From the arithmetic of Magnitsky. Oral arithmetic magazine for schoolchildren

Scientific and practical conference, dedicated to the life and work of L. F. Magnitsky

Solution of one problem “Kad drinking”

Introduction

1. Biography of L.F. Magnitsky

2. Magnitsky arithmetic

3. Solving a problem from Magnitsky Arithmetic

Conclusion

Bibliography

Introduction

INXVI- XVIIcenturies, handwritten mathematical literature begins to appear and spread in Russia (this is required by land surveying and measurement, the tax system, urban planning and military affairs, developing trade relations within the country and trade with other states). A significant number of mathematical manuscripts are currently knownXVIIcentury. They were mainly intended for merchants, traders, officials, artisans, land surveyors and were of a purely practical nature. Their material was distributed into “articles” containing instructions on how to proceed when solving certain problems. The rules were explained with various examples and problems. Some of these problems are interesting either because of their formulation or the way they are solved. Many of them were transferred to textbooks on arithmetic and algebraXVIIIcenturies, some have survived to this day.

In 1703, such a textbook was published by printing in an unusually large circulation for those times - 2,400 copies. It was called “Arithmetic, that is, the science of numbers...”. Its author was an outstanding teacher-mathematician - Leonty Filippovich Magnitsky. Taking as a basis the existing handwritten mathematical literature, Magnitsky created a book that for 50 years was the main textbook in mathematics for almost everyone educational institutions Russia.

Biography

Magnitsky Leonty Filippovich (1669-1739), mathematician, teacher.

Born on June 19, 1669 in the Ostashkovskaya settlement, Tver province. Descended from peasants. The future mathematician's father's name was Philip, his nickname was Telyashin, but at that time peasants were not given surnames. The boy learned to read independently as a child, thanks to which he at times served as a psalm-reader in the local church.

The young man’s fate changed dramatically when he was sent from his native settlement with a cart of frozen fish to the Joseph-Volokolamsk Monastery. Apparently, in the monastery the boy showed interest in books, and the abbot, making sure of his literacy, left Leonty as a reader. A year later, the abbot blessed the young man to study at the Slavic-Greek-Latin Academy, which was the main educational institution in Russia at that time. Leonty studied at the academy for about eight years.

At the end of the 17th century. lived in Moscow, giving private lessons to children and self-education. According to some information, he studied at the Slavic-Greek-Latin Academy. Legend has it that Peter I nicknamed him Magnitsky: “... in comparison to how a magnet attracts iron to itself, so he drew attention to himself with his natural and self-educated abilities.”

In 1701, Leonty Filippovich was appointed to help the English mathematicians teaching at the School of Mathematical and Navigational Sciences, which had just opened in Moscow. In 1715 Magnitsky became the senior teacher here and the head of its educational department. In addition, from 1714 he himself recruited teachers for the “digital schools” created in Russia.

Working continuously at the Navigation School for almost four decades, and then heading it, Magnitsky contributed to the success of Peter’s reforms in the field of education.

Magnitsky Arithmetic

Magnitsky is the author of the first Russian textbook on mathematics, “Arithmetic, that is, the science of numbers,” published in 1703 in a circulation of 2,400 copies. Book until the middle of the 18th century. was the main textbook on mathematics in Russia. It was a kind of encyclopedia of mathematical knowledge, containing material on geometry, trigonometry, astronomy and navigation and providing quite extensive applied information. Magnitsky also participated in the publication of the first logarithmic tables in Russia.

Surprisingly, the textbook was written and published in just two years. Moreover, it was not simply a translation of foreign textbooks; in structure and content it was a completely independent work, and there were no textbooks even remotely resembling it in Europe at that time. Naturally, the author used European textbooks and works on mathematics and took something from them, but presented it as he saw fit. In fact, Magnitsky created not a textbook, but an encyclopedia of mathematical and navigational sciences. Moreover, the book was written in simple, figurative and understandable language; it was possible to study mathematics from it, if you had certain basic knowledge.

According to the tradition of that time, the author gave the book a long title - “Arithmetic, that is, the science of numbers. Translated from different dialects into the Slavonic language, collected into one, and divided into two books.” The author did not forget to mention himself - “This book was written through the works of Leontius Magnitsky”, soon everyone began to call the book briefly and simply - “Mathematics of Magnitsky”.

In the book, containing more than 600 pages, the author examined in detail arithmetic operations with integer and fractional numbers, gave information about money accounts, measures and weights, and gave many practical problems in relation to the realities of Russian life. Then he outlined algebra, geometry and trigonometry. In the last section, entitled “Generally about earthly dimensions and what is necessary for navigation,” I examined the applied application of mathematics in maritime affairs.

In his textbook, Magnitsky not only sought to clearly explain mathematical rules, but also to arouse students’ interest in learning. He constantly emphasized the importance of knowledge of mathematics using specific examples from everyday life, military and naval practice. I even tried to formulate problems in such a way that they aroused interest; they often resembled jokes with an intricate mathematical plot.

The textbook turned out to be so successful that within several years it was spread throughout Russia. Apparently, even while writing the textbook, Magnitsky began teaching at the Navigation School, with which he was to connect his entire life. Until 1739, Leonty Filippovich first taught and then headed the Navigation School, raising a galaxy of students, many of whom became prominent military and statesmen Russia.

Magnitsky's authority among his contemporaries was enormous. Poet and philologist V.K. Trediakovsky wrote about him as a conscientious and unflattering person, the first Russian publisher and teacher of arithmetic and geometry. Admiral V.Ya. Chichagov called Magnitsky a great mathematician, and spoke of his book as a model of scholarship. M.V. considered “Magnitsky’s Arithmetic” to be the “gateway of his learning.” Lomonosov.

Solving a problem from Magnitsky Arithmetic

"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 that on how many days his wife will especially drink the same kad.

Solution:

1st method.

1 kad=839.71l ≈840l

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

2nd 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

3rd method

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

4th method

In 100 days he will drink 10 barrels of kvass, and together with his wife in 140 days they will drink 14 barrels of kvass. This means that in 140 days the wife will drink 14-10 = 4 kegs of kvass, and then she will drink one keg in 140:4 = 35 days.

5th method

Let the wife drink in 1 dayxqadi of drink, since in 1 day a person will drink 1/14 qadi of drink, and with his wife 1/10 of 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

Conclusion

While working with scientific literature, I learned a lot of interesting things from the history of the development of mathematics.It was Magnitsky who first introduced our ancestors to mathematics in a volume that was rare for his time and showed its great practical significance.L. F. Magnitsky first introduced the terms: multiplier, divisor, product, root extraction; replaced the obsolete words darkness, legion with the words million, billion, trillion, quadrillion. The book has significantly improved the system of presentation of the material: definitions are introduced, a smooth transition to something new is made, new sections and tasks appear, and additional information is provided.This is Magnitsky’s main merit to the history of mathematical education in our country.No less important is his merit as the first teacher of Russian sailors, who successfully overcame the enormous difficulties that he encountered when presenting the fundamentals of nautical science in Russian.

Bibliography.

1. Andronov I.K. The first mathematics teacher of Russian youth Leonty Filippovich Magnitsky // Mathematics at school. 1969. No. 6.

3. Glazer G.I. History of mathematics at school. Manual for teachers. – M.: “Enlightenment”, 1981. – 239 p.

4. Gnedenko B.V. and etc. encyclopedic Dictionary young mathematician.

M.: “Pedagogy”, 1985 – 349 p.

6. Olehnik S.N. et al. Ancient entertaining problems - 3rd ed. – M.: “Drofa”, 2006. – 173 p.

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Introduction

Chapter I. The influence of Peter I on development Russian education, starting from the end of the 17th century.

Chapter II. Features of the appearance of the textbook

Chapter III. Features of the content of the first domestic textbook on mathematics by Magnitsky in Russia in the 18th century.

Conclusion


Bibliography

Application

"Mathematics is the queen of sciences,

Arithmetic is the queen of mathematics."

Gauss.

Introduction

Every educated person knows such a branch of mathematics as arithmetic, but not everyone can say what contribution Magnitsky made to the development mathematical education Russia. To study the level of awareness about the history of the development of mathematical education in Russia at the beginning of the 18th century, we conducted a sociological survey, in which students in grades 10–11, their parents and school teachers were asked to answer the following questions:

1. Have you heard of such a branch of mathematics as arithmetic?

2. Did you know that in Russia the first arithmetic textbooks were published in 1703?

3. Did you know that the first domestic textbook on mathematics in Russia was published with the participation of Peter 1?

5. Are you familiar with the features of Magnitsky’s “Arithmetic”?

50 students in grades 10–11, 73 parents and 36 teachers from our school took part in the sociological survey. The survey results are shown in the diagram (Annex 1).

Analysis of the results of a sociological survey allows us to conclude that the majority of respondents have heard about such a branch of mathematics as arithmetic, but few are familiar with Magnitsky’s textbook and its features. The study of various sources of information convinces us that some areas of the scientist’s work remain poorly studied, which, of course, affects the low level of awareness about various areas practical activities Magnitsky.

This is what led to the choice Topics our research “The significance of Magnitsky’s “Arithmetic” for the development of mathematical education in Russia.” The topic raised in the research work is very relevant in our time and will be relevant in the near future. The problem of our society’s lack of awareness of Magnitsky’s activities in the field of mathematics is acute at the moment. With this work we would like to systematize information about Magnitsky’s role in the development of mathematical education in Russia and expand the knowledge of our contemporaries about the work of this great man in the field of mathematics.

Hypothesis: Magnitsky's "Arithmetic" has great scientific and methodological merits for its era.

Purpose of the study: determine the significance of Magnitsky’s “Arithmetic” for the development of mathematical education in Russia in the 18th century.

Research objectives:

1. Analyze the factors that influenced the development Russian science from the end of the 17th century.

2. Consider the features of the appearance of the textbook.

3. Study the features of the content of the textbook “Arithmetic”

Main method research work steel theoretical method: analysis of literature on this issue. It was interesting to get acquainted with the classic work of the scientist himself: Arithmetic. 1703 in electronic form, works by Galanin dedicated to Leonty Filippovich Magnitsky and his Arithmetic.

The question of the meaning of Magnitsky’s “Arithmetic” was addressed by many scientists, including modern ones: the historian and teacher of the 19th century Bobynin, Professor Berkov, and the Russian historian Depman.

A lot of material presented on Internet sites was studied.

Practical significance work is to systematize information on the topic of research, popularize knowledge about Magnitsky and his Arithmetic as “one of the most important phenomena of book-printing activity of Peter’s time”1, to develop visual material for use in lessons and extracurricular work in mathematics, in the work of school scientific society. Thus, consideration of issues related to this topic has both theoretical and practical significance.

Chapter I

The influence of Peter I on the development of Russian education,

since the end of the 17th century

In the second half of the 17th century, Russia was experiencing a deep crisis associated with the socio-economic lag behind the advanced countries of Europe. Peter I, with his energy, inquisitiveness, and interest in everything new, turned out to be a man capable of solving the problems facing the country. The transformations of Peter I affected all spheres of public life. The radical reforms he carried out contributed to rapid development in Russia industry, trade, restructuring of military equipment. During this period, the country increasingly needed educated people of various specialties. Peter I decided to open a number of technical educational institutions, but this was hampered by the lack of Russian teachers and comprehensive educational literature in physics, mathematics, and technical disciplines.

______________________________________________________________

It was during this period that the meeting between Peter I and Leonty Telyashin, a native of the Ostashkovskaya settlement of the Tver province, took place. in the field of mathematics surprised many. When they met, he made a very strong impression on Tsar Peter I with his extraordinary mental development and extensive knowledge. As a sign of respect and recognition of his merits, Peter I bestowed on him the surname Magnitsky, “in comparison with how a magnet attracts iron to itself, so he drew attention to himself with his natural and educated abilities”2. In January 1701, Peter issued a decree on the creation of a school of mathematical and navigational sciences in Moscow. Leonty Magnitsky began working as an assistant to Farvarson's mathematics teacher, and then as a teacher of arithmetic and, in all likelihood, geometry and trigonometry. Then he was instructed to write a textbook on mathematics and navigation. Peter I wished “to have in the new school a textbook not of foreign, but of Moscow origin”3. The fact that Magnitsky actually worked on arithmetic from the beginning of February 1701 is evidenced by his receipt for receiving feed money: “As a reward for its compilation, the author received feed money from February 2, 1701 to January 1, 1702 in the amount of 5 altyns per day , and only 49 rubles, 31 alt., 4 money, for which he issued a receipt, which was preserved in the files of the Naval Archive”4.

In 1715, the Moscow Academy was opened in St. Petersburg, the study of military sciences was transferred to the academy, and the Moscow school began to focus on teaching students arithmetic, geometry, and trigonometry.

2,3,4 // Encyclopedic Dictionary of Brockhaus and Efron: In 86 volumes (82 volumes and 4 additional ones). St. Petersburg: 1890-1907.

At the same time, Magnitsky was appointed head of the academic department and senior teacher of mathematics at the Moscow school. Magnitsky worked at the Moscow school until the day of his death, until October 1739. Magnitsky’s “Arithmetic” was published in January 1703, it marked the beginning of the printing of mathematical textbooks in Russia, and later Leonty Magnitsky actively participated in the publication of mathematical and astronomical literature, which was required for the new school.

Analysis of the above facts allows us to conclude that, starting from the second half of the 17th century, Russia began to realize that in order to overcome the crisis of traditionalism, modernization of the country was necessary. Peter I clearly understood the need to overcome the technical backwardness of Russia and in every possible way contributed to the development of Russian science and the level of education of people. Not in words, but in deeds, he considered mathematics the most important academic discipline, and education was the key to successful public policy. This is evidenced by such facts as:

· creation of a school of mathematical and navigational sciences in Moscow;

· opening of the Moscow Academy;

· interest and personal participation of Peter I in the publication of many textbooks.

Chapter II

Features of the appearance of the textbook

In January 1703, Magnitsky’s textbook with a long title was published: “Arithmetic, that is, the science of numbers, from different dialects to Slavic language translated and collected into one and divided into two books... This book was written through the works of Leonty Magnitsky", as stated on title page books. Magnitsky's textbook was published in a huge circulation (by the standards of that time) - 2,400 copies. What is Magnitsky’s “Arithmetic”? A lot has been written about this book. Researchers characterize the content in different ways, but always positively. The author of the book “The History of Mathematics in Russia before 1917,” Yushkevich believes that “for about 50 years it had no competitors and played an extraordinary role in the history of Russian mathematical education.”

Researchers still do not have a common opinion about which manuals Magnitsky used to compile his Arithmetic. Yushkevich believes that handwritten and printed material from an earlier time was used, which Leonty Filippovich carefully selected, substantially processed, composing a new, original work taking into account the knowledge and needs of the Russian reader. Let's turn to appearance and the composition of "Arithmetic". Book size 312 x 203 mm, 662 pages. The letters in this book are Church Slavonic, since there were still five years left before the introduction of a civil font in Russia that adopted the clarity of the Latin alphabet.

Printing in two colors - black and red on thick paper, pages framed from typesetting decorations. The text contains headers, endings, engravings. There is still no consensus on the method of printing a book: from wooden cut boards or movable type. Most researchers believe that “Arithmetic” was printed with movable type, as all books had been printed in Rus' up to that time, starting with Ivan Fedorov. Fonts: Cyrillic in three sizes. The numbers in the text are Slavic, in the examples, problems, tables - Arabic. Others believe that the book was printed using wooden boards on which the text was carved, and therefore it is possible that it was subsequently reprinted with the same boards, without mentioning new editions. Galanin in his book “Leonty Filippovich Magnitsky and his Arithmetic” notes: “If you take several copies of arithmetic and compare them, then in some places you can see how the letters, especially the numbers, have been erased over time, you get a slightly colored spot, and this could only have happened then when the seal was carved on the board. In addition, the surviving copies have the character of uneven print clarity, as if they were printed some earlier from better preserved boards, and others later, when the boards were already quite worn out.”

The book opens with the title page (Appendix 2), on which is written in cinnabar: “Arithmetic, that is, the science of numbers from different dialects into the Slavic language, translated and collected into one, and divided into two books.”

Further printed in black ink: “Now, by the command of the most pious great Sovereign of our Tsar and the great autocrat of all great and small and white Russia: Under the most noble great Sovereign of our Tsarevich and Grand Duke Alexy Petrovich, in the God-saved reigning city of Moscow, typographical embossing for the education of wise-loving Russian youths , and of every rank and age of people was brought into the world, first, in the year from the creation of the world 7211, from the birth of God in the flesh of the word 1703, indict 11, month of Januarius.” This title occupies the entire page, which is surrounded by a border; Below in this frame is printed in rather small letters: “This book was written through the works of Leonty Magnitsky.”

On the reverse side of the title page (Appendix 3) depicts a flower bush surrounded by a vignette with the words: “A man blooms like a village flower”, around there is a geometric pattern, at the top two young men are holding flowers. Under this picture there are poems “To the Young Reader” about the importance of learning arithmetic as necessary in many areas of life.

The next page of the book is the frontispiece. (Appendix 4). The frontispiece is a rather complex composition depicting the Russian coat of arms, below is an image of Pythagoras and Archimedes. Pythagoras with his head uncovered in clothes lined with fur. In his hands he has a board, scales, below - a compass, a ruler, a pen, an inkwell. On the right is Archimedes, wearing a turban and a fur collar. In his hands is a sphere, a table mathematical formulas; Below is a globe, a model of a ship. Near Pythagoras there is a casket and a bag of money, two forms and two bales of goods, a tied bag - in short, the attributes of trade and items necessary for teaching mathematics. Above them in the cartouche is the quatrain: “Arithmetic Politics and other Logistics. And many other publishers at different times of writers.” It must be assumed that the word “politics” attached to “Arithmetic” is given here in the sense of governing the laws of mathematics. Unfortunately, it is not known by whom and how this picture was compiled, whether it is a product of Magnitsky’s own creativity or whether he borrowed it from some foreign work.

Two plates show engravings on copper: the sphere of the world ( Appendix 5), a six-line engraved under the image, and a “wind rose” ( Appendix 6) – both beautifully executed.

The next 11 pages are occupied with “verses on the proposed coat of arms”: “On honor, a cross on the sovereign’s coat of arms to the face of His Royal Majesty the Tsar and Autocrat Peter Alexievich of all Russia.” These verses are a dedication in which the author sets out the purpose of the publication, the contents of the book and names the sources of his work. The author then describes the contents of each part of his book, ending the poetic preface with the words: “And we wish this work to be good for all Russian people.”

The book also has the usual prose preface: “The hardworking and wise-loving reader can rejoice.” It reiterates the purpose of this publication as a teaching aid for newly open school, the contents of the book are stated, there is a philosophical discussion about man as the highest “creatures” - “God created man and took away the dust of the earth, and breathed into him the spirit of life.”

Noteworthy screensaver (Appendix 7), placed before the beginning of the text. It shows an allegorical image of Arithmetic in the form of a woman wearing a crown, sitting on a throne, under a canopy supported by eight “pillars.” She holds a key in her right hand, and rests on a triangle with numbers in her left hand. The throne stands on a dais, five steps lead up to it, on which the following words (from below): number, addition, subtraction, multiplication, division. Around the throne on columns (“pillars”) on the left side of the reader: geometry, stereometry, astronomy, optics; on the right - Mercatorium, geography, fortification, architecture. At the base of the “pillars” on the left: “arithmetic what does”; on the right: “everything is on pillars.” At the top of the pediment in the rays is “Yahweh” - the name of God in Hebrew, below is the saying: “through care and teaching.” The engraving ends with a foliage ornament.

The above facts allow us to conclude that Leonty Magnitsky converted Special attention on the design of your textbook and the role of the preface. Reading it allows you to get answers to the following questions:

· about the importance of learning arithmetic as necessary in many areas of life,

· about the relationship of arithmetic with other sciences,

· about the purpose of creating this book and its contents.

Chapter III

Features of the content of the first domestic textbook on mathematics by Magnitsky in Russia in the 18th century

Let's turn to the content side of the textbook. The textbook, compiled according to the scheme outlined in the table of contents, has gone far from its name - “Arithmetic”. It includes information not only on arithmetic in the modern sense, but also on geometry, as well as applications on applied issues such as navigation, astronomy, and military affairs.

Magnitsky divided the entire work into two books. The actual arithmetic information is presented in the first three parts of the first book:

part 1 – “On integers”,

part 2 – “On numbers broken or with fractions.”

It should be noted that between the 1st and 2nd parts there is a section devoted to the description of ancient measures and coins, measures and weights of the “Moscow state and certain surrounding areas.” This information, of course, was necessary for business people of that time, especially in connection with the widespread development of economic and cultural relations between Russia and European countries.

Part 3 – “About similar rules, in three, five and seven lists.”

After the 3rd part there is an extensive addition “On various actions required for citizenship through the past parts”, in which the author cited a large number of examples of practical content.

Parts 4 and 5 - “On false and fortune-telling rules”, “On progression and square and cubic radixes” - contain, rather, algebraic rather than arithmetic material.

The second book is divided into three parts:

part 1 – “Arithmetic algebra”,

part 2 – “On geometric actions through arithmetic”,

part 3 – “Generally about earthly dimensions and how to navigate

belonging." Part 3 contains a lot of information about determining location necessary for navigation. The book ends with the addition “on the interpretation of various navigational problems through the above loxodromic tables” (“Interpretation of navigation problems through the above logarithmic tables”).

In addition to operations with literal expressions, these books present solutions to quadratic and biquadratic equations, the beginnings of plane and spherical trigonometry, and the calculation of areas and volumes. In Arithmetic, one form of presentation is strictly and consistently carried out: each new rule begins with simple example, then comes the general formulation, which is reinforced by a large number of examples and tasks. Each action is accompanied by a verification rule (“verification”); this is done for both arithmetic and algebraic operations.

Magnitsky's book played a significant role in the development of Russian terminology. He used many mathematical conceptual terms for the first time in Russian literature. Magnitsky first introduced the terms:

multiplier,

divisor,

work,

root extraction,

and replaced outdated words "darkness, legion" with the words "million, billion, trillion, quadrillion."

However, not everything proposed by Magnitsky was strengthened in Russian educational and scientific literature. So, for example, he called the root of a number “bok” or “radix”.

Of course, the progressive tendency of the book was systematic usage Russians names, explanation and replacement with them commonly used at that time in the scientific literature Latin terminology. Russian terminology in arithmetic began to be systematically used only after the publication of Magnitsky’s work. Magnitsky’s Arithmetic, like all textbooks of that time, discusses five operations: numbering, addition, subtraction, multiplication and division. Along with the Russians, Magnitsky also gives their Greek and Latin names in parallel. Magnitsky teaches Russia decimal calculus. What is interesting is that he gives the table of addition and multiplication not in the form in which it was customary to publish it on the last page of a 12-sheet notebook, but only half of it, that is, the commutability of these operations was given immediately. The textbook also covers geometry. For example, the Pythagorean theorem is studied on the problem that there is a tower of a certain height and a staircase of a certain length. How far must the bottom end of the ladder be moved so that the top of the ladder aligns with the top of the tower? The geometry of the circle, inscribed polygons, etc. is also studied. etc. Noteworthy is the large number of problems, the conditions of which are taken from life, everyday life, contemporary with Magnitsky. There are many problems and examples from commercial and military life, construction, etc.

There are tables on separate loose sheets. On one of them, in the first part, the names and comparison of ancient scales and coins are given; at the beginning of the book there are tables of Slavic, Arabic and Roman numbers.

Well, “Arithmetic” ends, of course, with applications of the studied material to life. In particular, the use of logarithmic tables in navigation.

In an effort to make arithmetic entertaining, the author resorts to using:

tasks and examples, interesting and exciting in content;

poems and drawings. The tasks are illustrated with images of the objects discussed in the task conditions. This is a chessboard, a city, towers, a fortress, tents, trees, barrels, cannonballs, bags, built troops, etc.;

entertaining tasks ( Appendix 8);

mathematical fun ( Appendix 9);

problems whose solutions are reduced to equations of the first degree ( Appendix 10).

The above facts allow us to conclude that Magnitsky served as an example of a Russian mathematician who closely linked theory with practice, in particular, he did not separate his scientific interests in mathematics from the problems and possibilities of their practical application in astronomy, geodesy, navigation and navigation. Comparative tables of old measures and measures of that time, original comparisons given in the text, undoubtedly testify to the author’s wide erudition and the fact that his scientific interests included not only mathematics.

Conclusion

Breaking through the cumbersome language of Peter’s time, reading Magnitsky’s “Arithmetic” allows one to discover many interesting features of “one of the most important phenomena of book-printing activity of Peter’s time,” according to Professor Berkov. Magnitsky’s “Arithmetic” truly has major scientific and methodological advantages for its era, thanks to the author’s specific innovations when creating his textbook. Magnitsky’s textbook uses the traditions of Russian mathematical manuscripts, but his work does not copy them; the system of presentation of the material is significantly improved in it:

The following scheme for studying the rules is introduced:

simple example → general formulation of a new rule → reinforced with a large number of examples and tasks → verification,

· there is a smooth transition to the new,

systematic use Russian names,

· definitions are introduced,

· new sections appear,

· tasks and additional information are provided,

· techniques are used to promote the reader’s interest in studying mathematics.

The first Russian textbook in mathematics is a link between the traditions of Moscow handwritten literature and the influences of new, Western European literature. Magnitsky’s “Arithmetic” became the first Russian encyclopedia on various branches of mathematics, astronomy, geodesy, navigation, and navigation, despite the fact that the title only mentioned the original mathematical field. Satisfying the requirements that could be presented to a mathematics textbook in Russia in the first half of the 18th century, Magnitsky’s “Arithmetic” was widely used for a long time and fell out of use around the mid-50s of the 18th century. Entire generations of workers in physical and mathematical sciences in Russia were brought up on it. Based on its content, one can form an idea about the direction and nature of teaching arithmetic in Russia in the first half of the 18th century and about the quality of knowledge delivered by this teaching.

Bibliography

1. Magnitsky. Arithmetic. 1703._ e-book

2. Magnitsky. Arithmetic (issue 1 of the reprint by P. Baranov). 1914. _ e-book

3. // Encyclopedic Dictionary of Brockhaus and Efron: In 86 volumes (82 volumes and 4 additional ones). St. Petersburg: 1890-1907.

4. P. Figures national history. Biographical reference book. Moscow, 1997

5. Journal “Physical and Mathematical Sciences in their Present and Past”, vol. VII, pp. 205-210 and 267-308, and vol. VIII, pp. 28-47 and 106-145.

6. Magnitsky and his Arithmetic. Issue_ e-book

7. Galanin. Leonty Filippovich Magnitsky and his Arithmetic. Issue 2,_e-book

Internet resources

1 . http://www. /ru/mov/magn/index. php

3. http://www. infantata. org/2007/08/24/magnickijj_lf_arifmetika. html

4. http://www. /science/mathematics/magnickiy/

5. http://dic. /dic. nsf/ruwiki/222703

6 . http:///forum/viewtopic. php? t=1132816

7. http:///magnitskij. html

Electronic manuals

1. Great Encyclopedia of Cyril and Methodius 2006

2. Great Soviet Encyclopedia

Annex 1

Appendix 2

Title page from “Arithmetic” by Magnitsky

Appendix 3

Reverse side of the title page from “Arithmetic” by Magnitsky.

Woodcut

Appendix 4

Frontispiece from “Arithmetic” by Magnitsky. Copper engraving by M. Karnovsky

Appendix 5

“Sphere of Peace”

Appendix 6

"Rose of Wind"

Copper engraving by M. Karnovsky from “Arithmetic” by Magnitsky

Appendix 7

“Arithmetic on the throne.”

Woodcut from “Arithmetic” by Magnitsky

Appendix 8

Entertaining tasks

From Magnitsky's Arithmetic: A certain man sells a horse for 156 rubles; Having repented, the merchant began to give it to the seller, saying: “I can’t afford to take a calico horse, unworthy of such high prices.” The seller offered to buy another, saying: “And it seems that the price of this horse of existence is great, because buy a nail, this horse will have them in the horseshoes of your feet, and take the horse for that purchase as a gift for yourself. And there are six nails in each horseshoe, and for one nail give me a half-ruble, for another - two half-rubles, and for the third a kopeck, and so buy all the nails.” The merchant, seeing such a small price and even taking the horse as a gift, promised to pay such a price, giving no more than 10 rubles per nail. And it’s in charge of how much the merchant has bargained with?

In modern Russian this means the following: One man sold a horse for 156 rubles; the buyer began to give the horse to the seller, saying: “It’s not good for me to buy this horse, since he is not worthy of such a high price.” Then the seller offered other conditions, saying: “If this price seems too high to you, pay only for the nails in the horseshoes, and take the horse as a gift. There are six nails in each horseshoe, and for the first nail give me half a ruble, for the second - two half rubles, for the third - a penny (that is, four half rubles), etc.” The buyer, seeing such a low price and wanting to receive a horse as a gift, agreed to this price, thinking that he would have to pay no more than 10 rubles for the nails. You need to find out how much the buyer bargained for.

Appendix 9

Math fun

In Magnitsky’s “Arithmetic,” fun forms a special section “On certain comforting actions used through arithmetic.” The author writes that he puts it in his book for pleasure and especially to sharpen the minds of students, although these amusements, in his opinion, “are not very necessary.”

First fun . One of the eight people in the company takes the ring and puts it on one of the fingers on a certain joint. You need to guess who has the ring, on which finger and on which joint.

Let the fourth person have the ring on the second joint of the fifth finger (it must be agreed that the joints and fingers are numbered the same for everyone).

The book gives this method of guessing. The guesser asks someone from the company to do the following without naming the resulting numbers:

1) the number of the person who has the ring, multiply by 2; the person asked in his head or on paper fulfills: 4 x 2 = 8

2) add 5 to the resulting product: 8+5=13

3) multiply the resulting amount by 5: 13 x 5=65

4) add to the product the number of the finger on which the ring is located: 65+5=70

5) multiply the amount by 10: 70 x 10 = 700

6) add to the product the number of the joint on which the ring is located: 700+2=702

The result is announced to the guesser.

From the resulting number the latter subtracts 250 and receives: 702 – 250 = 452

The first digit (going from left to right) gives the person's number, the second digit is the finger number, the third digit is the joint number. The ring is on the fourth person's fifth finger on the second knuckle.

It is not difficult to find an explanation for this technique. Let a person with number a have a ring on a finger with number b on a joint with number c

Let's perform the following actions on the numbers a, b c:

1) 2 x a = 2a

3)5 (2a+5)=10a+25

5)a+25+ b)=100a+250+10 b

6) 100a+10 b+250+s

7) 100a+10 b+250+s-250=100a+10 b+s

We got a number in which the person’s number is the hundreds digit, the finger number is the tens digit, and the joint number is the units digit. The rules of the game apply to any number of participants.

Second fun. We count the days of the week, starting from Sunday: first, second, third, and so on until the seventh (Saturday).

Has anyone thought about the day? You need to guess what day he has in mind.

Let Friday be the sixth day.

The guesser suggests performing the following actions silently:

1) multiply the number of the planned day by 2: 6 x 2=12

2) add 5 to the product: 12+5=17

3) multiply the amount by 5: 17 x 5=85

4) add zero to the product and call the result 850.

From this number the guesser subtracts 250 and gets: 850-250=600

The sixth day of the week was conceived - Friday

Appendix 10

False position rule or "false rule"

Let us present the solution to the problem using the false position method, or “false rule” from Magnitsky’s book:

Someone asked a teacher: how many students do you have in your class, since I want to enroll my son in your class? The teacher replied: if as many more students come as I have, and half as many and a quarter and your son, then I will have 100 students. The question is: how many students did the teacher have?

Magnitsky gives this solution.

Let's make the first assumption: there were 24 students.

Then, according to the meaning of the problem, to this number we need to add “that much, half that much, a quarter that much and 1”, we would have:

24+24+12+6+1=67,

that is, 100 – 67 = 33 less (than required by the conditions of the problem), the number 33 is called the “first deviation”.

We make the second assumption: there were 32 students. Then we would have:

32+32+16+8+1=89,

that is, 100 – 89 = 11 less, this is the “second deviation”.

In case both proposals result in less, the rule is given: multiply the first guess by the second deviation, and the second guess by the first deviation, subtract the smaller product from the larger product and divide the difference by the difference in deviations:

32 x 33 – 24 x 11

There were 36 students.

The same rule should be followed if, under both assumptions, the result is more than expected according to the condition. For example:

First guess: 52

52+52+26+13+1=114

We received 144 – 100 = 44 more (first deviation).

Second guess: 40

40+40+20+10+1=111

We received 111 – 100 = 11 more (second deviation)

40 x 44 – 52 x 11

If under one assumption we get more, and under another less, than required by the conditions of the problem, then in the above calculations it is necessary to take not the differences, but the sums.

With the help of the most basic information of algebra, these rules are easily justified.

With the enormous participation of Peter the Great, the first domestic textbook on mathematics was published in Russia. The year is 1703. Leonty Filippovich Magnitsky publishes Arithmetic. Leonty Filippovich's work was not translated; there were no analogues of the textbook at that time. This was a unique book. The textbook contains more than 600 pages and includes both the very beginning - a table of addition and multiplication of decimal numbers, and applications of mathematics to the navigational sciences.

From the preface of the book it is clear that it was printed by order of Peter Ⅰ “for the sake of teaching the wise-loving Russian youths and all ranks and ages of people.” Magnitsky did a great job to make the material presented in the book accessible and interesting to the reader. Many paragraphs end with poems that summarize what has been learned. Here, for example, is a wish from the preface to the book:

“And we wish this work to be

It’s good for all Russian people to use it.”

In Magintsky’s “Arithmetic”, for the first time in Russia, such “Arabic” numerals, which are now primary to us, were used for calculations.

The title page shows the emblem in the center Russian Empire, on the left is a merchant, symbolizing “politics”, on the right is a scientist, personifying “logistics”. On the vignette is the inscription “Arithmetic, politics with it, other logistics of the most eminent publishers in equal times written.” Pythagoras and Archimedes are written on the ribbons fluttering on the sides. The introduction says: “Arithmetic, or numerator, is an honest art, unenviable and understandable to everyone, most useful and much praised, invented and expounded by the most ancient and modern arithmeticians who appeared at different times.” In this definition, “art” must be understood as a skill, “honest” - worthy, “unenvious” - objective. Generations of Russian people studied from this book. Lomonosov called it “the gateway of his learning” and knew a lot by heart. Several copies of “Arithmetic” were carefully preserved in the Department of Rare Books and Manuscripts of the Moscow University Library.

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Ministry of Science and Education of the Russian Federation

State educational institution higher professional education

"Transbaikal State University"

Department of Hydrogeology and Engineering Geology

Report on the topic:

" ArithmeticL.F.Magnitsky"

Completed by: Kolesnikova K.O.

Chita 2014

Introduction

Our acquaintance with mathematics begins with arithmetic, the science of number. We enter with arithmetic, as M.V. said. Lomonosov, to the “gates of learning” and begin our long and difficult, but fascinating journey of understanding the world. arithmetic Magnitsky number

The word "arithmetic" comes from the Greek arithmos, which means "number". This science studies operations with numbers, various rules for handling them, and teaches how to solve problems that boil down to addition, subtraction, multiplication and division of numbers. Arithmetic is often imagined as some kind of first stage of mathematics, based on which one can study its more complex sections - algebra, mathematical analysis, etc. Even whole numbers - the main object of arithmetic - are referred when they are considered general properties and patterns, to higher arithmetic, or number theory.

One of the first Russian arithmetic textbooks, written by L.F. Magnitsky in 1703, began with the words: “Arithmetic, or the numerator, is an honest, unenviable art, and conveniently understandable for everyone, most useful and much praised, invented and expounded by the most ancient and modern arithmeticians who lived at different times.” It was Leonty Filippovich Magnitsky who laid the foundation for the development of Arithmetic in Russia.

Biography

Leonty Filippovich Magnitsky was born on June 9, 1669 in the Ostashkovskaya settlement of the Tver province. Russian mathematician, teacher. Author of the first educational reference book on mathematics in Russia.

From 1685 to 1694 he studied at the Slavic-Greek-Latin Academy. Mathematics was not taught there, which suggests that he acquired his mathematical knowledge through independent study of manuscripts, both Russian and foreign.

Leonty Filippovich's knowledge in the field of mathematics surprised many. When they met, he made a very strong impression on Tsar Peter I with his extraordinary mental development and extensive knowledge. As a sign of respect and recognition of his merits, Peter I “bestowed” him the surname Magnitsky “in comparison with how a magnet attracts iron to itself, so he drew attention to himself with his natural and self-educated abilities.”

In 1701, by order of Peter I, he was appointed teacher of the school of “mathematical and navigational, that is, nautical and cunning sciences of teaching,” located in the building of the Sukharev Tower.

In 1703, Magnitsky compiled the first educational encyclopedia in mathematics in Russia under the title “Arithmetic, that is, the science of numbers from different dialects into the Slavic language, translated and collected into one, and divided into two books” with a circulation of 2,400 copies. As a textbook, this book was used in schools for more than half a century due to its scientific, methodological and literary merits.

Leonty Filippovich died in Moscow in October 1739 at the age of 70.

Eastorigin of creation.

"Arithmetic" L.F. Magnitsky is one of the most famous Russian books, rightfully belonging to the monuments of national written culture. So, on February 22, 1702 L.F. Magnitsky was ordered a mathematics textbook, and funds were allocated for its compilation and printing. In an extremely short time - within 9 months - he created an educational mathematical book that was unique in its qualities, which was published in a large circulation for that time. It had a magnificent and long name according to the customs of that time: “Arithmetic, that is, the science of numbers. different languages translated into the Slavonic language, and collected together, and divided into two books."

It was published in Moscow in January 1703 and played an extraordinary role in the history of Russian mathematical education: for half a century it was unusually popular and had no competitors both in the few schools of that time and in wider reading circles, including among self-taught.

Characteristics of the book.

Such extraordinary popularity is largely due to the fact that despite the indication in the subtitle about the translated nature of the book, in fact it was quite original both in content and in methodologically an essay that was a connecting link between the traditions of Moscow handwritten educational literature and the influences of the new Western European. Well Knew foreign languages, Magnitsky studied a large number of European textbooks, books by Greek and Latin authors, Russian mathematical manuscripts and used all these materials in working on the textbook.

Magnitsky's "Arithmetic", directly or indirectly, in turn, had a great influence on all subsequent Russian mathematical literature. Much has been written in detail about Magnitsky’s Arithmetic. Let's give brief description this unique book.

Multifunctionality. Following the traditions of Russian handwritten educational literature, Magnitsky included purely, so to speak, “epic” material in “Arithmetic”: it described the “acts of Peter” and therefore could to some extent serve as a textbook of modern Russian history.

In addition, “Arithmetic” contained a large number of general philosophical discussions, advice to the reader, and general conclusions, often presented in poetic form, which enhanced its educational impact. Since it was a textbook for future navigators, it contained information on meteorology, astronomy and navigation, as well as numerous data on natural science and technology, which allows us to consider “Arithmetic” the forerunner of Russian printed popular science literature, although the main content of the book is all- it's mathematics.

The title of the book is much narrower than its mathematical content, since in addition to arithmetic information, it also presents significant algebraic, geometric material, elements of plane and spherical trigonometry. Thus, from a content point of view, “Arithmetic, that is, the science of numbers...” is more of an encyclopedia of mathematical knowledge contemporary to the author than a simple arithmetic textbook.

Number systems. Magnitsky uses the Indo-Arabic decimal positional number system in Arithmetic, only briefly explaining the Latin one and mentioning the Slavic one. Pagination (page numbering) is also Slavic. When characterizing the number system, Magnitsky uses a unique terminology that remained in mathematics textbooks until the end of the 18th century. He calls all the numbers in the first ten fingers; tens, hundreds, etc. (numbers like 30, 900, ...) - with joints, all other numbers - with compositions. Magnitsky calls significant figures signs, in contrast to zero, which is called a number.

Magnitsky's arithmetic operations have two names - Latin and Russian: numeratio, or notation; addicio, or addition; subtraction, or subtraction; division, or division. Numbering, as before, is highlighted as a special action.

Magnitsky pays special attention to numbers of the form 10n (n is a positive integer) and their names. The old counting of darkness, legions, etc. has been replaced by the generally accepted in Europe millions, billions, trillions and quadrillions (each class contains 6 decimal places).

Here, for the first time in Russian mathematical literature, 0 is elevated to the rank of a number: Magnitsky ranks it among the “fingers” (the first 10 numbers) and is thus far ahead of his time.

Structure of the book. Big volume, with a volume of over 600 pages, Magnitsky’s “Arithmetic” consists of 2 arithmetic books: “Arithmetic of politics, or civil” and “Arithmetic of logistics, not only to citizenship, but to the movement of celestial circles.” The third book is about navigation.

The book is unique not only for its history, but also for its content. It is interesting to note that, in addition to the amazing modern reader addition tables already on the second page of addition examples there are problems for finding the sum of six six-digit numbers, and on the third page an example of adding seventeen four-digit numbers is demonstrated. Squaring arises from the Pythagorean theorem using the example of a ladder 125 feet long attached to a tower 117 feet high.

What is Magnitsky’s “Arithmetic”? A lot has been written about this book. Researchers characterize the content in different ways, but always positively. Professor P.N. Berkov calls "Arithmetic" "one of the most important phenomena of book-printing activity of Peter's time." Nowadays it is called an encyclopedic book on various branches of mathematics and natural science (geodesy, navigation, astronomy). Researchers still do not have a common opinion about which manuals Magnitsky used to compile his Arithmetic. A.P. Yushkevich believes that handwritten and printed material from an earlier time was used, which Leonty Filippovich carefully selected, substantially processed, composing a new, original work taking into account the knowledge and needs of the Russian reader.

Magnitsky divided the entire work into two books. The actual arithmetic information is presented in the first three parts of the first book. Part 1 - “On whole numbers”, part 2 - “On broken numbers or with fractions”, part 3 - “On similar rules, in three, five and seven lists”, parts 4 and 5th - “On false and fortune-telling rules”, “On progression and radixes of square and cubic” - contain, rather, algebraic rather than arithmetic material. The second book is divided into three parts: part 1 - “Arithmetic and algebra.” Part 2 - “On geometrics operating through arithmetic”, part 3 - “General about earthly dimensions and how they belong to navigation.” In addition to operations with literal expressions, these books present solutions to quadratic and biquadratic equations, the beginnings of plane and spherical trigonometry, and the calculation of areas and volumes. Part 3 contains a lot of information about determining location necessary for navigation. The book ends with the addition “On the interpretation of various navigational problems through the above loxodromic tables.”

Magnitsky first introduced the terms “multiplier”, “divisor”, “product”, “root extraction”. Replaced the obsolete words "darkness, legion" with the words "million, billion, trillion, quadrillion."

In "Arithmetic" one form of presentation is strictly and consistently carried out: each new rule begins with a simple example, then comes a general formulation, which is reinforced by a large number of examples and problems. Each action is accompanied by a verification rule (“verification”); this is done for both arithmetic and algebraic operations.

Examples of problems and their solutions.

1. One person came to the teacher at school and asked the teacher: “How many students do you have? I just want to give you my son to study. Will I embarrass you?” In response, the teacher said: “No, your son will not embarrass my class. If as many as there were to come to me, half as much, and a quarter of that, and even your son, I would have 100 students.” How many students did the teacher have?

Let one set of students be X. Then we get the equation:

x + x + 1/2*x + 1/4*x + 1 =100

(2 + 3/4)*x = 99.

Hence x = 36 students. Answer: 36 students.

2. Someone sold a horse for 156 rubles. But the buyer, having acquired the horse, changed his mind and returned it to the seller, saying: “I have no reason to buy a horse for this price that is not worth that kind of money.” Then the seller offered other conditions: “If you think the price of a horse is high, then buy its horseshoe nails, and then you will get the horse for free. There are 6 nails in each horseshoe. For the first nail give me ¾ kopecks, for the second - ½ kopecks, for the third - 1 kopeck, etc." A buyer lured by a low price. And wanting to get a horse for free, he accepted the seller’s terms, calculating that he would have to pay no more than 10 rubles for the nails.

1. Let's create a sequence of numbers ј; S; 1; 2; 22;…221 .

2. This sequence is a geometric progression with denominator q=2, b=1/4, n=24.

4. Knowing the formula

Answer: 42,000 rubles.

Conclusion

The influence of this book on the development of physical and mathematical knowledge and research in Russia was very great. It is not for nothing that when they talk about Magnitsky’s “Arithmetic”, they always remember the words of M.V. Lomonosov, who called it “the gateway to his learning.” It was the “gateway of learning” not only for Lomonosov, but also for a number of generations of Russian people who did a lot to educate the country. In addition, it must be taken into account that, in addition to arithmetic knowledge, it also contained algebraic, geometric, trigonometric, astronomical and navigational information, so Magnitsky’s work was in fact a kind of encyclopedia of mathematical knowledge and provided quite extensive applied information.

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Municipal budgetary educational institution “Bernovskaya secondary school named after A.S. Pushkin"

Research work in mathematics

Klyuchnikova Valentina

8th grade

Head Zemtsova M.V.

Math teacher 1st category

S. Bernovo

year 2013

Introduction

Chapter 1 Biographical information about L.F. Magnitsky

Chapter 2 “Arithmetic” is a unique book.

2.1.Magnitsky arithmetic

2.2.Appearance of "Arithmetic"

2.3. Structure and content of the textbook

2.4.Forms of presentation

2.5.Words and symbols

Chapter 3 Problems from Arithmetic

3.1.Triple rule

3.2. False rule

3.3 Arithmetic fun

Conclusion

Bibliography

Applications

Annex 1

Appendix 2

Introduction.

Topic: Magnitsky Arithmetic

Relevance and choice of topicresearch work is 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.
L. F. Magnitsky comes from the Tver province
L. F. Magnitsky teacher of teachers

Problem:

Increasing interest in the history of mathematics
Learning ancient ways to solve problems
Instilling problem solving skills

Target:

Studying the history of mathematics education in Russia

Tasks:

Study biographical information about L.F. Magnitsky and his contribution to the development of mathematical education in Russia
Review the contents of the textbook
Solve some problems
Compare ancient and modern methods solutions

Hypothesis: If I get acquainted with the biography of L.F. Magnitsky and compare some methods of solving problems, I can tell school students about this, this will help increase interest in studying mathematics

Research methods. Studying literature, information found on the Internet, analysis, establishing connections between Magnitsky solutions and modern ones studied in a school mathematics course

Chapter 1

What do we know about L. F. Magnitsky

Leonty Filippovich Magnitsky is the first mathematics teacher of Russian youth, the author of the first mathematics textbook. He has not been forgotten for more than three centuries, but it is surprising that very little is known about his personality. Even the last name under which he arrived in Moscow and studied here is unknown. But I managed to find out some Interesting Facts from this person's life.

Leonty Filippovich Magnitsky (born Telyashin; June 9 (19), 1669, Ostashkov - October 19 (30), 1739, Moscow) - Russian mathematician, teacher. Mathematics teacher at the School of Mathematical and Navigational Sciences in Moscow (from 1701 to 1739), author of the first educational encyclopedia on mathematics in Russia.

Born in the Ostashkovskaya Patriarchal Settlement. The son of the peasant Philip Telyashin. WITH youth Leonty works with his father in the arable land, he himself learns to read and write, and was a passionate hunter to read and understand complicated and difficult things. He was the nephew of Archimandrite Nektariy, the organizer of the Nilova Heathland near Ostashkov, Tver province, and therefore had access to church books.

Leonty Filippovich's knowledge in the field of mathematics surprised many; upon meeting, he made a very strong impression on Tsar Peter I with his extraordinary mental development and extensive knowledge. As a sign of respect and recognition of his merits, Peter I bestowed on him the surname Magnitsky, “in comparison with how a magnet attracts iron to itself, so he drew attention to himself with his natural and self-educated abilities.”

1694-1701 Magnitsky lives in Moscow, teaches children in private homes and engages in self-education. 1701, by order of Peter I, he was appointed teacher of the school of “mathematical and navigational, that is, nautical and cunning sciences of teaching,” located in the building of the Sukharev Tower.

1703 compiled the first educational encyclopedia in mathematics in Russia under the title “Arithmetic, that is, the science of numbers from different dialects into the Slavic language, translated and collected into one, and divided into two books” with a circulation of 2,400 copies. As a textbook, this book was used in schools for more than half a century due to its scientific, methodological and literary merits.

From 1732 to last days During his life, L.F. Magnitsky was the head of the Navigat school.

He died in October 1739 at the age of 70.

“Magnitsky was buried in the Church of Our Lady of Grebnevskaya, which was located in Moscow at the corner of Lubyansky Proezd and Myasnitskaya Street.

In 1932, during the construction of the metro, this church was dismantled. On May 27, at a depth of one meter, a small slab of strong limestone was discovered, on back side which actually turned out to be a finely engraved “epitaph” of L.F.’s tombstone. Magnitsky. The next day, Magnitsky’s tomb was discovered under the monument slab at a depth of four meters. It was made of good brick and filled with lime on all sides. In the grave there was an oak log, in which lay the intact skeleton of Leonty Filippovich with some coverings preserved on it, in particular, the boots were relatively well preserved; Under the head there was a glass inkwell shaped like a lamp, and next to it lay a half-decayed goose feather. Together with the tomb of Leonty Filippovich there was the tomb of Maria Gavrilovna, Magnitsky’s wife, where an inscription was carved on the stone, announcing her sudden death during an unexpected meeting with her son, whom she considered dead.”

On the slab-monument to L.F. Magnitsky has a skillfully embossed text written by his son Ivan, from which one can obtain reliable biographical information about Magnitsky:

2. the surname Magnitsky was given by Tsar Peter I in 1700 and his surname was unknown until that time;

3. Magnitsky “learned science in a marvelous and incredible way”; This excludes him from being a student at the Theological Academy;

4. Magnitsky was appointed teacher of Russian youth;

Conclusion

While working with scientific literature, I learned a lot of interesting things from the history of the development of mathematics.

It was L.F. Magnitsky who created the textbook from which entire generations in Russia studied.

L. F. Magnitsky contributed to the success of Peter's reforms in the field of education.

L. F. Magnitsky was a permanent teacher at the Navigation School for almost four decades, and then its main leader.

L. F. Magnitsky first introduced the terms: multiplier, divisor, product, root extraction.

L. F. Magnitsky replaced the outdated words darkness, legion with the words million, billion, trillion, quadrillion.

Leonty Filippovich's work was not translated; there were no analogues of the textbook at that time. "Arithmetic" is a unique book.

Chapter 2

2.1 Magnitsky arithmetic

With the great participation of Peter, the first domestic textbook on mathematics is published in Russia. The year is 1703. Leonty Filippovich Magnitsky publishes Arithmetic. Leonty Filippovich's work was not translated; there were no analogues of the textbook at that time. The textbook contains more than 600 pages and includes both the very beginning - a table of addition and multiplication of decimal numbers, and applications of mathematics to the navigational sciences.

In 1703, the first Russian printed manual was published under the long title “Arithmetic, that is, the science of numbers, translated from different dialects into the Slovenian language and collected into one and divided into two books... This book was written through the works of Leonty Magnitsky.” The book contained information from mechanics, physics, hydraulics, meteorology, navigation, shipbuilding, etc., that is, scientific material that was of exceptional importance for the entire Russian people, including the Pomors and M.V. Lomonosov.

2.2.Appearance of “Arithmetic”

The design of the book is quite modest, but original. The frames are made of inlaid decorations, while the headpieces and endings are carved on wood. The size of the book is 312 x 203 mm, it has 331 sheets, that is, 662 pages typed in Slavic font. Printed in two colors - black and red on thick paper, pages framed from typesetting decorations. The text contains headers, endings, engravings.

2.3.Structure and content of the textbook.

Almost every old Russian manual on mathematics begins with an explanation of the meaning of this science for humans. The invention of arithmetic and geometry is most often attributed to Pythagoras (Greek philosopher and mathematician of the 6th century BC). Magnitsky continues this tradition. In his “Arithmetic” on the title page, he depicted, in addition to Pythagoras, also Archimedes, and wrote: Archimedes is presented here, The ancient philosopher is great, where with him another equal to him is presented to your face. The same Archimedes and Pythagoras, like water from the mountains, were the first to gain, writers of the sciences of China, pouring out like waters, publishing many sciences into the world

Magnitsky divided the entire work into two books. The actual arithmetic information is presented in the first three parts of the first book. Part 1 – “On whole numbers”, part 2 – “On broken numbers or with fractions”, part 3 – “On similar rules, in three, five and seven lists”, parts 4 and 5th - “On false and fortune-telling rules”, “On progression and radixes of square and cubic” - contain, rather, algebraic rather than arithmetic material.

2.4.Form of presentation.

The book strictly and consistently followed one form of presentation: each new rule began with a simple example, then its general formulation was given, and, finally, it was reinforced by a large number of tasks, mostly of practical content. Each action was accompanied by a verification rule - “behavior”.

Gate of learning

The great Russian scientist M.V. Lomonosov called Magnitsky’s “Arithmetic” “the gates of his learning.” This book was the “Gateway of Learning” for all those who strived for education in the first half of the 18th century. Many people's desire to always have Magnitsky's book at hand was so great that they copied it by hand.

2.5.Words and symbols

In “Arithmetic”, “numeration, or reckoning” is highlighted as a special action. It says: “numeration is the counting in words of all numbers that can be represented by ten such signs: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. Of these, nine are significant; the last one is 0, if there is one, then in itself it has no meaning. When it is added to some significant one, it increases it tenfold, as will be shown later.”

Conclusion:

In the process of research: I found out that Magnitsky’s textbook used the traditions of Russian mathematical manuscripts, but the system of presenting the material was significantly improved: definitions are introduced, a smooth transition to something new is carried out, new sections and problems appear, additional information is provided; I was convinced that Magnitsky’s “Arithmetic” played a big role in the dissemination of mathematical knowledge in Russia. No wonder Lomonosov called it “the gate of learning.”

Chapter 3.

Problems from Magnitsky Arithmetic using the Triple Rule

Problems solved by the triple rule have at all times constituted the majority of problems in practical arithmetic among all peoples. A person encounters quantities that are directly or inversely proportional to each other at every step, and he used common sense to solve problems about the meaning of such quantities.

The relationship of Russian mathematical manuscripts of the 17th century. To the triple rule:

This - “a commendable line and the best of other lines, which philosophers call the golden line”

Line called the triple rule because to mechanize calculations, data was written in a line. For directly proportional quantities, data should be written in one order, for inversely proportional quantities - in another. Examples:

For 2 rubles you can buy 6 items. How many of them can you buy for 4 rubles?

The data for this task should be written in a line like this: 2 – 6 – 4.

20 workers can complete a job in 30 days. How many workers can do the same work in 5 days?

The data for this task should be written in a line like this: 5 – 20 – 30.

In both cases, you need to multiply the second and third numbers and divide the product by the first. This rule is communicated to the student. Therefore, Magnitsky at the end of the section says:

And look above all

Reason (sense) in the task,

Because you know

How to write this.

Currently, such problems are solved using proportions (or by actions)

Entertaining tasks:

One person drinks a keg of kvass in 14 days, and together with his wife drinks the same keg of kvass in 10 days. You need to find out how many days it takes your wife to drink the same keg of kvass alone.

Solution: 1)14*10=140 2)14-10=4 3)140/4=35(days)

How much does a kaftan cost?

The owner hired a worker for a year and promised to give him 12 rubles and a caftan. But he, having worked only 7 months, wanted to leave. Upon settlement, he received a caftan and 5 rubles. How much does a kaftan cost?

Solution:

Problems from Arithmetic on "False Rule"

Starting to present the “false rule,” Magnitsky states:

This part is very cunning,

Like you can put everything with it,

Not only what is in citizenship,

But also higher sciences in space

As the wise have needs

Here is an example of the layout of calculations when applying Magnitsky's false rule:

Task

Someone asked the teacher: how many students do you have in your class, because I want to teach my son. The teacher answered: if as many more disciples come as I have, and half as many and a quarter and your son, then I will have 100 disciples.

Solution using a "fake rule". Let's assume that there were 24 students in the class. If the same number of students come and then half as many, then a quarter as many and finally one more student, then the total will be

24+24+12+6+1=67 students. You guessed wrong.

If we assume that there are 32 students in the class, then, after doing the same calculations, we get

32+32+16+8+1=89 students. We didn't guess right again.

24 33

100 - 67 =33 100 – 89 =11

24×11 =264 33×32 =1056

1056 – 264 =792 33 – 11 =22

32 11 therefore, there were 792 in the class: 22 =36 students.

Today we solve such problems using the equation

X +X +0.5X +0.25X + 1 =100

2.75X =99

X =99: 2.75

X =36

Answer: 36 students.

Conclusion:

Magnitsky’s “Arithmetic” contains many entertaining problems, as well as problems of practical content. I tried to solve some of them, and I succeeded. Problems from the textbook by L. F. Magnitsky develop logical thinking and force one to look for non-standard approaches to solving them. Solving them is fun.

Magnitsky's arithmetic fun

1.How to find out the day of the week?

After numbering the days of the week, starting from Monday, in order from 1 to 7, invite someone to wish for a certain day of the week. Then suggest serial number increase the planned day by 2 times and add 5 to this product. Offer to multiply the resulting amount by 5, and then multiply the result by 10. Based on the announced result, you name the day of the week that was planned.

How to find out the hidden day of the week?

2.Who has the ring?

Having renumbered those present and turned away from them, invite someone to take the ring and put it on some hand on some finger. Then ask to double the serial number of the person who took the ring, and add 5 to the result obtained. Ask to multiply the resulting amount by 5 and add the finger number to it, counting from the little finger. Ask the resulting amount to be multiplied by 10 again, and add the number 1 to the result if the ring is worn on the left hand and the number 2 if the ring is worn on the right hand. After announcing the result of the arithmetic operations you proposed, you will guess which of those present took the ring and on which finger of which hand they put it on.

How to determine this based on the announced result?

3. Guess several numbers.

Invite someone to think of several (you know the number) single-digit numbers. Then offer the first of the conceived numbers

multiply by 2 and add 5 to the resulting product. Ask the resulting number to be multiplied by 5 and to the result, ask to add 10 and the second number you have in mind. Then you need to carry out such operations as many times as there are unused planned numbers left. Multiply the number obtained from previous actions, but 10 and add the next intended number to the product. After announcing the result of your proposed actions, you announce what numbers were intended.

Conclusion

By carrying out this research work, I enriched my knowledge in the field of the history of mathematics, learned a lot from the biography of the great Russian scientist - the man who first published a printed textbook on mathematics in Russia. I learned a new way for me to solve problems, which at first glance seemed incredible to me, however, it leads to the right results. And once again I was convinced that mathematics is an unexpected, interesting science that develops human thinking and knowledge.

Acquired skills in conducting research work and preparing presentations for work.

In July 2013, with a group of students from our school, I visited a monastery in the Nilovo-Stolbenskaya hermitage. When visiting the museum, there was a meeting with the director of the Verkhnevolzhsky spiritual and educational center "Seliger's Legacy" named after Leonty Filippovich Magnitsky, who told us about the work to preserve the memory of the great scientist, the first teacher of mathematics, teacher of teachers, our fellow countryman. The center is working on naming the name L.F. Magnitsky Tver State University.

Bibliography.

1. Andronov I.K. The first mathematics teacher of Russian youth Leonty Filippovich Magnitsky // Mathematics at school. 1969. No. 6.

3. Glazer G.I. History of mathematics at school. Manual for teachers. – M.: “Enlightenment”, 1981. – 239 p.

From the arithmetic of Magnitsky. Oral arithmetic magazine for schoolchildren

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