كتاب مقدمه في علم المساحه by Mebuild

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

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

 

١٠٢

  

 ١٠٢

 ‫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 W‫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? ?? ?‫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     W    ‫א‬ ‫א‬  ‫א‬    ‫א‬  K‫א‬



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



  

 ١٠٢

 ‫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K

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫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

 W‫א‬K‫א‬‫א‬

  ‫א‬‫א‬‫א‬ ‫א‬‫א‬ •

 K‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬  ‫א‬‫א‬ • K‫א‬

K‫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

K‫א‬



  

 ١٠٢

 ‫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  K‫א‬‫א‬‫א‬



‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬      



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



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



 ‫א‬



‫א‬

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

 W‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

 W‫א‬‫א‬  W‫א‬‫א‬‫א‬  K‫• א‬  K‫א‬‫א‬ •

 K‫א‬‫• א‬

 K‫א‬‫א‬‫א‬‫• א‬  K‫א‬‫א‬‫• א‬  K‫א‬‫א‬ •



.%100‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬   ٤W‫א‬‫א‬ 

 W‫א‬‫א‬ K‫א‬ • 

 W‫א‬‫א‬  K١J ‫א‬

-١-

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

 ‫א‬  ‫א‬ .1

‫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

 K‫א‬‫א‬‫א‬‫א‬ 

‫א‬‫א‬K   ‫א‬

‫א‬‫א‬‫א‬،‫א‬‫א‬

‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬ 

‫א‬‫א‬ .2

 W‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬ •  K‫א‬‫א‬ • K‫א‬‫א‬ •



 W‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬ •

-٢-

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

 ‫א‬.1.2

Field Surveying‫א‬

Aerial SurveyingK‫א‬‫א‬K‫א‬  K‫א‬‫א‬ 

 Field Surveying‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬

 KE‫א‬F‫א‬‫א‬‫א‬‫א‬  Plane Surveying‫א‬‫• א‬

 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬ ‫א‬

‫א‬‫א‬،  ‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬٢٥٠‫א‬‫א‬

 W‫א‬‫א‬

 K‫א‬ •

 K‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬ •

‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬



 K‫א‬‫א‬‫א‬

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 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

Geodetic Surveying (‫)א‬‫א‬‫• א‬

‫א‬‫א‬‫א‬

‫א‬‫א‬

‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬E‫א‬F  K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ 

Aerial Surveying ‫א‬‫ א‬-‫ب‬

‫א‬،  ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬، ‫א‬ ‫א‬

 W‫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K  ‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬



‫א‬‫ א‬-‫ﺟـ‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

E ‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬، ‫א‬ .‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬

-٤-

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

‫א‬‫א‬ .2.2

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W 

Topographic Surveying

‫א‬‫א‬‫ א‬-‫أ‬

‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬Ground Control Points ‫א‬‫א‬‫א‬،‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬ 

Cadastral Surveying

‫א‬‫ א‬-‫ب‬

‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ ‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬ 

Route Surveying ‫א‬‫א‬ -‫ﺟـ‬

‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬ 

Hydrographic Surveying ‫א‬‫א‬‫ א‬-‫د‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬

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 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

Mine Surveying ‫א‬ -‫هـ‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬ 

Engineering Surveying ‫א‬‫ א‬-‫ﻣـ‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

KKK،،E،F‫א‬،E‫א‬،،F‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬W‫א‬ 

  .3

‫א‬  ‫א‬‫א‬‫א‬‫א‬

KKK‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬

 Ellipsoid of Revolution‫א‬‫א‬‫• א‬



‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  Plumb Bob‫• א‬



‫א‬E ‫א‬‫א‬F‫א‬

‫א‬‫א‬K ‫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  K‫א‬‫א‬

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 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

Vertical Line ‫א‬‫• א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

،‫א‬‫א‬K ‫א‬،‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬K‫א‬‫א‬‫א‬  KE‫א‬‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬

 

 Horizontal Line‫א‬‫• א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬  Horizontal plane ‫א‬‫• א‬



K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬ Vertical Plane ‫א‬‫• א‬



K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬ Level Surface‫א‬‫• א‬



 K‫א‬‫א‬‫א‬‫א‬‫א‬  Level Line ‫א‬‫• א‬



 K‫א‬‫א‬‫א‬‫א‬‫א‬

-٧-

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

Horizontal Distance ‫א‬‫• א‬



‫א‬ ‫א‬‫א‬‫א‬‫א‬

 K

 Vertical Distance ‫א‬‫• א‬



 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  Horizontal Angle ‫א‬‫א‬‫• א‬



‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬

 Vertical Angle ‫א‬‫א‬‫• א‬



‫א‬‫א‬K  ‫א‬‫א‬‫א‬‫א‬

K  ‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬  Zenith Angle ‫א‬‫א‬‫• א‬



‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K180‫א‬

 Elevation of a Point  •

 ‫א‬‫א‬‫א‬‫א‬



 K‫א‬

-٨-

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

 Elevation Difference ‫א‬ •

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬ 

 ‫א‬‫ א‬.4

 W‫א‬ 

E F‫א‬‫א‬ ‫א‬

‫א‬‫א‬

‫א‬‫א‬ ‫א‬‫א‬K ‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬

‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K 

‫א‬‫א‬‫א‬   ،‫א‬‫א‬K‫א‬ ‫א‬،E F‫א‬

‫א‬F‫א‬،E   ‫א‬F  KE‫א‬،

-٩-

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

 ‫א‬‫א‬‫א‬‫ א‬.5

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

K‫א‬‫א‬-1

‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬

‫א‬‫א‬K -2  K‫א‬‫א‬‫א‬‫א‬ 

‫א‬‫א‬E،،F‫א‬‫א‬‫א‬-3  K‫א‬‫א‬‫א‬K‫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‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

 ‫א‬‫א‬K6  ‫א‬‫ א‬1.6

‫א‬‫א‬W   ‫א‬

، ‫א‬‫א‬‫א‬‫א‬،  ‫א‬K  ‫א‬

E،F‫א‬‫א‬، ‫א‬E،،F‫א‬‫א‬‫א‬

K  EF‫א‬‫א‬،  ‫א‬

- ١٠ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬ 

Units of Measurement ‫א‬‫א‬ .٢٫٦

‫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‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K10000

‫א‬‫א‬‫א‬، E  F١٢‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬  ‫א‬K ٥٢٨٠‫א‬K ‫א‬ ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬K ٤٣٥٦٠‫א‬

English F‫א‬‫א‬‫א‬‫א‬‫א‬ ٢٫١‫ و א‬١٫١‫א‬K‫א‬

 KEMetric SystemF‫א‬‫א‬(System 

 E‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ :1.1‫א‬ 

 ‫א‬‫א‬ 1 Kilometer = 1000 meters 1 meter =100 centimeters 1 centimeter = 10 millimeters 1 decimeter = 10 centimeters 

 ‫א‬‫א‬ 1 mile = 5280 feet 1 mile = 1760 yard 1 mile = 320 rods 1 mile = 80 chains 1 foot=12 inches 1 yard= 3feet 1 rod=16.5 feet 1 chain=66 feet 1 chain =100 links 1 foot=0.3048 m 1 km=0.62137 miles 1 inch=25.4 mm

 

 ‫א‬‫א‬‫א‬

Units of length measurement



 - ١١ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

 E‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ :2.١‫א‬ 

 ‫א‬‫א‬

 ‫א‬‫א‬

1hectare (ha)= 1000 m2 1 square kilometer =1000000 m2 1 square kilometer = 100 hectares 1 hectare = 100 ares

1 acre = 43560 ft2 1 acre=10 square chains 1 are = 100 m2 1 hectare=2.471 acres 1 km2=247.1 acres

Cubic centimeter, Cubic meters

Cubic inch, Cubic feet, Cubic yard

‫א‬‫א‬ Units of area measurement

‫א‬‫א‬ Units of Volume measurement

1 revolution = 360degrees 1 degree=60 minutes 1 minute=60 seconds

revolution = 360degrees 1 degree=60 minutes 1 minute=60 seconds



 ‫א‬‫א‬‫א‬

Units of angles measurement

‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬



 W‫א‬‫א‬K‫א‬‫א‬‫א‬

٩٠‫א‬‫א‬‫א‬٣٦٠‫א‬‫א‬‫א‬‫• א‬



‫א‬DEG‫א‬‫א‬‫א‬‫א‬K 

 KDegree

١٠٠‫א‬‫א‬‫א‬٤٠٠‫א‬‫א‬‫א‬‫• א‬ ‫א‬GRA‫א‬‫א‬

 K‫א‬Gradient

- ١٢ -



 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

‫א‬π2 π ‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬  K‫א‬ π ‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬ 2



 ‫א‬‫א‬‫א‬‫א‬.٣٫٦ .‫א‬‫א‬‫א‬،‫א‬‫א‬،‫א‬‫א‬‫ א‬:٣٫١ ‫א‬  ‫א‬

 

 

2π

400

360

 ‫א‬‫א‬

200

180

 ‫א‬

π/2

100

 ‫א‬‫א‬‫א‬

π/4

 ‫א‬  

 60‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬ :  K60‫א‬‫א‬‫א‬

 1.11111Z‫א‬‫א‬

 54Z 0.9Z‫א‬‫א‬

 57°17'45" Z57.29578Z‫א‬‫א‬‫א‬

 ‫א‬‫א‬ .7

‫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K‫א‬

‫א‬‫א‬K ‫א‬‫א‬‫א‬ ‫א‬  ‫א‬K ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ - ١٣ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

 W‫א‬‫א‬ 

 ‫א‬‫א‬.1.7

‫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.2.7

‫א‬ ‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬K ‫א‬ ‫א‬‫א‬K  ‫א‬‫א‬ ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬ 

 ‫א‬‫א‬ .٣٫٧

‫א‬‫א‬‫א‬‫א‬‫א‬

K  ‫א‬‫א‬ ‫א‬‫א‬‫א‬K ‫א‬  K‫א‬‫א‬ 

 ‫א‬‫א‬‫א‬‫א‬‫א‬.٤٫٧

‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬

‫א‬‫א‬K  ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬K  ‫א‬K ‫א‬‫א‬‫א‬

K ‫א‬‫א‬‫א‬

‫א‬‫א‬ ‫א‬‫א‬،‫א‬‫א‬

‫א‬K  ‫א‬‫א‬‫א‬، - ١٤ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬ 

- ١٥ -

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



‫א‬‫א‬

 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 K‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬ 

 W‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬ ‫א‬ •

K‫א‬‫• א‬ K‫א‬ •



K٪100‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬   ٥W‫א‬‫א‬ 

 W‫א‬‫א‬ K‫א‬ • K‫א‬ •

K‫א‬ •

  W‫א‬‫א‬ .١–‫א‬ 

- ١٦ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 .1

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬K‫א‬‫א‬‫א‬‫א‬K‫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  K‫א‬‫א‬‫א‬‫א‬ 

Measurement of horizontal distance

‫א‬‫א‬ .2

 W‫א‬‫א‬‫א‬ 

Direct Method ‫א‬‫ א‬.1.2

K ‫א‬‫א‬،‫א‬



‫א‬، ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬

 K‫א‬1.2 ‫א‬



 ‫א‬‫א‬‫א‬‫א‬W1.2 ‫א‬ - ١٧ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

Indirect Method ‫א‬‫ א‬.2.2

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬ H‫א‬‫א‬ θ ‫א‬‫א‬‫א‬‫א‬‫א‬ S‫א‬‫א‬ 

H = S . Cos θ

: ١ 

 K‫א‬‫א‬‫א‬ 141.2162.2‫ا‬  .H‫א‬‫א‬

  ‫א‬‫א‬‫א‬‫א‬‫א‬W2.2‫א‬  Cos θ = H

 W‫א‬

 ،

 ‫א‬‫א‬J H  H = S .Cos θ =141.216 x Cos 1° 20′ = 141.178 m

 ‫א‬‫א‬- S



  ‫א‬    ،(٣٫٢  ‫ )א‬ ‫א‬‫ ا‬ ‫א‬  ‫ א‬ ‫א‬ -‫ب‬  W‫א‬‫א‬‫א‬(S)‫א‬‫א‬(h)‫א‬‫א‬

- ١٨ -

 ‫א‬‫א‬ ‫א‬‫א‬



 ١٠٢

 ‫א‬

 

 

 ‫א‬‫א‬‫א‬‫א‬‫א‬ : ٣٫٢‫א‬  H 2 + h 2 = S2

 H 2 = S2 - h 2

 H = S2 - h 2  ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬ ٤٫٢ ‫ א‬: ٢ ‫ﻣــﺜﺎل‬  K‫א‬

 ‫א‬‫א‬‫א‬‫א‬:4.2‫א‬

: ‫א‬

 W‫א‬‫א‬  H 2 + h 2 = S2

 H = S2 - h 2

 WH

 H = 253.1012 - 3.7212  H = 253.074 m

- ١٩ -



 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

.‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ -‫ﺟـ‬ 

 EhF‫א‬EθF‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬E5.2‫א‬F



 EhF‫א‬EθF‫א‬‫א‬‫א‬‫א‬‫א‬W5.2‫א‬ 

 Cotan θ =

H h

 H = h .Cotan θ

.()  ( Cotan ) 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٦٫٢‫ א‬:3 

 K‫א‬

  ‫א‬‫א‬‫א‬‫א‬: 6.2‫א‬

 W‫א‬

  θ = 0.85937°  h= 1.5 m - ٢٠ -

 WH‫א‬‫א‬

 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 H = 1.5 .Cotan 0.85937 = 113.268 m



Methods of measuring distances ‫א‬ .٣

 ‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬K‫א‬ 

(pacing) ‫ א‬‫א‬‫א‬ .1.3

‫א‬‫א‬‫א‬‫א‬‫א‬

.  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬

K  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬K  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬ ‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬K 

‫א‬‫א‬‫א‬  ‫א‬E‫א‬F

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬  K‫א‬‫א‬ 

Passometer‫א‬‫א‬،‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬ ‫א‬Pedometer‫א‬‫א‬K

‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬K ‫א‬‫א‬‫א‬

KK‫א‬‫א‬‫א‬‫א‬K   K‫א‬‫א‬‫א‬‫א‬ 

K1/1001/50‫א‬‫א‬‫א‬‫א‬

K  ‫א‬‫א‬‫א‬ - ٢١ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬

(Tapes) ‫ א‬‫א‬‫ א‬



.2.3

‫א‬K  ‫א‬  ‫א‬‫א‬‫א‬

 K‫א‬‫א‬

 ‫א‬‫ א‬- ‫أ‬

‫א‬‫א‬(Bronze)‫א‬‫א‬‫א‬

‫א‬Metallic Tape‫א‬‫א‬‫א‬‫א‬(Copper)‫א‬(Brass)

‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ٥٠،٣٠،  ٢٥،٢٠،١٥،١٠‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬K  ١–١{٥‫א‬

‫א‬(Feet)‫א‬‫א‬(Inches)‫א‬‫א‬،‫א‬‫א‬‫א‬ ‫א‬K‫א‬  ‫א‬‫א‬

 W‫א‬‫א‬ 

- ٢٢ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

  •  •

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •  W‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫• א‬

‫א‬ K



‫ א‬‫ א‬-‫ب‬

‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬   ١٠٠٣٠‫א‬‫א‬‫א‬١٠٠٠‫א‬٣٣٠٠١

‫א‬‫א‬K ١٠{٥‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬(Inches)‫א‬‫א‬  ‫א‬‫א‬

 K(Feet)

 W‫א‬‫א‬

 ‫א‬‫א‬ • K‫א‬‫א‬‫א‬ •



Invar Tape ‫א‬ -‫ﺟـ‬

‫א‬‫א‬‫א‬‫א‬

‫א‬EF٪35Nickel‫א‬٪65Steel ‫א‬

10030‫א‬6‫א‬‫א‬‫א‬K‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬KE‫א‬100‫א‬F  .(Triangulation)‫א‬‫א‬‫א‬‫א‬

- ٢٣ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 ‫א‬‫ א‬-‫د‬ 

‫א‬‫א‬،‫א‬‫א‬‫א‬ -1  K‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬ -2

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ -3

‫א‬‫ א‬-4

K‫א‬‫א‬ 

(‫א‬) ‫א‬ -‫هـ‬ 

 ‫א‬-1

‫א‬‫א‬ ‫א‬‫א‬‫א‬

 K‫א‬

 ‫א‬ -2 ‫א‬K ‫א‬

 K‫א‬ ‫א‬‫א‬‫ א‬-3

‫א‬‫א‬K ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬FK‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬EW ‫א‬‫א‬  K‫א‬‫א‬

- ٢٤ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

Equipment used for taping ‫א‬‫א‬‫א‬‫ א‬.٤  W‫א‬ Plumb Bob‫• א‬



‫א‬‫א‬‫א‬‫א‬

K‫א‬E  F‫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  Range Poles‫א‬‫• א‬



٣32‫א‬‫א‬‫א‬

K  ‫א‬‫א‬٦

 

- ٢٥ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 



E ‫א‬‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬ ‫א‬

‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬

‫א‬K ‫א‬‫א‬‫א‬‫א‬

K ‫א‬ ‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  Taping Pins‫א‬ •



4020 ٦3‫א‬

K‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬

- ٢٦ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 Pegs ‫• א‬

‫א‬‫א‬E٧٫٢‫א‬F‫א‬‫א‬

،  ‫א‬ 3020٦3 K‫א‬‫א‬‫א‬‫א‬

،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

20.5‫א‬‫א‬‫א‬‫א‬‫א‬

 K٣٠١٠   



 : 7.2‫א‬ 

 Level ‫א‬‫א‬‫א‬‫• א‬

‫א‬‫א‬ ‫א‬‫א‬‫א‬

E٨٫٢‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬

- ٢٧ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 ‫א‬‫א‬‫א‬‫א‬ : 8.2‫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K‫א‬

 W(TheodoliteF  (ClinometerF‫א‬

J 



‫א‬‫א‬‫א‬K  ‫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‫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K‫א‬ - ٢٨ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫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  W‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬ •

‫א‬‫א‬‫א‬‫א‬A‫א‬‫א‬ • K‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬ • ‫א‬‫א‬‫א‬‫א‬‫א‬ •

 K‫א‬‫א‬‫א‬‫א‬ 

 The Abney Level‫א‬J 

‫א‬K ‫א‬‫א‬

‫א‬‫א‬‫א‬ ‫א‬‫א‬ ‫א‬‫א‬‫א‬K  ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬E‫א‬F‫א‬‫א‬‫א‬  ‫א‬  K‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬ 

‫א‬‫א‬‫ א‬.٥  W‫א‬   •  K‫א‬‫א‬‫א‬‫א‬

- ٢٩ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 • ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬  •

‫א‬‫א‬‫א‬

 K

‫א‬‫ א‬.١٫٥  W‫א‬‫א‬‫א‬‫א‬‫א‬ : ‫א‬ 198‫א‬‫א‬‫א‬10

 K‫א‬

 W‫א‬‫א‬  20Z‫א‬‫א‬  19.90Z‫א‬‫א‬  198Z ‫א‬‫א‬  ‫؟‬Z‫א‬‫א‬  

- ٣٠ -

‫ ﻣﺘﺮ‬197.01 = ‫⇐ س‬

19.9 ‫س‬ = 20 198

 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 ‫א‬ ‫א‬‫ ) א‬‫א‬‫א‬‫א‬‫ א‬‫ א‬ ‫ اﻟﻨﺎﺷﺊ‬‫ א‬.2.5 Correction for Temperature (‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬ (‫ د‬- ١‫ )د‬α = ‫ﺣـ‬

 W  ‫א‬‫א‬J 

 ‫א‬‫א‬‫א‬J ١

‫א‬‫א‬ J 

K10-6x١١{٢‫א‬J α ‫א‬‫א‬‫א‬‫ א‬.٣٫٥

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬

 W

‫ ل‬.( ‫ ش‬- 1‫) ش‬ ‫ م‬.E

 = ‫ ﺣـ‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬J   ‫א‬‫א‬‫א‬J

١

 ‫א‬‫א‬‫א‬J 

 ‫א‬‫א‬J 

 ‫א‬‫א‬J 

 ‫א‬‫א‬‫א‬J E



E = 20 x 104N/mm2E =14.5 x 104N/mm2‫א‬

- ٣١ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

Electronic Distance Measurement ‫א‬ .٦

‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

‫א‬EGeodimeterF١٩٥٠‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬ K‫א‬ •



K‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫• א‬

E١٠FE٥٠F‫א‬ • K



‫א‬  ‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬EMicrowaves‫א‬F‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬Modulated Light Waves‫א‬‫א‬‫א‬ ‫א‬

 KModulated Radio Waves‫א‬ 

‫א‬‫א‬‫א‬

 K‫א‬‫א‬ 

‫א‬‫ א‬.1.6

‫א‬‫א‬‫א‬ .1.1.6

 W‫א‬٣‫א‬  K‫א‬‫א‬‫א‬ •  K‫א‬ •

 K‫• א‬

 K‫א‬EF‫א‬ • - ٣٢ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

‫א‬WEDM‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬ ‫א‬‫א‬K  ‫א‬‫א‬ F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬

 KE‫א‬‫א‬‫א‬‫א‬‫א‬

KEInfrared lightF‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬EDM‫א‬‫א‬‫א‬ A B ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬  K‫א‬

‫א‬EReflectorF‫א‬‫• א‬



 

‫א‬‫א‬‫א‬EDM‫א‬‫א‬‫א‬

 K



 WE9.2FAB‫א‬‫א‬‫א‬ 



 ‫א‬‫א‬‫א‬ :9.2‫א‬

- ٣٣ -



 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

A‫א‬E ،،F‫א‬EDM‫א‬ • .B‫א‬‫א‬‫א‬

‫א‬A‫א‬‫א‬ • KB‫א‬‫א‬‫א‬‫א‬‫א‬ A ‫א‬ EDM ‫א‬

B ‫א‬‫א‬‫א‬‫א‬ •



‫א‬ ‫א‬‫א‬‫א‬‫א‬

K‫א‬

‫א‬‫א‬‫א‬‫א‬ •



K‫א‬‫א‬

‫א‬EDM‫א‬‫א‬‫א‬ • ‫א‬‫א‬   KEDM‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬ESF‫א‬‫א‬ W‫א‬‫א‬‫א‬‫א‬‫א‬  S = 1/2 V.t

‫א‬‫א‬t ‫א‬‫א‬‫א‬v

‫א‬EDM‫א‬‫א‬‫א‬KS‫א‬  KEDM‫א‬E‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬

‫א‬‫א‬α ‫א‬‫א‬‫א‬،‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬EDM‫א‬‫א‬

B‫א‬hr‫א‬‫א‬‫א‬ • KAB‫א‬‫א‬A‫א‬he‫א‬EDM‫א‬ - ٣٤ -



 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

‫א‬‫א‬ BA‫א‬(DF‫א‬‫א‬

W‫א‬‫א‬S‫א‬‫א‬

D = S.Cos(α)

α‫א‬‫א‬‫א‬ESF‫א‬‫א‬(DF‫א‬‫א‬

EDM‫א‬‫א‬ h r B‫א‬‫א‬‫א‬B A‫א‬

 W‫א‬‫א‬ h e A‫א‬ 

 D = (S2 - d 2 )1/2



 K10.2‫א‬d



 K‫א‬،‫א‬‫א‬‫א‬W10.2‫א‬  ( h r + B ‫ ) ﻣﻨﺴﻮب اﻟﻨﻘﻄﺔ‬- ( h e + A ‫ = ) ﻣﻨﺴﻮب اﻟﻨﻘﻄﺔ‬d 



 K11.2‫א‬

- ٣٥ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 



 K‫א‬،‫א‬‫א‬‫א‬W11.2‫א‬ 



( h e + A ‫ﻣﻨﺴﻮب اﻟﻨﻘﻄﺔ‬

) - ( h r + B ‫ﻣﻨﺴﻮب اﻟﻨﻘﻄﺔ‬

)= d



‫א‬‫א‬‫א‬‫א‬ .2.1.6

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬



K ‫א‬‫א‬‫א‬‫א‬٢٠١‫א‬‫א‬‫א‬

‫א‬‫א‬F‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬E 

‫א‬‫א‬‫א‬ .3.1.6

‫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.2.6

 W‫א‬‫א‬ ‫א‬ 

- ٣٦ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

‫א‬‫א‬ .1.2.6

٠{٩٠{٤‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

‫א‬‫א‬‫א‬‫א‬‫א‬ .2.2.6

 K١٠٠{٨‫א‬‫א‬‫א‬‫א‬



‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ .3.2.6

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬



- ٣٧ -

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

‫א‬

‫א‬‫א‬

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

 K‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬ 

 W‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬  ‫א‬‫• א‬ ‫• א‬

 ‫א‬ •

 K‫א‬‫א‬ •



K٪100‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬   ٤W‫א‬‫א‬ 

 W‫א‬‫א‬ K‫א‬ • K‫א‬ •

  W‫א‬‫א‬  ١J ‫א‬

- ٣٨ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

 ‫א‬K١

‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬

 W‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬ •

.‫• ﺕﺴﺘﺨﺪم ﻓﻲ ﻋﻤﻠﻴﺎت اﻟﺤﺼﺮ اﻟﺰراﻋﻲ‬

K‫א‬‫א‬‫א‬ • K‫א‬ •

K‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬ • K‫א‬‫א‬ •

 W‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬-1

‫א‬‫א‬‫א‬‫א‬‫א‬ -2  ‫א‬

 W‫א‬‫א‬‫א‬‫א‬‫א‬

.‫א‬‫א‬‫א‬‫א‬ :‫ א‬-1 K‫א‬‫א‬‫א‬ :‫ א‬-2

‫א‬‫א‬‫א‬W‫ א‬-3 K‫א‬

‫א‬‫א‬‫א‬W  ‫א‬‫ א‬-4  K‫א‬‫א‬

- ٣٩ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

 .2 .‫א‬‫א‬‫א‬‫א‬ :‫א‬

 W

‫א‬‫א‬‫א‬‫א‬‫א‬W ‫א‬‫• א‬  K

 K‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫• א‬

 K‫א‬‫א‬W‫א‬‫• א‬

 K‫א‬‫א‬‫א‬W‫א‬‫• א‬

‫א‬‫א‬‫א‬‫א‬

 K‫א‬

 W

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬‫א‬

 K

 K‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬

 ‫א‬

 

 K‫א‬

‫א‬‫א‬(1.3‫א‬FE‫א‬F‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 - ٤٠ -

•

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

 ‫א‬:1.3‫א‬

‫א‬‫א‬‫א‬E‫א‬F‫א‬ •  K‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬ • KE2.3‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬ :2.3 ‫א‬

 ‫א‬.3

‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬E‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬ 

‫א‬‫א‬ .١٫٣

 K‫א‬‫א‬ 

 W‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬K - ٤١ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

‫א‬‫א‬W‫א‬

J 

 K‫א‬‫א‬ ‫א‬W‫א‬ J  

‫א‬‫א‬K‫א‬‫א‬

W

 K‫א‬‫א‬ •  K‫א‬‫א‬ •

 K١٢٠٣٠‫א‬‫א‬ •

 K‫א‬‫א‬‫א‬‫א‬ •

 K‫א‬‫א‬‫א‬‫א‬ •

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬ 

 W‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬



 K‫א‬‫א‬‫א‬‫א‬‫א‬ 

 K‫א‬‫א‬‫ א‬.2.3

‫א‬ • K‫א‬

 .(3.3‫א‬F‫א‬

- ٤٢ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

B 





 ‫א‬W3.3 ‫א‬

‫א‬‫א‬‫א‬ • K‫א‬

 KE4.3‫א‬F

2 E D C 



B A 1

 :4.3‫א‬

‫א‬‫א‬‫א‬‫א‬ • K‫א‬  WE5.3‫א‬F

- ٤٣ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

2 E D C 



B A 1



 :5.3‫א‬

‫א‬ •  E6.3‫א‬F‫א‬

   :6.3‫א‬

- ٤٤ -



 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

‫א‬ .٤

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬١٠٠٠‫א‬‫א‬١ 11000 

 ‫א‬ .1.4

 W‫א‬‫א‬

 ٢٠٠٠:١٥٠W١‫א‬-1

٥٠٠٠W١٥٠٠W١‫א‬ -2

١٠٠٠٠٠W١٥٠٠W١EF‫א‬‫א‬‫א‬‫א‬-3 ٥٠٠٠٠٠W١٢٥٠٠٠٠W١‫א‬‫א‬J 4

٥٠٠٠٠٠W١٢٥٠٠٠٠W١‫א‬-5

١٠٠٠٠٠٠W١٢٥٠٠٠٠W١‫א‬J 6 

 W‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ -1  K٥٠٠٠٠٠‫א‬

١٠٠٠٠٠٠W١٢٥٠٠٠٠W١‫א‬‫א‬ -2

٢٥٠٠٠٠W١٥٠٠W١‫א‬‫א‬-3

 ‫א‬‫א‬.٢٫٤

 W‫א‬‫א‬‫א‬‫א‬‫א‬ 

 Verbal statement ‫א‬‫א‬‫ א‬.1.2.4

‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬١٠٠٠‫א‬١WK‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬ 

- ٤٥ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

 Representative fraction ‫א‬‫ א‬.2.2.4

،٢،١‫א‬١‫א‬

 K١٠٨،٤،٢{٥ 

.... ، 1

1 1 1000 ، 100 ، 10  1 1 ......، 1 2000 ، 200 ، 20 1 1 ......، 1 2500 ، 250 ، 25 1 1 .....، 1 4000 ، 400 ، 40 1 1 .....، 1 5000 ، 500 ، 50 1 1 ....، 1 8000 ، 800 ، 80 

 W 

٥٠٠٠‫א‬٥٠٠٠‫א‬٥٠٠٠\١٥٠٠٠:١

 K‫א‬‫א‬‫א‬٥٠٠٠‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬ 

 ‫א‬‫ א‬.٣٫٢٫٤

‫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 K‫א‬

‫א‬،‫א‬‫א‬‫א‬

 W‫א‬‫א‬K‫א‬‫א‬‫א‬  J

 KJ - ٤٦ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 



Bar Scale or Graphic Scale ‫א‬‫א‬J 

‫א‬‫א‬،‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬  KE٧٫٣‫א‬F‫א‬‫א‬‫א‬



  :7.3‫א‬ 

Diagonal Scale ‫א‬‫ א‬-‫ب‬

‫א‬‫א‬‫א‬‫א‬‫א‬

 KE٨٫٣‫א‬F‫א‬‫א‬‫א‬‫א‬  

- ٤٧ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 



 KW8.3‫א‬ 

 ‫א‬‫א‬‫א‬‫ א‬.٥  .١٫٥

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬ 

 W‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫• א‬ ‫א‬‫א‬‫• א‬



 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  •

 • - ٤٨ -



 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

 ‫א‬‫א‬‫א‬K٢٫٥



 W 2 ‫ م‬‫א‬‫א‬ 1‫م‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬ 

 2 1‫م‬ 2 2‫م‬

‫م‬ 1 x‫א‬‫א‬Z‫א‬‫א‬ ‫م‬ 2

 x ‫א‬‫א‬Z‫א‬‫א‬

 W

K٥٠٠٢٠٠٠W١‫א‬٢٥٠٠W١  K‫؟‬٥٠٠٠W١‫א‬‫א‬ 

: ‫اﻟﺤﻞ‬



‫م‬ 1 x‫א‬Z‫א‬‫א‬ ‫م‬ 2



 ‫ ﻣﺘﺮ‬625 = 2500 x 1 x 500 = 1 x 3000



‫ ﺱﻢ‬12.5 = 100 x

625 Z‫א‬‫א‬ 5000



 ‫א‬‫א‬‫א‬K٣٫٥

‫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  - ٤٩ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

‫א‬‫א‬‫א‬EF‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬٩{٣‫א‬ 

  ‫א‬‫א‬‫א‬‫א‬W9.3‫א‬

- ٥٠ -

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



 ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 K‫א‬‫א‬‫א‬W‫א‬‫א‬

  W‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬  ‫א‬‫• א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬

 K‫א‬‫א‬‫• א‬

K‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬ • 

K٪100‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬   ٦W‫א‬‫א‬ 

  W‫א‬‫א‬  ١J ‫א‬

- ٥١ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

  .١

 WE١{٤‫א‬F‫א‬‫א‬ 

 K‫• א‬ K‫• א‬

K •

K‫• א‬

 



 W١{٤‫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

- ٥٢ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬،‫א‬ (Closed Traverse) ‫א‬ •



 ‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬

(Open Traverse) ‫א‬ •



‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ (Triangulation)  •



‫א‬‫א‬ 

 K‫א‬‫א‬

 

 ‫א‬‫א‬‫א‬‫ א‬.2

Magnetic Meridian ‫א‬‫ א‬.1.2

‫א‬‫א‬‫א‬‫א‬ ‫א‬،‫א‬‫א‬‫א‬‫א‬



 K‫א‬



Geographic Meridian ‫א‬‫א‬‫א‬K٢.2

‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬

 KE٣٫٤ ‫ و א‬٢٫٤‫א‬F

- ٥٣ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 K‫א‬‫א‬‫א‬‫א‬‫א‬:٢٫٤‫א‬ 

 ‫א‬‫א‬‫א‬‫ א‬:٣٫٤‫א‬ - ٥٤ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

Arbitrary or Assumed Meridian ‫א‬‫ א‬.3.2

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬ 

‫א‬ .٣

Azimuth‫א‬‫א‬‫א‬‫• א‬



 ‫א‬‫א‬‫א‬‫א‬W٤{٤‫א‬ 

‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬E  ‫א‬F‫א‬‫א‬‫א‬

 KE٤{٤‫א‬F٣٦٠‫א‬‫א‬،٣٦٠‫א‬  Bearing ‫א‬‫א‬‫א‬‫• א‬



‫א‬FJ  J  ‫א‬‫א‬ 

K  ‫א‬‫א‬٩٠‫א‬‫א‬‫א‬‫א‬‫א‬ KE٥{٤

‫א‬‫א‬‫א‬‫א‬‫א‬٩٠‫א‬‫א‬،‫א‬‫א‬

 KE٩٠FW‫א‬‫א‬ - ٥٥ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬



 ١٠٢

 ‫א‬

 

 

 ‫א‬‫א‬‫א‬‫א‬‫א‬W٥{٤‫א‬

 W‫א‬  W‫א‬  W‫א‬

 W‫א‬ 

 K??‫א‬??‫א‬??‫א‬??‫א‬W‫א‬ Deflection Angle‫א‬‫א‬‫א‬ •



 ‫א‬‫א‬‫א‬W٦{٤‫א‬

‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  KE٧{٤‫א‬F‫א‬‫א‬‫א‬‫א‬ - ٥٦ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

Angle to the Right ‫א‬‫א‬ •



 ‫א‬‫א‬W٧{٤‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 KE٧{٤‫א‬F‫א‬‫א‬‫א‬‫א‬ Interior Angles ‫א‬‫א‬‫ א‬‫א‬‫• א‬



KE٨{٤‫א‬F‫א‬ ‫א‬‫א‬‫א‬‫א‬

 E٢J F١٨٠W‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬J  



 ‫א‬‫א‬‫א‬‫א‬‫א‬W٨{٤‫א‬ 

: 

:(٩{٤‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ :١ 



- ٥٧ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 ‫א‬‫א‬‫א‬

‫א‬‫א‬

 ‫א‬

 ٤٠

‫ﺣـ‬



‫ﺟـ‬

‫ب ﺟـ‬

‫ش‬

‫ﺟـ د‬

‫ش‬

‫دأ‬

 ٣٠  ٣٥

 ٢٥



 ‫א‬‫א‬W٩{٤‫א‬

 ١٤٠Z٤٠–١٨٠Z‫א‬‫א‬‫א‬‫א‬

 ٢١٠Z٣٠H١٨٠Z‫א‬‫א‬‫א‬‫א‬  ٣٢٥Z٣٥–٣٦٠Z‫א‬‫א‬‫א‬‫א‬  K٢٥Z‫א‬‫א‬‫א‬‫א‬ 

.‫א‬‫א‬E١٠{٤‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ :٢ 

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K١١٠

- ٥٨ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬



 ١٠٢

 ‫א‬

 

 

 ‫א‬‫א‬W١٠{٤‫א‬

 

‫א‬‫א‬‫א‬‫א‬  

 ٩٢

 ٧٨





 ١٢٠



 ٢٠٨



 ٤٢





:‫א‬

 ١١٠Z‫א‬‫א‬‫א‬

 ٨٠Z١١٠–١٨٠Z١‫א‬‫א‬

 ٣٢Z٧٨–٨٠–١٨٠Z٢‫א‬‫א‬

 ٢١٢Z٣٢H١٨٠Z‫א‬‫א‬‫א‬  ٨٨Z٣٢–١٢٠Z١‫א‬‫א‬

 ٢٧٢Z٨٨–٣٦٠Z‫א‬‫א‬‫א‬

 ٥٠Z٤٢–E٨٨–١٨٠FZ‫א‬‫א‬‫א‬  ١٥٨Z٥٠–٢٠٨Z١‫א‬‫א‬

- ٥٩ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 ٢٢Z١٥٨–١٨٠Z١‫א‬‫א‬‫א‬ 

‫א‬،E١١{٤‫א‬F  ‫א‬‫א‬‫א‬‫א‬‫א‬ :٣   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬



 

 ٩٠

 ١٣٠  ٢٠

 ١٢٠



 ‫א‬‫א‬W١١{٤‫א‬









 W‫א‬‫א‬‫א‬ 

 ٩٠Z

 ١٣٠Z

 ٣٤٠Z٢٠–٣٦٠Z

 ١٦٠Z 

 W‫א‬‫א‬‫א‬‫א‬‫א‬ 

 ٩٠Z٩٠–١٨٠Z - ٦٠ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 ٥٠Z١٣٠–١٨٠Z

 ٢٠٠Z٢٠H١٨٠Z  ٢٠Z١٦٠–١٨٠Z 

،‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ ، (١٢٫٤ ‫ )א‬‫א‬ :٤  . 84ο 27′ 45′′ ‫و‬

28ο 40′ 30′′ 

:‫א‬



 W١٢٫٤‫א‬



: ‫ ﺟـ‬ ‫ ب‬‫א‬‫א‬ 



40′ 30′′

84 27′ 45′′ ___________ ο

111ο 67′ 75′′

 

- ٦١ -



112 ο 8′ 15′′ 

112 ο 8′ 15′′ - 180 ο = ‫ أ‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

‫א‬‫א‬.٤

 W‫א‬‫א‬  (Compass) ‫ א‬.١٫٤

‫א‬‫א‬‫א‬‫א‬

.‫א‬‫א‬    

:‫א‬‫א‬‫א‬ -‫أ‬

Graduated circle   ‫א‬ Magnetic Needle   :‫א‬

 Sighting marks ‫و‬

Compass Forms

‫א‬ -‫ب‬

 W‫א‬ 

Surveyor's Compass‫א‬J

 Prismatic Compass‫א‬‫א‬J 

Surveyor' s Compass ‫א‬ .١-‫ب‬

 W‫א‬‫א‬‫א‬‫א‬

 ‫א‬ • F‫א‬

‫א‬‫א‬‫א‬E‫א‬

 K‫א‬‫א‬‫א‬

‫א‬  • KE‫א‬‫א‬F‫א‬

‫א‬‫א‬‫א‬‫א‬(Two levels)‫א‬‫א‬‫• א‬ K

- ٦٢ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

‫א‬‫א‬‫א‬‫א‬‫א‬ •

‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬



 ‫א‬‫א‬‫א‬J

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E  ‫א‬F‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬S‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬J  ‫א‬F‫א‬‫א‬‫א‬

‫א‬‫א‬J  ‫א‬‫א‬‫א‬KE ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬AB‫א‬K  ‫א‬‫א‬‫א‬٩٠  W‫א‬‫א‬،‫א‬‫א‬

E ‫א‬‫א‬F‫א‬‫א‬ •

‫א‬ A‫א‬‫א‬

 KE‫א‬FBE‫א‬‫א‬F‫א‬



‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ • S‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬٦٥‫א‬‫א‬‫א‬‫א‬ (W)‫א‬EF KS٦٥ W‫א‬‫א‬ 

Prismatic Compass ‫א‬‫ א‬٢ -‫ب‬

 W‫א‬‫א‬‫א‬‫א‬‫א‬

١٥-٦ ‫א‬‫א‬‫א‬ (Compass Box)  • ‫א‬‫א‬‫א‬

 K‫א‬‫א‬

- ٦٣ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 



‫א‬ Pivot‫א‬ •  

K  ‫א‬‫א‬‫א‬،Compass Ring‫א‬ •

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬٣٦٠‫א‬٢٧٠‫א‬١٨٠ ٩٠

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬

 ١٨٠‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬

Prism •



K‫א‬‫א‬‫א‬

KObject Vane •

‫א‬‫א‬ Leveling Bubble • K‫א‬

 ‫א‬‫א‬‫א‬‫א‬J

،ABWhole Circle Bearing or Azimuth‫א‬‫א‬‫א‬‫א‬

Reference ‫א‬‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬KMeridian

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(A)

‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬



‫א‬‫א‬K ‫א‬  ‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬ 

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 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

EBF‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬KAB‫א‬‫א‬‫א‬‫א‬ 

Plane Table ‫א‬‫ א‬.٢٫٤

‫א‬‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬

‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

Sextant ‫ א‬.٣٫٤

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

Optical Square ‫א‬‫ א‬.٤٫٤

،٤٥‫א‬‫א‬،E١٣{٤‫א‬F‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬K

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K  ‫א‬

 K‫א‬

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 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬



 ١٠٢

 ‫א‬

 

 



 ‫א‬‫א‬W١٣{٤‫א‬ 

K  ‫א‬ ‫א‬‫א‬،‫א‬

K   K  ‫א‬‫א‬‫א‬K   ‫א‬

،‫א‬‫א‬،‫א‬‫א‬‫א‬

 K‫א‬ K‫א‬‫א‬

 E‫א‬F‫א‬‫א‬K٥٫٤

،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬

‫א‬K ‫א‬‫א‬‫א‬

 W

‫א‬‫א‬‫א‬‫א‬‫א‬  Transit ‫א‬‫א‬J

 K

 E‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬J

 K‫א‬‫א‬١٤{٤‫א‬K‫א‬‫א‬‫א‬ 

- ٦٦ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 METLAND FET 110‫א‬W١٤{٤‫א‬



 K‫א‬،‫א‬،‫א‬‫א‬W‫א‬‫א‬‫א‬ ‫א‬‫א‬‫ א‬



 WEAlidadeF‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬ E‫א‬‫א‬F‫א‬‫• א‬ ‫א‬ •

‫א‬‫• א‬

‫א‬‫א‬‫א‬E  ‫א‬‫א‬F‫א‬‫א‬ • ‫א‬‫א‬W  ‫א‬‫א‬‫א‬

،EVerticalFV‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬

KEHorizontalF(HzF  ‫ א‬-

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬ - ٦٧ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 ‫א‬ -

 W

‫א‬‫א‬‫א‬‫• א‬

‫א‬‫א‬EOptical PlummetF‫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‫א‬‫א‬‫א‬  ‫א‬ •

 W‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬K١ ‫א‬‫א‬،‫א‬‫א‬  K‫א‬

‫א‬‫א‬‫א‬‫א‬K٢ K‫א‬‫א‬

‫א‬‫א‬‫א‬E‫א‬‫א‬F‫א‬‫א‬K٣ K‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K٤ K‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬K٥ K‫א‬‫א‬ ‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬KK١

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K٢ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ - ٦٨ -



 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 ‫א‬‫א‬ •



 WE١٥٫٤‫א‬F‫א‬‫א‬‫א‬ EVF‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬

EAzF‫א‬‫א‬‫א‬‫א‬‫• א‬

‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬K‫א‬‫א‬‫א‬K‫א‬‫א‬

 K‫א‬‫א‬191.96،‫א‬‫א‬87.25 ‫א‬ 



 Wild‫א‬‫א‬‫א‬‫א‬W١٥{٤‫א‬  E‫א‬‫א‬‫א‬F

- ٦٩ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 ‫א‬‫א‬ •

 ‫א‬‫א‬،E  ‫א‬F‫א‬‫א‬‫א‬

‫א‬‫א‬K

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬

K ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬K ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

Calculation of Coordinates

‫א‬‫א‬K٥

‫א‬‫א‬E١٦٫٤‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬،‫א‬K‫א‬

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬ ∆ E = D Sin θ  ij ij ij     ∆ N ij = D ij Cos θ ij   

N j ∆Nj

θij

Dij

i E ∆Eij

Ei Ej

‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬:١٦٫٤‫א‬ E = E + ∆ E  i ij   j    N j = N i + ∆ E ij    - ٧٠ -

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

، ‫ﺣﻴﺚ أن‬  i‫א‬‫א‬‫א‬

i ‫א‬‫א‬‫א‬

j ‫א‬‫א‬‫א‬

j‫א‬‫א‬‫א‬

ij‫א‬‫א‬‫א‬

j ‫ و‬i ‫א‬‫א‬

Ej Nj

θ ij D ij

 W 1

D = ∆ E 2 + ∆ N 2  2 ij  ij ij 

∆E ij 1  θ ij = tan ∆N ij



- ٧١ -

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



 ‫א‬‫א‬

‫א‬‫א‬

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

‫א‬‫א‬‫א‬ ‫א‬‫א‬W‫א‬‫א‬  K‫א‬ 

 W‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬  K‫א‬‫• א‬ K‫א‬‫• א‬

 K‫א‬ •

 K‫א‬ •



K٪100‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬   ٧W‫א‬‫א‬ 

  W‫א‬‫א‬  ١J ‫א‬

- ٧٢ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

 .1 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K  ‫א‬‫א‬‫א‬

‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬K‫א‬‫א‬K،

 Trigonometric Leveling ‫א‬‫א‬‫א‬

 Checkerboard leveling ‫א‬‫א‬‫א‬

 Differential Leveling ‫א‬‫א‬‫א‬ 

  .2

‫א‬‫א‬ ‫א‬W‫א‬‫• א‬

‫א‬‫א‬‫א‬K  ‫א‬‫א‬

 K‫א‬

‫א‬‫א‬‫א‬W  ‫א‬ •

‫א‬‫א‬K  ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬

 KE١٫٥‫א‬F‫א‬‫א‬‫א‬‫א‬



K‫א‬‫א‬W١{٥‫א‬

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

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

K ‫א‬‫א‬‫א‬‫א‬‫א‬W ‫א‬ • ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬  KE٢٫٥‫א‬F‫א‬

 ‫א‬W٢٫٥‫א‬

 A‫א‬

 B‫א‬  C‫א‬ 

Bench Marks : ‫א‬‫א‬ •

 ‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬  ‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬  K‫א‬

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 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

‫א‬‫ א‬.٣

‫א‬ ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫א‬K  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 KE٣٫٥‫א‬F‫א‬‫א‬‫א‬

C B  

   ‫א‬

‫א‬

‫א‬‫א‬

A 

 ‫א‬‫א‬ :3.5‫א‬  

CE = DC sin α



 AB = AD + CE – BC



 WDE

 WCE

 WBA‫א‬

 A‫א‬‫א‬‫א‬WAB

 K‫א‬‫א‬B‫א‬‫א‬WBC 

 K٣٠٠‫א‬‫א‬

 W

B‫א‬300‫א‬‫א‬50,60 ‫א‬‫א‬‫א‬

‫א‬‫א‬1,40‫א‬‫א‬،245,00A‫א‬  K2,35

- ٧٥ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

DC α= AD BC

:‫א‬

= 50,25 m 300 = 1,40 m = 2,35 m



CE = DC sin α CE = 50,60 sin (300) = 25,30 m AB = AD + CE –BC AB = 1,40 + 25,30 – 2,35 = 24,35 m.

 B‫א‬

 K269.35= 24,35H245,00 

 ‫א‬‫א‬4K

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬ 

 ‫א‬‫א‬.1.4

‫א‬ ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬E  F  KE٤٫٥‫א‬F‫א‬‫א‬‫א‬

- ٧٦ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 



 ‫א‬‫א‬ :4.5‫א‬

K ‫א‬‫א‬BA‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 Kab‫א‬

 Aa‫א‬‫א‬‫א‬Wa

 Bb‫א‬‫א‬‫א‬Wb  W‫א‬

 b - a = ∆ z ‫א‬‫א‬

 b–aHAZB

 bJ aHZAZ ZB 

 ‫א‬‫ א‬.2.4  WE٥٫٥‫א‬F‫א‬‫א‬  

- ٧٧ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 



 METLAND‫א‬‫א‬W٥٫٥‫א‬

 ‫א‬‫א‬

 ‫א‬‫א‬

 ‫א‬‫א‬

 ‫א‬‫ א‬E

‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬ 

 ‫א‬‫א‬ :٥٫٥‫א‬

 ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬

J ١ J ٢

٣‫א‬‫א‬

 ‫א‬‫א‬J ٤  ‫א‬‫א‬J ٥

- ٧٨ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 



 ‫א‬‫א‬:٦٫٥‫א‬ 

 ‫א‬‫א‬‫א‬J ٦ 

 W‫א‬‫א‬ •

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬E٤F‫א‬ 

 W‫א‬‫א‬J 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬K‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬

 .(UF 

- ٧٩ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 



 ‫א‬‫א‬‫א‬‫א‬W٧{٥‫א‬ 



 ‫א‬‫א‬‫א‬‫א‬‫א‬W٨{٥‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬J 

‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬K‫א‬‫א‬‫א‬  W‫א‬‫א‬

- ٨٠ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬K‫א‬‫א‬

 V1‫א‬V1V2‫א‬ ‫א‬‫א‬F‫א‬‫א‬V1‫א‬V1 V′ ‫א‬ 1  KE٩٫٥ 

 ‫א‬‫א‬W٩{٥‫א‬



‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬

 ‫א‬K3K4 ٥٣‫א‬‫א‬‫א‬‫א‬

‫א‬K KE١٠٫٥‫א‬F‫א‬‫א‬

 K‫א‬   

- ٨١ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

 ‫ א‬:١٠٫٥ ‫א‬

‫א‬‫א‬‫א‬‫א‬

،‫א‬‫א‬‫א‬‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬  W



‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬ 

- ٨٢ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 



 W‫א‬

W‫א‬‫א‬  K

٩٠W‫א‬  K‫א‬١٠

 KW‫א‬‫א‬  ‫א‬Z‫א‬K

 ‫א‬ZKK

 KKKKKKK‫א‬ZKKK

  ‫א‬ : ١٠٫٥‫א‬



 ‫א‬‫א‬‫א‬‫א‬‫א‬W١١{٥‫א‬

- ٨٣ -



 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

W‫א‬‫א‬

‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬K‫א‬ ‫א‬

E

‫א‬‫א‬‫א‬‫א‬‫א‬K‫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

 K‫א‬

 : ‫ب( اﻟﻘﺮاءة ﻋﻠﻰ اﻟﻘﺎﻣﺔ‬



 ‫א‬‫א‬١٢{٥‫א‬ 



 W‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K(UF‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬    - ٨٤ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

 ‫א‬‫א‬‫א‬١٣{٥‫א‬ 0

‫א‬‫א‬

N0 2

N0 1

‫א‬‫א‬

‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬

0,225

0,763

1,397

‫א‬‫א‬ ‫א‬‫א‬ :١٫٥ ‫اﻟﺠﺪول‬



 W‫א‬‫א‬‫א‬

‫א‬K  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬100 ‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬ 

- ٨٥ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

  ‫א‬‫א‬‫א‬‫א‬ : ١٤٫٥ ‫א‬



 ‫א‬‫א‬٢{٥‫א‬



3

2

1

‫א‬‫א‬‫א‬

2075

1404

890

 ‫א‬‫א‬‫א‬

 2075 4150

 1404 2208

 890 1780

 ‫א‬

2275 1875

1468 1338

990 790

400  L40000 L40

130 L13000 L13

200  L20000  L20

‫א‬

 ‫א‬‫א‬ ‫א‬‫א‬

‫א‬ 100x‫א‬ 

‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬K‫א‬

 K

- ٨٦ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

‫א‬ .٥



 KW١٥{٥‫א‬  WA‫א‬‫א‬B‫א‬‫א‬

 K‫א‬B‫א‬A‫א‬‫א‬‫א‬  a‫א‬‫א‬A‫א‬‫א‬  b‫א‬‫א‬A‫א‬‫א‬

 B‫א‬A‫א‬‫א‬‫א‬‫א‬ 

 K‫א‬‫א‬‫א‬‫א‬‫א‬a‫א‬‫א‬

 K‫א‬‫א‬‫א‬b‫א‬‫א‬ 

 b - a = ∆ z ‫א‬‫א‬

 –Z‫א‬‫א‬

 K،‫א‬‫א‬ 

- ٨٧ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

  ‫א‬‫א‬W١٦{٥‫א‬



 ‫א‬‫א‬‫א‬W١٧{٥‫א‬   

- ٨٨ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 



 ‫א‬‫א‬‫א‬W١٨{٥‫א‬ 

‫א‬‫א‬‫ א‬.١٫٥

K‫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  K‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬K ‫א‬‫א‬‫א‬

A ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬KB‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬B‫א‬‫א‬‫א‬‫א‬‫א‬A

‫א‬B‫א‬‫א‬C‫א‬B‫א‬‫א‬

C‫א‬‫א‬‫א‬‫א‬C‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

- ٨٩ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 



 ‫א‬‫א‬‫א‬W١٩{٥‫א‬ 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬  ‫א‬‫א‬W  ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬

 W



 ‫ یﺒﻴﻦ اﻟﻤﻴﺰاﻥﻴﺔ اﻟﻔﺮﻗﻴﺔ اﻟﻤﻘﻔﻠﺔ‬:٢٠٫٥ ‫اﻟﺸﻜﻞ‬  ‫א‬

167,280 167,602 167,936 167,091 167,277

‫א‬

0,322 0,334 -0,845 0,186 -0,003

EJ F‫א‬

EHF‫א‬

1,310 1,183 1,731 1,489 5,713

5,710

1,632 1,517 0,886 1,675

‫א‬ R 1 2 3 R

 - ٩٠ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

-0,003=5,713-5,710 -0,003=167,28-167,277  3 =‫א‬‫א‬‫א‬

‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬

‫ﻃﻮل اﻟﻤﻴﺰاﻥﻴﺔ ﺏﺎﻟﻜﻴﻠﻮﻣﺘﺮ‬

 ZEF‫א‬‫א‬ 

 W‫א‬‫א‬‫א‬

 5=‫א‬‫א‬‫א‬

10 = ‫א‬‫א‬‫א‬

 20 = ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬ 

:‫א‬‫א‬‫ א‬.2.5

‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬

،B ‫א‬‫א‬A‫א‬‫א‬ 1A‫א‬‫א‬

W‫א‬‫א‬

 2B‫א‬‫א‬

W‫א‬‫א‬

 3C‫א‬‫א‬

W‫א‬‫א‬

1B‫א‬‫א‬

 2C‫א‬‫א‬



 3D‫א‬‫א‬ - ٩١ -

 KDC



 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 



‫א‬‫א‬‫א‬ :١٩٫٥ ‫اﻟﺸﻜﻞ‬ 

 ‫א‬.6

‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬30 ‫א‬ ‫א‬

 K30‫א‬ 

 ‫א‬‫א‬.1.6

 W‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •

‫א‬ •  K‫א‬

‫א‬‫א‬‫א‬ •  K

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •  K‫א‬‫א‬‫א‬ • - ٩٢ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ • ‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬



 ‫א‬‫א‬ .2.6

‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬-1

 ‫א‬‫א‬  ‫א‬‫א‬ •

 ‫א‬‫א‬‫א‬W‫• א‬

‫א‬‫א‬‫א‬‫א‬W  ‫א‬ •  ‫א‬

‫א‬‫א‬W ‫א‬ •  ‫א‬



 ١‫א‬‫א‬W٢٠٫٥ ‫א‬ - ٩٣ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬‫א‬

 

 

 .3.6

 W‫א‬‫א‬

W‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬ •

 ‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬ W‫א‬

 K‫א‬

‫א‬‫א‬‫א‬W ‫א‬‫א‬ •

‫א‬‫א‬،‫א‬

‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬W‫א‬ • K‫א‬‫א‬

 W‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫• א‬

‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫• א‬

 K‫א‬‫• א‬

   

- ٩٤ -



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



 ‫א‬‫א‬‫א‬

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

‫א‬‫א‬W‫א‬‫א‬  K‫א‬ 

 W‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬ •



K‫א‬‫א‬‫• א‬ K‫א‬‫א‬‫א‬‫• א‬ K‫א‬‫• א‬

 K‫א‬ •



  W‫א‬‫א‬  ١J ‫א‬

- ٩٦ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

.1

‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬

‫א‬K ‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬

 K‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬‫• א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬ K‫א‬‫א‬‫א‬‫• א‬  ‫א‬‫א‬‫א‬K 2

 K‫א‬‫א‬‫א‬‫א‬‫א‬ 

‫• א‬

 :١٫٦‫א‬  V = a3

 W

 ‫א‬a  ‫א‬V

- ٩٧ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

‫א‬‫א‬ •

 ‫א‬‫א‬:٢٫٦‫א‬ 

 V=bLh

 W

 ‫א‬Zb



 ‫א‬= L

 ‫ = א‬h

 K‫א‬‫א‬ =V ‫א‬‫• א‬

 ‫א‬‫א‬:٣٫٦‫א‬  V = 1 S h 3

- ٩٨ -



 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 W

 ‫א‬ZS

 ‫א‬Zh

 K‫א‬‫א‬=V ‫א‬‫• א‬



 ‫א‬‫א‬:٤٫٦‫א‬ 

 V = h  S + S + S S  1 2 3 1 2 

 W

 ‫א‬ZS1 

‫א‬= S2

 ‫א‬Zh

 K‫א‬‫א‬=V

  

- ٩٩ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 ‫א‬‫• א‬



 ‫א‬‫א‬:٥٫٦‫א‬ 

 V = π r2 h 

 W

 ‫א‬Zr

 ‫א‬Zh

 ‫א‬‫א‬=V



 ‫א‬‫• א‬  

 ‫א‬‫א‬:٦٫٦‫א‬ 

- ١٠٠ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 V = 1  π h r 2  3   W

 ‫א‬Zr  ‫א‬Zh

 ‫א‬‫א‬=V 

‫א‬‫• א‬ 

  ‫א‬‫א‬:٧٫٦‫א‬ 

 V = π  r 2 + r 2 + r r  h 3  1 2 1 2  W

 ‫א‬Zr1

 ‫א‬Zr2

 ‫א‬Zh    

- ١٠١ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 ‫א‬‫• א‬ 



 ‫א‬‫א‬:٨٫٦‫א‬   

V= 1 bLh 2

 W

 ‫א‬Zb

 ‫א‬ZL  ‫א‬Zh

 W‫א‬‫• א‬

 ‫א‬‫א‬:٩٫٦‫א‬ 

- ١٠٢ -



 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 V= 1 2

  

S + S  h 1 2



 W

 ‫א‬ZS1

 ‫א‬ZS2

 ‫א‬Zh 

 W‫א‬‫א‬S2‫א‬S1‫א‬ ‫א‬‫א‬ 

 V = h  S + S + 4S 2  6  1

 W

 ‫א‬ZS1

 ‫א‬ZS2

 h‫א‬‫א‬‫א‬ZS  ‫א‬Zh

 K‫א‬‫א‬ZV W‫א‬‫א‬‫א‬‫א‬ • 

  ‫א‬‫א‬‫א‬‫א‬ :١٠٫٦‫א‬ 

- ١٠٣ -



 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 



 V =S

    

h + h + h + h  1 2 3 4  4  

 W

 ‫א‬ZS

 ‫א‬‫א‬h4 h3، h2،h1 

‫א‬‫א‬‫א‬‫א‬ • 



 ‫א‬‫א‬‫א‬‫א‬:١١٫٦‫א‬

 V =S

    

h + h + h  1 2 3  3  

 W

 ‫א‬ZS

 ‫א‬‫א‬ h3، h2،h1 

 K‫א‬‫א‬‫א‬‫א‬-V - ١٠٤ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 

 W1

‫א‬‫א‬(22,00)E40,00F

 K‫א‬‫א‬‫א‬‫א‬15 x 30‫א‬‫א‬10 x 20‫א‬

 ‫א‬W‫א‬‫א‬

 W

 ‫א‬‫א‬ZS1

 ‫א‬‫א‬ZS2

 ‫א‬Zh

K‫א‬‫א‬‫א‬ZV 

V =  S + S  h 2 2  1  



450 =30 x 15ZS1

200 = 20 x 10ZS2

 18 = 40,00-22,00Zh  3 5850 = (450 +200) x  18 ZV 2  3 ‫ م‬5850 = V  ‫א‬W‫א‬‫א‬

 ‫א‬‫א‬ZS

 S=

 30 + 20     2  



 15 + 10     2  

 S = 25 . 12,5 = 2‫ م‬312.5  - ١٠٥ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 V= h 6

  

 ١٠٢

 ‫א‬

 

 

S + S + 4S 1 2 

 V = 18 (450 + 200 + 4 . 312,5) = 3‫ م‬5700 6



 V = 3‫ م‬5700



‫א‬‫א‬‫א‬‫א‬٪2,63 150‫א‬‫א‬

 K‫א‬‫א‬

 W2

‫א‬24،32  ‫א‬‫א‬‫א‬

‫א‬ 5‫א‬‫א‬ 812‫א‬‫א‬9‫א‬  K‫א‬‫א‬‫א‬، 6‫א‬‫א‬‫א‬

 K‫א‬W‫א‬‫א‬ 2

(24 + 32) = S1 2 (8 + 12) 2 ‫ م‬50 = 5 x = S2 2

‫ م‬252 = 9 x

 ٣

906= (50 + 252)

h 6 = (S + S ) = V 2 1 2 2

 

 ‫א‬W‫א‬‫א‬ 

1  9 + 5   8 + 24   12 + 32  ‫م‬133=  x  +  = S 2  2   2   2 

  ‫א‬

8 + 24  12 + 32 ‫א‬‫א‬Z S 2 2  K‫א‬ 9 + 5 2  3834= (133 x4 + 50 + 252) 6 = (S x 4 + S + S ) h = V 2 1 6 6 - ١٠٦ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬ 

 W‫א‬‫א‬‫א‬‫א‬.3

‫א‬‫א‬‫א‬Profiles‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬

 :١٢٫٦‫א‬ 

 K‫א‬‫א‬‫א‬‫א‬‫א‬



 :١٣٫٦‫א‬ 

‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ -1  ‫א‬‫א‬‫א‬‫א‬ -2

 ‫א‬‫א‬‫א‬J 3

- ١٠٧ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 ‫א‬‫א‬-4

 W‫א‬W  ‫א‬‫א‬‫א‬‫א‬ • ‫א‬‫א‬‫א‬ •

 W‫א‬‫א‬

 ‫א‬‫א‬1.2=‫א‬‫א‬

 ‫א‬‫א‬1.1=‫א‬‫א‬ 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ‫א‬‫א‬:١٤٫٦‫א‬



 L +L L +L L L L +L 3 4 2 3 1 1 2 )+S x 4  V =S x +S ( )+S ( )+S ( 5 2 4 1 2 2 3 2 2 2 

 ‫א‬‫א‬=V

- ١٠٨ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

‫א‬‫א‬‫א‬‫ א‬.4

K  ‫א‬‫א‬‫א‬

،h2،h1‫א‬‫א‬‫א‬

‫א‬ ‫א‬‫א‬‫א‬ h4،h3  W‫א‬‫א‬‫א‬ 

h +h +h +h 3 2 1) S= V  ( 4 4 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬

 W‫א‬‫א‬‫א‬ 

  V = S ( h + 2 h + 3 h + 4 h + ...... + n h n ) 2 3 4 4 1  

 ‫א‬‫א‬‫א‬‫א‬J S

 ‫א‬‫א‬‫א‬‫א‬‫א‬-h1

 KE‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬-h2

 KE‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬-h3  KE‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬-h4  KE‫א‬n‫א‬‫א‬F‫א‬n‫א‬‫א‬‫א‬‫א‬J hn

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

 V = S ( h + 2 h + 3 h + 4 h + ...... + n h n ) 1 2 3 4 3

- ١٠٩ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

: 

‫א‬‫א‬40‫א‬111‫א‬ ‫א‬‫א‬‫א‬‫א‬  KE6,00F‫א‬



 :١٥{٦‫א‬

‫א‬    ‫א‬‫א‬‫א‬

 K‫א‬

0.60 0.80

1.40

2 0.4 0.20 0.40 0.20   0.60 1.80

 ‫א‬‫א‬‫ א‬:١٫٦ h 1

0.8   0.4 0.4 1.60

‫א‬ 

 V=S(h +2h +4h ) 2 4 4 1 2 ‫ م‬740 = 20 x 37 = S - ١١٠ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 V = 740 ( 1.60 + 2 x 1.80 + 4 x 1.40) 4 3 ‫ م‬1998 = V 

‫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20  KE3,80F‫א‬ 

  :١٦٫٦‫א‬

- ١١١ -



 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 ‫א‬‫ א‬:٢٫٦ h

7 1.90 2.20

4.10

6 J

5  1.50

4 1.20

3 1.70 2.20 0.80 1.50

1.50

1.20

6.20

2 1.00 2.60 3.00 1.30  1.70 2.40 12.00



h 1 0.4

0.4 ‫א‬

200 = 1 x 20x20=S 2  V = S (h + 2h +3h + 4h +5h +6h +7h ) 5 7 2 3 4 6 3 1 

 V = 200 ( 0.4 + 2 x 12 + 3 x 6.20 + 4 x 1.20 + 5 x 1.50 + 0 + 7 x 4.10) 3 3 ‫ م‬5600 = V ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬K‫א‬ : 

‫א‬ ‫א‬40‫א‬111 ‫א‬

‫א‬‫א‬20x37 

 K‫א‬‫א‬E5,60F

- ١١٢ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬



 ١٠٢

 ‫א‬

 

 

 ‫א‬‫א‬:١٧٫٦‫א‬ 

 W‫א‬ 

   3 185=  0 + 0.40 + 0.20 + 0.4  x20x 37=EFV 4     3 83.25=  0.2 + 0.40 + 0 + 0  x( 10 + 20 )x 37=EFV 4 2     3 12.83=  0.20 + 0 + 0  x 10 x 37=EFV 3 2     3 83.25=  0.4 + 0.20 + 0 + 0  x( 10 + 20 ) x 37=EFV 4 2     3 55.5=  0.2 + 0.40 + 0 + 0  x10x 37=EFV 4     3 27.75=  0.2 + 0 + 0 + 0  x( 10 + 20 ) x 37=EFV 4 2    EFVHEFVHEFVHEFVHEFVHEFV=‫א‬

 27.75+55.50 + 83.25+12.33+83.25+185=‫א‬

 3447.08=‫א‬ 

- ١١٣ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 W‫א‬    3 12.33=  0.20 + 0 + 0  ( 10 x 37 )=E1FV 3 2     3 83.25=  0 + 0 + 0.4 + 0.2  x( 10 + 20 )x 37=E2FV 4 2     3 24.67=  0.40 + 0 + 0  x 10 x 37=E3FV 3 2     3 55.50=  0.2 + 0.40 + 0 + 0  x10 x 37=E4FV 4     3 12.33=  0.20 + 0 + 0  ( 10 x 37 ) =E5FV 3 2    E5FVHE4FVHE3FVHE2FVHE1FV=‫א‬  12.33+ 55.50 + 24.67+83.25+12.33=‫א‬  3188.08=‫א‬ 

‫א‬‫ א‬.5

‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬K  ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬ 6.00‫א‬‫א‬6.00  K6.00‫א‬‫א‬‫א‬6.00‫א‬‫א‬‫א‬

- ١١٤ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

  ‫א‬‫א‬:١٨{٦‫א‬

 

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 



E6.00FE7.00FE8.00F‫א‬‫א‬‫א‬J

 E7.00FE8.00F‫א‬‫א‬‫א‬J

‫ ﻣﺴﺎﺣﺔ‬+ (8.00) ‫ﻣﺴﺎﺣﺔ آﻨﺘﻮر‬ = 7 ← 8  2 (6.00) ‫ ﻣﺴﺎﺣﺔ آﻨﺘﻮر‬+ (7.00) ‫ ﻣﺴﺎﺣﺔ آﻨﺘﻮر‬= 6 ← 7   ‫א‬‫א‬x 2   6 ← 7 + 7 ← 8  = ‫א‬

 ‫א‬‫א‬x

(7.00)



‫آﻨﺘﻮر‬

E6.00F‫א‬‫א‬‫א‬E5.00F‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬ 

 E‫א‬‫א‬‫א‬‫א‬Fx[E6.00F‫א‬J E5.00F‫א‬] =‫א‬

- ١١٥ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 

:1 

‫א‬‫א‬

 W



٢٢٠Z١٧‫א‬‫א‬



٣٣٠Z١٦‫א‬‫א‬ ٤٤٠Z١٥‫א‬‫א‬

٥٥٠Z١٤‫א‬‫א‬ 

 K‫א‬‫א‬‫א‬‫א‬E١٥{٠٠F‫א‬‫א‬

 E١٥J ١٦FHE١٦J ١٧FZ‫א‬  

440 + 330 330 + 220 + 1x Z‫א‬ 2 2  ٣٦٦٠Z٣٨٥H٢٧٥Z‫א‬ 

 ٣٥٥Z 1 x

٣

٦٦٠Z‫א‬ 

440 − 550 Z‫א‬ 2 

 :٢ 

‫א‬‫א‬‫א‬‫א‬

 W‫א‬ 

 ٢١٣٠Z٢٦‫א‬ 

- ١١٦ -

٢٥٠Z٢٤‫א‬

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ١٠٢

 ‫א‬

 

   ٢

٣٦٠Z٢٢‫א‬ 



 

٤٨٠Z٢٠‫א‬ ٢

٥٦٠Z١٨‫א‬

٦٦٠Z١٦‫א‬

٧٨٠Z١٤‫א‬ 

 K‫א‬‫א‬‫א‬‫א‬(20.00F‫א‬‫א‬

 E٢٠٢٢FHE٢٢٢٦FHE٢٤٢٦FZ‫א‬

 ٨٤٠H٦١٠H٣٨٠Z‫א‬  ٣١٨٣٠Z‫א‬

 E٢٠١٤FHE٢٠١٦FHE٢٠١٨FZ‫א‬ 

 E

6+4 4+2 2 FE٦٦٠–٧٨٠FHE FE٥٦٠–٦٦٠FH E٤٨٠–٥٦٠FZ 2 2 2  ٦٠٠H٣٠٠H٨٠Z

 ٣٩٨٠Z

 ٣٩٨٠Z‫א‬ 

- ١١٧ -

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



‫א‬

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

 W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬ 

 W‫א‬‫א‬

 W‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬ •

 K‫א‬‫א‬‫א‬‫א‬‫א‬ •



K٪100‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬   ٨W‫א‬‫א‬ 

 W‫א‬‫א‬ ‫א‬ •

  W‫א‬‫א‬  ١J ‫א‬

        - ١١٨ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

 K١

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬

  ‫א‬K٢

 W‫א‬‫א‬  ‫א‬

J 

،‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬  ‫א‬‫א‬

J  



‫א‬‫א‬

 K

‫א‬ .٣

 W‫א‬‫א‬‫א‬‫א‬ 

 ‫א‬‫ א‬.١٫٣

Planimeter‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٫٧‫א‬‫א‬F  K‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬ 

- ١١٩ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 



 Placom KP 80W١{٧‫א‬



 K‫א‬‫א‬‫א‬‫א‬  W

 ‫א‬  ‫א‬   ‫א‬  ‫א‬   ‫א‬   • ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬

‫א‬‫א‬W‫א‬‫• א‬

 

 A = f (R f − Ri ) 

 ،

 EFinal ReadingF‫א‬‫א‬‫א‬J  R f  EInitial ReadingF‫א‬‫א‬‫א‬‫א‬J  R i ‫א‬f‫א‬‫א‬‫א‬،EInstrument FactorF‫א‬J f  K

 ‫א‬‫א‬‫א‬W‫א‬‫• א‬ - ١٢٠ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

 A = f (R f - R i ) + C Zero F‫א‬‫א‬C،

 K‫א‬‫א‬‫א‬ECircle ‫א‬‫ א‬.2.3

‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬،‫א‬،  K‫א‬‫א‬‫א‬ 

‫א‬‫א‬

‫א‬ ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬  W

Triangle ‫• א‬

 KArea   Area = S (S - a)(S - b)(S - c)

- ١٢١ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

a+b+c 2

، ‫ﺣﻴﺚ أن‬

SQUARE‫• א‬

 



 AB = BD = DC = CA = a 

‫د‬

 Area = a 2  RECTANGLE

‫• א‬

 

 - ١٢٢ -



 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

 AC = BD = a   BA = DC = b 

Area = a x b



Parallelogram ‫א‬‫א‬ •

 

  AB = DC = b 

 Area = b x h Trapezium

- ١٢٣ -

‫א‬ •



 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

Area = [(h1 +h2).b +a.h1 + c.h2]/2ِ 



 Area = [(h +h).b +a.h + a.h]/2 = b.h + a.hِ   

Area = (π.r2. θ)/360

Area = π.r2 

- ١٢٤ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

Area = (2.L.r )/3

Area = π.r1.r2

Area = r.L/2

Area = ِπ. r. r 2 + h 2 - ١٢٥ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

Area = ِ2 . π .r. h

Area = ِ π . s . (R + r)  

 ‫ א‬‫ א‬.3.3

‫א‬‫א‬‫א‬‫א‬

 W‫א‬

Trapezoidal Method ‫א‬ •



‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬ ‫א‬‫א‬  K‫א‬

- ١٢٦ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

 W٢{٧‫א‬  K‫א‬‫א‬J L 

 W ACDB‫א‬٧٫٢‫א‬   

h +h  Area = L. ( 1 n + h 2 + h 3 + h 4 + ..... + h n-1) 2 

:١ 

 K٧٫٣‫א‬  

 - ١٢٧ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

 W٣{٧‫א‬ 

 h n −1 = h 6  

h +h  Area = L. ( 1 7 + h 2 + h 3 + h 4 + h 5 + h 6 ) 2 

 W‫א‬‫א‬ 

 2 ‫ م‬1.06 = 2.16 x 0.81 = 1‫س‬ 2



 2 ‫ م‬1.11 = 2 x 1.11 = 2‫س‬ 2



 2 ‫ م‬2.17 = 2‫ س‬+ 1‫ س = س‬‫א‬ ‫أ‬ 

 K‫א‬

 W‫א‬ 

h +h  Area = L. ( 1 n + h 2 + h 3 + h 4 + ..... + h n-1) =‫א‬ 2 

 ،

 ‫א‬‫א‬‫א‬J

L



 ‫א‬‫א‬J h

 ‫א‬‫א‬J n

- ١٢٨ -



 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

 (2.50 + 3.03 + 4.05 + 4.51 + 4.18 + 3.48 + 3.52 + 2 + 2.61 ) 1.5 = ‫س ب‬ 2  

2‫ م‬41.36 = ‫سب‬



 W‫א‬‫א‬‫א‬

 2 ‫ م‬43.53 = 41.36 + 2.17 = ‫ س ب‬+ ‫س = س‬ ‫أ‬  Simpson‘s One Third Rule

 •

‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬  W 

 (4∑ ( ‫ )اﻷﻋﻤﺪة اﻟﺰوﺟﻴﺔ‬+ 2∑ ( ‫اﻟﻔﺮدیﺔ‬

L ‫ )اﻷﻋﻤﺪة‬+ h n + h ) =‫א‬ 1 3

 ‫א‬J

 ‫א‬J n  

:٢  

 W‫א‬‫א‬ 

 [(2.5 + 4.05 + 4.18 + 3.52 )4 + ( 3.03 + 4.51 + 3.48 )2 + 2 + 2.61)] 1.5 =‫א‬ 3



 2 ‫ م‬41.82 = ( 57 + 22.04 + 4.61) 1.5 =‫א‬ 3



2 ‫ م‬٤٣{٩٩Z٢{١٧H٤١{٨٢W‫א‬‫א‬‫א‬ - ١٢٩ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

 ‫א‬‫א‬K٤

 ‫א‬‫א‬‫א‬‫א‬‫א‬ •

‫א‬‫א‬،‫א‬EStationF‫א‬

‫א‬‫א‬‫א‬‫א‬٤٫٧‫א‬K‫א‬‫א‬‫א‬

 K٤،٣،٢،١‫א‬

 ‫א‬‫א‬‫א‬W٤{٧‫א‬  

 K‫א‬‫א‬‫א‬‫א‬‫א‬٥{٧‫א‬

- ١٣٠ -

 ‫א‬‫א‬

 ١٠٢

 ‫א‬

 ‫א‬

 

 

 ‫א‬‫א‬‫א‬‫א‬‫א‬W٥{٧‫א‬  ١‫א‬–٢‫א‬=‫א‬‫א‬

١‫א‬K 2′ 2 3 3′  3′ 3 4 4′ ‫א‬٢‫א‬  K 2′ 2 1 1′  1′ 1 4 4′ ‫א‬ 

 1 (X 4 + X 3 ) (Y4 − Y3 ) + 1 (X 3 + X 2 ) (Y3 − Y2 ) =٢‫א‬ 2 2 

 1 (X 4 + X1) (Y4 − Y1) + 1 (X1 + X 2 ) (Y1 − Y2 ) =١‫א‬ 2 2   ١‫א‬–٢‫א‬Z‫א‬‫א‬

Y =  ‫ و‬X = W ‫א‬‫א‬ 

 (( ‫ ع‬- ‫ س ( ) ع‬+ ‫ ) س‬+ ( ‫ ع‬- ‫ س ( ) ع‬+ ‫)) س‬ 1  2  2 3 2 3 3 4 3 4

= ‫א‬‫א‬

[ (( 2 ‫ ع‬- 1‫ ( ) ع‬2 ‫ س‬+ 1 ‫ ) س‬+ ( 1 ‫ ع‬- 4‫( ) ع‬1‫ س‬+ 4 ‫ ])) س‬12 − 

 ،‫א‬‫א‬



[ ( 3 ‫ ع‬- 1‫ ) ع‬4 ‫ س‬+ ( 2 ‫ ع‬- 4‫ ) ع‬3 ‫ س‬+ (1 ‫ ع‬- 3‫ ) ع‬2 ‫ س‬+ ( 4 ‫ ع‬- 2‫ ) ع‬1 ‫ ]) س‬12 =  

- ١٣١ -

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



‫א‬‫א‬

 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 W‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫ א‬‫א‬ 

 W‫א‬‫א‬  W‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬ •

 K‫א‬‫א‬‫א‬‫א‬ •

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬



 W‫א‬‫א‬ ‫א‬ •

  W‫א‬‫א‬ ١–‫א‬

- ١٣٢ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

 .١

‫א‬E١٫٨‫א‬F‫א‬‫א‬

،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬K ‫א‬‫א‬‫א‬‫א‬

 W،‫א‬ Horizontal Angle‫א‬‫א‬‫• א‬ Vertical Angle



‫א‬‫א‬‫• א‬

Slope Distance ‫א‬‫• א‬

 Horizontal Distance‫א‬‫• א‬

Vertical Distance‫א‬‫• א‬

‫ﻣﺘﻜﺎﻣ ﻞ‬Total Station ‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬ Electronic tacheometer ‫א‬‫א‬)

E ‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ (Data CollectorF

- ١٣٣ -

 ‫א‬‫א‬ ‫א‬‫א‬



 ١٠٢

 ‫א‬

 

 

 ‫א‬‫א‬:١٫٨‫א‬

 

‫א‬‫א‬‫א‬‫א‬ .٢  W‫א‬‫א‬ K‫א‬‫• א‬

KEKKK‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬F‫א‬‫• א‬ KE‫א‬F‫• א‬

K‫א‬‫א‬ •

K‫א‬‫א‬‫• א‬ ‫ ﻣﺴﺎوئ اﺳﺘﺨﺪام أﺟﻬﺰة اﻟﻤﺤﻄﺔ اﻟﺸﺎﻣﻠﺔ‬.٣  W‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬ • KEEDMF‫א‬

- ١٣٤ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

EF‫א‬‫א‬ • K‫א‬



‫א‬‫א‬‫א‬ (Traversing) ‫ א‬.٤ ‫א‬‫א‬EIF‫א‬ •  ‫א‬‫א‬‫א‬‫א‬E٢٫٨‫א‬F‫א‬  K‫א‬ ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬ •



E ‫א‬‫א‬‫א‬‫א‬F‫א‬E ‫א‬‫א‬‫א‬F

‫א‬‫א‬‫א‬

KE‫א‬‫א‬(IIFEIFF‫א‬



‫א‬‫א‬‫א‬‫א‬ Electronic tacheometer ‫א‬‫א‬)

E ‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬(Data CollectorF

‫א‬‫א‬‫א‬‫א‬E ‫א‬‫א‬F‫א‬E ‫א‬‫א‬F‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬K KEIF‫א‬EIIF‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ • ‫א‬F‫א‬‫א‬‫א‬‫א‬‫• א‬

‫א‬‫א‬‫א‬‫א‬ I‫א‬

‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬F‫א‬‫א‬KE‫א‬‫א‬ - ١٣٥ -



 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

‫א‬(E,D,C,B,AF‫א‬E  ‫א‬‫א‬ KE‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬



. .

D E .

III  ‫א‬‫א‬:٢٫٨‫א‬ F‫א‬‫א‬‫א‬ •



‫א‬‫א‬(AzimuthsF‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E ‫א‬ E, D, F‫א‬‫א‬(IE, ID, IC, IB, IA)‫א‬‫א‬

‫א‬‫א‬‫א‬F‫א‬L‫א‬EC, B, A

‫א‬EI‫א‬‫א‬ ‫א‬F‫א‬‫א‬‫א‬‫א‬

KE‫א‬‫א‬

EIIIF،EIF‫א‬‫א‬‫א‬‫א‬ •

‫א‬،2.8‫א‬

‫א‬‫א‬  ‫א‬KEIF‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬K(IIIFEIF‫א‬ - ١٣٦ -



 ‫א‬‫א‬ ‫א‬‫א‬

 ١٠٢

 ‫א‬

 

 

E  ‫א‬LF‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ KEIIF(IF‫א‬‫א‬‫א‬‫א‬‫א‬

 

  • ‫א‬L

 K‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬          

- ١٣٧ -

 ‫א‬‫א‬ 

 ١٠٢

 ‫א‬

 

 

 ‫א‬‫א‬  K‫א‬،،‫א‬‫א‬،‫א‬‫א‬،E١٩٩٧FKK1 

 K‫א‬،،‫א‬‫א‬،‫א‬،E١٩٨٣F،K2 

‫א‬‫א‬،E١٩٨٤F،‫א‬&‫א‬K3  K،‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ 

‫א‬‫א‬،E١٩٨٥F،‫א‬&‫א‬K٤

 K،‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ 

 K،‫א‬‫א‬‫א‬‫א‬،‫א‬،E١٩٧٤FK٥ ‫א‬W‫א‬‫א‬،E١٩٩٩F‫א‬&،K٦  K،‫א‬،‫א‬ 

‫א‬‫א‬،E١٩٨٣F‫א‬&‫א‬K٧  KK،‫א‬،‫א‬‫א‬ 

،‫א‬،‫א‬‫א‬‫א‬‫א‬،E١٩٩٨FK٨

 K

،‫א‬‫א‬،‫א‬‫א‬‫א‬،‫א‬،E١٩٩٩F&K٩  K‫א‬

- ١٣٨ -

 ‫א‬‫א‬ 

 ١٠٢

 ‫א‬

 

  

10. Barry F. kavanagh (1997), Surveying : with construction applications. 3 Edition, Prentice Hall, New Jersey, U.S.A.  11. James R. Wirshing & Roy H. Wirshing (1985) Theory and Problems of

 

Introductory Surveying, Schaum’s Outline Series, McGraw-Hill.

- ١٣٩ -



 ‫א‬ 

 ١٠٢

 ‫א‬

 

 

 ‫א‬‫א‬‫א‬ Right Angles .١

a = cos B c b cos A = = sin B c a tan A = = cot B b c sec A = = cosec B b c cosec A = = sec B a b cot A = = tan B a sin A =



Derived Relationships .٢

a = c sin A = c cos B = b tan A = b cot B = c 2 - b 2 b = c cos A = c sin B = a cot A = a tan B = c 2 - a 2 c=

b b a a = = = = sin A cos B sin B cos A - ١٣٢ -

a 2 + b2

 ‫א‬

 ١٠٢

 ‫א‬

 

 



Oblique Triangles .٣

Sine Law -a

a b c = = sin A sin B sin C Cosine Law -b

a 2 = b 2 + c 2 - 2 bc cos A

b 2 = a 2 + c 2 - 2 ac cos B c 2 = a 2 + b 2 - 2 ab cos C General Trigonometric Formulas .٤

sin A = 2 sin

1 2

A cos A = 2

1 - cos 2 A = tan A cos A

cos A = 2 cos 2 A - 1 = 1 - sin 2 A 1

cos A = cos 2 A - sin 2 A = 1 - sin 2 A tan A =

sin A sin 2A = = cos A 1 + cos 2A - ١٣٣ -

sec 2 A - 1

 ‫א‬ 

 ١٠٢

 ‫א‬

 

 

Addition and Subtraction Identities -a

sin (A ± B) = sin A . cos B ± sin B . cos A cos (A ± B) = cos A . cos B ± sin A . sin B tan (A ± B) =

tan A ± tan B 1 ± tan A . tan B 1

sin A + sin B = 2 sin ( A + B) . sin (A - B) sin A − sin B = 2 cos ( A + B) . sin (A - B) cos A + cos B = 2 cos ( A + B) . cos (A - B) cos A − cos B = 2 sin ( A + B) . sin (A - B) double-Angle Identities -b

sin 2A = 2 sin A . cos A cos 2A = cos 2 A - sin 2 A = 1 - 2 sin 2 A = 2 cos 2 A - 1

tan 2A =

2 tan A 1 − tan 2 A Half-Angle Identities -c

sin

A = 2

1 - cos A 2

cos

A = 2

1 + cos A 2

tan

A sin A = 2 1 + cos A - ١٣٤ -

 ‫א‬ 

 ‫א‬ ١

 ١٠٢

 ‫א‬

 

 

‫א‬

 ‫א‬  W‫א‬‫א‬  ‫א‬

٢ ٢ ٣ ٥ ٦ ٩ ١٠ ١٠ ١٠ ١١ ١٣ ١٣ ١٤ ١٤ ١٤ ١٤

 ‫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

 ١٠٢

 ‫א‬

 

 



 ‫א‬‫א‬W‫א‬‫א‬

 ١٧  ١٧  ٢٠  ٢١

 ٢١  ٢٢



١٨



K١



 

 ‫א‬‫א‬K٢{٢   ‫א‬K٣



‫א‬‫א‬K٢

‫א‬‫א‬K٢{١

‫א‬‫א‬‫א‬K١{٣

‫א‬‫א‬‫א‬K٢{٣

 ٢٥



‫א‬‫א‬‫א‬‫א‬K٤

 ٣٠



 ٢٩

 ٣١

 ٣٢  ٣٢



 

 ٣٢



 ٣٦



 ٣٦

 ٣٧



 ‫א‬‫א‬‫א‬K٥ 



‫א‬‫א‬K١{٥

‫א‬‫א‬‫א‬‫א‬‫א‬K٢{٥

 ‫א‬‫א‬‫א‬‫א‬K٣{٥  



 ‫א‬‫א‬‫א‬K1.1.6



 



‫א‬K٦

‫א‬‫א‬K١{٦

 ‫א‬‫א‬‫א‬‫א‬K2.1.6



‫א‬‫א‬‫א‬K3.1.6 



 ‫א‬‫א‬‫א‬‫א‬K٢{٦ 

 ٣٨



٣٨





‫א‬‫א‬K1.2.6

 ‫א‬‫א‬K2.2.6 















‫א‬‫א‬‫א‬



‫א‬‫א‬‫א‬‫א‬

  ‫א‬‫א‬K3.2.6

 ‫א‬

 ١٠٢

 ‫א‬

 

 



 ٣٩



 ‫א‬‫א‬W‫א‬‫א‬ 



 ‫א‬K١

    K٢

 ٤٠



 ٤١



٤١



‫א‬‫א‬K١{٣

 ٤٢



‫א‬‫א‬‫א‬K٢{٣

 ٤٥



 ٤٥



 ‫א‬K١{٤

 ٤٥



 ‫א‬‫א‬K٢{٤

 ٤٥



 ‫א‬‫א‬‫ א‬.1.2.4

 ٤٦



‫א‬K٣



 ‫א‬K٤

 ‫א‬‫א‬K2.2.4



 

 ٤٦



 ‫א‬‫א‬K٣{٢{٤

 ٤٨



 ٤٩



 ‫א‬‫א‬‫א‬K٢{٥

 ٥٢  ٥٣

 



 



٥٣

 ٥٥



  K١{٥



 ‫א‬‫א‬‫א‬K٣{٥



  ‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬ 



K١

 ‫א‬‫א‬‫א‬‫ א‬.2 ‫א‬‫א‬K١{٢

٥٣ 



‫א‬‫א‬‫א‬‫ א‬K٥

 ٤٨

 ٤٩



‫א‬‫א‬‫ א‬K٢{٢

 ‫א‬‫א‬K٣{٢ 

‫א‬ K٣

 ‫א‬

 ١٠٢

 ‫א‬

 

 



٦٢

٦٥

٦٥

‫א‬‫א‬ K٤ 



‫ א‬K١{٤

 ‫א‬‫ א‬K٢{٤ ‫א‬K٣{٤

٦٥

‫א‬‫א‬K٤{٤

 ٦٦ ٧٠



 E‫א‬F‫א‬‫א‬ K٥{٤

‫א‬‫א‬K٥

 ‫א‬‫א‬W‫א‬‫א‬

 ٧٣



 ٧٣



 K٢



 K١

٧٥



 ٧٦



 ‫א‬‫ א‬K٤

٧٦



‫א‬‫א‬K٣

 ‫א‬ ‫א‬ K١{٤

٧٧

‫א‬‫ א‬K٢{٤

٨١

‫א‬K٣{٤

٨٧

‫א‬K٥

٨٩



 ٩٢



 ٩٢



‫א‬‫א‬ K١{٦

٩٣



٩١

 ٩٤



 ‫א‬‫א‬‫א‬K١{٥

‫א‬‫א‬‫ א‬K٢{٥ 

 ‫א‬K٦

‫ א‬‫א‬K٢{٦

    K٣{٦

 ‫א‬‫א‬‫א‬W‫א‬‫א‬

٩٧



K١

 ٩٧



 ‫א‬‫א‬‫א‬K٢

 ‫א‬

 ١٠٢

 ‫א‬

 

 



 ١٠٧



 ‫א‬‫א‬‫א‬‫א‬K٣

١٠٩

‫א‬‫א‬‫א‬‫ א‬.4

١١٦ ١١٩

 ١١٩  ١١٩

‫א‬‫ א‬.5

 ‫א‬W‫א‬‫א‬ 



 .1

 ‫א‬K٢



‫א‬ K٣



 ‫א‬‫א‬K٢{٣

 ١٢١



 ‫א‬‫א‬K١{٣

١٢٨



  ‫ א‬‫ א‬.3.3

١٢٦

 ١٣٠



١٣٣



 ١٣٤



١٣٤

١٣٥



‫א‬‫א‬K٤  ‫א‬‫א‬W‫א‬‫א‬ 



 .1

 ‫א‬‫א‬‫א‬‫א‬ K٢  ‫א‬‫א‬‫א‬‫א‬ K٣

‫ اﻟﺸﺎﻣﻠﺔ‬‫א‬‫א‬ ‫ א‬K٤

 ١٣٨‫א‬‫א‬

      

      ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬E‫א‬F‫א‬‫א‬

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