Plane surv 2 level sec sur104 by Said Alhalawy

 ‫א‬‫א‬‫א‬

‫اﻟﻤﺆﺳﺴﺔ اﻟﻌﺎﻣﺔ ﻟﻠﺘﻌﻠﻴﻢ اﻟﻔﻨﻲ واﻟﺘﺪرﻳﺐ اﻟﻤﻬﻨﻲ‬ ‫א‬‫א‬‫א‬‫א‬

‫א‬ 2 104

  

 104

 ‫א‬

 2

 ‫א‬ 

 

 W،،‫א‬‫א‬،‫א‬



‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬،‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬ ‫א‬‫א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K ‫א‬‫א‬ 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬،‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،

‫א‬         ‫א‬   ،‫א‬ ‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬ ‫א‬‫א‬،‫ א‬  K‫א‬‫א‬،‫א‬ 

‫א‬ ?‫א‬?? 2?‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

،‫א‬،‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬ 

 K‫א‬‫א‬‫א‬‫א‬‫א‬

 

‫א‬‫א‬‫א‬‫א‬

  

 104

 ‫א‬

 2

 ‫א‬ 

 

 {‫א‬‫א‬‫א‬‫א‬ 

{‫א‬KKKKKKKKKKKKKK‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

‫א‬{‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬

 



 K{‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 ،،،‫א‬    



 ‫א‬‫א‬‫א‬

2

‫א‬

 ‫א‬‫א‬ ‫א‬

 104

 ‫א‬

 2

 ‫א‬

‫א‬W‫א‬‫א‬  ‫א‬‫א‬

 ‫א‬‫א‬‫א‬J   ( DATEM ) ‫א‬J   ( BENCH MARK ) ‫א‬J   ( BACK SIGHT ) ‫א‬‫א‬‫א‬J  (FORE SIGHT ) ‫א‬‫א‬‫א‬J  ( INTERME . SIGHT ) ‫א‬‫א‬‫א‬J  ( TURNING .POINT T .P ) ‫א‬J   ( Height of inst H. I ) ‫א‬‫א‬J   ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬  ‫א‬

 ‫א‬‫א‬  ‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬٪100‫א‬  3‫א‬‫א‬

 W‫א‬‫א‬

 ‫א‬‫א‬–1  ‫א‬–2 

-1-

 ‫א‬‫א‬ ‫א‬

 104

 ‫א‬

 2

 ‫א‬

  1-1 ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬

‫א‬‫א‬  ‫א‬‫א‬‫א‬ {

 

 ‫א‬ 2-1 ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬ –1‫א‬‫א‬‫א‬{

 K‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬–2  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬–3  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬–4  ‫א‬‫א‬‫א‬‫ א‬3-1  W‫א‬‫א‬‫א‬‫א‬  E‫א‬‫א‬‫א‬F–1  ‫א‬–2   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬{‫א‬‫א‬‫א‬‫א‬‫א‬{‫א‬

‫א‬{‫א‬‫א‬‫א‬

  ‫א‬‫א‬{‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬{‫א‬‫א‬ 

  ‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬{‫א‬

-2-

 ‫א‬‫א‬ ‫א‬

 104

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬‫א‬ 1-3-1  E1F‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬(1-1)  ‫א‬‫א‬  K‫א‬‫א‬–1  K‫א‬–2

 K‫א‬–3

-3-

 ‫א‬‫א‬ ‫א‬

 104

 ‫א‬

 2

 ‫א‬

 E‫א‬‫א‬F‫א‬‫א‬–1 {‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E2-1F‫א‬‫א‬ 



‫א‬‫א‬‫א‬E2-1F {W G

‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬

‫א‬{‫א‬W G ‫א‬‫א‬‫א‬‫א‬{‫א‬‫א‬

 K‫א‬‫א‬

‫א‬‫א‬W  ‫א‬‫א‬G ‫א‬‫א‬‫א‬‫א‬‫א‬{‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬{‫א‬‫א‬‫א‬

 K‫א‬

‫א‬‫א‬‫א‬‫א‬{  W G  K‫א‬‫א‬{‫א‬‫א‬‫א‬ -4-

 ‫א‬‫א‬ ‫א‬

 104

 ‫א‬

 2

 ‫א‬

 E‫א‬‫א‬F‫א‬–2 ‫א‬‫א‬‫א‬‫א‬{  { ‫א‬‫א‬‫א‬{  ‫א‬{  ‫א‬  KE3-1F‫א‬‫א‬‫א‬‫א‬‫א‬ 

  E3-1F

 

‫א‬‫א‬‫א‬{ ‫א‬‫א‬ ‫א‬‫א‬‫א‬  E4-1F‫א‬‫א‬‫א‬‫א‬ 

-5-

 ‫א‬‫א‬ ‫א‬



 104

 ‫א‬

 2

 ‫א‬



 EbFEaF‫א‬‫א‬E4-1F‫א‬ 

 ‫א‬J 3 ‫א‬‫א‬‫א‬{ ‫א‬‫א‬‫א‬  K‫א‬ 

 ‫א‬‫א‬–4  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬

 ‫א‬‫א‬2-3-1 ‫א‬ ‫א‬‫א‬‫א‬{‫א‬‫א‬

{{{‫א‬‫א‬‫א‬{‫א‬‫א‬

‫א‬{‫א‬‫א‬‫א‬

{‫א‬‫א‬{‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ -6-

 ‫א‬‫א‬ ‫א‬

 104

 ‫א‬

 2

 ‫א‬

‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬  E5 -1F‫א‬

  ‫א‬‫א‬E5-1F‫א‬

 

‫א‬ ‫א‬،‫א‬‫א‬‫א‬  K‫א‬‫א‬

 ‫ﺘﻌﺎﺭﻴﻑ‬4-1  W{‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬G  ‫א‬‫א‬‫א‬‫א‬{

 E‫א‬‫א‬F

 G  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

-7-

 ‫א‬‫א‬ ‫א‬

 104

 ‫א‬

 2

 ‫א‬

 ‫א‬G  E6-1F‫א‬‫א‬‫א‬ 



  ‫א‬‫א‬‫א‬E6-1F

 

 B.M‫א‬G K  ،‫א‬ 

،‫א‬‫א‬‫א‬،‫א‬  ‫א‬،‫א‬،‫א‬

‫א‬‫א‬ ،

 E7-1F‫א‬‫א‬K‫א‬‫א‬

-8-

 ‫א‬‫א‬ ‫א‬

 104

 ‫א‬

 2

 ‫א‬

  



 ‫א‬‫א‬‫א‬E7-1F‫א‬  EB.S‫א‬F‫א‬‫א‬‫א‬G  K‫א‬‫א‬‫א‬‫א‬  EF.S‫א‬F‫א‬‫א‬‫א‬G  K‫א‬‫א‬‫א‬‫א‬  EI.SF‫א‬‫א‬‫א‬G  ‫א‬‫א‬‫א‬‫א‬‫א‬

-9-

 ‫א‬‫א‬ ‫א‬

 104

 ‫א‬

 2

 ‫א‬

 E‫א‬‫א‬F‫א‬G  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  KE8-1F‫א‬



 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E8-1F  ‫א‬‫א‬G  K‫א‬،‫א‬‫א‬‫א‬



 ‫א‬ 5-1  ‫א‬‫א‬{‫א‬‫א‬

{‫א‬‫א‬ {‫א‬{B .M

‫א‬‫א‬‫א‬‫א‬{‫א‬‫א‬‫א‬‫א‬ {{ ‫א‬

{‫א‬{‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬{‫א‬{‫א‬  W‫א‬K‫א‬‫א‬

-10-

 ‫א‬‫א‬ ‫א‬

 104

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬{E‫א‬F‫א‬  K

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬{‫א‬‫א‬ {‫א‬‫א‬‫א‬‫א‬ {‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

-11-

 ‫א‬‫א‬ ‫א‬

 104

 ‫א‬

 2

 ‫א‬

 E‫א‬‫א‬F‫א‬ :‫א‬ 





 



 ‫א‬‫א‬‫א‬‫א‬

‫א‬



  



 ‫א‬‫א‬ 

 ‫א‬ ‫א‬‫א‬ ‫א‬ 

  ‫א‬ BM

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 

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 W‫א‬‫א‬  Z‫א‬–‫א‬‫א‬  Z–



-12-

 ‫א‬‫א‬ ‫א‬

 104

 ‫א‬

 2

 ‫א‬

 E‫א‬‫א‬F‫א‬  :‫א‬  

 ‫א‬  ‫א‬ (-)

‫א‬ (+)



   ‫א‬

 ‫א‬‫א‬‫א‬‫א‬  

 ‫א‬‫א‬

 ‫א‬

 

  ‫א‬ BM

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

 W‫א‬‫א‬  Z‫א‬–‫א‬‫א‬ Z–

 Z‫א‬–‫א‬ 

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 ‫א‬‫א‬ ‫א‬

 104

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬1-5-1 ‫א‬‫א‬{‫א‬‫א‬   ‫א‬

‫א‬{{‫א‬{‫א‬‫א‬

‫א‬ ‫א‬‫א‬{‫א‬‫א‬  K‫א‬‫א‬‫א‬

 KE9-1F‫א‬ 



 K‫א‬E9-1F   ‫א‬  W‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬–1

 K‫א‬‫א‬‫א‬{‫א‬–2  K‫א‬‫א‬{‫א‬‫א‬‫א‬–3

‫א‬‫א‬‫א‬{‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬–4  K‫א‬‫א‬‫א‬‫א‬

{E ‫א‬F‫א‬‫א‬‫א‬‫א‬ ‫א‬–5  K‫א‬‫א‬{‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬–6 -14-

 ‫א‬‫א‬ ‫א‬

 104

 ‫א‬

 2

 ‫א‬

‫א‬‫א‬‫א‬ {‫א‬‫א‬{‫א‬‫א‬ ‫א‬–7  K‫א‬

‫א‬‫א‬‫א‬{‫א‬ ‫א‬‫א‬‫א‬‫א‬ –8

 K‫א‬                     

-15-

 ‫א‬‫א‬ ‫א‬

 104

 ‫א‬

 2

 ‫א‬

 E1F 

 W‫א‬‫א‬‫א‬‫א‬E9-1F‫א‬

 ‫א‬‫א‬‫א‬{‫א‬‫א‬‫א‬EA,1,2,3,,4,5 ,B F

 W‫א‬‫א‬‫א‬‫א‬E3F  A = 3.2501 = 3.000 2 = 2.850 3 = 2.750,1.820 4 = 2.130 5 = 0.780 B = 0.680  EF‫א‬A , B   B = 550.810 A = 550.170  1 , 2 , 3 , 4, 5 , ‫א‬‫א‬  ‫א‬‫א‬{‫א‬‫א‬

 ‫א‬

‫א‬3‫א‬{‫א‬‫א‬{‫א‬‫א‬

 KB {A ‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬1 , 2, 4, 5 ,‫א‬

 E‫א‬‫א‬F‫א‬‫א‬‫א‬

 E‫א‬‫א‬F‫א‬‫א‬         

-16-

 ‫א‬‫א‬ ‫א‬

 104

 ‫א‬

 2

 ‫א‬

 E‫א‬‫א‬F‫א‬ :‫א‬



  



 ‫א‬‫א‬‫א‬‫א‬



 

  ‫א‬

 ‫א‬‫א‬

  550.170



 ‫א‬

‫א‬‫א‬

 ‫א‬  3.250

 ‫א‬



3.000



2.850



 3

2.750



  1.820



2.130



 4



0.780



 5



 B

 



0.680

 W‫א‬‫א‬  

=‫א‬–‫א‬‫א‬ =–

 

-17-

 ‫א‬‫א‬ ‫א‬

 104

 ‫א‬

 2

 ‫א‬

 E‫א‬‫א‬F‫א‬ :‫א‬



  



 ‫א‬‫א‬‫א‬‫א‬



 

  ‫א‬

 ‫א‬‫א‬

  550.170 553.420



 ‫א‬

‫א‬‫א‬

 ‫א‬  3.250

  ‫א‬



550.420



3.000



550.570



2.850



550.670 552.490 2.750



 3



550.360



2.130



 4



551.710



0.780



 5

  551.810



 B

  1.820

0.680

 W‫א‬‫א‬  1.640 = (0.680+2.750) – (1.820+3.250) = ‫א‬–‫א‬‫א‬  1.640 = 550.170- 551.810 = –  

     

-18-

 ‫א‬‫א‬ ‫א‬

 104

 ‫א‬

 2

 ‫א‬

 E‫א‬‫א‬F‫א‬ :‫א‬ 

  ‫א‬

‫ א‬ ‫א‬ (-)



550.170



550.420



(+)

 

   

 ‫א‬‫א‬‫א‬‫א‬ 



‫א‬

 ‫א‬‫א‬



‫א‬

 



‫א‬

3.250

 



3.000



 

2.850



 

  3



 

  4

0.780



 

  5



 



 

0.250



550.570

 

0.150



550.670

 

0.100 2.750



550.360

0.310

 



2.130



551.710

 

1.350



551.810

 

0.100 0.680

  1.820

B

 W‫א‬‫א‬  1.640Z‫א‬–‫א‬‫א‬ 1.640Z–

 1.640 Z‫א‬–‫א‬  

  

-19-

 ‫א‬‫א‬ ‫א‬

 104

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬‫א‬  ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  K  ‫א‬‫א‬  W‫א‬  K‫א‬‫א‬‫א‬‫א‬– 1  K‫א‬‫א‬‫א‬‫א‬– 2  K‫א‬‫א‬‫א‬‫א‬‫א‬– 3  K‫א‬‫א‬‫א‬‫א‬– 4  K‫א‬‫א‬‫א‬–5  K‫א‬‫א‬‫א‬‫א‬‫א‬– 6  ‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬– 1  K– 2  K‫א‬– 3

-20-

 ‫א‬‫א‬ ‫א‬

 104

 ‫א‬

 2

 ‫א‬

   W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬W1  ‫؟‬‫א‬‫א‬‫א‬‫א‬W2  K{‫א‬‫א‬‫א‬W3  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W4  W  W5  K‫א‬{‫א‬‫א‬{‫א‬{‫א‬{‫א‬{‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W6 

B M =2.330 1= 3.212 2= 3.415 3= 3.816 4 = 5.710

5= 3.400

Z‫א‬‫א‬‫א‬‫א‬ {‫א‬‫א‬  K‫א‬‫א‬‫א‬K‫א‬260.310

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W7  5 = 2.148 4 = 2.153 3 = 2.071 2= 2.068 B M = 1.115

1= 2.116 7 = 2.153

B M = 1.112 6 = 2.056

‫א‬‫א‬‫א‬{‫א‬‫א‬

 ‫א‬ 401.301=‫א‬

 ‫א‬(7, 6, 5, 4, 3, 2, 1)‫א‬‫א‬‫א‬‫א‬W8  W‫א‬4‫א‬‫א‬

 5 = 2.282 4 = 2.191 3 = 2.145 2= 2.183  B M = 1.508

1= 2.121B M = 1.511

7 = 2.291

6 = 2.315

2.305

 520.510‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬{E10J 1F ‫א‬{‫א‬  ‫א‬‫א‬‫א‬W9  W‫א‬‫א‬

-21-

 ‫א‬‫א‬ ‫א‬

 104

 ‫א‬

 2

 ‫א‬

1.612 , 1.652 , 1.443 , 1.171 , 3.820 , 1.730 , 1.650 , 2.350 ,1.930 , 1.740 2.052 ,2.351 , 0.751 , 1.821 , 0.562 , 1.162 , 2.051 , 2.441 ,   ‫א‬ ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   603.184 = ‫א‬‫א‬‫א‬‫א‬ 



 E10-1F

         

-22-

 ‫א‬‫א‬ ‫א‬

 104

 ‫א‬

 2

 ‫א‬

 K‫א‬‫א‬‫א‬WE‫א‬‫א‬F‫א‬‫א‬  W‫א‬



321W‫א‬ 

 KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKW‫א‬‫א‬  KKKKKKKKKKKKKKKKKKKKKKKW‫א‬

 K‫א‬

 K‫א‬٪80W‫א‬‫ א‬ KKKKKKKKKW‫א‬

 K‫א‬٪100W‫א‬‫א‬  ‫א‬



 ‫א‬



 ‫א‬‫א‬



 K‫א‬‫א‬



 ٪100‫א‬‫א‬



 ‫א‬

KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKW

KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK

 KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK  KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK  KKKKKKKKKKKKKKKKKKKKKKKKKKKKW‫א‬

     

-23-

 ‫א‬‫א‬ ‫א‬

 104

 ‫א‬

 2

 ‫א‬

 E‫א‬‫א‬F‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬ 

 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬E3F { ‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬{‫א‬

‫א‬ ‫א‬‫א‬‫א‬W  ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 E‫א‬‫א‬F‫א‬‫א‬   

   

 ‫א‬







 ‫א‬‫א‬‫א‬ K1



 ‫א‬‫א‬‫א‬ K2

  ‫א‬‫א‬‫א‬E‫א‬F‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬? ???‫א‬{  K‫א‬



-24-

 ‫א‬‫א‬‫א‬

2

‫א‬

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬W‫א‬‫א‬  ‫א‬‫א‬ (Differential Leveling F‫א‬‫א‬J ETrigonometric LevelingF‫א‬‫א‬J (Barometric . Leveling ) ‫א‬‫א‬J  ‫א‬‫א‬‫א‬J  ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬

 ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬

 

 ‫א‬‫א‬  ‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬٪100‫א‬ 

 9‫א‬‫א‬   W‫א‬‫א‬

 ‫א‬‫א‬– 1  ‫א‬– 2

-25-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬ 

1J 2

‫א‬‫א‬ {‫א‬ ‫א‬

 ‫א‬K‫א‬‫א‬  ‫א‬‫א‬-1

‫א‬{‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬{‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬-2 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬K‫א‬   ‫א‬‫א‬-3

 ‫א‬‫א‬‫א‬{‫א‬‫א‬ ‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬E‫א‬F

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K

‫א‬‫א‬‫א‬‫א‬‫א‬-4 ‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬{  ‫א‬‫א‬ 

-26-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬2–2 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬{‫א‬‫א‬

 K‫א‬

 ‫א‬‫א‬‫א‬‫א‬ 1-2-2 ‫א‬– 1

 E‫א‬F‫א‬‫א‬– 2

W‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬

 K‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬ •  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬E‫א‬F‫א‬‫א‬‫א‬ •  W‫א‬

‫א‬ ‫א‬   ،‫א‬‫א‬‫א‬‫א‬  ‫א‬E‫א‬F‫א‬‫א‬{‫א‬‫א‬

K ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 2-2-2  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬– 1

 K‫א‬

‫א‬E F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   – 2  KE‫א‬F‫א‬1.426‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬– 3  W‫א‬

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 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

‫א‬  ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬G  ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬G  K‫א‬

 W‫א‬‫ ﺍ‬3-2 ‫א‬ ‫א‬‫א‬ ‫א‬ ‫א‬‫א‬F‫א‬E‫א‬‫א‬F‫א‬

 KE‫א‬ 

  ‫א‬‫א‬4-2 {‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K   ‫א‬‫א‬5-2

E‫א‬‫א‬‫א‬F‫א‬

{‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   

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 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬‫א‬  ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  K  ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬J 1  K‫א‬‫א‬‫א‬‫א‬‫א‬J 2  K‫א‬‫א‬‫א‬‫א‬J 3  K‫א‬‫א‬‫א‬‫א‬‫א‬J 4  ‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬–1  K–2  K‫א‬–3   

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 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

    ‫א‬  W1  ‫א‬‫ א‬−‫א‬‫א‬− 

‫א‬‫א‬‫א‬− ‫א‬‫א‬−

 ‫א‬‫א‬‫א‬‫א‬‫א‬W2  K 

 ‫א‬‫א‬‫א‬‫א‬‫א‬W3 ‫א‬– 1

 E‫א‬F‫א‬‫א‬– 2

           

-30-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 WE‫א‬‫א‬F‫א‬‫א‬  K‫א‬‫א‬‫א‬  W‫א‬



321W‫א‬ 

 KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKW‫א‬‫א‬  KKKKKKKKKKKKKKKKKKKKKKKW‫א‬

 K‫א‬

 K‫א‬٪80W‫א‬‫ א‬ KKKKKKKKKW‫א‬

 K‫א‬٪100W‫א‬‫א‬  ‫א‬ 



 ‫א‬  ‫א‬‫א‬‫א‬



 ٪100‫א‬‫א‬



 ‫א‬

KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK  KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK

 KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK  KKKKKKKKKKKKKKKKKKKKKKKKKKKKW‫א‬

      

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 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 WE‫א‬‫א‬F‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬ 

 

‫א‬‫א‬ K‫א‬‫א‬‫א‬

E3F { ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬{‫א‬‫א‬‫א‬  ‫א‬‫א‬W‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬

 E‫א‬‫א‬F‫א‬‫א‬   

   

 ‫א‬







 ‫א‬‫א‬‫א‬



 ‫א‬‫א‬‫א‬

  ‫א‬‫א‬‫א‬E‫א‬F‫א‬‫א‬‫א‬

   

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 ‫א‬‫א‬‫א‬

2

‫א‬

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

‫א‬W‫א‬‫א‬   ‫א‬‫א‬‫א‬   ‫א‬‫א‬J  

 ‫א‬‫א‬‫א‬J   ‫א‬‫א‬  K‫א‬‫א‬‫א‬  ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬  K‫א‬

 ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬  K‫א‬‫א‬٪100‫א‬  3‫א‬‫א‬  W‫א‬‫א‬  ‫א‬– 1  K– 2

 K– 3  K– 4 



-33-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬ 

{ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

{  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬{ ‫א‬‫א‬‫א‬‫א‬{‫א‬  K‫א‬‫א‬‫א‬‫א‬ 

 E1F

 2.30 = ‫א‬‫א‬‫א‬A ‫א‬

  1: 50 ‫א‬‫א‬A 100 B ‫א‬

 ‫א‬

  2.00 = 100C

1 =‫א‬ 50

  0.30 = 2.00 - 2.30=B‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬{ B ∴

 0.30  

-34-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬‫א‬  ‫א‬‫א‬  K‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  K  ‫א‬‫א‬  KK‫א‬– 1  K{‫א‬‫א‬ – 2  ‫א‬{‫א‬‫א‬‫א‬‫א‬ – 3  K‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬{‫א‬‫א‬‫א‬{‫א‬ – 4  K‫א‬‫א‬‫א‬{‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬– 1  K – 2  K‫א‬ – 3   -35-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬

 ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬  K‫א‬‫א‬٪100‫א‬

 

 3‫א‬‫א‬   W‫א‬‫א‬  K– 1  K‫א‬‫א‬– 2 

 K– 3  K– 4  K– 5         -36-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫ א‬2-3 ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬ 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬{‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬

 KEF‫א‬‫א‬EF  ‫א‬‫א‬ 3-3  ‫א‬‫א‬J 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬-1

‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ {E1-3F



 ‫א‬‫א‬‫א‬‫א‬E1-3F

-37-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬‫א‬‫ א‬-2

‫א‬‫א‬‫א‬‫א‬‫א‬

{‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ {‫א‬‫א‬ ‫א‬‫א‬‫א‬{E2-3F‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬

 K ‫א‬‫א‬‫א‬‫א‬ 

  ‫א‬‫א‬‫א‬‫א‬E2-3F



‫א‬‫א‬‫א‬‫א‬-3

‫א‬‫א‬‫א‬‫ א‬‫א‬‫א‬‫א‬

‫א‬{‫א‬‫א‬‫א‬  KE3-3F  

-38-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬ 

  ‫א‬‫א‬‫א‬‫א‬E3-3F 



 ‫א‬-4

{‫א‬‫א‬

‫א‬‫א‬‫א‬ {E4-3F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬{‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬ 

-39-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 



 ‫א‬E4–3F



 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

{‫א‬‫א‬‫א‬‫א‬‫א‬{ ‫א‬

 K‫א‬‫א‬‫א‬‫א‬

-40-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 -1

 KE5-3F‫א‬‫א‬‫א‬ 



 E5-3F

 J 2

 KE6-3F ‫א‬‫א‬‫א‬‫א‬

E6-3F -41-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬ 4-2 EF‫א‬{E7- 3F‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬{‫א‬

 



 ‫א‬‫א‬‫א‬‫א‬‫א‬E7-3F



 K‫א‬‫א‬‫א‬ :

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬: 1  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ : 2  K‫א‬‫א‬ : 

 K‫א‬ : 

‫א‬EF‫א‬E1F‫א‬‫א‬‫א‬‫א‬ :   KEF‫א‬E2F‫א‬‫א‬‫א‬  =2 = 1W -42-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 K‫א‬21‫א‬‫א‬‫א‬‫א‬ : 

 K2{1‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬: 

 K‫א‬‫א‬‫א‬‫א‬‫א‬ : 

 K‫א‬‫א‬‫א‬‫א‬‫א‬ :   KEF‫א‬EF‫א‬‫א‬ :

 KEF‫א‬EF‫א‬‫א‬ : 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ :   KE21F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 –180Z‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ : ´ 

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬5–3 ‫א‬‫א‬‫א‬‫א‬‫א‬  KEF‫א‬‫א‬‫א‬EF‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬

{‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬EF‫א‬‫א‬ ‫א‬{‫א‬E 7 – 3F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬J   °90Z2‫א‬‫א‬Z1‫א‬‫א‬{‫א‬

  ‫ هـ‬Z2‫א‬‫א‬Z1‫א‬‫א‬2{1‫א‬– 2

 21‫א‬‫א‬Z ‫ و‬Z2Z1‫א‬‫א‬ 2

E7–3F‫א‬‫א‬‫א‬‫א‬‫א‬

 W

-43-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 EF‫א‬ 1-5-3

 ‫א‬‫א‬‫א‬‫א‬‫א‬Z°360‫א‬‫א‬‫א‬‫א‬‫א‬ 

‫ل‬ ‫هـ‬

= ‫ﻧﻖ‬

 E1-3FKKKKKKKKKKKK ‫× هـ‬

× ‫×ط‬2  360

‫ط× ﻧﻖ‬ 180



∴

  = 

∴



‫اﻟﻤﻘﺎﺑﻞ‬ ‫اﻟﻤﺠﺎور‬

 EF‫א‬2–5–3  =‫א‬‫א‬E7–3F‫א‬1‫א‬ 

‫ف‬ ‫ﻧﻖ‬



 =  ‫ هـ‬∴ 2



 E2–3FKKKKKKKKKKKKKKKK ‫ هـ‬ = ∴ 2

  EF‫א‬‫א‬2-5-3

 E7–3F‫א‬‫א‬‫א‬1‫א‬ 

‫اﻟﻤﻘﺎﺑﻞ‬ ‫اﻟﻮﺗﺮ‬



=‫א‬‫א‬ ‫و‬



‫ﻧﻖ‬

‫هـ‬



  = ‫ هـ‬ 2



K =  ‫ و‬∴ 2



 E3-3FKKKKKKKKKK ‫ هـ‬K2=∴ 2

 -44-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 EF‫א‬‫א‬‫א‬4–5-3  E7–3F‫א‬ 

 E1FKKKKKKKKKKKKKKKKKKKKKKKK– =

 

 ‫א‬‫א‬‫א‬1‫א‬ ‫ ت‬.‫م‬ ‫ﻧﻖ‬

 



 = ‫ هـ‬ 2



‫هـ‬ 2

K = ∴

 E1F‫א‬ 

  ‫ هـ‬J  =∴  KE4–3FKKKKKKKKKKKKKKKKE

‫هـ‬ 2

J 1F =∴ 

 EF‫א‬‫א‬5-5-3  E7–3F‫א‬  E1FKKKKKKKKKKKKKKKKKKKKK–=  1‫א‬‫א‬‫א‬1‫א‬ 

‫ﻧﻖ‬ ‫هـ‬ 2

=  

 E1F‫א‬  =J  ‫ﻧﻖ هـ‬ 2 -45-

‫ﺟﺘﺎ‬

=

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 KE5-3FKKKKKKKKKKKKKKKKKKE1J  ‫ هـ‬F = ∴ 2



 E1F

‫א‬200‫א‬

 K‫א‬‫א‬‫א‬‫א‬K °36 ´48 ‫א‬‫א‬‫א‬‫א‬EF‫א‬ 

 ‫א‬



 °18

´24  =  ‫ هـ‬°36 ´48 = 200 =  2

  

‫ط× ﻧﻖ × هـ‬ 180

 EF‫א‬-1

 = ∴ E1-3FKKKKKKKKKKKKKKKKK‫א‬   128.46  =  ‫ × ط‬200 × 36

180

48′

 = ∴  

 EF‫א‬–2

  ‫ هـ‬ =∴ E2J 3FKKKKKKKKKKKKKKKK‫א‬ 2

 ‫א‬66.53 =°18

-46-

 

´24 C200 =∴ 

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 EF‫א‬‫א‬–3 

  ‫א‬126.26 =°18

 E3–3FKKKKKKKKKKKKKKKKKKK‫א‬

‫هـ‬ 2

KC2=∴ 

´24 C 200 C 2 = 

 EF‫א‬‫א‬‫א‬-4  E4–3FKKKKKKKKKKKKKKKKKKK‫א‬

 E ‫ هـ‬–1F= 2

 10.22 =E°18

´24–1F200=∴ 

 EF‫א‬‫א‬-5

 E5 –3FKKKKKKKKKKKKKKKKKKK‫א‬ 1

 E1J  ‫هـ‬

 10.78 =E1J 

F=∴ 

1 °18

‫ﺣﺘﺎ‬

´24

‫ﺣﺘﺎ‬

FC200=∴          

-47-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

  ‫א‬‫א‬‫ א‬6-3 ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

 ‫א‬‫א‬1-6-3 ‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬

FEF‫א‬EF‫א‬EF‫א‬‫א‬

 WE8-3

  ‫א‬‫א‬‫א‬‫א‬E8–3F  E‫א‬F

‫د‬ 360

= 

‫اﻟﻘﻮس‬ ‫اﻟﺪاﺋﺮة‬ ‫د‬ 360

.‫ﻃﻮل‬ .‫ﻣﺤﻴﻂ‬

=

Q

‫س‬ ‫ × ط × ﻧﻖ‬2

 360C = CCC2 ∴ -48-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

180 × ‫ س‬o  E6-3FKKKKKKKKKKKKKKKKKK = ‫ط×د‬

 ‫א‬‫א‬2-6-3 ‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬

FEF‫א‬EF‫א‬EF‫א‬‫א‬

 E 9-3

   ‫א‬‫א‬‫א‬‫א‬E9-3F‫א‬  E9-3F‫א‬ ‫ر‬



‫ﻧﻖ‬

= ‫ ر‬ 2

‫ر‬ 2



-49-

‫ر‬ 2

= 

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 E2F  W‫א‬‫א‬°3 ‫א‬  K‫א‬20 ‫א‬‫א‬–  K‫א‬ 20 ‫א‬‫א‬–  W‫א‬  ‫א‬ 20  = ‫א‬20 = °3 =   E6-3F‫א‬‫א‬-‫ﺃ‬ 180 × ‫ س‬o  =  ‫ط×د‬

 ‫א‬381.97 = 

180 × 20 =  3o × ‫ط‬

 E7– 3F‫א‬‫א‬–‫ﺏ‬ ‫ر‬ 2



 ‫א‬ 382.02 = 

‫ر‬ 2

= 

20 2 o 3 2

=     

-50-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬   W‫א‬‫א‬‫א‬ 7-3 ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬{‫א‬

 K‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬

 EF‫א‬1-7-3

 W‫א‬EF

 K‫א‬‫א‬‫א‬‫א‬J 

 K‫א‬‫א‬‫א‬‫א‬J 

 K‫א‬‫א‬‫א‬‫א‬J  

 ‫א‬‫א‬‫א‬2-7-3

‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬، ‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬

،‫א‬‫א‬،‫א‬‫א‬‫א‬ ،‫א‬‫א‬20‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬ 

 EF‫א‬‫א‬‫א‬EF‫א‬3-7-3

،‫א‬‫א‬‫א‬‫א‬ -‫أ‬ ‫א‬E10-3F‫א‬‫א‬‫א‬‫א‬

-51-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬EF‫א‬2،1‫א‬ 

‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬

4،3{‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

E43،21F‫א‬‫א‬EF‫א‬

4،3‫א‬2،1‫א‬‫א‬  K‫א‬EF‫א‬‫א‬



(‫ ﺗﻮﻗﻴﻊ ﻧﻘﻄﺔ اﻟﺘﻘﺎﻃﻊ )ط( وﻗﻴﺎس زاوﻳﺔ اﻹﻧﺤﺮاف )هـ‬E10-3F‫א‬

‫א‬EF‫א‬‫א‬‫א‬EF‫א‬-‫ب‬ ‫א‬‫א‬EF‫א‬‫א‬‫א‬EF‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬E10-3FE2F‫א‬‫א‬ ‫א‬E2F‫א‬‫א‬‫א‬‫א‬

 KE´J °180F‫א‬EF‫א‬‫א‬‫א‬´‫א‬

 W‫א‬،EF‫א‬‫א‬ - ‫ﺟـ‬

 E،F‫א‬‫א‬EF‫א‬‫א‬J 1 -52-

 KE 11-3F

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 KEFJ 2  E،F

‫س ص‬

1 2 = ‫هَـ‬

‫ط ص‬

 

‫س ص‬ 1J ‫ ط ص‬2

W‫א‬J 3

= ‫هَـ‬

 2

∴  

 KE´J °180FEF‫א‬‫א‬‫א‬J 4 

  



 ‫א‬‫א‬EF‫א‬‫א‬‫א‬E11 –3F



 E‫א‬‫א‬F‫א‬ 4-7-3 -3F‫א‬EF‫א‬EF‫א‬‫א‬‫א‬EF‫א‬

1‫א‬‫א‬‫א‬‫א‬‫א‬EF‫א‬‫א‬‫א‬E2

‫א‬E12-3F2‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬EF‫א‬2{1  K‫א‬‫א‬

 K ( ‫ ) هـ‬12‫א‬‫א‬1‫א‬‫א‬ 2

-53-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 



  ‫א‬‫א‬E12-3F



 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬5-7-3 EF‫א‬‫א‬‫א‬EF‫א‬‫א‬ 1‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،2{1‫א‬

‫א‬‫א‬‫א‬،2‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

10{‫א‬20‫א‬ K10050‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬

-54-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 W‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬‫א‬J 1  

 K‫א‬‫א‬‫א‬J 

K‫א‬‫א‬‫א‬‫א‬J 

 KE‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬J 2

 KE‫א‬F‫א‬‫א‬‫א‬‫א‬J 3 

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 8-3  ‫א‬EF‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬EF‫א‬‫א‬‫א‬‫א‬

 

 

 E1F‫א‬‫א‬‫א‬E14-3FEF‫א‬‫א‬E13-3F



 EF‫א‬‫א‬ -1

 E13-3F‫א‬

 CC2  2  =  =‫سق‬ ‫هـ‬

 

‫و‬ 2

‫هـ‬ 2

-55-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 = E ‫ ﺟﺘﺎ‬J 1F= 2

 E8-3FKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ‫ هـ‬=EF‫א‬‫א‬ 2

 E9-3FKKKKKKKKKKKKKKKKKKKKKKKKKKKKKE ‫ هـ‬J 1F={ 2

 {1‫א‬‫א‬‫א‬‫א‬ -2

 E1F‫א‬E´1F‫א‬‫א‬E14 – 3F

‫א‬E1F‫א‬‫א‬E1F‫א‬E1F ‫א‬‫א‬‫א‬‫א‬‫א‬E1F‫א‬E´1F

 W‫א‬

 11–1= 1 

1J 2–= 1  2 2  E10 – 3F 1– –=   

≥

‫א‬E1F‫א‬‫א‬EF‫א‬ ‫א‬‫א‬E´1FE1FEF‫א‬

‫א‬E1F‫א‬E10-3F‫א‬E1F ‫א‬E1FKKKKKKK4{3{2KKKKKKK4{3{2‫א‬

4{3{2‫א‬KKKKKKKKKK{4{3{2‫א‬‫א‬EF  K‫א‬‫א‬‫א‬‫א‬‫א‬KKKKK{ 

‫א‬E2F‫א‬‫א‬‫א‬‫א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬

 K‫א‬ 

 E3F -56-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

‫א‬230 Z‫א‬

 ‫א‬‫א‬‫א‬‫א‬°40 ´48 Z‫א‬‫א‬‫א‬

 20 Z‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

´24 = ‫ هـ‬°40 ´48 =230 = 

 ‫א‬20=°20

 

 EF‫א‬ -1   ‫א‬ 85.54 =° 20

  80.17 = ° 20

‫هـ‬ 2

‫هـ‬

=

´24 C230 =∴  

 EF‫א‬‫א‬-2 C=E8 –3FKKKKKKKKKKKK‫א‬

´24 C 230 = 

 E ‫ هـ‬–1F=∴ E9 –3FKKKKKKKKKKKKKKKKKK‫א‬ 2

  14.43 =E° 20

´24–1F230=



 {1‫א‬‫א‬‫א‬‫א‬–3  E10–3 F‫א‬

 E10–3F2–2–=   ‫א‬0.87 =2 20J  ‫א‬3.50 = 2 40J

2

 



230– 230 = 1

‫א‬ 20

= 1

230–230= 2 

‫א‬ 40

= 2

‫א‬ 60

= 3

‫א‬ 80

= 4

60J

2

‫א‬14.36= 2 80J

2

 ‫א‬7.96 =

2

2



230 –230= 3 230– 230 = 4

-57-





  

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬80.17 ‫א‬‫א‬‫א‬‫א‬100= 

 E‫א‬‫א‬F‫א‬ 

 ‫א‬-4

 W‫א‬‫א‬ EF 0.78  3.50  7.96 14.36 14.43

EF ‫א‬  20  1  40  2  60  3  80  4 80.17    E4F

،46°‫א‬‫א‬‫א‬‫א‬115‫א‬

 K10‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬

 ‫א‬10=23°= 46 = ‫ هـ‬46°=‫א‬115= 2



 EF‫א‬-1

 E 2 – 3FKKKKKKKKKKK‫א‬ ‫ هـ‬ =  2

 ‫א‬48.81 = 23°C115 = ∴   EF‫א‬‫א‬ -2

 E8-3FKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK ‫ هـ‬= 2

 ‫א‬44.93 = 23°C115 =  

 E9J 3FKKKKKKKKKKKKKKKKKKKKKKKKKKKKKE ‫ هـ‬J 1F= 2

 

 ‫א‬9.14 = E23°J 1F115= 

-58-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ،1‫א‬‫א‬‫א‬‫א‬ -3  ‫א‬0.435 = ‫א‬

1.75 =

 E10 – 3F‫א‬

2

10J 2115– 115 = 1

2

20J 2115–115=

‫א‬ 3.98 = 2 30J  ‫א‬7.18=

40J

2

2

115–115= 3

2

115– 115 = 4

‫א‬ 10

‫א‬ 20 ‫א‬ 30 ‫א‬ 40

= 1

 

= 2

 

= 3



 

= 4

 

 44.93 ‫א‬‫א‬‫א‬‫א‬50= 5 

 ‫א‬‫א‬ -4 

EF 0.435  1.75  3.98  7.18  9.14

EF ‫א‬ 10  1  20  2  30  3  40  4 44.93   

 ‫א‬‫א‬‫א‬‫א‬‫ א‬1-8-3 ‫א‬‫א‬EF‫א‬‫א‬‫א‬  K‫א‬

 W‫א‬E10-3F‫א‬ 

2–2 –= 

   2E–F = E2–2F∴ 

 2J 2H2= 2J 2∴  -59-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬  2

–2= 2∴ 

 E–2F = 2∴ 



EFE2FEFEF

 W‫א‬‫א‬‫א‬‫א‬E2F‫א‬  2=2

 E11-3FKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK

‫س‬

‫ × ﻧﻖ‬2



=  E5F ‫ﻤﺜﺎل‬

K°42‫א‬‫א‬‫א‬‫א‬270‫א‬

‫א‬‫א‬‫א‬20‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬

 ‫א‬

 ‫א‬20=21°= ‫ هـ‬42°=‫א‬270= 2

 EF‫א‬-1

  ‫ هـ‬K=E2-3F‫א‬ 2

 ‫א‬103.64Z21°C 270=



 EF‫א‬‫א‬-2

E8-3FKKKKKKKKK‫א‬ ‫ هـ‬= 2

 ‫א‬96.76= 21°270=

 E9-3FKKKKKKKKKKK‫א‬E ‫ هـ‬J 1F= 2





 ‫א‬ 17.93 = E21°J 1 F270=  {1‫א‬‫א‬‫א‬‫א‬-3

 



‫س‬

=E11-3F‫א‬

‫ × ﻧﻖ‬2 2 ‫א‬0.74= (20) =1‫א‬20=1 270 × 2

 ‫א‬2.96= (40) =2‫א‬40=2 2

270 × 2

-60-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

2  ‫א‬6.67= (60) =3‫א‬60=3



270 × 2 2 ‫א‬11.85= (80) =4‫א‬80=4 270 × 2



 ‫א‬‫א‬-4  

 

EF E  0.74  2.96  6.67 11.85 17.93

  

   

   

-61-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 EF‫א‬‫א‬‫א‬



 ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  KE2FJ 1

 KJ 2

 K‫א‬‫א‬J 3  K‫א‬J 4

 ‫א‬‫א‬ ‫א‬‫א‬-1  K‫א‬{‫א‬

،EF‫א‬-2

‫א‬EF‫א‬

 KEF

 K‫א‬ EF‫א‬‫א‬‫א‬-3  KEF‫א‬-4

 E2-3F‫א‬EF‫א‬E2{1F‫א‬-5

 ‫א‬‫א‬‫א‬EF‫א‬‫א‬‫א‬E ‫ هـ‬=F 2

 E2F‫א‬‫א‬‫א‬‫א‬E1F

 KE2{1F  KE2{1F‫א‬

 E8- 3F‫א‬E{FEF‫א‬-6

EF‫א‬E ‫ هـ‬J 1F =F،E ‫ هـ‬=FE9–3F{ 2

‫א‬EFE´F‫א‬E1F‫א‬E1F‫א‬

 KE15-3FEF

-62-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

EF‫א‬‫א‬E1F‫א‬-7

E10-3F‫א‬EF‫א‬EF‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬E

‫ ﻧﻖ‬−‫ ن‬2 ‫س‬

J =F=

‫א‬EFE1F‫א‬‫א‬‫א‬‫א‬‫א‬-8

3{2´{1´F‫א‬E1F‫א‬E1F‫א‬E4{3{2{1F‫א‬

 E´4{ 



 ‫א‬‫א‬‫א‬‫א‬‫א‬E15-3F

F‫א‬KE15-3FKE´4{´3{2´{1´F‫א‬

 ‫א‬KE´4{´3{2´{1´F‫א‬E4{3{2{1

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E4{3{2{1F  KEF‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

E2F‫א‬E´8{´7{´6{´5F‫א‬E2F‫א‬‫א‬‫א‬

‫א‬EFEF‫א‬E2F‫א‬‫א‬E4{3{2{1F

{1F‫א‬‫א‬K‫א‬‫א‬E4{3{2{1F

 E8{7{6{5F‫א‬E4{3{2

-63-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

{3{2{1{1F‫א‬‫א‬‫א‬E5{6{7{8{{4{3{2{1F‫א‬

 K‫א‬‫א‬‫א‬‫א‬E2{5{6{7{8{{4

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 9-3  K‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬

 EF‫א‬‫א‬E2{1F‫א‬‫א‬ ‫א‬

 E{FEF‫א‬‫א‬E{F‫א‬‫א‬‫א‬  E16-3F 



 ‫א‬‫א‬‫א‬‫א‬E16-3F

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 

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

‫א‬EF‫א‬E1F‫א‬‫א‬‫א‬EFEF‫א‬ E{F‫א‬‫א‬EF‫א‬‫א‬

 W‫א‬‫א‬‫א‬E1F‫א‬‫א‬‫א‬‫א‬

 

1‫א‬E16-3F‫א‬



 2

E–FH2E ‫ و‬F=2 2

 E1FKKKKKKKKKKKKKK 2 E 1

⎛‫ ⎞و‬2 ⎜ ⎟ – F= ⎝2⎠

–∴ 

 1´1‫א‬

 2E´1FH 12= 2

 E2FKKKKKKKKKKKKKK2 E1HFH12=2∴   J =

 2 E1HJ FH12=2∴ 

 

 E3FKKKKKKKKKKKKKK2E1HJ FZ 2 E12J 2F 1

 WE3F‫א‬E1F‫א‬EJ F  1H E 1

  2 E 1

 E11 – 3FKKKKKKKKKKKKK

E

⎛‫⎞و‬ ⎜ ⎟J ⎝2⎠

2F

1 2 ⎛ ‫ ⎞ و‬2 ⎜ ⎟ J FZ 2 E1 J ⎝2⎠

2F

2FJ  2 E12J 2FZ1 1

- E2J 2F

= ‫صن‬ 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

EF‫א‬EF‫א‬EF‫א‬‫א‬E1F

‫א‬EF‫א‬‫א‬E2FE1F‫א‬‫א‬‫א‬EF‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E11-3F 

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 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 E6F

‫א‬EF‫א‬140‫א‬

‫א‬‫א‬‫א‬‫א‬{°84‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬20‫א‬

 

 W‫א‬

 ‫א‬20= °42=  ‫ هـ‬

°84= 

‫א‬140 =   

 EF‫א‬ -1  ‫ هـ‬ = ∴ 

 E2-3FKKKKKKKKKKKKKKKK‫א‬

 ‫א‬126.06 = °42 C140 =

 EF‫א‬‫א‬-2

 E3–3FKKKKKKKKKKKK‫א‬ ‫ هـ‬KC2=  2

 ‫א‬187.36 = °42‫ א‬C 140C2=

 ‫א‬93.68= 187.36 = ‫ و‬ 2



 EF‫א‬‫א‬-3  0.0=

 E ‫ هـ‬–1F=∴  2

 ‫א‬35.96 = E° 42 J 1F140=∴ 

 {1‫א‬‫א‬‫א‬‫א‬-4

 E11 – 3FKKKKKKKKKK‫א‬  ‫א‬34.52= 293.68 J 2140  ‫א‬

30.12 =   104.04

20 -

140  =1  20

-  2 20–2 140= 2  ‫א‬ 40

‫א‬22.45=104.04J   2 20–2 140 = 3 ‫א‬ 60 -66-





= 1





= 2



= 3

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

‫א‬10.85= 104.04 -   2 20– 2 140 = 4

‫א‬ 80



 

= 4



‫א‬EFE ‫ و‬F100Z5 2

 ‫א‬93.68 ‫א‬E ‫ و‬F‫א‬‫א‬ 2



 ‫א‬‫א‬-5 

EF EF ‫א‬ 35.96 34.52 30.12 22.45 10.85

   

   1 2  3  4

0.0 20 40 60 80

 E7F

‫א‬EF‫א‬100‫א‬

 K10‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ °64‫א‬‫א‬‫א‬

 ‫א‬

 10= °32=  ‫ هـ‬

°64= 

‫א‬100 =   

 EF‫א‬-1

 ‫א‬62.49 = °32 C100=  ‫ هـ‬ =∴ E2-3FKKKKKKKKKKKKKKKK‫א‬ 2



‫هـ‬ 2

EF‫א‬‫א‬-2 KC2= E3–3FKKKKKKKKKKKK‫א‬

 ‫א‬105.98 = °32C 100C2=

 ‫א‬ 52.99= 105.98 = ‫ و‬ 2

-67-



 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 EF‫א‬‫א‬ -3  0.0=

 E ‫ هـ‬–1F= 2

 ‫א‬15.195 = E° 32 J 1F100=∴  

 {1‫א‬‫א‬‫א‬‫א‬-4  E11-3F‫א‬

  2 E 1

⎛‫⎞و‬ ⎜ ⎟J ⎝2⎠

2FJ  2 E2J 2F= 1

 ‫א‬14.69 = ( 2 52.99 J 2100FJ

E 210J 2100F =1 ‫א‬ 10

 ‫א‬13.17 = 84.81J  2 E 220J 2100F= 1

 ‫א‬10.58= 84.81J  ‫א‬6.84=84.81  ‫א‬1.79=84.81J

 1 2  1 2  1 2

2

E 230J 2100F= 3

E 240J 2100F= 4

E 250J 2100F = 5

= 1



‫א‬ 20

= 2

‫א‬ 30

= 3

‫א‬ 40

= 4

‫א‬ 50

= 4







 ‫א‬‫א‬

 

EF EF ‫א‬ 15.195   0.0 14.69  10  1 13.17  20 2 10.58  30  3 6.84  40  4 1.79 50 5



-68-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 EF‫א‬‫א‬‫א‬  ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K

 ‫א‬‫א‬‫א‬‫א‬  KE2F -1

 K -2

 K‫א‬‫א‬-3  K‫א‬ -4

 ‫א‬‫א‬

 ‫א‬‫א‬-1  K‫א‬

 EF‫א‬-2

 ‫א‬EF‫א‬

 KEF

 KEF‫א‬‫א‬‫א‬ -3

 KEF‫א‬-4

 E2J 3F‫א‬EF‫א‬E2{1F‫א‬-5

 ‫א‬‫א‬‫א‬EF‫א‬‫א‬‫א‬E ‫ هـ‬=F 2

 E2F‫א‬‫א‬‫א‬‫א‬1

 ‫א‬KE2{1F  KE2{1F‫א‬

 ‫א‬EF‫א‬‫א‬EF‫א‬‫א‬-6

 ‫א‬‫א‬E ‫ و‬F‫א‬‫א‬E ‫ هـ‬2= FE3-3F 2

EF‫א‬‫א‬‫א‬EF‫א‬‫א‬E ‫ و‬F 2

EFEF‫א‬E{F‫א‬‫א‬‫א‬EF

 ‫א‬‫א‬EF‫א‬E1F‫א‬ -69-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 E17–3F

F{E=FEF‫א‬EF‫א‬ -7

‫א‬EFE21F‫א‬‫א‬E ‫ هـ‬J 1F= 2

 EF‫א‬EF‫א‬

 E17–3F 



 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E17–3F  ‫א‬‫א‬‫א‬EF‫א‬‫ ﻴﺘﻡ א‬-8  ‫א‬E ‫ و‬F‫א‬‫א‬ 2

 WE11-3F‫א‬EF‫א‬EF 

(

‫و‬ 2

 ) - 2 ‫ﻧﻖ‬

‫ن‬

‫ س‬- 2 ‫ﻧﻖ‬

= ‫صن‬

 

 K‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬-9

 ‫א‬‫א‬EF‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 2{1‫א‬EF‫א‬EF‫א‬ -70-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

‫א‬{‫א‬‫א‬  ‫א‬‫א‬EF‫א‬EF‫א‬ ‫א‬EFE1F‫א‬‫א‬‫א‬

‫א‬E´4{´3{2´{1´F‫א‬EF‫א‬  EF‫א‬

E´4{´3{2´{1´F‫א‬EF‫א‬‫א‬E4{3{2{1F  E 17-3 F

2{1F‫א‬E´4{´3{2´{1´F‫א‬E4{3{2{1F‫א‬

‫א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬E4{3{ ‫א‬‫א‬‫א‬E2F‫א‬EF‫א‬{ {‫א‬‫א‬E8{7{6{5F‫א‬‫א‬‫א‬

{{1{2{2{4{1F‫א‬‫א‬‫א‬E8{7{6{5{4{3{2{1F‫א‬

 E17-3 F‫א‬‫א‬‫א‬‫א‬E2{8{7{6{5 

 ‫א‬‫א‬‫א‬‫א‬‫א‬ 10-3  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  {‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬{

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬{‫א‬‫א‬‫א‬  K‫א‬

 E18-3F‫א‬‫א‬‫א‬ 

-71-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬E18-3F  E1F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W 1  E1F‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W´  ‫א‬E3–2F‫א‬E2-1F‫א‬E2‫א‬F‫א‬‫א‬E1F  K‫א‬{20{10E4-3F  E2 F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W2  E4J 2F‫א‬{E18-3FE4F‫א‬‫א‬  ‫א‬‫א‬E1F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬= 1 -72-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E11F‫א‬‫א‬E11F‫א‬  K‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬= ´  KE413F‫א‬‫א‬E312F‫א‬‫א‬E211F‫א‬‫א‬E1F‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬=  2  E214F‫א‬‫א‬E1F‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬1-10-3  E21F‫א‬E19–3F  E12J 3FKKKKKKKKKKKKK

‫و‬′ = ‫ ﻧﻖ‬2

´

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬KE1F‫א‬‫א‬

 K‫א‬ 

-73-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E19–3F  E´F‫א‬‫א‬‫א‬EF‫א‬E2-1F‫א‬  W‫א‬ ( 2-1 ) ‫ﻃﻮل اﻟﻘﻮس‬ ‫ـــــــــــــــــــــــــــــــ‬ ‫ﻧﻖ‬

 ( 2-1 ) ‫ﻃﻮل اﻟﻘﻮس‬ ‫ـــــــــــــــــــــــــــــــ‬ ‫ﻧﻖ‬2

-74-

 =E‫א‬‫א‬F´2   

 =´

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

E2-1F‫א‬‫א‬‫א‬E ‫ ﻧﻖ‬F≥E´F‫א‬‫א‬ 20

 ‫א‬‫א‬‫א‬E´F‫א‬E2-1F‫א‬ ( 2-1 ) ‫ﻃﻮل اﻟﻘﻮس‬ ‫ـــــــــــــــــــــــــــــــ‬ ‫ﻧﻖ‬2



   = E‫א‬‫א‬F´2  

 360 × ´‫و‬ ‫ـــــــــــــــــــــــــــــــ‬ ‫و‬′ ×90 ‫ ط‬2 × ‫ﻧﻖ‬2  = EF´

‫ﻧﻖ× ط‬



 ´‫ × و‬90  E13–3FKKKKKKKKKKK =EF´ ‫ــــــــــــــ‬ ‫ـــ‬ 

‫א‬E2{1F‫א‬‫א‬E13J 3F‫א‬  E 2{ 1F‫א‬‫א‬E1F‫א‬‫א‬‫א‬‫א‬              -75-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 E8F

‫א‬‫א‬ 200‫א‬

‫א‬‫א‬K‫א‬2256.59 EF‫א‬°30‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 ‫א‬10= °15=  ‫ هـ‬

°30= 

‫א‬200 = 

 ‫א‬‫א‬-‫أ‬

 ‫א‬53.59 = °15 C200=  ‫ هـ‬ =∴  

‫ط× ﻧﻖ × هـ‬ 180

  104.72

 = ∴ EF‫א‬ 30 × 200 × ‫ط‬ 180

=  ‫× هـ‬

‫ط× ﻧﻖ‬ 180

 = ∴ 

 ‫א‬{2{1-‫ب‬

 EF‫א‬–EF‫א‬=1E1F  ‫א‬2203.00 = 53.59 - 2256.59=

 EF‫א‬+E1F=2E2F

 ‫א‬2307.72 =104.72 + 2203.00 =

 ‫א‬2010E´F‫א‬‫א‬‫א‬‫א‬G  ‫ ﻧﻖ‬≥´ 20

 10= 200  ‫ﻧﻖ‬ 20

= 

 10= 

 E´F‫א‬= E1F‫א‬‫א‬‫א‬E3F  ‫א‬2210= ‫א‬E2203F

2‫א‬=‫א‬‫א‬‫א‬E4

 ‫א‬2300.00= E‫א‬2307.72F

 W21‫א‬‫א‬E5F 

-76-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

2280 , 2270 , 2260 , 2250 , 2240 , 2230 , 2220 , 2210 , 2203.00 F  E2307.72 , 2300 , 2290 ,

1–‫א‬‫א‬‫א‬=



 ‫א‬‫א‬‫א‬- ‫ﺟـ‬

E1F‫א‬‫א‬‫א‬E1F

 ‫א‬7.00= 2203.00J 2210.00= 

 E  ‫ ﻧﻖ‬≥F10=E´F‫א‬‫א‬‫א‬E2F 20

 ‫א‬‫א‬‫א‬–E2 F= E2F‫א‬‫א‬‫א‬E3F  ‫א‬7.72= 2300.00 - 2307.72=

 ‫א‬‫א‬J ‫א‬‫א‬ ‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬ ´‫و‬

= EF‫א‬‫א‬‫א‬E4F

 2210J 2300

 9 = ‫ = ـــــــــــــــــــــــــــــــــــــــــــــــــــ‬EF‫א‬‫א‬‫א‬E5F 10  1HEF‫א‬= ‫א‬‫א‬E6F  10= 1+9=

 ‫א‬‫א‬‫א‬‫א‬-‫د‬

 ‫א‬‫א‬‫א‬‫א‬E13–3F‫א‬ 

1‫و‬′ ×90 7×90 = =EF1 ‫ﻧﻖ × ط‬ ‫ × ط‬200  ‫و‬′ ×90 10×90 °1 ´25 ¨57 = = =EF´ ‫ﻧﻖ× ط‬ ‫ × ط‬200  7.72×90 ‫ و‬′ ×90 °1´06 ¨21=  =   =EF 2 ‫ × ط‬200 ‫ﻧﻖ× ط‬ 

 °1 ´00 ¨10 =

-77-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

  °15=  = 

‫هـ‬ 2

 ‫א‬‫א‬- ‫هـ‬ E2HCH1F

°1 ´00 ¨10 = E2HCH1F 9C °1 ´25 ¨57  °1´06

H

¨21H

  °15 ´ 00 ¨ 04 = 

  ‫א‬‫א‬{‫א‬‫א‬4¨

 ‫א‬-‫و‬ 







‫א‬‫א‬‫א‬

 ‫א‬





E1F‫א‬

 ‫א‬‫א‬‫א‬ ‫ א‬ ‫ א‬‫א‬  ‫א‬  E‫א‬ °1 ´00 ¨10 °1 ´00 ¨10  7.00 2210  1

2FZZ

°2 ´26 ¨07

 °1 ´25 ¨57

2220

E3FZZ

°3 ´52 ¨04

 °1 ´25 ¨57

2230

E4FZZ

°5 ´18 ¨01

 °1 ´25 ¨57

2240

E5FZZ

°6 ´43 ¨58

 °1 ´25 ¨57

2250

°08 ´09 ¨55  °1 ´25 ¨57

2260

°09 ´35 ¨52  °1 ´25 ¨57

2270

°11 ´01 ¨49  °1 ´25 ¨57

2280

°12 ´27 ¨46  °1 ´25 ¨57

2290

°13 ´53 ¨43  °1 ´25 ¨57

2300

7.72

2307.72

2

‫א‬‫א‬‫א‬F‫א‬

 E

E6FZZ E7FZZ E8FZZ E9FZZ E10FZZ 2‫א‬

°15 ´00 ¨04

°1´06 -78-

¨21

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬EF‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬ 

 E9F

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

956.67 EF‫א‬°24‫א‬‫א‬‫א‬‫א‬ 205‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 °12=  ‫ هـ‬

°24= 

205 = 

 956.67 = EF

 W‫א‬‫א‬-‫أ‬

 43.57 = °12 C205=  ‫ هـ‬ =EF‫א‬E1F 2



‫ط× ﻧﻖ × هـ‬ 180

 = EF‫א‬E2F 

  85.87

24o ×205 × ‫ط‬ 180

=  ‫× هـ‬

‫ط× ﻧﻖ‬ 180

= ∴ 

 ‫א‬{2{1-‫ب‬

 EF‫א‬–EF‫א‬=1E1F   913.10 = 43.57 - 956.67=

 EF‫א‬+E1F=2E2F

 998.97=85.87 + 913.10 =  10.25 = 

205 = ‫ﻧﻖ‬ 20 20



 E ‫ ﻧﻖ‬≥´F10=E´FG 20

 E´F‫א‬= E1F‫א‬‫א‬‫א‬E3F  920.00= E913.10F1

2‫א‬=‫א‬‫א‬‫א‬E4F

-79-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 990.00= E998.97F

 W21‫א‬‫א‬E5F

 E 998.97 , 990 , 980 , 970 ,960 ,950 ,940, 930, 920, 913.10 F 1–‫א‬‫א‬‫א‬=

 ‫א‬‫א‬‫א‬ - ‫ﺟـ‬

E1F‫א‬‫א‬‫א‬E1F

 ‫א‬6.90= 913.10J 920.00= 

 E  ‫ ﻧﻖ‬≥F10=E´F‫א‬‫א‬‫א‬E2F 2

 ‫א‬‫א‬‫א‬–E2 F= E2F‫א‬‫א‬‫א‬E3 F  8.97= 990.00 - 998.97=

 ‫א‬‫א‬J ‫א‬‫א‬ ‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬ ´‫و‬

‫ أوﺗﺎر‬7 =

= EF‫א‬‫א‬‫א‬E4F

920J 990 ‫ــــــــــــــــــــــــــــــــ‬= 10



8 = 7 + 1 =1 HEF‫א‬= ‫א‬‫א‬E5F 

 ‫א‬‫א‬‫א‬‫א‬-‫د‬

1‫× و‬90 6.90×90  °00´57 ¨51= = =E1F‫א‬‫א‬‫א‬‫א‬‫א‬E1F ‫ﻧﻖ × ط‬ ‫ × ط‬205  ´‫× و‬90 10×90  °01´23¨51= = =E´F‫א‬‫א‬‫א‬‫א‬‫א‬E2F ‫ﻧﻖ × ط‬ ‫ × ط‬205  

-80-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

8.97×90 2‫× و‬90  °01´15¨13 = =  =E2F‫א‬‫א‬‫א‬‫א‬‫א‬E3F ‫ × ط‬205 ‫ﻧﻖ × ط‬   ‫هـ‬

  °12 = 24 =  = 2



 ‫א‬‫ א‬- ‫هـ‬

E2HCH1F

°00 ´57 ¨51 = E2HCH1F 7C °01

´23

 °01´15

¨51

H

¨13H

   °12 ´ 00 ¨ 01 =   K‫א‬‫א‬{‫א‬‫א‬¨1

 ‫א‬ -‫و‬ 



‫א‬‫א‬‫א‬

 ‫א‬



 ‫א‬‫א‬‫א‬‫ א‬ ‫א‬‫א‬‫א‬ ‫ א‬ ‫א‬  ‫א‬  ‫א‬

E1F‫ א‬°00´57 ¨51 2FZZ °02 ´21 ¨42

°00´57 ¨51 °01´23¨51

E3FZZ

°03 ´45 ¨33

E4FZZ

‫א‬

920

 1

930

°01´23¨51

940

°05 ´09 ¨24

°01´23¨51

950

E5FZZ

°06 ´33 ¨15

°01´23¨51

960

E6FZZ

°07 ´57 ¨06

°01´23¨51

970

E7FZZ

°09 ´20 ¨57

°01´23¨51

980

E8FZZ

°10 ´44 ¨48

°01´23¨51

990

2‫א‬

°12 ´00 ¨01

°01´15¨13

8.97

998.97

2

 E

-81-

 6.90



 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬



 W

‫א‬‫א‬EF‫א‬‫א‬‫א‬EF‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬{EF ‫א‬‫א‬‫א‬E2{´F‫א‬KE´F‫א‬  W‫א‬‫א‬KE2{´F

 

 E10F

‫א‬‫א‬‫א‬°24‫א‬‫א‬‫א‬ 400‫א‬

 K

 ‫א‬

 °12=  ‫ هـ‬

°24= 

400 =  

 W‫א‬‫א‬-‫أ‬

 85.02 = °12 C400=  ‫ هـ‬ =EF‫א‬E1F 2



‫ط× ﻧﻖ × هـ‬ 180

 = EF‫א‬E2F 

  167.55 

24o ×400 × ‫ط‬ 180

=  ‫× هـ‬

‫ط× ﻧﻖ‬ 180

= ∴ 

 ‫א‬‫א‬‫א‬-‫ب‬  20 = 

400 = ‫ﻧﻖ‬ 20 20

 

E1F

  ‫ ﻧﻖ‬≥´Q  20

  20 = ´∴  

‫ل‬ ‫א‬‫א‬=E´F‫א‬‫א‬E2F ‫و‬′ -82-



 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 8.377=  167.55  =  ‫ ل‬Q ‫و‬′

 8= E´F‫א‬‫א‬∴

 ´CE´F‫א‬‫א‬=‫א‬‫א‬‫א‬E3F  160 = 20 C8=

 ‫א‬‫א‬‫א‬–= E2F‫א‬‫א‬‫א‬E4F

 7.55= 160 - 167.55=  ‫א‬‫א‬‫א‬‫א‬ - ‫ﺟـ‬  W‫א‬‫א‬‫א‬‫א‬E13–3F‫א‬ 

´‫× و‬o 90 20×90  °01´25 ¨57= = =E´F‫א‬‫א‬E´F‫א‬‫א‬E1F ‫ﻧﻖ × ط‬ ‫ × ط‬400  ´‫× و‬o 90 7.55×90  °00´32¨27= = = ( 2 )‫א‬‫א‬E2F‫א‬‫א‬E2F ‫ﻧﻖ × ط‬ ‫ × ط‬400  

  °12 = 24 =  = 2

‫هـ‬ 2

 ‫א‬‫א‬- ‫هـ‬

E2HCH1F

8C °01 ´25 ¨57 =W‫א‬‫א‬‫א‬‫א‬E1F  °00´32

¨27H

   °12 ´ 00 ¨ 03 =  ‫א‬‫א‬{‫א‬‫א‬¨3 °12= ‫ هـ‬E2F 2

 K

-83-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬-‫و‬ 





‫א‬‫א‬‫א‬‫א‬



 ‫א‬



E1F‫א‬

°01´25 ¨57

 ‫א‬‫א‬‫א‬ ‫ א‬‫א‬  ‫א‬ °01´25 ¨57 20  1

E2FZZ

°02 ´51 ¨54

°01´25 ¨57

E3FZZ

°04 ´17 ¨51

°01´25 ¨57

E4FZZ

°05 ´43 ¨48

°01´25 ¨57

E5FZZ

°07 ´09 ¨45

°01´25 ¨57

E6FZZ

°08 ´35 ¨42

°01´25 ¨57

E7FZZ

°10 ´01 ¨39

°01´25 ¨57

E8FZZ

°11 ´27 ¨36

°01´25 ¨57

2‫א‬

°12 ´00 ¨03

°00´32¨27

7.55

2

E‫א‬‫א‬‫א‬‫א‬F

           

-84-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 EF‫א‬‫א‬‫א‬  ‫א‬‫א‬  KE‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  -1  -2

 ‫א‬ ‫ ﺛﻼﺛﻪ‬-3   -4  ‫א‬‫א‬

 ‫א‬‫א‬-1  K،‫א‬

 ‫א‬EF‫א‬-2

 ‫א‬EF  KEF

 KEF‫א‬‫א‬‫א‬-3

 KEF‫א‬-4

 ‫א‬‫א‬‫א‬EF‫א‬‫א‬‫א‬E ‫ هـ‬=F 2

 ‫א‬‫א‬‫א‬EF‫א‬‫א‬E1F‫א‬‫א‬

KE2{1FE2F  KE2F

 W‫א‬‫א‬‫א‬-6

 ‫א‬‫א‬‫א‬‫א‬‫א‬EF‫א‬-‫ أ‬

 KEF‫א‬E‫א‬F‫א‬‫א‬

 EF‫א‬E ‫ هـ‬.‫ﻧﻖ‬

180

.‫ط‬

=F‫א‬-‫ب‬

 KE2،1F‫א‬ -85-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

‫א‬،‫א‬‫א‬E2،´،1F‫א‬‫א‬‫א‬- ‫ﺟـ‬

10‫א‬‫א‬‫א‬‫א‬‫א‬ E1F‫א‬‫א‬ E ‫ ﻧﻖ‬F،‫א‬‫א‬20 20

‫א‬‫א‬E´F‫א‬‫א‬‫א‬‫א‬ ‫א‬E ‫ ﻧﻖ‬F2010E´F‫א‬ 20

‫א‬‫א‬‫א‬E1F‫א‬‫א‬‫א‬E2F‫א‬‫א‬

 KEF‫א‬‫א‬E´CF

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬EF‫א‬-‫د‬  KE1F‫א‬

K‫א‬E ‫ هـ‬=E2HCH1F‫א‬‫א‬- ‫هـ‬ 2

 E20-3F‫א‬-7 

 E20-3F

 ‫א‬E1F‫א‬-‫أ‬  K‫א‬‫א‬‫א‬EF

-86-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬E1F‫א‬‫א‬‫א‬‫א‬‫א‬-‫ب‬

 E1F‫א‬E1F‫א‬‫א‬

 E1F‫א‬‫א‬‫א‬‫א‬E1F  KE1F‫א‬

‫א‬‫א‬‫א‬‫א‬E´F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬- ‫ﺟـ‬

‫א‬‫א‬E1F‫א‬E´F‫א‬E´H1F  KE2F‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬E´F‫א‬‫א‬‫א‬‫א‬‫א‬-‫د‬

 ،‫א‬‫א‬E2FE´F‫א‬E´2H1F  KE3F‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ - ‫هـ‬   ‫א‬‫א‬  ‫א‬‫א‬

E2F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E2F‫א‬‫א‬E2F‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬،‫א‬E2F‫א‬‫א‬‫א‬‫א‬ ‫א‬10J 5‫א‬،‫א‬‫א‬

E2F‫א‬‫א‬E2F‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬

 ‫א‬‫א‬

E215F‫א‬‫א‬E1FE2F‫א‬‫א‬‫א‬‫א‬‫א‬

،‫א‬E2F‫א‬‫א‬‫א‬‫א‬‫א‬E20-3F  ‫א‬‫א‬‫א‬‫א‬E2F‫א‬

 KE2HCH1F 

-87-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬ 11-3

،1F‫א‬‫א‬،E21-3 F

E12F،E11F‫א‬‫א‬E1F‫א‬E2

E3F‫א‬E22F{E21F‫א‬‫א‬E2F‫א‬

‫א‬‫א‬E32F‫א‬E31F‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 



 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E 21-3F

‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬،،‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬KE 21-3F‫א‬

 K‫א‬‫א‬‫א‬‫א‬E2،´،1F‫א‬ -88-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 EF‫א‬‫א‬‫א‬  W‫א‬‫א‬  KE2F‫א‬  ‫א‬‫א‬‫א‬‫א‬  KE2F-1  K-2

 K-3

 K-4  ‫א‬‫א‬  ‫א‬‫א‬ -1  K{‫א‬

 EF‫א‬-2  ‫א‬EF‫א‬

 KEF

 KEF‫א‬‫א‬‫א‬ -3

 KEF‫א‬-4

 E2J 3F‫א‬EF‫א‬E2{1F‫א‬-5

 ‫א‬‫א‬‫א‬EF‫א‬‫א‬‫א‬KE ‫ هـ‬=F 2

 ‫א‬‫א‬‫א‬EF‫א‬‫א‬E1F

 KE2{1F{E2F

 K‫א‬‫א‬‫א‬‫א‬E2{´{1F‫א‬‫א‬‫א‬‫א‬ -6

 ‫א‬‫א‬E1F‫א‬‫א‬‫א‬-7

 ‫א‬‫א‬{E2F‫א‬

 K‫א‬‫א‬‫א‬‫א‬EF

‫א‬E1F‫א‬‫א‬‫א‬E1F‫א‬‫א‬‫א‬‫א‬-8  ‫א‬‫א‬‫א‬E2F‫א‬‫א‬‫א‬

-89-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

‫א‬‫א‬E1H ‫ هـ‬J °360F 2

‫א‬‫א‬‫א‬{‫א‬‫א‬

 E22-3F‫א‬‫א‬E1F‫א‬

 

 E22-3F

‫א‬‫א‬‫א‬‫א‬‫א‬E1F‫א‬‫א‬‫א‬-9 E2F‫א‬‫א‬‫א‬‫א‬E´H1F‫א‬

‫א‬E´H1H ‫ هـ‬J 360F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 2

E2F‫א‬‫א‬‫א‬‫א‬

 KE2F{E22-3F{‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬-10  K‫א‬‫א‬‫א‬ 

 

-90-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬

E1F‫א‬E2F‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬{‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬{‫א‬E1F‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬E2F‫א‬‫א‬‫א‬‫א‬KE1F‫א‬‫א‬

 KE´H1F‫א‬‫א‬{      

-91-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

   ‫א‬225‫א‬W1  K‫א‬‫א‬‫א‬‫א‬K°30‫א‬‫א‬‫א‬‫א‬EF‫א‬  ‫א‬175‫א‬W2  K‫א‬‫א‬‫א‬‫א‬K°40 ´45‫א‬‫א‬‫א‬‫א‬EF‫א‬  W‫א‬‫א‬°4‫א‬W3  K‫א‬20‫א‬‫א‬J   K‫א‬20 ‫א‬‫א‬J   ‫א‬‫א‬245‫א‬W4  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K°44‫א‬‫א‬‫א‬  

K‫א‬20‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬140‫א‬W5  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K°48‫א‬  KE10F  ‫א‬‫א‬‫א‬‫א‬215‫א‬W6  ‫א‬20‫א‬‫א‬‫א‬‫א‬‫א‬K °50   K‫א‬‫א‬‫א‬  -92-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬ 150‫א‬W7  ‫א‬‫א‬‫א‬‫א‬K°80‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬(20)‫א‬  ‫א‬‫א‬‫א‬‫א‬120‫א‬W8  KE10F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K°56‫א‬  ‫א‬‫א‬‫א‬‫א‬185‫א‬W9  ‫א‬20‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K°62              

-93-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 E‫א‬‫א‬F‫א‬‫א‬  K‫א‬‫א‬‫א‬  W‫א‬

321W‫א‬ 



 KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKW‫א‬‫א‬  KKKKKKKKKKKKKKKKKKKKKKKW‫א‬

 K‫א‬

 K‫א‬٪80W‫א‬‫ א‬ KKKKKKKKKW‫א‬

 K‫א‬٪100W‫א‬‫א‬  ‫א‬



 ‫א‬ 

 ‫א‬‫א‬‫א‬



 ٪100‫א‬‫א‬



 ‫א‬

KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKW

 KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK  KKKKKKKKKKKKKKKKKKKKKKKKKKKKW‫א‬

      

-94-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 E‫א‬‫א‬F‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬ 

 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

E3F{‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬{‫א‬‫א‬‫א‬

 K

‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬

 E‫א‬‫א‬F‫א‬‫א‬ 

 ‫א‬



 

 



 ‫א‬ K1



 ‫א‬ K2



‫א‬‫א‬‫א‬E‫א‬F‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬? ???‫א‬{  K‫א‬

-95-

 ‫א‬‫א‬‫א‬

2

‫א‬

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

‫א‬W‫א‬‫א‬‫א‬  ‫א‬‫א‬  ‫א‬‫א‬J   ‫א‬‫א‬J   ‫א‬‫א‬J    ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬  ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬٪100‫א‬ 

-96-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬  1-4 ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

،‫א‬‫א‬{‫א‬‫א‬ ‫א‬،،‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬،‫א‬‫א‬‫א‬،

 E1-4F‫א‬

  E1-4F 

‫א‬EF‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬،‫א‬‫א‬

‫א‬،‫א‬‫א‬،‫א‬‫א‬

 K‫א‬

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 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬2-4  W‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬-1

 K‫א‬‫א‬،‫א‬‫א‬‫א‬-2   ‫א‬‫א‬    ‫א‬‫א‬  ‫א‬ ‫א‬    -3  K‫א‬

 ‫א‬‫א‬1-2-4 ‫א‬،‫א‬،  ‫א‬‫א‬

‫א‬،  ،‫א‬ ،‫א‬

، 50 – 10  ‫א‬  ‫א‬ ، ‫א‬ ‫א‬ ‫א‬     ‫א‬

،‫א‬‫א‬‫א‬‫א‬  ،30 – 20  ‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬،‫א‬‫א‬‫א‬،‫א‬‫א‬ ‫א‬ ‫א‬،‫א‬‫א‬‫א‬،‫א‬

 K‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬

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 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬2-2-4 ‫א‬‫א‬، ‫א‬‫א‬

‫א‬‫א‬،‫א‬‫א‬‫א‬ ‫א‬،‫א‬‫א‬‫א‬،‫א‬ 

 K‫א‬

 K‫א‬‫א‬G

 K‫א‬‫א‬،‫א‬‫א‬‫א‬G

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ ‫א‬G ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬{‫א‬‫א‬‫א‬،‫א‬

‫א‬‫א‬،‫א‬‫א‬‫א‬

 ‫א‬‫א‬ ،‫א‬ ،‫א‬   K‫א‬،‫א‬،‫א‬

،‫א‬‫א‬‫א‬‫א‬  ،‫א‬‫א‬‫א‬G  K‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬3-4  W‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E1  K‫א‬E2   W‫א‬  K‫א‬‫א‬،

 ،‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬،

‫א‬،   ‫א‬‫א‬  100‫א‬،٪1‫א‬‫א‬‫א‬،

 K‫א‬‫א‬‫א‬‫א‬‫א‬

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 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

W‫א‬‫א‬ E‫א‬‫א‬‫א‬C‫א‬F±Z‫א‬

   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬  ‫א‬‫א‬EHF  ‫א‬‫א‬EJ F ‫א‬ 72.20‫א‬‫א‬ ‫א‬‫א‬ E 1F

 K‫א‬‫א‬20‫א‬%2 ‫א‬  W‫א‬  W‫א‬‫א‬{{ 72.20=‫א‬‫א‬  K72.60Z20C0.02 H72.20= ‫א‬‫א‬  K73.00Z40C0.02 H72.20= ‫א‬‫א‬ K73.40Z60C0.02 H72.20= ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬-3

‫א‬‫א‬‫א‬ ،‫א‬ ‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬،‫א‬ 

 ‫א‬‫א‬ =‫א‬

 ‫א‬‫א‬

   ‫א‬ ‫א‬   ،   ‫א‬ ‫א‬ ‫א‬    ،‫א‬‫א‬ ‫א‬، ‫א‬  ‫א‬

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 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬



1 { 1 { 1 { 1 { 1 { 1 { 1 1000 750 500 300 250 200 100



 ‫א‬‫א‬ 1 { 1 { 1 { 1 { 1  100 75 25 20 10

 

 ‫א‬‫א‬‫א‬ -4 ، ،‫א‬‫א‬  ‫א‬‫א‬ ‫א‬،E،،FE2-4F‫א‬‫א‬K ، ،‫א‬‫א‬‫א‬‫א‬، ‫א‬  W‫א‬‫א‬‫א‬،‫א‬

K‫א‬– ‫א‬

‫א‬– ‫א‬

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 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 EFE2-4F

 EFE2-4F



 EFE2-4F -102-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

  ‫א‬-5 ‫א‬     ،  ‫א‬‫א‬

‫א‬‫א‬‫א‬،‫א‬

‫א‬‫א‬‫א‬،‫א‬‫א‬،‫א‬

‫א‬3L2،2L1،1L1‫א‬‫א‬‫א‬K‫א‬  E4-4FE3-4F‫א‬‫א‬K 

 

 ‫א‬  ‫א‬

 



‫א‬

 ‫א‬E3-4F

 



‫א‬C‫א‬Z‫א‬  ‫א‬ C ‫א‬‫א‬Z‫א‬



  

 ‫א‬ 

 ‫א‬‫א‬‫א‬‫א‬  ‫א‬ -103-

 



 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 

 ‫א‬E4-4F 

   xE‫א‬C‫א‬‫א‬F±‫א‬zC‫א‬=‫א‬  xE‫א‬‫א‬C‫א‬‫א‬F±‫א‬zC‫א‬‫א‬=‫א‬

 ‫א‬-6 ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬

K‫א‬‫א‬‫א‬‫א‬  ،‫א‬‫א‬‫א‬‫א‬

،،‫א‬

،‫א‬‫א‬،‫א‬‫א‬،  ،‫א‬‫א‬‫א‬‫א‬

 KE5-4F‫א‬‫א‬        

 E5-4F 

 ‫א‬

 ‫א‬‫א‬CZ‫א‬ 2 -104-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

‫א‬‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬K  ‫א‬

،‫א‬،‫א‬  ‫א‬

 E6-4FK‫א‬‫א‬  

1



2 1

 

2

 





 E6-4FW

 ‫א‬W1 ‫א‬‫א‬W

 ‫א‬W2





C2 C1

 ‫א‬W1

 ‫א‬W2



 

  =E2F‫א‬=E1F‫א‬         2 H1 2 H1  

 2

H1Z‫א‬ 

-105-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 2C21C1

Z‫א‬Z‫א‬ 2 2 

 

‫א‬،‫א‬‫א‬

 K‫א‬

 E2F ‫א‬‫א‬ ،120 ‫א‬‫א‬‫א‬

 ‫א‬‫א‬،30

‫ﺟﺪﻭﻝ ﺃﺭﺻﺎﺩ ﻣﻴﺰﺍﻧﻴﺔ ﶈﻮﺭ ﻃﻮﱄ ﺑﻄﺮﻳﻘﺔ – ﺳﻄﺢ ﺍﳌﻴﺰﺍﻥ‬ ‫ﺍﳌﻨﺴﻮﺏ‬ ‫ﻣﻠﺤﻮﻇﺎﺕ‬

‫ﻣﻨﺴﻮﺏ‬

‫ﺍﻟﻘﺮﺍﺀﺍﺕ ﻋﻠﻰ ﺍﻟﻘﺎﻣﺔ‬

‫ﺳﻄﺢ‬ ‫ﺍﳌﻴﺰﺍﻥ‬

‫ﻣﺴﺎﻓﺎت اﻷﻓﻘﻴﺔ‬

‫ﺭﻗﻢ‬

‫ﺟﺰﺋﻴﺔ ﺗﺮﺍﻛﻤﻴﺔ ﻣﺆﺧﺮﺓ ﻣﺘﻮﺳﻄﺔ ﻣﻘﺪﻣﺔ‬

‫ﺍﻟﻮﺗﺪ‬

1.7

B.M 1 2 3 4 5 B.M

80 2.4 2.03 2.7 2.06 2.3 1.68

:‫א‬  80‫א‬،‫א‬‫א‬‫א‬‫א‬J 1 K٪1‫א‬79.80‫א‬‫א‬،‫א‬-2  K1:25،1: 200 ‫א‬‫א‬-3  K‫א‬‫א‬‫א‬-4 -106-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

K1.2‫א‬‫א‬،-5  K‫א‬‫א‬-6  K‫א‬‫א‬ -7  ‫א‬ K‫א‬‫א‬‫א‬-1 ‫ﺟﺪﻭﻝ ﺃﺭﺻﺎﺩ ﻣﻴﺰﺍﻧﻴﺔ ﶈﻮﺭ ﻃﻮﱄ ﺑﻄﺮﻳﻘﺔ – ﺳﻄﺢ ﺍﳌﻴﺰﺍﻥ‬ ‫ﺍﳌﻨﺴﻮﺏ‬ ‫ﻣﻠﺤﻮﻇﺎﺕ‬

‫ﻣﻨﺴﻮﺏ‬

‫ﺍﻟﻘﺮﺍﺀﺍﺕ ﻋﻠﻰ ﺍﻟﻘﺎﻣﺔ‬

‫ﺳﻄﺢ‬

80 79.30 79.67 79.00 79.64 79.40 80.02

‫ﺍﳌﻴﺰﺍﻥ‬ 81.7

‫ﺭﻗﻢ‬

‫ﻣﺴﺎﻓﺎت اﻷﻓﻘﻴﺔ‬

‫ﺟﺰﺋﻴﺔ ﺗﺮﺍﻛﻤﻴﺔ ﻣﺆﺧﺮﺓ ﻣﺘﻮﺳﻄﺔ ﻣﻘﺪﻣﺔ‬

‫ﺍﻟﻮﺗﺪ‬

1.7

B.M 1 2 3 4 5 B.M

2.4 2.03 2.7 2.06 2.3 1.68

 W‫א‬‫א‬ 0.02Z‫א‬–‫א‬‫א‬ K1

 0.02Z

– K2  ‫א‬-2

 KE‫א‬‫א‬‫א‬C‫א‬FH‫א‬‫א‬=   79.80=‫א‬‫א‬  80.10=E30C0.01FH 79.80=‫א‬‫א‬   80.40=E60C0.01 FH 79.80=‫א‬‫א‬ -107-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

  80.70 =E90C0.01FH 79.80=‫א‬‫א‬‫א‬   81=E120C0.01FH 79.80=‫א‬‫א‬   ‫א‬‫א‬-3 -4F‫א‬‫א‬‫א‬  KE7               -108-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬



E7-4F ‫א‬‫א‬-4  ‫א‬‫א‬–‫א‬=‫א‬‫א‬  0.5=79.30–79.80=E 1F‫א‬‫א‬   0.43=79.67 –80.10=E2F‫א‬‫א‬   1.40= 79.00 –80.40=E3F‫א‬‫א‬   0.06 = 79.64–80.70=E 4F‫א‬‫א‬  K 1.06 =  79.40 –81=E5F‫א‬‫א‬  K‫א‬‫א‬ -5  ‫א‬‫א‬C‫א‬=‫א‬ 2

 2



0.516=0.43C1.20 =E2F‫א‬



0.6=0.5C 1.20=E1F‫א‬

1.68=1.40 C1.20=E3F‫א‬

1.272=1.06C1.20=E4F‫א‬ 2

1.92=1.60C1.20=E5F‫א‬  ‫א‬ -6

  ‫א‬

 ‫א‬‫א‬CZ‫א‬ -1092

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

  



  0.516 + 0.60  3  16.74 =30 C=‫א‬‫א‬‫א‬‫א‬ 2 1.68H0.516  3



 23.94 =30 C=‫א‬‫א‬‫א‬‫א‬  2 1.272H1.68

44.28 =30 C=‫א‬‫א‬‫א‬‫א‬‫א‬  2 1.92H1.272 

47.88 =30 C=‫א‬‫א‬‫א‬‫א‬‫א‬  2

 ‫א‬-7  K‫א‬‫א‬=‫א‬ 

141.84= 47.88H44.28H32.94H16.74=‫א‬        -110-



 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

  

-111-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

E3F ‫א‬،10‫א‬‫א‬،40  ‫א‬،‫א‬،‫א‬‫א‬‫א‬

 ‫א‬‫א‬–‫א‬ ‫ﻣﻠﺤﻮﻇﺎﺕ‬

‫ﺍﳌﻨﺴﻮﺏ‬

‫ﻣﻨﺴﻮﺏ‬

‫ﺍﻟﻘﺮﺍﺀﺍﺕ ﻋﻠﻰ ﺍﻟﻘﺎﻣﺔ‬

‫ﺳﻄﺢ‬ ‫ﺭﻭﺑﲑ‬

‫ﺍﳌﻴﺰﺍﻥ‬ 22.30

‫ﺭﻗﻢ‬

‫ﺟﺰﺋﻴﺔ ﺗﺮﺍﻛﻤﻴﺔ ﻣﺆﺧﺮﺓ ﻣﺘﻮﺳﻄﺔ ﻣﻘﺪﻣﺔ‬

‫ﺍﻟﻮﺗﺪ‬

2.3

B.M

3.21 3.41 3.81 2.71 3.40 ‫ﺭﻭﺑﲑ‬

‫ﻣﺴﺎﻓﺎت اﻷﻓﻘﻴﺔ‬

2.3

1 2 3 4 5 B.M

 J W‫א‬  K20‫א‬‫א‬‫א‬‫א‬ -1  %2 ‫א‬،19.50‫א‬‫א‬،‫א‬-2  1:20، 1 : 250‫א‬‫א‬ -3  K‫א‬‫א‬‫א‬-4  K 1.75‫א‬‫א‬،-5  K‫א‬‫א‬-6  K‫א‬‫א‬-7

 K‫א‬‫א‬-8    -112-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬  ‫א‬‫א‬‫א‬ -1  ‫א‬‫א‬–‫א‬ ‫ﻣﻠﺤﻮﻇﺎﺕ‬

‫ﺍﳌﻨﺴﻮﺏ‬

‫ﻣﻨﺴﻮﺏ‬ ‫ﺳﻄﺢ‬

‫ﺍﳌﻴﺰﺍﻥ‬ 22.30

‫ﺭﻭﺑﲑ‬

19.09 18.89 18.29 19.59 18.90 20

‫ﺍﻟﻘﺮﺍﺀﺍﺕ ﻋﻠﻰ ﺍﻟﻘﺎﻣﺔ‬

‫ﺭﻗﻢ‬

‫ﻣﺴﺎﻓﺎت اﻷﻓﻘﻴﺔ‬

‫ﺟﺰﺋﻴﺔ ﺗﺮﺍﻛﻤﻴﺔ ﻣﺆﺧﺮﺓ ﻣﺘﻮﺳﻄﺔ ﻣﻘﺪﻣﺔ‬

‫ﺍﻟﻮﺗﺪ‬

2.3

B.M

3.21 3.41 3.81 2.71 3.40

1 2 3 4 5 B.M

2.3

:‫اﻟﺘﺤﻘﻴﻖ اﻟﺤﺴﺎﺑﻲ‬

0.0 =

‫ ﳎﻤﻮﻉ ﺍﳌﺆﺧﺮﺍﺕ – ﳎﻤﻮﻉ ﺍﳌﻘﺪﻣﺎﺕ‬.1

0.0 = ‫ ﻣﻨﺴﻮﺏ ﺁﺧﺮ ﻧﻘﻄﺔ – ﻣﻨﺴﻮﺏ ﺃﻭﻝ ﻧﻘﻄﺔ‬.2  ‫א‬-2  KE‫א‬‫א‬‫א‬C‫א‬FH‫א‬‫א‬=   19.30=E10C0.02FJ



19.50=‫א‬‫א‬

19.50=‫א‬‫א‬

 19.10=E20C0.02 FJ  19.50=‫א‬‫א‬

 18.90 =E30C0.02FJ  19.50=‫א‬‫א‬‫א‬

  18.70=E40C0.02FJ  19.50=‫א‬‫א‬  ‫א‬‫א‬ -3

-4F‫א‬‫א‬‫א‬  KE8 -113-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬E8-4F                    ‫א‬‫א‬E8-4F -114-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬‫א‬-4  ‫א‬‫א‬–‫א‬=‫א‬‫א‬  ‫א‬J ‫א‬‫א‬=‫א‬  0.41 =19.09– 19.50 = ( 1)‫א‬‫א‬   0.41 = 18.89 –19.30=( 2)‫א‬‫א‬   0.61 = 18.29–19.10=( 3)‫א‬‫א‬  0.69 =19.59–18.90=( 4)‫א‬   0.20= 18.90 –18.70 = ( 5)‫א‬  ‫א‬ -5  ‫א‬‫א‬‫א‬C‫א‬=‫א‬ 2



0.718= 0.41C1.75=( 1)‫א‬



2 2

0.718=0.41C1.75 = ( 2)‫א‬ 1.068=0.61 C1.75=( 3)‫א‬

1.208=0.69 C 1.75=( 4)‫א‬

 20.35= 0. 2C 1.75=( 5)‫א‬  W‫א‬-6   ‫א‬

 ‫א‬‫א‬CZ‫א‬  2

-115-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

  0.718 + 0.718    3  E  F  7.18 =10 C=‫א‬‫א‬‫א‬‫א‬ 2  1.068H0.718 

 EF3 9.93 =10C=‫א‬‫א‬‫א‬‫א‬  2  0.35H1.208



 EF37.79 =10 C=‫א‬‫א‬‫א‬‫א‬‫א‬  2  

‫א‬‫א‬E4F{E3F‫א‬‫א‬‫א‬ -7

4.692

10C1.068+3 =

‫ـــــــــــــــــــــــــــــ‬

‫ـــــــــــــــــــــــــ‬

‫س‬

+ 3  10C1.208+4

 1.208 +1.0684

5.308

‫ـــــــــــــــــــــــــــــــ‬

‫ـــــــــــــــــــــــــ‬

‫س‬

+ 3

 1.208 + 1.0684



 10= 5.308 + 4.692=

‫س‬H

‫س‬

 4.692C1.068 1 ‫س‬×3 3

 2.506 =

‫ــــــــــــــــــــــــــــــــــــــ‬

 2

‫ــــــــــــــــــــــــ‬

2

=‫א‬

 



 

-116-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

5.308 C1.0682×4 3

 3.206 =

‫ـــــــــــــــــــــــــــــــــــــــ‬

 2

‫ـــــــــــــــــــــــــ‬

2

=‫א‬

 



 ‫א‬-8  K‫א‬‫א‬=‫א‬ 

 18.616 =  2.506H8.93H7.18=‫א‬ 

10.996 = 3.206H7.79=‫א‬               -117-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 EF‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬    ‫א‬‫א‬  ‫א‬  K‫א‬ -1

 K‫א‬‫א‬{‫א‬ -2

 K‫א‬‫א‬‫א‬-3  K‫א‬‫א‬-4

 K‫א‬‫א‬‫א‬-5  ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬-1  ‫א‬‫א‬‫א‬‫א‬‫א‬-2 ‫א‬‫א‬‫א‬{‫א‬‫א‬-3  K‫א‬  K‫א‬‫א‬-4  K‫א‬‫א‬‫א‬‫א‬‫א‬-5   -118-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 W‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬-1  K‫א‬-2  K‫א‬‫א‬J 3  K‫א‬‫א‬‫א‬J 4 K‫א‬‫א‬‫א‬‫א‬- 5  K‫א‬‫א‬‫א‬‫א‬J 6  K‫א‬‫א‬J 7     

        -119-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬

 4-4 ،‫א‬‫א‬ ‫א‬ ‫א‬{‫א‬‫א‬

‫א‬،‫א‬‫א‬ ‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬             

 E9–4F ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬K50–10  KE9-4F‫א‬‫א‬K‫א‬

-120-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

،‫א‬‫א‬،  ‫א‬‫א‬‫א‬

‫א‬‫א‬، ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬،‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬  K‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬1-4-4 ‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬{‫א‬‫א‬{‫א‬

E4F ‫א‬ ‫א‬ ،‫א‬‫א‬

‫א‬  ‫א‬‫א‬‫א‬ ،‫א‬‫א‬

،‫א‬‫א‬‫א‬،‫א‬‫א‬ ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬

،‫א‬،‫א‬

،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬ ،‫א‬  K‫א‬‫א‬،  ‫א‬‫א‬2-4-4

،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬،‫א‬،  ‫א‬3-4-4 ‫א‬‫א‬‫א‬،‫א‬‫א‬  W‫א‬  Z‫א‬‫א‬‫א‬‫א‬

E‫א‬‫א‬C‫א‬FH‫א‬‫א‬= -121-

 

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 

 K‫א‬‫א‬EJ F‫א‬‫א‬EHF ‫א‬،‫א‬  ‫א‬  ‫א‬  K‫א‬  ‫א‬‫א‬ 4-4-4 ‫א‬‫א‬  ،‫א‬‫א‬،‫א‬‫א‬

 ‫א‬‫א‬ {E2J 4F‫א‬ ‫א‬‫א‬

‫א‬،،،K  K‫א‬‫א‬

 ‫א‬

‫א‬CZ‫א‬ 2

 



   ‫א‬C‫א‬    Z‫א‬   2 

 E10-4F -122-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 C4C½=E1F‫א‬ 4‫ع‬+3‫ع‬  C=E2 F‫א‬  2 3 ‫ ع‬+ 2 ‫ ع‬  C = E3 F‫א‬  2  C2 ‫ع‬C½= E4F‫א‬ 







C2C4  Z{Z

2H15H4



 

 K‫א‬= ‫א‬ 

-123-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 E4F ‫א‬،5460

‫א‬‫א‬‫א‬‫א‬،20  ‫א‬4  

 K‫א‬‫א‬

W‫א‬ 32.111‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬-1

 K %2‫א‬ 32‫א‬‫א‬‫א‬‫א‬-2  K1: 25 {1:500‫א‬‫א‬ -3  K‫א‬‫א‬‫א‬- 4

 K‫א‬‫א‬‫א‬-5

 K 1 : 25 ، 1:200 ‫א‬‫א‬ -6

 K‫א‬‫א‬-7  K‫א‬‫א‬-8       

-124-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ?‫א‬‫א‬?‫א‬‫א‬ ‫ﻣﺘﻮﺳﻄﺔ‬

‫ﻣﺆﺧﺮﺓ‬

‫ﺍﳌﺴﺎﻓﺎﺕ‬ ‫ﻳﺴﺎﺭ‬

32.111

‫ﳏﻮﺭ‬

‫ﺭﻗﻢ ﺍﻟﻮﺗﺪ‬ ‫ﳝﲔ‬

0.905 2.196 2.207 2.033 2.028 1.871 1.998 1.916 1.653 1.564 0.973 2.536 1.231 1.610 1.213 1.273 0.789 1.173 1.084 1.201 1.238 0.905

4 4 0.0 4 4 4 4

20 4 4

4 4 40 4 4 4 4

B.M 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

‫ﺭﻗﻢ‬

‫ﺍﻟﻘﻄﺎﻉ‬

‫ﺍﻷﻭﻝ‬

‫ﺳﻄﺢ ﺍﳌﻴﺰﺍﻥ‬

‫ﻣﻘﺪﻣﺔ‬

‫ﺍﻟﺜﺎﱐ‬

‫ﻣﻨﺴﻮﺏ‬

‫ﺍﻟﺜﺎﻟﺚ‬

‫ﺍﳌﻨﺴﻮﺏ‬

16 60 4 4

17 18 19 20 B.M

‫ﺍﻟﺮﺍﺑﻊ‬

‫ﻣﻠﺤﻮﻇﺎﺕ‬

 W‫א‬‫א‬

Z‫א‬–‫א‬‫א‬ Z–

E1F E2F

    -125-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬



‫א‬

 ‫א‬‫א‬‫א‬ -1  ?‫א‬‫א‬?‫א‬‫א‬

‫ﺍﳌﻨﺴﻮﺏ‬

‫ﻣﺘﻮﺳﻄﺔ‬

‫ﻣﻘﺪﻣﺔ‬



33.016

 W‫א‬‫א‬‫א‬

‫ﺍﳌﺴﺎﻓﺎﺕ‬ ‫ﻳﺴﺎﺭ‬

‫ﺍﳌﻴﺰﺍﻥ‬



E4FW‫א‬

‫ﻣﺆﺧﺮﺓ‬

‫ﺳﻄﺢ‬

32.111 30.820 30.809 30.983 30.988 31.145 31.018 31.100 31.363 31.452 32.043 30.453 31.785 31.406 31.803 31.743 32.227 31.843 31.932 31.815 31.778 32.111



‫ﳏﻮﺭ‬

‫ﳝﲔ‬

0.905 2.196 2.207 2.033 2.028 1.871 1.998 1.916 1.653 1.564 0.973 2.536 1.231 1.610 1.213 1.273 0.789 1.173 1.084 1.201 1.238 0.905

4 4 0. 4 4 4 4

20 4 4

4 4 40 4 4 4 4

‫ﺭﻗﻢ‬

‫ﺍﻟﻮﺗﺪ‬

‫ﺍﻟﻘﻄﺎﻉ‬

B.M 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

‫ﺍﻷﻭﻝ‬

‫ﻣﻠﺤﻮﻇﺎﺕ‬



‫ﺍﻟﺜﺎﱐ‬

‫ﻣﻨﺴﻮﺏ‬

 W‫א‬



‫ﺍﻟﺜﺎﻟﺚ‬



16 60 4 4

17 18 19 20 B.M

‫ﺍﻟﺮﺍﺑﻊ‬

 W‫א‬

:‫ﺍﻟﺘﺤﻘﻴﻖ ﺍﳊﺴﺎﰊ‬ 0.0= 0.905–0.905= ‫א‬–‫א‬‫א‬E1F

 0.0= 32.111J 32.111=–E2F

-126-



 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 J W‫א‬2J  KE‫א‬‫א‬‫א‬C‫א‬FJ =  KE18،13،8،3F‫א‬‫א‬  K32=E3F‫א‬  31.600=E20C0.02F–32=E8F‫א‬  31.200= E40C0.02F–32=E13F‫א‬ 30. 800=E60C0.02F–32=E18F‫א‬  KE9-4F‫א‬‫א‬J W‫א‬‫א‬-3  ‫א‬‫א‬‫א‬-4  1.017= 30.983– 32.00 =‫א‬‫א‬  0.237=31.363– 31.60=‫א‬‫א‬  K0.206= 31.20–31.406=‫א‬‫א‬  K1.132= 30.80–31.932=‫א‬‫א‬‫א‬

-127-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 E9-4F‫א‬‫א‬J W‫א‬‫א‬-3                  E9-4F  -128-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬J 5

 E10-4 F‫א‬‫א‬‫א‬ =E5FE1F‫א‬  KE‫א‬‫א‬C‫א‬FJ ‫א‬‫א‬=  ‫א‬‫א‬EJ F{‫א‬‫א‬EHF  K30=E½C4F–32.000=  0.820= 30J 30.820= 1W  1.191= 32J 30.809 = 2  1.017= 32J 30.983= 3  1.012= 32J 30.988= 4  1.145= 30J 31.145= 5  {‫א‬W 4 × 1.012 ‫×ل‬4‫ع‬ 1.877 = ‫س = ـــــــــــــ = ــــــــــــــــــــــــــ‬ 1.145 + 1.012 5 ‫ع‬+ 4 ‫ع‬  4C1.191 C2





2.369 ===  1.191H0.8202H1

-129-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬W  2

‫م‬

4.416

= 4 ×

1.017 + 1.191 ‫= ـــــــــــــــــــــــــــ‬ 2

‫ل‬

4H3

1.012 + 1.017 2

‫م‬

4.058

= 4 ×

‫= ـــــــــــــــــــــــــــ‬ 2

‫ع‬+2‫ع‬ × ‫ ( = ـــــــــــــــــــــــ‬3 ) ‫ﻣﺴﺎﺣﺔ اﻟﺸﻜﻞ‬ 2 3

‫ل‬

× ‫ ( = ـــــــــــــــــــــــ‬2 ) ‫ﻣﺴﺎﺣﺔ اﻟﺸﻜﻞ‬ 2

 20.950 =1.877C1.191 C1/2 =C4 C1/2 =E1 F‫א‬  21.411 =2.369C1.191 C1/2 =C2 C1/2 =E4 F‫א‬  ‫א‬‫א‬ ‫إﺟﻤﺎﻟﻲ‬ 1.411+ 0.950 + 4.058+ 4.416 = ‫א‬‫א‬∴  3

 10.835 = 

 E10-4 F‫א‬‫א‬  

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 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬-5  ‫א‬‫א‬‫א‬                 ‫א‬‫א‬‫א‬  E10-4F -131-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬‫א‬  E11-4 F‫א‬‫א‬‫א‬ =E10F{E6F‫א‬  KE‫א‬‫א‬C‫א‬FJ ‫א‬‫א‬=  29.600=E½C4FJ 31.600 =  ‫א‬‫א‬‫א‬W   EFKKKKKKKKK1.418= 29.600J 31.018 = 6W  EFKKKKKKKKKKKK0.500= 31.600J 31.100 = 7  EFKKKKKKK0.237= 31.600J 31.363= 8  EFKKKKKKKKKKK0.148=31.600 J 31.452= 9  EFKKKKKKKKKKKK2.443= 29.600J 32.043= 10  {‫א‬W 4 × 0.148 ‫ ﻣﺘﺮ‬0.229 = ‫ــــــــــــــــــــــــــ‬ 2.443 + 0.148



‫×ل‬9‫ع‬ = ‫س = ـــــــــــــ‬ 10 ‫ع‬+ 9 ‫ع‬



 4C0.50 C7



 1.043 ===  1.418H0.57H6

   

-132-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬W  2

‫ م‬1.474

4 ×

(0.237 + 0.5) ‫= ـــــــــــــــــــــــــــ‬ 2

‫ع‬+7‫ع‬ ‫ ( = ـــــــــــــــــــــــ × ل‬3 ) ‫ﻣﺴﺎﺣﺔ اﻟﺸﻜﻞ‬ 2 8

9H8

(0.148 + 0.237) 2

‫م‬

0.77

= 4 ×

‫= ـــــــــــــــــــــــــــــــــ‬ 2

‫ل‬

× ‫ ( = ـــــــــــــــــــــــ‬2 ) ‫ﻣﺴﺎﺣﺔ اﻟﺸﻜﻞ‬ 2

 20.017 =0.229C0.148 C1/2 =C9 C1/2 =E1 F‫א‬  20.261 =1.043C0.5 C1/2 =C7 C1/2 =E4 F‫א‬  ‫א‬‫א‬ ‫إﺟﻤﺎﻟﻲ‬ 0.261+ 0.017 + 0.77+ 1.474 = ‫א‬‫א‬ 

 2.522 = 

 KE11- 4 F‫א‬‫א‬         -133-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬-5  ‫א‬‫א‬‫א‬                 ‫א‬‫א‬‫א‬  E11-4F -134-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬‫א‬  E12-4 F‫א‬‫א‬‫א‬ =E15F{E11F‫א‬  KE‫א‬‫א‬C‫א‬FJ ‫א‬‫א‬=  K33.20=E½C4F+31.200 =  ‫א‬‫א‬‫א‬W   EF2.747= 33.20 J 30.453 = 11W  EF0.585= 31.200J 31.785 = 12  EF0.206= 31.200J 31.406= 13  EF0.603= 31.200J 31.803= 14  EF1.457= 33.200J 31.743= 15  {‫א‬W 4 × 0.603 ‫ م‬1.171 = ‫ــــــــــــــــــــــــــ‬ 1.457 + 0.603

‫ × ل‬14 ‫ع‬ = ‫س = ـــــــــــــ‬ 15 ‫ع‬+ 14 ‫ع‬

  

4C0.585 C12 0.702 = ‫ص = ـــــــــــــــــ = ـــــــــــــــــــــــ‬  2.747H0.58512H11

-135-

 

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬W  2

‫م‬

1.582

4 ×

(0.206 + 0.585) ‫= ـــــــــــــــــــــــــــــــ‬ 2 (0.603 + 2.206)

‫م‬

1.618

= 4 ×

‫= ـــــــــــــــــــــــــــــــــ‬ 2

( 13 ‫ ع‬+ 12 ‫)ع‬ ‫ = ـــــــــــــــــــــــــــــ × ل‬E3 F‫א‬ 2

E14H13

)

‫ = ـــــــــــــــــــــــــــــ × ل‬E2 F‫א‬ 2

 20.353 =1.171C0.603 C1/2 =C14 C1/2 =E1 F‫א‬  20.205 =0.702C0.585 C1/2 =C12 C1/2 =E4 F‫א‬  ‫א‬‫א‬ ‫إﺟﻤﺎﻟﻲ‬ 0.205+ 0.353 + 1.618+ 1.582 = ‫א‬‫א‬  2

 3.758 = 

 KE12- 4 F‫א‬‫א‬        -136-



 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬‫א‬                   ‫א‬‫א‬‫א‬  E12-4F -137-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬  E13-4 F‫א‬‫א‬‫א‬‫א‬ =E20F{E16 F‫א‬  KE‫א‬‫א‬C‫א‬FH‫א‬‫א‬=  K32.80=E½C4F+31.200 =  ‫א‬‫א‬‫א‬W   EF0.573J = 32.80 J 32.227 = 16W  EF1.043= 30.80J 31.843 = 17  EF1.132= 30.80J 31.932= 18  EF1.015= 30.80J 31.815= 19  EF1.022J = 32.80J 31.778= 20  {‫א‬W   

4 × 1.015 ‫ م‬1.993 = ‫ــــــــــــــــــــــــــــ‬ 1.022 + 1.015 4 × 1.043 ‫ م‬2.582 = ‫= ــــــــــــــــــــــــــــ‬ 0.573 + 1.043

‫× ل‬19 ‫ع‬ = ‫س = ـــــــــــــ‬ 20 ‫ع‬+ 19 ‫ع‬  ‫× ل‬17 ‫ع‬ ‫س = ـــــــــــــ‬  18 ‫ع‬+ 17 ‫ع‬   

-138-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 ‫א‬W  2

‫م‬

4.35

= 4 ×

(1.132 + 1.043) ‫= ــــــــــــــــــــــــــــــ‬ 2

‫× ل‬

E19H18)

(1.015 + 1.132) 2

‫م‬

4.294

= 4 ×

‫= ـــــــــــــــــــــــــــــــــ‬ 2

(18 ‫ ع‬+ 17 ‫)ع‬ ‫ = ـــــــــــــــــــــــ‬E3 F‫א‬ 2

‫ل‬

× ‫ = ـــــــــــــــــــــــ‬E2 F‫א‬ 2

 21.012 =1.015C1.132 C1/2 =C19 C1/2 =E1 F‫א‬  21.347 =2.582C1.043 C1/2 =C17 C1/2 =E4 F‫א‬  ‫א‬‫א‬‫א‬ ‫إﺟﻤﺎﻟﻲ‬ 1.347+ 1.012 + 4.294+ 4.350 = ‫א‬‫א‬  2

 11.003 = 

 KE13 - 4 F‫א‬‫א‬         -139-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

                ‫א‬‫א‬‫א‬‫א‬  E13-4F   -140-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 K‫א‬‫א‬-7



‫ﻣﺠﻤﻮع ﻣﺴﺎﺣﺘﻲ‬ ‫اﻟﻘﻄﺎﻋﻴﻦ‬ × ‫ = ـــــــــــــــــــــــــــــــــــــــ‬‫א‬ 3

  

2.522+10.835  133.57 = 20

‫= ـــــــــــــــــــــــــــــــــــــــ‬

 2

EFE8 F{E3F‫א‬

3.758+2.522  62.800 = 20

× ‫= ـــــــــــــــــــــــــــــــــــــــ‬

EFE18F{E13F‫א‬

 2 1{‫א‬‫א‬E13F{E8F‫א‬‫א‬‫א‬



 K2

‫ ﻣﺘﺮ‬8.03 =

50.44 ‫ــــــــــــــــــ‬ 6.28

20 × 2.522 = ‫= ــــــــــــــــــــــــــــ‬ 3.758 + 2.522

‫× ل‬8 ‫م‬ ‫ = ـــــــــــــ‬1 ‫س‬ 13 ‫ م‬+ 8 ‫م‬

‫ ﻣﺘﺮ‬11.97 =

75.16 ‫ــــــــــــــــــ‬ 6.28

20 × 3.758 = ‫= ــــــــــــــــــــــــــــ‬ 3.758 + 2.522

‫× ل‬13 ‫م‬ ‫ = ـــــــــــــ‬2 ‫س‬ 13 ‫ م‬+ 8 ‫م‬

2.522 × 8.03 1‫×س‬8‫م‬ ‫ م‬10.128 = ‫= ــــــــــــــــــــــــ‬ ‫ = ـــــــــــــ‬‫א‬ 2 2 3.758 × 11.97 2 ‫ × س‬13 ‫م‬ 3 ‫ م‬22.47 = ‫= ــــــــــــــــــــــــــــ‬ ‫ = ــــــــــــــــــ‬‫א‬ 2 2 K‫א‬‫א‬-8  3   145.698=10.128H133.57=‫א‬ ‫إﺟﻤﺎﻟﻲ‬ 3

 3

85.27= 22.47 H62.800 =‫א‬ -141-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 EF‫א‬‫א‬‫א‬‫א‬    K،‫א‬‫א‬،   ‫א‬‫א‬‫א‬‫א‬    ‫א‬‫א‬  W‫א‬  K‫א‬-1  K‫א‬‫א‬‫א‬‫א‬-2  K‫א‬-3  K‫א‬‫א‬-4  K‫א‬‫א‬‫א‬‫א‬-5   ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬      -142-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

   K‫א‬‫א‬‫א‬‫א‬‫א‬W1  ‫؟‬‫א‬K‫א‬E‫א‬F‫א‬W2  ‫א‬‫א‬5،160‫א‬‫א‬‫א‬W3  W‫א‬‫א‬‫א‬،40 {2.2=5{2.46=4{2.00=32.75=2

{2.45=1،1.90=BM  J W‫ א‬1.89=BM

 K90‫א‬‫א‬‫א‬-1  K٪0.2‫א‬،89‫א‬‫א‬‫א‬‫א‬-2  25W1،1000W1‫א‬‫א‬-3  K‫א‬‫א‬‫א‬-4  K1.67‫א‬‫א‬،-5  K‫א‬‫א‬-6  K‫א‬‫א‬-7 ‫א‬ ،  6    ‫א‬100     ‫א‬‫א‬  ‫א‬   W 4  W‫א‬‫א‬‫א‬،20‫א‬  {1.007=5{1.11=42.62=3{2.015=2{1.113=1{1.650=BM  1.625=BM{1.725= 6   J W‫א‬  K14.687‫א‬‫א‬‫א‬-1 -143-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 K %3‫א‬15.60‫א‬‫א‬‫א‬‫א‬-2  1:50،1:500 ‫א‬‫א‬-3  K‫א‬‫א‬‫א‬-4  K 2.5‫א‬‫א‬،-5  K‫א‬‫א‬-6  K‫א‬‫א‬-7 ‫א‬‫א‬ ‫א‬،120‫א‬‫ א‬:5 ،‫א‬‫א‬،30  ‫א‬‫א‬،5‫א‬،  W‫א‬…  K%2 60Z‫א‬‫א‬،‫א‬-1  K1:50،1:500‫א‬‫א‬ -2  K‫א‬‫א‬‫א‬-3 ،1/1‫א‬‫א‬‫א‬‫א‬،-4  K10‫א‬ K‫א‬‫א‬-5  K‫א‬‫א‬-6  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬-7 K1:100،1:200  -144-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

     

-145-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 E‫א‬‫א‬F‫א‬‫א‬  K‫א‬‫א‬‫א‬  W‫א‬

321W‫א‬ 



 KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKW‫א‬‫א‬  KKKKKKKKKKKKKKKKKKKKKKKW‫א‬

 K‫א‬

 K‫א‬٪80W‫א‬‫ א‬ KKKKKKKKKW‫א‬

 K‫א‬٪100W‫א‬‫א‬  ‫א‬



 ‫א‬ 

 ‫א‬‫א‬ K1



 K‫א‬‫א‬ K2



 ٪100‫א‬‫א‬



 ‫א‬

KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKW

KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK

 KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK

 KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK  KKKKKKKKKKKKKKKKKKKKKKKKKKKKW‫א‬

      -146-

 ‫א‬‫א‬‫א‬

 104

 ‫א‬

 ‫א‬

 2

 ‫א‬

 E‫א‬‫א‬F‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬ 

 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ {‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬{‫א‬‫א‬‫א‬E3F  K‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬

 E‫א‬‫א‬F‫א‬‫א‬ 

 ‫א‬



 

 



 ‫א‬‫א‬‫א‬ K1



 ‫א‬‫א‬‫א‬ K2



   

-147-

 ‫א‬‫א‬‫א‬

2

‫א‬‫א‬

 ‫א‬‫א‬ ‫א‬‫א‬

 104

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬W‫א‬‫א‬  ‫א‬‫א‬  ‫א‬‫א‬J   ‫א‬‫א‬  ‫א‬‫א‬‫א‬  ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬

 

 ‫א‬‫א‬  ‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬٪100‫א‬ 

 3‫א‬‫א‬   W‫א‬‫א‬

 ‫א‬‫א‬–1

 ‫א‬–2      

-147-

 ‫א‬‫א‬ ‫א‬‫א‬

 104

 ‫א‬

 2

 ‫א‬

 ‫א‬‫ א‬1-5  ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬

 W‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ -1 ‫א‬{‫א‬E( Bench Mark ) 

‫א‬{‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬{

 K‫א‬‫א‬‫א‬‫א‬{‫א‬‫א‬‫א‬

 W

( Bench Mark ) ‫א‬‫א‬‫א‬‫א‬‫א‬ G {‫א‬ ‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬( Bench Mark ) ‫א‬‫א‬‫א‬‫א‬‫א‬ -2

‫א‬‫א‬{‫א‬{‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬  K‫א‬‫א‬

 W ( Bench Mark ) ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬G  

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬G Bench F‫א‬E1F  ‫א‬‫א‬‫א‬G  K‫א‬EMark 

-148-

 ‫א‬‫א‬ ‫א‬‫א‬

 104

 ‫א‬

 2

 ‫א‬

  

 ‫؟‬‫א‬‫א‬‫א‬‫א‬‫א‬W1 

 ‫؟‬‫א‬‫א‬‫א‬ W2 

 ( Bench Mark ) ‫א‬‫א‬‫א‬‫א‬‫א‬W3 

 ‫؟‬‫א‬{‫א‬ 

         

-149-

 ‫א‬‫א‬ ‫א‬‫א‬

 104

 ‫א‬

 2

 ‫א‬



321W‫א‬ 

 KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKW‫א‬‫א‬  KKKKKKKKKKKKKKKKKKKKKKKW‫א‬

 K‫א‬

 K‫א‬٪80W‫א‬‫ א‬ KKKKKKKKKW‫א‬

 K‫א‬٪100W‫א‬‫א‬  ‫א‬



 ‫א‬



 ‫א‬‫א‬‫א‬



 ٪100‫א‬‫א‬



 ‫א‬

KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK

        -150-

 ‫א‬‫א‬ ‫א‬‫א‬

 104

 ‫א‬

 2

 ‫א‬

 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ {‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬{‫א‬‫א‬‫א‬E3F  K‫א‬‫א‬

‫א‬‫א‬W  ‫א‬‫א‬‫א‬‫א‬‫א‬

K‫א‬

 E‫א‬‫א‬F‫א‬‫א‬    

    



 ‫א‬



 

 ‫א‬‫א‬

  ‫א‬‫א‬‫א‬E‫א‬F‫א‬‫א‬‫א‬



-151-

 ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬

2

‫א‬‫א‬‫א‬

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 104

 ‫א‬

 2

 ‫א‬

‫א‬‫א‬‫א‬W‫א‬‫א‬   ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬J    ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 

 ‫א‬‫א‬  ‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬٪100‫א‬  3‫א‬‫א‬ 

 ‫א‬‫א‬  ‫א‬‫א‬–1  ‫א‬–2       -152-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 104

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬‫א‬1-6 ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬{‫א‬‫א‬‫א‬{‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬، ‫א‬‫א‬–1

‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ {‫א‬‫א‬‫א‬‫א‬‫א‬ {‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

،‫א‬‫א‬‫א‬،‫א‬‫א‬

E‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬E‫א‬F‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬ –2

‫א‬‫א‬‫א‬{‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ –3

 KE1- 6F‫א‬‫א‬‫א‬ 

  E 1-6 F 

-153-



 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 104

 ‫א‬

 2

 ‫א‬

‫א‬EBench MarkF‫א‬–4

‫א‬‫א‬‫א‬‫א‬EBench MarkF‫א‬‫א‬ ‫א‬‫א‬‫א‬EBench MarkF‫א‬‫א‬

 KE2-6F‫א‬{‫א‬‫א‬



 E2-6F

 ‫א‬‫א‬‫א‬E3-6F{–5 



 E3 – 6 F

{‫א‬‫א‬‫א‬

‫א‬{‫א‬‫א‬‫א‬‫א‬ -154-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 104

 ‫א‬

 2

 ‫א‬

،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬

‫א‬‫א‬‫א‬{‫א‬–6 ‫א‬،‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬

‫א‬‫א‬{‫א‬‫א‬–7 ‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬

‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬{E‫א‬  KE4-6F‫א‬،‫א‬

  E4–6F



‫א‬{‫א‬‫א‬‫א‬J 8  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ -155-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 104

 ‫א‬

 2

 ‫א‬

  

 ‫א‬‫א‬‫א‬‫א‬‫א‬ W1  ‫؟‬‫א‬ 

 ‫א‬‫א‬‫א‬‫א‬W2  ‫؟‬‫א‬ 

 ‫؟‬‫א‬‫א‬‫א‬‫א‬‫א‬W3 

-156-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 104

 ‫א‬

 2

 ‫א‬



321W‫א‬ 

 KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKW‫א‬‫א‬  KKKKKKKKKKKKKKKKKKKKKKKW‫א‬

 K‫א‬

 K‫א‬٪80W‫א‬‫ א‬ KKKKKKKKKW‫א‬

 K‫א‬٪100W‫א‬‫א‬  ‫א‬



 ‫א‬



 ‫א‬‫א‬‫א‬‫א‬ K1



 K‫א‬‫א‬ K2



 ٪100‫א‬‫א‬



 ‫א‬

 KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK  KKKKKKKKKKKKKKKKKKKKKKKKKKKKW‫א‬

      -157-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 104

 ‫א‬

 2

 ‫א‬

 WE‫א‬‫א‬F‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬ 

 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

E3F { ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬{‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬

 E‫א‬‫א‬F‫א‬‫א‬    

    



 ‫א‬



 

 ‫א‬‫א‬

  ‫א‬‫א‬‫א‬E‫א‬F‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬? ???‫א‬{  K‫א‬

   

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 ‫א‬‫א‬‫א‬

2 ‫א‬‫א‬

‫א‬‫א‬

 ‫א‬‫א‬ ‫א‬‫א‬

 104

 ‫א‬

 2

 ‫א‬

‫א‬‫א‬W‫א‬‫א‬   ‫א‬‫א‬

 ‫א‬‫א‬J   ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬

 ‫א‬‫א‬  ‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬٪100‫א‬  3‫א‬‫א‬

 ‫א‬‫א‬  ‫א‬‫א‬–1  ‫א‬–2        

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 ‫א‬‫א‬ ‫א‬‫א‬

 104

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬ 1-7 ‫א‬،‫א‬

‫א‬‫א‬‫א‬،‫א‬

 J W

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬

‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬

K‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬ • K‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬ •

KEKKKKKKKK{‫א‬،،F‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬ •

K‫א‬EBench MarkF‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬ •  



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

 ‫א‬‫א‬ ‫א‬‫א‬

 104

 ‫א‬

 2

 ‫א‬

  

 ‫؟‬‫א‬‫א‬‫א‬‫א‬W1 

 ‫؟‬‫א‬‫א‬‫א‬‫א‬‫א‬W2 

 ‫؟‬‫א‬‫א‬‫א‬W3    



             

-161-

 ‫א‬‫א‬ ‫א‬‫א‬

 104

 ‫א‬

 2

 ‫א‬

 E‫א‬‫א‬F‫א‬‫א‬  K‫א‬‫א‬‫א‬  W‫א‬



321W‫א‬ 

 KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKW‫א‬‫א‬  KKKKKKKKKKKKKKKKKKKKKKKW‫א‬

 K‫א‬

 K‫א‬٪80W‫א‬‫ א‬ KKKKKKKKKW‫א‬

 K‫א‬٪100W‫א‬‫א‬  ‫א‬



 ‫א‬



 ‫א‬‫א‬‫א‬ K1



 K‫א‬‫א‬ K2



 ٪100‫א‬‫א‬



 ‫א‬

 KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK  KKKKKKKKKKKKKKKKKKKKKKKKKKKKW‫א‬

      -162-

 ‫א‬‫א‬ ‫א‬‫א‬

 104

 ‫א‬

 2

 ‫א‬

 

‫א‬‫א‬‫א‬‫א‬‫א‬

{‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬W ‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬

 E‫א‬‫א‬F‫א‬‫א‬    

    



 ‫א‬



 

 K‫א‬‫א‬

  ‫א‬‫א‬‫א‬E‫א‬F‫א‬‫א‬ ‫א‬



-163-

 ‫א‬‫א‬‫א‬

2

‫א‬‫א‬‫א‬

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬‫א‬‫א‬

 2

 ‫א‬

 ‫א‬‫א‬‫א‬W‫א‬‫א‬    ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬J   ‫א‬‫א‬‫א‬‫א‬J    ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬  ‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٪100‫א‬

 ‫א‬‫א‬  K‫א‬E1F        

-164-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬‫א‬‫א‬

 2

 ‫א‬

 ‫א‬‫א‬‫א‬1-8 ‫א‬{‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬–1

 ‫א‬‫א‬‫א‬‫א‬‫א‬ ±  mm

12 J

± 25

 mm

 ‫א‬‫א‬‫א‬‫א‬ k 

 ‫א‬‫א‬–2

 ‫א‬‫א‬‫א‬‫א‬‫א‬ ±  mm

4 J

± 12

 mm

 ‫א‬‫א‬‫א‬‫א‬‫א‬k

 W

 ‫א‬‫א‬‫א‬‫א‬‫א‬G

 K‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬G  ‫א‬‫א‬‫א‬‫א‬

 ±  mm

5 J

± 10

n 

mm= ‫א‬ 

 ‫א‬‫א‬‫א‬‫א‬‫א‬n

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬G  W‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬‫א‬G

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬=‫א‬‫א‬‫א‬

 ‫א‬‫א‬–‫א‬‫א‬=‫א‬

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬

-165-



 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬‫א‬‫א‬

 2

 ‫א‬





 E1F

1,2,3,4,5 ‫א‬‫א‬‫א‬‫א‬E1 – 8F 

 E 1-8F

             

-166-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬‫א‬‫א‬

 2

 ‫א‬

 ‫א‬‫א‬‫א‬  ‫א‬  ‫א‬‫א‬  ‫א‬‫א‬  ‫א‬ ‫א‬‫א‬ Point No . Measured (m) Correction (m) Adjusted h( m ) Elevation (m)

BM.23  1  2  3  4  5  BM .23 

823.651

 H0.004

 +8.111

 -17.212

 + 0.004

-17.208

 -0.525

 +0.003

 814.554

-0.522

 -2.387

 +0.004

 814.032

-2.383

 +2.790

 +0.004

 811.649

+2.794

 +9.206

 +0.003

 814.443

+9.209

 +0.022

 823.652

+0.001

 +8.107



∑ ∆h = −0.021



 831.762

  E2F 

 ‫א‬‫א‬‫א‬A,B,C,D ‫א‬‫א‬‫א‬

 K‫א‬‫א‬EBM F  ‫א‬

 K‫א‬‫א‬‫א‬-1

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬-2  ‫؟‬500 

-167-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬‫א‬‫א‬

 2

 ‫א‬

    ‫א‬

 

 ‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬  



764.723 767.013 



765.881



764.600



764.667 767.791 2.346

 

‫א‬‫א‬

 ‫א‬ 

‫א‬



1.132



2.413



3.124



765.993 768.338 1.798

2.345



764.728



2.290

 



3.610



 W‫א‬

 ‫א‬J 1

 3= ‫א‬‫א‬‫א‬‫א‬=‫א‬‫א‬‫א‬‫א‬ •  =‫א‬‫א‬‫א‬‫א‬–‫א‬‫א‬‫א‬‫א‬ •

 ‫א‬‫א‬‫א‬–‫א‬‫א‬‫א‬

 E7.759 – 7.754 ) =( 764.728 – 764.723 ) = .005m •

.005m = 5mm ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬-2  ،A,B,C,D ‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬

 4 J  ± 12 k  mm= k = 0.5 km =  mm - ± 4 0.5  ± 12 0.5 mm =  H 2.83mm - H8.49 mm = 

±  mm

 K

( +5mm )‫א‬‫א‬‫א‬‫א‬ 

-168-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬‫א‬‫א‬

 2

 ‫א‬

  

 ‫؟‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ W1

 ‫؟‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W2

‫א‬A,B,C,D,E ،‫א‬‫א‬‫א‬W3

‫א‬‫א‬500.123‫א‬BM ‫א‬‫א‬  W‫א‬،‫א‬

 K‫א‬‫א‬-1

 K‫א‬‫א‬-2

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬-3

 ‫א‬635

    

‫ א‬

 ‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬  



2.764



2.791



2.811

‫א‬‫א‬

 ‫א‬  2.56

  ‫א‬



2.113



2.410



 D



 E



  3.081 2.983



  2.516 

BM   

-169-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬‫א‬‫א‬

 2

 ‫א‬



321W‫א‬ 

 KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKW‫א‬‫א‬  KKKKKKKKKKKKKKKKKKKKKKKW‫א‬

 K‫א‬

 K‫א‬٪80W‫א‬‫ א‬ KKKKKKKKKW‫א‬

 K‫א‬٪100W‫א‬‫א‬  ‫א‬



 ‫א‬



 ‫א‬‫א‬‫א‬‫א‬



 ٪100‫א‬‫א‬



 ‫א‬

 KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK  KKKKKKKKKKKKKKKKKKKKKKKKKKKKW‫א‬

        -170-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬‫א‬‫א‬

 2

 ‫א‬

 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ {‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬W ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬ 

 E‫א‬‫א‬F‫א‬‫א‬    

    



 ‫א‬



 

 ‫א‬‫א‬

   

-171-

 ‫א‬‫א‬‫א‬

2

‫א‬‫א‬

-- 1 --

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬‫א‬

 2

 ‫א‬

‫א‬‫א‬W‫א‬‫א‬     ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬J    ‫א‬‫א‬  ‫א‬‫א‬‫א‬   ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬

 ‫א‬‫א‬  ‫א‬‫א‬‫א‬

 ‫א‬‫א‬٪100‫א‬  3‫א‬‫א‬        

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 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬‫א‬

 2

 ‫א‬

 ‫א‬‫א‬1-9 ‫א‬‫א‬‫א‬{‫א‬‫א‬  ‫א‬‫א‬

 K‫א‬،‫א‬،-1  K‫א‬‫א‬-2  K‫א‬-3

 K‫א‬‫א‬-4  K‫א‬‫א‬‫א‬‫א‬‫א‬-5

 K‫א‬150‫א‬‫א‬‫ א‬-6

 E‫א‬‫א‬‫א‬{‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ –7  K‫א‬‫א‬‫א‬‫א‬‫א‬–8  K‫א‬–9

 K‫א‬‫א‬–10

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬-11  ‫א‬G

 ‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬

 K‫א‬‫א‬ –1

 K‫א‬‫א‬‫א‬‫א‬‫– א‬2

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫– א‬3  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬ ‫– ﺣﻴﺚ إن‬4  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫– א‬5  ‫א‬‫א‬‫א‬ –6

 K‫א‬‫א‬‫א‬‫א‬ –7  K‫א‬‫א‬‫א‬‫א‬‫א‬ -8 -173-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬‫א‬

 2

 ‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬ –9

 K‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬EBench Mark F‫א‬‫א‬‫א‬–10 EBench Mark )

 K‫א‬‫א‬‫א‬‫א‬ –11

 K‫א‬‫א‬‫א‬‫א‬‫א‬ –12          



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 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬‫א‬

 2

 ‫א‬

  

 K‫א‬‫א‬‫א‬W1

 ‫؟‬‫א‬‫א‬‫א‬‫א‬‫א‬W2 ‫؟‬‫א‬‫א‬‫א‬‫א‬‫א‬W3

              -175-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬‫א‬

 2

 ‫א‬

 E‫א‬‫א‬F‫א‬‫א‬

 K‫א‬‫א‬‫א‬

 W‫א‬



321W‫א‬ 

 KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKW‫א‬‫א‬  KKKKKKKKKKKKKKKKKKKKKKKW‫א‬

 K‫א‬

 K‫א‬٪80W‫א‬‫ א‬ KKKKKKKKKW‫א‬

 K‫א‬٪100W‫א‬‫א‬  ‫א‬



 ‫א‬



 ‫א‬‫א‬



 ٪100‫א‬‫א‬



 ‫א‬

KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK

 KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK

 KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK  KKKKKKKKKKKKKKKKKKKKKKKKKKKKW‫א‬

      

-176-

 ‫א‬‫א‬

 104

 ‫א‬

 ‫א‬‫א‬

 2

 ‫א‬

 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬E3F { ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬‫א‬‫א‬  E‫א‬‫א‬F‫א‬‫א‬    

    



 ‫א‬



 

 ‫א‬‫א‬

‫א‬‫א‬‫א‬? ???‫א‬{  K‫א‬



-177-

  ‫א‬‫א‬

 104

 ‫א‬

 2

 ‫א‬

 ‫א‬‫א‬  ‫א‬‫א‬‫א‬

 K‫א‬-1

 ‫א‬‫א‬‫א‬‫א‬‫א‬ -2

 1408‫א‬K

 ‫א‬‫א‬‫א‬‫א‬‫ א‬-3

 1991KKK

 1987‫א‬‫א‬K‫א‬‫א‬-4  KE‫א‬‫א‬F‫א‬‫א‬-5

‫א‬K‫א‬K   K

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬-6  ‫א‬K‫א‬K

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ -7  ‫א‬K



‫א‬K

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ -8  ‫א‬‫א‬K



 K  

1-SURVEYING

-178-

 W‫א‬‫א‬‫א‬

B.C.PUNMIA

VOL

  ‫א‬

 104

 ‫א‬

 2

 ‫א‬

 ‫א‬ ............................................................................................................ ............................................................................................................  1 ................................................................. ‫א‬W‫א‬‫א‬ 25 ....................................................................‫א‬W‫א‬‫א‬ 33 ....................................................................... ‫א‬W‫א‬‫א‬ 96 ..................................................................... ‫א‬W‫א‬‫א‬‫א‬ 147............................................................ ‫א‬‫א‬W‫א‬‫א‬ 152............................................. ‫א‬‫א‬‫א‬W‫א‬‫א‬ 159.......................................................... ‫א‬‫א‬W‫א‬‫א‬ 164......................................................... ‫א‬‫א‬‫א‬W‫א‬‫א‬ 172................................................................. ‫א‬‫א‬W‫א‬‫א‬ 178...................................................................................................... ‫א‬‫א‬ 

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                  

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬E‫א‬F‫א‬‫א‬ GOTEVOT appreciates the financial support provided by BAE SYSTEMS