From the arithmetic of Magnitsky. The importance of Magnitsky’s “arithmetic” for the development of mathematical education in Russia

Many people have heard about “Arithmetic” by Leonty Filippovich Magnitsky, from which Russian youths studied for two centuries, but not everyone knows that it was created as a textbook for future, studied in.
Not much is known about the creator of the unique textbook, Leonty Magnitsky. Most of the information about him dates back to the years when he was already teaching at the Navigation School. All that is known about his childhood years is that he was born into a peasant family in the Ostashkovo monastery settlement on the shores of Lake Seliger. 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 at that time was the main educational institution in Russia. Leonty studied at the academy for about eight years.
It is curious that mathematics, which Magnitsky then studied for the rest of his life, was not taught at the academy. Consequently, Leonty studied it on his own, as well as the basics of navigation and astronomy. After graduating from the academy, Leonty did not become a clergyman, as the abbot who sent him to study had hoped, but began to teach mathematics, and possibly languages, to families .
It was in Moscow that he met with , who knew how to find people useful for Russia, no matter what strata of society they came from. The rootless teacher, who did not even have a surname, who pleased the king for his deep knowledge, received a unique gift from the monarch. Peter ordered him to henceforth be called Magnitsky, since he attracted youths to himself with his learning, like a magnet. For modern people the significance of this gift is not entirely clear, but at that time only representatives had surnames .
There are references in the literature that Leontius was protected by Archimandrite Nektary (Telyashin), who allegedly knew the tsar. This is a mistake; the coincidence of the archimandrite’s surname and the nickname of Leonty’s father does not mean that they were relatives, and Nektary died two years before the birth of the future mathematician.
The tsar's gift did not bring Magnitsky into the ranks of the Russian nobility, but soon he was appointed to public service, about which a record has been preserved: “On the 1st day of February (1701), the Ostashkovite Leonty Magnitsky was taken into the custody of the Armory Chamber, who was ordered, for the benefit of the people, to publish a book of arithmetic through his work in the Slovenian dialect. And he wants to have the Kadashevite Vasily Kiprianov with him for the sake of publishing the book soon.” Please note that he is not only tasked with creating a textbook, but is also allowed to hire an assistant at state expense.
During the preparation of the textbook, Magnitsky was assigned food money at the rate of 5 altyns per day, which is almost 50 rubles for a year - considerable money at that time. Apparently, Magnitsky set to work zealously, since already at the beginning of March, on the instructions of the tsar, a one-time cash award was made from the income of the Armory Chamber - 12 rubles from Magnitsky and 8 rubles from Kiprianov. Peter was interested not just in an arithmetic textbook, but in a comprehensive book with an accessible presentation of the main branches of mathematics, focused on the needs of naval and military affairs. Therefore, Magnitsky worked on the textbook at the Navigation School, opened this year in Moscow in . Here he could use the library, manuals and navigation tools, as well as advice and help from foreign teachers and , who apparently controlled the progress of writing the textbook.
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 a book containing more than 600 pages, the author examined in detail arithmetic operations with whole 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.
Magnitsky in his textbook not only sought to intelligibly explain mathematical rules, but also to stimulate 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.

Photo from the site ostashkov.ru

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. He considered Magnitsky’s Arithmetic to be the “gateway to his learning.” .
Leonty Filippovich Magnitsky died in 1739 at the age of 70. In the early 30s of the last century, during the construction of the Moscow metro, a grave was discovered at the corner of Lubyansky Proezd and Myasnitskaya. The half-erased inscription on the gravestone proclaimed the eternal memory of Leonty Filippovich Magnitsky, the first mathematics teacher in Russia, who was born on June 9, 1669, and died at 1 o’clock in the morning from October 19 to 20, 1739. Already in our time in Ostashkov in memory of his A small monument was erected to the famous fellow countryman Magnitsky.

student of class 10 "A"

Scientific supervisor: physics teacher

mathematic teacher

Vladimir, 2009

avenue Stroiteley house 10 "A"

telephone numbers for communication: (49–, (49– 07 –64

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 of mathematical education in 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 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 Brockhaus and Efron: In 86 volumes (82 volumes and 4 additional). 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 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 paid special attention to the design of his 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.

FROM FULL BOOK TITLE
In original:
“Arithmetic, that is, the science of numbers. Translated from different dialects into the Slavic language, collected into one, and divided into two books. Now, by the command of the most pious and great sovereign, our Tsar and Grand Duke Peter Alexievich of all great and small and white Russia, the autocrat. Under our most noble great sovereign Tsarevich, and Grand Duke Alexy Petrovich, in the God-saved reigning great city of Moscow, typographical embossing for the sake of teaching the wise-loving Russian youths, and of every rank and age of people was brought into the world, first, in the summer from the creation of the world 7211, from the birth of flesh of God words 1703, indict 11, month of Januarius."

In modern Russian it sounds something like this:
“Arithmetic is the science of numbers. This book, divided into two volumes, was written based on texts collected throughout the world in different languages. Published by order of our Tsar Peter Alekseevich and printed in the Moscow printing house. Recommended for teaching middle and older children school age, as well as for everyone who wants to expand their knowledge.
January 7211 SM or 1703 RH.”

SHORT REFERENCE
Magnitsky, Leonty Filippovich - mathematician (1669 - 1739). Studied at the Moscow Slavic-Greek-Latin Academy; then he independently studied the mathematical sciences, in a volume far exceeding the level of information reported in Russian arithmetic, land surveying and astronomical manuscripts of the 17th century. After the opening of a school of “mathematical and navigational sciences” in Moscow (1701), he was appointed there as a teacher of arithmetic and, in all likelihood, geometry and trigonometry. He compiled an educational encyclopedia on mathematics under the title “Arithmetic, that is, the science of numbers, etc.” (1703), containing a lengthy presentation of arithmetic, the most important articles of elementary algebra for practical applications, applications of arithmetic and algebra to geometry, practical geometry, concepts of the calculation of trigonometric tables and trigonometric calculations in general and the most necessary initial information from astronomy, geodesy and navigation (now published new edition of this Arithmetic; issue 1, Moscow, 1914, with a preface by P. Baranov). As a textbook, this book was used in schools for more than half a century. Magnitsky later participated in the first Russian edition of logarithmic tables by A. Vlakka. The government of Peter the Great did not appreciate Magnitsky's merits enough and placed him, as a teacher, below his fellow Englishmen, Farvarson and Gwin. He received a significantly lower salary, and when his comrades were transferred to St. Petersburg, to the naval academy that opened there (1715), he remained in Moscow in his previous position at the school, which took a secondary position in relation to the newly opened academy.

Leonty Filippovich Magnitsky (Telyashin)

On June 9 (19), 1669, in the Ostashkov Patriarchal Settlement (now the city of Ostashkov) of the Tver province, Leonty Filippovich Magnitsky, a Russian mathematician and teacher, author of the first Russian printed manual on mathematics - “Arithmetic...” (1703).
Leonty Telyashin grew up on the banks of the Seliger River, next to the Nilo-Stolobenskaya Monastery, which at that time was the center of spiritual culture in Russia. He acquired his first knowledge in the manuscript library of the monastery. It is noteworthy that the library was assembled by the abbot and builder of the Nile Hermitage, Metropolitan of Siberia and Tobolsk Nektary, who was Leonty’s great-uncle. The talented boy impressed the monks with his hard work and great desire to “read complex and difficult things in church.” In 1684, to improve his knowledge, he was sent to the Joseph-Volokolamsk Monastery, and then to the Moscow Simonov Monastery. Given Leonty’s strong desire to study, he was soon assigned to the Slavic-Greek-Latin Academy that had recently opened in Moscow.
At the academy, Leonty Telyashin studied Latin and Greek, and independently - German, Dutch and Italian. He also got the opportunity to independently study the mathematical sciences that were not taught at the academy, and, moreover, in a volume that far exceeded the level of information reported in Russian arithmetic, land surveying and astronomical manuscripts of the 17th century. In 1700, Leonty was introduced to Tsar Peter I and made a strong impression on the sovereign with his extraordinary mental development and extensive knowledge, especially in the field of mathematics. 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,” said Peter.
In 1694-1701 Magnitsky taught children in private homes, and he himself was engaged in self-education. In 1701, by order of Peter I, he was appointed teacher of the Moscow Navigation School, or the school of “mathematical and navigational, that is, nautical and cunning sciences of teaching,” located in the building of the Sukharev Tower. Magnitsky began working as an assistant to the Scottish mathematics teacher A. D. Farvarson, and then as a teacher of arithmetic and, in all likelihood, geometry and trigonometry. During these same years, he was commissioned to write a textbook on mathematics and navigation. “Arithmetic, that is, the science of numbers, from different dialects into the Slavic language was translated and collected into one, and divided into two books” by Leonty Magnitsky - the first educational encyclopedia in mathematics in Russia - was published in 1703 in a huge circulation for those years of 2400 copies.
Magnitsky’s “Arithmetic” contained a lengthy presentation of arithmetic, the most important articles of elementary algebra for practical applications, applications of arithmetic and algebra to geometry, practical geometry, concepts about the calculation of trigonometric tables and trigonometric calculations in general, and the necessary initial information from astronomy, geodesy and navigation. Educational book was compiled from sources, which, in addition to foreign books, also included Russian arithmetic manuscripts of the 17th century.
Leonty Magnitsky was a scientist who had deep theological knowledge. In his Arithmetic, he linked science with the Holy Scriptures, arguing that the “acceptance of the sciences” “reveals God’s unsearchable” beauty.” Using numerous examples, the mathematician explained that the “sciences” do not contradict the “law of God” - such an interpretation of the issue of “science and religion” was very progressive for that time. Much of the information contained in Arithmetic was reported for the first time in Russian literature. Thanks to its scientific, methodological and literary merits, this book played a significant role in the dissemination of mathematical knowledge in Russia: M. V. Lomonosov also studied from “Arithmetic,” who called it “the gateway of learning.”
In 1715, the Naval Academy was opened in St. Petersburg, where training in military sciences was transferred, and in the Moscow Navigation School they began to teach only arithmetic, geometry and trigonometry. From that moment on, Magnitsky was appointed senior teacher of the school, and from 1732 until the last days of his life he was the head of the school’s educational department.
Leonty Filippovich Magnitsky died on October 19 (30), 1739 and was buried in the Church of the Grebnevskaya Icon of the Mother of God at the Nikolsky Gate in Moscow.

In the year of the foundation of Moscow University, Mikhailo Vasilyevich Lomonosov wrote about Peter I: “Towards His great intentions, the wise monarch provided for the necessary task to spread all kinds of knowledge in the fatherland and people skilled in the high sciences...”. In January 2005, the 250th anniversary of the university was celebrated on a large scale. Russian President V.V. Putin came to the opening of the new Library building. In the hall where the flags of Russia, Moscow and Moscow University hung, there was also a plasma panel showing the video we bring to your attention. I wanted to remember what education meant to Peter I. With Peter’s enormous participation, the first domestic textbook on mathematics was published in Russia. The year is 1703. Leonty Filippovich Magnitsky publishes Arithmetic. “Arithmetic, that is, the science of numbers. Translated from different dialects into the Slavic language, both collected and divided into two parts.” Leonty Filippovich's work was not translated; there were no analogues of the textbook at that time. This was a unique book. “Arithmetic, or the numerator, is an honest, unenvious art...” Research on the textbook “Arithmetic” itself and the life of its author is given in the 1914 book by Dmitry Dmitrievich Galanin “Leonty Filippovich Magnitsky and his Arithmetic.” We'll just make a few touches. 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. Magnitsky teaches Russia decimal calculus. What’s interesting is that he gives the addition and multiplication table not in the form it is now customary to publish on the last page of a 12-sheet notebook, but only half of it. That is, the commutativity of these operations was given immediately. After the first three addition problems, the following examples already contain more than a dozen terms. The textbook also covers geometry. For example, the Pythagorean theorem is studied on the problem of 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,... All the problems used in the book are real-life. Well, “Arithmetic” ends, of course, with applications of the studied material to life. In particular, the use of logarithmic tables in navigation. Several copies of “Arithmetic” were carefully preserved in the Department of Rare Books and Manuscripts of the Moscow University Library. The second Russian textbook on mathematics was a book translated in 1708 from the German J. V. Bruce, “Geometry of Slovenian land surveying.” “Geometry” was based on the Austrian edition “Techniques of Compasses and Rulers”. The Northern War is going on, and in between battles, Peter I personally edits the textbook. The manuscript he sent to Bruce was riddled with corrections, notes, insertions and additions “in many places.” The Tsar also gave the textbook a new name. In this publication, Peter put into practice his requirement for Russian textbooks and translations from other languages. He considered it necessary to convey not the literal accuracy of the original text, but “having understood the text, [...] write in your own language as clearly as possible [...] and not in high Slovenian words, but in simple Russian language.” In the second edition of this book, published under the title “Methods of Compasses and Rulers,” the third part contained texts by Russian authors, and the chapter on building a sundial was written by Peter I. The textbook spreads presented in the video, as well as the situation in Russia, are amazingly Well-known quotes came up that I would like to remind the President of Russia. “Mathematics is the queen of sciences, arithmetic is the queen of mathematics.” K. F. Gauss. “To establish artillery according to the rules... which requires considerable knowledge of geometry, mechanics and chemistry...” M. V. Lomonosov. “...We lost to the Russians at the school desk.” J. Kennedy.

It was in Moscow that he met with Peter I, who knew how to find people useful for Russia, no matter what strata of society they came from. The rootless teacher, who did not even have a surname, who pleased the king for his deep knowledge, received a unique gift from the monarch. Peter ordered him to henceforth be called Magnitsky, since he attracted youths to himself with his learning, like a magnet. For modern people, the significance of this gift is not entirely clear, but at that time only representatives of the highest nobility had surnames.
There are references in the literature that Leontius was protected by Archimandrite Nektary (Telyashin), who allegedly knew the tsar. This is a mistake; the coincidence of the archimandrite’s surname and the nickname of Leonty’s father does not mean that they were relatives, and Nektary died two years before the birth of the future mathematician.
The tsar’s gift did not bring Magnitsky into the ranks of the Russian nobility, but soon he was appointed to the public service, about which a record has been preserved: “On the 1st day of February (1701) the Ostashkovite Leonty Magnitsky was taken into the payroll of the Armory Chamber, who was ordered for the benefit of the people to publish work your book of arithmetic in the Slovenian dialect. And he wants to have the Kadashevite Vasily Kiprianov with him for the sake of publishing the book soon.” Please note that he is not only tasked with creating a textbook, but is also allowed to hire an assistant at state expense.
During the preparation of the textbook, Magnitsky was assigned food money at the rate of 5 altyns per day, which is almost 50 rubles for a year - considerable money at that time. Apparently, Magnitsky set to work zealously, since already at the beginning of March, on the instructions of the tsar, a one-time cash award was made from the income of the Armory Chamber - 12 rubles from Magnitsky and 8 rubles from Kiprianov. Peter was interested not just in an arithmetic textbook, but in a comprehensive book with an accessible presentation of the main branches of mathematics, focused on the needs of naval and military affairs. Therefore, Magnitsky worked on the textbook at the Navigation School, opened that year in Moscow in the Sukharev Tower. Here he could use the library, manuals and navigation tools, as well as advice and help from foreign teachers and Jacob Bruce, who apparently supervised the progress of writing the textbook.
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”.
Fedor Alekseev. Lubyanka. On the left is the Church of the Grebnevskaya Mother of God, next to which L.F. was buried. 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 during the period of writing the textbook, Magnitsky
began teaching at the Navigation School, with which he was to connect his whole 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 government figures in 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. Lomonosov considered “Magnitsky’s Arithmetic” to be “the gateway to his learning.”
Leonty Filippovich Magnitsky died in 1739 at the age of 70. In the early 30s of the last century, during the construction of the Moscow metro, a grave was discovered at the corner of Lubyansky Proezd and Myasnitskaya. The half-erased inscription on the gravestone proclaimed the eternal memory of Leonty Filippovich Magnitsky, the first mathematics teacher in Russia, who was born on June 9, 1669, and died at 1 o’clock in the morning from October 19 to 20, 1739. Already in our time in Ostashkov in memory of his A small monument was erected to the famous fellow countryman Magnitsky.

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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 to everyone, most useful and most praiseworthy, from the most ancient and the newest, in different times the most famous arithmeticians who lived, invented and expounded." 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 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 there is 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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From the arithmetic of Magnitsky. The importance of Magnitsky’s “arithmetic” for the development of mathematical education in Russia

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