Presentation of ancient measures. Presentation "Old Russian measures of length." Proverbs and sayings

An ancient measure of length in Russia, equal to 71.12 cm. There are different versions of the origin of the arshin measure of length. Perhaps, initially, “arshin” denoted the length of a human step (about seventy centimeters, when walking on the plain, at an average pace) and was the base value for other large measures of determining length, distances (fathom, verst). Subsequently, they also began to use, under this name, an equal value - the length of the arm.

SMALL SPAND - the distance between the ends of the spread thumb and index (or middle) fingers = 17.78 cm. LARGE SPAND - the distance between the ends of the thumb and little finger (22-23 cm). SHARP WITH A TURN - a span with the addition of two joints of the index club = cm

Old Russian travel measure (its early name was “field”). This word originally referred to the distance traveled from one turn of the plow to another during plowing. The two names have long been used in parallel, as synonyms. "Verstoy" was also called a milestone on the road. The size of the verst changed repeatedly depending on the number of fathoms included in it and the size of the fathom. Before Tsar Alexei Mikhailovich, 1 verst was considered 1000 fathoms. Later, in the 18th century, along with it, a “travel mile” of 500 fathoms (“five hundredth mile”) began to be used.

One of the most common measures of length in Rus' is “Makhovaya fathom” - 1.76 m, the distance between the ends of the fingers of an adult man’s widely spaced hands. “Oblique fathom” - 2.48 m, the longest: the distance from the toe of the left foot to the end of the middle finger of the raised right hand. According to historians and architects, there were more than 10 fathoms and they had their own names, were incommensurable and not multiples of one another.

Elbow - “the distance in a straight line from the bend of the elbow to the end of the extended middle finger of the hand.” The size of this ancient measure of length, according to various sources, ranged from 38 to 47 cm. Since the 16th century, it was gradually replaced by the arshin and in the 19th century it was almost not used.

Pud - (from the Latin pondus - weight, heaviness) is not only a measure of weight, but also a weighing device. When weighing metals, the pud was both a unit of measurement and a unit of counting. Even when the results of weighings were reported to tens and hundreds of poods, they were not transferred to Berkovites. Back in the XI-XII centuries. they used various scales with equal-armed and unequal-armed beams: “pud” - a type of scale with a variable fulcrum and a fixed weight, “skalvy” - equal-armed scales (two-cup).

Proverbs and sayings “One, like a finger” - a person who has no relatives, no loved ones, no friends. “Two inches from the pot, and already a pointer” - a young man who has no life experience, but arrogantly teaches everyone. “Her Saturday has slipped two inches from Friday to Friday” - about a sloppy woman whose undershirt is longer than her skirt. “Every merchant measures by his own yardstick” - everyone judges any business one-sidedly, based on his own interests. “He sits and walks as if he could swallow a yardstick” - about an unnaturally upright person. “He found out what a pound is worth,” - this is what they say about a person who has suffered a lot of adversity. “Love is not measured by miles. A hundred miles is no detour for a young man” - distance cannot be an obstacle to love.

Ancient problems Problem 1 The dog saw a hare 150 fathoms away from him. A hare runs 500 fathoms in 2 minutes, and a dog runs 1300 fathoms in 5 minutes. How long will it take the dog to catch up with the hare? Solution: In one minute, the hare runs 250 fathoms, and the dog runs 260 fathoms. Consequently, in one minute the distance between the dog and the hare will decrease by 10 fathoms. Since there were 150 fathoms between the dog and the hare when the dog saw the hare, the dog will catch up with the hare in 150:10=15 minutes.

Interesting problems Problem Someone bought three quarters of an arshin of cloth and paid 3 altyns for them. How much should you pay for 100 arshins of the same cloth? (1 altyn = 3 k.) Solution: Since 3/4 arshin costs 3 altyn, then 3 arshin costs 12 altyn and 1 arshin costs 4 altyn. Consequently, 100 arshins cost 400 altyn, which is 1200 k. or 12 rubles.

Excerpts from works 1. P.P. Ershov “The Little Humpbacked Horse”: Yes, a toy horse Only three inches tall, On the back with two humps Yes, with arshin ears? ... 2. M.E. Saltykov - Shchedrin “Family Results”: ... But the economy in Pogorelovka was fussy, petty, requiring every minute personal supervision, and although in the heat of the moment it seemed to her that achieving accurate accounting where pennies are made up of half rubles, and pennies from pennies, does not amount to any wisdom , however, she soon had to admit that this belief was erroneous. ... 3. N.A. Nekrasov “Grandfather Mazai and the Hares”: ...I see one small island - With every minute the water was getting closer to the poor animals; Already under them there was less than an arshin of land in width, Less than a fathom in length, Then I drove up: their ears were chattering, They didn’t move; I took one, commanded the others: jump yourself! ….

Slide 1

Since ancient times, the measure of length and weight has always been a person: how far he can stretch his arm, how much he can lift on his shoulders, etc. The system of Old Russian measures of length included the following basic measures: verst, fathom, arshin, elbow, span and vershok.

Ancient Russian measures of length, weight, volume

Slide 2

ARSHIN is an ancient Russian measure of length, equal, in modern terms, to 0.7112 m. Arshin was also the name given to a measuring ruler, on which divisions in vershoks were usually applied.

STEP - the average length of a human step = 71 cm. One of the oldest measures of length.

PYAD (pyatnitsa) is an ancient Russian measure of length. SMALL SPAND (they said - “span”; since the 17th century it was called “quarter”) - the distance between the ends of the spread thumb and index (or middle) fingers = 17.78 cm.

SAZHEN is one of the most common length measures in Rus'. There were more than ten fathoms of different purposes (and, accordingly, size).

VERSTA is an old Russian travel measure (its early name was “field”).

Slide 3

For small measures of length, the base value was the measure used from time immemorial in Rus' - “span” (from the 17th century - a length equal to a span was called differently - “quarter arshin”, “quarter”, “chet”), from which it is easy to visualize it was possible to get smaller shares - two inches (1/2 inch) or an inch (1/4 inch).

Our old icon painters measured the size of icons in spans: “nine icons - seven spans (1 3/4 arshins). The Most Pure Tikhvin on gold - pyadnitsa (4 vershoks). Icon of St. George the Great deeds of four spans (1 arshin)"

ELBOW was equal to the length of the arm from the fingers to the elbow (according to other sources - “the distance in a straight line from the elbow to the end of the extended middle finger of the hand”). The size of this ancient measure of length, according to various sources, ranged from 38 to 47 cm. Since the 16th century, it was gradually replaced by the arshin and in the 19th century it was almost not used.

Slide 4

The basic Russian premetric measure of the volume of liquids is a bucket = 1/40 of a barrel = 10 mugs = 30 pounds of water = 20 vodka bottles (0.6) = 16 wine bottles (0.75) = 100 glasses = 200 scales = 12 liters (15 l - according to other sources, rarely) V. - iron, wooden or leather utensils, mostly cylindrical in shape, with ears or a bow for wearing. In everyday life, two buckets on the rocker should be in a “woman’s lift.” Division into smaller measures was carried out according to the binary principle: the bucket was divided into 2 half-buckets or 4 quarters of a bucket or 8 half-quarters, as well as into mugs and cups. The oldest “international” measure of volume is “handful”. The barrel, as a measure of liquids, was used mainly in the process of trade with foreigners, who were prohibited from conducting retail trade in wine in small quantities. Equal to 40 buckets (492 l)

Slide 5

BERKOVETS - this large measure of weight was used in wholesale trade mainly for weighing wax, honey, etc. Berkovets - from the name of the island of Bjerk. This is what was called in Rus' a measure of weight of 10 pounds, just a standard barrel of wax, which one person could roll onto a merchant boat sailing to this very island. (163.8 kg). There is a known mention of Berkovets in the 12th century in the charter of Prince Vsevolod Gabriel Mstislavich to the Novgorod merchants. The spool was equal to 1/96 of a pound, in modern terms 4.26 g. They said about it: “the spool is small and expensive.” This word originally meant a gold coin. POUND (from the Latin word “pondus” - weight, weight) was equal to 32 lots, 96 spools, 1/40 pood, in modern terms 409.50 g. Used in combinations: “not a pound of raisins”, “find out how much a pound of raisins is”. The Russian pound was adopted under Alexei Mikhailovich.

Slide 6

2 half rubles = 1 ruble Poltina = 50 kopecks Five-altyn = 15 kopecks Altyn = 3 kopecks Dime = 10 kopecks 2 money = 1 kopeck Grosh = ½ kopeck Polushka = ¼ kopeck

Ancient Russian monetary units.

Slide 7

Last = 72 pounds = 1.2t Kad = 14 pounds = 230 kg Berkovets = 10 pounds = 1.64 c Pud = 40 pounds = 16 kg Pound = 454 g Steelyard = 96 spools = 409.5g Spool = 4.3 g

Ancient Russian weight measures.

Slide 10

An arshin and a caftan, and two for patches. They were looking for a mosquito seven miles away, but the mosquito was on their nose. A yard's worth of beard, but an inch's worth of intelligence. I won't give in an inch. A hunter walks seven miles away to sip jelly. You are a span away from the truth (from service), and it is a fathom away from you. Stretch a mile, but don’t be easy. It's not bad that there's half a bun. Your own spool is more expensive than someone else's. He doesn't have half a spool of brain (mind) in his head. The bad comes in pounds, and the good comes in spools.

Proverbs and sayings.

Vintage Russians

weights

Mathematic teacher

MBOU Secondary School No. 19, Belovo

Kormina M.N.

Target research:

find out what measures of weight existed in Rus' in ancient times and why they are not used at the present time.

Tasks research:

Clarify what measures of weight are currently used;

Find out what measures of weight existed in ancient times in Rus';

Find out what instruments were used in ancient times to measure weight;

Find out in which literary sources the names of ancient weight measures are found;

Find out what proverbs, sayings, jokes mean,

phraseological units in which the names of ancient measures of weight are found;

Get acquainted with problems in which ancient weight measures are encountered;

Conduct an experiment with weight measurement;

Draw conclusions;

Hypothesis research:

We assume that the ancient weight measures

lost their significance due to

their inaccuracy and were replaced by

units of measurement accepted throughout the world.

Methods research:

• think for yourself what we know about modern and ancient

weight measures;

• study specialized literature;
• conduct an experiment: try

measure family weight using

vintage and modern units

measurements.

Object research

are vintage

weight measures.

Practical significance The work is that the use of ancient units of weight measurement when solving problems helps to increase interest in the study of mathematics and other academic subjects.

Novelty of the research: search for mathematical ideas among students about measures of weight in Ancient Rus'.

OLD RUSSIAN WEIGHT MEASURES

BERKOVETS - this large measure of weight was used in wholesale trade mainly for weighing wax, honey, etc. Berkovets - from the name of the island of Bjerk. This is what was called in Rus' a measure of weight of 10 pounds, just a standard barrel of wax, which one person could roll onto a merchant boat sailing to this very island. (163.8 kg). There is a known mention of Berkovets in the 12th century in the charter of Prince Vsevolod Gabriel Mstislavich to the Novgorod merchants.

Pud - (from the Latin pondus - weight, heaviness) is not only a measure of weight, but also a weighing device. When weighing metals, the pud was both a unit of measurement and a unit of counting. Even when the results of weighings were reported to tens and hundreds of poods, they were not transferred to Berkovites.

LB (from the Latin word "pondus" - weight, weight) was equal to 32 lots, 96 spools, 1/40 pood, in modern terms 409,50 d. Used in combinations: “not a pound of raisins”, “find out how much a pound of raisins is.” The Russian pound was adopted under Alexei Mikhailovich.

Sugar was sold by the pound. Apothecary pound (historical) - an ancient measure of apothecary weight, equal to approximately 360 grams or 12 ounces

LOT – old Russian unit of mass measurement, equal to three spools or 12.797 grams

Spool - about 4.3 years. In the 10th century. During the time of the Kyiv prince Vladimir Svyatoslavich, there was a coin called “zlatnik”. From the end of the 16th century. The spool serves as a unit of mass for precious metals and stones. Until 1927, Russia adopted a spool system for determining the content of precious metals (gold, silver, platinum) in an alloy, the so-called test. For example, an 84-karat silver item contains 84 spools, or 84 x 4.3 = 361.2 (g) fine silver per pound of alloy. Currently, the standard is expressed in the metric system.

Modern weight measures

Kilogram

1 kg = 1000 g

1 t = 1000 kg

An ancient measure of weight in literary works

Chukovsky "Telephone"

"What do you need? – chocolate.

For whom? - for my son.

Should I send too much?

– yes, about 5 or 6 poods:

he can't eat anymore

. He’s small for me!”

And in the work about Robinson Crusoe we encounter this description:

At the bottom of the chest I found three bags of money and several small ingots of gold, weighing, I think, about a pound."

Ancient weight measures

in proverbs and sayings

" Small spool but precious "

This is what they say about something seemingly insignificant, but very valuable.

"The pound must give way"

• one must have respect for elders,
• more experienced.

“You’ll lift a lot of grief off your shoulders, but you’ll choke on spool valves”

Even an insignificant danger should not be neglected.

“Weight and measure will not allow sin”

Those. to deception, error.

The peasant needs to pay rent for his

family of 12 people. For everyone you need

give away 30 pounds of grain. Will he be able to

take away the rent on horseback, if you yourself

weighs 5 pounds, and the horse lifts 15 pounds?

1) Let’s find how much the quitrent weighs: 30 * 12 = 360 pounds 2) Since 1 pood = 40 pounds, then: 360 / 40 = 9 poods 3) How much the owner weighs with the quitrent: 5 + 9 = 13 poods.

Answer: yes.

Problems with ancient weights

The merchant had 10 bags of grain, 1 berkovets per

everyone. The next day he bought

3 bags of 2 berks in each.

How many kg of grain did the merchant have in total?

Solution:

• Since 1 berk = 164 kg, then: 164*10=1640 (kg)

2) Since 2 berks = 328 kg, then: 328*3=984 (kg)

3) Total grain: 1640+984=2624 (kg)

Answer: 2624 kg

study

The most accurate way to measure weight is in modern units of measurement: kilograms.

conclusion

1. As a result of research: I have studied various weight measures.

2. Determined the use of ancient measures in literature.

3. Mastered the technique of converting ancient weights into modern ones and vice versa.

4. She showed how ancient weights are used when solving problems.

5. Old units of weight were inaccurate. Therefore, more accurate units of measurement that are common to all countries are now used: kilogram, gram, ton, centner

Slide 1

weights
Gran (from the Latin word "granum" - grain, grain) - in the Russian system of measures was used as a unit of weight (mass) for medicines and precious stones, in particular, for weighing pearls. One grain is equal to 62.209 mg.

Slide 2

weights
Zolotnik - about 4.3 years. In the 10th century. During the time of the Kyiv prince Vladimir Svyatoslavich, there was a coin called “zlatnik”. From the end of the 16th century. The spool serves as a unit of mass for precious metals and stones. Until 1927, Russia adopted a spool system for determining the content of precious metals (gold, silver, platinum) in an alloy, the so-called test. "small spool but precious".
They bought tea with gold coins.

Slide 3

The pound (from the German word "pfund" or the Latin "pondus" - weight, heaviness, weight) is an old Russian measure of weight (mass). Russian pound = 1/40 pood = 32 lot. = 96 spools = 409.51 grams. A pharmaceutical pound contains 358.8 g.
weights
“not a pound of raisins”, “find out how much a pound is worth.” Sugar was sold by the pound.

Slide 4

weights
PUD was equal to 40 pounds, in modern terms - 16.38 kg. It was already used in the 12th century. Pud - (from the Latin pondus - weight, heaviness) is not only a measure of weight, but also a weighing device. When weighing metals, the pud was both a unit of measurement and a unit of counting. Even when the results of weighings were reported to tens and hundreds of poods, they were not transferred to Berkovites. Back in the XI-XII centuries. they used various scales with equal-armed and unequal-armed beams: “pud” - a type of scale with a variable fulcrum and a fixed weight, “skalvy” - equal-armed scales (two-cup).

Slide 5

weights
In 1737, the bell suffered from the so-called Trinity Fire. Due to rapid and uneven cooling while extinguishing the fire, the red-hot bell cracked, and a piece weighing 11.5 tons broke off. After this, the bell lay in the pit for over a hundred years. In 1836, the bell was raised from the pit by the builder of St. Isaac's Cathedral and the Alexander Column, architect A. Morferrand, and placed on a stone pedestal.
The Tsar Bell. This is the largest bell of all existing bells in the world. He has no equal in artistic casting. The weight of the bell is more than 12 thousand poods, or 200 tons. The height of the bell is 5.87 m, diameter - 6.6 m. The Tsar Bell was cast in the Kremlin in 1733-1735. Russian foundry master Ivan Motorin and his son Mikhail.
12 thousand pounds
For the casting, an old broken bell from the time of Tsars Ivan Godunov and Alexei Mikhailovich was used

Slide 6

weights
The length of this gun is 5 meters 34 centimeters, caliber – 890 millimeters. The cannon is decorated with cast inscriptions; on the barrel itself is carved: “2400 poods” - the weight of the Tsar Cannon, which is 39312 kilograms. At the base of the gun lie four cast iron cannonballs, each weighing a ton. The name Tsar Cannon is associated with the image of Tsar Fyodor Ivanovich above the bracket, and also indicates the unsurpassed size of the weapon. In ancient times, the Tsar Cannon had another name: “Russian Shotgun,” since it was designed to fire “shot,” that is, buckshot. The Tsar Cannon did not have to participate in hostilities, but it was cast as a military weapon intended for the defense of the Moscow Kremlin. Initially, the cannon defended the main gate from Kitay-Gorod,
The Tsar Cannon, cast by Andrei Chokhov, is an ancient and one of the largest cannons in the world. Created in 1586 in Moscow, at the Cannon Yard

Slide 7

BERKOVETS - this large measure of weight was used in wholesale trade mainly for weighing wax, honey, etc. Berkovets - from the name of the island of Bjerk. This is what was called in Rus' a measure of weight of 10 pounds, just a standard barrel of wax, which one person could roll onto a merchant boat sailing to this very island. (163.8 kg). There is a known mention of Berkovets in the 12th century in the charter of Prince Vsevolod Gabriel Mstislavich to the Novgorod merchants.
weights

Objectives: get acquainted with the history of ancient measures of measurement; consider the relationship of these quantities with metric quantities; consider problems where ancient measures of measurement are found; generate interest in the study of these quantities and their further application; consider the use of these quantities in literary works

Objectives: get acquainted with the history of mathematics using ancient units of measurement as an example; study the relationship between ancient units of measurement and modern ones; examine problems and understand what modern concepts they are about; examine literary works in order to clarify and clarify the quantities used in this work

Why does a person need measurements? It is impossible to imagine the life of a person who would not make some, at least the simplest, measurements. Even for primitive man, who built his own home and made the simplest tools and utensils, the use of measures of length, weight and volume was necessary.

Pyad This word means hand (remember the modern word “wrist”). The span was defined as the distance between the ends of the extended thumb and index fingers; its value is approximately equal to cm.

Elbow, foot Elbow is a larger unit, as in most states, it was a unit equal to the distance from the elbow to the end of the extended middle finger. Old Russian kolot was approximately 46 - 47 cm. Foot - the average length of a human foot (30.48 cm)

Noah's Ark Quote "...the length of the ark is three hundred cubits; its breadth is fifty cubits, and its height is thirty cubits."

Fathom Oblique fathom from the big toe of the left foot to the middle finger of the outstretched right hand is about 42 vershoks, the swing in the size of both horizontally outstretched arms is about 2.5 arshins. At the same time, it is noteworthy that the fathom legalized in the Code of 1649, “which ... by sovereign decree was made 3 arshins,” is called new. Oblique fathom - the distance from the toe of the left foot to the end of the middle finger of the raised right hand.

Versta The largest of the ancient Russian units was the “verst” or field. The word “layout” meant to equalize, distribute. The verst was mentioned in the chronicle of 1097; it was 750 times larger than a fathom. Thus, it turns out that a mile is approximately 1140 meters. Old Russian travel measure - the distance traveled from one turn of the plow to another during plowing.

Kolomenskaya verst In the village of Kolomenskoye near Moscow there was the summer residence of Tsar Alexei Mikhailovich. The road there was busy and was considered the main one in the state. And when huge milestones were erected, the likes of which had never been seen in Russia, the glory of this road increased even more. The savvy people did not fail to take advantage of the new product and dubbed the lanky man the Kolomna milepost.

Versta The boundary verst existed in Rus' until the 18th century to determine the distance between settlements and for land surveying (from the word inter-border of land holdings in the form of a narrow strip). The length of such a mile is 1000 fathoms or 2.13 km. “verst” was a milestone on the road.

Mile – I wonder: how many miles have I already flown? - Alice said out loud. “I’m probably approaching the center of the Earth.” Let me remember...... This seems to be about four thousand miles down...... Mile (from the Latin word "milia" - a thousand (steps) - Russian measure of length. Used as a unit for measuring long distances, equal to seven versts or 7.468 km. Sailors measure distances in miles (1852 m) and cables (tenth of a mile), and speed in knots (1 mph).

Measures of liquid bodies From the measures of liquid bodies of Ancient Rus' the following are known: barrel, bucket, pot, nozzle, mug, cup... The main measure of liquid was a bucket. Honey and wax were measured using pots (12 kg). Nozzle 2.5 buckets. A barrel was equal to 4 nozzles or 10 buckets. A barrel could be equal to 40 buckets. Smaller measures: a shtof, a tenth of a bucket, a glass, a hundredth of a bucket, a scale, two glasses.

Units of mass The oldest unit of mass (weight) was the hryvnia, or hryvnia, which later became known as the pound. The Russian pound (400 g) was smaller than the English one (454 g). Pound, like pud, comes from a Latin root and means “weight, heaviness.” The pound was divided into 96 spools, and the spool into 96 shares. In addition to the trade pound, an apothecary pound was used, which was divided into 12 ounces. Larger units of weight were a pood, equal to 40 pounds, and a berkovets, equal to 10 poods. Berkovets comes from the word "berkun" - "a large wicker basket, a box for bringing feed to livestock, for carrying hay and straw."

Hryvnia and ruble The oldest unit of weight and monetary account in Rus', apparently, was the hryvnia. Its weight was 409.5 g. It is believed that the hryvnia came from the word “mane”: in terms of the amount of silver, the hryvnia was equal to the cost of a horse. There were different hryvnias: kun, silver and gold. Kunnies were made from low-grade silver and cost four times less than real silver ones. The gold hryvnia was 12.5 times more expensive than the silver one. Later, the hryvnia began to be cut in half into hryvnias, and a new bar of half a monetary hryvnia was called the ruble. The ruble (obviously, from the word “to chop”) became the main monetary unit in Rus'.

In 1535, coins were issued - “Novgorodki” with the image of a horseman with a spear in his hands, which were called kopek money. By the end of the 16th century, rubles and their hundredths – kopecks – remained. Under Peter I, the silver content in the ruble was reduced to 6 2/3 spools. At the same time, silver kopecks (10 kopecks) and fifty kopecks (50 kopecks) were first issued. In addition, the minting of kopecks and altyns, equal to three kopecks, continued. Under Catherine II, the silver content in the ruble was set at 4 spools 21 shares. This weight of the Russian ruble remained until 1917.

The main units for weighing were the foot and the pound. These words come from the same Latin word, pondus, meaning heaviness. The officials who checked the scales were called “pudovschiki” or “weights”. When weighing in Rus', two types of scales were used. A scale with a movable fulcrum and a fixed weight was called a steelyard. And in Novgorod, cup scales were called skalva.

By the end of the 17th century, a system of Russian weight measures had developed in the following form: Last = 72 pounds (= 1.18 tons); Berkovets = 10 pounds (= 1.64 c); Pud = 40 large hryvnias (or feet), or 80 small hryvnias, or 16 steelyards (=16.38 kg); Steelyard = 5 small hryvnias, or 1/16 pood (= 1 kg); Pound = 2 small hryvnias, or 4 small half-hryvnias, or 32 lots, or 96 spools (= 409.512); Spool = 96 shares (= 4.3 g). In Kievan Rus, the measure of grain was the kad. It contained 14 poods (= 230 kg) of rye and was divided into 2 ladles, or 4 quarters, or 8 ocmins. The kad was also called a fetter, since the eagled (checked by the authorities and equipped with a seal) kad was bound (chained) around the edges with an iron hoop. The Moscow kad was larger than the Kyiv one and contained 24 pounds of rye

You probably came across the word “arshin” in A.S. Pushkin. Remember the lines from the fairy tale “The Tale of Tsar Saltan, of his glorious son and the mighty hero Prince Guidon Saltanovich and of the beautiful Swan Princess”: Meanwhile, how far away he fights long and cruelly, the time of his homeland is coming; God gave them a son in arshin...

The Adventures of Gulliver One and a half thousand of the largest horses from the court stables, about four and a half inches high each, were needed to bring me to the capital, located, as has already been said, at a distance of half a mile from the place where I lay "...

This building was designated for my residence. The large door, facing north, was about four feet high and almost two feet wide, so that I could crawl through it quite freely. On either side of the door, at a distance of some six inches from the ground, were two small windows; through the left window, the court blacksmiths placed ninety-one chains, like those that our European ladies wear with their watches, and almost the same size...

A.S. Pushkin “Winter Road”. The moon makes its way through the wavy fogs, It pours a sad light onto the sad meadows. Along the winter, boring road, Three greyhounds are running, A monotonous bell is ringing tiresomely. Something familiar is heard in the long songs of the coachman6 Now a daring revelry, Now a heartfelt melancholy... No fire, no black hut, Wilderness and snow... towards me Only striped miles come across alone.

Ancient measures and tasks The plots of the tasks were not specially invented; some of them were prompted by everyday life, the peculiarities of life and traditions of the Russian people, others - by curious historical facts. In addition to historical ones, literary problems are also given. Nowhere do we come across old measures of length so often as in the writings of the classics.

In “Hegumen Daniel's Walk to the Holy Land,” the Russian cubit is mentioned among other measures of length. Describing the sights of Palestine, the author told about the Holy Sepulcher and indicated its dimensions: length - 4 cubits, width - 2 cubits. In the middle of the 17th century. Patriarch Nikon built the Resurrection New Jerusalem Monastery not far from Moscow, on the Istra River, and took the Church of the Resurrection in Jerusalem as a model for its main temple. In the new temple, a likeness of the Holy Sepulcher was made with an exact reproduction of its dimensions: the length was 2 arshins 9 vershoks, and the width was 1 arshin 5 vershoks. Based on a comparison of the indicated dimensions of the tomb, the size of the Old Russian cubit was found. What is it approximately equal to in centimeters? See the answer.

Harvesting logs Since ancient times, the Russian stove was heated with logs, which were prepared like this: they sawed a tree trunk into logs, chopped each into three logs, and a log into four parts. The log was inches long. Calculate how many logs could be obtained from a fathom-long log. Answer. 20 or 24 logs.

The tallest 1) Sobakevich to Chichikov: “And Cork Stepan, the carpenter? I'll lay my head if you can find such a guy anywhere. After all, what kind of power was that! If he had served in the guard, God knows what they would have given him, three arshins and an inch tall!” (N.V. Gogol, “Dead Souls”). 2) “Of all her servants, the most remarkable person was the janitor Gerasim, a man 12 inches tall, built like a hero and deaf-mute from birth” (I.S. Turgenev, “Mumu”). 3) “Nikitushka Lomov, a barge hauler who walked along the Volga years ago, was a giant of Herculean strength; 15 inches tall..." (N.G. Chernyshevsky, "What to do?"). Which of the mentioned literary characters is the shortest and who is the tallest? What is the height difference between these two? Answer. The shortest is Gerasim, the tallest is Stepan Cork

Hare Island The hero of the poem by N.A. Nekrasov’s “Grandfather Mazai and the Hares” recalls how he saved hares during the flood: I see one small island - Hares gathered in a crowd on it. From every minute the water was approaching the poor animals; Already under them there was less than an arshin of land in width, less than a fathom in length. How small was that island? What are its maximum dimensions in modern units of length and area? Answer: maximum dimensions: 0.71m, 2.13m, 1.51m2

“Arithmetic” L.F. Magnitsky The dog saw* a hare 150 fathoms away * from itself. A hare runs 500 fathoms in 2 minutes, and a dog runs 1300 fathoms in 5 minutes. How long will it take the dog to catch up with the hare? _______________________________________________ * Fathom is a measure of 3 arshins, 12 quarters, 2 meters. * See - see. Nowadays, this problem sounds like this: The dog saw a hare 300 meters away from itself. A hare runs 1000 meters in 2 minutes, and a dog runs 2600 meters in 5 minutes. How long will it take the dog to catch up with the hare? Solution: 1) 1000:2=500 (m) - the hare runs in 1 minute. 2) 2600:5=520 (m) - the dog runs in 1 minute. 3) =20 (m) - a dog runs more in 1 minute than a hare. 4) 300:20=15 (min.) – during this time the dog will catch up with the hare. Answer: the dog will catch the hare in 15 minutes.

The mill has three millstones*. On the first of them you can grind 60 quarters* of grain per day, on the second 54 quarters, and on the third 48 quarters. Someone wants to grind 81 quarters of grain in the least amount of time using these three millstones. In what shortest time can grain be ground and how much grain can be poured onto each millstone? __________________________ * Millstone - millstone. * A quarter is a measure of mass of 25 kg. Nowadays, this task sounds like this: There are three millstones in the mill. On the first of them, 1500 kg of grain can be ground per day, on the second 1350 kg, and on the third 1200 kg. Someone wants to grind 2025 kg of grain in the least amount of time using these three millstones. In what shortest time can grain be ground and how much grain can be poured onto each millstone? –Solution: 1) =4050 (kg) – three millstones are ground per day (24 hours). 2) 4050:2025=2 (times) - less time will be required to grind 2025 kg of grain. 3) 24:2=12 (hours) – it will be needed to grind 2025 kg of grain. 4) 1500:2=750 (kg) – grains must be poured onto the first millstone. 5) 1350:2=675 (kg) – grains must be poured onto the second millstone. 6) 1200:2=600 (kg) – grains must be poured onto the third millstone. Answer: in 12 hours, 750 kg, 675 kg, 600 kg.

On a hot day, 6 mowers drank kad* kvass in 8 hours. You need to find out how many mowers will drink the same tub of kvass in 3 hours. _______________________________________ * Kad is a cylindrical container made of wooden rivets (planks) and covered with metal or wooden hoops. Solution: 1) How many mowers will a Kad drink in one hour? 6x8 =48 (mows) 2) How many mows will Kad drink in three hours? 48:3 =16 (mowers) Answer: 16 mowers will drink a kad of kvass in 3 hours.

One man drinks a kad* of kvass in 14 days, and his wife and he will drink the same kad in 10 days. Surely there are* how many* days will his wife especially* drink the same Kad? _______________________ * Knowingly there is - you need to find out * In colic - for how much * Especially - alone, on your own Solution: 1) How many cups of kvass will a person drink in 140 days? 140:14=10 (kaday) 2) How many kadeys of kvass will a man drink in 140 days with his wife? 140:10 =14 (kaday) 3) How many kadays will the wife drink on her own in 140 days? 14-10=4 (kadi) 4) How many days will it take for the wife to drink kad kvass on her own? 140:4=35 (days) Answer: the wife will drink kad kvass in 35 days.

A man was sent from Moscow to Vologda, and he was ordered* to walk* 40 versts* every day; then another* person was sent on another day to follow* him, and he was ordered to go 45 versts a day, and knowingly*, on what* day the second will befall the first. ___________________________________ * Ordered - ordered * In your walk to do - to pass * For every day - every day * Versta - an old Russian unit of distance measurement, equal to meters * Another person - another person * Another day - the next day * After him - after him * Go for a day - to pass on a day * Knowingly there is - you need to find out * On what day - on what day In our time, this task sounds like this: One traveler set off on foot from Moscow to Vologda. He walked 40 km a day. Another traveler went after him the next day and walked 45 km a day. The question is, how many days will it take for the second traveler to catch up with the first?

A certain merchant bought 112 rams, old and young, and gave 49 rubles 20 altyns*. For the old one I paid 15 altyn and 2 money*, and for the young one 10 altyn. And in charge there are * how many * old and young rams he bought. _______________________________________ * Altyn is a monetary unit corresponding to 3 kopecks. * Denga is a monetary unit corresponding to half a penny. * Knowingly there is - you need to find out, you ask. *Koliko – how much. In our time, this problem sounds like this: One trader bought 112 rams, old and young, and paid 49 rubles 60 kopecks for them. For each old ram he paid 46 kopecks, and for each young ram - 30 kopecks. And we need to find out how many old and how many young rams he bought.

A certain man bought 96 geese. He bought half of the geese, paying 2 altyns* and 7 half rubles* for each goose. For each of the remaining geese, he paid 2 altyns less half a ruble. We know* how much do all the geese cost together? _____________________________ * Altyn - 3 kopecks * Ruble - 100 kopecks * Polushka - (half a marten's ear) the smallest coin, half money or a quarter of a penny * Denga - 2 half kopecks * Kopek - 4 half rubles, 2 money 57 conclusions I got acquainted with the texts of ancient mathematical problems from “Arithmetic” by Magnitsky I also learned the old measures of length (span, ell, verst, sazhen, arshin, weight (pud, pound), volume (quarter, kad), money (denga, polushka, kopeck, altyn) and their correspondence to modern measures I saw that in the old textbook much attention was paid to entertaining problems, to which L.F. Magnitsky devoted an entire section entitled “On certain comforting actions through arithmetic used.” I looked at literary works in which ancient units of measurement are found, and was convinced that there are a lot of them.

Literature 1.Mathematics. Subject week at school (methodology and scenarios for competitions, quizzes, etc.) / author - compiled by G.I. Grigoriev. – M.: Globus, 2008. – 198 p. – (learning with passion). 2.Vytautas Petkevicius. "Arshin, son of Vershka." Fairy tales, translation from Lithuanian; ed. “Children’s Literature”, Moscow – 226 p. 3. Entertaining mathematics in stories for children / author - composed by A.P. Savin, V.V. Stanzo, A.Yu. Kotova; artist A.E. Shabelnik, A.O. Khomenko. – M.AST: Astrel, 2011. – 382, ​​p.:ill. - (Extracurricular reading). 4. A.S. Pushkin. Essays. In three volumes (volume 1). Poems; Fairy tales; Ruslan and Lyudmila: poem. – Moscow: “Fiction”, – 735 p. 5. Swift Jonathan. Gulliver's Adventures. Ed. ABC - classic, 2009. – 64 s. 6.Ivanov M.I. Russian abacus and its use at school. M., Olehnik S.N., Nesterenko Yu.V., Potapov M.K. Vintage entertaining problems. M. Science I.Ya.Depman, N.Ya.Vilenkin. Behind the pages of a mathematics textbook: a manual for students in grades 5-6 of secondary school. – M.: Enlightenment, – 287 p.