We have written monuments of the mathematical knowledge of the Russian people starting from approximately the thousandth year of our chronology. This knowledge is the result of a long previous development and is based on the practical needs of man.
Interest in science appeared early in Rus'. Information has been preserved about schools under Vladimir Svyatoslavovich and Yaroslav the Wise (11th century). Even then there were “number lovers” who were interested in mathematics.
In ancient times in Rus', numbers were written using letters of the Slavic alphabet, above which a special icon was placed - title (~). In economic life they were content with relatively small numbers - the so-called “small count”, which reached the number 10,000. In the oldest monuments it is called “darkness”, that is, a dark number that cannot be clearly imagined.
Subsequently, the limit of small counting was pushed back to 108, to the number of “darkness of topics.” An ancient manuscript on this occasion states that “more than this number the human mind cannot comprehend.”
To designate these large numbers, our ancestors used an original method not found among any of the peoples known to us: the number of units of any of the listed higher ranks was denoted by the same letter as simple units, but surrounded by a corresponding border for each number.
But the problem of teaching mathematics remained very important. To solve it, a textbook was needed, which did not exist until the 18th century. Having become interested in the history of teaching mathematics and having studied a lot of historical literature, I came to the conclusion that the first printed textbook on teaching mathematics in Russia, “Arithmetic, that is, the science of numbers, was 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.” That’s why I called my work “In the beginning there was a book and this book by Magnitsky.” In his “Arithmetic” Magnitsky not only summarized the available mathematical information, but also introduced a lot of new things into the development of mathematics in Russia.
In June 1669, a boy was born into the family of a peasant from the Ostashkovskaya settlement of the Tver province, Philip Telyashin, who was named Leonty.
Already from childhood, Leonty began to stand out among his peers for his variety of interests. He taught himself to read, write, and count. The desire to learn as much as possible, to read not only Russian, but also foreign manuscripts and books, prompted Leonty to study foreign languages. He independently mastered Latin, Greek, German and Italian. The desire to study led him to the Moscow Slavic-Greek-Latin Academy.
During his years at the Academy, he devoted all his free time to studying mathematics. Leonty Telyashin carefully studied Russian arithmetic, geometric and astronomical manuscripts before the 17th century and the scientific literature of Western countries. Acquaintance with the works of Western European educational literature allowed him to realize the advantages and disadvantages of Russian handwritten literature. The study of mathematical works in Greek and Latin contributed to expanding Telyashin’s horizons. Leonty Filippovich's knowledge in the field of mathematics surprised many. Tsar Peter I also became interested in him.
The rapid development of industry, trade and military technology in Russia required educated people. Peter I decided to open a number of technical educational institutions. But this was hampered by the lack of Russian teaching staff and educational literature, especially in physics, mathematics, and technical disciplines.
At the first meeting with Peter I, Leonty Filippovich made a strong impression on him with his extraordinary mental development and extensive knowledge. In recognition of Leonty’s merits, Peter I granted him the surname Magnitsky, thereby emphasizing to numerous opponents of education that a developed mind and knowledge attracts other people to a person with the same force with which a magnet attracts iron.
In January 1701, Peter I issued a decree on the creation of a school of mathematical and navigational sciences in Moscow. The school was located in the Sukharev Tower and began to prepare young people for various military and civil services. L. F. Magnitsky began his teaching career in this mathematical school. Peter I entrusts him with the creation of a textbook on mathematics. Magnitsky starts work and during the period of work on the book he receives “feed money” - this is what the author’s salary was called before.
Leonty Filippovich is working hard to create a textbook. And a huge book called “Arithmetic, that is, the science of numbers,” was published in January 1703. She got the start of printing mathematical textbooks in Russia.
Subsequently, Magnitsky published mathematical and astronomical tables. At the same time, Magnitsky conscientiously treats his teaching responsibilities. The head of the navigation school, clerk Kurbatov, in a report to Peter I on the school for 1703, wrote: “By July 16, 200 people had been cleaned up and were studying. The English teach them science in an official manner, and when they have time they go on a spree, or, as is their custom, often sleep for a long time. We also have Leonty Magnitsky as his designated supporter, who is constantly at that school and always has an eye not only for the students’ zeal for science, but also for other good behavior.”
In 1715 The Naval Academy was opened in St. Petersburg, where training in military sciences was transferred. The Moscow school began to focus on teaching students arithmetic, geometry and trigonometry. Magnitsky is appointed head of its educational department and senior mathematics teacher. Magnitsky worked in this Moscow school until his last day. Died in October 1739. On his grave there is a tombstone inscription: “He learned science in a wondrous and incredible way.”
Chapter 2. “Arithmetic” by Magnitsky.
2. 1 Structure and content of L. F. Magnitsky’s textbook “Arithmetic”.
Magnitsky’s book “Arithmetic, that is, the science of numbers” is written in Slavic script in an accessible language. The book is huge, it has more than 600 large format pages. The material is enlivened with poetic stanzas and useful tips for the reader. Although this book was simply called "Arithmetic", there is a lot of non-arithmetic material in it. There are sections of elementary algebra, geometry, trigonometry; trigonometric, meteorological, astronomical and navigational information. Magnitsky’s book was called not just an arithmetic textbook of the early 18th century, but an encyclopedia of basic knowledge in mathematics of that time.
The title page of the book says that it was published “for the sake of teaching the wise-loving Russian youths and people of every rank and age.” And at that time teenage boys were called adolescents. Magnitsky Arithmetic is not only a textbook for school, but also a tool for self-education. The author, from his own experience, confidently states that “everyone can teach himself.”
The great Russian scientist M.V. Lomonosov called Magnitsky’s “Arithmetic” “the gateway of his learning.” This book was the “Gateway of Learning” for all those who strived for education in the first half of the 18th century. Many people's desire to always have Magnitsky's book at hand was so great that they copied it by hand.
In his “Arithmetic” Magnitsky outlined the calculations of profits and losses, operations on decimal fractions, basic algebraic rules, the doctrine of progressions, roots, and the solution of quadratic equations. In the geometric part, he provides solutions to problems using trigonometry. Using the tables he compiled, L. F. Magnitsky teaches how to determine the latitude of a place by the inclination of the magnetic needle, calculate the time of high and low tides for different points, and also gives Russian maritime terminology.
Magnitsky’s “Arithmetic” is by no means a rewriting of all the mathematical information accumulated before him; many problems were compiled by Magnitsky himself, additional information on a particular topic, entertaining problems and puzzles are given.
In addition to Arithmetic, he wrote a number of books on mathematics. He compiled “Tables of logarithms, sines, tangents and secants for the teaching of wise-loving scrupulers,” and in 1722 he published a “Nautical Handbook.” Leonty Filippovich Magnitsky’s great service to science and to the fatherland.
2. 2 Words and symbols found in the book.
It is interesting to note that in “Arithmetic” “numeration, or reckoning” is highlighted as a special action, and it is considered in a special section. It says: “numeration is the counting in words of all numbers that can be represented by ten such signs: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. Of these, nine are significant; the last one is 0, if there is one, then in itself it has no meaning. When it is added to some significant one, it increases it tenfold, as will be shown later.”
Magnitsky calls significant figures “signs” to distinguish them from zero. The author calls all single-digit numbers “fingers.” Numbers made up of ones and zeros (for example, 10, 40, 700, etc.) are “joints.” All other numbers (12, 37, 178, etc.) are “compositions”. Here he calls the number 0 “for nothing.”
Magnitsky L.F. was also the first to use such terms as “multiplier”, “divisor”, “product”, “root extraction”, “million”, “billion”, “trillion”, “quadrillion”.
Further in “Arithmetic” the names of numbers of the form one with one and several zeros are given. The table with the names of round numbers has been brought to a number with 24 zeros. Then in poetic form it is emphasized “The number is infinite”
Magnitsky’s “Arithmetic” uses modern Arabic numbers, and the year of publication and the numbering of sheets are given in Slavic numbering. This happened because the outdated Slavic numbering was being replaced with a more advanced one - Arabic.
Chapter 3. From the contents of ancient Russian manuals on mathematics.
3. 1 False position rule.
Ancient Russian manuals on mathematics, handwritten and printed, contain much that is useful to know for students of mathematics in our time. Let's talk about the false position rule, entertaining problems and mathematical fun.
False position rule. Old Russian manuals call a method of solving problems that is now known as the rule of false position, or otherwise the “false rule.”
Using this rule, in ancient manuals problems are solved that lead to equations of the first degree.
Let us present the solution to the problem using the method of a false position, 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 fourth clean and your son, then I will have 100 students. The question arises: how many students did the teacher have?
Magnitsky gives this solution. We make the first assumption: there were 24 students. Then, according to the meaning of the problem, we need to add “that much, half that much, a quarter that much and 1” to this number, 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”.
Let's make a 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 assumptions result in less, the rule is given: multiply the first assumption by the second deviation, and the second assumption by the first deviation, subtract the smaller product from the larger product and divide the difference by the difference in deviations:
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 = 144.
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).
If, under one assumption, we obtain 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.
I tried to solve this problem by identifying three stages of mathematical modeling. Here's my solution.
Let there be x students in the class, then x more students come to them. Then 1/2 students and another 1/4 students, and another student.
Since there will be 100 students in total, we get the equation: x+x+1/2x+1/4x+1=100
It is not difficult to solve this equation. Let's bring it to a common denominator and calculate x. We get x=36, i.e. there were 36 students in the class.
Answer: 36 students.
3. 2 Entertaining tasks.
Magnitsky's Arithmetic contains interesting problems. Here is one of them: A certain man is selling a horse for 156 rubles; Having repented, the merchant began to give it to the seller, saying: “It’s impossible for me to take a calico horse, unworthy of such high prices.” The seller offered to buy another, saying: “If you think the price of this horse is great, then boil the nails, they should have this horse in the horseshoes of your feet, take the horse for that purchase as a gift for yourself. And there are six nails in every horseshoe, and for one nail give me a half-ruble, for another - two half-rubles, and for the third a penny, 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, how much is the merchant - did he haggle?
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 is not good for me to buy this horse, since it 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.
I solved it this way: if there are only 4 horseshoes, and each horseshoe has 6 nails, then 4x6 = 24 nails in total. From the conditions of the problem we conclude that the price of each nail needs to be doubled. Let's solve this problem using geometric progression. One half is ¼ kopeck. 1 nail costs ¼ kopeck, 2 nails ½ kopeck, 3 nails 1 kopeck. Let 1 kopeck be 1 term of a geometric progression, the difference is 2, let’s find the 22nd term.
b22=b1xq21=1x221=2097152 kopecks - costs the 24th nail. Let's find the cost of all nails Sn=(bnxq-b1)/(q-1) =(2097152x2-1)/(2-1)=4194303 kopecks. This means that the buyer bargained for 41940-10 = 41930 rubles.
This problem is similar to the problem about the inventor of the game of chess. In Dante's famous "Divine Comedy" we read:
“The beauty of all those circles sparkled,
And there was an immense fire in those sparks;
The number of sparks is hundreds of times more abundant,
Than counting cells twice on a chessboard.”
“Double counting” means increasing numbers by doubling the previous number, that is, we have here a reference to the same old problem.
It turns out that it is found in our time not only in collections of entertaining problems. According to one newspaper in 1914, a judge in the city of Novocherkassk was hearing a case about the sale of a herd of 20 sheep under the condition: pay 1 kopeck for the first sheep, 2 kopecks for the second, 4 kopecks for the third, etc. Obviously, the buyer was tempted hope to buy cheap. I calculated how much he had to pay. Using the formula for the sum of the geometric progression S20=b1x(q20-1)/(q-1), we get 1x(220-1)/(2-1)=1048575 kopecks=10486 rubles. It turns out that Magnitsky, not without reason, provided the solution to his problem with a warning:
“You want to be attractive.
From whom do you take what?
Yes, he sees himself as dangerous. “, that is, if someone is tempted by the apparent cheapness of the purchase, he may find himself in an unpleasant situation.
3. 3 Math fun.
In Magnitsky’s “Arithmetic,” fun forms a special section “On certain comforting actions used through arithmetic.” The author writes that he includes 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 performs in his mind or on paper: 4 ∙ 2 = 8;
2) add 5 to the resulting product: 8 + 5 = 13;
3) multiply the resulting amount by 5: 13 ∙ 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 ∙ 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.
The latter subtracts 250 from the resulting number and gets: 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 ∙ a = 2a;
3) 5(2a + 5)=10a + 25;
4) 10a + 25 + b;
5) 10(10a + 25 + b) = 100a + 250 +10b;
6) 100a + 10b + 250 + c;
7) 100a + 10b + 250 + c – 250 = 100a + 10b + c.
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 ∙ 2 = 12;
2) add 5 to the product: 12 + 5 = 17;
3) multiply the amount by 5: 17 ∙ 5 = 85;
4) add zero to the product and call the result: 850.
From this number, the guesser subtracts 250 and receives: 850–250= 600.
The sixth day of the week was conceived - Friday. The rationale for the rule is the same as in the previous case.
I performed these games in my class, and the kids really liked them.
Conclusion.
In the 18th century there was not a single printed textbook on mathematics, so L. F. Magnitsky’s book was of great importance for the development of industry and the army, construction and navy, education and science in Russia. “Arithmetic” was useful to every person: both an artist and a rower, as mentioned above. But who, if not Magnitsky, could so clearly explain and summarize already known mathematical information, as well as add explanations to this or that topic, compile many tables, find methods and rules for solving problems!?
It is very important to study the history of the development of mathematics in order to cultivate respect for the cultural heritage of Russian science, which is what I tried to do in this research work “First there was a book and this book by Magnitsky.”
I believe that the main goal of the work has been achieved, the tasks have been solved. I will definitely continue working on this topic, as I am very interested in the history of the development of mathematics.
One of the stages of work on the project “Ancient Mathematical Problems” was the collection of material about mathematicians of past times. I chose a topic about L.F. Magnitsky. I found interesting material about him, his textbook “Arithmetic”.
Download:
Preview:
Leonty Filippovich Magnitsky
Leonty Filippovich Magnitsky is the first teacher of mathematics and marine sciences in Russia. From 1701 until the end of his life he taught mathematics at the Moscow School of Mathematical and Navigational Sciences.
Not much is known about Leonty Magnitsky. Most of the information about him dates back to the years when he was already teaching at the Navigation School. All that is known about his childhood years is that he was born into a peasant family in the Ostashkovo monastery settlement on the shores of Lake Seliger. The future mathematician's father's name was Philip, his nickname was Telyashin, but at that time peasants were not given surnames. The boy learned to read independently as a child, thanks to which he at times served as a psalm-reader in the local church.
The young man’s fate changed dramatically when he was sent from his native settlement with a cart of frozen fish to the Joseph-Volokolamsk Monastery. Apparently, in the monastery the boy showed interest in books, and the abbot, making sure of his literacy, left Leonty as a reader. A year later, the abbot blessed the young man to study at the Slavic-Greek-Latin Academy, which was the main educational institution in Russia at that time. Leonty studied at the academy for about eight years.
It is curious that mathematics, which Magnitsky then studied for the rest of his life, was not taught at the academy. Consequently, Leonty studied it on his own, as well as the basics of navigation and astronomy. After graduating from the academy, Leonty did not become a clergyman, as the abbot who sent him to study had hoped, but began teaching mathematics, and possibly languages, to the families of Moscow boyars.
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 I loved Magnitsky for his lively mind and great knowledge, and as a sign of deep respect for the mathematical talent of Leonty Filippovich and his educational activities, he came up with the name “Magnitsky” for him, since he attracted youths to himself with his learning like a magnet. Only representatives of the highest nobility had surnames.
As the best Russian mathematician, L. F. Magnitsky was entrusted with compiling a textbook on arithmetic, which he completed with great talent. Although the textbook was called "Arithmetic", it can be considered as an encyclopedia of mathematical knowledge of that time. In it, in addition to a detailed presentation of the basics of arithmetic, it provides information on algebra (rules for extracting square and cubic roots, progression), applications of arithmetic and algebra to geometry, concepts about the calculation of trigonometric tables and trigonometric calculations in general, information on astronomy, geodesy and navigation. The textbook contains many problems and examples, and most of them are interesting and even exciting in content. The author, trying to make arithmetic entertaining, uses poetry and drawings.
Magnitsky’s “Arithmetic” as a textbook was in school use almost until the middle of the 18th century. M.V. Lomonosov also studied according to it. An epitaph is carved on the gravestone in memory of L.F. Magnitsky. She tells descendants about a selfless worker of science, a man of great soul, a faithful son of his fatherland. Here is the inscription:
“In eternal memory... to the virtuous life of Leonty Filippovich Magnitsky, the first mathematics teacher in Russia, buried here, husband..., who began the path of this temporary and regrettable life on the 9th day of June 1669, studied the sciences in a marvelous and incredible way, His Majesty Peter the First, for his wit in the sciences, was appointed in 1700 and from His Majesty, at the discretion of his disposition towards everyone and attracted to himself, was granted, named Magnitsky and appointed to the Russian noble youth as a teacher of mathematics, in which title zealously, faithfully, honestly , having served diligently and blamelessly and having lived in peace for 70 years, 4 months and 10 days, 1739, October 19th day, about midnight at 1 o'clock, having left an example for those who followed him with his virtuous life, he died piously...Not in office wrote the bitter-tearful Ivan, the lowest slave, his dear son»
The main advantage of Magnitsky's Arithmetic is its completeness of content. This is not just arithmetic, but a whole course of mathematics with its application to navigation. True, Magnitsky considered arithmetic the cornerstone of mathematical education and treated it extremely carefully in his book. He used innovations in the field of arithmetic, introduced new names; “million”, “billion”, etc., thereby taking a major step forward, elevated zero to the rank of a number, classifying it among the “fingers” (the first ten numbers) and thereby was much ahead of its time; placed many explanatory examples (“butts”), including examples of “certain entertainment actions used through arithmetic,” and revealed great pedagogical talent in presenting operations on integers and ordinary fractions.
Magnitsky's "Arithmetic" was a response to this demand of the time. It had great scientific and methodological advantages for its era, and its advantages are especially clear when compared with similar Western European textbooks that were contemporary to it.
In the preface to Arithmetic, Magnitsky wrote: “all Russian people will make good use of this work.” This wish came true. His book helped students of the mathematics and navigation school provide material for the first “general map of all Rus'” and the first geographical atlas in 1726-1734.
Magnitsky is an outstanding mathematics teacher of the first half of the 18th century, the author of “Arithmetic,” one of the most remarkable books of the 18th century, which M. V. Lomonosov called “the gates of learning.”
Magnitsky was the first to introduce our ancestors to mathematics in a volume that was rare for his time and showed its great practical significance. This is Magnitsky’s main merit to the history of mathematical education in our country.
No less important is his merit as the first teacher of Russian sailors, who successfully overcame the enormous difficulties that he encountered when presenting the fundamentals of nautical science in Russian. Information about Magnitsky's life and activities is very scarce; Most of this information has not yet been documented.
Magnitsky was born on June 9 (10), 1669. According to some sources, he was born in Moscow. This birthplace of Magnitsky is indicated in the article “The author of the first Russian arithmetic, Leonty Magnitsky” (“Moskovskie Vedomosti”, 1836, No. 76), the name of the author of which could not be established. The author of this article, in his own words, presented all the information about Magnitsky on the basis of “reliable sources,” but did not indicate these sources.
According to other sources, Magnitsky was born in the Ostashkovskaya patriarchal settlement of the Tver province. For example, N. A. Krinitsky, one of Magnitsky’s biographers, based on archival materials he found in 1903, argued that Magnitsky was the son of a peasant of the Ostashkovskaya Patriarchal Settlement, nicknamed Telyashin, and “was a close relative of the second organizer of the Nilova Hermitage - Archimandrite Nectarius, who came from the Telyashin family.”
Magnitsky’s parents were Russian people, but to what class they belonged and what they did remained unknown until the last days.
Nothing is also known about whether Magnitsky studied, where or with whom, or whether he was, in the full sense of the word, a nugget and self-taught.
N.I. Novikov in his “Experience of a Historical Dictionary on Russian Writers” (St. Petersburg, 1772) directly states that nothing is known about the place of Magnitsky’s teachings.
S. Smirnov in “History of the Moscow Slavic-Greek-Latin Academy” (Moscow, 1855, p. 252) states the opposite: Magnitsky studied at the Moscow Academy, probably under the Likhud brothers; but at the same time does not indicate any sources from which he borrowed this statement.
One thing is certain that among the students of the mentioned academy for the first 15 years of its existence (1685-1700) neither Magnitsky’s name nor Telyashin’s name appears.
It is difficult to imagine that Magnitsky - “a pious, well-behaved and grateful man” - could remain silent about his teachers and the place of his teaching. In the preface to his Arithmetic, Magnitsky, with his characteristic frankness, declares himself simply and directly:
"naturally Russian, not Nemchin."
Or elsewhere in the same preface we read:
“And for me, like you and your mother, be,
That anyone can teach himself.”
These words, as well as the words on Magnitsky’s tombstone: “He learned the sciences in a marvelous and incredible way,” give reason to think that Magnitsky owes his broad education not so much to school as to his natural talent, which allowed him to find ways and means to study the ancients and new languages, mathematics, church literature, literature and rhetoric.
N.A. Krinitsky in the above article cites an interesting excerpt characterizing Leonty Filippovich in his youth: “In his youth, an inglorious and insufficient person who fed himself with the work of his hands, he became famous only for the fact that, having learned to read and write, he was a passionate hunter read in church and sort out the tricky and difficult things.”
At the age of thirty-two, Magnitsky became a mathematics teacher at the first Russian school in which the study of this science was given a prominent place, namely, the mathematical and navigation school, established in 1701. In this school, Russian youths, “those who voluntarily wanted to, some more so under compulsion,” were taught arithmetic, geometry, trigonometry with applications to geodesy and astronomy, flat and Mercator navigation, mathematical geography, and keeping a logbook (“diurnal”).
The teachers of the mathematics and navigation school were Englishmen appointed back in 1698: for “mathematical science” - Andrei Farkhvarson, for “navigational science” - Stefan Gwin and Richard Grace.
Magnitsky, known to the leadership of the school of mathematics and navigation as the best mathematician in Moscow at that time, was appointed assistant to Farkhvatson in 1702. At the same time, funds were allocated for the compilation and printing of Magnitsky’s textbook on mathematics.
Teaching in this school proceeded in the following order: students studying arithmetic, after an exam with Magnitsky, were transferred to the next class, the geometry class; those studying geometry were transferred to the trigonometry class, etc.
Magnitsky, who taught arithmetic, geometry and trigonometry, initially also taught navigation. But after a quarrel with the British, he taught only trigonometry to his students, and the students were transferred from him to foreign teachers.
At the end of the course, Farkhvatson and Magnitsky submitted lists of “those who had completed training and were ready for practice” first to the armory and then to the order of the navy.
An idea of the level of teaching mathematical sciences in the navigation school is given by the fact that Peter I demanded “to write to the mathematical teachers in Moscow (at the Sukharev Tower) so that they could calculate how many eclipses the sun would have in Voronezh, and, having drawn them, send them to us "
The given fact indicates that the teachers of the mathematics and navigation school were able to carry out complex astronomical observations and calculations.
Magnitsky performed his teaching duties with his characteristic conscientiousness, as evidenced by the following letter from clerk Kurbatov in 1703, the de facto head of the mathematics and navigation school: “By July 16, 200 people were cleaned up and studying. The British teach them that science in an official manner. We have as their helper Leonty Magnitsky, who is constantly at that school, and always has care not only for the students’ zeal for science, but also for other good behavior, in which those Englishmen, seeing his management in schools not the last, obliged themselves to him, Leonty, with hatred.”
This letter provides a comparative assessment of the school's teachers and outlines the relationship between Magnitsky and the English teachers at the beginning of their joint teaching activities.
Magnitsky’s wages were low compared to English teachers. But for his diligent attitude towards teaching duties, Magnitsky, apparently, sometimes received additional remuneration.
In 1715, Peter I decreeed the establishment of a maritime academy in St. Petersburg. From this year, the mathematics and navigation school changed its character somewhat: teaching military sciences was transferred to the newly opened naval academy, and in the Moscow school they began to teach only arithmetic, geometry and trigonometry.
Since the opening of the maritime academy, Magnitsky became the senior teacher of the mathematics and navigation school and the head of its educational department. He, by the way, was entrusted, starting in 1714, with the recruitment of teachers for the digital schools then established throughout Russia. It was prescribed to recruit such teachers “not from noble breeds,” and Magnitsky reported in 1716 that he chose only 6 people from his school and that “no more worthy ones from such noble breeds appeared.”
Since 1832, Magntsky was in charge of the administrative and economic part of the mathematics and navigation school. In this regard, the following facts are interesting, which are reported in the article “The author of the first Russian arithmetic, Leonty Magnitsky.”
“From the files of the Sukharevsky archive it is clear that Magnitsky, managing the Moscow academic office under Anna Ivanovna, submitted reports to the Collegium that forced him to redo them, and received a salary of 260 rubles per year. This circumstance and the words in the tombstone inscription that he was “the most patient of insults from the enemy,” give reason to assume that he, too, suffered insults in that time when Biron’s cruel hand weighed heavily on the Russians.”
Another evidence of the role and significance of Magnitsky for the school of mathematics and navigation has been preserved. Vasily Yakovlevich Chichagov (1726-1809), later a famous military admiral who won a brilliant naval victory over the Swedes in 1789, studied at this school under Magnitsky. This is what he told his son P.V. Chichagov about his studies at the mathematics and navigation school, from whose words we relay this story: “One of the teachers, Magnitsky, was reputed to be a great mathematician... He even published a sheet of work printed in Slavic script, which was in my hands, which contained arithmetic, geometry, trigonometry and the rudiments of algebra. Subsequently, this book was recognized as an example of scholarship. It was here that my father gained his knowledge.”
Magnitsky devoted more than half of his life to serving in the mathematics and navigation school. To a large extent, thanks to his leadership of this school, mathematical knowledge began to spread in our country and acquire corresponding significance.
Magnitsky led the school of mathematics and navigation until the last days of his life. He died on October 19 (30), 1739 and was buried in Moscow. On Magnitsky’s tombstone there was an inscription made by his son, shedding some light on the personality of Leonty Filippovich.
“An honest life, the quietest disposition, an honest demeanor, a lover of righteousness, the most pleasant to everyone and shuns all sorts of insults, passions and evil deeds with all his might, the most dangerous keeper of the truth about both spiritual and civil matters, he studied the sciences in a marvelous and inconceivable way, to His Majesty Peter I, for the sake of wit in the sciences, was appointed, we know, in 1700, and from His Majesty, at the discretion of his disposition towards everyone, who was most pleasant and attracted to himself, was granted, named Magnitsky, and appointed to the Russian noble youth as a teacher of mathematics, in which title zealously, faithfully, honestly, diligently and blamelessly, served and lived in peace for 70 years, 4 months and 10 days on October 19, 1739, at midnight at 1 o’clock, due to a six-day illness and which he died piously.”
Magnitsky owns several manuals on mathematics, the most important of which is “Arithmetic, that is, the science of numbers” (1703).
It was stated above that Magnitsky submitted his “Arithmetic” on November 21, 1701 for publication. Magnitsky's Arithmetic was written in Slavic.
Magnitsky’s “Arithmetic” consists of two books: “Arithmetic of politics, or civil” and “Arithmetic of logistics, not only to citizenship, but also to the movement of celestial circles.”
The first book is divided into five parts, the second into three parts. The first part of the first book sets out the rules of numbering, the four operations on integers, and how to test them. Next come named numbers, which are preceded by an extensive treatise on ancient Jewish, Greek and Roman money, measures and weights of Holland and Prussia, measures and money of the Moscow state, three comparative tables of measures, weights and money. This treatise, distinguished by its remarkable detail, clarity and accuracy, testifies to Magnitsky's deep erudition and erudition.
Even now, this section of Magnitsky’s “Arithmetic” can be of some use in historical research, since it provides information about how our ancestors measured land, bulk substances, what kind of money they had, etc.
The second part sets out fractions in detail, the third and fourth - “rule problems”, very cleverly composed and of practical importance for that time (“required for citizenship”); the fifth part sets out the basic rules of algebraic operations, progressions and roots. This part contains many examples of the application of algebraic material to military and naval affairs. The fifth part ends with a discussion “about another order of arithmetic, called decimal or tenth.” Here Magnitsky sets out the initial operations on decimal fractions, which at that time were news in educational and mathematical literature.
Throughout the first book of Magnitsky's arithmetic, syllabic verses are generously scattered, which follow each rule. Each part of the Arithmetic is also preceded by a poem; for example, the second part begins with verses:
O dear thorough one
Hear my helpful voice.
Magnitsky prefaces the second book, containing arithmetic-logistics, with a preface in which he explains the meaning of arithmetic-logistics and argues for the need for its study for an engineer and navigator.
Magnitsky divides arithmetic and logistics into three parts.
The first part provides a further presentation of algebra - solving quadratic equations; in the second part, geometric problems on measuring areas are solved and those theorems are considered that make it possible to calculate trigonometric functions of various angles; the third part contains information necessary for the navigator, and is an application to navigation of the previously stated rules of arithmetic, algebra, geometry, and trigonometry.
The material in Magnitsky’s “Arithmetic” is presented in question-and-answer form; for example, the chapter on subtracting integers begins: “What is subtraction? Subtraction, or subtraction, is also subtracting a small number from a large one and declaring the excess... as when you happen to subtract the list of 57 from 89, and declare the rest; and you put the smaller list under the larger one 89 57, draw a line under them, just like there is 57, and start subtracting from the right hand, think 7 out of 9, there will be 2 left, put it against 7 under the line
89
57
2
then think about it: 5 out of 8 will remain 3: and you put that against 5 under the line
89
57
32
and declare the excess of the larger list before the smaller one under the line.”
The main advantage of Magnitsky’s “Arithmetic” is its completeness of content. This is not just arithmetic, but a whole course of mathematics with its application to navigation. True, Magnitsky considered arithmetic the cornerstone of mathematical education and treated it extremely carefully in his book. He used innovations in the field of arithmetic, introduced new names; “million”, “billion”, etc., thereby taking a major step forward, elevated zero to the rank of a number, classifying it among the “fingers” (the first ten numbers) and thereby was much ahead of its time; placed many explanatory examples (“butts”), including examples of “certain entertainment actions used through arithmetic,” and revealed great pedagogical talent in presenting operations on integers and ordinary fractions.
In Magnitsky's presentation of algebra and geometry we will no longer find this completeness and thoroughness. There are no definitions, no axioms, no proofs; often the rules are not even stated - the reader is left to do it himself.
Despite these shortcomings, algebraic and arithmetic information in Magnitsky’s “Arithmetic” played its role as the first time that publicly available mathematical information was brought into a certain system, going beyond the boundaries of arithmetic itself.
Magnitsky's mathematics textbook was difficult to understand not only for students, but also for teachers of that time. The more accessible part of it was arithmetic; but even this part needed significant processing in order to be widely used in digital schools and home teaching.
Both Magnitsky’s textbook and his adaptations were distinguished by the dogmatism of their presentation. In Magnitsky’s era, it was important to teach how to perform actions without explaining the reasons why it was done one way and not another.
Magnitsky's "Arithmetic" was a response to this demand of the time. It had great scientific and methodological advantages for its era, and its advantages are especially clear when compared with similar Western European textbooks that were contemporary to it.
In the preface to Arithmetic, Magnitsky wrote: “all Russian people will make good use of this work.” This wish came true. His book helped students of the mathematics and navigation school provide material for the first “general map of all Rus'” and the first geographical atlas in 1726-1734. His book stimulated M.V. Lomonosov to natural science education.
Leonty Filippovich Magnitsky
An absolutely amazing person.
One of the first Russian teachers, the creator of a unique textbook, from which Russian youths studied for two centuries. By the way, for the first time this textbook was published under the editorship of who do you think? Peter I himself.
Who in his youth went with a fish train to Moscow, entered the best educational institution there, and soon after graduation became famous as a scientist?
That's right - Lomonosov.
But the same episodes determined the biography of Leonty Filippovich Magnitsky half a century earlier. This is who Mikhail Vasilyevich modeled himself on!
A fellow villager brought Magnitsky’s work on sign arithmetic to Lomonosov’s home village of Denisovka in northern Russia. Already at the height of his fame, Lomonosov called “Arithmetic” by Leonty Magnitsky and “Grammar” by Melety Smotritsky “to the gates 
and his learning."
All that is known about his childhood years is that he was born into a peasant family in the Ostashkovo monastery settlement on the shores of Lake Seliger. The future mathematician's father's name was Philip, his nickname was Telyashin, but at that time peasants were not given surnames. The boy learned to read independently as a child, thanks to which he at times served as a psalm-reader in the local church.
The young man’s fate changed dramatically when he was sent from his native settlement with a cart of frozen fish to the Joseph-Volokolamsk Monastery. Apparently, in the monastery the boy showed interest in books, and the abbot, making sure of his literacy, left Leonty as a reader. A year later, the abbot blessed the young man to study at the Slavic-Greek-Latin Academy, which was the main educational institution in Russia at that time. 
Leonty studied at the academy for about eight years. It is curious that mathematics, which Magnitsky then studied for the rest of his life, was not taught at the academy. Consequently, Leonty studied it on his own, as well as the basics of navigation and astronomy. After graduating from the academy, Leonty did not become a clergyman, as the abbot who sent him to study had hoped, but began teaching mathematics, and possibly languages, to the families of Moscow boyars.
What was going on in Russia then? On the throne was Peter I. Tsar reformer. He himself studied in Europe and, having arrived back in Russia, launched an extremely vigorous activity. He forced the boyars to take on beards and dress in European dress. Created new governing bodies. The Northern War was fought. There was a huge need for our own fleet.
The urgent need for educated people for the purposes of the state in its increasing development should have caused and did cause the emergence of a number of schools for teaching children of all ranks, including those of the same household, from 10 to 15 years old in numbers (arithmetic) and geometry. It was ordered to establish them in every significant city and place them at the most prosperous monasteries and bishops' houses, or in buildings specially arranged for this purpose at the military offices.
For children of the clergy, education in these schools was mandatory: those who did not want to study were threatened with military service or taxation; young men who did not complete the digital school course should not even be given permission to marry.
The practical creation of schools began in 1715, when, with the relocation of the School of Mathematical and Navigational Sciences to St. Petersburg, Peter I ordered that two students from this school be sent to the provinces, who had learned geometry and geography for “the science of young children from all ranks of people.” Already in the next 1716, twelve schools were opened in different cities of Russia, and in 1720-1722 thirty more were opened. The new schools taught arithmetic and geometry, which is why they were called digital (and also, occasionally, arithmetic).
Peter 1 was looking for teachers who could teach in navigation schools. I was looking for my own, Russian teachers. Young Leonty Fillipovich made a very strong impression on Tsar Peter I with his extraordinary mental development and extensive knowledge. As a sign of respect and recognition of his merits, Peter I “bestowed” him the surname Magnitsky “in comparison with how a magnet attracts iron to itself, so he drew attention to himself with his natural and self-educated abilities.” For modern people, the significance of this gift is not entirely clear, but at that time only representatives of the highest nobility had surnames.
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.
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 navigational tools, as well as advice and assistance from foreign teachers.
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.
Magnitsky problems
1. Someone asked a certain teacher how many students you have, since I want to send my son to your school. The teacher answered: if as many more students come to me as I have, and half as many and a quarter and your son, then I will have 100 students.
How many students did the teacher have? (Ans. 36).
2. A certain man sold a horse for 156 rubles; repentant 
The merchant began to give it to the seller, saying that the horse was not worthy of such a high price. The seller offered him another purchase, saying: if you think the price of a horse is high, then buy only the nails that are in the horse’s shoes, take the horse for free, and there are 6 nails in each horseshoe. For the 1st nail, give me half a ruble (1/4 kopecks), for another 2 half rubles, for the 3rd - a kopeck, for the 4th - two kopecks, etc. for all the nails. The merchant, believing that all the nails would cost no more than 10 rubles, wanted to receive a horse as a gift and agreed to that price. It’s obvious how much the merchant bargained with. (Ans. 4 178 703 3/4 kop.).
3. A certain man hired a worker for a year, promising to give him 12 rubles and a caftan. But by chance, after working for 7 months, he wanted to leave and asked for a decent salary with a caftan. He was given his due 5 rubles and a caftan. What was the price of this caftan? (Ans. 4 4/5 rubles or 48 hryvnia).
4. One man will drink a kad on the 14th day, and his wife and he will drink the same kad on the 10th day. And you know, in how many days will his wife especially drink the same Kad? (Ans. 35 days)
In 1704, Magnitsky was granted nobility by royal decree. Peter I was especially disposed towards Leonty Filippovich, granted him villages in the Vladimir and Tambov provinces, ordered him to build a house on Lubyanka, and awarded him a “Saxon caftan” and other clothes for his “incessant and diligent work in navigational schools.”
In 1714, Magnitsky was entrusted with recruiting teachers for digital schools.
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 this moment on, Magnitsky becomes the senior teacher of the school and leads its educational part.
From 1732 until the last days of his life, L. F. Magnitsky was the head of the Navigation School.
He died in October 1739 at the age of 70. He was buried in the Church of the Grebnevskaya Icon of the Mother of God at the Nikolsky Gate. Magnitsky's ashes found peace for almost two centuries next to the remains of princes and counts (from the Shcherbatov, Urusov, Tolstoy, Volynsky families).
In 1932, during the construction of the metro on May 27, at a depth of one meter, a slab of strong limestone was discovered, on the back of which was the “epitaph” of L. F. Magnitsky’s tombstone, written by his son Ivan, finely engraved. The next day, a tomb was discovered under the monument slab at a depth of four meters. It was made of good brick and filled with lime on all sides. In the grave there was an oak log, in it lay the intact skeleton of Leonty Filippovich with some of the integument preserved on it, under the head there was a glass inkwell shaped like a lamp, and next to it lay a half-decayed goose feather.
Website materials used:
- http://shkolazhizni.ru http://www.peoples.ru/science/mathematics/
- http://bozhoklv.ucoz.ru/news/uchebnik_magnickogo/
- http://azbukivedi-istoria.ru/publ/prochee/