Scientific and practical conference dedicated to the life and work of L. F. Magnitsky
Solution of one problem “Kad drinking”
Introduction
1. Biography of L.F. Magnitsky
2. Magnitsky arithmetic
3. Solving a problem from Magnitsky Arithmetic
Conclusion
Bibliography
Introduction
INXVI- XVIIcenturies, handwritten mathematical literature begins to appear and spread in Russia (this is required by land surveying and measurement, the tax system, urban planning and military affairs, developing trade relations within the country and trade with other states). A significant number of mathematical manuscripts are currently knownXVIIcentury. They were mainly intended for merchants, traders, officials, artisans, land surveyors and were of a purely practical nature. Their material was distributed into “articles” containing instructions on how to proceed when solving certain problems. The rules were explained with various examples and problems. Some of these problems are interesting either because of their formulation or the way they are solved. Many of them were transferred to textbooks on arithmetic and algebraXVIIIcenturies, some have survived to this day.
In 1703, such a textbook was published by printing in an unusually large circulation for those times - 2,400 copies. It was called “Arithmetic, that is, the science of numbers...”. Its author was an outstanding teacher-mathematician - Leonty Filippovich Magnitsky. Taking the existing handwritten mathematical literature as a basis, Magnitsky created a book that for 50 years was the main textbook in mathematics for almost all educational institutions in Russia.
Biography
Magnitsky Leonty Filippovich (1669-1739), mathematician, teacher.
Born on June 19, 1669 in the Ostashkovskaya settlement, Tver province. Descended from peasants. The future mathematician's father's name was Philip, his nickname was Telyashin, but at that time peasants were not given surnames. The boy learned to read independently as a child, thanks to which he at times served as a psalm-reader in the local church.
The young man’s fate changed dramatically when he was sent from his native settlement with a cart of frozen fish to the Joseph-Volokolamsk Monastery. Apparently, in the monastery the boy showed interest in books, and the abbot, making sure of his literacy, left Leonty as a reader. A year later, the abbot blessed the young man to study at the Slavic-Greek-Latin Academy, which was the main educational institution in Russia at that time. Leonty studied at the academy for about eight years.
At the end of the 17th century. lived in Moscow, giving private lessons to children and self-education. According to some information, he studied at the Slavic-Greek-Latin Academy. Legend has it that Peter I nicknamed him Magnitsky: “... in comparison to how a magnet attracts iron to itself, so he drew attention to himself with his natural and self-educated abilities.”
In 1701, Leonty Filippovich was appointed to help the English mathematicians teaching at the School of Mathematical and Navigational Sciences, which had just opened in Moscow. In 1715 Magnitsky became the senior teacher here and the head of its educational department. In addition, from 1714 he himself recruited teachers for the “digital schools” created in Russia.
Working continuously at the Navigation School for almost four decades, and then heading it, Magnitsky contributed to the success of Peter’s reforms in the field of education.
Magnitsky Arithmetic
Magnitsky is the author of the first Russian textbook on mathematics, “Arithmetic, that is, the science of numbers,” published in 1703 in a circulation of 2,400 copies. Book until the middle of the 18th century. was the main textbook on mathematics in Russia. It was a kind of encyclopedia of mathematical knowledge, containing material on geometry, trigonometry, astronomy and navigation and providing quite extensive applied information. Magnitsky also participated in the publication of the first logarithmic tables in Russia.
Surprisingly, the textbook was written and published in just two years. Moreover, it was not simply a translation of foreign textbooks; in structure and content it was a completely independent work, and there were no textbooks even remotely resembling it in Europe at that time. Naturally, the author used European textbooks and works on mathematics and took something from them, but presented it as he saw fit. In fact, Magnitsky created not a textbook, but an encyclopedia of mathematical and navigational sciences. Moreover, the book was written in simple, figurative and understandable language; it was possible to study mathematics from it, if you had certain basic knowledge.
According to the tradition of that time, the author gave the book a long title - “Arithmetic, that is, the science of numbers. Translated from different dialects into the Slavonic language, collected into one, and divided into two books.” The author did not forget to mention himself - “This book was written through the works of Leontius Magnitsky”, soon everyone began to call the book briefly and simply - “Mathematics of Magnitsky”.
In the book, containing more than 600 pages, the author examined in detail arithmetic operations with integer and fractional numbers, gave information about money accounts, measures and weights, and gave many practical problems in relation to the realities of Russian life. Then he outlined algebra, geometry and trigonometry. In the last section, entitled “Generally about earthly dimensions and what is necessary for navigation,” I examined the applied application of mathematics in maritime affairs.
In his textbook, Magnitsky not only sought to clearly explain mathematical rules, but also to arouse students’ interest in learning. He constantly emphasized the importance of knowledge of mathematics using specific examples from everyday life, military and naval practice. I even tried to formulate problems in such a way that they aroused interest; they often resembled jokes with an intricate mathematical plot.
The textbook turned out to be so successful that within several years it was spread throughout Russia. Apparently, even while writing the textbook, Magnitsky began teaching at the Navigation School, with which he was to connect his entire life. Until 1739, Leonty Filippovich first taught and then headed the Navigation School, raising a galaxy of students, many of whom became prominent military and 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. considered “Magnitsky’s Arithmetic” to be the “gateway of his learning.” Lomonosov.
Solving a problem from Magnitsky Arithmetic
"Kad of drinking"
One man will drink a kad in 14 days, and he and his wife will drink the same kad in 10 days, and it is known that on how many days his wife will especially drink the same kad.
Solution:
1st method.
1 kad=839.71l ≈840l
1) 840:14=60 (l) - a person will drink in 1 day.
2) Let the wife drink x liter in 1 day, since a man drinks a kad in 14 days, and his wife drinks the same kad in 10 days, let’s create an equation:
(60+X)∙10=840
60+X=840:10
60+X=84
X=84−60
X=24 (l) - wife drinks in 1 day
3) 840:24=35 (days) - the wife will drink a pot of drink
2nd method
1) 14∙5=70 (days) - equalized the time during which a person drinks a pot of drink with the time during which a man and his wife drink the same pot of drink
2) 10∙7=70 (days) - equalized the time during which a man and his wife would drink a tub of drink with the time during which a person would drink the same tub
3) 70:14=5 (k.) - a person will drink in 70 days
4) 70:10=7 (k.) - a man and his wife will drink in 70 days
5) 7−5=2 (k.) - the wife will drink in 70 days
6) 70:2=35 (days) - the wife will drink a kad of drink
3rd method
1) 840:10=84 (l) - a man and his wife will drink in 1 day
2) 840:14=60 (l) - a person will drink in 1 day
3) 84−60=24 (l) - the wife will drink in 1 day
4) 840:24=35 (days) - wife drinks in 1 day
4th method
In 100 days he will drink 10 barrels of kvass, and together with his wife in 140 days they will drink 14 barrels of kvass. This means that in 140 days the wife will drink 14-10 = 4 kegs of kvass, and then she will drink one keg in 140:4 = 35 days.
5th method
Let the wife drink in 1 dayxqadi of drink, since in 1 day a person will drink 1/14 qadi of drink, and with his wife 1/10 of qadi of drink, let’s create an equation:
1) X + 1/14 = 1/10
X = 1/10 - 1/14
X = (14 - 10) / 140 = 4/140 = 1/35 (kadi drink) - wife drinks in 1 day
2) 1/35∙35=35/35=1 (drink) - drinks 1 dram of drink in 35 days
Conclusion
While working with scientific literature, I learned a lot of interesting things from the history of the development of mathematics.It was Magnitsky who first introduced our ancestors to mathematics in a volume that was rare for his time and showed its great practical significance.L. F. Magnitsky first introduced the terms: multiplier, divisor, product, root extraction; replaced the obsolete words darkness, legion with the words million, billion, trillion, quadrillion. The book has significantly improved the system of presentation of the material: definitions are introduced, a smooth transition to something new is made, new sections and tasks appear, and additional information is provided.This is Magnitsky’s main merit to the history of mathematical education in our country.No less important is his merit as the first teacher of Russian sailors, who successfully overcame the enormous difficulties that he encountered when presenting in Russian the fundamentals of nautical science.
Bibliography.
1. Andronov I.K. The first mathematics teacher of Russian youth Leonty Filippovich Magnitsky // Mathematics at school. 1969. No. 6.
3. Glazer G.I. History of mathematics at school. Manual for teachers. – M.: “Enlightenment”, 1981. – 239 p.
4. Gnedenko B.V. and others. Encyclopedic Dictionary of a Young Mathematician.
M.: “Pedagogy”, 1985 – 349 p.
6. Olehnik S.N. et al. Ancient entertaining problems - 3rd ed. – M.: “Drofa”, 2006. – 173 p.
L. F. Magnitsky
(The first teacher of mathematics and marine sciences in Russia)
The textbook written by Magnitsky is an encyclopedia of mathematics and its applications and, according to the custom of that time, bears a long title: “Arithmetic, that is, the science of numbers. Translated from different dialects into the Slavic language... Now... for the sake of teaching the wise-loving Russian youths and every rank and age of people, it was born in the summer from the creation of the world 7211 (1703) of the month of Januaria. This book was written through the works of Leonty Magnitsky.”
On the back of the title page, the author addresses the future, the student:
“Kindly learn arithmetic,
Stick to different rules and things in it,
Because there is a need for citizenship in business...
And he will decide the paths in the sky, and on the sea,
It’s also useful in war, and in politics...”
The meaning of the entire poem is this: mathematics gives a person the opportunity to calculate and think about his actions in different circumstances.
In Russia, before Magnitsky's book appeared, there were only handwritten mathematical books. Only in 1682 was it published “A convenient calculation, with which every person buying or selling can conveniently find the number of all sorts of things. And what is the number of things and the number of things the price of finding, and reading about this in the preface to the reader will become completely clear.”
The leaflet has such a long title - a table for multiplying all numbers up to 100 in pairs. This table apparently found wide circulation, since in 1714 it was republished by order of Peter I under the title: “The Book of Calculation, convenient for use by anyone who wants to easily know the price or measure of some things.” This book is in no way a textbook.
Since during the renewal of Russian life by Peter the question of textbooks in general and an arithmetic textbook in particular could not help but arise, then in 1699 in Amsterdam from the Russian printing house of Jan Tessing, to whom Peter gave the privilege “to set up a printing house and print in it ... mathematical and architectural and city planning and all sorts of military and artistic books,” the book “A Brief and Useful Guide to Arrhythmetic or to the Training and Knowledge of Every Account” was published. The author of the book was the Pole Ilya Kopievsky or Kopievich, who also lived in Amsterdam.
Since neither the author nor the publisher of Russia knew or had any idea about it. What information on mathematics was known to Russian readers from handwritten mathematical books, this book turned out to be so elementary and unnecessary in Russia that it almost did not gain distribution, and the publisher suffered material damage.
Magnitsky’s textbook was destined to become a conductor of mathematical knowledge to the broad Russian masses.
Magnitsky came from the “lower classes” of the Russian people. He understood the need of Russian society for mathematics and, being a very educated man, he also understood that it was impossible for the Russian reader to offer a foreign mathematical book that did not take into account the readers’ knowledge of mathematics, developed over centuries.
Magnitsky made extensive use of Russian handwritten mathematical literature in his arithmetic, supplementing it with the achievements of European scientific and methodological thought. He rightfully declared that he had collected the science of arithmetic in his book from multilingual books - Greek, Latin, German, Italian and Old Church Slavonic. He reworked the science borrowed from European books in the spirit of Russian manuscripts and adapted it to the needs of his reader, whom he knew well.
He emphasized in the preface:
“The whole mind has gathered and the rank
Naturally Russian, not German.”
As a result of all this, a new original Russian mathematics textbook was created, which remained the only textbook for schools for 50 years and influenced mathematics education in Russia for at least 100 years. Russian mathematical literature does not know any other book that would have such great historical significance.
What made this book such a success?
Firstly, its content. This is not a textbook in the usual sense of the word, but an encyclopedia of mathematics and its applications. Magnitsky arithmetic includes algebra, basic geometry, trigonometry and astronomy. Everywhere theory is accompanied by practice - “butts, to civil 
necessities." Problems from everyday practice are solved - all sorts of calculations of “companies” (partnerships), mixtures, samples, losses and profits, deadlines; areas and volumes are calculated; issues of military equipment and system are resolved, and at the end of the book a detailed guide to ship navigation and solutions to all the main “navigational problems” are given, i.e., issues of nautical astronomy and navigation.
Secondly, the success of the book depended on the tireless agitation about the benefits of science in general and mathematics in particular, which the author waged in poetry and prose throughout the book.
He never tired of citing historical examples of how:
“In ancient times, the kings of the Greeks
And the current ones are all German
Unanimously it (science) is accepted
And they strengthen their kingdom.”
The author also repeatedly emphasized that the importance of mathematics is not limited to solving particular practical problems. Teaching, for example, to determine the composition of alloys, he indicated:
“If anyone knows how much ore there is.
He also knows others by example.”
Regarding the second part of his book, in which mathematics is applied to solving astronomical and nautical issues, Magnitsky explained that he cannot do without mastering it:
“At least you’re a sea swimmer.
Is it a navigator or a rower?
So what: 
"Nowadays every best warrior
He deserves to know science”...
With the enormous participation of Peter the Great, the first domestic textbook on mathematics was published in Russia. The year is 1703. Leonty Filippovich Magnitsky publishes Arithmetic. Leonty Filippovich's work was not translated; there were no analogues of the textbook at that time. This was a unique book. The textbook contains more than 600 pages and includes both the very beginning - a table of addition and multiplication of decimal numbers, and applications of mathematics to the navigational sciences.
From the preface of the book it is clear that it was printed by order of Peter Ⅰ “for the sake of teaching the wise-loving Russian youths and all ranks and ages of people.” Magnitsky did a great job to make the material presented in the book accessible and interesting to the reader. Many paragraphs end with poems that summarize what has been learned. Here, for example, is a wish from the preface to the book:
“And we wish this work to be
It’s good for all Russian people to use it.”
In Magintsky’s “Arithmetic”, for the first time in Russia, such “Arabic” numerals, which are now primary to us, were used for calculations.
The title page depicts the emblem of the Russian Empire in the center, a merchant on the left, symbolizing “politics,” and a scientist, symbolizing “logistics,” on the right. On the vignette is the inscription “Arithmetic, politics with it, other logistics of the most eminent publishers in equal times written.” Pythagoras and Archimedes are written on the ribbons fluttering on the sides. The introduction says: “Arithmetic, or numerator, is an honest art, unenviable and understandable to everyone, most useful and much praised, invented and expounded by the most ancient and modern arithmeticians who appeared at different times.” In this definition, “art” must be understood as a skill, “honest” - worthy, “unenvious” - objective. Generations of Russian people studied from this book. Lomonosov called it “the gateway of his learning” and knew a lot by heart. Several copies of “Arithmetic” were carefully preserved in the Department of Rare Books and Manuscripts of the Moscow University Library.
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Introduction | |
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Chapter I. The influence of Peter I on the development of Russian education, starting from the end of the 17th century. | |
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Chapter II. Features of the appearance of the textbook | |
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Chapter III. Features of the content of the first domestic textbook on mathematics by Magnitsky in Russia in the 18th century. | |
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Conclusion | |
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Bibliography | |
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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 the various areas of Magnitsky’s practical activities.
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 of Russian science since 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 The research work became a theoretical method: analysis of the 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 The work consists of systematizing information on the topic of research, popularizing knowledge about Magnitsky and his Arithmetic as “one of the most important phenomena of book-printing activity of Peter’s time”1, developing visual material for use in lessons and extracurricular work in mathematics, and in the work of the 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 the rapid development of industry and trade in Russia, and the restructuring of military equipment. During this period, the country increasingly needed educated people of various specialties. Peter I decided to open a number of technical educational institutions, but this was hampered by the lack of Russian teachers and comprehensive educational literature in physics, mathematics, and technical disciplines.
______________________________________________________________
It was during this period that the meeting between Peter I and Leonty Telyashin, a native of the Ostashkovskaya settlement of the Tver province, took place. in the field of mathematics surprised many. When they met, he made a very strong impression on Tsar Peter I with his extraordinary mental development and extensive knowledge. As a sign of respect and recognition of his merits, Peter I bestowed on him the surname Magnitsky, “in comparison with how a magnet attracts iron to itself, so he drew attention to himself with his natural and educated abilities”2. In January 1701, Peter issued a decree on the creation of a school of mathematical and navigational sciences in Moscow. Leonty Magnitsky began working as an assistant to Farvarson's mathematics teacher, and then as a teacher of arithmetic and, in all likelihood, geometry and trigonometry. Then he was instructed to write a textbook on mathematics and navigation. Peter I wished “to have in the new school a textbook not of foreign, but of Moscow origin”3. The fact that Magnitsky actually worked on arithmetic from the beginning of February 1701 is evidenced by his receipt for receiving feed money: “As a reward for its compilation, the author received feed money from February 2, 1701 to January 1, 1702 in the amount of 5 altyns per day , and only 49 rubles, 31 alt., 4 money, for which he issued a receipt, which was preserved in the files of the Naval Archive”4.
In 1715, the Moscow Academy was opened in St. Petersburg, the study of military sciences was transferred to the academy, and the Moscow school began to focus on teaching students arithmetic, geometry, and trigonometry.
2,3,4 // Encyclopedic Dictionary of Brockhaus and Efron: In 86 volumes (82 volumes and 4 additional ones). St. Petersburg: 1890-1907.
At the same time, Magnitsky was appointed head of the academic department and senior teacher of mathematics at the Moscow school. Magnitsky worked at the Moscow school until the day of his death, until October 1739. Magnitsky’s “Arithmetic” was published in January 1703, it marked the beginning of the printing of mathematical textbooks in Russia, and later Leonty Magnitsky actively participated in the publication of mathematical and astronomical literature, which was required for the new school.
Analysis of the above facts allows us to conclude that, starting from the second half of the 17th century, Russia began to realize that in order to overcome the crisis of traditionalism, modernization of the country was necessary. Peter I clearly understood the need to overcome the technical backwardness of Russia and in every possible way contributed to the development of Russian science and the level of education of people. Not in words, but in deeds, he considered mathematics the most important academic discipline, and education as 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, translated from different dialects into the Slavic language and collected into one and divided into two books... This book was written through the works of Leonty Magnitsky”, as stated on the title page of the book. 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 us turn to the appearance and 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 of 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 again talks about the purpose of this publication as a teaching aid for a newly opened school, sets out the contents of the book, and contains 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 gave 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 a simple example, then comes a general formulation, which is reinforced by a large number of examples and problems. Each action is accompanied by a verification rule (“verification”); this is done for both arithmetic and algebraic operations.
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 of 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 of Russian 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 children of middle and high 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. The 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 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 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.
