home Social science Non-standard ways of solving problems on mixtures and alloys. Title page of the book "Youth Honest Mirror"

Non-standard ways of solving problems on mixtures and alloys. Title page of the book "Youth Honest Mirror"

An outstanding figure in education in the era of Peter the Great was a prominent mathematician, teacher at the School of Mathematical and Navigational Sciences in Moscow Leonty Filippovich Magnitsky(1669–1739). He made a huge contribution to the methodology of secular schooling of his time and in the development of vocational education. According to the tradition that came from the literacy masters of Moscow Russia, he created his own textbook - “Arithmetic, that is, the science of numerals”, publishing it after a two-year practical test in 1703. This educational book marked the birth of a truly new textbook that combined the domestic tradition with achievements Western European methods of teaching exact sciences. "Arithmetic" L.F. Magnitsky was the main educational book on mathematics until the middle of the 18th century; M.V. Lomonosov.

Textbook L.F. Magnitsky had the character of an applied, in fact, even a utilitarian manual for teaching all basic mathematical operations, including algebraic, geometric, trigonometric and logarithmic. The students of the navigational school copied the content of the textbook, formulas and drawings on slate boards, mastering almost various branches of mathematics.

Mathematical knowledge was studied sequentially according to the principle from simple to complex; mathematical calculations were closely connected with the professional training of specialists in the field of fortification, geodesy, artillery, etc.

L.F. were widely used. Magnitsky various visual aids. Various tables and layouts were attached to the textbook. In the learning process, visual aids were used - ship models, engravings, drawings, instruments, drawings, etc.

Already the title page of "Arithmetic" was a kind of symbolic visual aid, displaying the contents of the textbook. Arithmetic itself as a science was depicted in the form of an allegorical female figure with a scepter - a key and an orb, seated on a throne, to which the stairs lead with a sequential enumeration of arithmetic operations: "calculation, addition, subtraction, multiplication, division." The throne was placed in the "temple of sciences", the vaults of which are supported by two groups of columns of four each. The first group of columns had inscriptions: "geometry, stereometry, astronomy, optics" and rested on the foundation, on which the question was written: "What gives arithmetic?" The second group of columns had inscriptions: "mercatorium (as navigational sciences were called in those days), geography, fortification, architecture."

Thus, Magnitsky's "Arithmetic" was essentially a kind of mathematical encyclopedia, which had a pronounced applied character. This textbook marked the beginning of a fundamentally new generation of educational books. It not only was not inferior to Western European models, but was also compiled in line with the Russian tradition, for Russian students.

L.F. Magnitsky supervised all the educational work of the school, starting from its first stage. To prepare students for studying in the navigation school itself, two primary classes were organized under her, which were called the “Russian school”, where they taught reading and writing in Russian, and the “digital school”, where children were introduced to the beginnings of arithmetic, and for those who wished, they taught more fencing.

Title page books by L. F. Magnitsky "Arithmetic"

All subjects were studied sequentially at the navigation school, there were no transfer and final exams, students were transferred from class to class as they learned, and the very concept of “class” meant not an element of the class-lesson system, which did not exist in Russia yet, but the content of education : navigation class, geometry class, etc. They were released from school as the student was ready for a specific state activity or at the request of various departments that were in dire need of educated specialists. New students were immediately recruited to the vacated places.

Teaching in the navigation school was equated with service, so the students received the so-called "feed money". Pupils upon admission were provided with books and the necessary teaching aids, which were required to be returned at the end of the class in safety. The students were given tables of logarithms, geographical maps, for recording calculations - slates, slates, pencils, as well as rulers and compasses. In fact, the school was completely on state support.

The students lived in the school itself, some in apartments near the school. In 1711 the number of pupils in the school grew to 400.

L.F. Magnitsky introduced into practice the selection of the "tenth" students from among the best students, who monitored their behavior in their top ten.

Graduates of the navigational school served not only in the navy; in the decree of Peter I of 1710, it was said that graduates of this school were suitable for service in artillery, in civil departments, as elementary school teachers, architects, etc. Individual graduates of the navigation school were sent abroad to continue their education.

Simultaneously with the navigational school, in the same 1701, following its model, an artillery, or Pushkar, school was opened in Moscow, which was supposed to train specialists for the army and navy. Students were recruited into it at the age of 7 to 25, taught Russian literacy, arithmetic, and immediately began to prepare for the profession of an engineer. Teachers in both navigational and Pushkar schools were trained right on the spot from the most capable and appropriate students for this function.

In addition to state schools, which set the task of rapid primary education and vocational training, private schools began to open in the Petrine era, which in many ways served as a model for the subsequent development of schooling in Russia.

Back in the 17th century. in Moscow, on the Yauza River, a German settlement was formed, where immigrants from Western Europe organized schools for their children according to the European model. The inhabitants of this settlement had a certain educational impact on the young Peter I and his inner circle.

In July 1701, pastor and head of the school at the German church in the Novo-Nemetskaya Sloboda in Moscow Nikolai Schwimmer By royal decree, he was appointed translator of Latin, German and Dutch at the Posolsky Prikaz - the state body of international relations. At the same time, he was charged with the duty to create a school in which everyone would study, regardless of rank. In November 1701, N. Schwimmer began teaching the first six students Latin and German based on Western European methods. First, he taught them to read and write in German, then spoken language, and only then - Latin, which opened the way to science.

The textbook was the book of N. Schwimmer himself “Entrance Latin”, testifying to his acquaintance with the famous textbook of the Latin language Ya.A. Comenius. However, in 1703 this school was closed, and his students were handed over to the pastor Ernst Gluck.

E. Gluck was an educated person, well acquainted with the latest pedagogical ideas of Western Europe. Back in 1684, he developed a project for a system of teaching in his native language among the Russian Old Believers in Livonia, where he himself lived at that time. For them, he translated the Slavic Bible into colloquial Russian, wrote the Russian ABC and a number of school textbooks. During Russian-Swedish war E. Gluck was captured and taken to Moscow, where at the beginning of 1703 he was instructed by Peter I to teach Russian youths German, Latin and other languages. Somewhat later, in 1705, in Moscow, at the corner of Maroseyka Street and Zlatoustinsky Lane, in the chambers of the boyar Vasily Fedorovich Naryshkin, E. Gluck's own school was opened by royal decree. The children of boyars, officials, merchants were supposed to study there. 300 rubles were allocated from the state treasury for the maintenance of the school, at that time a huge amount. The school taught geography, ethics, politics, history, poetics, philosophy; Latin, French and German. Attention was also paid to the "secular sciences" - dancing, secular manners, horse riding. In addition to the listed subjects, the study of which was mandatory, those who wished could study Swedish and Italian.

Classes at the school began at 8 o'clock in the morning and ended at 6 o'clock in the evening for junior classes and at 8 o'clock in the evening for seniors. The daily routine of the school allows us to conclude that elements of a new form of organization of education for Russian schools were used here - class-lesson, in which children of the same age group united to study a particular subject; lessons were practiced to repeat and memorize already studied material, which was a mandatory form of educational work for teachers and students.

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Report on the topic:

" ArithmeticL.F.Magnitsky"

Completed by: Kolesnikova K.O.

Chita 2014

Introduction

With arithmetic, the science of numbers, our acquaintance with mathematics begins. With arithmetic, we enter, as M.V. Lomonosov, into the "gates of learning" and we begin our long and difficult, but fascinating journey of knowing the world. arithmetic magnitsky number

The word "arithmetic" comes from the Greek arithmos, which means "number". This science studies operations on numbers, various rules for handling them, teaches how to solve problems that boil down to addition, subtraction, multiplication and division of numbers. Arithmetic is often imagined as some first step in mathematics, based on which it is possible to study its more complex sections - algebra, mathematical analysis, etc. Even integers - the basic object of arithmetic - are related 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 art that is honest, unenviable, and conveniently understood by everyone, most useful and much praised, from the oldest and the newest, who lived at different times, the fairest arithmeticians, 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 Russian textbook on mathematics.

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

Knowledge of Leonty Filippovich in the field of mathematics surprised many. At the meeting, he made a very strong impression on Tsar Peter I with his outstanding mental development and extensive knowledge. As a sign of respect and recognition of his merits, Peter I "granted" him the name Magnitsky "in comparison with how a magnet attracts iron to itself, so with its natural and self-educated abilities it drew attention to itself."

In 1701, by order of Peter I, he was appointed teacher at the school of "mathematical and navigational, that is, nautical cunning sciences of learning," which was 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 numerals from different dialects into the Slavic language, translated and collected into one, and divided into two books" edition of 2400 copies. As a textbook, this book has been 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.

Eastoriya of creation.

"Arithmetic" L.F. Magnitsky is one of the most famous Russian books, rightfully belonging to the monuments of the national written culture. So, on February 22, 1702, L.F. Magnitsky was ordered a mathematics textbook, funds were allocated for its compilation and printing. In an extremely short time - in 9 months - he created a unique educational mathematical book, which was published in a large circulation for that time. It had a magnificent and long title according to the customs of that time: "Arithmetic, that is, the science of numerals. Translated from different languages 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 extremely 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 of the translation nature of the book, in fact it was a rather original work, both in content and in methodological terms, which was a link between the traditions of Moscow handwritten educational literature and the influences of the new Western European. well known 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 the work on the textbook.

"Arithmetic" Magnitsky directly or indirectly, in turn, had big influence to all subsequent domestic mathematical literature. Much has been written about Magnitsky's "Arithmetic" in detail. Let's give brief description this unique book.

Polyfunctionality. Following the traditions of Russian handwritten educational literature, Magnitsky included in "Arithmetic" purely, so to speak, "epic" material: 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 reasoning, advice to the reader, general conclusions, often stated in poetic form, which increased 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 the domestic printed popular science literature, although the main content of the book is still mathematics.

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

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

Magnitsky's arithmetic operations have two names - Latin and Russian: numeration, or reckoning; addizio, or addition; subtraction, or subtraction; division, or division. Numbering, as before, stands out as a special action.

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

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

The structure of the book. big volume, with a volume of over 600 pages, "Arithmetic" Magnitsky 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 belonging." The third book is devoted to navigation.

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

What is Magnitsky's "Arithmetic"? Much 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 the book-printing activity of the Petrine era." Today 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 on what guidelines Magnitsky compiled his "Arithmetic". A.P. Yushkevich believes that handwritten and printed material of an earlier time was used, which Leonty Filippovich carefully selected, substantially processed, compiling 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 the numbers of integers", part 2 - "On the numbers of broken lines or with fractions", part 3 - "On the rules of similar, in three, five and seven lists", parts 4 and 5th - "On the rules of false and fortune-telling", "On the 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 Algebraic". Part 2 - "On the geometric through arithmetic acting", part 3 - "General about earthly measurement and how to belong to navigation." In these books, in addition to operations with literal expressions, solutions of square and bi quadratic equations, the beginning of plane and spherical trigonometry, the calculation of areas and volumes. The 3rd part contains a lot of information about determining the position necessary for navigation. The book ends with the addition "On the interpretation of various navigational problems through the loxodromic tables above."

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 the general formulation, which is fixed large quantity examples and tasks. Each action is accompanied by a verification rule ("verification"); this is done for both arithmetic and algebraic operations.

Examples of problems and their solution.

1. One person came to the teacher at the 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 constrain my class. If I had as many as there are, yes, half as many, yes 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 found the horse, changed his mind and returned it to the seller, saying: "I have no reason to buy a horse for this price, which 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, then you will get a horse for free. There are 6 nails in each horseshoe. 1 kopeck, etc." A buyer seduced by a low price. And wanting to get a horse for free, he accepted the conditions of the seller, hoping that he would have to pay no more than 10 rubles for nails.

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

2. This sequence is a geometric progression with the 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. No wonder when they talk about Magnitsky's Arithmetic, they always remember the words of M.V. Lomonosov, who called it "the gates of his learning." It was the "gate 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 should be taken into account that, in addition to arithmetic knowledge, it also contained algebraic, geometric, trigonometric, astronomical and navigational information, so that Magnitsky's work was in fact a kind of encyclopedia of mathematical knowledge and provided quite extensive applied information.

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

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

ARITHMETICS OF THE MAGNITSKY PROBLEM and RESEARCH METHODS Research objectives. Do short review retrospective of the creation of Arithmetic, a biography of Leonty Filippovich Magnitsky, get acquainted with the history of the creation of Arithmetic and identify the degree of influence of Arithmetic on the spread of mathematics in Russia. Research methods. As research methods, such general scientific methods as the empirical method, the method of comparison, and generalization were used.

ARITHMETICS OF MAGNITSKY main content Historical retrospective of the emergence of Magnitsky's Arithmetic About Leonty Filippovich Magnitsky About the textbook Magnitsky's Arithmetic Conclusion

ARITHMETICS OF MAGNITSKY Historical retrospective of the emergence of Magnitsky Arithmetics North War 1700-1721 – many qualified specialists are required There were few textbooks. There were no textbooks in Russian. There were textbooks in Latin, Greek, kept in "closed" libraries, for example, bishops' schools, rare manuscripts of the Sukharev Tower - the building of the Navigation School, created in 1701

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

ARITHMETICS OF MAGNITSKY Peter I commanded L.F. Magnitsky to write a textbook of mathematics for the navigational school, established on January 14, 1701 in Russian

ARITHMETICS OF MAGNITSKY About the textbook of Magnitsky's arithmetic

Magnitsky's Arithmetic conclusions The textbook Magnitsky's Arithmetic contributed to the emergence of the Russian mathematical tradition of teaching mathematics in a format new to Peter the Great's time, to the development of a uniform approach to teaching and studying mathematics The historical significance of Magnitsky's Arithmetic, as study guide in mathematics, in that he introduces a convenient numbering similar to Arabic, writes down the advanced algorithms of that time for addition, subtraction, multiplication, division. The presentation of the material is based on the solution of practical problems, which allows using the textbook for self-education. Scientific novelty. At each time step, comparison modern methods education, solution algorithms math problems with those given in Magnitsky's Arithmetic justified with scientific point of view, as it allows assessing the level of evolution of mathematical scientific thought, the level of evolution of general education.

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

ARITHMETICS OF MAGNITSKY sources THANK YOU FOR YOUR ATTENTION

Usanova Yana

Research work "Solution of the problem from Magnitsky's Arithmetic". The work tells about the life and work of Leonty Filippovich Magnitsky. The solution of the problem "Kad' drinking" (4 ways) and the problem on the "triple rule" is considered.

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Municipal educational institution

average comprehensive school No. 2 of the city of Kuznetsk

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Solving a problem from Magnitsky Arithmetic

Research work

Prepared by a 6th grade student

Usanova Ya.

Head: Morozova O.V.-

Mathematic teacher

Kuznetsk, 2015

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

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

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

3. Solution of the problem "Kad' drinking" from Arithmetic of Magnitsky. Tasks for the “Three Rule”……………………………………………………………….. 11

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

References…………………………………………………………….16

Introduction

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

Before the appearance of L.F. Magnitsky's book "Arithmetic" in Russia there was no printed textbook for teaching mathematics;

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

Target:

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

Tasks:

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

Consider the content of his textbook;

Solve the problem "Kad drinking" in different ways;

Hypothesis:

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

Research methods:

The study of literature, information found on the Internet, analysis, establishing links between solutions according to L. F. Magnitsky and modern methods of solving mathematical problems.

Biography of L.F. Magnitsky

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

As time went. The boy grew and became stronger in spirit. He helped his father, who “feeded himself with the work of his hands” and his family, and in free time"There was a passionate hunter to read intricate and difficult things in church." Ordinary peasant children did not have the opportunity to have books, learn to read and write. And the lad Leonty had such an opportunity. His great-uncle, St. Nectarios, was the second rector and builder of the Nilo-Stolobenskaya desert, which arose on the site of the exploits of the great Russian saint, the Monk Nile. Two years before the birth of Leonty, the relics of this saint were found, and on the island of Stolbny, where the hermitage is located, many people began to rush to the pilgrimage. The Telyashin family also went to this miraculous place. And visiting the monastery, Leonty lingered for a long time in the monastery library. He read ancient handwritten books, not noticing the time, reading absorbed him.

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

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

Visiting his students, Leonty Filippovich ran into a problem. In mathematics, or, as they said then, arithmetic, there was not a single manual and not a single textbook for children and young men. The young man began to compose examples and interesting problems himself. He explained his subject with such fervor that he could interest even the most lazy and unwilling to study student, which was not a small number in rich families.

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

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

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

At the Navigation School, Leonty Filippovich worked as a teacher for 38 years - more than half a lifetime. He was a modest man, devoted to science, cared about his students.

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

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

Arithmetic of Magnitsky

In the stories about the engineers of the Petrine era, one story is often repeated: having received a task from the sovereign-emperor Peter Alekseevich, they first of all took L. F. Magnitsky's "Arithmetic" in their hands, and then proceeded to the calculations. To determine what outstanding Russian inventors found in Magnitsky's book, let's look at his work. For more than half a century, this fundamental work of L. F. Magnitsky had no equal in Russia. It was studied in schools, it was addressed by the widest circles of people who aspired to education or, as already noted, were working on some technical problem. It is known that M. V. Lomonosov called Magnitsky's "Arithmetic" along with Smotrytsky's "Grammar" "the gates of his learning."

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

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

The second part is devoted to fractions, the third and fourth - "tasks for the rule", the fifth - the basic rules of algebraic operations, progression and roots. There are many examples of the application of algebra to military and naval affairs. The fifth part ends with a consideration of actions with decimals, which was a novelty in the mathematical literature of the time.

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

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

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

The solution of the problem "Kad drink" from Arithmetic of Magnitsky. Tasks for the "Three Rule"

"Kad of Drinking"

One man will drink a cad of drink in 14 days, and with his wife he will drink the same cad in 10 days, and knowingly eat, in how many days his wife will especially drink the same cad.

I found this problem in the electronic form of the textbook "Arithmetic" along with the solution. L.F. Magnitsky solves it arithmetically. I solved this problem in 4 ways: two of them arithmetic, two algebraic.

Decision:

1st way.

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

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

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 woman will drink the drink

2nd way

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

1) 840:10 = 84 (l) - a man and a 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) - the wife drinks in 1 day

3rd way

1) 840:14 = 60 (l) - a person will drink for 1d.

2) Let the wife drink in 1 day x l., since a person will drink a cad of drink in 14 days, and with his wife he will drink the same cad in 10 days, we will make an equation:

(60+X)∙10=840

60+X=840:10

60+X=84

X=84−60

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

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

4th way

Let the wife drink for 1 day x kadi of drinking, because in 1 day a person will drink 1/14 of the kadi of drinking, and with his wife 1/10 of the kadi of drinking, we will make the equation:

1) X + 1/14 = 1/10

X = 1/10 - 1/14

X \u003d (14 - 10) / 140 \u003d 4/140 \u003d 1/35 (kadi drinking) - the wife drinks in 1 day

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

In the 3rd quarter, in mathematics lessons, we began to study the topic of direct and inverse proportional dependencies. This task is directly related to this topic. And analyzing the solution of this problem and those similar to this one presented in Magnitsky's book, I found out that he solved problems of this type using a very interesting rule - the "Triple Rule".

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

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

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

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

Here are examples of these tasks.

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

Decision.