoples used the abacus counting device in calculations.

Abacus is a counting board used for arithmetic calculations in Ancient Greece and Rome. The abacus board was divided by lines into stripes, the count was carried out with the help of 5 stones and bones placed on the strips. In China and Japan, oriental abacuses of 7 bones were common: Chinese suan-pan and Japanese - soroban.

Russian abacus - abacus, appeared at the end of the 15th century. They have horizontal knitting needles with underwire and are based on the decimal system. Russian abacus was widely used for calculations. They are easy and quick to add and subtract.

For almost three centuries, talented scientists, engineers and designers have been creating mechanical calculating machines that make it easier to perform the four mathematical operations.

At the beginning of the 19th century, the French inventor Karl Thomas, took advantage of the ideas of the famous German scientist Leibniz and invented a calculating machine for performing 4 arithmetic operations and called it an adding machine. Adding machines until the early 1970s remained good helpers of calculators of all countries.

And 20 years ago, small devices were made that perform complex calculations in a matter of seconds - calculators. A calculator is an electronic computing device. Calculators can be desktop or (pocket) calculators, calculators built into computers, cell phones, and even wristwatches. But even faster than a calculator, a computer performs various mathematical operations. All these are assistants to a person in counting. Despite all the advantages of the computer age, there is the fact that many adults have forgotten how to count without a calculator. And many children even count on their fingers - this is very inconvenient. Therefore, I propose to learn how to count "in an adult way", using mathematical tricks - ways to memorize the addition table within 20 and quick counting without a calculator and fingers. Cunning mathematical tricks will allow you to instantly add in your mind. At first glance, these techniques seem confusing and incomprehensible. But having understood them and bringing the execution to automaticity, you will understand how simple, convenient and easy these techniques are. Count faster, count better!

From interviews with subject teachers, we learned that the action of addition is actively used in other sciences.

Russian language . Topic: "Word formation" (primary school teacher)

As a result of addition, a complex word-word with several roots is formed: snowfall, cinema, forest park.

Biology . Topic: "Human nutrition" (biology teacher)

Addition of calories is performed to determine the energy value of the product (proteins, fats, carbohydrates)

Geography . Topic: "Climate" (geography teacher)

Temperatures are added up for a certain period to find the average daily, average monthly, average annual temperature.

Physics . Topic "Interference" (physics teacher)

The addition in space of two (or several) waves, in which at different points an increase or decrease in the amplitude of the wave is obtained - wave interference.

We can see the action of addition everywhere: in the construction of houses, in the design and construction of a rocket, a car, in tailoring, for cooking, for raising animals, for making medicines and in many other areas of activity.

Conclusions :

• Addition has been used for a long time to count various objects.
• addition action is used in many sciences
• most often in life, both adults and children use addition
• the easiest way to add numbers on a calculator
• there are "easy" ways of mental counting when adding