, 2002

2

. - . . - . - . . .

, , 2002

3

, , . I II . . , , . , , . . , , , , , , , , , . I II . :

. : 1521, 3642, 4951, 6164, 66, 67, 7173; . : 1113, 2225, 5255, 65, 74, 75; . : 2635, 6870, 76; . : 710, 14, 4345; . : 16, 4648, 5660.

4

0 ............................................... 17

11. ............................................................................................... 17 22. ............................................................................................ 17 33. .................................................................................................................................... 17 44. . ..................................................................................................................................... 18

54.1. ................................................................................................................................................ 18 64.2. ....................................................................................................................................................... 110

75. .............................................................................................. 111 86. , ....................................................... 114

9 ............................................................................................ 119 17. ........................................................................................................................ 119 18. ............................................................................................ 119 19. ............................................................................... 121 110. ......................................................................... 121

110.1. ................................................ 121 110.2. . .................... 122 110.3. . ............. 123 110.4. ............................................................................................ 125 110.5. . ...................................................... 125 110.6. .................................................................................. 126 210.7. ............................................................... 127

2 ........................................................................................................... 229 211. ................................................................................................................................. 229 212. .................................................. 230 213. . ... 233

2 ...................................................................................................... 236 214. ....................................................................................... 236

2 .......................................................................................................................................... 239 215. ....................................................................................... 239

215.1. ................................................................................................................................... 239 315.2. ...................................................................................................................... 239 315.3. .................................................... 241

316. - ..................................................................................................................... 242 316.1. , , ................................................... 242 316.2. ....................................................................... 250 316.3. ............................................................................................... 253

317. .................................................................................................................................. 256 317.1. , , , ................ 256 317.2. ................................................... 261

318. ................................................................................................................ 265 418.1. ................................................................................................................. 268 418.2. ........................................................................................................... 269

419. ............................................................................................................ 270 419.1. ............................................................................ 270 419.2. ............................................................................... 271

420. () . .................................................................... 272 420.1. .......................................................................................... 272 420.2. ..................................................................................................................... 274

421. . .......................................................................... 274 4 ................................................................................................................................ 277

522. ..................................................................................................... 277 523. ................................... 278

523.1. .................................................................................................................................. 279 523.2. .......................................................................................................................... 279

524. . , , .............. 280 524.1. ............................................................................................................. 280

525. ......................................................................................................................................... 283 525.1. ...................................................................... 284

5 ......................................................................................................................... 287 526. . . ............................................. 287

626.1. .................................................................................................................................... 287

5

626.2. ................................................................................................... 287 626.3. .................................................................................................................... 288

627. . ............................................................ 289 628. . .................................. 291 629. ......................................................................................... 293

629.1. ....................................................................................................................... 293 629.2. ................................................................................................................ 295

630. ................................................................................................................................... 295 631. ............................................... 2106 732. ....................................................................................................... 2108

732.1. .......................................................................................................................... 2108 732.2. ..................................................................................................................... 2111

733. ...................................................................................................................... 2115 734. .......................................................................................................................... 2118 735. ............................................................................................................................ 2119

7 ............................................................................................... 2122 736. .............................................................................................. 2122

736.1. ........................................................................................................ 2122 736.2. .................................................................................................................................... 2123 836.3. ............................................................................................................................... 2124

837. ................................................................................................... 2125 8 () ......................................................................................................... 2128

838. ......................................................................................................... 2128 838.1. .............................................................................................................. 2128 838.2. ......................................................................................................... 2129

839. .................................................................................................................................................... 2132 839.1. .................................................................................................................................. 2132 839.2. .............................................................................. 2139

840. ............................................................................................................. 2139 941. ................................................................................................................ 2151 942. ............................................................................................................. 2152

942.1. ........................................................................................... 2153 942.2. ......................................................................... 2155 942.3. ....................................................................................................................................... 2158 942.4. ................................................................................................................................... 2158 942.5. ......................................................................................................... 2158

9 .................................................................................................................................. 2159 943. ......................................................................................................... 2159 944. ......................................................................................................... 2161 145. ............................................................................................ 2162

1 .......................................................................................................................................... 2163 146. , ......................................................................................... 2163

146.1. .................................................................................. 2163 146.2. , ................................................................. 2164

147. .................................................................................. 2165 147.1. .................................................................................................................................... 2165 147.2. ................................................................................................................................... 2165

148. ................................................ 2168 148.1. ............................................................................................................ 2168 148.2. .......................................................................................................... 2169

1 .................................................................................................................. 2170 149. ........................................................................................................................................... 2170 150. ........................................................................................................................................ 2171

1 () ......................................................................................... 2172 151. .............................................................. 2172

1 ................................................................................................................................. 2179 152. ............................................................................................................................................... 2179

152.1. ........................................................ 2179 152.2. ............................................................................................................... 2181 152.3. ................................................................................................................... 2182 152.4. .......................................................... 3183 152.5. ............................................. 3183

6

153. ........................................................................................................................................... 3184 153.1. ............................................................................................................... 3186

154. .......................................................................................................................................... 3188 155. ................................................................................................................................. 3189

1 ............................................................................................................................................................ 3205 156. . , , ........................ 3205

156.1. ........................................................................................................................ 3205 156.2. ........................................................................ 3205 156.3. ......................................................................................................... 3206 156.4. ............................................................................. 3206 156.5. ............................................................................ 3206 156.6. ........................................................................ 3207

157. , .......................................................................................................... 3208 157.1. ....................................................................................................................................... 3208 157.2. ..................................................................................................................................... 3212 157.3. ................................................................................................................................... 3217

158. ............................................................................................................................ 3220 159. ....................................................................... 3224 160. .......................................................................................................................................... 3227

1 .......................................................................................................... 3230 161. ..................................................................................................................... 3230

161.1. .............................................................................................. 3230 161.2. ............................................................................................ 3231

162. ................................................................... 3233 162.1. .......................................................................................................... 3233 162.2. ........................................................................................................ 3236

163. ...................................................................................................... 3237 164. - .......................................................... 3246 165. .................................................................................................................. 3259

165.1. ....................................................................... 3259 165.2. ............................................................................................... 3262

1 ............................................................................... 3264 166. .................................................................... 3264 167. ................................... 3267

1 ..................................................................................... 3268 168. ........................................................................ 3268

168.1. ................................................................................................................................... 3269 168.2. .......................................................................... 3274 168.3. ......................................................... 3275

169. ....................................................................... 3287 169.1. ( ) ........ 3287 169.2. .......................................................... 3289 169.3. ( , .) .................................................................................................................................. 3289

170. ............................. 3291 170.1. .......................................................................................................... 3291 170.2. MKAD ................................................................................................................... 3303

1 . .................... 3311 171. ........................................................................................ 3311 172. ............................................................................................................ 3312 173. .............................................................................................................. 3314

1 ........................................................ 3319 174. I ....................................................................................................... 3319 175. II ...................................................................................................... 3322 176. ................................................................... 3324

1....................................................................................................................................................... 3347 1 ......................................................................................................................................................... 3365

7

1. , . . , . . . 251,45 0,005, 1,316 0,0005 , . , n- , - 5. - 5, n- . 35,18 35,176. , , 5 : 152,.25 152,2, 0,435 0,44 .. . , , . , : 55,35

g.

, . , , , , . . 350 000 . 3 5. 0,0015 , 102,350 . , . , - . , - .

2. , . . , . : 1. , - . 28,17+3,2+0,025+12,3854=43,7804 43,8. 2. , - . = 34,215 0,102 0,48 = 1,6751664 1,68. 3. , . : 2,752 = 7,56. 4. , . : 6, 25 2,50= . 5. . 6. - .

3. , - . - , . () . , . , . () . , .

8

, , . , . . . .

4. . 4.1. Sistem international Si ( , 1965 .) (rad). , , . (). .

. 1.

. 360 , . (10) 60 (60) (1) 60 (60). 10 = 60; 1 = 60. 31501830. - . . 400 , (g). (1

g)

100 , (). (1) 100

, (). 1

g = 100

c; 1

c = 100

cc. , : 125

g 75

c 85

cc 125,7585

g.

(gon) (mgon) (mmgon) 1

gon = 100

mgon; 1 mgon = 100 mmgon.

(4.1) g

g360 400 = .

, :

(4.2) g 109 9

= = + ,

(4.3) g

g g910 10

= = . 1: = 62 45 32. , (4.2), - . (32 / 60 = 0,53), 45,53. (45,53 / 60 = 0,7588), 62,7588. (4.2) :

g g

62.758862.758862.7588 69.7320 .

9

= = + =

2: g = 85.1735g. , (4.3).

85.173585.1735 77.142110

= = . 0,1421 60 = 8,526 0,526 60 = 31,56.

O

R

. 4.1

9

= 77.1421 77 08 32. 2.

. - . (rad). , (. 4.1). :

(4.4) g

g360 2400 = =

)

R.

R = 1 (4.4) :

(4.5) ""

= = = )

(4.6) g c cc

g c cc = = =

) ,

:

(4.7) ;

;" "

= =

=

)))

(4.8)

g g

c c

cc cc

;

;

= = =

)))

, : 180 57, 2958 = = = 3437,75 = 206265

gg g200 63,6620 = =

c = 6366,20c cc = 636620cc. , , , , . 3: (. 4.2) CD , = 4. f,

, S = 20 m. : CDD =D D f

tg= CDf S . - , tg : =) f

S,

= )f S . f , , :

. 4.2

10

c c

c4 .20 m 1,2 cm

6366,20= = =f S .

4.2. 1. () (),

:

(4.9) 1 1:= =a MA M

.

, . . 250, 500, 1000, 2000, 5000, 10 000 .. -, -, , -, -. (4.9) : 1: =150,45 m 1:2500.

150,45 0,0602 60, 2 mm2500

= = = =AaM

.

2: 1:5000 = 52,5 mm . A = a M = 52,5 * 5000 = 262 500 mm = 262,5 m. 3: , , = 21,8 mm = 214,25 m .

214,25 9828 100000,0218

= = = AMa

= 10 000. . .. . ().

2. , . . , . , . , , . 1 5 cm. , , (, 2, 3 ..). - n 0,5 2 mm. n , , t.

(4.10) = Atn

.

- , , (. 4.3). 0,1 . , t. 4: 1:500 t = 0,5 m. , . 1 cm = 5,00 m.

(4.10) 5 100,5

= = =ant

.

1 cm (. 4.4), 10 . ( 6,4 m).

. 4.3

11

. 4.4

, - . 3. ()

. , n p q, n = p.q. . (3 5 mm) q . - q . - , . q , .., -1 - . . t , . 5: 1:5 000 t = 1 m. , = 2 cm, 100 m.

: 100 1001

= = =Ant

. q: n = 100 = 10.10 = 5.20.

- p = 10 q = 10. = 10 q=10 (. 4.5). L = 163,4 m.

. 4.5

5.

. ( ) .

, - . 25 mm. - , . , (. 5.1). , . , (. 5.1), , . (. 5.1)

. 5.1

12

, , .

. 5.1a . 5.1a

, . .

. 5.1

. . (. 5.2) , R. , , .

. 5.2 . 5.2a (- 2 mm) (. 5.2).

. . , , (. 5.2).

. 5.3

13

, (. 5.3). , , . , , N (. 5.4). N, (m) . 200

g (. 5.4).

, . , m , .

. 5.4 . 5.4

, , m. , , N, . . . - , , . R. - -. , , . , 2 mm. :

(5.1) " = MmnR

,

n , ; Mm . , = 12. -. : 3040 m (. 5.5).

. 5.5

, . l1 [mm]. , n l2. . 5.5 :

2 1 2 1tg( ) " = = l l l lnS S

,

" = lnS

.

14

- , , . .. . (. 5.6).

. 5.6 . 5.7

, . , . , (. 5.7). , . . , . , .

6. , . , . , , . , .

. 6.1

, , , (. 6.1). - , , , . ,

. 6.2

15

, - . , . , (. 6.2). , , . - (, , , .. .) (. 6.3). (. 6.4).

. 6.3 . 6.4 , - , (. 6.5). , , . , , ( 0,07 m). () .. 12 , .. 26 . - 20 m. () , . . ,

. , , 1,01,5 m, 0,20,3 m. , . , , , . , , . . , ( , , .) . , , . . .

. 6.5

16

. 6.6

. 34 cm 1,5 3 m. 0,5 m . , . , - , (. 6.6). , , . , . -, (. 6.7). .

, , . - , , (. 6.8). , (. 6.9). .

. 6.8 . 6.9

, - . , .

. 6.10

. 6.7

17

. 6.11 , (. 6.10). C D 23 m . , . . , , . . . , - . . . . . , , , , (. 6.11). . , . , - . , 30. 100 m 15 mm. . , , . , . (. 6.12). , . 1, , . D1 1. D1 1 , D1B1, .. . 2. . D . D, : , . (. 6.13).

. 6.12

18

. 6.13 , (. 6. 14).

. 6.14

19

II

7.

. . . .

. - . , , , .

, . .

, , . , - .

, . , . . , .. , .

, . B L H

, X Y

H, . - X Y, H.

8. . 6. , . . , .

. 8.1 .

. 6 4 . , 180 . 60 . 4 , . 1:1 000 000. . : -34; -35; L-34; L-35.

20

1:1 000 000 1:500 000, 1:200 000, 1:100 000.

: 1:1 000 000 1:500 000,

, , , . 1:200 000 1:1 000 000 36 ,

I XXXVI. 144 1:100 000

1 144 (. 8.3). 1:100 000 1:50 000, 1:25 000, 1:10 000 :

1:100 000 1:50 000 , , , .

. 8.2 . 8.3 1:50 000 4 , : , , ,

1:25 000. 1:10 000, 1 4 (. 8.4). 1:100 000 1:5 000, 1: 100 000 256 1:5 000, (1) (256) (. 8.5). [17] 1:2 000 1:10 000. 1:10 000 25 1:2 000 (. 8.6). - 1:2 000 .

1:100000, 1:50 000, 1:25 000

1:10 000 1:100000

1:5 000

1:100000

. 8.4 . 8.5 8.1

1:2 000

1:10 000

1: 500 000 K-34-

21

1: 200 000 K-34-XXXVI 1: 100 000 K-34-144 1: 50 000 K-34-144- 1: 25 000 K-34-- 1: 10 000 K-34---4 1: 5 000 K-34-144-(256)

. 8.6 1: 2 000 K-34--4-XXV 9.

: , , , . , . , . , h (. 9.1).

. 9.1

, - , (.. -), . .

. 9.2 10. 10.1.

, . . : . . . , - . , , - . (. 10.1).

. 10.1 . 10.2

22

, , . : , . , (. 10.2). (. 10.3): 0.2 m, , . 136.4 4. , . 4 6 137.5. , , . . .

: , , (. 10.4). = SAB. , . 134.4

.

(10.1) 1=

AB

A AB

Sah H

,

(10.2) 1 134.4 134.2. .0,25135.0 134.2

= = = A

AB AB ABAB

ha S S S

H.

. , . . . , . : , , . . -

, . 1/2 , 1/4 . . (. 10.5). 10.2. . - . - , . -

, - 10 .

. 10.3

. 10.4

. 10.5

23

- . X Y . . XA YA, .

(10.3) .

= + = +

K A

K A

X X XY Y Y

X Y . (. 10.6).

. 10.6

. . . 3 = S X 2 = S Y . : (10.4)

.

= =

K B

K B

X X XY Y Y

. , 1 2+S S 3 4+S S d X Y A B. . :

(10.5) 4

3 4

11 2

,

.

= + += + +

K A

K A

dX X SS SdY Y S

S S

X Y - . .

10.3. .

. , . . 10.7 . 307 m. (. 10.8) . .

24

. 10.7 . 10.8 , . .

S, , h. h = 1 m.

hCB = x . - H1, SCB. :

(10.6) =CB AB

x hS S

.= CBAB

Sx h

S.

.

(10.7) 1 .= + CBCAB

SH H h

S.

:

. . . 10.9 .

. 10.9 . . . i , (. 10.10) h

(10.8) arctg = ha

tg= = hia

.

, i (10.9) % 100 tg 100= =i i . : h = 2 m, = 6.7m. :

g

2tg 0.2985076.7

18.4675 .

= = = = =

hia

% 100 tg 29.85%= =i .

: :

. 10.10

25

h (. 10.10), .

:

(. 10.11). , . . 10.11 , = 330.

10.4.

, i% h

(10.10) .100%

= hai

.

,

(10.11) tg

= ha .

, , , . .

. 10.12 :

1. , - ; 2. , ; 3. , - . , . . , . . . . . , . D. ADB.

10.5. . ,

.

: , . . (. 10.13).

. 10.11

26

. 10.13

, , , , . . . - , , .

.

. . , . (. 10.14 ).

. 10.14 . 10.14

. , . , (. 10.15).

, - , ', , . ' . . .

' ' , . ' ', , .

. 10.15

10.6. , .

, .

27

, , , .

. 10.16 , . .

. 10.16

10.7. ,

h. , (. 10.17).

. 10.17

:

(10.12) ( )112 = +i i iV h S S . n :

(10.13) 1 2 31 ( 2 2 ... )2

= + + + + nV h S S S S . ,

h'.

(10.14) 13

= nV h S . :

(10.15) 1 2 31 1( 2 2 ... ) '2 3

= + + + + +n nV h S S S S h S . : D (. 10.21) .

. : HA = 104.3 m, HC = 99.7 m h = 1 m. 0 1 5, ,...,S S S 0 600=S m2; 1 =S 580 m2; 2 =S 420 m2; 3 =S 380 m2; 4 =S 320 m2; 5 =S 210 m2.

28

. 10.18 :

1 2 3 4 5 0 1 51 1 1( 2 2 2 ) '( ) ''2 2 3

= + + + + + + +V h S S S S S h S S h S . 1 1 1(600 2.580 2.420 2.380 2.320 210) .0,3(600 580) .0,3.210 23032 2 3

= + + + + + + + + =V m3.

29

III

11.

, , , . . : , , .

. . , , . . Y n 1 2 3, , , ,K nx x x x , : (11.1) ( )1 2 3, , , ,= K nY f x x x x . Y,

( 1,2, , )= Kix i n

(11.2) 22 2

2 2 21 2

1 2

= + + + KY n

n

f f fM m m mx x x

,

YM ; im ix ;

i

fx

ix

il . (11.2) , YM , im .

(. cm mm 15.6 cm, 9.3 cm, 6.7

). ,

. :

1. . 2. . :

; . 3. , .

, :

1. . 2. , , . 3. . 4.

YM . : a = 137.28 m, b = 185.72 m = 57.8500g, : ma = 5 cm, mb = 7 cm, m = 2

c.

. 1. ,

. 11.1

30

(11.3) sin2

= abS . 2. (11.2)

(11.4) 222 2

2 2 = + + s a bmS S Sm m m

a b.

3. :

(11.5) sin2

=s ba

; sin ;2

=s ab

cos2

=s ab

4. (11.5) (11.4).

(11.6) 22 2 2

2 2sin sin cos2 2 2

= + + s a bmb a abm m m .

, , cm c .

2 2 2 22 2185.0,789 173.0,789 185.137.0,615 20,05. 0,07

2 2 2 6366 = + + sm

33.62=sm = 5,8 m2. 12. ,

, , - , - . , - , - . ( ), , . , . :

1. - (-) . 2. .

, - , , - , . 1 2 3, , , ,K nl l l l n l, . - , x , lm - xM . - . . 1. il (12.1) 0 = i il l x , 0x - il (i = 1, 2, 3, n).

2. - x :

(12.2) [ ]

0= + lx xn

.

x . 3. . (12.3) = i ix l . :

31

(12.4) [ ] 0 = , (12.5) [ ] [ ] = l . (12.4) (12.5) [ ]l n. , : (12.6) [ ] = n , (12.7) [ ] [ ] [ ]{ } = l l . : (12.8)

[ ] [ ] = l l

n n,

, - , , . 4. :

(12.9) [ ]( 1)= m n .

5. - :

(12.10) [ ]( 1)= =

mMn nn

.

. :

(12.11) 2( 1)

= mmmn

,

(12.12) 2 ( 1)

= = m

Mm mm

n n n.

- , . , - , , ..

(12.13) 1= =mM

x N; = xN

m.

: 6 . . 12.1. - x m, M M . (12.1) (12.13) . 12.1.

12.1 l, m l, cm l . 1 2 2 4 5 6

135,27 135,24 135,28 135,22 135,25 135,26

5 2 6 0 3 4

-1,7 +1,3 -2,7 +3,3 +0,3 -0,7

2,89 1,69 7,29 10,89 0,09 0,49

-8,5 +2,6 -16,2

0 +0,9 -2,8

23,34 / 5 2,1= =m cm2,1/ 6 0,9= =M cm .

0,9 :135, 2= =M = 1:15000

0 =x 135,22 20 -0,2 23,34 -24,00

[ ] =ln

3,3 [ ]l [ ] [ ] [ ]l

=x 135,253

0,033 = 0, 2 = n [ ] 0,66 = l[ ]

ln

3,3

[ ] l

n 3,333

. 12.1 , (12.6) (12.7) .

32

: 1. - x = 135.253 m. 2. m = 2.1 cm. 3. - Mx, = 0.9 cm. 4. M, 1:15 000.

(, , ). .

il , il i- ( 1, 2, , )= Ki n , a id , (12.14) = i i id l l .

il , . ,

(12.15) 2

2 [ ]2

= dmn

.

-

(12.16) 21 [ ]

22= =m dM

n.

(12.15) (12.16) . ,

(12.17) [ ] = id

n.

, , (12.18) = i id d , (12.15) (12.16). , (12.19) [ ] 0,25 d d . : . . 12.2. - , .

12.2 l , m l , m d , cm x ,m 2d . 1 2 3 4 5 6 7 8 9

10

135,27 165,84 103,18 115,02 141,75 95,21

128,98 101,31 65,76 99,15

135,25 165,80 103.23 115,06 141,83 95,19

128,94 101,29 65,74 99,12

+2 +4 -5 -4 -8 +2 +4 +2 +2 +3

135,260 165,820 103,205 115,040 141,790 95,200

128,960 101,300 65,750 99,135

4 16 25 16 64 4

16 4 4 9

162 / 20 2,8= =m cm 2,8 / 2 2,0= =M cm

2 /165,82 1: 8 291= =M 2 / 65,75 1: 3 287= =M

2 [ ]d

36 d

162 2 d

2 < 0,25 36 [ ] 0, 25< d d

. 12.2 , . - . - (165,84 m) - (65,75 m) , .

33

13. .

12 . . - - - . , . p :

(13.1) 2=ii

kpm

,

k , im i- , i =1,2,3,, n. - . k , . k . - . . : cc1 25=m , cc2 30=m , cc3 20=m , cc4 50=m . , . k

22m , .

230 900= =k . (13.1) 1

900625

=p , 2 900900=p , 3900400

=p , 4 9002500=p =9002500

,

1 1, 44=p , 2 1,00=p , 3 2, 25=p , 4 0,36=p . . 1. . . (13.1). 2. . , . 3. . , - . - . (13.2). : - x , , i- im , - xM . , : 1. 0x 12 (13.2) 0 = i il l x . 2. (13.1). 3. ( ):

(13.3) 0[ ][ ]= + p lx xp

.

4. : (13.4) = i ix l . 5. , : (13.5) [ ] 0 =p , (13.6) [ ] [ ] = p p l .

34

(13.5) (13.6), [pl] [p]. , : (13.7) [ ] [ ] = p p , (13.8) [ ] [ ] [ ]{ } = p p l p l . : (13.9)

[ ] [ ][ ] [ ]

= p l p lp p

,

, 12. 6. :

(13.10) [ ]1

= pn

.

7. :

(13.11) [ ]( 1)

= = i iipm

p np.

8. - :

(13.12) [ ][ ]( 1)[ ]

= = pM

p np.

. . - x , , 5m , M . . 13.1.

13.1 g ccm p l p l p p p l 1 2 3 4 5

65,8920 65,8945 65,8975 65,8930 65,8950

30 17 40 35 25

1,36 4,24 0,76 1,00 1,96

0 25 55 10 30

0 106 41,8 10

58,8

23,2 -1,8

-31,8 13,2 -6,8

31,55 -7,63

-24,17 13,20

-13,33

731,96 13,73

768,61 174,24 90,64

0 -190,75

-1329,40 132,00

-399,90

0x = 65,8920g [ ]p [ ]p l [ ]p [ ]p [ ]p l

[ ][ ]p lp

= +23,2cc

9,32 216,6 -0,38 1779,18 -1788,0

x = 65,89432g 0, 04 = [ ] 0, 373 = p [ ] 8,8 = p l

24 1225= =k m , , .

. 13 .1 , [ ]p l [p] (13.7) (13.8),

cc

[ ] 23, 2[ ]

= p lp

,

cc

[ ] 23, 240[ ]

= p lp

,

cc0,04 = . : 1. :

cc1779, 2 214

= = . 2. :

cc521 151,96

= =m . 3. - :

35

cc21 79,23

= =M . - , : g cc65,89432 7x = .

, . . , , (13.12) 0,25

36

IV

14. , ,

X, Y, H. X Y, ..

AB (. 14.1) ABS , . ABS . ABS , BA . AB BA 200

g, .. AB = BA 200

g.

BA . BA < 200g "+"

, BA > 200g "".

. 14.1 . 14.2

: X Y

, ; SAB,

SAB S. 1. , ,

ABX ABY . . 14.2 ,

(14.1) cos

sin .

= = = =

AB AB AB B A

AB AB AB B A

X S X X

Y S Y Y

ABX ABY X Y

(14.2) cos

sin .

= + = + = + = +

B A AB A AB AB

B A AB A AB AB

X X X X S

Y Y Y Y S

: 1409.08=AX m, 2104.43=AY m, 103.04ABS m g129.3814 =AB . B (XB, YB).

:

cos 45.88 m

sin 92.26 m

= = = =

AB AB AB

AB AB AB

X S

Y S

1409.08 45.88 1363.20 m

2104.43 92.26 2196.69 m.

= + = == + = + =

B AB AB

B AB AB

X X X

Y Y Y

37

2. SAB S AB BA

SAB = S

(14.5) arctg =

ABAB

AB

YX

.

. 14.3

. 14.3 , AB 0g 400

g.

X Y: XAB YAB , AB 0

g

100g. XAB , YAB , 100

g

38

r, , , AB (. 14.4)

(14.7)

, 0 0,

200 , 0 0,

200 , 0 0,

400 , 0 0

= > > = < > = + < > = > >

AB AB AB

AB AB AB

AB AB AB

AB AB AB

r X Y

r X Y

r X Y

r X Y

(14.8) g200 = BA AB .

ABS :

(14.9) 2 2cos sin = = + = =

AB ABAB BA AB AB

AB AB

X YS S X Y

: , B, C, D X Y. , , ,AB BC CD DAS S S S , , , AB BC CD DA . . 14.1

X Y X12 Y12 r = arctg| || |

AB

AB

YX

12 S12

1 A 4023.48 2113.38 -2003.34 2887.88 61.3897 200-r 3514.71 2 B 2020.14 5001.26 138.6103 1 B 2020.14 5001.26 -488.69 -1886.08 83.8599 200+r 1948.36 2 C 1531.45 3115.18 283.8599 1 C 1531.45 3115.18 998.85 -1902.06 69.2158 400-r 2148.38 2 D 2530.30 1213.12 330.7842 1 D 2530.30 1213.12 1493.18 900.26 34.5404 r 1743.58 2 A 4023.48 2113.38 34.5404

39

V

15.

, .. . , , , - .

15.1. . , . . 15.1. (1) (2) .

, . . 15.2.

, (. 15.2), , (. 15.2). , , (200

g).

. 15.2 . 15.2

. 15.1

40

. . , , . . , . 1

. , , , (. 15.3). , , . 1 , . , . , . 2 (. 15.3). . ( ), , . , , (. 15.3). . . . , . , ( 1,52 m), , . . ,

, (. 15.4) . , , . , . . .

. 15.3

. 15.4

41

, . . , . . , . 24

.

15.3.

(. 15.5). ( X) . 1, 2, ,K Ki 1 , 2 , , K Ki , . X . , ,

iX iY . (. 15.6) - .

, . ( ) . 1, 2, ,K Ki (. 15.5), iX

iY , . , . iX 1 , 2 , , K Ki , . iY 1, 2, ,K Ki . , .

. 15.5

42

(23), , .

16. - () . - : -, - , , (), -.

16.1. , , 1.

. 16.1, . 16.2. : ( ) (1), () (2), (3) (6) 7. : Z , V (4), H (5),

. , ,

: , . - (. 16.2 16.3) : 1, 1.1, 1.2, - 1.3 ( - ) , 1.4 1.5 , . 16.4. . () 2 6. .

. 15.6

. 16.1

43

3, , - 3.1 3.2. ,

, . . - . . : I , II , . 200

g.

V (4) () 4.1 4.2 . . (5)

() 5.1 5.2 . . 7 6, . : 6.1 , 6.2, 6.3, 6.4 ( ), 6.5 , 6.6 6.7 (1 . 16.16), (8 . 16.16) (2 . 16.14). () 8, , 8.1 8.2 ( ), , . 9 (. 16.1), - , 9.1, , , , . . . , . . - , , . , 1015 - . , . , , : ( ), ( ) , (- ), , , , .

2. .

16 2

44

, . 16.3, () . : 1, 2 ( , ), 3 ( ), 4 ( ) 5 ( ), 6 ( , ) 1, 2 3 (. 16.4).

. 16.3

. 16.4

. 16.5. , , 1 1B A . ( ) , , , 1 1B A . , . , () , 2 2B A , , W .

. 16.5

45

. 16.6

W - . , , .. W . . Z . . 16.6 - . , , : hh, vv () dd 1 1d -d . (), .. . , , , , , . : 1. . (- ) , - W . . () : 2. , . 3. , 1 1A B , . ( ), , , . 4. , ( ) ( ) .

3. . . : ) , - 30

(10

II);

) 5

30 (1,5

II10

II),

: 10 30

(3II

10II

) 5 10

(1,5II

3II

); ) , - 5

(1,5

II).

. - : , ( ). , , , . , , ZEISS/Jena (), .

. .

46

h 080 (. 16.7.). , (1), , (2). (3), , (4) . (. 16.8) : (-) 100, (-) 50. (. 16.8) (5) (. 16.7), . . (Hz) (V) , . -

c10=a , . , , 12

.

. 16.8 : 208,23g 220,08

g .

. 16.8a . 16.8 , , . - heo 080 heo 120, . Theo 080 A : T05 (Wild/), Th51 (Opton/), KO-S (Kern/) .

. . Theo 030 (. 16.9). , , (1) (2). , , . (3). (6.3 . 16.1) , (4), . - g1=a . , (. 16.10). , : Hz V, , . n = 100 , 1 10 . , - c/ 1= =t a n . . (0,10,2) cc10 20= t . , , , ,

. 16.7

47

. . 16.10 : 372,08g

291,86g .

. 16.9 . 16.10 (5) , , (18). Theo 020 (. 16.11) - . (1), ( 2), 10. (3) , ( , 4).

. 16.11 . 16.12 . 16.13

Theo 020 (. 16.12), , . (1) (2) , (3) (4), , . (5) (6). Theo 020 (. 16.13). (1) , . : T16 (Wild/), Th41 Th42 (Opton/), DKM1 (Kern/), T5 T10 (), T60E (Sokkia/) . .

48

Theo 015 (. 16.14). (1) (2) . (3) . , , - , . , . (1) (. 16.15). , Hz V , ( ), . . , . . : , - , ( ). . . g1=a , 500=n , cc/ 20= =t a n . , 20

. .

16.14 373,766g.

. 16.14 . 16.15

(4) . : T1 1A(Wild/), K1A 1 (Kern/) . . . cc1 2= t . . . - . , , - , . , , . , . .

49

Theo 010 (. 16.16). -. (1) , (1.1) . . (2) (3) . (4) . (5) (6) , (. 16.17) . , , - c20=a . , n = 1000 cc/ 2= =t a n .

. 16.17a

. 16.17

, (7) , .. (. 16.17). ( 200

g).

: ( 291); ( c c7 10 70 = ); ( 6), 0, 2, : 291,7602

g.

, - (4) (2) (3). heo 010 A (. 16.18). -, . (1)

. 16.16

. 16.18

50

(2) Theo020A (. 16.12). - , . (. 16.19). - . . : , , . , . (4) (. 16.19) 126,1990

g.

, (5).

. 16.19a

. 16.19

heo 010 (. 16.20) (1) , . . : T2 (Wild/), Th2 (Opton/), DKM2 DKM2-A (Kern/), Te-B1 (/), T2 (), TM1A (Sokkia/) .

16.2.

- , , . , . , - . , , .. , . - : H , V , Z ,

. 16.20

51

L , L , .. () , hh , vv . , , , , , : , , 100

g .

( , ):

1. L V, ( L V) . , . : , , . 200

g. 1/2 , ,

. . . , () . . , 1/2 . , , .. L V. , . ( )f L V (16.1) ( ) .sin .tgf = , , , . , , = 0 (200)g = 0g. L V , . 2. hh V ( vv V ) , . , . : , (. 16.21). . , (. 16.21). , .

52

. 16.21 , . : 3 (. 16.4). , . . , , , , - . 3. Z H . , H Z , . 100

g

. ( )f c c :

(16.2) ( ) .seccos

cf c c= = ,

, . = 0g, ( ) =f c c . : ( ) , (. 16.22) O1 . , 200

g

( ) (. 16.22) O2. ( )f c c

, ( ) =f c c , 1 (2 200g) = 2c, 1 2

. : 1 = 115,3150

g, 1 = 1 = 115,3300

g,

O2 = 315,3450g, 2 = 2+ = 315,3300

g.

2c=1 ( 2 200g)= 3,00

c c = 1,5

c.

, . , 2 ( ).

53

. 16.22 : 2 - , , : : 1 2, (. 16.22). (1) (. 16.4), , . : 1 2 , ( ) ( ). . , . 4. V (.. ). , , . ( )f i i : (16.3) ( ) .tgf i i= . ( = 0g) , - , -. Z H . : , 1 2 . (16.4) ( ) 1 22 O O 200= gf i , , , .. Z H . , H V . : - , . , 1 2 , ..

(16.5) ( )g1 2

cp

O + O 200O =

2,

( )f i . 16.3.

54

1. . ,

, v . : , , , ( ). L 5 , , . (. 16.23): 5 1 = 1400, 2 = 2602 L = 2 1 = 120,2 . v = L / 5 = 120.2 / 5 = 24 . - , -, .

: , , , . - 16 40 . . , , , . , , . 1 3. (. 16.24): D , . 1 2 , 2 1O O= L . (16.6) 22arctg = L L

D D.

. 16.24

. , . : , , 5, 20, 50, 100, 200, 500, 1000 m, I II

I

II .

= I II (. . 3).

. 16.23

55

, . .

2. . (0 10) , , . , . : (. 20

g),

, . (. 100

) 0,1 - .

. . . (. 20

g),

. ( ) ( ). . (. 100

10,00

). 0,1

, . 34.

. 3.

(. 16.25) E C , e . O ( ) : (5060 m), , 2050g . I II ,

I O

II

= OI OII. . 2( ) = i ic , c ,

Y , (. 16.26). , . Y = 2c, X, i . .

. 16.25

56

. 16.26 4.

, , .. . : , , .. , . , 1Z .

1g 2Z .

, , , .

g2 1 1 = Z Z Z .

, 1A . , 2A . 1A . 2A . 2A 1A .

34 , 200g 1A 2A , .

(16.7) =

i ,

(16.7) arcsin(sin sin ) sin sin = = i Z A Z A , ( ) 2 1 = A A A .

17. , - .

- . 17.1. , , , 1. - (. 17.1). , , , . (1) , () (2), , (3),

. 17.1

57

( ) . (ON/OFF) . - (-), , . ( ) , . .

2. . . , () () , - , (. 17.2). () , , . , , . , . , .. , . , . ( ) , . . .

. 17.2

, - . - : , (. 17.3). , , , . , . ( ) , . - .

. 17.3

58

. 17.4 (. 17.4). , , , ( 1: 1,01). . , . . - . - , , 90.

. 17.5

(. 17.5). , , , , . . , , . , . , . , , , . , . , , , . - . - . 1

.

. , (. 17.6), () . . - , 256 . . - 1,6

g.

128 .

. 17.6

59

. ( ) 1000 128 000 31,25

. -

4096 , 1000 4 096 000 , 1. -, , - , : () , ( ). , , . - , . , .. . : ) ; ) ) - . - . .

3. - . . , () , , , , , . () , , , - , , , , . - , , - , . , 39. : ( ). . .

4. . , : - ( ), . ( - ) , , , , . . . - , (), . . -. . Kern /, Opton/ . . (. 17.7). ( , , , , .) () . , (. , .).

60

( , .).

. 17.7

(39) , -.

5. () , . , : , , , . , .. , . . : ( ) ( ). THEOMAT T2000 Wild/ (. 17.1). , , 0,1

.

, . . (. 17.7): 1. : ON ( OFF); : SET TIME t RUN ( t = 0 20 ., t = 1 1 .); : SET MODE 40 RUN 2 RUN ; n : SET FIX n RUN, n 1 5; 2. ON. DSP HzV 2 3 . : , , : Hz, V HzV. REP, , . STOP. : SET Hz0 RUN. 3. ( ). - : SET MODE 78 RUN RUN. REC . NR RUN NR RUN, REC. 4. . ERROR

61

: 11 12 , 5158 .. TEST 0, 1 BATT, 2 . , CE. : T1000, T1010, T1610, T1100, T1800, T105 T107 (Wild, Leica/), 2 (Kern/), Eth2 Eth50 (Zeiss/ ), DT2E, DT4E, DT500 DT600 (Sokkia/), DT101, DT 102, DT 103, DT 104 DT106 (Topcon/) . ( ) 39.

17.2. , -: 1. L V, . LI V; 2. hh V; 3. Z H 4. H V. - . . , , . . , , . , () . , . ( ) , , - : 1) , , - , , ( ) 2) ( ) , . , , , . , (. ), . . , - , , , . . (THEOMAT T 2000) . THEOMAT T2000 (. 17.1 17.7): ( ). , , . ( ) SET MODE 15 RUN, . , RUN, . 200

g,

( ), RUN . 3 . , 0. ,

62

1II, 100g, , . , , , STOP RUN. . . , - 100 . , . SET MODE 11 RUN. 1 Hz C, 2 3 . RUN 3 100,0000, . , 1 2 , 3 . - 45 , , , RUN CE . ( ). , . 1 , . 200

g 2 .

, : , . 3 1 2 . 3. , 200

g

3. , . SET 2 C II SET 4C II ( SOKKIA/) (. 17.8 17.8) , 2

20

.

. , . 15- () - . , , 60 - . . ( ) . .

. 17.8 . 17.8

.. , .. , . : YES, , , , . SHFT 0 SET, . PROG,

63

2 Correction (). Tilt offset ( 2) , Tilt angle . , , SHFT 0 SET, . 200

g, ,

SHFT 0 SET, , . CECA. , Tilt angle, X Y 100

g.

. - 100 m (). PROG. 2.Correction, 2.Collimation ( ). YES, . , . ( YES), . YES , NO . NO (Re-observe?). YES . , , , () . , -. . . SET5F (. 17.9 17.9) SOKKIA/, , 20

,

, , 4 , 3000 , . () : (THEO), (EDM), (SO) (CONF). . 4 , . .

. 17.9 . 17.9a () : , . , , . . , (CONF), 2.Tilt correction ( ).

64

: = 90,0000g 1X 1Y

. , , 200

g,

= 270,0000g, ,

2X 2Y . 1 1( ) / 2= +X X Y 2 2( ) / 2= +Y X Y . - - - 10

II,

EXIT . : 0 SET, 0,0000

g. SET 1X 1Y .

200g ( ), , 2X 2Y

, SET . , .. . - 400 120, EXIT. ENTER, . 3X 3Y , .

200g , 4X 4Y .

X Y 3 4 10II, EXIT , . . REC ELTA 13 C (ZEISS/) (. 17.10 17.10) , , , 4 , 40 , 24 , , -.

. 17.10 . 17.10a (ADJUST/PREPARE) 5 , . 1, . ENTER (Input and measurement), : Measure pos. 1: ENTER. ENT , . ENT : 1. ; 2. 3. 0 . MEN . 4,95

,

ERROR: LIMIT EXCEEDED MEN INPUT AND MEASUREMENT MENU. 2, SZ SK .

65

, ENT. 200

g,

ENT . SZ SK NZ NK . (+) , () . MEN SZ SK . SZ SK 2,55

5,15, ERROR: LIMIT EXCEEDED. MEN

ADJUST/ PREPARE. , 1.Levelling, , , SZ, SK , NZ NK . MEN . LEV ().

18. , , , . , , , (6). . , R , (. 18.1). , , ( ). -, 400

g.

( 18.1). : 1. , . , .

. 18.1

66

18.1

-

.

. 2c

= R-OR

cc

=

cc

I

OI

g c cc

II OII

g c cc

= OI+(OII 200)

2 g c cc

OR

g c cc

R

g c cc 1 2 3 4 5 6 7 8 9 10 11 24 28 0, 15 24 200, 14 82 42 0, 15 03 0 ,00 00 0, 00 00 0,0 -2,6 12.08.1999. 40 161, 20 42 361, 19 94 48 161, 20 18 161, 05 15 161 ,05 080 -7,0 -9,6 17 15 260, 01 98 160, 01 44 54 260, 01 71 259, 86 68 259,86 757 7,7 5,1 : , 16 330, 79 72 130, 79 34 38 330, 79 53 330, 64 50 330,64 597 9,7 7,1 (17 36) (15 54) (182) (16 45) (56 33) (56 434) +10,4 0.0 + 15 03 x 4 = 60 12 1= +2,6 [ ] = 411,18 (16 45)

24 28 66, 64 82 266, 64 48 34 66, 64 65 0, 00 00 0,0 1,4 40 227, 69 88 27, 69 38 50 227, 69 63 161, 04 98 10,0 11,4 cc411,18 /(3 2) 8,3m = = 15 326, 51 74 126, 51 26 48 326, 51 50 259, 86 85 9,3 -7,9 16 396, 29 50 196, 29 12 38 396, 29 31 330, 64 66 6,3 -4,9 cc cc8,3 / 3 4,8= =M (15 94) (14 24) (170) (15 09) (56 49) 5,6 0,0 + 64 65 4 = 58 60 2= -1.4 fmax (15 09)

24 28 133, 38 62 333, 38 12 50 133, 38 37 0, 00 00 56 33 0,0 1,2 40 294, 43 66 94, 43 30 36 294, 43 48 161, 05 11 56 49 -3,0 -1,8 No f cc 15 393, 25 32 193, 24 90 42 393, 25 11 259, 86 74 56 48 1,7 2,9 . 1 2 3 max 16 64, 03 20 264, 02 80 40 64, 03 00 330, 64 63 169 30 : 3 = -3,3 -2,1 28 00 00 00 0 (10 80) (09 12) (168) (09 96) (56 48) 56 433 -4.6 0.2 40 115 98 111 17 38 37 x 4 = 53 48 3= -1.2 15 68 85 74 17 09 96 16 50 66 63 16

67

, , . 2. , , ( ) . . 3. ( ). , , . , , : 4. . , . . 5. . , , .. , , , , . : 6. , () . , . 0,5 cm. - , , , . 7. , . - , , : , , 100

g .

, . , , , . , , : . . , - . , (, ) , . 0,2 2 mm. . , , , , , 100

g.

, ( ) . 8. , .. - . . : ; ; , ( , , - ); , .

68

, , . , , .

18.1. , , - . , , . (. 18.2) : ( - , , ). ( 18.1), , , ,

, . 3 . , 200

g

, , , , 4 . . , , 200

g.

, - , , .. , n . , . , = 200g/n. n = 3 ( 18.1) , = 6667g. , 0

g, 2.

: : , - 0

g,

, , . . , - , , - 0

g,

, . : , , , 0

g, - 66

g,

. : , , , - 133

g.

: 1. 5 ( )I II g2 O O 200= c . , , , .

. 18.2

69

. . , , - . , ( ). .: I IIO O 2 = c : 17 36 15 54 = 1 82 .. 2. 6 O , , : ( )I II g O O 200

2

+ = .

, .. 6 3 4. : 16 45 = (17 36 + 15 54 )/2 .. 3. 7

R ,

6 , 0,00 00

g. ,

R ,

, , .. . . , . : 7 4 ( ) , 6. : 56 33 + 415 03 = 16 45 .. 4. 8 R

R .

: 7 : (56 33 + 56 49 + 56 48)/ 3 = 56 434.

: 1. 9 , .. = R R. 2. 10 i = i , : = []/, (i = 1, 2, ..., ). [ ] = 0 . [ ].

(18.1) [ ]

( )( )1 1= m n k ,

R

(18.2) mMn

= . 18.2.

, - . (), .

70

. 18.3 : (. 18.3) . , . , - 0

g ( ,

).

, . ,

, . (

I ) (. 18.3). ,

. , . , . . (. 18.3). . (

II), , ,

. , . () .

=

III.

(. 18.3). - , 3, n ,

n

(18.3) ( ) gO O .400k

n

= ,

k = 1, 2, ... . , O O = . :

= 0, 76 24

g :

= 0, 76 24

g

= 7, 83 68 = 3, 12 13 (3) = = 7, 07 44 = = 2, 35 89 = (3)/3 = 2, 35 813 .

19. : 1. , .. , ; 2. .

19.1. ( , .) 12, (. 19.1). mm, , , .. 12. i ,

(19.1) sin

arcsin iii

eS = ,

i . 19.1

71

, iS () , . , ( 19.1) : 1. 2 , 3 eR . 2. 4 i , . . 3. 5 iS e ( ). 4. 6 7 sin i i . 5. i 3 , i ( 8) R 9 = + e RR R . 7, 8 9 .

19.1. 12

.

. .

eR (g c cc)

.

= eR R(g c cc)

S e

(m)

sin sin = eS

.

(g)

7 = R

(g)

= + ReR R (g c cc)

1 2 3 4 5 6 7 8 9

12e

7 0,0000 63,8468 646,320 0,001874 0,1193 0,0000 0,0000 14 73,1481 136,9952 781,570 0,001537 0,0978 -0,0215 73,1269 28 182,4658 246,3126 524,350 -0,001822 -0,1160 -0,2353 182,2305 10 311,5362 375,3830 758,430 -0.000715 -0,0455 -0,1648 311,3714

12() 336,1532 0,0000 1,437

(3036) (5376) 0,0556 -0,4216 (7288) +15325 = 7660 +0,11934 = +0,4772 +4216

(1504) 3036 0,0556 1504 19.2.

(. 19.2) : () , ,

. 19.2

72

(. ). (. ) , . -, , . = mm, . . 19.2, , 19.1, .

20. () . , (. 20.1). h . , , . , - , (. 20.2). z () . - 100

g, 100

g,

- 100g. 100

g: (20.1) g100 + =z .

. 20.1 . 20.2 , , , . , , . - , . - , . ( 810I). 100

g (300

g

). - , i . i.

20.1. 1. -

. . 30 m (. 20.3). , , , , ,

73

. 1z . (. 20.3), 2z . : (20.2) ( ) g1 22 400= + i z z .

. 20.3

, . . . . -

g g g g1 1 1

c2 2 2

99, 85 50 , 2 400 3 , 99, 87 00 ,

300, 11 50 , 1,5 , 300, 13 00

399, 97 00 400, 00 00 .

= = = = == = = == =

z i z z i

z i z z i

. , 1z 1z ( 2z 2z ). , . . . , 1z 1z ( 2z 2z ). (. 20.3). 2 (. 16.4).

2. , - , . - , . . , . - , . . THEOMAT T 2000 (. 17.1). : SET MODE 10 RUN. . 2 3 . RUN, . . , 2 3 . RUN, CE . SET 2 CII (SET 4CII) (. 17.8). V indexing, 2.Manual. ()

74

3 ZA Face 1. 30 . SHFT 0 SET. ZA Face 2. SHFT 0 SET, . REC ELTA 15 C (ZEISS/) (. 17.10). (ADJUST/PREPARE) 5 V INDEX/HZ COLLIMATION COMPENSATOR, . 1 . (. 17.2).

20.2. , . , . . ( 20.1). 20.1.

. . 4002 += III OOi( )I II

400O O

2

=

+Z

J m

S m

I OI = ZI

g c cc

II OII = ZII

g c cc cc g c cc 24

1,48 28

2,01 97,4616 302,5362 -22 97,4627 40

1,51 100,7694 299,2270 -36 100,7712 15

0,00 103,8964 296,1008 -28 103,8978 16

1,51 101,1852 298,8130 -18 101,1861 - (33). J ( ) iS ( , ). 2i , , .

I

II

:

(20.3) ( )I II

cp

O 400 O

2Z

+ = .

21. . , . (. 21.1). A, A

,

, , , , : N , M +X .

. 21.1

75

: , , I . , . , () () , . . , (, , ) . . , . , , (). . , .. , . , , .. , , , . . , . , , , , , , . , . (. 21.2) - - , , 0180 (0200

g), 1 (1

g).

, , .

. 21.2 . 21.3

(. XI) (. 21.3), , , 2040 ( ). , , , . , , .

76

. 21.4 . 21.5

- , . (. 21.4) (. 21.5). , (. 21.6). , , , (. 21.6) (. 21.6). , O . , i .

MAi

(21.1) M MA O O= i i .

. 21.6 , , , 0g . : (21.2) MA = A +i i : (21.3) M= A +i i + . , . , , . . 410. , .

77

VI

22.

, . . - 1/4000 (2.5 cm 100 m), - . 20, 30 50 m, , 10 cm . ( ), . (20C), (10 kg). - 12 mm. - . - , - . () (. 22.1, . 22.2).

. 22.2

. , :

, ;

, . . , , , , 11 . : 1. . 2. - (. 22.1), . 3. , , . (20 m). 4. , . , , , . 5. , , 10 kg, 45 . . 1 (. 22.1). 6. , 1 . , . 1 , . 7. . . - , , .

. 22.1

78

8. () , , ( ) . (22.1) D nl l= + , l, , l . 9. , . . . . . . . , : 1. 56 cm, . 2. - 1020 cm. 3. , . 4. , , . 5. . .

I

II

(I +

II)

. I II

No

No

.

12 15 136,45 136,39 136,42 4 6 16,45 6 16,39 10 89,36 89,33 89,345 5 4 9,36 6 9,33

1 2 121,98 121,96 121,97 4 6 1,98 6 1,96 8 56,67 56,68 56,675 4 2 16,67 2 16,68 18 139,75 139,67 139,71 5 6 19,75 6 19,71

, , , . . 22. 1.

22.1

1:500 1:1000 1:2000

.

100

m

.

100

m

.

100

m

4% 4% 8% 8%

1:4000

1:3000

1:2000

2,5cm

3,3cm

5,0cm

1:3000

1:2000

1:1500

3,3cm

5,0cm

6,5cm

1:2000

1:1500

1:1000

5,0cm

6,5cm

10cm

, . (11), , - .

23.

. , , , . () . : ; ; . .

79

23.1. , . : , . . 1. , , . . (. 23.1) . N, A B, M N AB . a, b, h D :

(23.1) 22+= + a bD a b hab

.

. 23.1 . 23.2 (. 23.2) A B . . 1M . 2M 1 3M M 2 4M M . m, b . a, b, c (23.2) = + +D a b c . 2. . AN. . B . x, y (. 23.3)

(23.3) 2 2= +D x y . - , , . . A . B x, 1y , 2y (. 23.4).

(23.4) ( )22 2 1= + D x y y .

. 23.3 . 23.4 , . . . , , , 2 - .

23.2.

80

. - . , . 1. . A B, (. 23.5). . C, A B. AC = a BC = b. (23.5) 2 cos= + D a b ab . 6. . A B, (. 23.6). . C , , a.

200 = ++ f . = 3 f

, :

(23.6) sinsin

= aD .

. 23.6 . 23.7 7. . . A B . , (. 23.7). . 1C 2C .

, , a b. : (23.7) sin

sin( )= +

aD ;

(23.8) sinsin( )

= + bD .

. , 11 .

24. . , , 24.1.

, (. 24.1, 24.1a).

. 24.1 . 24.1

. 23.5

81

() . b, S. :

(24.1) tg

= b bS .

, : ) ; ) . , . : 1. ( ); : 1.1.

: 1.1.1 ( ); 1.1.2 ( 002, , .). 1.2. , (BRT 006, .) 2. ( ). : ( ); ( ). - ( ), . , 6366

.

. (. 24.2), :

. 24.2 . 24.3

; 3 4 ; , (. 24.3). , 1L 2L 2 1= L L L . (1000, 2000, 3000), . : (24.2) = +S KL c , ctg= K , c . K - 100, 50 200. (24.2) : (24.3) =S KL . (. 24.3), 1 1400=L ;

2 1626=L , : 2 1( ) 100 (1,626 1,400) 100 0,226 22,60S KL K L L= = = = = m.

82

- . D z. : 2 2cos cos= = D S KL , 2 2sin sin= =D S z KL z . , . . . 1% , . . , , ( 3 5 m) ( 100 m) (. 24.4). , K c, : 1 1= +S KL c 2 2= +S KL c . : 1 4,62=S m 2 98,43=S m, L1= 10461000 = 0,046 m; L2= 19861000 = 0,986 m. : 4,62 = 0,046K + c; 93,81 = 0,940K; c = 4,62 0,046K; 98,43 = 0,986K+c; K = 99,80; c = 0,03 m. - 1%, , K = 100 c = 0. : , , , ., 1% . :

(24.4) 2 2 = + S

m mm SK L

.

, 1:100 300 m 1:400 100 m. - . , , . . , . . . 002. . 170 m 2 5 cm. . , - . . , BRT-006, . 60 180 m. 60 m . - . , . BRT-006 6 10 cm 100 m. . - . ( ) .

-2 1 m, . (. 24.5) ,

(24.6) ctg2 2

= bD ,

. 24.4

. 24. 5

83

b =2 m e ; . : . ; . ; ; :

(24.7) ctg2

=D . . .

25. -, . - . . , . ( ),

. A B (. 25.1), . A, . B, . , , 1t . , . A

2t . 2 1 = t t . . - , ,

(25.1) 2=S v ,

v ; , . :

(25.2) = Cvn

,

C = 299 792 458 m/s ; n , ( ). . . (25.1)

(25.3) 2 2 2

= + S vm m m

S v,

Sm , vm , m S, v . , (25.1) , . : , . - , ,

. 25.1

84

. - , . , , ( ), . - , . . ( ). , (25.4) = . :

(25.5) 2

= vS .

- ( 2 ) = f f , :

(25.6) 4=

vSf

.

f, v , : (25.7)

2 2 = S .

, 2 , . - (25.8) 02 = + N , (25.9) ( )

2= + S N N ,

0 / 2 = N , . N ,

. (25.9) . 25.2. 25.1. , . :

1. . 2. , ,

, , , . 3. , . 4. , , . (25.6), :

(25.10) 2 22

2 2 24

= + + f v

S vm mvm m S S

f f v.

. 1 . 4 : (25.11) ( )= +L kmm a bS , mm = +Lm a bppm , Lm S ; a , ; b , ppm .

. 25.2

85

a b . = +k k k . 25.1, , . . [48]. , . , , , : - 400 m - 1000 m; /2 ; . () , 0,4 m . , 1,3 m, . 24 m, . - , , 5 10 m. 1 m, 2 m, . 25.3. .

. 25.3

, . 5 10 , : (25.12) = i mk S S , 1, 2, ,= Ki n , S , mS . n - , :

(25.13) 1

( ) = n mS Sk n . k ik .. .

. k .

.

() 1550 km. - . 1/300 000. . () 2 5 km. . . . () - 0,3 3 km . .

86

- . (0,1 + 0,1 ppm). , , .

87

VII

26. . . 26.1.

, . .

, (. 26.1). . 26.1 , (26.1) = + B A ABH H h . ABh , B , , A. A B : = AB B Ah H H , (26.2) = BA A Bh H H , = AB BAh h . , :

; ; ; .

- , , , . , . 12 , . , , .

26.2. A B ,

. , . a , A b , B.

. 26.2 , ABh : (26.3) = ABh a b . . 26.3 - 3.5 m, A B 150 m. , - -

. 26.1

. 26.2

88

-, , , , . , A B . ( ) . . 26.3, A , . A ( ). AJ .

b B . : (26.4) = AB Ah J b . , , . 26.3. , . , . . , () . , , , .

, - . . :

1 km , - 0,5 mm. I II , - . .

1 km 0,5 mm 3 mm. III IV , - , .

1 km 3 mm 10 mm. , - . :

;

( ) .

4 m, 3 m 2 m, , . , , . . , .

. 26.4

. 26.3

89

. - 4- . , .

. . , . , , , , (. 26.5). 27. .

, . , (. 27.1). . - , , .. - , , .. . :

() ; .

H . , , . . , . , - - .

, .

. 27.1

. 27.2

. 26.5

90

, , . 27.2, , . 27.2. , . , , . 27.1, :

V, ; L; L; Z; (hh) (vv) .

: 1. V. . (. 27.3). 200

g

. , . (. 27.3) , , . . 2. (hh) V.

, , . . , , a, b, c d (. 27.4) , . . 3. L Z . , .

. 27.5

. 27.3

a

b c

d

A

B

C

D

. 27.4

91

, A B (. 27.5). 6070 m. , , . A, 1a . , . B, 1b . . 27.5 , ABh : (27.1) 1 1 = ABh a b , A B, . . 27.1 , . , , . ( 34 m) , . . B, , , 2b . . 2