Activities l. F. Magnitsky and the further development of schools. Research work "solving a problem from Magnitsky arithmetic" Assignments from entrance exams at Moscow State University

Borzenkova Angela, Surkov Mikhail, Sokolov Andrey

Authors, students of grade 7B of State Budget Educational Institution Secondary School 134, St. Petersburg, under the guidance of mathematics teacher A.E. Nechaeva. Research work was carried out on the topic “Magnitsky Arithmetic”. The in-person defense of the study took place on April 15, 2017 at IV scientific-practical conference students of the Krasnogvardeisky district of St. Petersburg "WORLD OF SCIENCE" (without publication). This action involves the publication of the work in the media.

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MAGNITSKY ARITHMETICS Relevance The relevance of the chosen topic is determined by: the opportunity to get acquainted with the first Russian textbook on mathematics, the history of its creation, identify the historical significance of its appearance and influence on the development of mathematical science in Russia.

MAGNITSKY'S ARITHMETICS The Magnitsky's Arithmetic hypothesis, becoming the first Russian textbook in mathematics, contributed to: the formation of a unified approach to the study of mathematics in Russia; an increase in the number of students studying the basics of mathematics in Russia due to the fact that it was written in Russian and became the main textbook in mathematics in the newly created Navigation School; and it also became historical evidence of certain aspects of the life of Russian citizens at the beginning of the 18th century.

MAGNITSKY ARITHMETICS PROBLEMS and METHODS of research Research objectives. Make a brief overview of the retrospective of the creation of Arithmetic, the biography of Leonty Filippovich Magnitsky, get acquainted with the history of the creation of Arithmetic and identify the degree of influence of Arithmetic on the spread of mathematics in Russia. Research methods. General scientific methods such as the empirical method, the method of comparison, and generalization were used as research methods.

MAGNITSKY'S ARITHMETICS main contents Historical retrospective of the origins of Magnitsky's Arithmetic About Leonty Filippovich Magnitsky About the textbook Magnitsky's Arithmetic Conclusion

MAGNITSKY ARITHMETICS Historical retrospective of the origins of Magnitsky Arithmetic Northern War 1700-1721. – many qualified specialists are required. There were few textbooks. There were no textbooks in Russian. There were textbooks in Latin and Greek, kept in “closed” libraries, for example, of bishops’ schools, rare manuscripts Sukharev Tower - the building of the Navigation School, created in 1701

ARITHMETICS OF MAGNITSKY About Leonty Filippovich Magnitsky On June 9, 1669, according to the old style, the future mathematician Leonty was born into the family of the peasant Philip, nicknamed Telyashin, Ostashkovsky patriarchal settlement, Tver province. In 1684, at the age of 14, Leonty was sent to the Joseph-Volokolamsk monastery. A year later, the abbot blessed Leonty to study at the Slavic-Greek-Latin Academy, which in those years was the main educational institution Russia, where he studied for about eight years. In 1700, Peter I ordered Leonty to be called Leonty Filippovich Magnitsky. After which, in 1701, Magnitsky became a civil servant, to whom Tsar Peter I set the task of creating the first Russian-language mathematics textbook. From the same year until 1739, the life of L.F. Magnitsky is inextricably linked with the activities of the Navigation School, opened by Peter I in 1701. In 1739, at the age of 70, L.F. Magnitsky died.

ARITHMETICS OF MAGNITSKY Peter I commanded L.F. about Magnitsky’s arithmetic textbook. Magnitsky to write a mathematics textbook for the navigation school established on January 14, 1701 in Russian

MAGNITSKY ARITHMETICS About the Magnitsky Arithmetic textbook

MAGNITSKY'S ARITHMETICS conclusions The Magnitsky's Arithmetic textbook contributed to the emergence of the Russian mathematical tradition of teaching mathematics in a new format for Peter's times, the development of a uniform approach to teaching and learning mathematics. The historical significance of Magnitsky's Arithmetic, as teaching aid in mathematics, in that he introduces convenient numbering, similar to Arabic, and writes down the advanced algorithms of that time for addition, subtraction, multiplication, and division. The presentation of the material is based on solving practical problems, which allows you to use the textbook for self-education. Scientific novelty. At each time stage comparison modern methods education, algorithms for solving mathematical problems given in Magnitsky Arithmetic is justified from a scientific point of view, since it allows us to assess the level of evolution of mathematical scientific thought, the level of evolution of general education.

MAGNITSKY'S ARITHMETICS sources Magnitsky's Arithmetic. Exact reproduction of the original. With the application of an article by P. Baranov. - M.: Publishing house P. Baranov, 1914. URL: http://elibrary.orenlib.ru/index.php?dn=down&to=open&id=1261 Belenchuk L.N., Enlightenment in the era of Peter the Great // Domestic and foreign pedagogy. I. Institute for Educational Development Strategy Russian Academy education. - 2016. - No. 3 (30). - pp. 54-68. URL: http://elibrary.ru/download/elibrary_26286817_93418862.pdf Denisov A.P., Leonty Filippovich Magnitsky (1669–1739)// M.: Enlightenment. - 1967. - 143 p. Magnitsky Leonty Filippovich // Encyclopedic Dictionary of Brockhaus and Efron: In 86 volumes (82 volumes and 4 additional), St. Petersburg: 1890-1907. Malykh A.E., Danilova V.I., Leonty Filippovich Magnitsky (1669–1739) // Bulletin Perm University,Mathematics. Mechanics. Informatics. – 2010. – Issue. 4 (4). – pp. 84-94. URL: http://elibrary.ru/download/elibrary_15624452_71219613.pdf Stepanenko G.A., Magnitsky Arithmetic and modern elementary school mathematics textbooks // Tauride Scientific Observer, I. Limited Liability Company "Interregional Institute for Territorial Development", Yalta. – 2016. – 1-3 (6) – P. 38-43. URL: http://elibrary.ru/download/elibrary_25473094_94425485.pdf Tikhonova O. Yu. Leonty Filippovich Magnitsky - mathematician and Christian // Scientific and methodological electronic journal "Concept". – 2016. – No. 3 (March). – pp. 71–75. – URL: http://e-koncept.ru/2016/16053.htm Chekin A.L., Borisova E.V., The first domestic printed textbook “Arithmetic” L.F. Magnitsky// Magazine “Primary School”, I. Limited Liability Company Publishing House “Primary School and Education”, Moscow. – 2013. - No. 9. – P.12-15. URL: http://elibrary.ru/download/elibrary_21131169_20173013.pdf 9. http://museum.lomic.ru/trip.html - website of the museum M.V. Lomonosov in the village of Lomonosovo,

MAGNITSKY ARITHMETICS sources THANKS FOR YOUR ATTENTION

The first part of the book - "Arithmetic of Politics", volume of 218 double pages, is devoted to the presentation of arithmetic itself, as well as progressions and roots (square and cubic). It consists of 5 parts:
1. About integers.
2. About broken numbers, or with fractions.
3. About similar rules, in three, five and seven lists.
4. About false rules, even fortune-telling ones.
5. On the rules of radixes, square and cubic, belonging to geometry.

Let us briefly describe each of the parts of the first book.

The first part covers integers and 5 operations - numbering, addition, subtraction, multiplication and division. Unlike the manuscripts of the 17th century, Magnitsky, in addition to the rules for their implementation, gives definitions of actions:
"What is numeration? Numeration is the calculation of absolutely all numbers in speech, even in ten signs, or images, contained and depicted even: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, of which nine are significant: the last 0 (even if it is called a number or nothing) always stands alone, then in itself it means nothing. Whenever these signs are applied to someone, then it multiplies by ten.”

The definitions of arithmetic operations were apparently borrowed by Magnitsky from contemporary Western European literature. "Addition, or the addition of two or many numbers into a single collection, or into a single list of copulation", - this is how Magnitsky defines addition. Magnitsky defined subtraction not as an action inverse to addition, but as an independent operation, which can be considered natural at the first stage of learning. “Subtraction, or subtraction, is where a small number is subtracted from a larger one and the excess is declared”.

Multiplication and division were also defined as independent actions that solved certain problems. “Multiplication is where we multiply by numbers, or distribute many things by many other things: and we show their quantity by number.”. Thus, Magnitsky reduced multiplication to repeated addition of collections of objects. “Division is a larger number, or a list is divided into equal parts by smaller ones, and from them we show a single number.”.

Of course, these definitions are extremely imperfect both from a substantive and methodological point of view. We will not engage in fruitless criticism of them, if only because it is ahistorical. The very fact of attempting to define arithmetic operations is productive, since it marked the beginning of a process as a result of which modern definitions were born in the course of analysis and improvement.

Action properties were not considered. The main attention, naturally, was paid to the rules of action and the analysis of numerous examples. Moreover, Magnitsky, like his predecessors, cited several methods of division and multiplication. Action signs were not used (as in foreign textbooks of that time). Magnitsky paid considerable attention to methods of checking arithmetic operations. To check subtraction and division, reverse operations were used, for all operations - verification using 9.

Next come named numbers, which are preceded by an extensive treatise on ancient Greek, Roman and Jewish money, measures and weights of Holland and Prussia, measures and money of the “Muscovite state and some surrounding ones,” 3 comparative tables of measures, weights and money. This treatise, distinguished by its remarkable detail, clarity and accuracy, testifies to Magnitsky's deep erudition. Moreover, it has undoubted historical significance, as it provides information about the systems of measures and monetary circulation in Russia. As for named numbers, Magnitsky introduces the reader to their addition and subtraction, as well as “fragmentation” and “transformation,” which he views as division and multiplication. Operations with named numbers are performed in the usual way.

The second part of The Arithmetic of Politics covers fractions in detail. Magnitsky for the first time in Russian mathematical literature gives the definition of fractions: “A broken number is nothing other than a part of a thing, declared as a number, that is, half a ruble is half a ruble, but it is also written as 1/2 of a ruble, or a quarter of a 1/4, or a fifth of 1/5, or two fifths of 2/5 and all sorts of things any part declared as a number: i.e. a broken number".

It is no coincidence that the study of fractions followed the department on named numbers and systems of measures: a fraction was understood by Magnitsky not as an abstract number or a fraction of an abstract unit, but as a fraction of a quantity, a thing. In this case, a fraction was thought of as a kind of whole, consisting of smaller units (half - 50 kopecks, for example). Magnitsky then goes into detail about arithmetic operations with fractions - numbering, reduction, addition, subtraction, multiplication and division.

The third part of the "Arithmetic of Politics" contains threefold rules, set out, in contrast to the manuscripts of the 17th century. detailed and dissected. In addition to the usual triple rule, the “reflexive” is distinguished in wholes and fractions, i.e. reverse triple rule; the “triple contractile rule”, in which preliminary reduction of the terms of the proportion is possible, and the rules of 5, as well as 7 quantities. Magnitsky directly connected the triple rule with the proportionality of quantities, but he does not have any developed doctrine of proportions. Therefore, even the simple triple rule is not described clearly enough in Arithmetic of Politics.

The fourth part of the Arithmetic of Politics sets out the rules of falsehood. Magnitsky, unlike his Russian and foreign predecessors, considered not 2, but 3 cases of the rule of 2 false provisions: 1) when both provisions are greater than the desired one; 2) when both of them are smaller; 3) when one is more and the other is less. Magnitsky also has problems that can be solved using the rule of one false position, which he, however, did not specifically highlight. This ends the part of “Arithmetic” that related it to the manuscripts of the 17th century. The rest of its content was new for the Russian reader.

In the last, fifth part of “The Arithmetic of Politics,” Magnitsky placed the doctrine of progressions and the extraction of square and cubic roots. He rightly attributes these questions to algebra. Magnitsky sets out the elements of algebra in the second part of the book, however, considering that few will study it, he decides to offer some questions “in addition to many, in the previous parts of various rules...”. Taking into account the needs of practice, he gives many examples of the application of algebraic material to military and naval affairs.

In the fifth part, Magnitsky returns to “similarities”, or, as he now calls them, proportions and progressions - arithmetic, geometric, only mentioning “harmonic”. He continues the tradition of introducing definitions that he introduced into the Russian textbook:
“Progressio is the proportion or similarity of numbers to numbers in multiplication, or in reduction, or list.”
“An arithmetic progression or proportion is when there are three or many numbers, each of them equal in difference from each other, but having different proportions, and this either in a single progression, like 2, 4, 6, 8, 10, 12, or not in a single progression, like 2, 4, 5, 7, 8, 10, 11, 13".
“Geometric progression or proportion is, when there are three or many numbers, one and the same proportion among themselves, but they have different differences, and this is either in the same progression, like 2, 4, 8, 16, 32, 64, 128, or not in the same way, like 2, 4, 6, 12, 18".

Decreasing and increasing progressions, properties of arithmetic progressions and the rule for calculating its sum are considered: “Add the first limit and the last, and then add the sum with half of all limits.”. Naturally, the formula for the general term is not given; the rule is formulated for the specific (14th) term of the progression: “The difference of the sum is 13 places, and add the first limit to that, and there will be a final limit.”. The presentation of a geometric progression begins by defining its denominator: “It is worth considering that when two numbers are a geometric progression, and one is divided by the other, and the product becomes a proportion, or a multiplied number, in which the progression rises or falls.”. Magnitsky has no formulas for finding the common term and the sum of the terms of a geometric progression; when solving problems, he uses a descriptive method.

The article “On the square radix” is devoted to the square root. Magnitsky gives a geometric definition of the square root, as he later uses it mainly in geometric applications. Having determined the side of a square by its area and placed a table of squares from 1 to 12, Magnitsky notes that any number can be a square and describes in detail, using an example, the method of extracting the square root of integers and fractions. It obtains an approximate value of the root by assigning pairs of zeros to the right.

By analogy, the concept of a cube root is introduced, to which the article “On the cubic radix” is devoted.

The problems in this article are interesting, among which there are problems for replacing a cube with several cubes of equal size: “A certain cube has a side of 28 vershoks. You need to make 8 identical smaller cubes from it. Determine the side of the cube.”

Due to the large number of calculations in the fifth part of “Arithmetic of Politics”, Magnitsky for the first time in Russian mathematical literature provides information about decimal fractions: “another member of arithmetic... also called decimal or tenth, that is, in tenths, or in hundredths, or in thousandths and multiples”. He examines the addition of decimal fractions and formulates the rules for their subtraction and multiplication.

School and pedagogical thought in Russia XVIII V.
- Enlightenment in Russia at the beginning of the 18th century.
  - Enlightenment in Russia at the beginning of the 18th century. - page 2
  - Enlightenment in Russia at the beginning of the 18th century. - page 3
- Activities of L.F. Magnitsky
  - Activities of L.F. Magnitsky - page 2
  - Activities of L.F. Magnitsky - page 3
- V.N. Tatishchev and the beginning vocational education in Russia
  - V.N. Tatishchev and the beginning of vocational education in Russia - page 2
- Education and school after Peter I
- Pedagogical activity M.V. Lomonosov
  - Pedagogical activity of M.V. Lomonosov - page 2
  - Pedagogical activity of M.V. Lomonosov - page 3
- Enlightenment in Russia in the era of Catherine the Great
- Pedagogical views and activities of I.I. Betsky
  - Pedagogical views and activities of I.I. Betsky - page 2
  - Pedagogical views and activities of I.I. Betsky - page 3
  - Pedagogical views and activities of I.I. Betsky - page 4
  - Pedagogical views and activities of I.I. Betsky - page 5
School and pedagogical thought in Western Europe and the USA in the 19th century. (until the 90s)
- Development of the school in the 19th century. (until the 90s)
  - Development of the school in the 19th century. (until the 90s) - page 2
  - Development of the school in the 19th century. (until the 90s) - page 3
- Pedagogical thought in Western Europe by the 90s of the nineteenth century.
  - Pedagogical thought in Western Europe by the 90s of the nineteenth century. - page 2
  - Pedagogical thought in Western Europe by the 90s of the nineteenth century. - page 3
  - Pedagogical thought in Western Europe by the 90s of the nineteenth century. - page 4
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  - Pedagogical thought in Western Europe by the 90s of the nineteenth century. - page 7
  - Pedagogical thought in Western Europe by the 90s of the nineteenth century. - page 8
  - Pedagogical thought in Western Europe by the 90s of the nineteenth century. - page 9
  - Pedagogical thought in Western Europe by the 90s of the nineteenth century. - page 10
  - Pedagogical thought in Western Europe by the 90s of the nineteenth century. - page 11
- School and pedagogical thought in the USA in the 19th century. (until the 90s)
  - School and pedagogical thought in the USA in the 19th century. (until the 90s) - page 2
  - School and pedagogical thought in the USA in the 19th century. (until the 90s) - page 3
- Issues of education in European social teachings
  - Issues of education in European social teachings - page 2
  - Issues of education in European social teachings - page 3
- The idea of a class approach to issues of upbringing and education
  - The idea of a class approach to issues of upbringing and education - page 2
  - The idea of a class approach to issues of upbringing and education - page 3
School and pedagogical thought in Russia until the 90s of the 19th century.
- School development and formation of the school system
  - School development and formation of the school system - page 2
  - School development and formation of the school system - page 3
  - School development and formation of the school system - page 4
  - School development and formation of the school system - page 5
- Pedagogical thought in Russia in the 19th century (until the 90s)
  - Pedagogical thought in Russia in the 19th century (until the 90s) - page 2
  - Pedagogical thought in Russia in the 19th century (until the 90s) - page 3
  - Pedagogical thought in Russia in the 19th century (until the 90s) - page 4
  - Pedagogical thought in Russia in the 19th century (until the 90s) - page 5
  - Pedagogical thought in Russia in the 19th century (until the 90s) - page 6
  - Pedagogical thought in Russia in the 19th century (until the 90s) - page 7
  - Pedagogical thought in Russia in the 19th century (until the 90s) - page 8
  - Pedagogical thought in Russia in the 19th century (until the 90s) - page 9
  - Pedagogical thought in Russia in the 19th century (until the 90s) - page 10
Foreign school and pedagogy in late XIX- early 20th century
- School reform movement at the end of the 19th century.
- The main representatives of reform pedagogy
  - The main representatives of reform pedagogy - page 2
  - The main representatives of reform pedagogy - page 3
  - The main representatives of reform pedagogy - page 4
  - The main representatives of reform pedagogy - page 5
- Experience in organizing schools based on the ideas of reform pedagogy
  - Experience in organizing schools based on the ideas of reform pedagogy - page 2
  - Experience in organizing schools based on the ideas of reform pedagogy - page 3
  - Experience in organizing schools based on the ideas of reform pedagogy - page 4
School and pedagogy in Russia at the end of the 19th - beginning of the 20th centuries. (until 1917)
- Public education in Russia at the end of the 19th - beginning of the 20th century.
  - Public education in Russia at the end of the 19th - beginning of the 20th centuries. - page 2
  - Public education in Russia at the end of the 19th - beginning of the 20th centuries. - page 3
  - Public education in Russia at the end of the 19th - beginning of the 20th century. - page 4
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  - Public education in Russia at the end of the 19th - beginning of the 20th century. - page 6
  - Public education in Russia at the end of the 19th - beginning of the 20th century. - page 7
  - Public education in Russia at the end of the 19th - beginning of the 20th century. - page 8
- Pedagogical thought in Russia at the end of the 19th - beginning of the 20th century.
  - Pedagogical thought in Russia at the end of the 19th - beginning of the 20th century. - page 2
  - Pedagogical thought in Russia at the end of the 19th - beginning of the 20th century. - page 3
  - Pedagogical thought in Russia at the end of the 19th - beginning of the 20th century. - page 4
  - Pedagogical thought in Russia at the end of the 19th - beginning of the 20th century. - page 5
  - Pedagogical thought in Russia at the end of the 19th - beginning of the 20th century. - page 6
  - Pedagogical thought in Russia at the end of the 19th - beginning of the 20th century. - page 7
  - Pedagogical thought in Russia at the end of the 19th - beginning of the 20th century. - page 8
  - Pedagogical thought in Russia at the end of the 19th - beginning of the 20th century. - page 9
  - Pedagogical thought in Russia at the end of the 19th - beginning of the 20th century. - page 10
School and pedagogy in Western Europe and the USA between the First and Second World Wars (1918-1939)
- School and pedagogy in Western Europe and the USA between the world wars
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  - School and pedagogy in Western Europe and the USA between the world wars - page 6
School in Russia from the February Revolution to the end of the Great Patriotic War
- General education after the February Revolution and the October Revolution of 1917.
  - General education after the February Revolution and the October Revolution of 1917 - page 2
  - General education after the February Revolution and the October Revolution of 1917 - page 3
  - General education after the February Revolution and the October Revolution of 1917 - page 4
  - General education after the February Revolution and the October Revolution of 1917 - page 5
- Problems of content and methods of educational work in school in the 20s
  - Problems of the content and methods of educational work in school in the 20s - page 2
  - Problems of the content and methods of educational work in school in the 20s - page 3
- Pedagogical science in Russia after 1918
  - Pedagogical science in Russia after 1918 - page 2
  - Pedagogical science in Russia after 1918 - page 3
  - Pedagogical science in Russia after 1918 - page 4
  - Pedagogical science in Russia after 1918 - page 5
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  - Pedagogical science in Russia after 1918 - page 8
  - Pedagogical science in Russia after 1918 - page 9
- Pedagogical science during the Great Patriotic War
  - Pedagogical science during the Great Patriotic War - page 2

Activities of L.F. Magnitsky

Leonty Filippovich Magnitsky (1669-1739) made a huge contribution to the methods of secular school education of the Petrine era and to the training of domestic personnel. According to the tradition that came from the masters of literacy in Moscow Rus', he created his own textbook - “Arithmetic, that is, the science of numbers” - publishing it after a two-year practical test in 1703. This educational book marked the birth of a truly new textbook, combining the domestic tradition with achievements of Western European methods of teaching exact sciences. Arithmetic L.F. Magnitsky was the main educational book on mathematics until the middle of the 18th century; M.V. studied from it. Lomonosov.

Textbook L.F. Magnitsky had the character of an applied, in fact even utilitarian, manual for teaching all basic mathematical operations, including algebraic, geometric, trigonometric and logarithmic. Pupils of the navigation school copied the contents of the textbook, formulas and drawings on slate boards, mastering not theoretically, but practically the listed branches of mathematics.

L.F. were widely used. Magnitsky a variety of visual aids. Various tables and layouts were included with the textbook. The navigation school used a wide range of visual aids - ship models, engravings, drawings, instruments, drawings, etc.

Already the title page of “Arithmetic” was a kind of symbolic visual aid that reflected the contents of the textbook, which to a certain extent made it easier for schoolchildren to master mathematics, since the text itself was written in a language difficult for children to understand. Arithmetic itself as a science was depicted in the form of an allegorical female figure with a scepter - a key and an orb, seated on a throne, to which the steps of a staircase lead with a sequential listing of arithmetic operations: “numeration, addition, subtraction, multiplication, division.” The throne was placed in the "temple of sciences", the vaults of which are supported by two groups of columns of four each. The first group of columns had the inscriptions: “geometry, stereometry, astronomy, optics” and rested on a foundation on which the question was written: “What does arithmetic give?” The second group of columns had the inscriptions: “mercatorium (that’s what the navigational sciences were called in those days), geography, fortification, architecture.”

Thus, “Arithmetic” by L. F. Magnitsky was essentially a kind of mathematical encyclopedia, which had a clearly applied nature. This textbook marked the beginning of a fundamentally new generation of educational books. It was not only not inferior to Western European models, but was also compiled in line with the Russian tradition, for Russian students.

L.F. Magnitsky was in charge of the entire academic work school, starting from the first stage. To prepare students for training in the navigation school itself, two primary school, which were called the “Russian school”, where they taught reading and writing in Russian, and the “number school”, where children were introduced to the beginnings of arithmetic, and fencing was also taught for those who wished.

All academic subjects were studied in the navigation school sequentially, there were no transfer or final exams, students were transferred from class to class as they learned, and the concept of “class” itself did not mean an element of the class-lesson system, which did not yet exist in Russia, but the content of education : navigation class, geometry class, etc. Released from school as soon as the student was ready for a specific government activities or at the request of various departments that were in dire need of educated specialists. New students were immediately recruited to fill the vacant position.

Pages: 1 2 3

Usanova Yana

Research work "Solving a problem from Magnitsky Arithmetic." The work tells about the life and work of Leonty Filippovich Magnitsky. The solution to the problem of "Kad drinking" (4 methods) and the problem of the "triple rule" is considered.

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Municipal educational institution

average secondary school No. 2 of the city of Kuznetsk

__________________________________________________________________

Solving a problem from Magnitsky Arithmetic

Research work

Prepared by a 6th grade student

Usanova Ya.

Head: Morozova O.V.-

Math teacher

Kuznetsk, 2015

Introduction………………………………………………………………………………….3

1. Biography of L.F. Magnitsky…………………………………………………………….4

2. Magnitsky Arithmetic…………………………………………………….7

3. Solution of the problem “Kad of drinking” from Magnitsky Arithmetic. Problems for the “Triple Rule”…………………………………………………………….. 11

Conclusion…………………………………………………………………………………15

References…………………………………………………………….16

Introduction

Relevance and choicemy topic research work determined by the following factors:

Before the appearance of L. F. Magnitsky’s book “Arithmetic,” there was no printed textbook for teaching mathematics in Russia;

L. F. Magnitsky not only systematized the existing knowledge in mathematics, but also compiled many tables and introduced new notations.

Target:

- Studying the history of mathematics and solving problems from the book by L.F. Magnitsky.

Tasks:

Study the biography of L.F. Magnitsky and his contribution to the development mathematics education in Russia;

Consider the contents of his textbook;

Solve the problem “Kad drinking” in different ways;

Hypothesis:

If I study the biography of L.F. Magnitsky and ways to solve problems, I will be able to tell students of our school about the role of mathematics in modern society. It will be fun and will increase interest in learning mathematics.

Research methods:

Studying literature, information found on the Internet, analysis, establishing connections between decisions according to L. F. Magnitsky and in modern ways solving mathematical problems.

Biography of L.F. Magnitsky

On June 19, 1669, 3 centuries have already passed since then, in the city of Ostashkov, on the land where the great Russian river Volga originates, a boy was born. He was born in a small wooden house, located near the walls of the Znamensky Monastery, on the shores of Lake Seliger. He was born into a large peasant family, the Telyashins, famous for their religiosity. He was born at a time when the Nilova Monastery was flourishing on the Seliger land. At baptism, the child was given the name Leonty, which translated from Greek means “lion.”

Time passed. The boy grew and became stronger in spirit. He helped his father, who “fed himself” and his family with the work of his hands, and in his free time “he was a passionate hunter of reading complex and difficult things in church.” Ordinary peasant children did not have the opportunity to have books or learn to read and write. And the youth Leonty had such an opportunity. His great-uncle, Saint Nektarios, was the second abbot and builder of the Nilo-Stolobensk hermitage, which arose on the site of the exploits of the great Russian saint, Venerable Nile. Two years before the birth of Leonty, the relics of this saint were found, and many people began to flock to Stolbny Island, where the hermitage is located. The Telyashin family also went to this miraculous place. And while visiting the monastery, Leonty spent a long time in the monastery library. He read ancient handwritten books, not noticing the time, reading absorbed him.

Lake Seliger is rich in fish. As soon as the sled track was established, convoys with frozen fish were sent to Moscow, Tver and other cities. The young man Leonty was sent with this convoy. He was then about sixteen years old.

The monastery was amazed at the unusual abilities of an ordinary peasant son: he could read and write, which most ordinary peasants could not do. The monks decided that this young man would become a good reader and kept him “for reading.” Then Telyashin was sent to the Moscow Simonov Monastery. The young man amazed everyone there with his extraordinary abilities. The abbot of the monastery decided that such a genius needed to study further and sent him to study at the Slavic-Greek-Latin Academy. Of particular interest to young man called up math problems. And since mathematics was not taught at the academy at that time, and there were a limited number of Russian mathematical manuscripts, he studied this subject, according to his son Ivan, “in a marvelous and incredible way.” To do this, he studied Latin, Greek at the academy, German, Dutch, Italian on his own. Having studied languages, he re-read many foreign manuscripts and mastered mathematics so much that he was invited to teach this subject to rich families.

While visiting his students, Leonty Filippovich encountered a problem. In mathematics, or as they called arithmetic then, there was not a single manual or textbook for children and young people. The young man began to compose examples and interesting problems himself. He explained his subject with such fervor that he could interest even the laziest and most unwilling student, of whom there were many in rich families.

Rumors about a talented teacher reached Peter I. The Russian autocrat needed Russians educated people, because almost all literate people came from other countries. Peter I's profit-maker, A.A. Kurbatov, introduced Telyashin to the Tsar. The emperor really liked the young man. He was amazed by his knowledge of mathematics. Peter I gave Leonty Filippovich a new surname. Remembering the expression of his spiritual mentor Simeon of Polotsk, “Christ, like a magnet, attracts the souls of people to himself,” Tsar Peter called Telyashin Magnitsky - a man who, like a magnet, attracts knowledge to himself. Tsar Peter appointed Leonty Filippovich “to the Russian noble youth as a teacher of mathematics” at the newly opened Moscow Navigation School.

Peter opened a mathematics and navigation school, but there were no textbooks. Then the tsar, having thought well, instructed Leonty Filippovich to write a textbook on arithmetic.

Magnitsky, relying on his ideas for children, on examples and problems invented for them, in two years created the most important work of his life - a textbook on arithmetic. He called it “Arithmetic - that is, the science of numbers.” This book was published in a huge circulation for that time - 2400 copies.

Leonty Filippovich worked as a teacher at the Navigatskaya school for 38 years - more than half his life. He was a modest man, cared about science, and cared about his students.

Magnitsky cared about the fate of his students and appreciated their talent. In the winter of 1830, a young man approached Magnitsky with a request to accept him into the Navigation School. Leonty Filippovich was amazed that this young man himself learned to read from church books and mastered mathematics himself using the textbook “Arithmetic - that is, the science of numbers.” Magnitsky was also struck by the fact that this young man, just like himself, came to Moscow with a fish train. This young man's name was Mikhailo Lomonosov. Assessing the talent in front of him, Leonty Filippovich did not leave the young man at the Navigation School, but sent Lomonosov to study at the Slavic-Greek-Latin Academy.

Magnitsky was amazingly talented: an outstanding mathematician, the first Russian teacher, theologian, politician, statesman, associate of Peter, poet, author of the poem “The Last Judgment.” Magnitsky died at the age of 70. He was buried in the Church of the Grebnevskaya Icon Mother of God at the Nikolsky Gate. Magnitsky’s ashes found peace for almost two centuries next to the remains of princes and counts (from the Shcherbatov, Urusov, Tolstoy, Volynsky families).

Magnitsky Arithmetic

In stories about engineers of the Petrine era, one plot is often repeated: having received an assignment from the Emperor Peter Alekseevich, they first of all picked up L. F. Magnitsky’s “Arithmetic”, and then began to calculate. To determine what outstanding Russian inventors found in Magnitsky’s book, let’s look at his work. For more than half a century, this fundamental work of L. F. Magnitsky had no equal in Russia. It was studied in schools, and was approached by a wide range of people who were seeking education or, as already noted, working on some technical problem. It is known that M.V. Lomonosov called Magnitsky’s “Arithmetic” along with Smotritsky’s “Grammar” “the gates of his learning.”

At the very beginning, in the preface, Magnitsky explained the importance of mathematics for practical activities. He pointed out its importance for navigation, construction, and military affairs, i.e., he emphasized the value of this science for the state. In addition, he noted the benefits of mathematics for merchants, artisans, people of all ranks, that is, the general civil significance of this science. The peculiarity of Magnitsky’s “Arithmetic” was that the author was sure that Russian people have a great thirst for knowledge, that many of them study mathematics on their own. For them, engaged in self-education, Magnitsky provided each rule, each type of problem with a huge number of solved examples. Moreover, given the importance of mathematics for practical activities, Magnitsky included material on natural science and technology in his work. Thus, the meaning of “Arithmetic” went beyond the boundaries of mathematical literature itself and acquired a general cultural influence, developing the scientific worldview of a wide range of readers.

Arithmetic consists of two books. The first includes five parts and is devoted directly to arithmetic. This part outlines the rules for numbering, operations with integers, and verification methods. Then there are named numbers, which are preceded by an extensive section on ancient Jewish, Greek, Roman money, containing information about measures and weights in Holland, Prussia, about measures, weights and money of the Moscow state. Dans comparison tables measures, weights, money. This section is distinguished by great accuracy and clarity of presentation, which testifies to Magnitsky’s deep erudition.

The second part is devoted to fractions, the third and fourth - “rule problems”, the fifth - the basic rules of algebraic operations, progression and roots. There are many examples of the application of algebra to military and naval affairs. The fifth part ends with a discussion of operations with decimal fractions, which was news in the mathematical literature of that time.

It is worth saying that in the first book of “Arithmetic” there is a lot of material from old Russian handwritten books of a mathematical nature, which indicates cultural continuity and has educational value. The author also makes extensive use of foreign mathematical literature. At the same time, Magnitsky’s work is characterized by great originality. Firstly, all the material is arranged with a systematicity that did not occur in other educational books. Secondly, the problems have been significantly updated, many of them are not found in other mathematical textbooks. In Arithmetic, modern numbering finally supplanted the alphabetical one, and the old counting (for darkness, legions, etc.) was replaced by counting for millions, billions, etc. Here, for the first time in Russian scientific literature, the idea of the infinity of the natural series of numbers is affirmed, and this is done it is in poetic form. In general, in the first part of Arithmetic, syllabic verses follow each rule. The poems were composed by Magnitsky himself, which confirms the idea that a talented person is always multifaceted.

L. Magnitsky called the second book of “Arithmetic” “Astronomical Arithmetic”. In the preface, he pointed out its necessity for Russia. Without it, he argued, it is impossible to be a good engineer, surveyor or warrior and navigator. This book "Arithmetic" consists of three parts. The first part provides further exposition of algebra, including solving quadratic equations. The author examined in detail several problems in which linear, quadratic and biquadratic equations were encountered. The second part provides solutions to geometric problems involving measuring areas. Among them are the calculation of the area of a parallelogram, regular polygons, and a segment of a circle. In addition, a method for calculating the volumes of round bodies is shown. The diameter, surface area and volume of the Earth are also indicated here. This section provides some geometric theorems. Next, we consider mathematical formulas that make it possible to calculate trigonometric functions of various angles. The third part contains information necessary for navigators: tables of magnetic declinations, tables of latitude of sunrise and sunset points of the Sun and Moon, coordinates of the most important ports, hours of tides in them, etc. In this part, Russian maritime terminology is encountered for the first time, which has not been lost meaning up to now. It should be noted that in his “Arithmetic” Magnitsky did a great job of improving Russian scientific terminology. It was thanks to this outstanding scientist that our mathematical vocabulary included such terms as “multiplier”, “product”, “divisible and quotient”, “square number”, “average proportional number”, “proportion”, “progression”, etc. .

Thus, it is clear why L. Magnitsky’s “Arithmetic” was studied a lot and diligently for more than half a century, why it became the basis for a number of courses that were created and published later.Outstanding Russian inventors turned to Magnitsky’s work not just as an encyclopedia or reference book; among the solutions to hundreds of practical problems given in the book, they found those that could provide an analogy, suggest a new fruitful thought, because these problems had practical significance and demonstrated the capabilities of mathematics in search of a good technical solution.

Solution of the problem “Kad of drinking” from Magnitsky Arithmetic. Problems for the “Triple Rule”

"Kad of drinking"

One man will drink a kad in 14 days, and he and his wife will drink the same kad in 10 days, and it is known how many days his wife will drink the same kad.

I found this problem in the electronic version of the textbook “Arithmetic” along with the solution. L.F. Magnitsky solves it in an arithmetic way. I solved this problem in 4 ways: two of them arithmetic, two of them algebraic.

Solution:

1st method.

1) 14∙5=70 (days) - equalized the time during which a person drinks a pot of drink with the time during which a man and his wife drink the same pot of drink

2) 10∙7=70 (days) - equalized the time during which a man and his wife would drink a tub of drink with the time during which a person would drink the same tub

3) 70:14=5 (k.) - a person will drink in 70 days

4) 70:10=7 (k.) - a man and his wife will drink in 70 days

5) 7−5=2 (k.) - the wife will drink in 70 days

6) 70:2=35 (days) - the wife will drink a kad of drink

2nd method

Based on the fact that 1 kad=839.71l ≈840l

1) 840:10=84 (l) - a man and his wife will drink in 1 day

2) 840:14=60 (l) - a person will drink in 1 day

3) 84−60=24 (l) - the wife will drink in 1 day

4) 840:24=35 (days) - wife drinks in 1 day

3rd method

1) 840:14=60 (l) - a person will drink in 1 day.

2) Let the wife drink x liter in 1 day, since a man drinks a kad in 14 days, and his wife drinks the same kad in 10 days, let’s create an equation:

(60+X)∙10=840

60+X=840:10

60+X=84

X=84−60

X=24 (l) - wife drinks in 1 day

3) 840:24=35 (days) - the wife will drink a pot of drink

4th method

Let the wife drink x qadi of drink in 1 day, since in 1 day a person will drink 1/14 of the qadi of drink, and with his wife 1/10 of the qadi of drink, let’s create an equation:

1) X + 1/14 = 1/10

X = 1/10 - 1/14

X = (14 - 10) / 140 = 4/140 = 1/35 (kadi drink) - wife drinks in 1 day

2) 1/35∙35=35/35=1 (drink) - drinks 1 dram of drink in 35 days

In the 3rd quarter, during mathematics lessons, we began studying the topic of direct and inverse proportional relationships. This task is directly related to this topic. And analyzing the solution to this problem and similar ones presented in Magnitsky’s book, I found out that he solved problems of this type using a very interesting rule - the “Triple Rule”.

He called this rule a line because to mechanize calculations, data was written in a line.

The correctness of the solution depends entirely on the correct recording of the problem data.

RULE: multiply the second and third numbers and divide the product by the first.

And in mathematics lessons we decided to check whether this rule works on modern problems presented in the textbook by N.Ya. Vilenkina. First we solved problems by composing proportions, and then we checked whether the “triple rule” worked. My classmates were very interested in this rule; everyone was surprised how, after more than 300 years, it works for modern problems. For some guys, the solution using the triple rule seemed easier and more interesting.

Here are examples of these tasks.

No. 783. A steel ball with a volume of 6 cubic centimeters has a mass of 46.8 g. What is the mass of a ball made of the same steel if its volume is 2.5 cubic centimeters? (direct proportionality)

Solution.