In the 4th grade, children studied length measures in the world around them. We also touched upon ancient Russian measures of length. To help her classmates better present and remember this information, my daughter prepared a presentation. The presentation contains a selection of illustrations and includes materials about ancient length measures.

Presentation of ancient Russian measures of length

Since ancient times, the measure of length has always been a person: how far he will stretch out his hand, what step he will take, etc. The system of Old Russian measures of length included the following basic measures: verst, fathom, arshin, elbow, span and vershok.

presentation Ancient Russian measures of length

Vershok- Old Russian unit of measurement, originally equal to the length of the main phalanx of the index finger, 4.45 cm

Span(pyadnitsa) is an ancient Russian measure of length. Small span - the distance between the ends of the spread thumb and index (or middle) fingers = 17.78 cm. Large span - the distance between the ends of the thumb and little finger (22-23 cm). A span with a somersault - a span with the addition of two joints of the index club = 27-31 cm

Elbow- an ancient measure of length corresponding to the distance from the elbow joint to the end of the extended middle finger of the hand or to the fingers gathered into a fist. Suppressed by arshin

Arshin- 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.

Fathom- one of the most common length measures in Rus'. There were more than ten fathoms, varying in purpose and size. “Makhovaya fathom” is the distance between the ends of the fingers of an adult man’s widely spaced hands. “Oblique fathom” is the longest: the distance from the toe of the left foot to the end of the middle finger of the raised right hand.

Verst- distance traveled from one plow turn to another, 1.067 km

And finally, in order to better understand the material, a small selection of proverbs and sayings with an explanation of their meaning.

Proverbs and sayings about ancient Russian measures of length

1. A beard as big as an inch, and words as big as a bag - It is not becoming for young people to brag to their elders.
2. The pot is two inches away, and already the pointer is about a young man who has no life experience, but arrogantly teaches everyone.
3. We don’t need an inch of someone else’s land, but we won’t give up even an inch of our own.
4. Seven spans in the forehead - about a very smart person.
5. If you give in an inch, you will lose a fathom.
6. He sees three arshins into the ground - visionary man.
7. Like an arshin swallowed - about a person who holds himself unnaturally straight, “toe the line”
8. Each merchant measures with his own yardstick - everyone judges any matter one-sidedly, based on their own interests.
9. A beard as long as a beard, but a mind as long as an inch - about an adult but stupid person.
10. Log to log - fathom - about the accumulation of reserves, wealth through saving
11. Oblique fathoms in the shoulders - about a hero, a broad-shouldered man.
12. They were looking for a mosquito for seven miles, and the mosquito was on the nose - about fools.
13. A hunter walks seven miles away to sip jelly - travel, walk far unnecessarily.
14. Moscow is miles away, but close to my heart - This is how Russian people characterized their attitude towards the capital.
15. Love is not measured by miles, Seven miles is not a detour for a young man - distance cannot be an obstacle to love.
16. From word to deed - a whole mile - promising does not mean doing.
17. You can see him a mile away, Kolomenskaya Versta - about a tall man

Thank you for your attention!

1 inch = cm? About whom do they say: “He has seven spans in his forehead”? About a smart, wise person.

1 vershok = 4.45 cm Vershok is the length of the top of the finger. ? About what kind of person can you say: “The pot is two inches away”? Two inches is about nine centimeters: 4.45 2 = 8.9 cm. People of this height do not exist. What is the solution? The fact is that when indicating a person’s height, previously the count was made after two arshins, that is, after 142.24 centimeters. This means that two inches from the pot is a little more than one and a half meters: 142.24 + 8.9 = 151.14 (cm). 1 cubit = cm

Versta - a distance 500 times larger than a fathom 1 verst = 1540 m? What does the saying mean: “You can eat jelly seven miles away”? Travel, walk far without any particular need? What does the expression “measure miles” mean? Walk long distances? About whom do they say: “Kolomenskaya verst”? This is what they call a very tall person, a brute.

What does the expression mean: “Measure by your own yardstick”? To judge someone or something from your personal point of view, to evaluate according to your taste. ? What does the expression mean: “Measure with a common yardstick”? Treat someone or something as normal. ? About whom do they say: “Like an arshin swallowed”? This is what they say about a person who holds himself unnaturally straight, “toe the line.” ? What does the expression mean: “To see two arshins underground”? This means being distinguished by great insight. Arshin is the length of the entire arm. 1 arshin = 71.12 cm

200 years ago in different countries, including Rus', different systems of units were used to measure length. The first units of length were associated with the sizes of parts of the human body. In connection with the development of trade, there is a need to establish clear definitions of units and the relationships between them. Under Peter I, Russian measures were brought into a certain system. Traditionally, the old units are sometimes used today. Proverbs and sayings related to ancient length measures also appeared.

Dictionary of a young mathematician. – M.: Pedagogy, rol_00/ rol_00/

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Presentation on the topic: Ancient Russian measures

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Introduction In order to understand the essence of what is happening, we need to look into the distant past. It is by studying it that we can find the answer to the question of what the heritage of Rus' means to us. The question of the significance of units of measurement is always relevant. The history of measures is the history of trade, craft, agriculture, and ultimately, it is part of the history of man. Most of the old measures have been forgotten and fallen out of use, but many of them appear in literary works, historical monuments, found in ancient buildings, in many medicinal recipes and all kinds of foods. How did the measures come about? How did they change? What did they bring to the peoples and how did they influence their lives? This is still interesting today. Therefore, we chose “Ancient Russian Measures” as the topic of our research activity.

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Measures of length The system of ancient Russian measures of length included the following basic measures: verst, fathom, arshin, cubit, span and vershok. But the first measures of length were the fingers and toes of a person, and then the step, fathom, palm, elbow, five. PALM = 1/6 cubit (six-palmed cubit)

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STEP - the average length of a human step = 71cm. To count steps there is a special device - a pedometer. With each step or foot hitting the ground, the pedometer needle moves through one division, and on the pedometer dial you can read the number of steps from the beginning of the moment when the arrows were set to the beginning of the movement.

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Elbow - the distance from the end of 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”). The cubit was widely used in trade as a particularly convenient measure. In the retail trade of canvas, cloth, and linen, the cubit was the main measure. It was convenient to wrap the fabric being measured around such a standard. A complete turn of tissue near the elbow was called a double elbow. 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.

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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. There are different versions of the origin of the arshin measure of length. Perhaps, initially, “arshin” denoted the length of a human step (about 70 cm, when walking on the plain at an average pace) and was the base value for other large measures of determining length and distance (fathom, verst). The root "AR" in the word a r sh i n - in the Old Russian language means "EARTH", "surface of the earth", and indicates that this measure could be used in determining the length of the path traveled on foot. There was another name for this measure - STEP. Subsequently, they also began to use, under this name, an equal value - the length of the arm. Merchants, selling goods, as a rule, measured it with their arshin (ruler) or quickly - measuring “from the shoulder”. To exclude measurements, the authorities introduced, as a standard, the “official yardstick,” which is a wooden ruler with metal tips with a state mark riveted at the ends.

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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 it was possible to get smaller shares - two vershok (1/2 span) or a vershok (1/4 span). PYAD (pyatnitsa) is an ancient Russian measure of length. The name span comes from the Old Russian word “past”, i.e. wrist. SMALL SPAND - the distance between the outstretched thumb and index fingers and is equal to 17.78 cm. Since the 17th century it was called “quarter”<аршина>.BIG SPAND - the distance between the ends of the thumb and the little finger and is equal to 22-23 cm. SPAND WITH A TUMPLER ("span with a somersault", according to Dahl - 'span with a somersault') - a span with the addition of two joints of the index finger - 27- 31 cm. Our old icon painters measured the size of icons in spans: “Nine icons” - seven spans (1 3/4 arshins in gold - pyadyatnitsa (4 vershoks).

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VERSHOK - an ancient Russian measure of length, equal to the width of two fingers (index and middle). Vershok - equal to 1/16 of an arshin, 1/4 of a quarter. In modern terms -4.44 cm. The name "Vershok" comes from the word "top". In the literature of the 17th century. there are also fractions of an inch - half an inch and a quarter inch. When determining the height of a person or animal, counting was carried out after two arshins (mandatory for a normal adult): if it was said that the person being measured was 15 vershoks in height, then this meant that he was 2 arshins 15 vershoks, those. 209 cm. For a person, two methods were used to fully express height: 1 - a combination of “height *** elbows, *** spans” 2 - a combination of height arshin, vershkovs 18th century - “*** feet, *** inches” For households small animals were used - "height *** arshins" For trees - "height *** arshins"

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One of the most common measures of length in Rus' is the fathom. There were more than ten fathoms of different purposes and sizes and they had their own names, were incommensurable and not multiples of one another. Fathoms: 1. city ​​-284.8 cm 2. without name - 258.4 cm 3. great - 244.0 cm 4. Greek - 230.4 cm 5. state - 217.6 cm 6. royal - 197.4 cm 7. church - 186.4 cm 8. folk - 176.0 cm 9. masonry - 159.7 cm 10. simple - 150.8 cm 11. small - 142.4 cm and another one without a name - 134.5 cm, as well as - courtyard, pavement. The most famous are “machaya fathom” and “oblique fathom”.

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“Makhovaya fathom” is the distance between the ends of the fingers of an adult man’s widely spaced hands. Fly fathom - 1.76 m.

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“Oblique fathom” is the longest: the distance from the toe of the left foot to the end of the middle finger of the raised right hand. Oblique fathom (originally “oblique”) - 2.48 m. Used in the phrase: “he has oblique fathom in his shoulders” (meaning - hero, giant)

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To measure large distances in Rus' they used the unit “field”, which was later replaced by verstoy.VERSTA - an old Russian travel measure. 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. There are known mentions in written sources of the 11th century. In manuscripts of the 15th century. there is an entry: “field of 7 hundred and 50 fathoms” (750 fathoms long). Before Tsar Alexei Mikhailovich, 1 verst was considered 1000 fathoms. Under Peter the Great, one verst was equal to 500 fathoms. In modern calculation: 213.36 500 = 1066.8 m. “Verstoy” was also called a milepost on the road.

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The size of the verst changed repeatedly depending on the number of fathoms included in it and the size of the fathom. The Code of 1649 established a “boundary mile” of 1 thousand fathoms. Later, in the 18th century, along with it, a “travel verst” of 500 fathoms (“five hundredth verst”) began to be used. Mezhevaya verst is an old Russian unit of measurement equal to two versts. A verst of 1000 fathoms (2.16 km) was widely used as a boundary measure, usually when determining pastures around large cities, and on the outskirts of Russia, especially in Siberia, and to measure distances between populated areas. The 500-fathom verst was used somewhat less frequently, mainly for measuring distances in the European part of Russia. Long distances, especially in Eastern Siberia, were determined in days of travel. In the 18th century boundary versts are gradually being replaced by travel ones, and the only verst in the 19th century. there remains a “travel” mileage equal to 500 fathoms. In addition, “transitions,” “halts,” and “days of movement” were also used to measure large distances.

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Measures of length (used in Russia after the Decree of 1835 and before the introduction of the metric system): 1 verst = 500 fathoms = 50 poles = 10 chains = 1.0668 km 1 fathom = 3 arshins = 7 feet = 48 vershoks = 2.1336 meter Oblique fathom = 2.48 m. Flying fathom = 1.76 m. 1 arshin = 4 quarters (spans) = 16 vershok = 28 inches = 71.12 cm (divisions in vershoks were usually applied to the arshin) 1 cubit = 44 cm ( according to various sources from 38 to 47 cm) 1 foot = 1/7 fathom = 12 inches = 30.479 cm1 quarter<четверть аршина>(span, small span, span, span, span, span) = 4 vershka = 17.78 cm Large span = 1/2 cubit = 22-23 cm Since the 17th century, “span” was replaced by “quarter arshin” PALM = 1/6 cubit (six-palmed cubit) “A span with a somersault” is equal to a small span plus two or three joints of the index or middle finger = 27-31 cm. 1 vershok = 4 nails (width - 1.1 cm) = 1/4 span = 1/16 arshin = 4.445 cm 1 finger ~ 2 cm.

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The foot and inch, which were used in Russia, are equal in size to English measures. The decree of 1835 determined the relationship between Russian and English measures: Fathom = 7 feet Arshin = 28 inches A number of units of measurement (verst divisions) are abolished, and new measures of length come into use: inch , line, point, borrowed from English measures.

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New measures of length (introduced from the 18th century): 1 inch = 10 lines = 2.54 cm The name comes from the Dutch - “thumb”. Equal to the width of the thumb or the length of three dry grains of barley taken from the middle part of the ear. 1 line = 10 points = 1/10 inch = 2.54 millimeters (example: Mosin’s “three-ruler” - d = 7.62 mm.) Line - width of a wheat grain, approximately 2.54 mm. 1 hundredth fathom = 2.134 cm 1 point = 0.254 millimeters 1 geographical mile (1/15 degree of the earth's equator) = 7 versts = 7.42 km (from the Latin word "milia" - a thousand (steps) )1 nautical mile (1 arc minute of the earth's meridian) = 1.852 km 1 English mile = 1.609 km 1 yard = 91.44 cm

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In the 18th century, the weight of a pound (kryvnia) was specified as 25,019 cubic meters. inches of water at its highest density and the division of a pound into 32 lots, a lot into 3 spools, and a spool into 96 shares was introduced. It is currently believed that the normal weight of the hryvnia was 409.512 grams, which is 96 spools. Lot is an old Russian unit of mass measurement equal to three spools or 12.797 grams. A share is the smallest old Russian unit of mass measurement, equal to 1/96 of a spool or 0.044 grams. 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. Berkovets - this large measure of weight was used in wholesale trade mainly for weighing wax, honey, etc.

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Vladimir's "Zlatnik" weight is a gold coin weighing 4 grams. On the obverse of the coin there is an image of the Grand Duke in a headdress with a staff in his hand and a circular inscription: “Vladimir and all his gold” or “Vladimir on the table.” On the reverse side there is a waist-length image with the inscription “Jesus Christ”. Silver weight: on the front side there is an image almost the same as on the gold coin and the same inscriptions. On the reverse side there is the end of the inscription on the front side and a special sign. Copper weight of Prince Gleb (12th century), found in Kyiv caves during the collapse of the walls. The weight of this weight is 516.5 shares.

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The origin of the word pud from the Latin word pondus - weight is not very convincing. The term pud was used in the sense of weight or heaviness. A pud 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). The officials who checked the scales were called pudovschiki, or weighers

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For a long time there was a measure of weight called the “steelyard”. The steelyard was equal to 1kg. In addition, hand scales with an unequal lever and a movable support point were called steelyards. The marks on the steelyard first show fractions of a pound (quarters of an octam; this is 1/8 of a pound or 50 grams), then whole pounds up to 10; then two pounds 20; then 5 pounds each up to 40. In the North and Siberia, a steelyard is a weight of 2.5 ounces when purchasing certain goods: oil, caviar, fish, hops.

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Measures of areas In "Russkaya Pravda", a legislative monument, different lists of which date back to the 11th-13th centuries, the land measure plow is used as an economic unit to which tribute was paid. There are some reasons to consider a plow equal to 8-9 hectares. In the 16th-17th centuries, the measure of fields was already a tithe (equal to 1.1 hectares), as well as shares of a tithe: half a tithe and a quarter (a quarter was 40 fathoms in length and 30 in breadth; a field on which a quarter of the grain was sown). The tithe was sometimes called a korobye. The “Book of Soshnogo Letters,” compiled in 1629 as a guide for accounting for taxes on land, mentions a tithe equal to 8030 = 2400 square meters. fathoms. The tax unit of land was the plow, in Novgorod it was the obzha, which had different sizes, depending on the quality of the land and the social status of the owner (servants, clergy, peasants, etc.) The most commonly used yield measure was the hay. Gradually, this measure acquired a meaning linked to the tithe, and was divided into 2 half-shocks, 4 quarter-shocks, 8 half-quarters of a hay, etc. Over time, a haystack, as a measure of area, was equated to 0.1 tithes (i.e., it was believed that an average of 10 copecks of hay were taken from a tithe). Labor and sowing measures were expressed through a geometric measure - tithe.

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Volume measures 1. Liquid measures The original sizes of liquid measures are a barrel and a bucket and it remains unknown which of them came first. In addition, liquids were measured in bottles, “shtofas” (2 bottles), “scales” (61g), “hundreds” (a glass or 2 scales). The oldest “international” measure of volume is a “handful”. 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) A ​​barrel as a measure of liquids was used mainly in the process of trade with foreigners who were prohibited from conducting small retail trade in wine. The barrel was equal to 40 buckets (492 l). The material for making the barrel was chosen depending on its purpose: oak - for beer and vegetable oils; spruce - under water; linden - for milk and honey. Barrels were also used for washing (beating) linen.

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In the 15th century Ancient measures were also common - golvazhnya, lukno and harvesting. In the XVI-XVII centuries. Along with the fairly common korobya and belly, the Vyatka grain measure marten, the Perm sapsa (measure of salt and bread), the Old Russian bast and poshev are often found. The Vyatka marten was considered equal to 3 Moscow quarters, the saptsa could hold 6 pounds of salt and approximately 3 pounds of rye, bast - 5 pounds of salt, poshev - about 15 pounds of salt. A variety of household vessels were used in everyday life and in trade: boilers, jugs, pots, bratins , valleys. The significance of such household measures varied in different places: for example, the capacity of boilers ranged from half a bucket to 20 buckets. In the 17th century, a system of cubic units based on the 7-foot fathom was introduced, and the term cubic (or "cubic") was introduced. 1 cubic fathom = 27 cubic arshins = 343 cubic feet 1 cubic arshin = 4096 cubic inches = 21952 cubic inches

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Wine measures The Charter on Wine of 1781 established that every drinking establishment should have “measures certified in the Treasury Chamber.” Bucket = 12 liters Quarter (fourth of a bucket) = 3 liters (previously it was a narrow-necked glass bottle) The “bottle” measure appeared in Russia under Peter I. Russian bottle = 1/20 of a bucket = 1/2 of a damask = 5 glasses = 0, 6 liters (half a liter appeared later - in the twenties of the 20th century) Since the bucket held 20 bottles (2 0 0.6 = 12 liters), and in trade the bill was on buckets, the box still holds 20 bottles. For wine, the Russian bottle was more than 0.75 liters. A flat bottle is called a flask.

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Shtof (from the German Stof) = 1/10 of a bucket = 10 glasses = 1.23 l Shtof appeared under Peter I and served as a measure of the volume of all alcoholic drinks. The shape of the damask was like a quarter. Mug (the word means “for drinking in a circle”) = 10 glasses = 1.23 liters. A modern faceted glass was formerly called “doskan” (“planed boards”), consisting of fret-boards tied with rope around a wooden bottom. Russian measure of liquid) = 1/10 shtofa = 2 scales = 0.123 l. Stack = 1/6 bottle = 100 grams (considered the size of a single dose) Scale (popular name - “kosushka”, from the word “mow”, based on the characteristic movement hands) = 1/2 cup = 0.06 l. Quarter (half a scale or 1/16 part of a bottle) = 37.5 grams. Barrel utensils are utensils for liquids and bulk solids. It was distinguished by a variety of names depending on the place of production (baklazhka, baklusha, bochaty), on the size and volume (badiya, pudovka, sorokovka), its main purpose (resin, salt, wine, tar) and the wood used for their production (oak, pine, linden, aspen). Finished cooperage products were divided into buckets, tubs, vats, kegs and casks.

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An endova is a wooden or metal utensil (often decorated with ornaments) used for serving drinks to the table. It was a low bowl with a spout. The metal valley was made of copper or brass. Wooden valleys were made from aspen, linden or birch. Leather bag (skin) = up to 60 l Pot = 12 l Attachment - 2.5 buckets (Nogorod liquid measure, 15th century) Tub - vessel height - 30-35 centimeters, diameter - 40 centimeters, volume - 2 buckets or 22-25 liters Box - made of solid pieces of bast, sewn with strips of bast. The bottom and top cover are made of boards. Sizes - from small boxes to large "chests of drawers" Balakir - a dugout wooden vessel, 1/4-1/5 in volume, buckets.

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In the central and western parts of Russia, measuring containers for storing milk were proportional to the daily needs of the family. They were a variety of clay pots, pots, milk pans, jars, jugs, throats, milking bowls, birch bark with lids, tubs, the capacity of which was approximately 1/4-1/2 of a bucket (about 3-5 liters). The containers of makhotok, stavtsy, tueskov, in which fermented milk products were kept - sour cream, yogurt and cream, approximately corresponded to 1/8 of a bucket. Kvass was prepared for the whole family in vats, tubs, barrels and tubs (lagushki, izhemki, etc.) with a capacity of up to 20 buckets, and for a wedding - 40 or more pounds. In drinking establishments in Russia, kvass was usually served in kvass pots, decanters and jugs, the capacity of which varied in different areas from 1/8-1/16 to about 1/3-1/4 of a bucket. The commercial measure of kvass in the central regions of Russia was a large clay (drinking) glass and jug. Under Ivan the Terrible, eagle-shaped (branded with the sign of an eagle), that is, standardized drinking measures: bucket, octah, krynki, sudentsy, misa, tuesa, ladle, jug, foot and mug. Moreover, valleys, ladles, staves, shot glasses remained in use, and for small sales - hooks (cups with a long hook at the end instead of a handle, hanging along the edges of the valley). In Old Russian measures and in vessels used for drinking, the principle of correlation is laid down volumes - 1:2:4:8:16.

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2. Measures of bulk solids In Kievan Rus there was a measure of grain - a tub, which contained 14 pounds (about 230 kg) of rye and was divided into 2 ladles or 4 quarters, or 8 octagons. The tub was called a fetter, since “the eagle tub was edged with an iron hoop to eliminate the possibility of cutting off the edge.” In trade practice and in everyday life, the following measures of bulk solids were used for a long time, they were also called “grain measures”: Last = 12 quarters Quarter (chet) = 1/4 part of a tub Kad (tub, fetter) = 20 buckets Large tub - larger than a tub K In the 18th century, the system of measures of bulk solids took the form: Quarter = 8 chetverikam = 2.0991 hectoliters = 209.9 liters Quarter = 8 garnets = 26.239 liters 1 chetyrek (“measure”) = 2.624 deciliters = 26.24 liters Garnets = 3.279 liters . By decree of 1835, the garnet was set at 200.15 cubic cm. In Kievan Rus there was a measure of grain - a kad, which contained 14 poods (about 230 kg) of rye and was divided into 2 ladles or 4 quarters, or 8 octagons.

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Conclusion The system of old Russian measures was inconvenient in all respects. In 1842, the first metrological institution in Russia was created in St. Petersburg, which was called the “Depot of Exemplary Weights and Measures”. In 1893, the Depot was transformed into the Main Chamber of Weights and Measures, which was headed by Mendeleev until 1907. Currently there is an international system for calculating quantities. In the future, we would like to study the history of the formation of the monetary system in Rus' and establish the connection between old Russian measures and the modern calculation system.

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”: While he fights far away 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 easily. 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.

Preparing logs For a long time, Russian stoves were 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 used through arithmetic”, he examined literary works in which ancient units of measurement were 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.

7th grade students of Ninorovskaya secondary school, Uglich district, Yaroslavl region

There are only 7 students in the class. The guys performed this presentation all together, each making their own page, selecting material and proverbs. Crossword puzzles were completed collectively in groups: one was done by boys, the other by girls.

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Ancient length measures

Goals and objectives: 1. Find out what units of length were used previously in Rus'. 2. How ancient units of length are related to the modern system of measures. 3. Where can you find ancient units of length nowadays? 4. Establish a connection between mathematics and literature.

Vershok Vershok is an old Russian unit of length measurement, originally equal to the length of the main phalanx of the index finger. Top = 4.445 cm Tops were usually used to measure height: small animals and people.

Span An ancient measure of length, equal to approximately a quarter of an arshin, that is, a fourth of 71.1 cm. Simple calculations show that there were about 18 centimeters in a span. The span is the distance between the tips of the extended thumb and index fingers.

Elbow The elbow is a unit of length that has no specific meaning and roughly corresponds to the distance from the elbow joint to the end of the extended middle finger. Elbow = 45 cm

Arshin Arshin - Old Russian measure of length. In the 16th-17th centuries. was divided into 4 quarters and was equal to 72 cm. In Rus', the eastern measure “arshin” has long been adopted. As a unit of measurement, the arshin was widely used in the textile industry and in trade, as well as in the weapons industry. In 1899, the arshin was legalized as one of the main units of measurement, and the length of the arshin was expressed both through English measures and through metric ones.

Fathom Straight simple fathom - arm span from the tips of the thumbs. A simple fathom is equal to 152cm. In construction and engineering, a fathom was often divided into 100 parts. Before 1835, fathom flywheel and fathom oblique were often used in everyday life.

Oblique fathom Oblique fathom =2.48m. This is the distance from the fingertips of the outstretched right hand to the toes of the left foot. There were more than 10 fathoms and they had their own names. Fathom was used in the construction of various structures, shipbuilding, land surveying and cartographic work.

Versta Versta is a Russian unit of length equal to 500 fathoms (1.0668 km). This word originally referred to the distance traveled from one turn of the plow to another during plowing. “Verstoy” was also called a milestone on the road.

Proverbs and sayings The pot is two inches away. He's about the size of an inch, and his head is about the size of a pot. Seven spans in the forehead. We don’t need an inch of someone else’s land, but we won’t give up even an inch of our own (words from a song). Measure to your own yardstick. Oblique fathoms in the shoulders. Versta Kolomenskaya. Straight as a ramrod. It’s a sin to carry it away an arshin, but God ordered it to be carried away with scissors. Seven miles to heaven and everything is forest. To sip jelly seven miles away.

Research results We noticed that most ancient units of measurement are associated with parts of the human body, so they are inaccurate and are not currently used for measurements. - But in Russian sayings and proverbs, ancient measures of length are used very often and accurately convey the features of our language.

Crossword D L I N A

1. The distance between the tips of the extended thumb and index fingers. 2. Distance from the elbow joint to the extended middle finger of the hand. 3.A unit of distance used at sea. 4.Used in textiles. 5. Distance of arm span from the tips of the thumbs.

Crossword Length

1 . One tenth of a meter. 2. This is the distance from the elbow joint to the end of the extended middle finger. 3.A unit of distance used by sailors. 4. This is a unit that was used in the textile industry, in trade, as well as in weapons. 5. The black and white pillar on the road is called exactly the same.