Антропова Н.А., Садыков Т.Д. Геодезическое обеспечение нефтегазопроводов и газонефтехранилищ

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ɆɂɇɂɋɌȿɊɋɌȼɈ ɈȻɊȺɁɈȼȺɇɂə ɂ ɇȺɍɄɂ ɊɈɋɋɂɃɋɄɈɃ ɎȿȾȿɊȺɐɂɂ

Ƚɨɫɭɞɚɪɫɬɜɟɧɧɨɟ ɨɛɪɚɡɨɜɚɬɟɥɶɧɨɟ ɭɱɪɟɠɞɟɧɢɟ ɜɵɫɲɟɝɨ ɩɪɨɮɟɫɫɢɨɧɚɥɶɧɨɝɨ ɨɛɪɚɡɨɜɚɧɢɹ

«ɇȺɐɂɈɇȺɅɖɇɕɃ ɂɋɋɅȿȾɈȼȺɌȿɅɖɋɄɂɃ

ɌɈɆɋɄɂɃ ɉɈɅɂɌȿɏɇɂɑȿɋɄɂɃ ɍɇɂȼȿɊɋɂɌȿɌ»

ɇ.Ⱥ. Ⱥɧɬɪɨɩɨɜɚ, Ɍ.Ⱦ. ɋɚɞɵɤɨɜ,

Ⱥ.ȼ. ɒɚɞɪɢɧɚ, Ⱥ.ɋ. ɉɚɲɤɨɜɚ

ȽȿɈȾȿɁɂɑȿɋɄɈȿ ɈȻȿɋɉȿɑȿɇɂȿ

ɗɄɋɉɅɍȺɌȺɐɂɂ ɇȿɎɌȿȽȺɁɈɉɊɈȼɈȾɈȼ

ɂ ȽȺɁɈɇȿɎɌȿɏɊȺɇɂɅɂɓ

ɋɛɨɪɧɢɤ ɡɚɞɚɧɢɣ

ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɣ ɪɚɛɨɬɵ ɫɬɭɞɟɧɬɨɜ

ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ

ɂɡɞɚɬɟɥɶɫɬɜɨ

Ɍɨɦɫɤɨɝɨ ɩɨɥɢɬɟɯɧɢɱɟɫɤɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ

2011

ɍȾɄ 528.48(076)

ȻȻɄ 26.12ɹ73

Ⱥ72

Ⱥɧɬɪɨɩɨɜɚ ɇ.Ⱥ.

Ⱥ72 Ƚɟɨɞɟɡɢɱɟɫɤɨɟ ɨɛɟɫɩɟɱɟɧɢɟ ɧɟɮɬɟɝɚɡɨɩɪɨɜɨɞɨɜ ɢ ɝɚɡɨɧɟɮɬɟ-

ɯɪɚɧɢɥɢɳ. ɋɛɨɪɧɢɤ ɡɚɞɚɧɢɣ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɣ ɪɚɛɨɬɵ ɫɬɭɞɟɧ-

ɬɨɜ: ɭɱɟɛɧɨɟ ɩɨɫɨɛɢɟ / ɇ.Ⱥ. Ⱥɧɬɪɨɩɨɜɚ, Ɍ.Ⱦ. ɋɚɞɵɤɨɜ, Ⱥ.ȼ. ɒɚɞ-

ɪɢɧɚ, Ⱥ.ɋ. ɉɚɲɤɨɜɚ; Ɍɨɦɫɤɢɣ ɩɨɥɢɬɟɯɧɢɱɟɫɤɢɣ ɭɧɢɜɟɪɫɢɬɟɬ. –

Ɍɨɦɫɤ: ɂɡɞ-ɜɨ Ɍɨɦɫɤɨɝɨ ɩɨɥɢɬɟɯɧɢɱɟɫɤɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ, 2011. –

164 ɫ.

ȼ ɩɨɫɨɛɢɢ ɪɚɫɫɦɨɬɪɟɧɨ ɪɟɲɟɧɢɟ ɩɪɚɤɬɢɱɟɫɤɢɯ ɜɨɩɪɨɫɨɜ ɞɢɫɰɢɩɥɢɧɵ

«Ƚɟɨɞɟɡɢɱɟɫɤɨɟ ɨɛɟɫɩɟɱɟɧɢɟ ɫɬɪɨɢɬɟɥɶɫɬɜɚ ɧɟɮɬɟɝɚɡɨɩɪɨɜɨɞɨɜ ɢ ɝɚɡɨɧɟɮɬɟ-

ɯɪɚɧɢɥɢɳ», ɩɨɷɬɨɦɭ ɨɧɨ ɦɨɠɟɬ ɛɵɬɶ ɪɟɤɨɦɟɧɞɨɜɚɧɨ ɞɥɹ ɜɵɩɨɥɧɟɧɢɹ ɥɚɛɨɪɚ-

ɬɨɪɧɵɯ ɢ ɪɚɫɱɟɬɧɨ-ɝɪɚɮɢɱɟɫɤɢɯ ɪɚɛɨɬ ɩɨ ɬɨɩɨɝɪɚɮɢɱɟɫɤɨɣ ɤɚɪɬɟ, ɝɟɨɞɟɡɢɱɟ-

ɫɤɢɦ ɩɪɢɛɨɪɚɦ ɢ ɨɛɪɚɛɨɬɤɟ ɝɟɨɞɟɡɢɱɟɫɤɢɯ ɢɡɦɟɪɟɧɢɣ.

ɉɪɟɞɧɚɡɧɚɱɟɧɨ ɞɥɹ ɫɬɭɞɟɧɬɨɜ, ɨɛɭɱɚɸɳɢɯɫɹ ɩɨ ɫɩɟɰɢɚɥɶɧɨɫɬɢ 130501

«ɉɪɨɟɤɬɢɪɨɜɚɧɢɟ, ɫɨɨɪɭɠɟɧɢɟ ɢ ɷɤɫɩɥɭɚɬɚɰɢɹ ɝɚɡɨɧɟɮɬɟɩɪɨɜɨɞɨɜ ɢ ɝɚɡɨɧɟɮ

ɬɟɯɪɚɧɢɥɢɳ» ɧɚɩɪɚɜɥɟɧɢɹ 131000 «ɇɟɮɬɟɝɚɡɨɜɨɟ ɞɟɥɨ», ɬɚɤɠɟ ɦɨɠɟɬ ɛɵɬɶ ɩɨ-

ɥɟɡɧɨ ɫɬɭɞɟɧɬɚɦ ɞɪɭɝɢɯ ɧɚɩɪɚɜɥɟɧɢɣ, ɢɡɭɱɚɸɳɢɯ ɝɟɨɞɟɡɢɸ.

ɍȾɄ 528.48(076)

ȻȻɄ 26.12ɹ73

Ɋɟɰɟɧɡɟɧɬɵ

Ƚɥɚɜɧɵɣ ɦɚɪɤɲɟɣɞɟɪ ɈȺɈ «Ɍɨɦɫɤɇɂɉɂɧɟɮɬɶ»

ɘ.ɇ. Ⱥɪɟɫɬɨɜ

ɇɚɱɚɥɶɧɢɤ ɨɬɞɟɥɚ ɝɟɨɞɟɡɢɢ ɢ ɤɚɪɬɨɝɪɚɮɢɢ

ɍɩɪɚɜɥɟɧɢɹ Ɋɨɫɪɟɟɫɬɪɚ ɩɨ Ɍɨɦɫɤɨɣ ɨɛɥɚɫɬɢ

ȼ.Ɋ. Ʉɪɚɣɧɨɜɚ

ɒɚɞɪɢɧɚ Ⱥ.ȼ., ɉɚɲɤɨɜɚ Ⱥ.ɋ., 2011

ɩɨɥɢɬɟɯɧɢɱɟɫɤɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ, 2011

ʝˆˎ˃˅ˎˈːˋˈ

ʦ̛̖̖̦̖̏̔..........................................................................................................................................5

1. ˀʫʶʽʺʫʻʪʤˉʰʰˁ˃˄ʪʫʻ˃ʤʺʿʽˁʤʺʽˁ˃ʽ˔˃ʫʸːʻʽʱˀʤʥʽ˃ʫ........................................7

2. ʺʤˁˌ˃ʤʥˏʶʤˀ˃ʰʿʸʤʻʽʦ,˃ʽˋʻʽˁ˃ːʺʤˁˌ˃ʤʥʽʦ.ʸʰʻʫʱʻˏʫʰʯʺʫˀʫʻʰ˔.........10

2.1. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ........................................................................ 10

2.2. Ɂɚɞɚɧɢɹ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɜɵɩɨɥɧɟɧɢɹ ........................................ 18

2.3. Ɉɬɜɟɬɵ ɤ ɡɚɞɚɧɢɹɦ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɜɵɩɨɥɧɟɧɢɹ ...................... 19

2.4. Ɋɚɫɱɟɬɧɨ-ɝɪɚɮɢɱɟɫɤɚɹ ɪɚɛɨɬɚ «Ʌɢɧɟɣɧɵɟ ɢɡɦɟɪɟɧɢɹ ɧɚ

ɬɨɩɨɝɪɚɮɢɱɟɫɤɨɣ ɤɚɪɬɟ» .............................................................................................. 21



3. ʽʿˀʫʪʫʸʫʻʰʫʧʫʽʧˀʤˇʰˋʫˁʶʰˈʰʿˀ˔ʺʽ˄ʧʽʸːʻˏˈʶʽʽˀʪʰʻʤ˃˃ʽˋʫʶʿʽ

˃ʽʿʽʧˀʤˇʰˋʫˁʶʽʱʶʤˀ˃ʫ...........................................................................................................23

3.1. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ........................................................................ 23

3.2. Ɂɚɞɚɧɢɹ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɜɵɩɨɥɧɟɧɢɹ ........................................ 33

3.3. Ɉɬɜɟɬɵ ɤ ɡɚɞɚɧɢɹɦ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɜɵɩɨɥɧɟɧɢɹ ...................... 34

3.4. Ɋɚɫɱɟɬɧɨ-ɝɪɚɮɢɱɟɫɤɚɹ ɪɚɛɨɬɚ «Ɉɩɪɟɞɟɥɟɧɢɟ ɤɨɨɪɞɢɧɚɬ ɬɨɱɟɤ ɧɚ

ɬɨɩɨɝɪɚɮɢɱɟɫɤɨɣ ɤɚɪɬɟ» .............................................................................................. 36



4. ʽˀʰʫʻ˃ʰˀʽʦʤʻʰʫʸʰʻʰʱʰʽʥˎʫʶ˃ʽʦʿʽ˃ʽʿʽʧˀʤˇʰˋʫˁʶʽʱʶʤˀ˃ʫ........................38

4.1. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ........................................................................ 38

4.2. Ɂɚɞɚɧɢɹ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɜɵɩɨɥɧɟɧɢɹ ........................................ 49

4.3. Ɉɬɜɟɬɵ ɤ ɡɚɞɚɧɢɹɦ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɜɵɩɨɥɧɟɧɢɹ ...................... 51

4.4. ɊȺɋɑȿɌɇɈ-ȽɊȺɎɂɑȿɋɄȺə ɊȺȻɈɌȺ «Ɉɩɪɟɞɟɥɟɧɢɟ ɭɝɥɨɜ

ɨɪɢɟɧɬɢɪɨɜɚɧɢɹ ɩɨ ɬɨɩɨɝɪɚɮɢɱɟɫɤɨɣ ɤɚɪɬɟ» ............................................................ 53



5. ˀʫˌʫʻʰʫʯʤʪʤˋʿʽ˃ʽʿʽʧˀʤˇʰˋʫˁʶʽʱʶʤˀ˃̖...............................................................56

5.1. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ........................................................................ 56

5.2. Ɂɚɞɚɧɢɹ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɜɵɩɨɥɧɟɧɢɹ ........................................ 85

5.3. Ɉɬɜɟɬɵ ɤ ɡɚɞɚɧɢɹɦ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɜɵɩɨɥɧɟɧɢɹ ...................... 87

5.4. Ɋɚɫɱɟɬɧɨ-ɝɪɚɮɢɱɟɫɤɚɹ ɪɚɛɨɬɚ ʋ 4 «ɉɨɫɬɪɨɣɬɟ ɩɪɨɮɢɥɶ ɦɟɫɬɧɨɫɬɢ ɩɨ

ɬɨɩɨɝɪɚɮɢɱɟɫɤɨɣ ɤɚɪɬɟ ɩɨ ɡɚɞɚɧɧɨɦɭ ɧɚɩɪɚɜɥɟɧɢɸ» .............................................. 89



6. ʽʥˀʤʥʽ˃ʶʤˀʫʯ˄ʸː˃ʤ˃ʽʦ˃ʫʽʪʽʸʰ˃ʻʽʱˁˎʭʺʶʰ.........................................................90

6.1. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ........................................................................ 90

6.2. Ɂɚɞɚɧɢɹ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɜɵɩɨɥɧɟɧɢɹ ...................................... 113

6.3. Ɉɬɜɟɬɵ ɤ ɡɚɞɚɧɢɹɦ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɜɵɩɨɥɧɟɧɢɹ ɩɨ ɬɟɦɟ ʋ5 118

6.4. ɊȺɋɑȿɌɇɈ-ȽɊȺɎɂɑȿɋɄȺə ɊȺȻɈɌȺ «ɉɨɫɬɪɨɟɧɢɟ ɩɥɚɧɚ

ɦɟɫɬɧɨɫɬɢ ɩɨ ɪɟɡɭɥɶɬɚɬɚɦ ɬɟɨɞɨɥɢɬɧɨɣ ɫɴɺɦɤɢ» .................................................... 121



7. ʽʥˀʤʥʽ˃ʶʤˀʫʯ˄ʸː˃ʤ˃ʽʦ̵̸̡̨̨̛̯̖̦̖̭̐̨̛̛̛̦̖̣̬̦̏̏̌́...............................................127

7.1. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ...................................................................... 127

7.2. Ɂɚɞɚɧɢɹ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɜɵɩɨɥɧɟɧɢɹ ...................................... 140

7.3. Ɉɬɜɟɬɵ ɤ ɡɚɞɚɧɢɹɦ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɜɵɩɨɥɧɟɧɢɹ ɞɥɹ ɬɟɦɵ ʋ7

142



7.4. ɊȺɋɑȿɌɇɈ-ȽɊȺɎɂɑȿɋɄȺə ɊȺȻɈɌȺ «ɉɨɫɬɪɨɟɧɢɟ ɩɪɨɮɢɥɹ

ɦɟɫɬɧɨɫɬɢ ɩɨ ɪɟɡɭɥɶɬɚɬɚɦ ɬɟɯɧɢɱɟɫɤɨɝɨ ɧɢɜɟɥɢɪɨɜɚɧɢɹ» ..................................... 143



8. ˀ̛̖̹̖̦̖̨̨̬̯̦̜̍̌̸̨̡̨̛̖̖̖̭̜̐̔̚̸̛̌̔̌̚........................................................................147

8.1. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ...................................................................... 147

8.2. Ɂɚɞɚɧɢɹ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɜɵɩɨɥɧɟɧɢɹ ...................................... 149

8.3. Ɉɬɜɟɬɵ ɤ ɡɚɞɚɧɢɹɦ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɜɵɩɨɥɧɟɧɢɹ .................... 150

8.4. Ɋɚɫɱɟɬɧɨ-ɝɪɚɮɢɱɟɫɤɚɹ ɪɚɛɨɬɚ «Ɋɟɲɟɧɢɟ ɨɛɪɚɬɧɨɣ ɝɟɨɞɟɡɢɱɟɫɤɨɣ

ɡɚɞɚɱɢ» 153



ʿˀʰʸʽʮʫʻʰʫ1.ʽ̶̬̖̍̌̚̴̸̡̨̨̛̬̖̭̐̌̐̛̣̭̯̌̴̨̬̥̯̌̌ʤ4̣̔́̨̛̼̪̣̦̖̦̏́̸̨̬̭̖̯̦̌Ͳ

̴̸̵̡̛̛̬̖̭̐̌̨̬̯̌̍.......................................................................................................................154

ʿˀʰʸʽʮʫʻʰʫ2.˃̛̯̱̣̦̼̜̽̛̣̭̯..............................................................................................155

ʿˀʰʸʽʮʫʻʰʫ3.ˁ̵̖̥̌̨̛̛̥̭̏̌̏́̚̚̨̛̥̱̯̌̏̚̛̨̬̱̥̍̏.......................................................156

ʿˀʰʸʽʮʫʻʰʫ4.ʯ̡̛̦̌̛̛̪̬̬̺̖̦̜̌̡̨̨̛̬̦̯̔̌̨̪̸̖̯̖̬̯̥̏́...............................................156

ʿˀʰʸʽʮʫʻʰʫ5.ʫ̶̛̛̦̼̔̛̛̥̖̬̖̦̜̚,̛̪̬̥̖̦̖̥̼̖́̏̨̛̛̖̖̐̔̚.........................................157

ɉɊɂɅɈɀȿɇɂȿ 6. Ʉɪɚɬɧɵɟ ɢ ɞɨɥɶɧɵɟ ɩɪɢɫɬɚɜɤɢ ɤ ɟɞɢɧɢɰɚɦ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ..........158

ɉɊɂɅɈɀȿɇɂȿ 7. Ⱥɧɚɥɢɬɢɱɟɫɤɢɣ ɫɩɨɫɨɛ (ɜɵɜɨɞ ɮɨɪɦɭɥɵ) ................... 159

ɉɊɂɅɈɀȿɇɂȿ 8. Ɉɩɪɟɞɟɥɟɧɢɟ ɤɨɨɪɞɢɧɚɬ ɩɭɧɤɬɨɜ ɤɚɪɬɨɦɟɬɪɢɱɟɫɤɢɦ

ɫɩɨɫɨɛɨɦ ...................................................................................................................... 160

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ȼɜɟɞɟɧɢɟ

ɍɱɟɛɧɵɣ ɩɪɨɰɟɫɫ ɩɨ ɤɭɪɫɭ ɂɧɠɟɧɟɪɧɚɹ ɝɟɨɞɟɡɢɹ ɫɨɫɬɨɢɬ ɢɡ ɥɟɤɰɢɣ

ɢ ɥɚɛɨɪɚɬɨɪɧɵɯ ɡɚɧɹɬɢɣ, ɧɚ ɤɨɬɨɪɵɯ ɫɬɭɞɟɧɬɵ ɪɟɲɚɸɬ ɡɚɞɚɱɢ ɩɨ ɬɨɩɨ-

ɝɪɚɮɢɱɟɫɤɨɣ ɤɚɪɬɟ, ɡɧɚɤɨɦɹɬɫɹ ɫ ɭɫɬɪɨɣɫɬɜɨɦ ɢ ɪɚɛɨɬɨɣ ɝɟɨɞɟɡɢɱɟɫɤɢɯ

ɢɧɫɬɪɭɦɟɧɬɨɜ, ɨɛɪɚɛɚɬɵɜɚɸɬ ɪɟɡɭɥɶɬɚɬɵ ɝɟɨɞɟɡɢɱɟɫɤɢɯ ɢɡɦɟɪɟɧɢɣ.

Ⱦɚɧɧɨɟ ɭɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɩɪɢɡɜɚɧɨ ɨɤɚɡɚɬɶ ɩɨɦɨɳɶ ɫɬɭɞɟɧɬɚɦ ɜ ɜɵ-

ɩɨɥɧɟɧɢɢ ɢɦɢ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɣ ɪɚɛɨɬɵ ɫɨɝɥɚɫɧɨ ɭɱɟɛɧɨɦɭ ɩɥɚɧɭ ɩɨ

ɞɢɫɰɢɩɥɢɧɟ «ɂɧɠɟɧɟɪɧɚɹ ɝɟɨɞɟɡɢɹ». ɋɚɦɨɫɬɨɹɬɟɥɶɧɚ

ɹ ɪɚɛɨɬɚ ɫɬɭɞɟɧɬɨɜ

ɫɨɫɬɨɢɬ ɜ ɪɟɲɟɧɢɢ ɪɚɡɥɢɱɧɵɯ ɝɟɨɞɟɡɢɱɟɫɤɢɯ ɡɚɞɚɱ (ɤɚɤ ɩɨ ɤɚɪɬɟ, ɬɚɤ ɢ

ɩɨ ɨɛɪɚɛɨɬɤɟ ɪɟɡɭɥɶɬɚɬɨɜ ɝɟɨɞɟɡɢɱɟɫɤɢɯ ɢɡɦɟɪɟɧɢɣ), ɚ ɬɚɤɠɟ ɩɨ ɜɵɩɨɥ-

ɧɟɧɢɸ ɪɚɫɱɺɬɧɨ-ɝɪɚɮɢɱɟɫɤɢɯ ɪɚɛɨɬ (ɤɨɧɬɪɨɥɶɧɵɯ ɪɚɛɨɬ).

ȼ ɩɨɫɨɛɢɢ ɩɪɢɜɟɞɺɧ ɦɚɬɟɪɢɚɥ ɩɨ 8-ɦɢ ɬɟɦɚɦ, ɧɚɱɢɧɚɹ ɫ ɥɢɧɟɣɧɵɯ

ɢɡɦɟɪɟɧɢɣ ɩɨ ɤɚɪɬɚɦ ɢ ɩɥɚɧɚɦ ɢ ɡɚɤɚɧɱɢɜɚɹ ɨɛɪɚɛɨɬɤɨɣ ɪɟɡɭɥɶɬɚɬɨɜ ɚɷ-

ɪɨɮɨɬɨɫɴɺɦɤɢ. ɉɨ ɤɚɠɞɨɣ ɬɟɦɟ ɦɚɬɟɪɢɚɥ ɫɬɪɭɤɬɭɪɢɪɨɜɚɧ ɧɚ ɱɟɬɵɪɟ

ɱɚɫɬɢ: ɩɪɢɦɟɪɵ ɫ ɪɟɲɟɧɢɹɦɢ, ɡɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɜɵɩɨɥɧɟɧɢɹ,

ɨɬɜɟɬɵ ɤ ɧɢɦ ɢ ɡɚɞɚɧɢɹ ɧɚ ɪɚɫɱɺɬɧɨ-ɝɪɚɮɢɱɟɫɤɢɟ ɪɚɛɨɬɵ ɫ ɜɚɪɢɚɧɬɚɦɢ.

Ʉɪɨɦɟ ɬɨɝɨ, ɜ ɬɟɤɫɬɟ

ɩɨɫɨɛɢɹ ɩɪɢɜɨɞɢɬɫɹ ɬɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ,

ɪɚɧɠɢɪɨɜɚɧɧɵɣ ɫɨɝɥɚɫɧɨ ɩɢɤɬɨɝɪɚɦɦɚɦ.

Ɍɟɨɪɟɬɢɱɟɫɤɢɣ

ɦɚɬɟɪɢɚɥ, ɮɨɪɦɭɥɵ, ɧɟɨɛɯɨɞɢ-

ɦɵɟ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱ.



ɂɧɮɨɪɦɚɰɢɹ ɞɥɹ ɪɚɡɦɵɲɥɟɧɢɹ.



Ⱦɨɩɨɥɧɢɬɟɥɶɧɵɟ ɫɜɟɞɟɧɢɹ ɞɥɹ ɪɟɲɟɧɢɹ ɤɨɧɤɪɟɬɧɵɯ

ɡɚɞɚɱ.



ɂɧɮɨɪɦɚɰɢɹ

ɞɥɹ ɪɚɡɦɵɲ-

ɥɟɧɢɹ

ɂɫɬɨɪɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ ɢ ɥɸɛɨɩɵɬɧɵɟ ɫɜɟɞɟɧɢɹ.

ȼɨ ɜɬɨɪɨɣ ɱɚɫɬɢ ɩɨɫɨɛɢɹ ɩɪɢɜɨɞɹɬɫɹ ɬɟɫɬɨɜɵɟ ɡɚɞɚɧɢɢ ɩɨ ɤɚɠɞɨɣ

ɬɟɦɟ ɫ ɨɬɜɟɬɚɦɢ.

ɇɚɫɬɨɹɳɟɟ ɭɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɜ ɩɨɦɨɳɶ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɣ ɪɚɛɨɬɟ

ɫɬɭɞɟɧɬɨɜ ɢɡɞɚɺɬɫɹ ɜɩɟɪɜɵɟ.

1. ɊȿɄɈɆȿɇȾȺɐɂɂ ɋɌɍȾȿɇɌȺɆ ɉɈ ɋȺɆɈɋɌɈəɌȿɅɖ-

ɇɈɃ ɊȺȻɈɌȿ

ɉɪɢ ɩɪɨɟɤɬɧɵɯ ɪɚɛɨɬɚɯ ɱɚɫɬɨ ɥɢɧɟɣɧɵɟ ɪɚɡɦɟɪɵ, ɩɥɨɳɚɞɢ ɡɟɦɥɹ-

ɧɵɯ ɭɝɨɞɢɣ, ɜɨɞɨɡɚɛɨɪɧɨɝɨ ɛɚɫɫɟɣɧɚ, ɨɛɴɟɦɵ ɡɟɦɥɹɧɵɯ ɦɚɫɫ, ɨɩɪɟɞɟ-

ɥɹɸɬɫɹ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɫ ɱɟɪɬɟɠɚ, ɩɨɷɬɨɦɭ ɜɫɟ ɩɨɫɬɪɨɟɧɢɹ ɧɚ ɱɟɪɬɟ-

ɠɚɯ, ɜ ɱɚɫɬɧɨɫɬɢ ɧɚ ɬɨɩɨɝɪɚɮɢɱɟɫɤɨɦ ɩɥɚɧɟ, ɞɨɥɠɧɵ ɛɵɬɶ ɜɵɩɨɥɧɟɧɵ ɫ

ɩɪɟɞɟɥɶɧɨ ɜɨɡɦɨɠɧɨɣ ɞɥɹ ɱɟɥɨɜɟɱɟɫɤɨɝɨ ɝɥɚɡɚ ɬɨɱɧɨɫɬɶɸ (0,1 ɦɦ). ȼ

ɫɜɹɡɢ ɫ ɷɬɢɦ ɩɟɪɟɞ ɧɚɱɚɥɨɦ ɝɪɚɮɢɱɟɫɤɢɯ ɪɚɛɨɬ, ɫɬɭɞɟɧɬ ɞɨɥɠɟɧ ɢɦɟɬɶ

ɧɟɨɛɯɨɞɢɦɵɟ ɢɧɫɬɪɭɦɟɧɬɵ ɢ ɩɪɢɧɚɞɥɟɠɧɨɫɬɢ: ɝɟɨɞɟɡɢɱɟɫɤɢɣ ɬɪɚɧɫɩɨɪ-

ɬɢɪ, ɦɟɬɚɥɥɢɱɟɫɤɭɸ ɥɢɧɟɣɤɭ ɫ ɩɨɩɟɪɟɱɧɵɦ ɦɚɫɲɬɚɛɨɦ, ɢɡɦɟɪɢɬɟɥɶ ɫ

ɮɢɤɫɢɪɨɜɚɧɢɟɦ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɢɝɥɚɦɢ ɢ ɞɪ. ȼɨ ɢɡɛɟɠɚɧɢɟ ɡɚɝɪɹɡɧɟ-

ɧɢɹ ɱɟɪɬɟɠɚ ɩɪɢ ɪɚɛɨɬɟ, ɦɟɬɚɥɥɢɱɟɫɤɢɟ ɢ ɩɥɚɫɬɦɚɫɫɨɜɵɟ ɩɨɜɟɪɯɧɨɫɬɢ

ɱɟɪɬɟɠɧɵɯ ɩɪɢɧɚɞɥɟɠɧɨɫɬɟɣ, ɤɚɤ ɢ ɪɭɤɢ, ɞɨɥɠɧɵ ɛɵɬɶ ɩɪɨɦɵɬɵ ɢ ɧɚ-

ɫɭɯɨ ɜɵɬɟɪɬɵ.

ȼɵɱɢɫɥɢɬɟɥɶɧɵɟ ɪɚɛɨɬɵ ɞɨɥɠɧɵ ɜɵɩɨɥɧɹɬɶɫɹ ɫ ɫɨɛɥɸɞɟɧɢɟɦ ɬɪɟ-

ɛɨɜɚɧɢɣ ɢ ɩɪɚɜɢɥ, ɢɡɥɨɠɟɧɧɵɯ ɜ (2). ȼ ɩɪɚɤɬɢɤɟ ɜɵɱɢɫɥɢɬɟɥɶɧɵɯ ɪɚ-

ɛɨɬ ɧɟ ɜɫɟɝɞɚ ɢɦɟɟɬɫɹ ɞɨɫɬɭɩ ɤ ɜɵɱɢɫɥɢɬɟɥɶɧɨɣ ɬɟɯɧɢɤɟ, ɩɨɷɬɨɦɭ ɫɬɭ-

ɞɟɧɬ ɞɨɥɠɟɧ ɫɨɜɟɪɲɟɧɫɬɜɨɜɚɬɶ ɧɚɜɵɤɢ ɜ ɪɭɱɧɨɦ ɫɱɟɬɟ ɢ ɭɦɟɬɶ ɜɵɩɨɥ-

ɧɹɬɶ ɩɪɨɫɬɵɟ ɞɟɣɫɬɜɢɹ ɩɨ ɩɪɚɜɢɥɚɦ ɦɚɬɟɦɚɬɢɤɢ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɬɚɛ-

ɥɢɰ, ɡɧɚɱɟɧɢɹ ɜ ɤɨɬɨɪɵɯ ɬɳɚɬɟɥɶɧɨ ɩɪɨɜɟɪɟɧɵ. ɋɥɟɞɭɟɬ ɩɨɦɧɢɬɶ, ɱɬɨ

ɜɟɥɢɱɢɧɵ ɨɞɧɨɣ ɪɚɡɦɟɪɧɨɫɬɢ ɞɨɥɠɧɵ ɩɨɞɫɱɢɬɵɜɚɬɶɫɹ ɫ ɨɞɢɧɚɤɨɜɨɣ

ɬɨɱɧɨɫɬɶɸ.

Ɉɛɳɢɟ ɬɪɟɛɨɜɚɧɢɹ ɤ ɜɟɞɟɧɢɸ ɢ ɨɮɨɪɦɥɟɧɢɸ ɜɵɱɢɫɥɟɧɢɣ

 ȼɵɛɢɪɚɸɬ ɪɚɰɢɨɧɚɥɶɧɭɸ ɫɯɟɦɭ (ɚɥɝɨɪɢɬɦ), ɨɛɟɫɩɟɱɢɜɚɸɳɭɸ

ɩɪɨɫɬɨɬɭ, ɧɚɝɥɹɞɧɨɫɬɶ ɢ ɨɞɧɨɬɢɩɧɨɫɬɶ ɜɵɱɢɫɥɟɧɢɣ; ɧɚɩɪɢɦɟɪ ɪɟɡɭɥɶɬɚ-

ɬɵ ɢɡɦɟɪɟɧɢɣ ɢ ɩɨɥɟɜɵɯ ɜɵɱɢɫɥɟɧɢɣ ɡɚɩɢɫɵɜɚɸɬ ɜ ɫɬɚɧɞɚɪɬɧɵɯ ɠɭɪ-

ɧɚɥɚɯ, ɛɥɚɧɤɚɯ ɢɥɢ ɜɟɞɨɦɨɫɬɹɯ.

 ȼɫɟ ɜɵɱɢɫɥɟɧɢɹ ɫɨɩɪɨɜɨɠɞɚɸɬ ɤɨɧɬɪɨɥɟɦ – ɬɟɤɭɳɢɦ (ɩɪɨɜɟ-

ɪɹɸɬ ɩɪɚɜɢɥɶɧɨɫɬɶ ɩɪɨɦɟɠɭɬɨɱɧɵɯ ɜɵɱɢɫɥɟɧɢɣ) ɢ ɡɚɤɥɸɱɢɬɟɥɶɧɵɦ

(ɩɪɚɜɢɥɶɧɨɫɬɶ ɨɤɨɧɱɚɬɟɥɶɧɨɝɨ ɪɟɡɭɥɶɬɚɬɚ). Ⱦɥɹ ɷɬɨɝɨ ɜɵɱɢɫɥɟɧɢɹ ɜɵ-

ɩɨɥɧɹɸɬ ɞɜɚ ɪɚɛɨɬɧɢɤɚ, ɩɚɪɚɥɥɟɥɶɧɨ

ɢ ɧɟɡɚɜɢɫɢɦɨ ɞɪɭɝ ɨɬ ɞɪɭɝɚ, ɥɢɛɨ

ɪɟɡɭɥɶɬɚɬɵ ɩɪɨɜɟɪɹɸɬ ɩɨ ɤɨɧɬɪɨɥɶɧɵɦ ɮɨɪɦɭɥɚɦ.

 Ɂɚɩɢɫɢ ɜɟɞɭɬ ɱɺɬɤɨ ɢ ɪɚɡɛɨɪɱɢɜɨ, ɧɟ ɞ

ɨɩɭɫɤɚɟɬ

ɫɹ ɢɫɩɪɚɜɥɟɧɢɟ

ɩɨ ɪɚɧɟɟ ɧɚɩɢɫɚɧɧɨɦɭ ɱɢɫɥɭ; ɧɭɠɧɨ ɨɲɢɛɨɱɧɨɟ ɱɢɫɥɨ ɡɚɱɟɪɤɧɭɬɶ ɢ

ɫɜɟɪɯɭ ɧɚɩɢɫɚɬɶ ɩɪɚɜɢɥɶɧɨɟ ɱɢɫɥɨ. ɉɪɚɤɬɢɤɚ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɧɟɱɺɬɤɚɹ

ɢ ɧɟɛɪɟɠɧɚɹ ɡɚɩɢɫɶ ɱɢɫɟɥ ɱɚɫɬɨ ɩɪɢɜɨɞɢɬ ɤ ɩɨɝɪɟɲɧɨɫɬɹɦ

 ȼɵɱɢɫɥɟɧɢɹ ɜɟɞɭɬ ɫ ɱɢɫɥɚɦɢ, ɧɚ ɨɞɢɧ ɡɧɚɤ ɛɨɥɶɲɢɦɢ, ɱɟɦ ɩɨ-

ɥɭɱɟɧɧɵɟ ɢɡ ɢɡɦɟɪɟɧɢɣ. Ɂɚɬɟɦ ɪɟɡɭɥɶɬɚɬ ɨɤɪɭɝɥɹɸɬ.

ɉɪɚɜɢɥɚ ɨɤɪɭɝɥɟɧɢɹ (Ƚɚɭɫɫɚ):

 ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɜɵɱɢɫɥɟɧɢɣ ɱɢɫɥɨ ɡɧɚɱɚɳɢɯ ɰɢɮɪ ɩɪɨɦɟɠɭ-

ɬɨɱɧɵɯ ɪɟɡɭɥɶɬɚɬɨɜ ɧɟ ɞɨɥɠɧɨ ɩɪɟɜɵɲɚɬɶ ɱɢɫɥɚ ɜɟɪɧɵɯ ɰɢɮɪ ɛɨɥɟɟ ɱɟɦ

ɧɚ 1 ɢɥɢ 2 ɟɞɢɧɢɰɵ. Ɉɤɨɧɱɚɬɟɥɶɧɵɣ ɪɟɡɭɥɶɬɚɬ ɦɨɠɟɬ ɫɨɞɟɪɠɚɬɶ ɧɟ ɛɨ-

ɥɟɟ ɨɞɧɨɣ ɥɢɲɧɟɣ ɡɧɚɱɚɳɟɣ ɰɢɮɪɵ.

 ɑɢɫɥɚ ɨɤɪɭɝɥɹɸɬ ɩɨ ɨɛɳɢɦ ɩɪɚɜɢɥɚɦ: ɟɫɥɢ ɩɨɫɥɟɞɭɸɳɚɹ ɩɨ-

ɫɥɟ ɨɫɬɚɜɥɹɟɦɨɣ ɰɢɮɪɵ ɰɢɮɪɚ ɦɟɧɶɲɟ ɩɹɬɢ, ɬɨ ɟɺ ɩɪɨɫɬɨ

ɨɬɛɪɚɫɵɜɚɸɬ;

ɟɫɥɢ ɛɨɥɶɲɟ ɩɹɬɢ – ɬɨ ɤ ɩɨɫɥɟɞɧɟɣ ɨɫɬɚɜ

ɥɹɟɦɨɣ ɰɢɮɪɟ ɞɨɛɚɜɥɹɸɬ ɟɞɢ-

ɧɢɰɭ; ɟɫɥɢ ɩɨɫɥɟɞɧɹɹ ɰɢɮɪɚ 5, ɬɨ ɟɺ ɨɬɛɪɚɫɵɜɚɸɬ, ɚ ɩɪɟɞɵɞɭɳɭɸ ɰɢɮɪɭ

ɨɤɪɭɝɥɹɸɬ ɞɨ ɱɺɬɧɨɣ ɰɢɮɪɵ.

10,375 – ɞɨ 10,38; 0,245 – ɞɨ 0,24.

 ɉɪɢ ɫɥɨɠɟɧɢɢ ɢɥɢ ɜɵɱɢɬɚɧɢɢ ɱɢɫɟɥ ɫ ɧɟɨɞɢɧɚɤɨɜɵɦ ɤɨɥɢɱɟ-

ɫɬɜɨɦ ɞɟɫɹɬɢɱɧɵɯ ɡɧɚɤɨɜ ɨɫɬɚɜɥɹɸɬ ɫɬɨɥɶɤɨ ɞɟɫɹɬɢɱɧɵɯ ɡɧɚɤɨɜ, ɫɤɨɥɶ-

ɤɨ ɢɯ ɢɦɟɟɬ ɱɢɫɥɨ ɫ ɧɚɢɦɟɧɶɲɢɦ

ɤɨɥɢɱɟɫɬɜɨɦ ɞɟɫɹɬɢɱɧɵɯ ɡɧɚɤɨɜ.

24,36+0,783=25,14; 17,866-4,31=13,56.

 ɉɪɢ ɭɦɧɨɠɟɧɢɢ ɢɥɢ ɞɟɥɟɧɢɢ

ɱɢɫɟɥ ɫ ɧɟɨɞɢɧɚɤɨɜɵɦ ɤɨɥɢɱɟɫɬ-

ɜɨɦ ɡɧɚɱɚɳɢɯ ɰɢɮɪ ɨɫɬɚɜɥɹɸɬ ɫɬɨɥɶɤɨ ɡɧɚɱɚɳɢɯ ɰɢɮɪ, ɫɤɨɥɶɤɨ ɢɯ ɢɦɟ-

ɟɬ ɱɢɫɥɨ ɫ ɧɚɢɦɟɧɶɲɢɦ ɤɨɥɢɱɟɫɬɜɨɦ ɡɧɚɱɚɳɢɯ ɰɢɮɪ, ɩɥɸɫ ɨɞɧɚ ɡɚɩɚɫ-

ɧɚɹ ɰɢɮɪɚ. ȼ ɩɪɨɢɡɜɟɞɟɧɢɢ ɢɥɢ ɱɚɫɬɧɨɦ ɨɫɬɚɜɥɹɸɬ ɫɬɨɥɶɤɨ ɡɧɚɱɚɳɢɯ

ɰɢɮɪ, ɫɤɨɥɶɤɨ ɢɦɟɟɬ ɱɢɫɥɨ ɫ ɧɚɢɦɟɧɶɲɢɦ ɤɨɥɢɱɟɫɬɜɨɦ ɡɧɚɱɚɳɢɯ ɰɢɮɪ

;

25,36ɯ2,63=66,6968=66,7;

53,644:5,43=53,64:5,

43=9,88.

 ɉɪɢ ɜɨɡɜɟɞɟɧɢɢ ɜ

ɫɬɟɩɟɧɶ ɜ ɪɟɡɭɥɶɬɚɬɟ ɨɫɬɚɜɥɹɸɬ ɫɬɨɥɶɤɨ ɡɧɚ-

ɱɚɳɢɯ ɰɢɮɪ, ɫɤɨɥɶɤɨ ɢɯ ɛɵɥɨ ɜ ɱɢɫɥɟ, ɜɨɡɜɨɞɢɦɨɦ ɜ ɫɬɟɩɟɧɶ;

15,63

=244,2969=244,3;

24,2

=585,64=586.

 ɉɪɢ ɢɡɜɥɟɱɟɧɢɢ ɤɨɪɧɹ ɢɡ ɱɢɫɥɚ ɜ ɪɟɡɭɥɶɬɚɬɟ ɫɨɯɪɚɧɹɸɬ ɫɬɨɥɶ-

ɤɨ ɡɧɚɱɚɳɢɯ ɰɢɮɪ, ɫɤɨɥɶɤɨ ɜɟɪɧɵɯ ɰɢɮɪ ɢɦɟɟɬ ɩɨɞɤɨɪɟɧɧɨɟ ɱɢɫɥɨ

126,928.83

 ȿɫɥɢ ɩɪɨɢɡɜɨɞɢɬɫɹ ɧɟɫɤɨɥɶɤɨ ɚɪɢɮɦɟɬɢɱɟɫɤɢɯ ɞɟɣɫɬɜɢɣ, ɬɨ ɜ

ɩɪɨɦɟɠɭɬɨɱɧɵɯ ɪɟɡɭɥɶɬɚɬɚɯ ɫɨɯɪɚɧɹɟɬɫɹ ɧɚ ɨɞɢɧ ɡɧɚɤ ɛɨɥɶɲɟ.

1,507,54,148,053,346,24,14835,0528,346,2  

Ɋɚɛɨɬɚ ɫ ɛɨɥɶɲɢɦ ɱɢɫɥɨɦ ɡɧɚɤɨɜ ɧɟ ɭɜɟɥɢɱɢɜɚɟɬ ɬɨɱɧɨɫɬɶ ɪɟɡɭɥɶ-

ɬɚɬɨɜ, ɚ ɡɚɬɪɭɞɧɹɟɬ ɜɵɱɢɫɥɟɧɢɹ ɢ ɬɪɟɛɭɟɬ ɛɨɥɶɲɟɝɨ ɜɪɟɦɟɧɢ.

2. ɆȺɋɒɌȺȻɕ ɄȺɊɌ ɂ ɉɅȺɇɈȼ, ɌɈɑɇɈɋɌɖ ɆȺɋɒɌȺ-

ȻɈȼ. ɅɂɇȿɃɇɕȿ ɂɁɆȿɊȿɇɂə

2.1. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ

Ɂɚɞɚɱɚ 2.1. ɇɚ ɩɥɚɧɟ

ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɬɨɱɤɚɦɢ ɫɨɫɬɚɜ-

ɥɹɟɬ 5 ɫɦ. Ɉɩɪɟɞɟɥɢɬɟ ɝɨɪɢɡɨɧɬɚɥɶɧɨɟ ɩɪɨɥɨɠɟɧɢɟ ɦɟɠɞɭ ɷɬɢɦɢ ɠɟ

ɬɨɱɤɚɦɢ ɧɚ ɦɟɫɬɧɨɫɬɢ.

ɑɢɫɥɟɧɧɵɣ ɦɚɫɲɬɚɛ ɤɚɪɬɵ (ɩɥɚɧɚ) – ɨɬɧɨɲɟɧɢɟ ɞɥɢɧɵ

ɥɢɧɢɢ ɧɚ ɤɚɪɬɟ (ɩɥɚɧɟ) ɤ ɞɥɢɧɟ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɩɪɨɟɤ-

ɰɢɢ ɥɢɧɢɢ ɦɟɫɬɧɨɫɬɢ:

. (2.1)

ɑɢɫɥɟɧɧɵɣ ɦɚɫɲɬɚɛ ɦɨɠɧɨ ɜɵɪɚɡɢɬɶ ɜ ɜɢɞɟ ɩɪɨɫɬɨɣ ɞɪɨɛɢ:

, (2.2)

ɝɞɟ m – ɫɬɟɩɟɧɶ ɭɦɟɧɶɲɟɧɢɹ ɢɥɢ ɡɧɚɦɟɧɚɬɟɥɶ ɱɢɫɥɟɧɧɨɝɨ ɦɚɫɲɬɚɛɚ.

Ɋɟɲɟɧɢɟ

. ɉɨ ɮɨɪɦɭɥɚɦ (1, 2) ɢɦɟɟɦ: ; ;

Ɂɚɞɚɱɚ 2.2. Ɉɩɪɟɞɟɥɢɬɟ ɱɢɫɥɟɧɧɵɣ ɦɚɫɲɬɚɛ ɩɥɚɧɚ, ɟɫɥɢ ɝɨɪɢɡɨɧ-

ɬɚɥɶɧɨɟ ɩɪɨɥɨɠɟɧɢɟ ɥɢɧɢɢ, ɞɥɢɧɨɸ 50 ɦ ɧɚ ɦɟɫɬɧɨɫɬɢ, ɜɵɪɚɠɚɟɬɫɹ ɧɚ

ɩɥɚɧɟ ɨɬɪɟɡɤɨɦ 5 ɫɦ.

Ɋɟɲɟɧɢɟ.

ɉɨɞɫɬɚɜɢɦ ɢɫɯɨɞɧɵɟ ɞɚɧɧɵɟ ɜ ɮɨɪɦɭɥɭ (2), ɩɨɥɭɱɢɦ:

Ɂɚɞɚɱɚ 2.3. Ƚɨɪɢɡɨɧɬɚɥɶɧɨɟ ɩɪɨɥɨɠɟɧɢɟ ɦɟɠɞɭ ɞɜɭɦɹ ɬɨɱɤɚɦɢ ɧɚ

ɦɟɫɬɧɨɫɬɢ ɪɚɜɧɨ 40 ɦ. Ɉɩɪɟɞɟɥɢɬɟ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɷɬɢɦɢ ɠɟ ɬɨɱɤɚɦɢ

ɧɚ ɩɥɚɧɟ Ɇ = 1:2000.

Ɋɟɲɟɧɢɟ

. ɉɨɞɫɬɚɜɢɦ ɜ ɮɨɪɦɭɥɭ (2) ɢɡɜɟɫɬɧɵɟ ɞɚɧɧɵɟ, ɡɚɩɢɲɟɦ: