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10- كيفية حل المسائل الحسابية (1).pdf

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M
MOHAMEDALNAZEEREZ

المساحة

Engineering
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‫اﻟﻤﺴﺎﺣﺔ‬ ‫ﻋﻠﻢ‬ ‫ﻓﻰ‬ ‫اﻹﻟﻴﻜﺘﺮوﻧﻴﺔ‬ ‫اﻟﻤﺤﺎﺿﺮات‬ ‫ﺳﻠﺴﻠﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫ﻋﻠﻢ‬ ‫ﻓﻰ‬ ‫اﻹﻟﻴﻜﺘﺮوﻧﻴﺔ‬ ‫اﻟﻤﺤﺎﺿﺮات‬ ‫ﺳﻠﺴﻠﺔ‬ E E – – Learning courses Learning courses ‫اﻟﻤﺴﺎﺣﻴﺔ‬ ‫اﻟﻤﺴﺎﺋﻞ‬ ‫ﺣﻞ‬ ‫آﻴﻔﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﻴﺔ‬ ‫اﻟﻤﺴﺎﺋﻞ‬ ‫ﺣﻞ‬ ‫آﻴﻔﻴﺔ‬ How to solve How to solve Surveying Problems Surveying Problems ‫أ‬ ‫أ‬ . . ‫د‬ ‫د‬ / / ‫اﻟﻤﻐﺮﺑﻰ‬ ‫ﺳﻌﻴﺪ‬ ‫اﻟﻤﻐﺮﺑﻰ‬ ‫ﺳﻌﻴﺪ‬ ‫ﻣﺪﻧﻰ‬ ‫ﻗﺴﻢ‬ ‫ﻣﺪﻧﻰ‬ ‫ﻗﺴﻢ‬ - - ‫اﻷزهﺮ‬ ‫هﻨﺪﺳﺔ‬ ‫اﻷزهﺮ‬ ‫هﻨﺪﺳﺔ‬
٢ ٢ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﻤﺤﺘﻮﻳﺎت‬ ‫اﻟﻤﺤﺘﻮﻳﺎت‬ ‫اﻷول‬ ‫اﻟﺒﺎب‬ ‫اﻷول‬ ‫اﻟﺒﺎب‬ : : ‫اﻟﺘﺮاﻓﻴﺮﺳﺎت‬ ‫ﺑﺎب‬ ‫ﻋﻠﻰ‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫اﻟﺘﺮاﻓﻴﺮﺳﺎت‬ ‫ﺑﺎب‬ ‫ﻋﻠﻰ‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﺒﺎب‬ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﺒﺎب‬ : : ‫اﻟﻤﻴﺰاﻧﻴﺔ‬ ‫ﺑﺎب‬ ‫ﻋﻠﻰ‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫اﻟﻤﻴﺰاﻧﻴﺔ‬ ‫ﺑﺎب‬ ‫ﻋﻠﻰ‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﺒﺎب‬ ‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﺒﺎب‬ : : ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫اﻟﺮاﺑﻊ‬ ‫اﻟﺒﺎب‬ ‫اﻟﺮاﺑﻊ‬ ‫اﻟﺒﺎب‬ : : ‫اﻷراﺿﻰ‬ ‫ﺗﺴﻮﻳﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫اﻷراﺿﻰ‬ ‫ﺗﺴﻮﻳﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬
٣ ٣ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻷول‬ ‫اﻟﺒﺎب‬ ‫اﻷول‬ ‫اﻟﺒﺎب‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺘﺮاﻓﻴﺮﺳﺎت‬ ‫ﺑﺎب‬ ‫اﻟﺘﺮاﻓﻴﺮﺳﺎت‬ ‫ﺑﺎب‬
٤ ٤ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ١ ١ ) ) ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫واﻟﺰواﻳﺎ‬ ‫اﻟﻘﻔﻞ‬ ‫ﺧﻄﺄ‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫واﻟﺰواﻳﺎ‬ ‫اﻟﻘﻔﻞ‬ ‫ﺧﻄﺄ‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ :( :( ‫ﻳﻠ‬ ‫آﻤﺎ‬ ‫ﻓﻜﺎﻧﺖ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻓﻰ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰواﻳﺎ‬ ‫ﻗﻴﺴﺖ‬ ‫ﻳﻠ‬ ‫آﻤﺎ‬ ‫ﻓﻜﺎﻧﺖ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻓﻰ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰواﻳﺎ‬ ‫ﻗﻴﺴﺖ‬ ‫ﻰ‬ ‫ﻰ‬ : : ‫اﻟﺰواﻳﺎ‬ ‫ﻗﻴﻢ‬ ‫وﺣﺴﺎب‬ ‫اﻟﺰاوى‬ ‫اﻟﻘﻔﻞ‬ ‫ﺧﻄﺄ‬ ‫ﻗﻴﻤﺔ‬ ‫ﺣﺴﺎب‬ ‫واﻟﻤﻄﻠﻮب‬ ‫اﻟﺰواﻳﺎ‬ ‫ﻗﻴﻢ‬ ‫وﺣﺴﺎب‬ ‫اﻟﺰاوى‬ ‫اﻟﻘﻔﻞ‬ ‫ﺧﻄﺄ‬ ‫ﻗﻴﻤﺔ‬ ‫ﺣﺴﺎب‬ ‫واﻟﻤﻄﻠﻮب‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ . . ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ا‬ 22 46 99 ‫ب‬ 47 50 122 ‫ﺟـ‬ 15 26 72 ‫د‬ 32 56 64 ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫ااﻟﺰاوﻳﺔ‬
٥ ٥ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١ ١ : : ‫ﻣﺠﻤﻮع‬ ‫ﺣﺴﺎب‬ ‫ﻳﺘﻢ‬ ‫ﻣﺠﻤﻮع‬ ‫ﺣﺴﺎب‬ ‫ﻳﺘﻢ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰواﻳﺎ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰواﻳﺎ‬ ‫اﻟﺰاوى‬ ‫اﻟﻘﻔﻞ‬ ‫ﺧﻄﺄ‬ ‫اﻟﺰاوى‬ ‫اﻟﻘﻔﻞ‬ ‫ﺧﻄﺄ‬ = = ٠٠ ٠٠ ٠٠ ٠٠ ٣٦٠ ٣٦٠ – – ٥٦ ٥٦ ٥٩ ٥٩ ٣٥٩ ٣٥٩ = = ٤ ٤ ‫ﺛﻮاﻧﻰ‬ ‫ﺛﻮاﻧﻰ‬ ‫ﻧﻮزع‬ ‫ﺣﻴﺚ‬ ‫ﻧﻮزع‬ ‫ﺣﻴﺚ‬ ١ ١ ‫زاوﻳﺔ‬ ‫آﻞ‬ ‫ﻋﻠﻰ‬ ‫ﺛﺎﻧﻴﺔ‬ ‫زاوﻳﺔ‬ ‫آﻞ‬ ‫ﻋﻠﻰ‬ ‫ﺛﺎﻧﻴﺔ‬ . . ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ا‬ 22 46 99 23 46 99 ‫ب‬ 47 50 122 48 50 122 ‫ﺟـ‬ 15 26 72 16 26 72 ‫د‬ 32 56 64 33 56 64 ‫اﻟﻤﺠﻤﻮع‬ 116 178 357 120 178 357 56 59 359 0 0 360 ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫ااﻟﺰاوﻳﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰاوﻳﺔ‬
٦ ٦ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٢ ٢ ) ) ‫اﻻﻧﺤﺮاف‬ ‫ﺣﺴﺎب‬ ‫آﻴﻔﻴﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻻﻧﺤﺮاف‬ ‫ﺣﺴﺎب‬ ‫آﻴﻔﻴﺔ‬ ‫ﻋﻠﻰ‬ :( :( ‫اﻟﺨﻂ‬ ‫آﺎن‬ ‫إذا‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻰ‬ ‫اﻟﺨﻂ‬ ‫آﺎن‬ ‫إذا‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻰ‬ ‫ﻓﺎﺣﺴﺐ‬ ‫اﻟﺸﺮق‬ ‫ﻧﺤﻮ‬ ‫ﻳﺘﺠﻪ‬ ‫ب‬ ‫ا‬ ‫ﻓﺎﺣﺴﺐ‬ ‫اﻟﺸﺮق‬ ‫ﻧﺤﻮ‬ ‫ﻳﺘﺠﻪ‬ ‫ب‬ ‫ا‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻷﺿﻼع‬ ‫اﻟﺪاﺋﺮى‬ ‫اﻻﻧﺤﺮاف‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻷﺿﻼع‬ ‫اﻟﺪاﺋﺮى‬ ‫اﻻﻧﺤﺮاف‬ . . ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٢ ٢ : : ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰواﻳﺎ‬ ‫ﻗﻴﻢ‬ ‫آﺎﻧﺖ‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻣﻦ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰواﻳﺎ‬ ‫ﻗﻴﻢ‬ ‫آﺎﻧﺖ‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻣﻦ‬ ) ) ‫ﺑﻌﺪ‬ ‫ﺑﻌﺪ‬ ‫اﻟﺰاوى‬ ‫اﻟﻘﻔﻞ‬ ‫ﺧﻄﺄ‬ ‫ﺗﺼﺤﻴﺢ‬ ‫اﻟﺰاوى‬ ‫اﻟﻘﻔﻞ‬ ‫ﺧﻄﺄ‬ ‫ﺗﺼﺤﻴﺢ‬ ( ( ‫ﻳﻠﻰ‬ ‫آﻤﺎ‬ ‫ﻳﻠﻰ‬ ‫آﻤﺎ‬ : : ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ا‬ 23 46 99 ‫ب‬ 48 50 122 ‫ﺟـ‬ 16 26 72 ‫د‬ 33 56 64 ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰاوﻳﺔ‬
٧ ٧ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٢ ٢ : : ‫آﺮوآﻰ‬ ‫رﺳﻢ‬ ‫ﻳﺘﻢ‬ ‫آﺮوآﻰ‬ ‫رﺳﻢ‬ ‫ﻳﺘﻢ‬ ‫ﻟﻠﺘﺮاﻓﻴﺮس‬ ‫ﻟﻠﺘﺮاﻓﻴﺮس‬ ‫اﻻﻧﺤﺮاف‬ ‫ﻋﻠﻴﻪ‬ ‫ﻣﻮﺿﺢ‬ ‫اﻻﻧﺤﺮاف‬ ‫ﻋﻠﻴﻪ‬ ‫ﻣﻮﺿﺢ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰواﻳﺎ‬ ‫وﻗﻴﻢ‬ ‫ب‬ ‫ا‬ ‫ﻟﻠﺨﻂ‬ ‫اﻟﺪاﺋﺮى‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰواﻳﺎ‬ ‫وﻗﻴﻢ‬ ‫ب‬ ‫ا‬ ‫ﻟﻠﺨﻂ‬ ‫اﻟﺪاﺋﺮى‬ ‫ﻟﻠﺨﻂ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻻﻧﺤﺮاف‬ ‫ﻟﻠﺨﻂ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻻﻧﺤﺮاف‬ = = ‫اﻟﺴﺎﺑﻖ‬ ‫ﻟﻠﺨﻂ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻻﻧﺤﺮاف‬ ‫اﻟﺴﺎﺑﻖ‬ ‫ﻟﻠﺨﻂ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻻﻧﺤﺮاف‬ ± ± ١٨٠ ١٨٠ – – ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰاوﻳﺔ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰاوﻳﺔ‬ ‫ا‬ ‫ب‬ ‫ﺟـ‬ ‫د‬ ‫اﻟﻘﺎﻋﺪة‬ ‫ﻧﻄﺒﻖ‬ ‫ﺛﻢ‬ ‫اﻟﻘﺎﻋﺪة‬ ‫ﻧﻄﺒﻖ‬ ‫ﺛﻢ‬ : :
٨ ٨ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ا‬ ‫ب‬ ‫ﺟـ‬ ‫د‬ ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٢ ٢ : :
٩ ٩ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٣ ٣ ) ) ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ :( :( ‫أﻃﻮال‬ ‫آﺎﻧﺖ‬ ‫إذا‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻰ‬ ‫أﻃﻮال‬ ‫آﺎﻧﺖ‬ ‫إذا‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻰ‬ ‫ﺛﻢ‬ ‫اﻟﻀﻠﻌﻰ‬ ‫اﻟﺨﻄﺄ‬ ‫ﻗﻴﻤﺔ‬ ‫ﻓﺎﺣﺴﺐ‬ ‫ﺑﺎﻟﺸﺮﻳﻂ‬ ‫ﻗﻴﺴﺖ‬ ‫اﻟﺨﻄﻮط‬ ‫ﺛﻢ‬ ‫اﻟﻀﻠﻌﻰ‬ ‫اﻟﺨﻄﺄ‬ ‫ﻗﻴﻤﺔ‬ ‫ﻓﺎﺣﺴﺐ‬ ‫ﺑﺎﻟﺸﺮﻳﻂ‬ ‫ﻗﻴﺴﺖ‬ ‫اﻟﺨﻄﻮط‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫اﺣﺴﺐ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫اﺣﺴﺐ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻷﺿﻼع‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻷﺿﻼع‬ ‫ا‬ ‫ا‬ ( ( ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻷﻃﻮال‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻷﻃﻮال‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ Bowditch method Bowditch method ‫ب‬ ‫ب‬ ( ( ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ Transit method Transit method
١٠ ١٠ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٣ ٣ ) ) ‫ا‬ ‫ا‬ :( :( ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻷﻃﻮال‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻷﻃﻮال‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ Bowditch method Bowditch method ‫ا‬ ‫ب‬ ‫ا‬ 61.31 0 0 90 61.310 0.000 61.299 0.025 ‫ب‬ ‫ﺟـ‬ ‫ب‬ 71.85 12 9 147 38.971 -60.363 38.958 -60.334 ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ 120.31 56 42 254 -116.055 -31.715 -116.076 -31.666 ‫د‬ ‫هـ‬ ‫د‬ 93.29 23 46 9 15.836 91.936 15.819 91.974 ‫ا‬ ‫اﻟﻤﺠﻤﻮع‬ 346.76 0.062 -0.142 0.000 0.000 ‫اﻟﺨﻂ‬ ‫اﻟﻄﻮل‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻟﻨﻘﻄﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬
١١ ١١ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٣ ٣ ) ) ‫ب‬ ‫ب‬ :( :( ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ Transit method Transit method ‫ا‬ ‫ب‬ ‫ا‬ 61.31 0 0 90 61.310 0.000 61.294 0.000 ‫ب‬ ‫ﺟـ‬ ‫ب‬ 71.85 12 9 147 38.971 -60.363 38.961 -60.316 ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ 120.31 56 42 254 -116.055 -31.715 -116.086 -31.691 ‫د‬ ‫هـ‬ ‫د‬ 93.29 23 46 9 15.836 91.936 15.831 92.007 ‫ا‬ ‫اﻟﺠﺒﺮى‬ ‫ﻣﺠـ‬ 346.76 0.062 -0.142 0.000 0.000 ‫اﻟﻌﺪدى‬ ‫ﻣﺠـ‬ 232.171 184.014 ‫اﻟﺨﻂ‬ ‫اﻟﻄﻮل‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻟﻨﻘﻄﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬
١٢ ١٢ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٤ ٤ ) ) ‫اﻻﺣﺪاﺛﻴﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ ‫اﻻﺣﺪاﺛﻴﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ :( :( ‫ﻧﻘﻄ‬ ‫إﺣﺪاﺛﻴﺎت‬ ‫آﺎﻧﺖ‬ ‫إذا‬ ‫اﻟﻤﻀﻠﻊ‬ ‫ﻧﻘﺎط‬ ‫إﺣﺪاﺛﻴﺎت‬ ‫اﺣﺴﺐ‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻰ‬ ‫ﻧﻘﻄ‬ ‫إﺣﺪاﺛﻴﺎت‬ ‫آﺎﻧﺖ‬ ‫إذا‬ ‫اﻟﻤﻀﻠﻊ‬ ‫ﻧﻘﺎط‬ ‫إﺣﺪاﺛﻴﺎت‬ ‫اﺣﺴﺐ‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻰ‬ ‫ﺔ‬ ‫ﺔ‬ ‫ا‬ ‫ا‬ ) ) ٥٠٠ ٥٠٠ ‫ﺷﺮﻗﺎ‬ ‫ﺷﺮﻗﺎ‬ ، ، ١٠٠٠ ١٠٠٠ ‫ﺷﻤﺎﻻ‬ ‫ﺷﻤﺎﻻ‬ ( ( ‫ﺑﺎﻟﻄﺮﻳﻘﺘﻴﻦ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻰ‬ ‫وذﻟﻚ‬ ‫ﺑﺎﻟﻄﺮﻳﻘﺘﻴﻦ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻰ‬ ‫وذﻟﻚ‬ : : ‫ا‬ ‫ا‬ ( ( ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻷﻃﻮال‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻷﻃﻮال‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ Bowditch method Bowditch method ‫ب‬ ‫ب‬ ( ( ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ Transit method Transit method
١٣ ١٣ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٤ ٤ ) ) ‫ا‬ ‫ا‬ : ( : ( ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻷﻃﻮال‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻷﻃﻮال‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ Bowditch method Bowditch method ‫ا‬ 500.000 1000.000 ‫ب‬ ‫ا‬ 61.31 61.299 0.025 ‫ب‬ 561.299 1000.025 ‫ﺟـ‬ ‫ب‬ 71.85 38.958 -60.334 ‫ﺟـ‬ 600.257 939.691 ‫د‬ ‫ﺟـ‬ 120.31 -116.076 -31.666 ‫د‬ 484.181 908.026 ‫هـ‬ ‫د‬ 93.29 15.819 91.974 ‫ا‬ 500.000 1000.000 ‫اﻟﻤﺠﻤﻮع‬ 346.76 0.000 0.000 ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﺨﻂ‬ ‫اﻻﺣﺪاﺛﻰ‬ ‫اﻷﻓﻘﻰ‬ ‫اﻻﺣﺪاﺛﻰ‬ ‫اﻟﺮأﺳﻰ‬ ‫اﻟﻄﻮل‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬
١٤ ١٤ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٤ ٤ ) ) ‫ب‬ ‫ب‬ : ( : ( ‫ب‬ ‫ب‬ ( ( ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ Transit method Transit method ‫ا‬ 500.000 1000.000 ‫ب‬ ‫ا‬ 61.31 61.294 0.000 ‫ب‬ 561.294 1000.000 ‫ﺟـ‬ ‫ب‬ 71.85 38.961 -60.316 ‫ﺟـ‬ 600.254 939.684 ‫د‬ ‫ﺟـ‬ 120.31 -116.086 -31.691 ‫د‬ 484.169 907.993 ‫هـ‬ ‫د‬ 93.29 15.831 92.007 ‫ا‬ 500.000 1000.000 ‫اﻟﺠﺒﺮى‬ ‫ﻣﺠـ‬ 346.76 0.000 0.000 ‫اﻟﻌﺪدى‬ ‫ﻣﺠـ‬ ‫اﻻﺣﺪاﺛﻰ‬ ‫اﻷﻓﻘﻰ‬ ‫اﻻﺣﺪاﺛﻰ‬ ‫اﻟﺮأﺳﻰ‬ ‫اﻟﻄﻮل‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﺨﻂ‬
١٥ ١٥ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ب‬ ‫ا‬ 107.12 0 20 85 ‫ﺟـ‬ ‫ب‬ 63.18 10 46 163 ‫د‬ ‫ﺟـ‬ 126.84 40 46 262 ‫هـ‬ ‫د‬ 27.99 50 30 348 ‫ا‬ ‫هـ‬ 40.04 10 29 6 ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫اﻟﺨﻂ‬ ‫اﻟﻄﻮل‬ ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٥ ٥ ) ) ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ :( :( ‫ﻷﺿﻼع‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫اﺣﺴﺐ‬ ‫ﻷﺿﻼع‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫اﺣﺴﺐ‬ ‫ﺗﺮاﻓﻴﺮس‬ ‫ﺗﺮاﻓﻴﺮس‬ ‫اﻟﺘﻴﻮدوﻟﻴﺖ‬ ‫اﻟﺘﻴﻮدوﻟﻴﺖ‬ ‫اﻟﺘﺎﻟﻰ‬ ‫ﺑﺎﻟﺠﺪول‬ ‫ﻣﻮﺿﺤﺔ‬ ‫اﻷرﺻﺎد‬ ‫ﺑﺄن‬ ‫ﻋﻠﻤﺎ‬ ‫هـ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ ‫اﻟﺘﺎﻟﻰ‬ ‫ﺑﺎﻟﺠﺪول‬ ‫ﻣﻮﺿﺤﺔ‬ ‫اﻷرﺻﺎد‬ ‫ﺑﺄن‬ ‫ﻋﻠﻤﺎ‬ ‫هـ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ : :
١٦ ١٦ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ا‬ ‫ب‬ ‫ا‬ 107.12 0 20 85 106.765 8.715 107.774 8.754 ‫ب‬ ‫ﺟـ‬ ‫ب‬ 63.18 10 46 163 17.659 -60.662 17.826 -60.392 ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ 126.84 40 46 262 -125.834 -15.946 -124.644 -15.875 ‫د‬ ‫هـ‬ ‫د‬ 27.99 50 30 348 -5.574 27.429 -5.521 27.552 ‫هـ‬ ‫ا‬ ‫هـ‬ 40.04 10 29 6 4.523 39.784 4.566 39.961 ‫ا‬ ‫اﻟﺠﺒﺮى‬ ‫ﻣﺠـ‬ -2.460 -0.680 0.000 0.000 ‫اﻟﻌﺪدى‬ ‫ﻣﺠـ‬ 260.354 152.536 ‫اﻟﻨﻘﻄﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫اﻟﺨﻂ‬ ‫اﻟﻄﻮل‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٥ ٥ : : ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬
١٧ ١٧ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ب‬ ‫ا‬ 363.900 363.900 ‫ﺟـ‬ ‫ب‬ 341.360 0.000 ‫د‬ ‫ﺟـ‬ 0.000 -324.150 ‫هـ‬ ‫د‬ -231.180 -400.420 ‫و‬ ‫هـ‬ -334.180 193.220 ‫ا‬ ‫و‬ -138.980 167.200 ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺨﻂ‬ ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٦ ٦ ) ) ‫اﻻﺣﺪاﺛﻴﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ ‫اﻻﺣﺪاﺛﻴﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ :( :( ‫ﻓﻰ‬ ‫ﻓﻰ‬ ‫ﺗﺮاﻓﻴﺮس‬ ‫ﺗﺮاﻓﻴﺮس‬ ‫اﻟﺘﻴﻮدوﻟﻴﺖ‬ ‫اﻟﺘﻴﻮدوﻟﻴﺖ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻗﻴﻤﺔ‬ ‫ﻣﻌﻠﻮم‬ ‫و‬ ‫هـ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻗﻴﻤﺔ‬ ‫ﻣﻌﻠﻮم‬ ‫و‬ ‫هـ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ ‫آﺎﻧﺖ‬ ‫إذا‬ ‫اﻟﻤﻀﻠﻊ‬ ‫ﻧﻘﺎط‬ ‫اﺣﺪاﺛﻴﺎت‬ ‫ﺣﺴﺎب‬ ‫وﻣﻄﻠﻮب‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫آﺎﻧﺖ‬ ‫إذا‬ ‫اﻟﻤﻀﻠﻊ‬ ‫ﻧﻘﺎط‬ ‫اﺣﺪاﺛﻴﺎت‬ ‫ﺣﺴﺎب‬ ‫وﻣﻄﻠﻮب‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫ا‬ ‫اﺣﺪاﺛﻴﺎت‬ ‫ا‬ ‫اﺣﺪاﺛﻴﺎت‬ ) ) ‫ﺷﺮﻗﺎ‬ ‫ﺻﻔﺮ‬ ‫ﺷﺮﻗﺎ‬ ‫ﺻﻔﺮ‬ ، ، ‫ﺷﻤﺎﻻ‬ ‫ﺻﻔﺮ‬ ‫ﺷﻤﺎﻻ‬ ‫ﺻﻔﺮ‬ ( (
١٨ ١٨ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ا‬ 0.000 0.000 ‫ب‬ ‫ا‬ 363.900 363.900 363.662 363.963 ‫ب‬ 363.662 363.963 ‫ﺟـ‬ ‫ب‬ 341.360 0.000 341.137 0.000 ‫ﺟـ‬ 704.800 363.963 ‫د‬ ‫ﺟـ‬ 0.000 -324.150 0.000 -324.094 ‫د‬ 704.800 39.869 ‫هـ‬ ‫د‬ -231.180 -400.420 -231.331 -400.351 ‫هـ‬ 473.469 -360.482 ‫و‬ ‫هـ‬ -334.180 193.220 -334.398 193.253 ‫و‬ 139.071 -167.229 ‫ا‬ ‫و‬ -138.980 167.200 -139.071 167.229 ‫ا‬ 0.000 0.000 ‫ﺟﺒﺮى‬ ‫ﻣﺠـ‬ 0.920 -0.250 0.000 0.000 ‫ﻋﺪدى‬ ‫ﻣﺠـ‬ 1409.600 1448.890 ‫اﻟﻨﻘﻄﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺨﻂ‬ ‫اﻻﺣﺪاﺛﻰ‬ ‫اﻷﻓﻘﻲ‬ ‫اﻻﺣﺪاﺛﻰ‬ ‫اﻟﺮأﺳﻲ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٦ ٦ : : ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬
١٩ ١٩ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٧ ٧ ) ) ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻣﺴﺎﺣﺔ‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻣﺴﺎﺣﺔ‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ :( :( ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻣﺴﺎﺣﺔ‬ ‫اﺣﺴﺐ‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻣﺴﺎﺣﺔ‬ ‫اﺣﺴﺐ‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻰ‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻰ‬ . . ‫ا‬ 0.000 0.000 ‫ب‬ 363.662 363.963 704.800 256520.865 ‫ﺟـ‬ 704.800 363.963 341.137 124161.249 ‫د‬ 704.800 39.869 -231.331 -9222.866 ‫هـ‬ 473.469 -360.482 -565.729 203935.225 ‫و‬ 139.071 -167.229 -473.469 79177.645 ‫ا‬ 0.000 0.000 224.592 0.000 ‫ب‬ 363.662 363.963 ‫اﻟﻤﺴﺎﺣﺔ‬ ‫ﺿﻌﻒ‬ 654572.118 ‫اﻟﻤﺴﺎﺣﺔ‬ 327286.059 ‫اﻟﻨﻘﻄﺔ‬ ‫ﻓﺮق‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫اﻷﻓﻘﻴﺔ‬ * ‫اﻟﺮأﺳﻴﺔ‬ (‫اﻟﻤﺮآﺒﺎت‬ ‫)ﻓﺮق‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬
٢٠ ٢٠ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٨ ٨ ) ) ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ : : ‫واﻧﺤﺮاﻓﻪ‬ ‫ﺧﻂ‬ ‫ﻃﻮل‬ ‫واﻧﺤﺮاﻓﻪ‬ ‫ﺧﻂ‬ ‫ﻃﻮل‬ : ( : ( ‫ﺑﺎﻟﺠﺪول‬ ‫اﻟﻤﻮﺿﺤﺔ‬ ‫اﻷرﺻﺎد‬ ‫أﺧﺬت‬ ‫ﺑﺎﻟﺠﺪول‬ ‫اﻟﻤﻮﺿﺤﺔ‬ ‫اﻷرﺻﺎد‬ ‫أﺧﺬت‬ ‫ﻟﻠﺘﺮاﻓﻴﺮس‬ ‫ﻟﻠﺘﺮاﻓﻴﺮس‬ ‫ﺣﺴﺎب‬ ‫واﻟﻤﻄﻠﻮب‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ ‫ﺣﺴﺎب‬ ‫واﻟﻤﻄﻠﻮب‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ ‫ب‬ ‫ا‬ ‫اﻟﺨﻂ‬ ‫واﻧﺤﺮاف‬ ‫ﻃﻮل‬ ‫ب‬ ‫ا‬ ‫اﻟﺨﻂ‬ ‫واﻧﺤﺮاف‬ ‫ﻃﻮل‬ . . ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ﺟـ‬ ‫ا‬ 130.75 0 0 0 ‫د‬ ‫ﺟـ‬ 210.75 0 39 54 ‫ب‬ ‫د‬ 65.00 0 57 328 ‫ا‬ ‫ب‬ L α ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺨﻂ‬ ‫اﻟﻄﻮل‬
٢١ ٢١ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٨ ٨ : : ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ : : ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ا‬ ‫ﺟـ‬ ‫ا‬ 130.75 0 0 0 0.000 130.750 ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ 210.75 0 39 54 171.895 121.934 ‫د‬ ‫ب‬ ‫د‬ 65.00 0 57 328 -33.526 55.687 ‫ب‬ ‫ا‬ ‫ب‬ L L sin α L cos α ‫ا‬ ‫اﻟﻤﺠﻤﻮع‬ 138.369 308.370 L sin α L cos α α ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺨﻂ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻄﻮل‬
٢٢ ٢٢ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٨ ٨ : : ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ = = ‫ل‬ ‫ل‬ ‫ﺟﺎ‬ ‫ﺟﺎ‬ α α + + ١٣٨٫٣٦٩ ١٣٨٫٣٦٩ = = ‫ﺻﻔﺮ‬ ‫ﺻﻔﺮ‬ ‫ل‬ ‫ل‬ ‫ﺟﺎ‬ ‫ﺟﺎ‬ α α = = - - ١٣٨٫٣٦٩ ١٣٨٫٣٦٩ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ = = ‫ل‬ ‫ل‬ ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ α α + + ٣٠٨٫٣٧ ٣٠٨٫٣٧ = = ‫ﺻﻔﺮ‬ ‫ﺻﻔﺮ‬ ‫ل‬ ‫ل‬ ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ α α = = - - ٣٠٨٫٣٧ ٣٠٨٫٣٧ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫ﺑﻘﺴﻤﺔ‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫ﺑﻘﺴﻤﺔ‬ ‫ﻇﺎ‬ ‫ﻇﺎ‬ α α = = ٠٫٤٤٨٧١ ٠٫٤٤٨٧١ ‫إذا‬ ‫إذا‬ α α = = ٥٩ ٥٩ ‫ث‬ ‫ث‬ ٩ ٩ ‫ق‬ ‫ق‬ ٢٤ ٢٤ ‫د‬ ‫د‬ ‫ﻓﻰ‬ ‫اﻟﺨﻂ‬ ‫ﻓﻴﻜﻮن‬ ‫ﺳﺎﻟﺒﺔ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫ﻣﻦ‬ ‫آﻼ‬ ‫ﻷن‬ ‫وﻧﻈﺮا‬ ‫ﻓﻰ‬ ‫اﻟﺨﻂ‬ ‫ﻓﻴﻜﻮن‬ ‫ﺳﺎﻟﺒﺔ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫ﻣﻦ‬ ‫آﻼ‬ ‫ﻷن‬ ‫وﻧﻈﺮا‬ ‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﺮﺑﻊ‬ ‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﺮﺑﻊ‬ ‫اﻻﻧﺤﺮاف‬ ‫اﻻﻧﺤﺮاف‬ = = ٥٩ ٥٩ ‫ث‬ ‫ث‬ ٩ ٩ ‫ق‬ ‫ق‬ ٢٤ ٢٤ ‫د‬ ‫د‬ + + ١٨٠ ١٨٠ ‫د‬ ‫د‬ = = ٥٩ ٥٩ ‫ث‬ ‫ث‬ ٩ ٩ ‫ق‬ ‫ق‬ ٢٠٤ ٢٠٤ ‫د‬ ‫د‬ ‫ل‬ ‫اﻟﻄﻮل‬ ‫ﻳﻜﻮن‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫اﺣﺪى‬ ‫ﻓﻰ‬ ‫وﺑﺎﻟﺘﻌﻮﻳﺾ‬ ‫ل‬ ‫اﻟﻄﻮل‬ ‫ﻳﻜﻮن‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫اﺣﺪى‬ ‫ﻓﻰ‬ ‫وﺑﺎﻟﺘﻌﻮﻳﺾ‬ = = ٣٧٧٫٩٩ ٣٧٧٫٩٩ ‫ﻣﺘﺮ‬ ‫ﻣﺘﺮ‬
٢٣ ٢٣ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻓﻰ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻘﻖ‬ ‫ﻣﺜﺎل‬ ‫ﻓﻰ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻘﻖ‬ ٨ ٨ : : ‫اﻷرﺻﺎد‬ ‫ﻣﻮﺿﻊ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫اﻷرﺻﺎد‬ ‫ﻣﻮﺿﻊ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫اﻟﺘﺤﻘﻴﻖ‬ ‫وﻳﻜﻮن‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫إﻋﺎدة‬ ‫ﺛﻢ‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻟﺘﺤﻘﻴﻖ‬ ‫وﻳﻜﻮن‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫إﻋﺎدة‬ ‫ﺛﻢ‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫ﻟﻠﺼﻔﺮ‬ ‫ﻣﺴﺎوﻳﺎ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻤﺠﻤﻮع‬ ‫ﻟﻠﺼﻔﺮ‬ ‫ﻣﺴﺎوﻳﺎ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻤﺠﻤﻮع‬ : : ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ا‬ ‫ﺟـ‬ ‫ا‬ 130.75 0 0 0 0.000 130.750 ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ 210.75 0 39 54 171.895 121.934 ‫د‬ ‫ب‬ ‫د‬ 65.00 0 57 328 -33.526 55.687 ‫ب‬ ‫ا‬ ‫ب‬ 337.99 59 9 204 -138.369 -308.369 ‫ا‬ ‫اﻟﻤﺠﻤﻮع‬ 0.000 0.000 ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺨﻂ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻄﻮل‬
٢٤ ٢٤ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ب‬ ‫ا‬ 500.0 0 0 0 ‫ﺟـ‬ ‫ب‬ L 0 0 45 ‫د‬ ‫ﺟـ‬ 854.0 0 33 110 ‫هـ‬ ‫د‬ 1019.8 0 41 168 ‫و‬ ‫هـ‬ 1118.0 ‫ا‬ ‫و‬ 656.8 0 54 305 α ‫اﻟﻄﻮل‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺨﻂ‬ ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٩ ٩ ) ) ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ : : ‫ﺁﺧﺮ‬ ‫ﺧﻂ‬ ‫واﻧﺤﺮاف‬ ‫ﺧﻂ‬ ‫ﻃﻮل‬ ‫ﺁﺧﺮ‬ ‫ﺧﻂ‬ ‫واﻧﺤﺮاف‬ ‫ﺧﻂ‬ ‫ﻃﻮل‬ : ( : ( ‫و‬ ‫هـ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻓﻰ‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ ‫اﺣﺴﺐ‬ ‫و‬ ‫هـ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻓﻰ‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ ‫اﺣﺴﺐ‬ . .
٢٥ ٢٥ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ا‬ ‫ب‬ ‫ا‬ 500.00 0 0 0 0.000 500.000 ‫ب‬ ‫ﺟـ‬ ‫ب‬ L 0 0 45 0.707 L 0.707 L ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ 854.00 0 33 110 799.657 -299.775 ‫د‬ ‫هـ‬ ‫د‬ 1019.80 0 41 168 200.117 -999.973 ‫هـ‬ ‫و‬ ‫هـ‬ 1118.00 1118 sin α 1118 cos α ‫و‬ ‫ا‬ ‫و‬ 656.80 0 54 305 -532.035 385.129 ‫ا‬ ‫اﻟﻤﺠﻤﻮع‬ 467.738 -414.618 0.707 L 0.707 L 1118 sin α 1118 cos α ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺨﻂ‬ α ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻄﻮل‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٩ ٩ : : ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ : :
٢٦ ٢٦ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٩ ٩ : : ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ = = ٤٦٧٫٧٣٨ ٤٦٧٫٧٣٨ + + ٠٫٧٠٧ ٠٫٧٠٧ ‫ل‬ ‫ل‬ + + ١١١٨ ١١١٨ ‫ﺟﺎ‬ ‫ﺟﺎ‬ α α = = ‫ﺻﻔﺮ‬ ‫ﺻﻔﺮ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ = = - - ٤١٤٫٦١٨ ٤١٤٫٦١٨ + + ٠٫٧٠٧ ٠٫٧٠٧ ‫ل‬ ‫ل‬ + + ١١١٨ ١١١٨ ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ α α = = ‫ﺻﻔﺮ‬ ‫ﺻﻔﺮ‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫ﺑﻄﺮح‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫ﺑﻄﺮح‬ ) ) ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ α α – – ‫ﺟﺎ‬ ‫ﺟﺎ‬ α α = ( = ( ٠٫٧٨٩٢٢٧ ٠٫٧٨٩٢٢٧ ٢ ٢ ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ ٢ ٢ ) ) ٤٥ ٤٥ + + α α = ( = ( ٠٫٧٨٩٢٢٧ ٠٫٧٨٩٢٢٧ ‫اذا‬ ‫اذا‬ α α = = ٣٩ ٣٩ ‫ث‬ ‫ث‬ ٤ ٤ ‫ق‬ ‫ق‬ ١١ ١١ ‫د‬ ‫د‬ ‫و‬ ‫هـ‬ ‫اﻟﺨﻂ‬ ‫اﻧﺤﺮاف‬ ‫وﻳﻜﻮن‬ ‫و‬ ‫هـ‬ ‫اﻟﺨﻂ‬ ‫اﻧﺤﺮاف‬ ‫وﻳﻜﻮن‬ )= )= ٠٠ ٠٠ ‫ث‬ ‫ث‬ ٠٠ ٠٠ ‫ق‬ ‫ق‬ ٢٧٠ ٢٧٠ ‫د‬ ‫د‬ ( ( – – ) ) ٣٩ ٣٩ ‫ث‬ ‫ث‬ ٤ ٤ ‫ق‬ ‫ق‬ ١١ ١١ ‫د‬ ‫د‬ = ( = ( ٢١ ٢١ ‫ث‬ ‫ث‬ ٥٥ ٥٥ ‫ق‬ ‫ق‬ ٢٥٨ ٢٥٨ ‫د‬ ‫د‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫إﺣﺪى‬ ‫ﻓﻰ‬ ‫وﺑﺎﻟﺘﻌﻮﻳﺾ‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫إﺣﺪى‬ ‫ﻓﻰ‬ ‫وﺑﺎﻟﺘﻌﻮﻳﺾ‬ ‫ﺟـ‬ ‫ب‬ ‫اﻟﻀﻠﻊ‬ ‫ﻃﻮل‬ ‫ﻗﻴﻤﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻧﺤﺼﻞ‬ ‫ﺟـ‬ ‫ب‬ ‫اﻟﻀﻠﻊ‬ ‫ﻃﻮل‬ ‫ﻗﻴﻤﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻧﺤﺼﻞ‬ ) ) ‫ل‬ ‫ل‬ = ( = ( ٨٩٠٫١٥٩ ٨٩٠٫١٥٩ ‫م‬ ‫م‬
٢٧ ٢٧ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ا‬ ‫ب‬ ‫ا‬ 500.00 0 0 0 0.000 500.000 ‫ب‬ ‫ﺟـ‬ ‫ب‬ 890.16 0 0 45 629.437 629.437 ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ 854.00 0 33 110 799.657 -299.775 ‫د‬ ‫هـ‬ ‫د‬ 1019.80 0 41 168 200.117 -999.973 ‫هـ‬ ‫و‬ ‫هـ‬ 1118.00 21 55 258 -1097.170 -214.809 ‫و‬ ‫ا‬ ‫و‬ 656.80 0 54 305 -532.035 385.129 ‫ا‬ ‫اﻟﻤﺠﻤﻮع‬ 0.000 0.000 ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻄﻮل‬ ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺨﻂ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻘﻖ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻘﻖ‬ ٩ ٩ : : ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ : :
٢٨ ٢٨ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ١٠ ١٠ ) ) ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ : : ‫ﺿﻠﻌﻴﻦ‬ ‫ﻃﻮﻻ‬ ‫ﺿﻠﻌﻴﻦ‬ ‫ﻃﻮﻻ‬ : ( : ( ‫وﻗ‬ ‫ﻟﻸﺿﻼع‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻻﻧﺤﺮاف‬ ‫ﻗﻴﺎس‬ ‫ﺗﻢ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻓﻰ‬ ‫وﻗ‬ ‫ﻟﻸﺿﻼع‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻻﻧﺤﺮاف‬ ‫ﻗﻴﺎس‬ ‫ﺗﻢ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻓﻰ‬ ‫ﻃﻮل‬ ‫ﻴﺎس‬ ‫ﻃﻮل‬ ‫ﻴﺎس‬ ‫ب‬ ‫ا‬ ‫اﻟﻀﻠﻌﻴﻦ‬ ‫ﻣﻦ‬ ‫آﻞ‬ ‫ب‬ ‫ا‬ ‫اﻟﻀﻠﻌﻴﻦ‬ ‫ﻣﻦ‬ ‫آﻞ‬ ، ، ‫د‬ ‫ﺟـ‬ ‫اﻟﻀﻠﻌﻴﻦ‬ ‫ﻃﻮل‬ ‫ﻗﻴﺎس‬ ‫وﺗﻌﺬر‬ ‫ﺟـ‬ ‫ب‬ ‫د‬ ‫ﺟـ‬ ‫اﻟﻀﻠﻌﻴﻦ‬ ‫ﻃﻮل‬ ‫ﻗﻴﺎس‬ ‫وﺗﻌﺬر‬ ‫ﺟـ‬ ‫ب‬ ، ، ‫ا‬ ‫د‬ ‫ا‬ ‫د‬ . . ‫واﻟﻤﻄﻠﻮب‬ ‫واﻟﻤﻄﻠﻮب‬ ‫اﻟﺘﺎﻟﻰ‬ ‫ﺑﺎﻟﺠﺪول‬ ‫ﻣﻮﺿﺤﺔ‬ ‫اﻷرﺻﺎد‬ ‫ﺑﺄن‬ ‫ﻋﻠﻤﺎ‬ ‫أﻃﻮاﻟﻬﻤﺎ‬ ‫ﺣﺴﺎب‬ ‫اﻟﺘﺎﻟﻰ‬ ‫ﺑﺎﻟﺠﺪول‬ ‫ﻣﻮﺿﺤﺔ‬ ‫اﻷرﺻﺎد‬ ‫ﺑﺄن‬ ‫ﻋﻠﻤﺎ‬ ‫أﻃﻮاﻟﻬﻤﺎ‬ ‫ﺣﺴﺎب‬ : : ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ب‬ ‫ا‬ 150.0 0 30 178 ‫ﺟـ‬ ‫ب‬ 224.0 0 20 102 ‫د‬ ‫ﺟـ‬ L 0 45 31 ‫ا‬ ‫د‬ M 0 20 282 ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺨﻂ‬ ‫اﻟﻄﻮل‬
٢٩ ٢٩ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ا‬ ‫ب‬ ‫ا‬ 150.0 0 30 178 3.927 -149.949 ‫ب‬ ‫ﺟـ‬ ‫ب‬ 224.0 0 20 102 218.830 -47.846 ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ L 0 45 31 0.526L 0.850L ‫د‬ ‫ا‬ ‫د‬ M 0 20 282 -0.977M 0.214M ‫ا‬ ‫اﻟﻤﺠﻤﻮع‬ 222.757 -197.795 0.526L 0.850L -0.977M 0.214M ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺨﻂ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻄﻮل‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١٠ ١٠ : : ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ : :
٣٠ ٣٠ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١٠ ١٠ : : ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ = = ٢٢٢٫٧٥٧ ٢٢٢٫٧٥٧ + + ٠٫٥٢٦ ٠٫٥٢٦ ‫ل‬ ‫ل‬ - - ٠٫٩٧٧ ٠٫٩٧٧ ‫م‬ ‫م‬ = = ‫ﺻﻔﺮ‬ ‫ﺻﻔﺮ‬ ‫ل‬ ‫ل‬ = = - - ٤٢٣٫٤٩٢ ٤٢٣٫٤٩٢ + + ١٫٨٥٧ ١٫٨٥٧ ‫م‬ ‫م‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ = = - - ١٩٧٫٧٩٥ ١٩٧٫٧٩٥ + + ٠٫٨٥٠ ٠٫٨٥٠ ‫ل‬ ‫ل‬ + + ٠٫٢١٤ ٠٫٢١٤ ‫م‬ ‫م‬ = = ‫ﺻﻔﺮ‬ ‫ﺻﻔﺮ‬ ‫ل‬ ‫ل‬ = = ٢٣٢٫٧ ٢٣٢٫٧ – – ٠٫٢٥٢ ٠٫٢٥٢ ‫م‬ ‫م‬ ‫ﻣﺠﻬﻮﻟﻴﻦ‬ ‫ﻓﻰ‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫ﺑﺤﻞ‬ ‫ﻣﺠﻬﻮﻟﻴﻦ‬ ‫ﻓﻰ‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫ﺑﺤﻞ‬ ‫م‬ ‫اﻟﻄﻮل‬ ‫ﻳﻜﻮن‬ ‫م‬ ‫اﻟﻄﻮل‬ ‫ﻳﻜﻮن‬ = = ٣١١٫١٨٣ ٣١١٫١٨٣ ‫ﻣﺘﺮ‬ ‫ﻣﺘﺮ‬ ‫ل‬ ‫واﻟﻄﻮل‬ ‫ل‬ ‫واﻟﻄﻮل‬ = = ١٥٤٫٣٧٥ ١٥٤٫٣٧٥ ‫ﻣﺘﺮ‬ ‫ﻣﺘﺮ‬
٣١ ٣١ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻓﻰ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻘﻖ‬ ‫ﻣﺜﺎل‬ ‫ﻓﻰ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻘﻖ‬ ١٠ ١٠ : : ‫ﻣﻮﺿﻊ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫ﻣﻮﺿﻊ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫وﻳﻜﻮن‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫إﻋﺎدة‬ ‫ﺛﻢ‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ ‫وﻳﻜﻮن‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫إﻋﺎدة‬ ‫ﺛﻢ‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ ‫ﻟﻠﺼﻔﺮ‬ ‫ﻣﺴﺎوﻳﺎ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻤﺠﻤﻮع‬ ‫اﻟﺘﺤﻘﻴﻖ‬ ‫ﻟﻠﺼﻔﺮ‬ ‫ﻣﺴﺎوﻳﺎ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻤﺠﻤﻮع‬ ‫اﻟﺘﺤﻘﻴﻖ‬ : : ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ا‬ ‫ب‬ ‫ا‬ 150.0 0 30 178 3.927 -149.949 ‫ب‬ ‫ﺟـ‬ ‫ب‬ 224.0 0 20 102 218.830 -47.846 ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ 154.4 0 45 31 81.234 131.273 ‫د‬ ‫ا‬ ‫د‬ 311.2 0 20 282 -304.001 66.468 ‫ا‬ ‫اﻟﻤﺠﻤﻮع‬ 0.000 0.000 ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺨﻂ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻄﻮل‬
٣٢ ٣٢ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ١١ ١١ ) ) ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ : : ‫ﺿﻠﻌﻴﻦ‬ ‫اﻧﺤﺮاف‬ ‫ﺿﻠﻌﻴﻦ‬ ‫اﻧﺤﺮاف‬ : ( : ( ‫ﻓﻴﻪ‬ ‫ا‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻀﻠﻊ‬ ‫ﻓﻴﻪ‬ ‫ا‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻀﻠﻊ‬ : : ‫ب‬ ‫ا‬ 200.00 ‫ﺟـ‬ ‫ب‬ 350.00 0 0 102 ‫د‬ ‫ﺟـ‬ 150.00 ‫هـ‬ ‫د‬ 400.00 0 0 270 ‫اﻟﺨﻂ‬ ‫اﻟﻄﻮل‬ α β ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ب‬ ‫ا‬ ‫اﻟﻀﻠﻌﻴﻦ‬ ‫اﻧﺤﺮاف‬ ‫إﻳﺠﺎد‬ ‫واﻟﻤﻄﻠﻮب‬ ‫ب‬ ‫ا‬ ‫اﻟﻀﻠﻌﻴﻦ‬ ‫اﻧﺤﺮاف‬ ‫إﻳﺠﺎد‬ ‫واﻟﻤﻄﻠﻮب‬ ، ، ‫د‬ ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬
٣٣ ٣٣ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١١ ١١ : : ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ : : ‫ا‬ ‫ب‬ ‫ا‬ 200.00 α‫ﺟﺎ‬200 α‫ﺟﺘﺎ‬200 ‫ب‬ ‫ﺟـ‬ ‫ب‬ 350.00 0 0 102 342.352 -72.769 ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ 150.00 β‫ﺟﺎ‬150 β‫ﺟﺘﺎ‬150 ‫د‬ ‫هـ‬ ‫د‬ 400.00 0 0 270 -400.000 0.000 ‫ا‬ ‫اﻟﻤﺠﻤﻮع‬ 1100.00 -57.648 -72.769 α‫ﺟﺎ‬200 α‫ﺟﺘﺎ‬200 β‫ﺟﺎ‬150 β‫ﺟﺘﺎ‬150 ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ α β ‫اﻟﻨﻘﻄﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺨﻂ‬ ‫اﻟﻄﻮل‬
٣٤ ٣٤ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ٢٠٠ ٢٠٠ ‫ﺟﺎ‬ ‫ﺟﺎ‬ α α = = ٥٧٫٦٤٨ ٥٧٫٦٤٨ – – ١٥٠ ١٥٠ ‫ﺟﺎ‬ ‫ﺟﺎ‬ β β ‫ﺟﺎ‬ ‫ﺟﺎ‬ α α = = ٠٫٢٨٨٣٤ ٠٫٢٨٨٣٤ – – ٠٫٧٥ ٠٫٧٥ ‫ﺟﺎ‬ ‫ﺟﺎ‬ β β ‫ﻣﻌﺎدﻟﺔ‬ ‫ﻣﻌﺎدﻟﺔ‬ ) ) ١ ١ ( ( ٢٠٠ ٢٠٠ ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ α α = = ٧٢٫٧٦٩ ٧٢٫٧٦٩ – – ١٥٠ ١٥٠ ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ β β ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ α α = = ٠٫٣٦٣٨ ٠٫٣٦٣٨ – – ٠٫٧٥ ٠٫٧٥ ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ β β ‫ﻣﻌﺎدﻟﺔ‬ ‫ﻣﻌﺎدﻟﺔ‬ ) ) ٢ ٢ ( ( ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١١ ١١ : : ‫ﺟﺎ‬ ‫ﺟﺎ‬ ٢ ٢ α α = = ٠٫٠٨٣ ٠٫٠٨٣ + + ٠٫٥٦٢٥ ٠٫٥٦٢٥ ‫ﺟﺎ‬ ‫ﺟﺎ‬ ٢ ٢ β β - - ٢ ٢ ) ) ٠٫٢٨٨٢٤ ٠٫٢٨٨٢٤ x x ٠٫٧٥ ٠٫٧٥ ‫ﺟﺎ‬ ‫ﺟﺎ‬ β β ( ( ‫ﻣﻌﺎدﻟﺔ‬ ‫ﻣﻌﺎدﻟﺔ‬ ) ) ٣ ٣ ( ( ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫ﺑﺘﺮﺑﻴﻊ‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫ﺑﺘﺮﺑﻴﻊ‬ ١ ١ ، ، ٢ ٢ ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ ٢ ٢ α α = = ٠٫١٣٢٣ ٠٫١٣٢٣ + + ٠٫٥٦٢٥ ٠٫٥٦٢٥ ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ ٢ ٢ β β - - ٢ ٢ ) ) ٠٫٣٦٣٨ ٠٫٣٦٣٨ x x ٠٫٧٥ ٠٫٧٥ ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ β β ( ( ‫ﻣﻌﺎدﻟﺔ‬ ‫ﻣﻌﺎدﻟﺔ‬ ) ) ٤ ٤ ( (
٣٥ ٣٥ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ ) ) β β - - δ δ ) = ( ) = ( - - ٠٫٢٢٢٢ ٠٫٢٢٢٢ ( ( )) )) ‫س‬ ‫س‬ ٢ ٢ + + ‫ص‬ ‫ص‬ ٢ ٢ ( ( ½ ½ ( ( ) ) β β - - δ δ = ( = ( ٤٢ ٤٢ ‫ث‬ ‫ث‬ ٣٦ ٣٦ ‫ق‬ ‫ق‬ ١٠٨ ١٠٨ ‫أو‬ ‫د‬ ‫أو‬ ‫د‬ = = ١٨ ١٨ ‫ث‬ ‫ث‬ ٢٣ ٢٣ ‫ق‬ ‫ق‬ ٢٥١ ٢٥١ ‫د‬ ‫د‬ β β = = ٠٥ ٠٥ ‫ث‬ ‫ث‬ ٠٠ ٠٠ ‫ق‬ ‫ق‬ ١٤٧ ١٤٧ ‫أو‬ ‫د‬ ‫أو‬ ‫د‬ = = ٤١ ٤١ ‫ث‬ ‫ث‬ ٤٦ ٤٦ ‫ق‬ ‫ق‬ ٢٨٩ ٢٨٩ ‫د‬ ‫د‬ α α = = ٤٢ ٤٢ ‫ث‬ ‫ث‬ ٠٥ ٠٥ ‫ق‬ ‫ق‬ ٣٥٣ ٣٥٣ ‫أو‬ ‫د‬ ‫أو‬ ‫د‬ = = ٠٩ ٠٩ ‫ث‬ ‫ث‬ ٤٣ ٤٣ ‫ق‬ ‫ق‬ ٨٣ ٨٣ ‫د‬ ‫د‬ ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١١ ١١ : : ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫ﺑﺠﻤﻊ‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫ﺑﺠﻤﻊ‬ ٣ ٣ ، ، ٤ ٤ ٠٫٤٣٢٣٦ ٠٫٤٣٢٣٦ ‫ﺟﺎ‬ ‫ﺟﺎ‬ β β + + ٠٫٥٤٥٧ ٠٫٥٤٥٧ ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ β β = = - - ٠٫٢٢٢٢ ٠٫٢٢٢٢ ‫اﻟﺤﺪ‬ ‫أن‬ ‫وﺑﻔﺮض‬ ‫اﻟﺤﺪ‬ ‫أن‬ ‫وﺑﻔﺮض‬ ٠٫٤٣٢٣٦ ٠٫٤٣٢٣٦ = = ‫س‬ ‫س‬ ، ، ‫واﻟﺤﺪ‬ ‫واﻟﺤﺪ‬ ٠٫٥٤٥٧ ٠٫٥٤٥٧ = = ‫ﻣﻊ‬ ‫ص‬ ‫ﻣﻊ‬ ‫ص‬ ‫ﻣﺴﺎﻋﺪة‬ ‫ﺑﺰاوﻳﺔ‬ ‫اﻻﺳﺘﻌﺎﻧﺔ‬ ‫ﻣﺴﺎﻋﺪة‬ ‫ﺑﺰاوﻳﺔ‬ ‫اﻻﺳﺘﻌﺎﻧﺔ‬ δ δ ‫ﺣﻴﺚ‬ ‫ﺣﻴﺚ‬ ‫ﻇﺎ‬ ‫ﻇﺎ‬ δ δ = = ‫س‬ ‫س‬ ‫ص‬ ‫ص‬ = = ٠٫٧٩٢٣ ٠٫٧٩٢٣ ‫إذا‬ ‫إذا‬ δ δ = = ٢٣ ٢٣ ‫ث‬ ‫ث‬ ٢٣ ٢٣ ‫ق‬ ‫ق‬ ٣٨ ٣٨ ‫د‬ ‫د‬
٣٦ ٣٦ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻘﻖ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻘﻖ‬ ١١ ١١ ) ) ‫اﻷول‬ ‫اﻟﺤﻞ‬ ‫اﻷول‬ ‫اﻟﺤﻞ‬ :( :( ‫اﻟ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺄآﺪ‬ ‫آﻴﻔﻴﺔ‬ ‫ﻳﻮﺿﺢ‬ ‫اﻟﺘﺎﻟﻰ‬ ‫ﻓﺎﻟﺠﺪول‬ ‫ﺣﻼن‬ ‫ﻟﻬﺎ‬ ‫اﻟﻤﺴﺄﻟﺔ‬ ‫ﻷن‬ ‫ﻧﻈﺮا‬ ‫اﻟ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺄآﺪ‬ ‫آﻴﻔﻴﺔ‬ ‫ﻳﻮﺿﺢ‬ ‫اﻟﺘﺎﻟﻰ‬ ‫ﻓﺎﻟﺠﺪول‬ ‫ﺣﻼن‬ ‫ﻟﻬﺎ‬ ‫اﻟﻤﺴﺄﻟﺔ‬ ‫ﻷن‬ ‫ﻧﻈﺮا‬ ‫اﻷول‬ ‫ﺑﺎﻟﺤﻞ‬ ‫ﻨﺘﺎﺋﺞ‬ ‫اﻷول‬ ‫ﺑﺎﻟﺤﻞ‬ ‫ﻨﺘﺎﺋﺞ‬ ‫ا‬ ‫ب‬ ‫ا‬ 200.00 42 5 353 -24.045 198.549 ‫ب‬ ‫ﺟـ‬ ‫ب‬ 350.00 0 0 102 342.352 -72.769 ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ 150.00 5 0 147 81.693 -125.803 ‫د‬ ‫هـ‬ ‫د‬ 400.00 0 0 270 -400.000 0.000 ‫ا‬ ‫اﻟﻤﺠﻤﻮع‬ 1100.00 0.000 0.000 ‫اﻟﻨﻘﻄﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫اﻟﺨﻂ‬ ‫اﻟﻄﻮل‬
٣٧ ٣٧ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ا‬ ‫ب‬ ‫ا‬ 200.00 9 43 83 198.800 21.880 ‫ب‬ ‫ﺟـ‬ ‫ب‬ 350.00 0 0 102 342.352 -72.769 ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ 150.00 9 46 289 -141.159 50.735 ‫د‬ ‫هـ‬ ‫د‬ 400.00 0 0 270 -400.000 0.000 ‫ا‬ ‫اﻟﻤﺠﻤﻮع‬ 1100.00 0.000 0.000 ‫اﻟﻨﻘﻄﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫اﻟﺨﻂ‬ ‫اﻟﻄﻮل‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻘﻖ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻘﻖ‬ ١١ ١١ ) ) ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﺤﻞ‬ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﺤﻞ‬ :( :( ‫اﻟﺜﺎﻧﻰ‬ ‫ﺑﺎﻟﺤﻞ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺄآﺪ‬ ‫آﻴﻔﻴﺔ‬ ‫ﻳﻮﺿﺢ‬ ‫اﻟﺘﺎﻟﻰ‬ ‫اﻟﺠﺪول‬ ‫اﻟﺜﺎﻧﻰ‬ ‫ﺑﺎﻟﺤﻞ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺄآﺪ‬ ‫آﻴﻔﻴﺔ‬ ‫ﻳﻮﺿﺢ‬ ‫اﻟﺘﺎﻟﻰ‬ ‫اﻟﺠﺪول‬
٣٨ ٣٨ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﺒﺎب‬ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﺒﺎب‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﻴﺰاﻧﻴﺔ‬ ‫ﺑﺎب‬ ‫اﻟﻤﻴﺰاﻧﻴﺔ‬ ‫ﺑﺎب‬
٣٩ ٣٩ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ١ ١ : : ‫ﻋﻠﻰ‬ ‫اﻟﻘﺮاءة‬ ‫ﻓﻜﺎﻧﺖ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻣﻨﺘﺼﻒ‬ ‫ﻓﻰ‬ ‫ﻣﻴﺰان‬ ‫وﺿﻊ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻘﺮاءة‬ ‫ﻓﻜﺎﻧﺖ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻣﻨﺘﺼﻒ‬ ‫ﻓﻰ‬ ‫ﻣﻴﺰان‬ ‫وﺿﻊ‬ ‫ا‬ ‫اﻟﻘﺎﻣﺔ‬ ‫ا‬ ‫اﻟﻘﺎﻣﺔ‬ ) ) ١٫٦٨ ١٫٦٨ ‫م‬ ‫م‬ ( ( ‫ب‬ ‫اﻟﻘﺎﻣﺔ‬ ‫وﻋﻠﻰ‬ ‫ب‬ ‫اﻟﻘﺎﻣﺔ‬ ‫وﻋﻠﻰ‬ ) ) ١٫٩٥ ١٫٩٥ ‫م‬ ‫م‬ ( ( ‫اﻟﺠﻬﺎز‬ ‫ﻧﻘﻞ‬ ‫ﺛﻢ‬ ‫اﻟﺠﻬﺎز‬ ‫ﻧﻘﻞ‬ ‫ﺛﻢ‬ ‫ا‬ ‫اﻟﻘﺎﻣﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻘﺮاءة‬ ‫ﻓﻜﺎﻧﺖ‬ ‫ب‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻣﻦ‬ ‫ﻗﺮﻳﺒﺎ‬ ‫ووﺿﻊ‬ ‫ا‬ ‫اﻟﻘﺎﻣﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻘﺮاءة‬ ‫ﻓﻜﺎﻧﺖ‬ ‫ب‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻣﻦ‬ ‫ﻗﺮﻳﺒﺎ‬ ‫ووﺿﻊ‬ ) ) ١٫٣١ ١٫٣١ ‫م‬ ‫م‬ ( ( ‫ب‬ ‫اﻟﻘﺎﻣﺔ‬ ‫وﻋﻠﻰ‬ ‫ب‬ ‫اﻟﻘﺎﻣﺔ‬ ‫وﻋﻠﻰ‬ ) ) ١٫٧٤ ١٫٧٤ ‫م‬ ‫م‬ .( .( ‫ووﺿﺢ‬ ‫اﻟﻨﻈﺮ‬ ‫ﺧﻂ‬ ‫ﻳﻮﺿﺢ‬ ‫ﺷﻜﻼ‬ ‫ارﺳﻢ‬ ‫ووﺿﺢ‬ ‫اﻟﻨﻈﺮ‬ ‫ﺧﻂ‬ ‫ﻳﻮﺿﺢ‬ ‫ﺷﻜﻼ‬ ‫ارﺳﻢ‬ ‫ﻟﻤﻌﺎﻳﺮة‬ ‫اﻟﻼزم‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻗﻴﻤﺔ‬ ‫وﻣﺎ‬ ‫ﺑﺎﻟﻤﻴﺰان‬ ‫اﻟﺮﺻﺪ‬ ‫ﻳﻤﻜﻦ‬ ‫هﻞ‬ ‫ﻟﻤﻌﺎﻳﺮة‬ ‫اﻟﻼزم‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻗﻴﻤﺔ‬ ‫وﻣﺎ‬ ‫ﺑﺎﻟﻤﻴﺰان‬ ‫اﻟﺮﺻﺪ‬ ‫ﻳﻤﻜﻦ‬ ‫هﻞ‬ ‫اﻟﻤﻴﺰان‬ ‫اﻟﻤﻴﺰان‬ . .
٤٠ ٤٠ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ب‬ ‫ب‬ ١٫٩٥ ١٫٩٥ ١٫٦٨ ١٫٦٨ ‫ﻟﻠﻤﻴﺰان‬ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﻮﺿﻊ‬ ‫ﻟﻠﻤﻴﺰان‬ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﻮﺿﻊ‬ ‫ﻟﻠﻤﻴﺰان‬ ‫اﻷول‬ ‫اﻟﻮﺿﻊ‬ ‫ﻟﻠﻤﻴﺰان‬ ‫اﻷول‬ ‫اﻟﻮﺿﻊ‬ ١٫٣١ ١٫٣١ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١ ١ : : ‫اﻟﺤﺎﻟﺘﻴﻦ‬ ‫ﻓﻰ‬ ‫اﻟﺠﻬﺎز‬ ‫وﺿﻌﻰ‬ ‫رﺳﻢ‬ ‫ﻳﺘﻢ‬ ‫اﻟﺤﺎﻟﺘﻴﻦ‬ ‫ﻓﻰ‬ ‫اﻟﺠﻬﺎز‬ ‫وﺿﻌﻰ‬ ‫رﺳﻢ‬ ‫ﻳﺘﻢ‬ ‫اﻷول‬ ‫اﻟﻮﺿﻊ‬ ‫ﻓﻰ‬ ‫اﻷول‬ ‫اﻟﻮﺿﻊ‬ ‫ﻓﻰ‬ : : ‫ا‬ ‫ﺑﻴﻦ‬ ‫اﻟﺤﻘﻴﻘﻰ‬ ‫اﻟﻤﻨﺴﻮب‬ ‫ﻓﺮق‬ ‫ا‬ ‫ﺑﻴﻦ‬ ‫اﻟﺤﻘﻴﻘﻰ‬ ‫اﻟﻤﻨﺴﻮب‬ ‫ﻓﺮق‬ ، ، ‫ب‬ ‫ب‬ = = ١٫٩٥ ١٫٩٥ - - ١٫٦٨ ١٫٦٨ = = ٠٫٢٧ ٠٫٢٧ ‫م‬ ‫م‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ب‬ ‫ب‬ ١٫٧٤ ١٫٧٤ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﻮﺿﻊ‬ ‫ﻓﻰ‬ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﻮﺿﻊ‬ ‫ﻓﻰ‬ : : ‫ا‬ ‫ﺑﻴﻦ‬ ‫اﻟﻤﻨﺴﻮب‬ ‫ﻓﺮق‬ ‫ﻳﻜﻮن‬ ‫ا‬ ‫ﺑﻴﻦ‬ ‫اﻟﻤﻨﺴﻮب‬ ‫ﻓﺮق‬ ‫ﻳﻜﻮن‬ ، ، ‫ب‬ ‫ب‬ = = ١٫٧٤ ١٫٧٤ - - ١٫٣١ ١٫٣١ = = ٠٫٤٣ ٠٫٤٣ ‫م‬ ‫م‬ ‫اﻟﻤﻨﺴﻮب‬ ‫ﻓﺮق‬ ‫ﻻﺧﺘﻼف‬ ‫ﻧﻈﺮا‬ ‫اﻟﻤﻨﺴﻮب‬ ‫ﻓﺮق‬ ‫ﻻﺧﺘﻼف‬ ‫ﻧﻈﺮا‬ ‫اﻟﺮﺻﺪ‬ ‫ﻳﻤﻜﻦ‬ ‫ﻻ‬ ‫إذا‬ ‫اﻟﻮﺿﻌﻴﻦ‬ ‫ﻓﻰ‬ ‫اﻟﺮﺻﺪ‬ ‫ﻳﻤﻜﻦ‬ ‫ﻻ‬ ‫إذا‬ ‫اﻟﻮﺿﻌﻴﻦ‬ ‫ﻓﻰ‬ ‫ﻣﻌﺎﻳﺮة‬ ‫اﻟﻰ‬ ‫وﻳﺤﺘﺎج‬ ‫ﺑﺎﻟﻤﻴﺰان‬ ‫ﻣﻌﺎﻳﺮة‬ ‫اﻟﻰ‬ ‫وﻳﺤﺘﺎج‬ ‫ﺑﺎﻟﻤﻴﺰان‬ . . ‫ﻓﻰ‬ ‫ب‬ ‫ﻋﻨﺪ‬ ‫اﻟﺨﻄﺄ‬ ‫ان‬ ‫وﺑﺎﻋﺘﺒﺎر‬ ‫ﻓﻰ‬ ‫ب‬ ‫ﻋﻨﺪ‬ ‫اﻟﺨﻄﺄ‬ ‫ان‬ ‫وﺑﺎﻋﺘﺒﺎر‬ ‫ﺻﻔﺮ‬ ‫ﻳﺴﺎوى‬ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﻮﺿﻊ‬ ‫ﺻﻔﺮ‬ ‫ﻳﺴﺎوى‬ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﻮﺿﻊ‬ ، ، ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻗﻴﻤﺔ‬ ‫ﻓﺘﻜﻮن‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻗﻴﻤﺔ‬ ‫ﻓﺘﻜﻮن‬ : : ١٫٧٤ ١٫٧٤ = = ٠٫٢٧ ٠٫٢٧ + + ١٫٣١ ١٫٣١ - - ‫س‬ ‫س‬ ‫س‬ ‫س‬ = = ٠٫١٦ ٠٫١٦ ‫م‬ ‫م‬ ‫س‬ ‫س‬
٤١ ٤١ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٢ ٢ : : ‫ﻟﻄﺮﻳﻖ‬ ‫ﻃﻮﻟﻰ‬ ‫ﻣﺤﻮر‬ ‫ﻋﻠﻰ‬ ‫ﺑﺎﻟﻤﻴﺰان‬ ‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﻘﺮاءات‬ ‫أﺧﺬت‬ ‫ﻟﻄﺮﻳﻖ‬ ‫ﻃﻮﻟﻰ‬ ‫ﻣﺤﻮر‬ ‫ﻋﻠﻰ‬ ‫ﺑﺎﻟﻤﻴﺰان‬ ‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﻘﺮاءات‬ ‫أﺧﺬت‬ : : ) ) ٢٫١٩ ٢٫١٩ ( ( ، ، ٢٫٥٠ ٢٫٥٠ ، ، ٢٫٣٢ ٢٫٣٢ ، ، ١٫٤٩ ١٫٤٩ ، ، ) ) ٣٫٠١ ٣٫٠١ ( ( ، ، ٢٫٥١ ٢٫٥١ ، ، ٢٫٨١ ٢٫٨١ ، ، ) ) ١٫٧٥ ١٫٧٥ ( ( ، ، ٣٫٨١ ٣٫٨١ . . ‫ﻧﻘﻄﺔ‬ ‫أول‬ ‫وﻣﻨﺴﻮب‬ ‫ﻣﺆﺧﺮات‬ ‫اﻷﻗﻮاس‬ ‫ﺑﻴﻦ‬ ‫اﻟﻘﺮاءات‬ ‫آﺎﻧﺖ‬ ‫ﻓﺈذا‬ ‫ﻧﻘﻄﺔ‬ ‫أول‬ ‫وﻣﻨﺴﻮب‬ ‫ﻣﺆﺧﺮات‬ ‫اﻷﻗﻮاس‬ ‫ﺑﻴﻦ‬ ‫اﻟﻘﺮاءات‬ ‫آﺎﻧﺖ‬ ‫ﻓﺈذا‬ +) +) ٣٠ ٣٠ ‫م‬ ‫م‬ ( ( ، ، ‫ﻣﺨﺘﻠﻔﺘﻴﻦ‬ ‫ﺑﻄﺮﻳﻘﺘﻴﻦ‬ ‫اﻟﻨﻘﻂ‬ ‫ﺑﺎﻗﻰ‬ ‫ﻣﻨﺎﺳﻴﺐ‬ ‫ﻓﺎﺣﺴﺐ‬ ‫ﻣﺨﺘﻠﻔﺘﻴﻦ‬ ‫ﺑﻄﺮﻳﻘﺘﻴﻦ‬ ‫اﻟﻨﻘﻂ‬ ‫ﺑﺎﻗﻰ‬ ‫ﻣﻨﺎﺳﻴﺐ‬ ‫ﻓﺎﺣﺴﺐ‬ . .
٤٢ ٤٢ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٢ ٢ : : ‫اﻟﻤﻴﺰان‬ ‫ﺳﻄﺢ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻤﻴﺰان‬ ‫ﺳﻄﺢ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﻤﺆﺧﺮة‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﻤﻘﺪﻣﺔ‬ ‫ﺳﻄﺢ‬ ‫ﻣﻨﺴﻮب‬ ‫اﻟﻤﻴﺰان‬ ‫ﻣﻨﺴﻮب‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻣﻼﺣﻈﺎت‬ ‫ا‬ 2.19 32.19 30.00 ‫روﺑﻴﺮ‬ ‫ب‬ 2.50 29.69 ‫ﺟـ‬ 2.32 29.87 ‫د‬ 3.01 1.49 33.71 30.70 ‫دوران‬ ‫هـ‬ 2.51 31.20 ‫و‬ 1.75 2.81 32.65 30.90 ‫دوران‬ ‫ز‬ 3.81 28.84 ‫اﻟﻤﺠﻤﻮع‬ 6.95 8.11 ‫اﻟﻔﺮق‬ 1.16 1.16 ‫اﻟﺘﺤﻘﻴﻖ‬ O.K
٤٣ ٤٣ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٢ ٢ : : ‫واﻻﻧﺨﻔﺎض‬ ‫اﻻرﺗﻔﺎع‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫واﻻﻧﺨﻔﺎض‬ ‫اﻻرﺗﻔﺎع‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﻤﺆﺧﺮة‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﻤﻘﺪﻣﺔ‬ ‫ارﺗﻔﺎع‬ (+) ‫اﻧﺨﻔﺎض‬ (-) ‫ﻣﻨﺴﻮب‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻣﻼﺣﻈﺎت‬ ‫ا‬ 2.19 30.00 ‫روﺑﻴﺮ‬ ‫ب‬ 2.50 0.31 29.69 ‫ﺟـ‬ 2.32 0.18 29.87 ‫د‬ 3.01 1.49 0.83 30.70 ‫دوران‬ ‫هـ‬ 2.51 0.50 31.20 ‫و‬ 1.75 2.81 0.30 30.90 ‫دوران‬ ‫ز‬ 3.81 2.06 28.84 ‫اﻟﻤﺠﻤﻮع‬ 6.95 8.11 ‫اﻟﻔﺮق‬ 1.16 1.16 ‫اﻟﺘﺤﻘﻴﻖ‬ O.K
٤٤ ٤٤ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٣ ٣ : : ‫اﻟﻤﻴﺰان‬ ‫ﺳﻄﺢ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻤﻴﺰان‬ ‫ﺳﻄﺢ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﻤﺆﺧﺮة‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﻤﻘﺪﻣﺔ‬ ‫ﺳﻄﺢ‬ ‫ﻣﻨﺴﻮب‬ ‫اﻟﻤﻴﺰان‬ ‫ﻣﻨﺴﻮب‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻣﻼﺣﻈﺎت‬ ‫ا‬ 2.19 26.35 24.16 ‫ب‬ 2.50 23.85 ‫ﺟـ‬ 2.32 24.03 ‫د‬ 3.01 1.49 27.87 24.86 ‫دوران‬ ‫هـ‬ 2.51 25.36 ‫و‬ 1.75 2.81 26.81 25.06 ‫دوران‬ ‫ز‬ 3.81 23.00 ‫روﺑﻴﺮ‬ ‫اﻟﻤﺠﻤﻮع‬ 6.95 8.11 ‫اﻟﻔﺮق‬ 1.16 1.16 ‫اﻟﺘﺤﻘﻴﻖ‬ O.K ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٣ ٣ : : ‫ﺑﻄﺮﻳﻘﺘﻴﻦ‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻰ‬ ‫اﻟﻨﻘﻂ‬ ‫ﻣﻨﺎﺳﻴﺐ‬ ‫ﺣﺴﺎب‬ ‫اﻟﻤﻄﻠﻮب‬ ‫ﺑﻄﺮﻳﻘﺘﻴﻦ‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻰ‬ ‫اﻟﻨﻘﻂ‬ ‫ﻣﻨﺎﺳﻴﺐ‬ ‫ﺣﺴﺎب‬ ‫اﻟﻤﻄﻠﻮب‬ ‫ﻧﻘﻄﺔ‬ ‫ﺁﺧﺮ‬ ‫ﻣﻨﺴﻮب‬ ‫آﺎن‬ ‫إذا‬ ‫ﻣﺨﺘﻠﻔﺘﻴﻦ‬ ‫ﻧﻘﻄﺔ‬ ‫ﺁﺧﺮ‬ ‫ﻣﻨﺴﻮب‬ ‫آﺎن‬ ‫إذا‬ ‫ﻣﺨﺘﻠﻔﺘﻴﻦ‬ +) +) ٢٣ ٢٣ ‫م‬ ‫م‬ .( .(
٤٥ ٤٥ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٣ ٣ : : ‫واﻻﻧﺨﻔﺎض‬ ‫اﻻرﺗﻔﺎع‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫واﻻﻧﺨﻔﺎض‬ ‫اﻻرﺗﻔﺎع‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﻤﺆﺧﺮة‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﻤﻘﺪﻣﺔ‬ ‫ارﺗﻔﺎع‬ (+) ‫اﻧﺨﻔﺎض‬ (-) ‫ﻣﻨﺴﻮب‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻣﻼﺣﻈﺎت‬ ‫ا‬ 2.19 24.16 ‫روﺑﻴﺮ‬ ‫ب‬ 2.50 0.31 23.85 ‫ﺟـ‬ 2.32 0.18 24.03 ‫د‬ 3.01 1.49 0.83 24.86 ‫دوران‬ ‫هـ‬ 2.51 0.50 25.36 ‫و‬ 1.75 2.81 0.30 25.06 ‫دوران‬ ‫ز‬ 3.81 2.06 23.00 ‫اﻟﻤﺠﻤﻮع‬ 6.95 8.11 ‫اﻟﻔﺮق‬ 1.16 1.16 ‫اﻟﺘﺤﻘﻴﻖ‬ O.K
٤٦ ٤٦ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﺒﺎب‬ ‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﺒﺎب‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻋﻠﻰ‬ ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺴﺎب‬ ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺴﺎب‬
٤٧ ٤٧ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ١ ١ : : ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺴﺎب‬ ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻣﻦ‬ ‫ﻣﻦ‬ ‫اﻟﺸﺒﻜﻴﺔ‬ ‫اﻟﻤﻴﺰاﻧﻴﺔ‬ ‫اﻟﺸﺒﻜﻴﺔ‬ ‫اﻟﻤﻴﺰاﻧﻴﺔ‬ - - ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻣﻄﻠﻮب‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻣﻄﻠﻮب‬ ‫اﻷرض‬ ‫ﻟﺘﺴﻮﻳﺔ‬ ‫اﻟﻼزﻣﺔ‬ ‫واﻟﺮدم‬ ‫اﻷرض‬ ‫ﻟﺘﺴﻮﻳﺔ‬ ‫اﻟﻼزﻣﺔ‬ ‫واﻟﺮدم‬ ‫ﻣﻨﺴﻮب‬ ‫ﻋﻠﻰ‬ ‫ﺑﺎﻟﺸﻜﻞ‬ ‫اﻟﻤﻮﺿﺤﺔ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻋﻠﻰ‬ ‫ﺑﺎﻟﺸﻜﻞ‬ ‫اﻟﻤﻮﺿﺤﺔ‬ + + ٧٫٠٠ ٧٫٠٠ ‫ﻣﺮﺑﻌﺔ‬ ‫اﻟﻮﺣﺪة‬ ‫ﺑﺄن‬ ‫ﻋﻠﻤﺎ‬ ‫ﻣﺘﺮ‬ ‫ﻣﺮﺑﻌﺔ‬ ‫اﻟﻮﺣﺪة‬ ‫ﺑﺄن‬ ‫ﻋﻠﻤﺎ‬ ‫ﻣﺘﺮ‬ ‫وأﺑﻌﺎدهﺎ‬ ‫اﻟﺸﻜﻞ‬ ‫وأﺑﻌﺎدهﺎ‬ ‫اﻟﺸﻜﻞ‬ ٣٠ ٣٠ x x ٣٠ ٣٠ ‫م‬ ‫م‬ . . ٦٫٥ ٦٫٥ ٧٫٥ ٧٫٥ ٦٫٨ ٦٫٨ ٨٫١ ٨٫١ ٨٫٣ ٨٫٣ ٧٫٣ ٧٫٣ ٧٫٠ ٧٫٠ ٧٫٢ ٧٫٢ ٧٫٥ ٧٫٥ ٦٫١ ٦٫١ ٦٫٨ ٦٫٨ ٦٫٥ ٦٫٥ ٦٫٦ ٦٫٦ ٦٫٧ ٦٫٧ ٦٫٠ ٦٫٠ ٥٫٨ ٥٫٨ ٥٫٥ ٥٫٥ ٦٫٠ ٦٫٠ ٥٫٣ ٥٫٣ ٩٫١ ٩٫١ ٨٫٥ ٨٫٥ ٨٫٥ ٨٫٥
٤٨ ٤٨ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١ ١ : : ٦٫٥ ٦٫٥ ٧٫٥ ٧٫٥ ٦٫٨ ٦٫٨ ٨٫١ ٨٫١ ٨٫٣ ٨٫٣ ٧٫٣ ٧٫٣ ٧٫٠ ٧٫٠ ٧٫٢ ٧٫٢ ٧٫٥ ٧٫٥ ٦٫١ ٦٫١ ٦٫٨ ٦٫٨ ٦٫٥ ٦٫٥ ٦٫٦ ٦٫٦ ٦٫٧ ٦٫٧ ٦٫٠ ٦٫٠ ٥٫٨ ٥٫٨ ٥٫٥ ٥٫٥ ٦٫٠ ٦٫٠ ٥٫٣ ٥٫٣ ٩٫١ ٩٫١ ٨٫٥ ٨٫٥ ٨٫٥ ٨٫٥ - - ‫رﺳﻢ‬ ‫ﻳﺘﻢ‬ ‫رﺳﻢ‬ ‫ﻳﺘﻢ‬ ‫آﻨﺘﻮر‬ ‫آﻨﺘﻮر‬ + + ٧٫٠٠ ٧٫٠٠ ‫م‬ ‫م‬ - - ‫اﻷﻋﻠﻰ‬ ‫اﻟﻘﻴﻤﺔ‬ ‫ذات‬ ‫اﻷرآﺎن‬ ‫اﻷﻋﻠﻰ‬ ‫اﻟﻘﻴﻤﺔ‬ ‫ذات‬ ‫اﻷرآﺎن‬ ‫ﻣﻨﺴﻮب‬ ‫ﻣﻦ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻣﻦ‬ + + ٧٫٠٠ ٧٫٠٠ ‫م‬ ‫م‬ ‫اﻷﻗﻞ‬ ‫واﻷرآﺎن‬ ‫ﺣﻔﺮ‬ ‫ﻣﻨﺎﻃﻖ‬ ‫اﻷﻗﻞ‬ ‫واﻷرآﺎن‬ ‫ﺣﻔﺮ‬ ‫ﻣﻨﺎﻃﻖ‬ ‫ردم‬ ‫ﻣﻨﺎﻃﻖ‬ ‫ردم‬ ‫ﻣﻨﺎﻃﻖ‬ . . ‫ﺣﻔﺮ‬ ‫ﺣﻔﺮ‬ ‫ردم‬ ‫ردم‬
٤٩ ٤٩ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١ ١ : : ٠٫٥ ٠٫٥ ٠٫٥ ٠٫٥ ٠٫٢ ٠٫٢ ١٫١ ١٫١ ١٫٣ ١٫٣ ٠٫٣ ٠٫٣ ٠٫٠ ٠٫٠ ٠٫٢ ٠٫٢ ٠٫٥ ٠٫٥ ٠٫٩ ٠٫٩ ٠٫٢ ٠٫٢ ٠٫٥ ٠٫٥ ٠٫٤ ٠٫٤ ٠٫٣ ٠٫٣ ١٫٠ ١٫٠ ١٫٢ ١٫٢ ١٫٥ ١٫٥ ١٫٠ ١٫٠ ١٫٧ ١٫٧ ٢٫١ ٢٫١ ١٫٥ ١٫٥ ١٫٥ ١٫٥ - - ‫ﻃﺮح‬ ‫ﻳﺘﻢ‬ ‫ﻃﺮح‬ ‫ﻳﺘﻢ‬ + + ٧٫٠٠ ٧٫٠٠ ‫ﻣﻦ‬ ‫م‬ ‫ﻣﻦ‬ ‫م‬ ‫وﻧﻀﻊ‬ ‫اﻷرآﺎن‬ ‫ﺟﻤﻴﻊ‬ ‫ﻣﻨﺎﺳﻴﺐ‬ ‫وﻧﻀﻊ‬ ‫اﻷرآﺎن‬ ‫ﺟﻤﻴﻊ‬ ‫ﻣﻨﺎﺳﻴﺐ‬ ‫أو‬ ‫ﺟﺪﻳﺪ‬ ‫رﺳﻢ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻔﺮق‬ ‫أو‬ ‫ﺟﺪﻳﺪ‬ ‫رﺳﻢ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻔﺮق‬ ‫اﻟﺮﺳﻢ‬ ‫ﻧﻔﺲ‬ ‫ﻋﻠﻰ‬ ‫ﺁﺧﺮ‬ ‫ﺑﻠﻮن‬ ‫اﻟﺮﺳﻢ‬ ‫ﻧﻔﺲ‬ ‫ﻋﻠﻰ‬ ‫ﺁﺧﺮ‬ ‫ﺑﻠﻮن‬ . . ‫ﺣﻔﺮ‬ ‫ﺣﻔﺮ‬ ‫ردم‬ ‫ردم‬
٥٠ ٥٠ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١ ١ : : - - ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺠﻢ‬ ‫ﺣﺴﺎب‬ ‫ﻳﺘﻢ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺠﻢ‬ ‫ﺣﺴﺎب‬ ‫ﻳﺘﻢ‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻟﺮدم‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻟﺮدم‬ ) ) ‫ﻋﺪد‬ ‫ﻋﺪد‬ ٦ ٦ ‫ﻣﺮﺑﻌﺎت‬ ‫ﻣﺮﺑﻌﺎت‬ :( :( ٠٫٥ ٠٫٥ ٠٫٥ ٠٫٥ ٠٫٢ ٠٫٢ ١٫١ ١٫١ ١٫٣ ١٫٣ ٠٫٣ ٠٫٣ ٠٫٠ ٠٫٠ ٠٫٢ ٠٫٢ ٠٫٥ ٠٫٥ ٠٫٩ ٠٫٩ ٠٫٢ ٠٫٢ ٠٫٥ ٠٫٥ ٠٫٤ ٠٫٤ ٠٫٣ ٠٫٣ ١٫٠ ١٫٠ ١٫٢ ١٫٢ ١٫٥ ١٫٥ ١٫٠ ١٫٠ ١٫٧ ١٫٧ ٢٫١ ٢٫١ ١٫٥ ١٫٥ ١٫٥ ١٫٥ ‫ﺣﻔﺮ‬ ‫ﺣﻔﺮ‬ ‫ردم‬ ‫ردم‬ ١‫ع‬ ٢‫ع‬ ٣‫ع‬ ٤‫ع‬ 1 1.2 0.3 1.7 1.5 0.4 0.9 1 0.5 0.2 0.2 0.5 4.1 4.6 0 0.7 ‫اﻟﺤﺠﻢ‬ ‫اﻟﺤﺠﻢ‬ )) = )) = ٣٠ ٣٠ x x ٣٠ ٣٠ ( ( ٤ ٤ ( ( x x ) ) ١ ١ x x ٤٫١ ٤٫١ + + ٢ ٢ x x ٤٫٦ ٤٫٦ + + ٤ ٤ x x ٠٫٧ ٠٫٧ = ( = ( ٣٦٢٢٫٥ ٣٦٢٢٫٥ ‫م‬ ‫م‬ ٣ ٣
٥١ ٥١ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١ ١ : : - - ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺠﻢ‬ ‫ﺣﺴﺎب‬ ‫ﻳﺘﻢ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺠﻢ‬ ‫ﺣﺴﺎب‬ ‫ﻳﺘﻢ‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫اﻟﺮدم‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫اﻟﺮدم‬ ) ) ‫ﻋﺪد‬ ‫ﻋﺪد‬ ٣ ٣ ‫أﺟﺰاء‬ ‫أﺟﺰاء‬ :( :( ٠٫٥ ٠٫٥ ٠٫٥ ٠٫٥ ٠٫٢ ٠٫٢ ١٫١ ١٫١ ١٫٣ ١٫٣ ٠٫٣ ٠٫٣ ٠٫٠ ٠٫٠ ٠٫٢ ٠٫٢ ٠٫٥ ٠٫٥ ٠٫٩ ٠٫٩ ٠٫٢ ٠٫٢ ٠٫٥ ٠٫٥ ٠٫٤ ٠٫٤ ٠٫٣ ٠٫٣ ١٫٠ ١٫٠ ١٫٢ ١٫٢ ١٫٥ ١٫٥ ١٫٠ ١٫٠ ١٫٧ ١٫٧ ٢٫١ ٢٫١ ١٫٥ ١٫٥ ١٫٥ ١٫٥ ‫ﺣﻔﺮ‬ ‫ﺣﻔﺮ‬ ‫ردم‬ ‫ردم‬ I I II II III III ‫ﺣﺠﻢ‬ ‫ﺣﺠﻢ‬ I I ) = ) = ١٥ ١٥ x x ٣٠ ٣٠ ( ( x x )) )) ٠٫٥ ٠٫٥ + + ٠٫٢ ٠٫٢ + + ٠٫٠ ٠٫٠ + + ٠٫٠ ٠٫٠ ( ( ٤ ٤ =( =( ٧٨٫٧٥ ٧٨٫٧٥ ‫م‬ ‫م‬ ٣ ٣ ‫ﺣﺠﻢ‬ ‫ﺣﺠﻢ‬ II II ))= ))= ١٥ ١٥ + + ٣٠ ٣٠ ( ( ٢ ٢ ( ( x x ٣٠ ٣٠ ( ( x x )) )) ٠٫٢ ٠٫٢ + + ٠٫٢ ٠٫٢ + + ٠٫٠ ٠٫٠ + + ٠٫٠ ٠٫٠ ( ( ٤ ٤ =( =( ٦٧٫٥ ٦٧٫٥ ‫م‬ ‫م‬ ٣ ٣ ‫ﺣﺠﻢ‬ ‫ﺣﺠﻢ‬ III III ))= ))= ٢٢٫٥ ٢٢٫٥ + + ٣٠ ٣٠ ( ( ٢ ٢ ( ( x x ٣٠ ٣٠ ( ( x x )) )) ٠٫٩ ٠٫٩ + + ٠٫٢ ٠٫٢ + + ٠٫٠ ٠٫٠ + + ٠٫٠ ٠٫٠ ( ( ٤ ٤ =( =( ٢١٦٫٥٦ ٢١٦٫٥٦ ‫م‬ ‫م‬ ٣ ٣ ‫اﻟﺮدم‬ ‫ﺣﺠﻢ‬ ‫اﺟﻤﺎﻟﻰ‬ ‫اﻟﺮدم‬ ‫ﺣﺠﻢ‬ ‫اﺟﻤﺎﻟﻰ‬ = = ٣٦٢٢٫٥ ٣٦٢٢٫٥ + + ٧٨٫٧٥ ٧٨٫٧٥ + + ٦٧٫٥ ٦٧٫٥ + + ٢١٦٫٥٦ ٢١٦٫٥٦ = = ٣٩٨٥٫٣١ ٣٩٨٥٫٣١ ‫م‬ ‫م‬ ٣ ٣
٥٢ ٥٢ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١ ١ : : - - ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺠﻢ‬ ‫ﺣﺴﺎب‬ ‫ﻳﺘﻢ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺠﻢ‬ ‫ﺣﺴﺎب‬ ‫ﻳﺘﻢ‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻟﺤﻔﺮ‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻟﺤﻔﺮ‬ ) ) ‫ﻋﺪد‬ ‫ﻋﺪد‬ ٤ ٤ ‫ﻣﺮﺑﻌﺎت‬ ‫ﻣﺮﺑﻌﺎت‬ :( :( ٠٫٥ ٠٫٥ ٠٫٥ ٠٫٥ ٠٫٢ ٠٫٢ ١٫١ ١٫١ ١٫٣ ١٫٣ ٠٫٣ ٠٫٣ ٠٫٠ ٠٫٠ ٠٫٢ ٠٫٢ ٠٫٥ ٠٫٥ ٠٫٩ ٠٫٩ ٠٫٢ ٠٫٢ ٠٫٥ ٠٫٥ ٠٫٤ ٠٫٤ ٠٫٣ ٠٫٣ ١٫٠ ١٫٠ ١٫٢ ١٫٢ ١٫٥ ١٫٥ ١٫٠ ١٫٠ ١٫٧ ١٫٧ ٢٫١ ٢٫١ ١٫٥ ١٫٥ ١٫٥ ١٫٥ ‫ﺣﻔﺮ‬ ‫ﺣﻔﺮ‬ ‫ردم‬ ‫ردم‬ ١‫ع‬ ٢‫ع‬ ٣‫ع‬ ٤‫ع‬ 0.5 0.2 1.5 0 2.1 0.3 1.3 1.5 0.5 1.1 5.4 3.6 0 0 ‫اﻟﺤﺠﻢ‬ ‫اﻟﺤﺠﻢ‬ )) = )) = ٣٠ ٣٠ x x ٣٠ ٣٠ ( ( ٤ ٤ ( ( x x ) ) ١ ١ x x ٥٫٤ ٥٫٤ + + ٢ ٢ x x ٣٫٦ ٣٫٦ = ( = ( ٢٨٣٥ ٢٨٣٥ ‫م‬ ‫م‬ ٣ ٣ I I II II III III
٥٣ ٥٣ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١ ١ : : - - ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺠﻢ‬ ‫ﺣﺴﺎب‬ ‫ﻳﺘﻢ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺠﻢ‬ ‫ﺣﺴﺎب‬ ‫ﻳﺘﻢ‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫اﻟﺤﻔﺮ‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫اﻟﺤﻔﺮ‬ ) ) ‫ﻋﺪد‬ ‫ﻋﺪد‬ ٣ ٣ ‫أﺟﺰاء‬ ‫أﺟﺰاء‬ :( :( ٠٫٥ ٠٫٥ ٠٫٥ ٠٫٥ ٠٫٢ ٠٫٢ ١٫١ ١٫١ ١٫٣ ١٫٣ ٠٫٣ ٠٫٣ ٠٫٠ ٠٫٠ ٠٫٢ ٠٫٢ ٠٫٥ ٠٫٥ ٠٫٩ ٠٫٩ ٠٫٢ ٠٫٢ ٠٫٥ ٠٫٥ ٠٫٤ ٠٫٤ ٠٫٣ ٠٫٣ ١٫٠ ١٫٠ ١٫٢ ١٫٢ ١٫٥ ١٫٥ ١٫٠ ١٫٠ ١٫٧ ١٫٧ ٢٫١ ٢٫١ ١٫٥ ١٫٥ ١٫٥ ١٫٥ ‫ﺣﻔﺮ‬ ‫ﺣﻔﺮ‬ ‫ردم‬ ‫ردم‬ I I II II III III ‫ﺣﺠﻢ‬ ‫ﺣﺠﻢ‬ IV IV ) = ) = ١٥ ١٥ x x ٣٠ ٣٠ ( ( x x )) )) ٠٫٥ ٠٫٥ + + ٠٫٢ ٠٫٢ + + ٠٫٠ ٠٫٠ + + ٠٫٠ ٠٫٠ ( ( ٤ ٤ =( =( ٧٨٫٧٥ ٧٨٫٧٥ ‫م‬ ‫م‬ ٣ ٣ ‫ﺣﺠﻢ‬ ‫ﺣﺠﻢ‬ V V )) = )) = ١٥ ١٥ x x ٣٠ ٣٠ ( ( ٢ ٢ ( ( x x )) )) ٠٫٢ ٠٫٢ + + ٠٫٠ ٠٫٠ + + ٠٫٠ ٠٫٠ ( ( ٣ ٣ =( =( ١٥٫٠ ١٥٫٠ ‫م‬ ‫م‬ ٣ ٣ ‫ﺣﺠﻢ‬ ‫ﺣﺠﻢ‬ VI VI )) = )) = ٧٫٥ ٧٫٥ x x ٣٠ ٣٠ ( ( ٢ ٢ ( ( x x )) )) ٠٫٣ ٠٫٣ + + ٠٫٠ ٠٫٠ + + ٠٫٠ ٠٫٠ ( ( ٣ ٣ =( =( ١١٫٢٥ ١١٫٢٥ ‫م‬ ‫م‬ ٣ ٣ ‫اﻟﺮدم‬ ‫ﺣﺠﻢ‬ ‫اﺟﻤﺎﻟﻰ‬ ‫اﻟﺮدم‬ ‫ﺣﺠﻢ‬ ‫اﺟﻤﺎﻟﻰ‬ = = ٢٨٣٥ ٢٨٣٥ + + ٧٨٫٧٥ ٧٨٫٧٥ + + ١٥٫٠ ١٥٫٠ + + ١١٫٢٥ ١١٫٢٥ = = ٢٩٤٠٫٠ ٢٩٤٠٫٠ ‫م‬ ‫م‬ ٣ ٣ IV IV V V VI VI
٥٤ ٥٤ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٢ ٢ : : ‫أﺑﻌﺎدﻩ‬ ‫ﺳﺒﺎﺣﺔ‬ ‫ﺣﻮض‬ ‫ﻹﻧﺸﺎء‬ ‫أﺑﻌﺎدﻩ‬ ‫ﺳﺒﺎﺣﺔ‬ ‫ﺣﻮض‬ ‫ﻹﻧﺸﺎء‬ ٢٠ ٢٠ x x ٥٠ ٥٠ ‫ﻣﻴﺰاﻧﻴﺔ‬ ‫أﺟﺮﻳﺖ‬ ‫م‬ ‫ﻣﻴﺰاﻧﻴﺔ‬ ‫أﺟﺮﻳﺖ‬ ‫م‬ ‫ﻳﻠﻰ‬ ‫آﻤﺎ‬ ‫ﻓﻜﺎﻧﺖ‬ ‫اﻟﻄﻮﻟﻰ‬ ‫اﻟﻤﺤﻮر‬ ‫ﻋﻠﻰ‬ ‫ﻃﻮﻟﻴﺔ‬ ‫ﻳﻠﻰ‬ ‫آﻤﺎ‬ ‫ﻓﻜﺎﻧﺖ‬ ‫اﻟﻄﻮﻟﻰ‬ ‫اﻟﻤﺤﻮر‬ ‫ﻋﻠﻰ‬ ‫ﻃﻮﻟﻴﺔ‬ : : ‫اﻟﻤﺴﺎﻓﺔ‬ 0 10 20 30 40 50 ‫اﻷرض‬ ‫ﻣﻨﺴﻮب‬ ‫اﻟﻄﺒﻴﻌﻴﺔ‬ 39.30 40.00 41.50 39.70 39.50 37.70 ‫اﻟﺤﻮض‬ ‫ﺑﺪاﻳﺔ‬ ‫ﻋﻨﺪ‬ ‫اﻹﻧﺸﺎء‬ ‫ﺧﻂ‬ ‫ﻣﻨﺴﻮب‬ ‫آﺎن‬ ‫ﻓﺈذا‬ ‫اﻟﺤﻮض‬ ‫ﺑﺪاﻳﺔ‬ ‫ﻋﻨﺪ‬ ‫اﻹﻧﺸﺎء‬ ‫ﺧﻂ‬ ‫ﻣﻨﺴﻮب‬ ‫آﺎن‬ ‫ﻓﺈذا‬ ٣٨٫٥ ٣٨٫٥ ‫م‬ ‫م‬ ‫اﻟﺤﻮض‬ ‫ﻗﺎع‬ ‫واﻧﺤﺪار‬ ‫اﻟﺤﻮض‬ ‫ﻗﺎع‬ ‫واﻧﺤﺪار‬ ٥ ٥ % % ‫اﻟﻰ‬ ‫ﺻﻔﺮ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫ﻣﻦ‬ ‫ﻷﺳﻔﻞ‬ ‫اﻟﻰ‬ ‫ﺻﻔﺮ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫ﻣﻦ‬ ‫ﻷﺳﻔﻞ‬ ٢٠ ٢٠ ‫م‬ ‫م‬ ‫ﺛﻢ‬ ‫ﺛﻢ‬ ٤ ٤ % % ‫ﻣﻦ‬ ‫ﻷﺳﻔﻞ‬ ‫ﻣﻦ‬ ‫ﻷﺳﻔﻞ‬ ٢٠ ٢٠ ‫اﻟﻰ‬ ‫اﻟﻰ‬ ٣٠ ٣٠ ‫ﻣﻦ‬ ‫أﻓﻘﻰ‬ ‫ﺛﻢ‬ ‫م‬ ‫ﻣﻦ‬ ‫أﻓﻘﻰ‬ ‫ﺛﻢ‬ ‫م‬ ٣٠ ٣٠ ‫اﻟﻰ‬ ‫اﻟﻰ‬ ٥٠ ٥٠ ‫م‬ ‫م‬ . . ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫وﺣﺴﺎب‬ ‫ﻃﻮﻟﻰ‬ ‫ﻗﻄﺎع‬ ‫رﺳﻢ‬ ‫واﻟﻤﻄﻠﻮب‬ ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫وﺣﺴﺎب‬ ‫ﻃﻮﻟﻰ‬ ‫ﻗﻄﺎع‬ ‫رﺳﻢ‬ ‫واﻟﻤﻄﻠﻮب‬ . .
٥٥ ٥٥ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ٣٧ ٣٨ ٣٩ ٤٠ ٤١ ٣٦ ٣٥ ‫ء‬‫ﺎ‬‫ﺸ‬‫ﻧ‬‫ﻹ‬‫ا‬ ‫ﻂ‬‫ﺧ‬ ‫ﺔ‬‫ﻴ‬‫ﻌ‬‫ﻴ‬‫ﺒ‬‫ﻄ‬‫ﻟ‬‫ا‬ ‫ض‬‫ر‬‫ﻷ‬‫ا‬ ‫اﻟﻤﺴﺎﻓﺔ‬ 0 10 20 30 40 50 ‫اﻟﻄﺒﻴﻌﻴﺔ‬ ‫اﻷرض‬ ‫ﻣﻨﺴﻮب‬ 39.30 40.00 41.50 39.70 39.50 37.70 ‫اﻹﻧﺸﺎء‬ ‫ﺧﻂ‬ ‫ﻣﻨﺴﻮب‬ 38.50 38.00 37.50 37.10 37.10 37.10 ‫اﻟﺤﻔﺮ‬ ‫ارﺗﻔﺎع‬ 0.80 2.00 4.00 2.60 2.40 0.60 ‫اﻟﺤﻔﺮ‬ ‫ﻣﺴﺎﺣﺔ‬ 16.00 40.00 80.00 52.00 48.00 600.00 ‫اﻟﺤﻔﺮ‬ ‫ﺣﺠﻢ‬ 1120 2400 2640 2000 12960 ‫اﻟﻜﻠﻰ‬ ‫اﻟﺤﺠﻢ‬ 21120 : :٢ ٢ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬
٥٦ ٥٦ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٣ ٣ : : ‫آﻞ‬ ‫ﻃﻮﻟﻴﺔ‬ ‫ﻣﻴﺰاﻧﻴﺔ‬ ‫أﺟﺮﻳﺖ‬ ‫ﻃﺮﻳﻖ‬ ‫إﻧﺸﺎء‬ ‫ﺑﻬﺪف‬ ‫آﻞ‬ ‫ﻃﻮﻟﻴﺔ‬ ‫ﻣﻴﺰاﻧﻴﺔ‬ ‫أﺟﺮﻳﺖ‬ ‫ﻃﺮﻳﻖ‬ ‫إﻧﺸﺎء‬ ‫ﺑﻬﺪف‬ ١٠٠ ١٠٠ ‫ﻋﻠﻰ‬ ‫م‬ ‫ﻋﻠﻰ‬ ‫م‬ ‫ﻳﻠﻰ‬ ‫آﻤﺎ‬ ‫ﻓﻜﺎﻧﺖ‬ ‫اﻟﻄﻮﻟﻰ‬ ‫اﻟﻤﺤﻮر‬ ‫ﻳﻠﻰ‬ ‫آﻤﺎ‬ ‫ﻓﻜﺎﻧﺖ‬ ‫اﻟﻄﻮﻟﻰ‬ ‫اﻟﻤﺤﻮر‬ : : ‫اﻟﻤﺴﺎﻓﺔ‬ 0 100 200 300 400 500 ‫اﻷرض‬ ‫ﻣﻨﺴﻮب‬ ‫اﻟﻄﺒﻴﻌﻴﺔ‬ 26.00 27.50 25.00 23.00 23.00 24.00 ‫واﺣﺪ‬ ‫ﻣﺘﺮ‬ ‫ﻳﺴﺎوى‬ ‫اﻟﻄﺮﻳﻖ‬ ‫ﺑﺪاﻳﺔ‬ ‫ﻋﻨﺪ‬ ‫اﻟﺤﻔﺮ‬ ‫ارﺗﻔﺎع‬ ‫آﺎن‬ ‫ﻓﺈذا‬ ‫واﺣﺪ‬ ‫ﻣﺘﺮ‬ ‫ﻳﺴﺎوى‬ ‫اﻟﻄﺮﻳﻖ‬ ‫ﺑﺪاﻳﺔ‬ ‫ﻋﻨﺪ‬ ‫اﻟﺤﻔﺮ‬ ‫ارﺗﻔﺎع‬ ‫آﺎن‬ ‫ﻓﺈذا‬ ، ، ‫واﻟﻄﺮﻳﻖ‬ ‫واﻟﻄﺮﻳﻖ‬ ‫ﺑﻨﺴﺒﺔ‬ ‫أﺳﻔﻞ‬ ‫اﻟﻰ‬ ‫ﻳﻨﺤﺪر‬ ‫ﺑﻨﺴﺒﺔ‬ ‫أﺳﻔﻞ‬ ‫اﻟﻰ‬ ‫ﻳﻨﺤﺪر‬ ٢٠٠:١ ٢٠٠:١ ‫ﻣﺴﺎﻓﺔ‬ ‫اﻟﻰ‬ ‫ﺻﻔﺮ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫ﻣﻦ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫اﻟﻰ‬ ‫ﺻﻔﺮ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫ﻣﻦ‬ ٢٠٠ ٢٠٠ ‫م‬ ‫م‬ ، ، ‫ﻣﺴﺎﻓﺔ‬ ‫ﻣﻦ‬ ‫أﻓﻘﻰ‬ ‫ﺛﻢ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫ﻣﻦ‬ ‫أﻓﻘﻰ‬ ‫ﺛﻢ‬ ٢٠٠ ٢٠٠ ‫اﻟﻰ‬ ‫اﻟﻰ‬ ٣٠٠ ٣٠٠ ‫م‬ ‫م‬ ، ، ‫ﺑﻨﺴﺒﺔ‬ ‫أﻋﻠﻰ‬ ‫اﻟﻰ‬ ‫ﺛﻢ‬ ‫ﺑﻨﺴﺒﺔ‬ ‫أﻋﻠﻰ‬ ‫اﻟﻰ‬ ‫ﺛﻢ‬ ١٠٠:١ ١٠٠:١ ‫اﻟﻄﺮﻳﻖ‬ ‫ﻧﻬﺎﻳﺔ‬ ‫ﺣﺘﻰ‬ ‫اﻟﻄﺮﻳﻖ‬ ‫ﻧﻬﺎﻳﺔ‬ ‫ﺣﺘﻰ‬ . . ‫اﻟﻄﺮﻳﻖ‬ ‫وﻋﺮض‬ ‫اﻟﻄﺮﻳﻖ‬ ‫وﻋﺮض‬ ١٥ ١٥ ‫وﻣﻴﻮﻟﻪ‬ ‫م‬ ‫وﻣﻴﻮﻟﻪ‬ ‫م‬ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ٢:١ ٢:١ . . ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫وﺣﺴﺎب‬ ‫ﻟﻠﻄﺮﻳﻖ‬ ‫ﻃﻮﻟﻰ‬ ‫ﻗﻄﺎع‬ ‫رﺳﻢ‬ ‫واﻟﻤﻄﻠﻮب‬ ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫وﺣﺴﺎب‬ ‫ﻟﻠﻄﺮﻳﻖ‬ ‫ﻃﻮﻟﻰ‬ ‫ﻗﻄﺎع‬ ‫رﺳﻢ‬ ‫واﻟﻤﻄﻠﻮب‬ . .
٥٧ ٥٧ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ٢٤ ٢٥ ٢٦ ٢٧ ٢٨ ٢٣ ٢٢ ‫ء‬‫ﺎ‬‫ﺸ‬‫ﻧ‬‫ﻹ‬‫ا‬ ‫ﻂ‬‫ﺧ‬ ‫ﺔ‬‫ﻴ‬‫ﻌ‬‫ﻴ‬‫ﺒ‬‫ﻄ‬‫ﻟ‬‫ا‬ ‫ض‬ ‫ر‬‫ﻷ‬‫ا‬ : :٣ ٣ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٢ ١ ١٥ ‫م‬ ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻓﻰ‬ ‫اﻟﻘﻄﺎع‬ ‫ﻣﺴﺎﺣﺔ‬ ‫ﻣﻌﺎدﻟﺔ‬ = ‫ع‬ x ) ١٥ + ١٥ + ٤ ‫ع‬ ( ٢ = ‫ع‬ x ) ١٥ + ٢ ‫ع‬ ( ‫ع‬ ١٥ + ٤ ‫ع‬ ‫اﻟﺤﻔﺮ‬ ‫اﻟﺮدم‬ ‫اﻟﻔﺎﺻﻞ‬ ‫اﻟﺤﺪ‬
٥٨ ٥٨ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﻤﺴﺎﻓﺔ‬ 0.0 100.0 200.0 300.0 400.0 500.0 ‫اﻷرض‬ ‫ﻣﻨﺴﻮب‬ ‫اﻟﻄﺒﻴﻌﻴﺔ‬ 26.0 27.5 25.0 23.0 23.0 24.0 ‫ﺧﻂ‬ ‫ﻣﻨﺴﻮب‬ ‫اﻹﻧﺸﺎء‬ 25.0 24.5 24.0 24.0 25.0 26.0 ‫اﻟﺤﻔﺮ‬ ‫ارﺗﻔﺎع‬ 1 3 1 ‫اﻟﺮدم‬ ‫ارﺗﻔﺎع‬ 1 2 2 ‫اﻟﺤﻔﺮ‬ ‫ﻣﺴﺎﺣﺔ‬ 17 63 17 0 ‫اﻟﺮدم‬ ‫ﻣﺴﺎﺣﺔ‬ 0 17 38 38 ‫اﻟﺤﻔﺮ‬ ‫ﺣﺠﻢ‬ 4000 4000 425 ‫اﻟﺮدم‬ ‫ﺣﺠﻢ‬ 425 2750 3800 ‫اﻟﺤﻔﺮ‬ ‫إﺟﻤﺎﻟﻰ‬ ‫اﻟﺮدم‬ ‫ﺣﺠﻢ‬ 6975 8425 2 5 0 .0 : :٣ ٣ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫اﻟﻔﺎﺻﻞ‬ ‫اﻟﺤﺪ‬ ‫اﻟﻔﺎﺻﻞ‬ ‫اﻟﺤﺪ‬
٥٩ ٥٩ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٤ ٤ : : ‫ﻣﻘﺘﺮح‬ ‫ﻃﺮﻳﻖ‬ ‫ﻣﺤﻮر‬ ‫ﻋﻠﻰ‬ ‫واﻟﻤﻨﺎﺳﻴﺐ‬ ‫اﻟﻤﺴﺎﻓﺎت‬ ‫أﺧﺬت‬ ‫ﻣﻘﺘﺮح‬ ‫ﻃﺮﻳﻖ‬ ‫ﻣﺤﻮر‬ ‫ﻋﻠﻰ‬ ‫واﻟﻤﻨﺎﺳﻴﺐ‬ ‫اﻟﻤﺴﺎﻓﺎت‬ ‫أﺧﺬت‬ ‫ﻳﻠﻰ‬ ‫آﻤﺎ‬ ‫ﻓﻜﺎﻧﺖ‬ ‫ﻳﻠﻰ‬ ‫آﻤﺎ‬ ‫ﻓﻜﺎﻧﺖ‬ : : ‫اﻟﻤﺴﺎﻓﺔ‬ 0 100 200 300 400 500 ‫اﻷرض‬ ‫ﻣﻨﺴﻮب‬ ‫اﻟﻄﺒﻴﻌﻴﺔ‬ 23.50 24.50 25.70 23.90 21.60 21.50 ‫ﺻﻔﺮ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫ﻋﻨﺪ‬ ‫اﻹﻧﺸﺎء‬ ‫ﺧﻂ‬ ‫ﻣﻨﺴﻮب‬ ‫آﺎن‬ ‫ﻓﺈذا‬ ‫ﺻﻔﺮ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫ﻋﻨﺪ‬ ‫اﻹﻧﺸﺎء‬ ‫ﺧﻂ‬ ‫ﻣﻨﺴﻮب‬ ‫آﺎن‬ ‫ﻓﺈذا‬ ٢٣٫٣٠ ٢٣٫٣٠ ‫م‬ ‫م‬ ، ، ‫وﻋﺮض‬ ‫وﻋﺮض‬ ‫اﻟﻄﺮﻳﻖ‬ ‫اﻟﻄﺮﻳﻖ‬ ١٠ ١٠ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫وﻣﻴﻮﻟﻪ‬ ‫م‬ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫وﻣﻴﻮﻟﻪ‬ ‫م‬ ١:١ ١:١ ‫أﻋﻠﻰ‬ ‫اﻟﻰ‬ ‫ﻳﻤﻴﻞ‬ ‫واﻟﻄﺮﻳﻖ‬ ‫أﻋﻠﻰ‬ ‫اﻟﻰ‬ ‫ﻳﻤﻴﻞ‬ ‫واﻟﻄﺮﻳﻖ‬ ‫ﺑﻨﺴﺒﺔ‬ ‫ﺑﻨﺴﺒﺔ‬ ٥٠٠:١ ٥٠٠:١ ‫ﻣﺴﺎﻓﺔ‬ ‫اﻟﻰ‬ ‫ﺻﻔﺮ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫ﻣﻦ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫اﻟﻰ‬ ‫ﺻﻔﺮ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫ﻣﻦ‬ ٣٠٠ ٣٠٠ ‫م‬ ‫م‬ ، ، ‫اﻟﻰ‬ ‫ﻳﻤﻴﻞ‬ ‫ﺛﻢ‬ ‫اﻟﻰ‬ ‫ﻳﻤﻴﻞ‬ ‫ﺛﻢ‬ ‫ﺑﻨﺴﺒﺔ‬ ‫أﺳﻔﻞ‬ ‫ﺑﻨﺴﺒﺔ‬ ‫أﺳﻔﻞ‬ ٤٠٠:١ ٤٠٠:١ ‫اﻟﻄﺮﻳﻖ‬ ‫ﻧﻬﺎﻳﺔ‬ ‫ﺣﺘﻰ‬ ‫اﻟﻄﺮﻳﻖ‬ ‫ﻧﻬﺎﻳﺔ‬ ‫ﺣﺘﻰ‬ . . ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫وﺣﺴﺎب‬ ‫ﻟﻠﻄﺮﻳﻖ‬ ‫ﻃﻮﻟﻰ‬ ‫ﻗﻄﺎع‬ ‫رﺳﻢ‬ ‫واﻟﻤﻄﻠﻮب‬ ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫وﺣﺴﺎب‬ ‫ﻟﻠﻄﺮﻳﻖ‬ ‫ﻃﻮﻟﻰ‬ ‫ﻗﻄﺎع‬ ‫رﺳﻢ‬ ‫واﻟﻤﻄﻠﻮب‬ . .
٦٠ ٦٠ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ٢٤ ٢٥ ٢٦ ٢٧ ٢١ ٢٣ ٢٢ ‫ء‬‫ﺸﺎ‬‫ﻹﻧ‬‫ا‬ ‫ﻂ‬‫ﺧ‬ ‫ﺔ‬‫ﻴ‬‫ﻌ‬‫ﻴ‬‫ﺒ‬‫ﻄ‬‫ﻟ‬‫ا‬ ‫ض‬‫ر‬‫ﻷ‬‫ا‬ : :٤ ٤ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١ ١ ١٠ ‫م‬ ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻓﻰ‬ ‫اﻟﻘﻄﺎع‬ ‫ﻣﺴﺎﺣﺔ‬ ‫ﻣﻌﺎدﻟﺔ‬ = ‫ع‬ x ) ١٠ + ١٠ + ٢ ‫ع‬ ( ٢ = ‫ع‬ x ) ١٠ + ‫ع‬ ( ‫ع‬ ١٠ + ٢ ‫ع‬ ‫اﻟﺤﻔﺮ‬ ‫اﻟﺮدم‬ ‫اﻟﻔﺎﺻﻞ‬ ‫اﻟﺤﺪ‬
٦١ ٦١ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﻤﺴﺎﻓﺔ‬ 0.0 100.0 200.0 300.0 400.0 500.0 ‫اﻷرض‬ ‫ﻣﻨﺴﻮب‬ ‫اﻟﻄﺒﻴﻌﻴﺔ‬ 23.50 24.50 25.70 23.90 21.60 21.50 ‫ﺧﻂ‬ ‫ﻣﻨﺴﻮب‬ ‫اﻹﻧﺸﺎء‬ 23.30 23.50 23.70 23.90 23.65 23.40 ‫اﻟﺤﻔﺮ‬ ‫ارﺗﻔﺎع‬ 0.20 1.00 2.00 0.00 ‫اﻟﺮدم‬ ‫ارﺗﻔﺎع‬ 0.00 2.05 1.90 ‫اﻟﺤﻔﺮ‬ ‫ﻣﺴﺎﺣﺔ‬ 2.04 11.00 24.00 0.00 ‫اﻟﺮدم‬ ‫ﻣﺴﺎﺣﺔ‬ 0.00 24.70 22.61 ‫اﻟﺤﻔﺮ‬ ‫ﺣﺠﻢ‬ 652.0 1750.0 1200.0 ‫اﻟﺮدم‬ ‫ﺣﺠﻢ‬ 1235.13 2365.63 ‫اﻟﺤﻔﺮ‬ ‫إﺟﻤﺎﻟﻰ‬ ‫اﻟﺮدم‬ ‫ﺣﺠﻢ‬ 3600.75 3602.00 : :٤ ٤ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﺪ‬‫ﺤ‬‫ﻟ‬‫ا‬ ‫ﺪ‬‫ﺤ‬‫ﻟ‬‫ا‬ ‫ﻞ‬‫ﺻ‬ ‫ﺎ‬‫ﻔ‬‫ﻟ‬‫ا‬ ‫ﻞ‬‫ﺻ‬ ‫ﺎ‬‫ﻔ‬‫ﻟ‬‫ا‬
٦٢ ٦٢ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﻜﻨﺘﻮر‬ ‫ﺧﻂ‬ ‫رﻗﻢ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ 33 300 32 500 31 600 30 750 29 800 28 1000 27 1200 26 1720 ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٥ ٥ : : ‫ﺧﻄﻮط‬ ‫داﺧﻞ‬ ‫اﻟﻤﺤﺼﻮرة‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫ﻳﻮﺿﺢ‬ ‫اﻟﺘﺎﻟﻰ‬ ‫اﻟﺠﺪول‬ ‫ﺧﻄﻮط‬ ‫داﺧﻞ‬ ‫اﻟﻤﺤﺼﻮرة‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫ﻳﻮﺿﺢ‬ ‫اﻟﺘﺎﻟﻰ‬ ‫اﻟﺠﺪول‬ ‫اﻟﻜﻨﺘﻮر‬ ‫اﻟﻜﻨﺘﻮر‬ ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫آﻤﻴﺎت‬ ‫ﺣﺴﺎب‬ ‫واﻟﻤﻄﻠﻮب‬ ‫ﺗﻞ‬ ‫ﺑﻬﺎ‬ ‫ﻟﻤﻨﻄﻘﺔ‬ ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫آﻤﻴﺎت‬ ‫ﺣﺴﺎب‬ ‫واﻟﻤﻄﻠﻮب‬ ‫ﺗﻞ‬ ‫ﺑﻬﺎ‬ ‫ﻟﻤﻨﻄﻘﺔ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻋﻠﻰ‬ ‫اﻷرض‬ ‫ﻟﺘﺴﻮﻳﺔ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻋﻠﻰ‬ ‫اﻷرض‬ ‫ﻟﺘﺴﻮﻳﺔ‬ ٣٠ ٣٠ ‫م‬ ‫م‬ . .
٦٣ ٦٣ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﻜﻨﺘﻮر‬ ‫ﺧﻂ‬ ‫رﻗﻢ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫اﻟﺤﺠﻢ‬ ‫ﻣﻌﺎدﻟﺔ‬ ‫اﻟﻜﻤﻴﺔ‬ 33 300 (٥٠٠+٣٠٠)١ * ٠٫٥= ‫ح‬ 400.00 32 500 (٦٠٠+٥٠٠)١ * ٠٫٥= ‫ح‬ 550.00 31 600 (٧٥٠+٦٠٠)١ * ٠٫٥ = ‫ح‬ 675.00 30 750 ‫اﻟﺤﻔﺮ‬ ‫اﺟﻤﺎﻟﻰ‬ 1625.00 30 750 3250.00 (٧٥٠-٨٠٠)١ * ٠٫٥ = ‫ح‬ 25.00 29 800 (٨٠٠ - ١٠٠٠) ١٫٥ = ‫ح‬ 300.00 28 1000 (١٠٠٠ - ١٢٠٠) ٢٫٥ = ‫ح‬ 500.00 27 1200 (١٢٠٠- ١٧٢٠) ٣٫٥ = ‫ح‬ 1820.00 26 1720 ‫اﻟﺮدم‬ ‫اﺟﻤﺎﻟﻰ‬ 2645.00 ‫اﻟﺮدم‬ ‫ﻣﻜﻌﺒﺎت‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ : :٥ ٥ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬
٦٤ ٦٤ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﻜﻨﺘﻮر‬ ‫ﺧﻂ‬ ‫رﻗﻢ‬ ‫ﻣﺮﺑﻊ‬ ‫ﻣﺘﺮ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ 40 22080 45 56340 50 58060 55 61940 60 68060 65 70960 ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٦ ٦ : : ‫ﺻﺨﺮﻳﺔ‬ ‫ﺑﻤﻨﻄﻘﺔ‬ ‫اﻟﻤﻴﺎﻩ‬ ‫ﻟﺤﺠﺰ‬ ‫ﺧﺰان‬ ‫ﺑﻨﺎء‬ ‫ﺗﻢ‬ ‫ﺻﺨﺮﻳﺔ‬ ‫ﺑﻤﻨﻄﻘﺔ‬ ‫اﻟﻤﻴﺎﻩ‬ ‫ﻟﺤﺠﺰ‬ ‫ﺧﺰان‬ ‫ﺑﻨﺎء‬ ‫ﺗﻢ‬ ، ، ‫اﻟﺘﺎﻟﻰ‬ ‫واﻟﺠﺪول‬ ‫اﻟﺘﺎﻟﻰ‬ ‫واﻟﺠﺪول‬ ‫ﺧﻄﻮط‬ ‫وﻣﺴﺎﺣﺔ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻳﻮﺿﺢ‬ ‫ﺧﻄﻮط‬ ‫وﻣﺴﺎﺣﺔ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻳﻮﺿﺢ‬ ‫اﻟﻜﻨﺘﻮر‬ ‫اﻟﻜﻨﺘﻮر‬ ‫اﻟﻤﻨﻄﻘﺔ‬ ‫ﻟﻬﺬﻩ‬ ‫اﻟﻤﻨﻄﻘﺔ‬ ‫ﻟﻬﺬﻩ‬ ، ، ‫واﻟﻤﻄﻠﻮب‬ ‫واﻟﻤﻄﻠﻮب‬ ‫اﻟﺨﺰان‬ ‫ﺳﻌﺔ‬ ‫ﻣﻨﺤﻨﻰ‬ ‫رﺳﻢ‬ ‫اﻟﺨﺰان‬ ‫ﺳﻌﺔ‬ ‫ﻣﻨﺤﻨﻰ‬ ‫رﺳﻢ‬ . .
٦٥ ٦٥ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﻣﺴﺎﺋﻞ‬ ‫ﻣﺜﻞ‬ ‫ﺗﺤﺴﺐ‬ ‫اﻟﺨﺰان‬ ‫ﺳﻌﺔ‬ ‫ﻣﺴﺎﺋﻞ‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﻣﺴﺎﺋﻞ‬ ‫ﻣﺜﻞ‬ ‫ﺗﺤﺴﺐ‬ ‫اﻟﺨﺰان‬ ‫ﺳﻌﺔ‬ ‫ﻣﺴﺎﺋﻞ‬ : :٦ ٦ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫اﻟﻜﻨﺘﻮر‬ ‫ﺧﻂ‬ ‫رﻗﻢ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫آﻨﺘﻮر‬ ‫ﺧﻄﻲ‬ ‫آﻞ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻤﻴﺎﻩ‬ ‫ﺣﺠﻢ‬ ‫ﻣﻌﺎدﻟﺔ‬ ‫اﻟﺠﺰﺋﻰ‬ ‫اﻟﺤﺠﻢ‬ ‫اﻟﻜﻠﻰ‬ ‫اﻟﺤﺠﻢ‬ 40 22080 (٥٦٣٤٠+٢٢٠٨٠)٥ * ٠٫٥= ‫ح‬ 196050 196050 45 56340 (٥٦٣٤٠+٥٨٠٦٠)٥ * ٠٫٥= ‫ح‬ 286000 482050 50 58060 (٥٨٠٦٠+٦١٩٤٠)٥ * ٠٫٥ = ‫ح‬ 300000 782050 55 61940 (٦١٩٤٠+٦٨٠٦٠)٥ * ٠٫٥ = ‫ح‬ 325000 1107050 60 68060 (٦٨٠٦٠+٧٠٩٦٠)٥ * ٠٫٥ = ‫ح‬ 347550 1454600 65 70960 ‫اﻟﻜﻠﻰ‬ ‫اﻟﺤﺠﻢ‬ 1454600
٦٦ ٦٦ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ٥٠ ٥٥ ٦٠ ٦٥ ٤٥ ٤٠ ‫اﻟﺴﻌﺔ‬ ‫اﻟﻤﻜﻌﺐ‬ ‫ﺑﺎﻟﻤﺘﺮ‬ ‫ﺻﻔﺮ‬ ٢٥٠٠٠٠ ٥٠٠٠٠٠ ٧٥٠٠٠٠ ١٠٠٠٠٠٠ ١٢٥٠٠٠٠ ١٥٠٠٠٠٠ ‫اﻟﻤﻨﺴﻮب‬ ‫ﺔ‬‫ﻌ‬‫ﺴ‬‫ﻟ‬‫ا‬ ‫ﻰ‬‫ﻨ‬‫ﺤ‬‫ﻨ‬‫ﻣ‬ ** ** ‫ﺑﻴﻨﻰ‬ ‫ﻣﻨﺴﻮب‬ ‫أى‬ ‫ﻋﻨﺪ‬ ‫اﻟﻤﺨﺰﻧﺔ‬ ‫اﻟﻤﻴﺎﻩ‬ ‫آﻤﻴﺔ‬ ‫ﻟﺘﺤﺪﻳﺪ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻣﻨﺤﻨﻰ‬ ‫ﻳﺴﺘﺨﺪم‬ ‫ﺑﻴﻨﻰ‬ ‫ﻣﻨﺴﻮب‬ ‫أى‬ ‫ﻋﻨﺪ‬ ‫اﻟﻤﺨﺰﻧﺔ‬ ‫اﻟﻤﻴﺎﻩ‬ ‫آﻤﻴﺔ‬ ‫ﻟﺘﺤﺪﻳﺪ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻣﻨﺤﻨﻰ‬ ‫ﻳﺴﺘﺨﺪم‬ ‫ﻣﻨﺴﻮب‬ ‫ﻋﻨﺪ‬ ‫اﻟﻤﺨﺰﻧﺔ‬ ‫اﻟﻤﻴﺎﻩ‬ ‫آﻤﻴﺔ‬ ‫ﻳﻮﺿﺢ‬ ‫اﻷﺳﻮد‬ ‫اﻟﺴﻬﻢ‬ ‫اﻟﻤﺜﺎل‬ ‫ﺳﺒﻴﻞ‬ ‫ﻋﻠﻰ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻋﻨﺪ‬ ‫اﻟﻤﺨﺰﻧﺔ‬ ‫اﻟﻤﻴﺎﻩ‬ ‫آﻤﻴﺔ‬ ‫ﻳﻮﺿﺢ‬ ‫اﻷﺳﻮد‬ ‫اﻟﺴﻬﻢ‬ ‫اﻟﻤﺜﺎل‬ ‫ﺳﺒﻴﻞ‬ ‫ﻋﻠﻰ‬ ٦٣ ٦٣ ‫م‬ ‫م‬
٦٧ ٦٧ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﻜﻨﺘﻮر‬ ‫ﺧﻂ‬ ‫رﻗﻢ‬ ‫ﻣﺮﺑﻊ‬ ‫ﻣﺘﺮ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ 120 4600 125 7100 130 8900 135 11200 140 12300 145 14100 ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٧ ٧ : : ‫ﺧﻄﻮط‬ ‫داﺧﻞ‬ ‫ﺧﺮﻳﻄﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺴﺎﺣﺎت‬ ‫ﻗﻴﺴﺖ‬ ‫ﺧﻄﻮط‬ ‫داﺧﻞ‬ ‫ﺧﺮﻳﻄﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺴﺎﺣﺎت‬ ‫ﻗﻴﺴﺖ‬ ‫اﻟﻜﻨﺘﻮر‬ ‫اﻟﻜﻨﺘﻮر‬ ‫ﻟﻤﻮﻗﻊ‬ ‫ﻟﻤﻮﻗﻊ‬ ‫ﻓﻜﺎﻧﺖ‬ ‫اﻟﺨﺰاﻧﺎت‬ ‫أﺣﺪ‬ ‫ﻹﻧﺸﺎء‬ ‫ﻣﻘﺘﺮح‬ ‫ﻓﻜﺎﻧﺖ‬ ‫اﻟﺨﺰاﻧﺎت‬ ‫أﺣﺪ‬ ‫ﻹﻧﺸﺎء‬ ‫ﻣﻘﺘﺮح‬ : : ‫ﻣﻨﺴﻮب‬ ‫ﻋﻠﻰ‬ ‫ﻳﻘﻊ‬ ‫اﻟﺨﺰان‬ ‫ﻗﺎع‬ ‫أن‬ ‫ﻋﻠﻤﺖ‬ ‫ﻓﺈذا‬ ‫ﻣﻨﺴﻮب‬ ‫ﻋﻠﻰ‬ ‫ﻳﻘﻊ‬ ‫اﻟﺨﺰان‬ ‫ﻗﺎع‬ ‫أن‬ ‫ﻋﻠﻤﺖ‬ ‫ﻓﺈذا‬ ١٢٠ ١٢٠ ‫ﺑﺎﻟﺨﺰان‬ ‫اﻟﻤﻴﺎﻩ‬ ‫وﺳﻄﺢ‬ ‫م‬ ‫ﺑﺎﻟﺨﺰان‬ ‫اﻟﻤﻴﺎﻩ‬ ‫وﺳﻄﺢ‬ ‫م‬ ‫ﻣﻨﺴﻮب‬ ‫ﻋﻠﻰ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻋﻠﻰ‬ ١٤٢ ١٤٢ ‫ﻓﺎﺣﺴﺐ‬ ‫م‬ ‫ﻓﺎﺣﺴﺐ‬ ‫م‬ : : ‫ا‬ ‫ا‬ ( ( ‫إرﺳﻢ‬ ‫إرﺳﻢ‬ ‫اﻟﺨﺰان‬ ‫ﺳﻌﺔ‬ ‫ﻣﻨﺤﻨﻰ‬ ‫اﻟﺨﺰان‬ ‫ﺳﻌﺔ‬ ‫ﻣﻨﺤﻨﻰ‬ ‫ب‬ ‫ب‬ ( ( ‫اﻟﺨﺰان‬ ‫داﺧﻞ‬ ‫اﻟﻤﻴﺎﻩ‬ ‫ﺣﺠﻢ‬ ‫اﻟﺨﺰان‬ ‫داﺧﻞ‬ ‫اﻟﻤﻴﺎﻩ‬ ‫ﺣﺠﻢ‬ ‫ﺟـ‬ ‫ﺟـ‬ ( ( ‫ﺳﻌﺔ‬ ‫ﻋﻨﺪ‬ ‫ﺑﺎﻟﺨﺰان‬ ‫اﻟﻤﻴﺎﻩ‬ ‫ﺳﻄﺢ‬ ‫ﻣﻨﺴﻮب‬ ‫ﺳﻌﺔ‬ ‫ﻋﻨﺪ‬ ‫ﺑﺎﻟﺨﺰان‬ ‫اﻟﻤﻴﺎﻩ‬ ‫ﺳﻄﺢ‬ ‫ﻣﻨﺴﻮب‬ ١٠٠٠٠ ١٠٠٠٠ ‫ﻣﻜﻌﺐ‬ ‫ﻣﺘﺮ‬ ‫ﻣﻜﻌﺐ‬ ‫ﻣﺘﺮ‬
٦٨ ٦٨ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﻜﻨﺘﻮر‬ ‫ﺧﻂ‬ ‫رﻗﻢ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫آﻨﺘﻮر‬ ‫ﺧﻄﻲ‬ ‫آﻞ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻤﻴﺎﻩ‬ ‫ﺣﺠﻢ‬ ‫ﻣﻌﺎدﻟﺔ‬ ‫اﻟﺠﺰﺋﻰ‬ ‫اﻟﺤﺠﻢ‬ ‫اﻟﻜﻠﻰ‬ ‫اﻟﺤﺠﻢ‬ 120 4600 (٧١٠٠+٤٦٠٠)٥ * ٠٫٥= ‫ح‬ 29250 29250 125 7100 (٨٩٠٠+٧١٠٠)٥ * ٠٫٥= ‫ح‬ 40000 69250 130 8900 (١١٢٠٠+٨٩٠٠)٥ * ٠٫٥ = ‫ح‬ 50250 119500 135 11200 (١٢٣٠٠+١١٢٠٠)٥ * ٠٫٥ = ‫ح‬ 58750 178250 140 12300 (١٤١٠٠+١٢٣٠٠)٥ * ٠٫٥ = ‫ح‬ 66000 244250 145 14100 ‫اﻟﻜﻠﻰ‬ ‫اﻟﺤﺠﻢ‬ 244250 : :٧ ٧ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬
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10- كيفية حل المسائل الحسابية (1).pdf

  • 1. ‫اﻟﻤﺴﺎﺣﺔ‬ ‫ﻋﻠﻢ‬ ‫ﻓﻰ‬ ‫اﻹﻟﻴﻜﺘﺮوﻧﻴﺔ‬ ‫اﻟﻤﺤﺎﺿﺮات‬ ‫ﺳﻠﺴﻠﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫ﻋﻠﻢ‬ ‫ﻓﻰ‬ ‫اﻹﻟﻴﻜﺘﺮوﻧﻴﺔ‬ ‫اﻟﻤﺤﺎﺿﺮات‬ ‫ﺳﻠﺴﻠﺔ‬ E E – – Learning courses Learning courses ‫اﻟﻤﺴﺎﺣﻴﺔ‬ ‫اﻟﻤﺴﺎﺋﻞ‬ ‫ﺣﻞ‬ ‫آﻴﻔﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﻴﺔ‬ ‫اﻟﻤﺴﺎﺋﻞ‬ ‫ﺣﻞ‬ ‫آﻴﻔﻴﺔ‬ How to solve How to solve Surveying Problems Surveying Problems ‫أ‬ ‫أ‬ . . ‫د‬ ‫د‬ / / ‫اﻟﻤﻐﺮﺑﻰ‬ ‫ﺳﻌﻴﺪ‬ ‫اﻟﻤﻐﺮﺑﻰ‬ ‫ﺳﻌﻴﺪ‬ ‫ﻣﺪﻧﻰ‬ ‫ﻗﺴﻢ‬ ‫ﻣﺪﻧﻰ‬ ‫ﻗﺴﻢ‬ - - ‫اﻷزهﺮ‬ ‫هﻨﺪﺳﺔ‬ ‫اﻷزهﺮ‬ ‫هﻨﺪﺳﺔ‬
  • 2. ٢ ٢ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﻤﺤﺘﻮﻳﺎت‬ ‫اﻟﻤﺤﺘﻮﻳﺎت‬ ‫اﻷول‬ ‫اﻟﺒﺎب‬ ‫اﻷول‬ ‫اﻟﺒﺎب‬ : : ‫اﻟﺘﺮاﻓﻴﺮﺳﺎت‬ ‫ﺑﺎب‬ ‫ﻋﻠﻰ‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫اﻟﺘﺮاﻓﻴﺮﺳﺎت‬ ‫ﺑﺎب‬ ‫ﻋﻠﻰ‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﺒﺎب‬ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﺒﺎب‬ : : ‫اﻟﻤﻴﺰاﻧﻴﺔ‬ ‫ﺑﺎب‬ ‫ﻋﻠﻰ‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫اﻟﻤﻴﺰاﻧﻴﺔ‬ ‫ﺑﺎب‬ ‫ﻋﻠﻰ‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﺒﺎب‬ ‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﺒﺎب‬ : : ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫اﻟﺮاﺑﻊ‬ ‫اﻟﺒﺎب‬ ‫اﻟﺮاﺑﻊ‬ ‫اﻟﺒﺎب‬ : : ‫اﻷراﺿﻰ‬ ‫ﺗﺴﻮﻳﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫اﻷراﺿﻰ‬ ‫ﺗﺴﻮﻳﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬
  • 3. ٣ ٣ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻷول‬ ‫اﻟﺒﺎب‬ ‫اﻷول‬ ‫اﻟﺒﺎب‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺘﺮاﻓﻴﺮﺳﺎت‬ ‫ﺑﺎب‬ ‫اﻟﺘﺮاﻓﻴﺮﺳﺎت‬ ‫ﺑﺎب‬
  • 4. ٤ ٤ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ١ ١ ) ) ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫واﻟﺰواﻳﺎ‬ ‫اﻟﻘﻔﻞ‬ ‫ﺧﻄﺄ‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫واﻟﺰواﻳﺎ‬ ‫اﻟﻘﻔﻞ‬ ‫ﺧﻄﺄ‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ :( :( ‫ﻳﻠ‬ ‫آﻤﺎ‬ ‫ﻓﻜﺎﻧﺖ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻓﻰ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰواﻳﺎ‬ ‫ﻗﻴﺴﺖ‬ ‫ﻳﻠ‬ ‫آﻤﺎ‬ ‫ﻓﻜﺎﻧﺖ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻓﻰ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰواﻳﺎ‬ ‫ﻗﻴﺴﺖ‬ ‫ﻰ‬ ‫ﻰ‬ : : ‫اﻟﺰواﻳﺎ‬ ‫ﻗﻴﻢ‬ ‫وﺣﺴﺎب‬ ‫اﻟﺰاوى‬ ‫اﻟﻘﻔﻞ‬ ‫ﺧﻄﺄ‬ ‫ﻗﻴﻤﺔ‬ ‫ﺣﺴﺎب‬ ‫واﻟﻤﻄﻠﻮب‬ ‫اﻟﺰواﻳﺎ‬ ‫ﻗﻴﻢ‬ ‫وﺣﺴﺎب‬ ‫اﻟﺰاوى‬ ‫اﻟﻘﻔﻞ‬ ‫ﺧﻄﺄ‬ ‫ﻗﻴﻤﺔ‬ ‫ﺣﺴﺎب‬ ‫واﻟﻤﻄﻠﻮب‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ . . ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ا‬ 22 46 99 ‫ب‬ 47 50 122 ‫ﺟـ‬ 15 26 72 ‫د‬ 32 56 64 ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫ااﻟﺰاوﻳﺔ‬
  • 5. ٥ ٥ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١ ١ : : ‫ﻣﺠﻤﻮع‬ ‫ﺣﺴﺎب‬ ‫ﻳﺘﻢ‬ ‫ﻣﺠﻤﻮع‬ ‫ﺣﺴﺎب‬ ‫ﻳﺘﻢ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰواﻳﺎ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰواﻳﺎ‬ ‫اﻟﺰاوى‬ ‫اﻟﻘﻔﻞ‬ ‫ﺧﻄﺄ‬ ‫اﻟﺰاوى‬ ‫اﻟﻘﻔﻞ‬ ‫ﺧﻄﺄ‬ = = ٠٠ ٠٠ ٠٠ ٠٠ ٣٦٠ ٣٦٠ – – ٥٦ ٥٦ ٥٩ ٥٩ ٣٥٩ ٣٥٩ = = ٤ ٤ ‫ﺛﻮاﻧﻰ‬ ‫ﺛﻮاﻧﻰ‬ ‫ﻧﻮزع‬ ‫ﺣﻴﺚ‬ ‫ﻧﻮزع‬ ‫ﺣﻴﺚ‬ ١ ١ ‫زاوﻳﺔ‬ ‫آﻞ‬ ‫ﻋﻠﻰ‬ ‫ﺛﺎﻧﻴﺔ‬ ‫زاوﻳﺔ‬ ‫آﻞ‬ ‫ﻋﻠﻰ‬ ‫ﺛﺎﻧﻴﺔ‬ . . ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ا‬ 22 46 99 23 46 99 ‫ب‬ 47 50 122 48 50 122 ‫ﺟـ‬ 15 26 72 16 26 72 ‫د‬ 32 56 64 33 56 64 ‫اﻟﻤﺠﻤﻮع‬ 116 178 357 120 178 357 56 59 359 0 0 360 ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫ااﻟﺰاوﻳﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰاوﻳﺔ‬
  • 6. ٦ ٦ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٢ ٢ ) ) ‫اﻻﻧﺤﺮاف‬ ‫ﺣﺴﺎب‬ ‫آﻴﻔﻴﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻻﻧﺤﺮاف‬ ‫ﺣﺴﺎب‬ ‫آﻴﻔﻴﺔ‬ ‫ﻋﻠﻰ‬ :( :( ‫اﻟﺨﻂ‬ ‫آﺎن‬ ‫إذا‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻰ‬ ‫اﻟﺨﻂ‬ ‫آﺎن‬ ‫إذا‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻰ‬ ‫ﻓﺎﺣﺴﺐ‬ ‫اﻟﺸﺮق‬ ‫ﻧﺤﻮ‬ ‫ﻳﺘﺠﻪ‬ ‫ب‬ ‫ا‬ ‫ﻓﺎﺣﺴﺐ‬ ‫اﻟﺸﺮق‬ ‫ﻧﺤﻮ‬ ‫ﻳﺘﺠﻪ‬ ‫ب‬ ‫ا‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻷﺿﻼع‬ ‫اﻟﺪاﺋﺮى‬ ‫اﻻﻧﺤﺮاف‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻷﺿﻼع‬ ‫اﻟﺪاﺋﺮى‬ ‫اﻻﻧﺤﺮاف‬ . . ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٢ ٢ : : ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰواﻳﺎ‬ ‫ﻗﻴﻢ‬ ‫آﺎﻧﺖ‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻣﻦ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰواﻳﺎ‬ ‫ﻗﻴﻢ‬ ‫آﺎﻧﺖ‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻣﻦ‬ ) ) ‫ﺑﻌﺪ‬ ‫ﺑﻌﺪ‬ ‫اﻟﺰاوى‬ ‫اﻟﻘﻔﻞ‬ ‫ﺧﻄﺄ‬ ‫ﺗﺼﺤﻴﺢ‬ ‫اﻟﺰاوى‬ ‫اﻟﻘﻔﻞ‬ ‫ﺧﻄﺄ‬ ‫ﺗﺼﺤﻴﺢ‬ ( ( ‫ﻳﻠﻰ‬ ‫آﻤﺎ‬ ‫ﻳﻠﻰ‬ ‫آﻤﺎ‬ : : ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ا‬ 23 46 99 ‫ب‬ 48 50 122 ‫ﺟـ‬ 16 26 72 ‫د‬ 33 56 64 ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰاوﻳﺔ‬
  • 7. ٧ ٧ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٢ ٢ : : ‫آﺮوآﻰ‬ ‫رﺳﻢ‬ ‫ﻳﺘﻢ‬ ‫آﺮوآﻰ‬ ‫رﺳﻢ‬ ‫ﻳﺘﻢ‬ ‫ﻟﻠﺘﺮاﻓﻴﺮس‬ ‫ﻟﻠﺘﺮاﻓﻴﺮس‬ ‫اﻻﻧﺤﺮاف‬ ‫ﻋﻠﻴﻪ‬ ‫ﻣﻮﺿﺢ‬ ‫اﻻﻧﺤﺮاف‬ ‫ﻋﻠﻴﻪ‬ ‫ﻣﻮﺿﺢ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰواﻳﺎ‬ ‫وﻗﻴﻢ‬ ‫ب‬ ‫ا‬ ‫ﻟﻠﺨﻂ‬ ‫اﻟﺪاﺋﺮى‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰواﻳﺎ‬ ‫وﻗﻴﻢ‬ ‫ب‬ ‫ا‬ ‫ﻟﻠﺨﻂ‬ ‫اﻟﺪاﺋﺮى‬ ‫ﻟﻠﺨﻂ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻻﻧﺤﺮاف‬ ‫ﻟﻠﺨﻂ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻻﻧﺤﺮاف‬ = = ‫اﻟﺴﺎﺑﻖ‬ ‫ﻟﻠﺨﻂ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻻﻧﺤﺮاف‬ ‫اﻟﺴﺎﺑﻖ‬ ‫ﻟﻠﺨﻂ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻻﻧﺤﺮاف‬ ± ± ١٨٠ ١٨٠ – – ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰاوﻳﺔ‬ ‫اﻟﺪاﺧﻠﻴﺔ‬ ‫اﻟﺰاوﻳﺔ‬ ‫ا‬ ‫ب‬ ‫ﺟـ‬ ‫د‬ ‫اﻟﻘﺎﻋﺪة‬ ‫ﻧﻄﺒﻖ‬ ‫ﺛﻢ‬ ‫اﻟﻘﺎﻋﺪة‬ ‫ﻧﻄﺒﻖ‬ ‫ﺛﻢ‬ : :
  • 8. ٨ ٨ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ا‬ ‫ب‬ ‫ﺟـ‬ ‫د‬ ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٢ ٢ : :
  • 9. ٩ ٩ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٣ ٣ ) ) ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ :( :( ‫أﻃﻮال‬ ‫آﺎﻧﺖ‬ ‫إذا‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻰ‬ ‫أﻃﻮال‬ ‫آﺎﻧﺖ‬ ‫إذا‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻰ‬ ‫ﺛﻢ‬ ‫اﻟﻀﻠﻌﻰ‬ ‫اﻟﺨﻄﺄ‬ ‫ﻗﻴﻤﺔ‬ ‫ﻓﺎﺣﺴﺐ‬ ‫ﺑﺎﻟﺸﺮﻳﻂ‬ ‫ﻗﻴﺴﺖ‬ ‫اﻟﺨﻄﻮط‬ ‫ﺛﻢ‬ ‫اﻟﻀﻠﻌﻰ‬ ‫اﻟﺨﻄﺄ‬ ‫ﻗﻴﻤﺔ‬ ‫ﻓﺎﺣﺴﺐ‬ ‫ﺑﺎﻟﺸﺮﻳﻂ‬ ‫ﻗﻴﺴﺖ‬ ‫اﻟﺨﻄﻮط‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫اﺣﺴﺐ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫اﺣﺴﺐ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻷﺿﻼع‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻷﺿﻼع‬ ‫ا‬ ‫ا‬ ( ( ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻷﻃﻮال‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻷﻃﻮال‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ Bowditch method Bowditch method ‫ب‬ ‫ب‬ ( ( ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ Transit method Transit method
  • 10. ١٠ ١٠ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٣ ٣ ) ) ‫ا‬ ‫ا‬ :( :( ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻷﻃﻮال‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻷﻃﻮال‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ Bowditch method Bowditch method ‫ا‬ ‫ب‬ ‫ا‬ 61.31 0 0 90 61.310 0.000 61.299 0.025 ‫ب‬ ‫ﺟـ‬ ‫ب‬ 71.85 12 9 147 38.971 -60.363 38.958 -60.334 ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ 120.31 56 42 254 -116.055 -31.715 -116.076 -31.666 ‫د‬ ‫هـ‬ ‫د‬ 93.29 23 46 9 15.836 91.936 15.819 91.974 ‫ا‬ ‫اﻟﻤﺠﻤﻮع‬ 346.76 0.062 -0.142 0.000 0.000 ‫اﻟﺨﻂ‬ ‫اﻟﻄﻮل‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻟﻨﻘﻄﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬
  • 11. ١١ ١١ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٣ ٣ ) ) ‫ب‬ ‫ب‬ :( :( ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ Transit method Transit method ‫ا‬ ‫ب‬ ‫ا‬ 61.31 0 0 90 61.310 0.000 61.294 0.000 ‫ب‬ ‫ﺟـ‬ ‫ب‬ 71.85 12 9 147 38.971 -60.363 38.961 -60.316 ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ 120.31 56 42 254 -116.055 -31.715 -116.086 -31.691 ‫د‬ ‫هـ‬ ‫د‬ 93.29 23 46 9 15.836 91.936 15.831 92.007 ‫ا‬ ‫اﻟﺠﺒﺮى‬ ‫ﻣﺠـ‬ 346.76 0.062 -0.142 0.000 0.000 ‫اﻟﻌﺪدى‬ ‫ﻣﺠـ‬ 232.171 184.014 ‫اﻟﺨﻂ‬ ‫اﻟﻄﻮل‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻟﻨﻘﻄﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬
  • 12. ١٢ ١٢ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٤ ٤ ) ) ‫اﻻﺣﺪاﺛﻴﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ ‫اﻻﺣﺪاﺛﻴﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ :( :( ‫ﻧﻘﻄ‬ ‫إﺣﺪاﺛﻴﺎت‬ ‫آﺎﻧﺖ‬ ‫إذا‬ ‫اﻟﻤﻀﻠﻊ‬ ‫ﻧﻘﺎط‬ ‫إﺣﺪاﺛﻴﺎت‬ ‫اﺣﺴﺐ‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻰ‬ ‫ﻧﻘﻄ‬ ‫إﺣﺪاﺛﻴﺎت‬ ‫آﺎﻧﺖ‬ ‫إذا‬ ‫اﻟﻤﻀﻠﻊ‬ ‫ﻧﻘﺎط‬ ‫إﺣﺪاﺛﻴﺎت‬ ‫اﺣﺴﺐ‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻰ‬ ‫ﺔ‬ ‫ﺔ‬ ‫ا‬ ‫ا‬ ) ) ٥٠٠ ٥٠٠ ‫ﺷﺮﻗﺎ‬ ‫ﺷﺮﻗﺎ‬ ، ، ١٠٠٠ ١٠٠٠ ‫ﺷﻤﺎﻻ‬ ‫ﺷﻤﺎﻻ‬ ( ( ‫ﺑﺎﻟﻄﺮﻳﻘﺘﻴﻦ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻰ‬ ‫وذﻟﻚ‬ ‫ﺑﺎﻟﻄﺮﻳﻘﺘﻴﻦ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻰ‬ ‫وذﻟﻚ‬ : : ‫ا‬ ‫ا‬ ( ( ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻷﻃﻮال‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻷﻃﻮال‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ Bowditch method Bowditch method ‫ب‬ ‫ب‬ ( ( ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ Transit method Transit method
  • 13. ١٣ ١٣ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٤ ٤ ) ) ‫ا‬ ‫ا‬ : ( : ( ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻷﻃﻮال‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻷﻃﻮال‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ Bowditch method Bowditch method ‫ا‬ 500.000 1000.000 ‫ب‬ ‫ا‬ 61.31 61.299 0.025 ‫ب‬ 561.299 1000.025 ‫ﺟـ‬ ‫ب‬ 71.85 38.958 -60.334 ‫ﺟـ‬ 600.257 939.691 ‫د‬ ‫ﺟـ‬ 120.31 -116.076 -31.666 ‫د‬ 484.181 908.026 ‫هـ‬ ‫د‬ 93.29 15.819 91.974 ‫ا‬ 500.000 1000.000 ‫اﻟﻤﺠﻤﻮع‬ 346.76 0.000 0.000 ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﺨﻂ‬ ‫اﻻﺣﺪاﺛﻰ‬ ‫اﻷﻓﻘﻰ‬ ‫اﻻﺣﺪاﺛﻰ‬ ‫اﻟﺮأﺳﻰ‬ ‫اﻟﻄﻮل‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬
  • 14. ١٤ ١٤ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٤ ٤ ) ) ‫ب‬ ‫ب‬ : ( : ( ‫ب‬ ‫ب‬ ( ( ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻨﺴﺒﺔ‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻃﺮﻳﻘﺔ‬ Transit method Transit method ‫ا‬ 500.000 1000.000 ‫ب‬ ‫ا‬ 61.31 61.294 0.000 ‫ب‬ 561.294 1000.000 ‫ﺟـ‬ ‫ب‬ 71.85 38.961 -60.316 ‫ﺟـ‬ 600.254 939.684 ‫د‬ ‫ﺟـ‬ 120.31 -116.086 -31.691 ‫د‬ 484.169 907.993 ‫هـ‬ ‫د‬ 93.29 15.831 92.007 ‫ا‬ 500.000 1000.000 ‫اﻟﺠﺒﺮى‬ ‫ﻣﺠـ‬ 346.76 0.000 0.000 ‫اﻟﻌﺪدى‬ ‫ﻣﺠـ‬ ‫اﻻﺣﺪاﺛﻰ‬ ‫اﻷﻓﻘﻰ‬ ‫اﻻﺣﺪاﺛﻰ‬ ‫اﻟﺮأﺳﻰ‬ ‫اﻟﻄﻮل‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﺨﻂ‬
  • 15. ١٥ ١٥ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ب‬ ‫ا‬ 107.12 0 20 85 ‫ﺟـ‬ ‫ب‬ 63.18 10 46 163 ‫د‬ ‫ﺟـ‬ 126.84 40 46 262 ‫هـ‬ ‫د‬ 27.99 50 30 348 ‫ا‬ ‫هـ‬ 40.04 10 29 6 ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫اﻟﺨﻂ‬ ‫اﻟﻄﻮل‬ ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٥ ٥ ) ) ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ :( :( ‫ﻷﺿﻼع‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫اﺣﺴﺐ‬ ‫ﻷﺿﻼع‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫اﺣﺴﺐ‬ ‫ﺗﺮاﻓﻴﺮس‬ ‫ﺗﺮاﻓﻴﺮس‬ ‫اﻟﺘﻴﻮدوﻟﻴﺖ‬ ‫اﻟﺘﻴﻮدوﻟﻴﺖ‬ ‫اﻟﺘﺎﻟﻰ‬ ‫ﺑﺎﻟﺠﺪول‬ ‫ﻣﻮﺿﺤﺔ‬ ‫اﻷرﺻﺎد‬ ‫ﺑﺄن‬ ‫ﻋﻠﻤﺎ‬ ‫هـ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ ‫اﻟﺘﺎﻟﻰ‬ ‫ﺑﺎﻟﺠﺪول‬ ‫ﻣﻮﺿﺤﺔ‬ ‫اﻷرﺻﺎد‬ ‫ﺑﺄن‬ ‫ﻋﻠﻤﺎ‬ ‫هـ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ : :
  • 16. ١٦ ١٦ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ا‬ ‫ب‬ ‫ا‬ 107.12 0 20 85 106.765 8.715 107.774 8.754 ‫ب‬ ‫ﺟـ‬ ‫ب‬ 63.18 10 46 163 17.659 -60.662 17.826 -60.392 ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ 126.84 40 46 262 -125.834 -15.946 -124.644 -15.875 ‫د‬ ‫هـ‬ ‫د‬ 27.99 50 30 348 -5.574 27.429 -5.521 27.552 ‫هـ‬ ‫ا‬ ‫هـ‬ 40.04 10 29 6 4.523 39.784 4.566 39.961 ‫ا‬ ‫اﻟﺠﺒﺮى‬ ‫ﻣﺠـ‬ -2.460 -0.680 0.000 0.000 ‫اﻟﻌﺪدى‬ ‫ﻣﺠـ‬ 260.354 152.536 ‫اﻟﻨﻘﻄﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫اﻟﺨﻂ‬ ‫اﻟﻄﻮل‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٥ ٥ : : ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬
  • 17. ١٧ ١٧ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ب‬ ‫ا‬ 363.900 363.900 ‫ﺟـ‬ ‫ب‬ 341.360 0.000 ‫د‬ ‫ﺟـ‬ 0.000 -324.150 ‫هـ‬ ‫د‬ -231.180 -400.420 ‫و‬ ‫هـ‬ -334.180 193.220 ‫ا‬ ‫و‬ -138.980 167.200 ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺨﻂ‬ ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٦ ٦ ) ) ‫اﻻﺣﺪاﺛﻴﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ ‫اﻻﺣﺪاﺛﻴﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ :( :( ‫ﻓﻰ‬ ‫ﻓﻰ‬ ‫ﺗﺮاﻓﻴﺮس‬ ‫ﺗﺮاﻓﻴﺮس‬ ‫اﻟﺘﻴﻮدوﻟﻴﺖ‬ ‫اﻟﺘﻴﻮدوﻟﻴﺖ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻗﻴﻤﺔ‬ ‫ﻣﻌﻠﻮم‬ ‫و‬ ‫هـ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻗﻴﻤﺔ‬ ‫ﻣﻌﻠﻮم‬ ‫و‬ ‫هـ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ ‫آﺎﻧﺖ‬ ‫إذا‬ ‫اﻟﻤﻀﻠﻊ‬ ‫ﻧﻘﺎط‬ ‫اﺣﺪاﺛﻴﺎت‬ ‫ﺣﺴﺎب‬ ‫وﻣﻄﻠﻮب‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫آﺎﻧﺖ‬ ‫إذا‬ ‫اﻟﻤﻀﻠﻊ‬ ‫ﻧﻘﺎط‬ ‫اﺣﺪاﺛﻴﺎت‬ ‫ﺣﺴﺎب‬ ‫وﻣﻄﻠﻮب‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫ا‬ ‫اﺣﺪاﺛﻴﺎت‬ ‫ا‬ ‫اﺣﺪاﺛﻴﺎت‬ ) ) ‫ﺷﺮﻗﺎ‬ ‫ﺻﻔﺮ‬ ‫ﺷﺮﻗﺎ‬ ‫ﺻﻔﺮ‬ ، ، ‫ﺷﻤﺎﻻ‬ ‫ﺻﻔﺮ‬ ‫ﺷﻤﺎﻻ‬ ‫ﺻﻔﺮ‬ ( (
  • 18. ١٨ ١٨ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ا‬ 0.000 0.000 ‫ب‬ ‫ا‬ 363.900 363.900 363.662 363.963 ‫ب‬ 363.662 363.963 ‫ﺟـ‬ ‫ب‬ 341.360 0.000 341.137 0.000 ‫ﺟـ‬ 704.800 363.963 ‫د‬ ‫ﺟـ‬ 0.000 -324.150 0.000 -324.094 ‫د‬ 704.800 39.869 ‫هـ‬ ‫د‬ -231.180 -400.420 -231.331 -400.351 ‫هـ‬ 473.469 -360.482 ‫و‬ ‫هـ‬ -334.180 193.220 -334.398 193.253 ‫و‬ 139.071 -167.229 ‫ا‬ ‫و‬ -138.980 167.200 -139.071 167.229 ‫ا‬ 0.000 0.000 ‫ﺟﺒﺮى‬ ‫ﻣﺠـ‬ 0.920 -0.250 0.000 0.000 ‫ﻋﺪدى‬ ‫ﻣﺠـ‬ 1409.600 1448.890 ‫اﻟﻨﻘﻄﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺨﻂ‬ ‫اﻻﺣﺪاﺛﻰ‬ ‫اﻷﻓﻘﻲ‬ ‫اﻻﺣﺪاﺛﻰ‬ ‫اﻟﺮأﺳﻲ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺼﺤﺤﺔ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٦ ٦ : : ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬
  • 19. ١٩ ١٩ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٧ ٧ ) ) ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻣﺴﺎﺣﺔ‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻣﺴﺎﺣﺔ‬ ‫ﺣﺴﺎب‬ ‫ﻋﻠﻰ‬ :( :( ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻣﺴﺎﺣﺔ‬ ‫اﺣﺴﺐ‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻣﺴﺎﺣﺔ‬ ‫اﺣﺴﺐ‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻰ‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻰ‬ . . ‫ا‬ 0.000 0.000 ‫ب‬ 363.662 363.963 704.800 256520.865 ‫ﺟـ‬ 704.800 363.963 341.137 124161.249 ‫د‬ 704.800 39.869 -231.331 -9222.866 ‫هـ‬ 473.469 -360.482 -565.729 203935.225 ‫و‬ 139.071 -167.229 -473.469 79177.645 ‫ا‬ 0.000 0.000 224.592 0.000 ‫ب‬ 363.662 363.963 ‫اﻟﻤﺴﺎﺣﺔ‬ ‫ﺿﻌﻒ‬ 654572.118 ‫اﻟﻤﺴﺎﺣﺔ‬ 327286.059 ‫اﻟﻨﻘﻄﺔ‬ ‫ﻓﺮق‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫اﻷﻓﻘﻴﺔ‬ * ‫اﻟﺮأﺳﻴﺔ‬ (‫اﻟﻤﺮآﺒﺎت‬ ‫)ﻓﺮق‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬
  • 20. ٢٠ ٢٠ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٨ ٨ ) ) ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ : : ‫واﻧﺤﺮاﻓﻪ‬ ‫ﺧﻂ‬ ‫ﻃﻮل‬ ‫واﻧﺤﺮاﻓﻪ‬ ‫ﺧﻂ‬ ‫ﻃﻮل‬ : ( : ( ‫ﺑﺎﻟﺠﺪول‬ ‫اﻟﻤﻮﺿﺤﺔ‬ ‫اﻷرﺻﺎد‬ ‫أﺧﺬت‬ ‫ﺑﺎﻟﺠﺪول‬ ‫اﻟﻤﻮﺿﺤﺔ‬ ‫اﻷرﺻﺎد‬ ‫أﺧﺬت‬ ‫ﻟﻠﺘﺮاﻓﻴﺮس‬ ‫ﻟﻠﺘﺮاﻓﻴﺮس‬ ‫ﺣﺴﺎب‬ ‫واﻟﻤﻄﻠﻮب‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ ‫ﺣﺴﺎب‬ ‫واﻟﻤﻄﻠﻮب‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ ‫ب‬ ‫ا‬ ‫اﻟﺨﻂ‬ ‫واﻧﺤﺮاف‬ ‫ﻃﻮل‬ ‫ب‬ ‫ا‬ ‫اﻟﺨﻂ‬ ‫واﻧﺤﺮاف‬ ‫ﻃﻮل‬ . . ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ﺟـ‬ ‫ا‬ 130.75 0 0 0 ‫د‬ ‫ﺟـ‬ 210.75 0 39 54 ‫ب‬ ‫د‬ 65.00 0 57 328 ‫ا‬ ‫ب‬ L α ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺨﻂ‬ ‫اﻟﻄﻮل‬
  • 21. ٢١ ٢١ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٨ ٨ : : ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ : : ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ا‬ ‫ﺟـ‬ ‫ا‬ 130.75 0 0 0 0.000 130.750 ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ 210.75 0 39 54 171.895 121.934 ‫د‬ ‫ب‬ ‫د‬ 65.00 0 57 328 -33.526 55.687 ‫ب‬ ‫ا‬ ‫ب‬ L L sin α L cos α ‫ا‬ ‫اﻟﻤﺠﻤﻮع‬ 138.369 308.370 L sin α L cos α α ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺨﻂ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻄﻮل‬
  • 22. ٢٢ ٢٢ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٨ ٨ : : ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ = = ‫ل‬ ‫ل‬ ‫ﺟﺎ‬ ‫ﺟﺎ‬ α α + + ١٣٨٫٣٦٩ ١٣٨٫٣٦٩ = = ‫ﺻﻔﺮ‬ ‫ﺻﻔﺮ‬ ‫ل‬ ‫ل‬ ‫ﺟﺎ‬ ‫ﺟﺎ‬ α α = = - - ١٣٨٫٣٦٩ ١٣٨٫٣٦٩ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ = = ‫ل‬ ‫ل‬ ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ α α + + ٣٠٨٫٣٧ ٣٠٨٫٣٧ = = ‫ﺻﻔﺮ‬ ‫ﺻﻔﺮ‬ ‫ل‬ ‫ل‬ ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ α α = = - - ٣٠٨٫٣٧ ٣٠٨٫٣٧ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫ﺑﻘﺴﻤﺔ‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫ﺑﻘﺴﻤﺔ‬ ‫ﻇﺎ‬ ‫ﻇﺎ‬ α α = = ٠٫٤٤٨٧١ ٠٫٤٤٨٧١ ‫إذا‬ ‫إذا‬ α α = = ٥٩ ٥٩ ‫ث‬ ‫ث‬ ٩ ٩ ‫ق‬ ‫ق‬ ٢٤ ٢٤ ‫د‬ ‫د‬ ‫ﻓﻰ‬ ‫اﻟﺨﻂ‬ ‫ﻓﻴﻜﻮن‬ ‫ﺳﺎﻟﺒﺔ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫ﻣﻦ‬ ‫آﻼ‬ ‫ﻷن‬ ‫وﻧﻈﺮا‬ ‫ﻓﻰ‬ ‫اﻟﺨﻂ‬ ‫ﻓﻴﻜﻮن‬ ‫ﺳﺎﻟﺒﺔ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫ﻣﻦ‬ ‫آﻼ‬ ‫ﻷن‬ ‫وﻧﻈﺮا‬ ‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﺮﺑﻊ‬ ‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﺮﺑﻊ‬ ‫اﻻﻧﺤﺮاف‬ ‫اﻻﻧﺤﺮاف‬ = = ٥٩ ٥٩ ‫ث‬ ‫ث‬ ٩ ٩ ‫ق‬ ‫ق‬ ٢٤ ٢٤ ‫د‬ ‫د‬ + + ١٨٠ ١٨٠ ‫د‬ ‫د‬ = = ٥٩ ٥٩ ‫ث‬ ‫ث‬ ٩ ٩ ‫ق‬ ‫ق‬ ٢٠٤ ٢٠٤ ‫د‬ ‫د‬ ‫ل‬ ‫اﻟﻄﻮل‬ ‫ﻳﻜﻮن‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫اﺣﺪى‬ ‫ﻓﻰ‬ ‫وﺑﺎﻟﺘﻌﻮﻳﺾ‬ ‫ل‬ ‫اﻟﻄﻮل‬ ‫ﻳﻜﻮن‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫اﺣﺪى‬ ‫ﻓﻰ‬ ‫وﺑﺎﻟﺘﻌﻮﻳﺾ‬ = = ٣٧٧٫٩٩ ٣٧٧٫٩٩ ‫ﻣﺘﺮ‬ ‫ﻣﺘﺮ‬
  • 23. ٢٣ ٢٣ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻓﻰ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻘﻖ‬ ‫ﻣﺜﺎل‬ ‫ﻓﻰ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻘﻖ‬ ٨ ٨ : : ‫اﻷرﺻﺎد‬ ‫ﻣﻮﺿﻊ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫اﻷرﺻﺎد‬ ‫ﻣﻮﺿﻊ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫اﻟﺘﺤﻘﻴﻖ‬ ‫وﻳﻜﻮن‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫إﻋﺎدة‬ ‫ﺛﻢ‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻟﺘﺤﻘﻴﻖ‬ ‫وﻳﻜﻮن‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫إﻋﺎدة‬ ‫ﺛﻢ‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫ﻟﻠﺼﻔﺮ‬ ‫ﻣﺴﺎوﻳﺎ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻤﺠﻤﻮع‬ ‫ﻟﻠﺼﻔﺮ‬ ‫ﻣﺴﺎوﻳﺎ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻤﺠﻤﻮع‬ : : ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ا‬ ‫ﺟـ‬ ‫ا‬ 130.75 0 0 0 0.000 130.750 ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ 210.75 0 39 54 171.895 121.934 ‫د‬ ‫ب‬ ‫د‬ 65.00 0 57 328 -33.526 55.687 ‫ب‬ ‫ا‬ ‫ب‬ 337.99 59 9 204 -138.369 -308.369 ‫ا‬ ‫اﻟﻤﺠﻤﻮع‬ 0.000 0.000 ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺨﻂ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻄﻮل‬
  • 24. ٢٤ ٢٤ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ب‬ ‫ا‬ 500.0 0 0 0 ‫ﺟـ‬ ‫ب‬ L 0 0 45 ‫د‬ ‫ﺟـ‬ 854.0 0 33 110 ‫هـ‬ ‫د‬ 1019.8 0 41 168 ‫و‬ ‫هـ‬ 1118.0 ‫ا‬ ‫و‬ 656.8 0 54 305 α ‫اﻟﻄﻮل‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺨﻂ‬ ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٩ ٩ ) ) ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ : : ‫ﺁﺧﺮ‬ ‫ﺧﻂ‬ ‫واﻧﺤﺮاف‬ ‫ﺧﻂ‬ ‫ﻃﻮل‬ ‫ﺁﺧﺮ‬ ‫ﺧﻂ‬ ‫واﻧﺤﺮاف‬ ‫ﺧﻂ‬ ‫ﻃﻮل‬ : ( : ( ‫و‬ ‫هـ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻓﻰ‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ ‫اﺣﺴﺐ‬ ‫و‬ ‫هـ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻓﻰ‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ ‫اﺣﺴﺐ‬ . .
  • 25. ٢٥ ٢٥ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ا‬ ‫ب‬ ‫ا‬ 500.00 0 0 0 0.000 500.000 ‫ب‬ ‫ﺟـ‬ ‫ب‬ L 0 0 45 0.707 L 0.707 L ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ 854.00 0 33 110 799.657 -299.775 ‫د‬ ‫هـ‬ ‫د‬ 1019.80 0 41 168 200.117 -999.973 ‫هـ‬ ‫و‬ ‫هـ‬ 1118.00 1118 sin α 1118 cos α ‫و‬ ‫ا‬ ‫و‬ 656.80 0 54 305 -532.035 385.129 ‫ا‬ ‫اﻟﻤﺠﻤﻮع‬ 467.738 -414.618 0.707 L 0.707 L 1118 sin α 1118 cos α ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺨﻂ‬ α ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻄﻮل‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٩ ٩ : : ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ : :
  • 26. ٢٦ ٢٦ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٩ ٩ : : ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ = = ٤٦٧٫٧٣٨ ٤٦٧٫٧٣٨ + + ٠٫٧٠٧ ٠٫٧٠٧ ‫ل‬ ‫ل‬ + + ١١١٨ ١١١٨ ‫ﺟﺎ‬ ‫ﺟﺎ‬ α α = = ‫ﺻﻔﺮ‬ ‫ﺻﻔﺮ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ = = - - ٤١٤٫٦١٨ ٤١٤٫٦١٨ + + ٠٫٧٠٧ ٠٫٧٠٧ ‫ل‬ ‫ل‬ + + ١١١٨ ١١١٨ ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ α α = = ‫ﺻﻔﺮ‬ ‫ﺻﻔﺮ‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫ﺑﻄﺮح‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫ﺑﻄﺮح‬ ) ) ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ α α – – ‫ﺟﺎ‬ ‫ﺟﺎ‬ α α = ( = ( ٠٫٧٨٩٢٢٧ ٠٫٧٨٩٢٢٧ ٢ ٢ ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ ٢ ٢ ) ) ٤٥ ٤٥ + + α α = ( = ( ٠٫٧٨٩٢٢٧ ٠٫٧٨٩٢٢٧ ‫اذا‬ ‫اذا‬ α α = = ٣٩ ٣٩ ‫ث‬ ‫ث‬ ٤ ٤ ‫ق‬ ‫ق‬ ١١ ١١ ‫د‬ ‫د‬ ‫و‬ ‫هـ‬ ‫اﻟﺨﻂ‬ ‫اﻧﺤﺮاف‬ ‫وﻳﻜﻮن‬ ‫و‬ ‫هـ‬ ‫اﻟﺨﻂ‬ ‫اﻧﺤﺮاف‬ ‫وﻳﻜﻮن‬ )= )= ٠٠ ٠٠ ‫ث‬ ‫ث‬ ٠٠ ٠٠ ‫ق‬ ‫ق‬ ٢٧٠ ٢٧٠ ‫د‬ ‫د‬ ( ( – – ) ) ٣٩ ٣٩ ‫ث‬ ‫ث‬ ٤ ٤ ‫ق‬ ‫ق‬ ١١ ١١ ‫د‬ ‫د‬ = ( = ( ٢١ ٢١ ‫ث‬ ‫ث‬ ٥٥ ٥٥ ‫ق‬ ‫ق‬ ٢٥٨ ٢٥٨ ‫د‬ ‫د‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫إﺣﺪى‬ ‫ﻓﻰ‬ ‫وﺑﺎﻟﺘﻌﻮﻳﺾ‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫إﺣﺪى‬ ‫ﻓﻰ‬ ‫وﺑﺎﻟﺘﻌﻮﻳﺾ‬ ‫ﺟـ‬ ‫ب‬ ‫اﻟﻀﻠﻊ‬ ‫ﻃﻮل‬ ‫ﻗﻴﻤﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻧﺤﺼﻞ‬ ‫ﺟـ‬ ‫ب‬ ‫اﻟﻀﻠﻊ‬ ‫ﻃﻮل‬ ‫ﻗﻴﻤﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻧﺤﺼﻞ‬ ) ) ‫ل‬ ‫ل‬ = ( = ( ٨٩٠٫١٥٩ ٨٩٠٫١٥٩ ‫م‬ ‫م‬
  • 27. ٢٧ ٢٧ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ا‬ ‫ب‬ ‫ا‬ 500.00 0 0 0 0.000 500.000 ‫ب‬ ‫ﺟـ‬ ‫ب‬ 890.16 0 0 45 629.437 629.437 ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ 854.00 0 33 110 799.657 -299.775 ‫د‬ ‫هـ‬ ‫د‬ 1019.80 0 41 168 200.117 -999.973 ‫هـ‬ ‫و‬ ‫هـ‬ 1118.00 21 55 258 -1097.170 -214.809 ‫و‬ ‫ا‬ ‫و‬ 656.80 0 54 305 -532.035 385.129 ‫ا‬ ‫اﻟﻤﺠﻤﻮع‬ 0.000 0.000 ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻄﻮل‬ ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺨﻂ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻘﻖ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻘﻖ‬ ٩ ٩ : : ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ : :
  • 28. ٢٨ ٢٨ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ١٠ ١٠ ) ) ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ : : ‫ﺿﻠﻌﻴﻦ‬ ‫ﻃﻮﻻ‬ ‫ﺿﻠﻌﻴﻦ‬ ‫ﻃﻮﻻ‬ : ( : ( ‫وﻗ‬ ‫ﻟﻸﺿﻼع‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻻﻧﺤﺮاف‬ ‫ﻗﻴﺎس‬ ‫ﺗﻢ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻓﻰ‬ ‫وﻗ‬ ‫ﻟﻸﺿﻼع‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻻﻧﺤﺮاف‬ ‫ﻗﻴﺎس‬ ‫ﺗﻢ‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻘﻔﻞ‬ ‫اﻟﺘﺮاﻓﻴﺮس‬ ‫ﻓﻰ‬ ‫ﻃﻮل‬ ‫ﻴﺎس‬ ‫ﻃﻮل‬ ‫ﻴﺎس‬ ‫ب‬ ‫ا‬ ‫اﻟﻀﻠﻌﻴﻦ‬ ‫ﻣﻦ‬ ‫آﻞ‬ ‫ب‬ ‫ا‬ ‫اﻟﻀﻠﻌﻴﻦ‬ ‫ﻣﻦ‬ ‫آﻞ‬ ، ، ‫د‬ ‫ﺟـ‬ ‫اﻟﻀﻠﻌﻴﻦ‬ ‫ﻃﻮل‬ ‫ﻗﻴﺎس‬ ‫وﺗﻌﺬر‬ ‫ﺟـ‬ ‫ب‬ ‫د‬ ‫ﺟـ‬ ‫اﻟﻀﻠﻌﻴﻦ‬ ‫ﻃﻮل‬ ‫ﻗﻴﺎس‬ ‫وﺗﻌﺬر‬ ‫ﺟـ‬ ‫ب‬ ، ، ‫ا‬ ‫د‬ ‫ا‬ ‫د‬ . . ‫واﻟﻤﻄﻠﻮب‬ ‫واﻟﻤﻄﻠﻮب‬ ‫اﻟﺘﺎﻟﻰ‬ ‫ﺑﺎﻟﺠﺪول‬ ‫ﻣﻮﺿﺤﺔ‬ ‫اﻷرﺻﺎد‬ ‫ﺑﺄن‬ ‫ﻋﻠﻤﺎ‬ ‫أﻃﻮاﻟﻬﻤﺎ‬ ‫ﺣﺴﺎب‬ ‫اﻟﺘﺎﻟﻰ‬ ‫ﺑﺎﻟﺠﺪول‬ ‫ﻣﻮﺿﺤﺔ‬ ‫اﻷرﺻﺎد‬ ‫ﺑﺄن‬ ‫ﻋﻠﻤﺎ‬ ‫أﻃﻮاﻟﻬﻤﺎ‬ ‫ﺣﺴﺎب‬ : : ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ب‬ ‫ا‬ 150.0 0 30 178 ‫ﺟـ‬ ‫ب‬ 224.0 0 20 102 ‫د‬ ‫ﺟـ‬ L 0 45 31 ‫ا‬ ‫د‬ M 0 20 282 ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺨﻂ‬ ‫اﻟﻄﻮل‬
  • 29. ٢٩ ٢٩ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ا‬ ‫ب‬ ‫ا‬ 150.0 0 30 178 3.927 -149.949 ‫ب‬ ‫ﺟـ‬ ‫ب‬ 224.0 0 20 102 218.830 -47.846 ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ L 0 45 31 0.526L 0.850L ‫د‬ ‫ا‬ ‫د‬ M 0 20 282 -0.977M 0.214M ‫ا‬ ‫اﻟﻤﺠﻤﻮع‬ 222.757 -197.795 0.526L 0.850L -0.977M 0.214M ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺨﻂ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻄﻮل‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١٠ ١٠ : : ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ : :
  • 30. ٣٠ ٣٠ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١٠ ١٠ : : ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ = = ٢٢٢٫٧٥٧ ٢٢٢٫٧٥٧ + + ٠٫٥٢٦ ٠٫٥٢٦ ‫ل‬ ‫ل‬ - - ٠٫٩٧٧ ٠٫٩٧٧ ‫م‬ ‫م‬ = = ‫ﺻﻔﺮ‬ ‫ﺻﻔﺮ‬ ‫ل‬ ‫ل‬ = = - - ٤٢٣٫٤٩٢ ٤٢٣٫٤٩٢ + + ١٫٨٥٧ ١٫٨٥٧ ‫م‬ ‫م‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﻣﺠـ‬ = = - - ١٩٧٫٧٩٥ ١٩٧٫٧٩٥ + + ٠٫٨٥٠ ٠٫٨٥٠ ‫ل‬ ‫ل‬ + + ٠٫٢١٤ ٠٫٢١٤ ‫م‬ ‫م‬ = = ‫ﺻﻔﺮ‬ ‫ﺻﻔﺮ‬ ‫ل‬ ‫ل‬ = = ٢٣٢٫٧ ٢٣٢٫٧ – – ٠٫٢٥٢ ٠٫٢٥٢ ‫م‬ ‫م‬ ‫ﻣﺠﻬﻮﻟﻴﻦ‬ ‫ﻓﻰ‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫ﺑﺤﻞ‬ ‫ﻣﺠﻬﻮﻟﻴﻦ‬ ‫ﻓﻰ‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫ﺑﺤﻞ‬ ‫م‬ ‫اﻟﻄﻮل‬ ‫ﻳﻜﻮن‬ ‫م‬ ‫اﻟﻄﻮل‬ ‫ﻳﻜﻮن‬ = = ٣١١٫١٨٣ ٣١١٫١٨٣ ‫ﻣﺘﺮ‬ ‫ﻣﺘﺮ‬ ‫ل‬ ‫واﻟﻄﻮل‬ ‫ل‬ ‫واﻟﻄﻮل‬ = = ١٥٤٫٣٧٥ ١٥٤٫٣٧٥ ‫ﻣﺘﺮ‬ ‫ﻣﺘﺮ‬
  • 31. ٣١ ٣١ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻓﻰ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻘﻖ‬ ‫ﻣﺜﺎل‬ ‫ﻓﻰ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻘﻖ‬ ١٠ ١٠ : : ‫ﻣﻮﺿﻊ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫ﻣﻮﺿﻊ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫وﻳﻜﻮن‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫إﻋﺎدة‬ ‫ﺛﻢ‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ ‫وﻳﻜﻮن‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫إﻋﺎدة‬ ‫ﺛﻢ‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ ‫ﻟﻠﺼﻔﺮ‬ ‫ﻣﺴﺎوﻳﺎ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻤﺠﻤﻮع‬ ‫اﻟﺘﺤﻘﻴﻖ‬ ‫ﻟﻠﺼﻔﺮ‬ ‫ﻣﺴﺎوﻳﺎ‬ ‫واﻟﺮأﺳﻴﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻤﺮآﺒﺎت‬ ‫ﺑﻤﺠﻤﻮع‬ ‫اﻟﺘﺤﻘﻴﻖ‬ : : ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ا‬ ‫ب‬ ‫ا‬ 150.0 0 30 178 3.927 -149.949 ‫ب‬ ‫ﺟـ‬ ‫ب‬ 224.0 0 20 102 218.830 -47.846 ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ 154.4 0 45 31 81.234 131.273 ‫د‬ ‫ا‬ ‫د‬ 311.2 0 20 282 -304.001 66.468 ‫ا‬ ‫اﻟﻤﺠﻤﻮع‬ 0.000 0.000 ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺨﻂ‬ ‫اﻟﻤﺮآﺒﺔ‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻄﻮل‬
  • 32. ٣٢ ٣٢ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ١١ ١١ ) ) ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ ‫اﻟﻨﺎﻗﺼﺔ‬ ‫اﻷرﺻﺎد‬ : : ‫ﺿﻠﻌﻴﻦ‬ ‫اﻧﺤﺮاف‬ ‫ﺿﻠﻌﻴﻦ‬ ‫اﻧﺤﺮاف‬ : ( : ( ‫ﻓﻴﻪ‬ ‫ا‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻀﻠﻊ‬ ‫ﻓﻴﻪ‬ ‫ا‬ ‫د‬ ‫ﺟـ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﻀﻠﻊ‬ : : ‫ب‬ ‫ا‬ 200.00 ‫ﺟـ‬ ‫ب‬ 350.00 0 0 102 ‫د‬ ‫ﺟـ‬ 150.00 ‫هـ‬ ‫د‬ 400.00 0 0 270 ‫اﻟﺨﻂ‬ ‫اﻟﻄﻮل‬ α β ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫ب‬ ‫ا‬ ‫اﻟﻀﻠﻌﻴﻦ‬ ‫اﻧﺤﺮاف‬ ‫إﻳﺠﺎد‬ ‫واﻟﻤﻄﻠﻮب‬ ‫ب‬ ‫ا‬ ‫اﻟﻀﻠﻌﻴﻦ‬ ‫اﻧﺤﺮاف‬ ‫إﻳﺠﺎد‬ ‫واﻟﻤﻄﻠﻮب‬ ، ، ‫د‬ ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬
  • 33. ٣٣ ٣٣ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١١ ١١ : : ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ ‫آﺎﻵﺗﻰ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫اﻟﺤﺴﺎب‬ ‫ﺛﻢ‬ ‫اﻷرﺻﺎد‬ ‫وﺿﻊ‬ ‫ﻳﺘﻢ‬ : : ‫ا‬ ‫ب‬ ‫ا‬ 200.00 α‫ﺟﺎ‬200 α‫ﺟﺘﺎ‬200 ‫ب‬ ‫ﺟـ‬ ‫ب‬ 350.00 0 0 102 342.352 -72.769 ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ 150.00 β‫ﺟﺎ‬150 β‫ﺟﺘﺎ‬150 ‫د‬ ‫هـ‬ ‫د‬ 400.00 0 0 270 -400.000 0.000 ‫ا‬ ‫اﻟﻤﺠﻤﻮع‬ 1100.00 -57.648 -72.769 α‫ﺟﺎ‬200 α‫ﺟﺘﺎ‬200 β‫ﺟﺎ‬150 β‫ﺟﺘﺎ‬150 ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ α β ‫اﻟﻨﻘﻄﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻟﺨﻂ‬ ‫اﻟﻄﻮل‬
  • 34. ٣٤ ٣٤ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ٢٠٠ ٢٠٠ ‫ﺟﺎ‬ ‫ﺟﺎ‬ α α = = ٥٧٫٦٤٨ ٥٧٫٦٤٨ – – ١٥٠ ١٥٠ ‫ﺟﺎ‬ ‫ﺟﺎ‬ β β ‫ﺟﺎ‬ ‫ﺟﺎ‬ α α = = ٠٫٢٨٨٣٤ ٠٫٢٨٨٣٤ – – ٠٫٧٥ ٠٫٧٥ ‫ﺟﺎ‬ ‫ﺟﺎ‬ β β ‫ﻣﻌﺎدﻟﺔ‬ ‫ﻣﻌﺎدﻟﺔ‬ ) ) ١ ١ ( ( ٢٠٠ ٢٠٠ ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ α α = = ٧٢٫٧٦٩ ٧٢٫٧٦٩ – – ١٥٠ ١٥٠ ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ β β ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ α α = = ٠٫٣٦٣٨ ٠٫٣٦٣٨ – – ٠٫٧٥ ٠٫٧٥ ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ β β ‫ﻣﻌﺎدﻟﺔ‬ ‫ﻣﻌﺎدﻟﺔ‬ ) ) ٢ ٢ ( ( ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١١ ١١ : : ‫ﺟﺎ‬ ‫ﺟﺎ‬ ٢ ٢ α α = = ٠٫٠٨٣ ٠٫٠٨٣ + + ٠٫٥٦٢٥ ٠٫٥٦٢٥ ‫ﺟﺎ‬ ‫ﺟﺎ‬ ٢ ٢ β β - - ٢ ٢ ) ) ٠٫٢٨٨٢٤ ٠٫٢٨٨٢٤ x x ٠٫٧٥ ٠٫٧٥ ‫ﺟﺎ‬ ‫ﺟﺎ‬ β β ( ( ‫ﻣﻌﺎدﻟﺔ‬ ‫ﻣﻌﺎدﻟﺔ‬ ) ) ٣ ٣ ( ( ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫ﺑﺘﺮﺑﻴﻊ‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫ﺑﺘﺮﺑﻴﻊ‬ ١ ١ ، ، ٢ ٢ ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ ٢ ٢ α α = = ٠٫١٣٢٣ ٠٫١٣٢٣ + + ٠٫٥٦٢٥ ٠٫٥٦٢٥ ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ ٢ ٢ β β - - ٢ ٢ ) ) ٠٫٣٦٣٨ ٠٫٣٦٣٨ x x ٠٫٧٥ ٠٫٧٥ ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ β β ( ( ‫ﻣﻌﺎدﻟﺔ‬ ‫ﻣﻌﺎدﻟﺔ‬ ) ) ٤ ٤ ( (
  • 35. ٣٥ ٣٥ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ ) ) β β - - δ δ ) = ( ) = ( - - ٠٫٢٢٢٢ ٠٫٢٢٢٢ ( ( )) )) ‫س‬ ‫س‬ ٢ ٢ + + ‫ص‬ ‫ص‬ ٢ ٢ ( ( ½ ½ ( ( ) ) β β - - δ δ = ( = ( ٤٢ ٤٢ ‫ث‬ ‫ث‬ ٣٦ ٣٦ ‫ق‬ ‫ق‬ ١٠٨ ١٠٨ ‫أو‬ ‫د‬ ‫أو‬ ‫د‬ = = ١٨ ١٨ ‫ث‬ ‫ث‬ ٢٣ ٢٣ ‫ق‬ ‫ق‬ ٢٥١ ٢٥١ ‫د‬ ‫د‬ β β = = ٠٥ ٠٥ ‫ث‬ ‫ث‬ ٠٠ ٠٠ ‫ق‬ ‫ق‬ ١٤٧ ١٤٧ ‫أو‬ ‫د‬ ‫أو‬ ‫د‬ = = ٤١ ٤١ ‫ث‬ ‫ث‬ ٤٦ ٤٦ ‫ق‬ ‫ق‬ ٢٨٩ ٢٨٩ ‫د‬ ‫د‬ α α = = ٤٢ ٤٢ ‫ث‬ ‫ث‬ ٠٥ ٠٥ ‫ق‬ ‫ق‬ ٣٥٣ ٣٥٣ ‫أو‬ ‫د‬ ‫أو‬ ‫د‬ = = ٠٩ ٠٩ ‫ث‬ ‫ث‬ ٤٣ ٤٣ ‫ق‬ ‫ق‬ ٨٣ ٨٣ ‫د‬ ‫د‬ ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١١ ١١ : : ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫ﺑﺠﻤﻊ‬ ‫اﻟﻤﻌﺎدﻟﺘﻴﻦ‬ ‫ﺑﺠﻤﻊ‬ ٣ ٣ ، ، ٤ ٤ ٠٫٤٣٢٣٦ ٠٫٤٣٢٣٦ ‫ﺟﺎ‬ ‫ﺟﺎ‬ β β + + ٠٫٥٤٥٧ ٠٫٥٤٥٧ ‫ﺟﺘﺎ‬ ‫ﺟﺘﺎ‬ β β = = - - ٠٫٢٢٢٢ ٠٫٢٢٢٢ ‫اﻟﺤﺪ‬ ‫أن‬ ‫وﺑﻔﺮض‬ ‫اﻟﺤﺪ‬ ‫أن‬ ‫وﺑﻔﺮض‬ ٠٫٤٣٢٣٦ ٠٫٤٣٢٣٦ = = ‫س‬ ‫س‬ ، ، ‫واﻟﺤﺪ‬ ‫واﻟﺤﺪ‬ ٠٫٥٤٥٧ ٠٫٥٤٥٧ = = ‫ﻣﻊ‬ ‫ص‬ ‫ﻣﻊ‬ ‫ص‬ ‫ﻣﺴﺎﻋﺪة‬ ‫ﺑﺰاوﻳﺔ‬ ‫اﻻﺳﺘﻌﺎﻧﺔ‬ ‫ﻣﺴﺎﻋﺪة‬ ‫ﺑﺰاوﻳﺔ‬ ‫اﻻﺳﺘﻌﺎﻧﺔ‬ δ δ ‫ﺣﻴﺚ‬ ‫ﺣﻴﺚ‬ ‫ﻇﺎ‬ ‫ﻇﺎ‬ δ δ = = ‫س‬ ‫س‬ ‫ص‬ ‫ص‬ = = ٠٫٧٩٢٣ ٠٫٧٩٢٣ ‫إذا‬ ‫إذا‬ δ δ = = ٢٣ ٢٣ ‫ث‬ ‫ث‬ ٢٣ ٢٣ ‫ق‬ ‫ق‬ ٣٨ ٣٨ ‫د‬ ‫د‬
  • 36. ٣٦ ٣٦ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻘﻖ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻘﻖ‬ ١١ ١١ ) ) ‫اﻷول‬ ‫اﻟﺤﻞ‬ ‫اﻷول‬ ‫اﻟﺤﻞ‬ :( :( ‫اﻟ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺄآﺪ‬ ‫آﻴﻔﻴﺔ‬ ‫ﻳﻮﺿﺢ‬ ‫اﻟﺘﺎﻟﻰ‬ ‫ﻓﺎﻟﺠﺪول‬ ‫ﺣﻼن‬ ‫ﻟﻬﺎ‬ ‫اﻟﻤﺴﺄﻟﺔ‬ ‫ﻷن‬ ‫ﻧﻈﺮا‬ ‫اﻟ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺄآﺪ‬ ‫آﻴﻔﻴﺔ‬ ‫ﻳﻮﺿﺢ‬ ‫اﻟﺘﺎﻟﻰ‬ ‫ﻓﺎﻟﺠﺪول‬ ‫ﺣﻼن‬ ‫ﻟﻬﺎ‬ ‫اﻟﻤﺴﺄﻟﺔ‬ ‫ﻷن‬ ‫ﻧﻈﺮا‬ ‫اﻷول‬ ‫ﺑﺎﻟﺤﻞ‬ ‫ﻨﺘﺎﺋﺞ‬ ‫اﻷول‬ ‫ﺑﺎﻟﺤﻞ‬ ‫ﻨﺘﺎﺋﺞ‬ ‫ا‬ ‫ب‬ ‫ا‬ 200.00 42 5 353 -24.045 198.549 ‫ب‬ ‫ﺟـ‬ ‫ب‬ 350.00 0 0 102 342.352 -72.769 ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ 150.00 5 0 147 81.693 -125.803 ‫د‬ ‫هـ‬ ‫د‬ 400.00 0 0 270 -400.000 0.000 ‫ا‬ ‫اﻟﻤﺠﻤﻮع‬ 1100.00 0.000 0.000 ‫اﻟﻨﻘﻄﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫اﻟﺨﻂ‬ ‫اﻟﻄﻮل‬
  • 37. ٣٧ ٣٧ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ا‬ ‫ب‬ ‫ا‬ 200.00 9 43 83 198.800 21.880 ‫ب‬ ‫ﺟـ‬ ‫ب‬ 350.00 0 0 102 342.352 -72.769 ‫ﺟـ‬ ‫د‬ ‫ﺟـ‬ 150.00 9 46 289 -141.159 50.735 ‫د‬ ‫هـ‬ ‫د‬ 400.00 0 0 270 -400.000 0.000 ‫ا‬ ‫اﻟﻤﺠﻤﻮع‬ 1100.00 0.000 0.000 ‫اﻟﻨﻘﻄﺔ‬ ‫اﻷﻣﺎﻣﻰ‬ ‫اﻹﻧﺤﺮاف‬ ‫اﻷﻓﻘﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺮأﺳﻴﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫ﻣﺼﺤﺤﺔ‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪﻗﻴﻘﺔ‬ ‫اﻟﺪرﺟﺔ‬ ‫اﻟﺨﻂ‬ ‫اﻟﻄﻮل‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻘﻖ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻘﻖ‬ ١١ ١١ ) ) ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﺤﻞ‬ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﺤﻞ‬ :( :( ‫اﻟﺜﺎﻧﻰ‬ ‫ﺑﺎﻟﺤﻞ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺄآﺪ‬ ‫آﻴﻔﻴﺔ‬ ‫ﻳﻮﺿﺢ‬ ‫اﻟﺘﺎﻟﻰ‬ ‫اﻟﺠﺪول‬ ‫اﻟﺜﺎﻧﻰ‬ ‫ﺑﺎﻟﺤﻞ‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺄآﺪ‬ ‫آﻴﻔﻴﺔ‬ ‫ﻳﻮﺿﺢ‬ ‫اﻟﺘﺎﻟﻰ‬ ‫اﻟﺠﺪول‬
  • 38. ٣٨ ٣٨ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﺒﺎب‬ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﺒﺎب‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﻴﺰاﻧﻴﺔ‬ ‫ﺑﺎب‬ ‫اﻟﻤﻴﺰاﻧﻴﺔ‬ ‫ﺑﺎب‬
  • 39. ٣٩ ٣٩ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ١ ١ : : ‫ﻋﻠﻰ‬ ‫اﻟﻘﺮاءة‬ ‫ﻓﻜﺎﻧﺖ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻣﻨﺘﺼﻒ‬ ‫ﻓﻰ‬ ‫ﻣﻴﺰان‬ ‫وﺿﻊ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻘﺮاءة‬ ‫ﻓﻜﺎﻧﺖ‬ ‫ب‬ ‫ا‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻣﻨﺘﺼﻒ‬ ‫ﻓﻰ‬ ‫ﻣﻴﺰان‬ ‫وﺿﻊ‬ ‫ا‬ ‫اﻟﻘﺎﻣﺔ‬ ‫ا‬ ‫اﻟﻘﺎﻣﺔ‬ ) ) ١٫٦٨ ١٫٦٨ ‫م‬ ‫م‬ ( ( ‫ب‬ ‫اﻟﻘﺎﻣﺔ‬ ‫وﻋﻠﻰ‬ ‫ب‬ ‫اﻟﻘﺎﻣﺔ‬ ‫وﻋﻠﻰ‬ ) ) ١٫٩٥ ١٫٩٥ ‫م‬ ‫م‬ ( ( ‫اﻟﺠﻬﺎز‬ ‫ﻧﻘﻞ‬ ‫ﺛﻢ‬ ‫اﻟﺠﻬﺎز‬ ‫ﻧﻘﻞ‬ ‫ﺛﻢ‬ ‫ا‬ ‫اﻟﻘﺎﻣﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻘﺮاءة‬ ‫ﻓﻜﺎﻧﺖ‬ ‫ب‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻣﻦ‬ ‫ﻗﺮﻳﺒﺎ‬ ‫ووﺿﻊ‬ ‫ا‬ ‫اﻟﻘﺎﻣﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻘﺮاءة‬ ‫ﻓﻜﺎﻧﺖ‬ ‫ب‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻣﻦ‬ ‫ﻗﺮﻳﺒﺎ‬ ‫ووﺿﻊ‬ ) ) ١٫٣١ ١٫٣١ ‫م‬ ‫م‬ ( ( ‫ب‬ ‫اﻟﻘﺎﻣﺔ‬ ‫وﻋﻠﻰ‬ ‫ب‬ ‫اﻟﻘﺎﻣﺔ‬ ‫وﻋﻠﻰ‬ ) ) ١٫٧٤ ١٫٧٤ ‫م‬ ‫م‬ .( .( ‫ووﺿﺢ‬ ‫اﻟﻨﻈﺮ‬ ‫ﺧﻂ‬ ‫ﻳﻮﺿﺢ‬ ‫ﺷﻜﻼ‬ ‫ارﺳﻢ‬ ‫ووﺿﺢ‬ ‫اﻟﻨﻈﺮ‬ ‫ﺧﻂ‬ ‫ﻳﻮﺿﺢ‬ ‫ﺷﻜﻼ‬ ‫ارﺳﻢ‬ ‫ﻟﻤﻌﺎﻳﺮة‬ ‫اﻟﻼزم‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻗﻴﻤﺔ‬ ‫وﻣﺎ‬ ‫ﺑﺎﻟﻤﻴﺰان‬ ‫اﻟﺮﺻﺪ‬ ‫ﻳﻤﻜﻦ‬ ‫هﻞ‬ ‫ﻟﻤﻌﺎﻳﺮة‬ ‫اﻟﻼزم‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻗﻴﻤﺔ‬ ‫وﻣﺎ‬ ‫ﺑﺎﻟﻤﻴﺰان‬ ‫اﻟﺮﺻﺪ‬ ‫ﻳﻤﻜﻦ‬ ‫هﻞ‬ ‫اﻟﻤﻴﺰان‬ ‫اﻟﻤﻴﺰان‬ . .
  • 40. ٤٠ ٤٠ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ب‬ ‫ب‬ ١٫٩٥ ١٫٩٥ ١٫٦٨ ١٫٦٨ ‫ﻟﻠﻤﻴﺰان‬ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﻮﺿﻊ‬ ‫ﻟﻠﻤﻴﺰان‬ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﻮﺿﻊ‬ ‫ﻟﻠﻤﻴﺰان‬ ‫اﻷول‬ ‫اﻟﻮﺿﻊ‬ ‫ﻟﻠﻤﻴﺰان‬ ‫اﻷول‬ ‫اﻟﻮﺿﻊ‬ ١٫٣١ ١٫٣١ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١ ١ : : ‫اﻟﺤﺎﻟﺘﻴﻦ‬ ‫ﻓﻰ‬ ‫اﻟﺠﻬﺎز‬ ‫وﺿﻌﻰ‬ ‫رﺳﻢ‬ ‫ﻳﺘﻢ‬ ‫اﻟﺤﺎﻟﺘﻴﻦ‬ ‫ﻓﻰ‬ ‫اﻟﺠﻬﺎز‬ ‫وﺿﻌﻰ‬ ‫رﺳﻢ‬ ‫ﻳﺘﻢ‬ ‫اﻷول‬ ‫اﻟﻮﺿﻊ‬ ‫ﻓﻰ‬ ‫اﻷول‬ ‫اﻟﻮﺿﻊ‬ ‫ﻓﻰ‬ : : ‫ا‬ ‫ﺑﻴﻦ‬ ‫اﻟﺤﻘﻴﻘﻰ‬ ‫اﻟﻤﻨﺴﻮب‬ ‫ﻓﺮق‬ ‫ا‬ ‫ﺑﻴﻦ‬ ‫اﻟﺤﻘﻴﻘﻰ‬ ‫اﻟﻤﻨﺴﻮب‬ ‫ﻓﺮق‬ ، ، ‫ب‬ ‫ب‬ = = ١٫٩٥ ١٫٩٥ - - ١٫٦٨ ١٫٦٨ = = ٠٫٢٧ ٠٫٢٧ ‫م‬ ‫م‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ب‬ ‫ب‬ ١٫٧٤ ١٫٧٤ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﻮﺿﻊ‬ ‫ﻓﻰ‬ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﻮﺿﻊ‬ ‫ﻓﻰ‬ : : ‫ا‬ ‫ﺑﻴﻦ‬ ‫اﻟﻤﻨﺴﻮب‬ ‫ﻓﺮق‬ ‫ﻳﻜﻮن‬ ‫ا‬ ‫ﺑﻴﻦ‬ ‫اﻟﻤﻨﺴﻮب‬ ‫ﻓﺮق‬ ‫ﻳﻜﻮن‬ ، ، ‫ب‬ ‫ب‬ = = ١٫٧٤ ١٫٧٤ - - ١٫٣١ ١٫٣١ = = ٠٫٤٣ ٠٫٤٣ ‫م‬ ‫م‬ ‫اﻟﻤﻨﺴﻮب‬ ‫ﻓﺮق‬ ‫ﻻﺧﺘﻼف‬ ‫ﻧﻈﺮا‬ ‫اﻟﻤﻨﺴﻮب‬ ‫ﻓﺮق‬ ‫ﻻﺧﺘﻼف‬ ‫ﻧﻈﺮا‬ ‫اﻟﺮﺻﺪ‬ ‫ﻳﻤﻜﻦ‬ ‫ﻻ‬ ‫إذا‬ ‫اﻟﻮﺿﻌﻴﻦ‬ ‫ﻓﻰ‬ ‫اﻟﺮﺻﺪ‬ ‫ﻳﻤﻜﻦ‬ ‫ﻻ‬ ‫إذا‬ ‫اﻟﻮﺿﻌﻴﻦ‬ ‫ﻓﻰ‬ ‫ﻣﻌﺎﻳﺮة‬ ‫اﻟﻰ‬ ‫وﻳﺤﺘﺎج‬ ‫ﺑﺎﻟﻤﻴﺰان‬ ‫ﻣﻌﺎﻳﺮة‬ ‫اﻟﻰ‬ ‫وﻳﺤﺘﺎج‬ ‫ﺑﺎﻟﻤﻴﺰان‬ . . ‫ﻓﻰ‬ ‫ب‬ ‫ﻋﻨﺪ‬ ‫اﻟﺨﻄﺄ‬ ‫ان‬ ‫وﺑﺎﻋﺘﺒﺎر‬ ‫ﻓﻰ‬ ‫ب‬ ‫ﻋﻨﺪ‬ ‫اﻟﺨﻄﺄ‬ ‫ان‬ ‫وﺑﺎﻋﺘﺒﺎر‬ ‫ﺻﻔﺮ‬ ‫ﻳﺴﺎوى‬ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﻮﺿﻊ‬ ‫ﺻﻔﺮ‬ ‫ﻳﺴﺎوى‬ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﻮﺿﻊ‬ ، ، ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻗﻴﻤﺔ‬ ‫ﻓﺘﻜﻮن‬ ‫اﻟﺘﺼﺤﻴﺢ‬ ‫ﻗﻴﻤﺔ‬ ‫ﻓﺘﻜﻮن‬ : : ١٫٧٤ ١٫٧٤ = = ٠٫٢٧ ٠٫٢٧ + + ١٫٣١ ١٫٣١ - - ‫س‬ ‫س‬ ‫س‬ ‫س‬ = = ٠٫١٦ ٠٫١٦ ‫م‬ ‫م‬ ‫س‬ ‫س‬
  • 41. ٤١ ٤١ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٢ ٢ : : ‫ﻟﻄﺮﻳﻖ‬ ‫ﻃﻮﻟﻰ‬ ‫ﻣﺤﻮر‬ ‫ﻋﻠﻰ‬ ‫ﺑﺎﻟﻤﻴﺰان‬ ‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﻘﺮاءات‬ ‫أﺧﺬت‬ ‫ﻟﻄﺮﻳﻖ‬ ‫ﻃﻮﻟﻰ‬ ‫ﻣﺤﻮر‬ ‫ﻋﻠﻰ‬ ‫ﺑﺎﻟﻤﻴﺰان‬ ‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﻘﺮاءات‬ ‫أﺧﺬت‬ : : ) ) ٢٫١٩ ٢٫١٩ ( ( ، ، ٢٫٥٠ ٢٫٥٠ ، ، ٢٫٣٢ ٢٫٣٢ ، ، ١٫٤٩ ١٫٤٩ ، ، ) ) ٣٫٠١ ٣٫٠١ ( ( ، ، ٢٫٥١ ٢٫٥١ ، ، ٢٫٨١ ٢٫٨١ ، ، ) ) ١٫٧٥ ١٫٧٥ ( ( ، ، ٣٫٨١ ٣٫٨١ . . ‫ﻧﻘﻄﺔ‬ ‫أول‬ ‫وﻣﻨﺴﻮب‬ ‫ﻣﺆﺧﺮات‬ ‫اﻷﻗﻮاس‬ ‫ﺑﻴﻦ‬ ‫اﻟﻘﺮاءات‬ ‫آﺎﻧﺖ‬ ‫ﻓﺈذا‬ ‫ﻧﻘﻄﺔ‬ ‫أول‬ ‫وﻣﻨﺴﻮب‬ ‫ﻣﺆﺧﺮات‬ ‫اﻷﻗﻮاس‬ ‫ﺑﻴﻦ‬ ‫اﻟﻘﺮاءات‬ ‫آﺎﻧﺖ‬ ‫ﻓﺈذا‬ +) +) ٣٠ ٣٠ ‫م‬ ‫م‬ ( ( ، ، ‫ﻣﺨﺘﻠﻔﺘﻴﻦ‬ ‫ﺑﻄﺮﻳﻘﺘﻴﻦ‬ ‫اﻟﻨﻘﻂ‬ ‫ﺑﺎﻗﻰ‬ ‫ﻣﻨﺎﺳﻴﺐ‬ ‫ﻓﺎﺣﺴﺐ‬ ‫ﻣﺨﺘﻠﻔﺘﻴﻦ‬ ‫ﺑﻄﺮﻳﻘﺘﻴﻦ‬ ‫اﻟﻨﻘﻂ‬ ‫ﺑﺎﻗﻰ‬ ‫ﻣﻨﺎﺳﻴﺐ‬ ‫ﻓﺎﺣﺴﺐ‬ . .
  • 42. ٤٢ ٤٢ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٢ ٢ : : ‫اﻟﻤﻴﺰان‬ ‫ﺳﻄﺢ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻤﻴﺰان‬ ‫ﺳﻄﺢ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﻤﺆﺧﺮة‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﻤﻘﺪﻣﺔ‬ ‫ﺳﻄﺢ‬ ‫ﻣﻨﺴﻮب‬ ‫اﻟﻤﻴﺰان‬ ‫ﻣﻨﺴﻮب‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻣﻼﺣﻈﺎت‬ ‫ا‬ 2.19 32.19 30.00 ‫روﺑﻴﺮ‬ ‫ب‬ 2.50 29.69 ‫ﺟـ‬ 2.32 29.87 ‫د‬ 3.01 1.49 33.71 30.70 ‫دوران‬ ‫هـ‬ 2.51 31.20 ‫و‬ 1.75 2.81 32.65 30.90 ‫دوران‬ ‫ز‬ 3.81 28.84 ‫اﻟﻤﺠﻤﻮع‬ 6.95 8.11 ‫اﻟﻔﺮق‬ 1.16 1.16 ‫اﻟﺘﺤﻘﻴﻖ‬ O.K
  • 43. ٤٣ ٤٣ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٢ ٢ : : ‫واﻻﻧﺨﻔﺎض‬ ‫اﻻرﺗﻔﺎع‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫واﻻﻧﺨﻔﺎض‬ ‫اﻻرﺗﻔﺎع‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﻤﺆﺧﺮة‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﻤﻘﺪﻣﺔ‬ ‫ارﺗﻔﺎع‬ (+) ‫اﻧﺨﻔﺎض‬ (-) ‫ﻣﻨﺴﻮب‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻣﻼﺣﻈﺎت‬ ‫ا‬ 2.19 30.00 ‫روﺑﻴﺮ‬ ‫ب‬ 2.50 0.31 29.69 ‫ﺟـ‬ 2.32 0.18 29.87 ‫د‬ 3.01 1.49 0.83 30.70 ‫دوران‬ ‫هـ‬ 2.51 0.50 31.20 ‫و‬ 1.75 2.81 0.30 30.90 ‫دوران‬ ‫ز‬ 3.81 2.06 28.84 ‫اﻟﻤﺠﻤﻮع‬ 6.95 8.11 ‫اﻟﻔﺮق‬ 1.16 1.16 ‫اﻟﺘﺤﻘﻴﻖ‬ O.K
  • 44. ٤٤ ٤٤ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٣ ٣ : : ‫اﻟﻤﻴﺰان‬ ‫ﺳﻄﺢ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻤﻴﺰان‬ ‫ﺳﻄﺢ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﻤﺆﺧﺮة‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﻤﻘﺪﻣﺔ‬ ‫ﺳﻄﺢ‬ ‫ﻣﻨﺴﻮب‬ ‫اﻟﻤﻴﺰان‬ ‫ﻣﻨﺴﻮب‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻣﻼﺣﻈﺎت‬ ‫ا‬ 2.19 26.35 24.16 ‫ب‬ 2.50 23.85 ‫ﺟـ‬ 2.32 24.03 ‫د‬ 3.01 1.49 27.87 24.86 ‫دوران‬ ‫هـ‬ 2.51 25.36 ‫و‬ 1.75 2.81 26.81 25.06 ‫دوران‬ ‫ز‬ 3.81 23.00 ‫روﺑﻴﺮ‬ ‫اﻟﻤﺠﻤﻮع‬ 6.95 8.11 ‫اﻟﻔﺮق‬ 1.16 1.16 ‫اﻟﺘﺤﻘﻴﻖ‬ O.K ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٣ ٣ : : ‫ﺑﻄﺮﻳﻘﺘﻴﻦ‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻰ‬ ‫اﻟﻨﻘﻂ‬ ‫ﻣﻨﺎﺳﻴﺐ‬ ‫ﺣﺴﺎب‬ ‫اﻟﻤﻄﻠﻮب‬ ‫ﺑﻄﺮﻳﻘﺘﻴﻦ‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻤﺜﺎل‬ ‫ﻓﻰ‬ ‫اﻟﻨﻘﻂ‬ ‫ﻣﻨﺎﺳﻴﺐ‬ ‫ﺣﺴﺎب‬ ‫اﻟﻤﻄﻠﻮب‬ ‫ﻧﻘﻄﺔ‬ ‫ﺁﺧﺮ‬ ‫ﻣﻨﺴﻮب‬ ‫آﺎن‬ ‫إذا‬ ‫ﻣﺨﺘﻠﻔﺘﻴﻦ‬ ‫ﻧﻘﻄﺔ‬ ‫ﺁﺧﺮ‬ ‫ﻣﻨﺴﻮب‬ ‫آﺎن‬ ‫إذا‬ ‫ﻣﺨﺘﻠﻔﺘﻴﻦ‬ +) +) ٢٣ ٢٣ ‫م‬ ‫م‬ .( .(
  • 45. ٤٥ ٤٥ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٣ ٣ : : ‫واﻻﻧﺨﻔﺎض‬ ‫اﻻرﺗﻔﺎع‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫واﻻﻧﺨﻔﺎض‬ ‫اﻻرﺗﻔﺎع‬ ‫ﻃﺮﻳﻘﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻨﻘﻄﺔ‬ ‫اﻟﻤﺆﺧﺮة‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﻤﻘﺪﻣﺔ‬ ‫ارﺗﻔﺎع‬ (+) ‫اﻧﺨﻔﺎض‬ (-) ‫ﻣﻨﺴﻮب‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻣﻼﺣﻈﺎت‬ ‫ا‬ 2.19 24.16 ‫روﺑﻴﺮ‬ ‫ب‬ 2.50 0.31 23.85 ‫ﺟـ‬ 2.32 0.18 24.03 ‫د‬ 3.01 1.49 0.83 24.86 ‫دوران‬ ‫هـ‬ 2.51 0.50 25.36 ‫و‬ 1.75 2.81 0.30 25.06 ‫دوران‬ ‫ز‬ 3.81 2.06 23.00 ‫اﻟﻤﺠﻤﻮع‬ 6.95 8.11 ‫اﻟﻔﺮق‬ 1.16 1.16 ‫اﻟﺘﺤﻘﻴﻖ‬ O.K
  • 46. ٤٦ ٤٦ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﺒﺎب‬ ‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﺒﺎب‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫ﻣﺤﻠﻮﻟﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻋﻠﻰ‬ ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺴﺎب‬ ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺴﺎب‬
  • 47. ٤٧ ٤٧ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ١ ١ : : ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺴﺎب‬ ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻣﻦ‬ ‫ﻣﻦ‬ ‫اﻟﺸﺒﻜﻴﺔ‬ ‫اﻟﻤﻴﺰاﻧﻴﺔ‬ ‫اﻟﺸﺒﻜﻴﺔ‬ ‫اﻟﻤﻴﺰاﻧﻴﺔ‬ - - ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻣﻄﻠﻮب‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺴﺎب‬ ‫ﻣﻄﻠﻮب‬ ‫اﻷرض‬ ‫ﻟﺘﺴﻮﻳﺔ‬ ‫اﻟﻼزﻣﺔ‬ ‫واﻟﺮدم‬ ‫اﻷرض‬ ‫ﻟﺘﺴﻮﻳﺔ‬ ‫اﻟﻼزﻣﺔ‬ ‫واﻟﺮدم‬ ‫ﻣﻨﺴﻮب‬ ‫ﻋﻠﻰ‬ ‫ﺑﺎﻟﺸﻜﻞ‬ ‫اﻟﻤﻮﺿﺤﺔ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻋﻠﻰ‬ ‫ﺑﺎﻟﺸﻜﻞ‬ ‫اﻟﻤﻮﺿﺤﺔ‬ + + ٧٫٠٠ ٧٫٠٠ ‫ﻣﺮﺑﻌﺔ‬ ‫اﻟﻮﺣﺪة‬ ‫ﺑﺄن‬ ‫ﻋﻠﻤﺎ‬ ‫ﻣﺘﺮ‬ ‫ﻣﺮﺑﻌﺔ‬ ‫اﻟﻮﺣﺪة‬ ‫ﺑﺄن‬ ‫ﻋﻠﻤﺎ‬ ‫ﻣﺘﺮ‬ ‫وأﺑﻌﺎدهﺎ‬ ‫اﻟﺸﻜﻞ‬ ‫وأﺑﻌﺎدهﺎ‬ ‫اﻟﺸﻜﻞ‬ ٣٠ ٣٠ x x ٣٠ ٣٠ ‫م‬ ‫م‬ . . ٦٫٥ ٦٫٥ ٧٫٥ ٧٫٥ ٦٫٨ ٦٫٨ ٨٫١ ٨٫١ ٨٫٣ ٨٫٣ ٧٫٣ ٧٫٣ ٧٫٠ ٧٫٠ ٧٫٢ ٧٫٢ ٧٫٥ ٧٫٥ ٦٫١ ٦٫١ ٦٫٨ ٦٫٨ ٦٫٥ ٦٫٥ ٦٫٦ ٦٫٦ ٦٫٧ ٦٫٧ ٦٫٠ ٦٫٠ ٥٫٨ ٥٫٨ ٥٫٥ ٥٫٥ ٦٫٠ ٦٫٠ ٥٫٣ ٥٫٣ ٩٫١ ٩٫١ ٨٫٥ ٨٫٥ ٨٫٥ ٨٫٥
  • 48. ٤٨ ٤٨ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١ ١ : : ٦٫٥ ٦٫٥ ٧٫٥ ٧٫٥ ٦٫٨ ٦٫٨ ٨٫١ ٨٫١ ٨٫٣ ٨٫٣ ٧٫٣ ٧٫٣ ٧٫٠ ٧٫٠ ٧٫٢ ٧٫٢ ٧٫٥ ٧٫٥ ٦٫١ ٦٫١ ٦٫٨ ٦٫٨ ٦٫٥ ٦٫٥ ٦٫٦ ٦٫٦ ٦٫٧ ٦٫٧ ٦٫٠ ٦٫٠ ٥٫٨ ٥٫٨ ٥٫٥ ٥٫٥ ٦٫٠ ٦٫٠ ٥٫٣ ٥٫٣ ٩٫١ ٩٫١ ٨٫٥ ٨٫٥ ٨٫٥ ٨٫٥ - - ‫رﺳﻢ‬ ‫ﻳﺘﻢ‬ ‫رﺳﻢ‬ ‫ﻳﺘﻢ‬ ‫آﻨﺘﻮر‬ ‫آﻨﺘﻮر‬ + + ٧٫٠٠ ٧٫٠٠ ‫م‬ ‫م‬ - - ‫اﻷﻋﻠﻰ‬ ‫اﻟﻘﻴﻤﺔ‬ ‫ذات‬ ‫اﻷرآﺎن‬ ‫اﻷﻋﻠﻰ‬ ‫اﻟﻘﻴﻤﺔ‬ ‫ذات‬ ‫اﻷرآﺎن‬ ‫ﻣﻨﺴﻮب‬ ‫ﻣﻦ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻣﻦ‬ + + ٧٫٠٠ ٧٫٠٠ ‫م‬ ‫م‬ ‫اﻷﻗﻞ‬ ‫واﻷرآﺎن‬ ‫ﺣﻔﺮ‬ ‫ﻣﻨﺎﻃﻖ‬ ‫اﻷﻗﻞ‬ ‫واﻷرآﺎن‬ ‫ﺣﻔﺮ‬ ‫ﻣﻨﺎﻃﻖ‬ ‫ردم‬ ‫ﻣﻨﺎﻃﻖ‬ ‫ردم‬ ‫ﻣﻨﺎﻃﻖ‬ . . ‫ﺣﻔﺮ‬ ‫ﺣﻔﺮ‬ ‫ردم‬ ‫ردم‬
  • 49. ٤٩ ٤٩ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١ ١ : : ٠٫٥ ٠٫٥ ٠٫٥ ٠٫٥ ٠٫٢ ٠٫٢ ١٫١ ١٫١ ١٫٣ ١٫٣ ٠٫٣ ٠٫٣ ٠٫٠ ٠٫٠ ٠٫٢ ٠٫٢ ٠٫٥ ٠٫٥ ٠٫٩ ٠٫٩ ٠٫٢ ٠٫٢ ٠٫٥ ٠٫٥ ٠٫٤ ٠٫٤ ٠٫٣ ٠٫٣ ١٫٠ ١٫٠ ١٫٢ ١٫٢ ١٫٥ ١٫٥ ١٫٠ ١٫٠ ١٫٧ ١٫٧ ٢٫١ ٢٫١ ١٫٥ ١٫٥ ١٫٥ ١٫٥ - - ‫ﻃﺮح‬ ‫ﻳﺘﻢ‬ ‫ﻃﺮح‬ ‫ﻳﺘﻢ‬ + + ٧٫٠٠ ٧٫٠٠ ‫ﻣﻦ‬ ‫م‬ ‫ﻣﻦ‬ ‫م‬ ‫وﻧﻀﻊ‬ ‫اﻷرآﺎن‬ ‫ﺟﻤﻴﻊ‬ ‫ﻣﻨﺎﺳﻴﺐ‬ ‫وﻧﻀﻊ‬ ‫اﻷرآﺎن‬ ‫ﺟﻤﻴﻊ‬ ‫ﻣﻨﺎﺳﻴﺐ‬ ‫أو‬ ‫ﺟﺪﻳﺪ‬ ‫رﺳﻢ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻔﺮق‬ ‫أو‬ ‫ﺟﺪﻳﺪ‬ ‫رﺳﻢ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻔﺮق‬ ‫اﻟﺮﺳﻢ‬ ‫ﻧﻔﺲ‬ ‫ﻋﻠﻰ‬ ‫ﺁﺧﺮ‬ ‫ﺑﻠﻮن‬ ‫اﻟﺮﺳﻢ‬ ‫ﻧﻔﺲ‬ ‫ﻋﻠﻰ‬ ‫ﺁﺧﺮ‬ ‫ﺑﻠﻮن‬ . . ‫ﺣﻔﺮ‬ ‫ﺣﻔﺮ‬ ‫ردم‬ ‫ردم‬
  • 50. ٥٠ ٥٠ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١ ١ : : - - ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺠﻢ‬ ‫ﺣﺴﺎب‬ ‫ﻳﺘﻢ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺠﻢ‬ ‫ﺣﺴﺎب‬ ‫ﻳﺘﻢ‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻟﺮدم‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻟﺮدم‬ ) ) ‫ﻋﺪد‬ ‫ﻋﺪد‬ ٦ ٦ ‫ﻣﺮﺑﻌﺎت‬ ‫ﻣﺮﺑﻌﺎت‬ :( :( ٠٫٥ ٠٫٥ ٠٫٥ ٠٫٥ ٠٫٢ ٠٫٢ ١٫١ ١٫١ ١٫٣ ١٫٣ ٠٫٣ ٠٫٣ ٠٫٠ ٠٫٠ ٠٫٢ ٠٫٢ ٠٫٥ ٠٫٥ ٠٫٩ ٠٫٩ ٠٫٢ ٠٫٢ ٠٫٥ ٠٫٥ ٠٫٤ ٠٫٤ ٠٫٣ ٠٫٣ ١٫٠ ١٫٠ ١٫٢ ١٫٢ ١٫٥ ١٫٥ ١٫٠ ١٫٠ ١٫٧ ١٫٧ ٢٫١ ٢٫١ ١٫٥ ١٫٥ ١٫٥ ١٫٥ ‫ﺣﻔﺮ‬ ‫ﺣﻔﺮ‬ ‫ردم‬ ‫ردم‬ ١‫ع‬ ٢‫ع‬ ٣‫ع‬ ٤‫ع‬ 1 1.2 0.3 1.7 1.5 0.4 0.9 1 0.5 0.2 0.2 0.5 4.1 4.6 0 0.7 ‫اﻟﺤﺠﻢ‬ ‫اﻟﺤﺠﻢ‬ )) = )) = ٣٠ ٣٠ x x ٣٠ ٣٠ ( ( ٤ ٤ ( ( x x ) ) ١ ١ x x ٤٫١ ٤٫١ + + ٢ ٢ x x ٤٫٦ ٤٫٦ + + ٤ ٤ x x ٠٫٧ ٠٫٧ = ( = ( ٣٦٢٢٫٥ ٣٦٢٢٫٥ ‫م‬ ‫م‬ ٣ ٣
  • 51. ٥١ ٥١ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١ ١ : : - - ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺠﻢ‬ ‫ﺣﺴﺎب‬ ‫ﻳﺘﻢ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺠﻢ‬ ‫ﺣﺴﺎب‬ ‫ﻳﺘﻢ‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫اﻟﺮدم‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫اﻟﺮدم‬ ) ) ‫ﻋﺪد‬ ‫ﻋﺪد‬ ٣ ٣ ‫أﺟﺰاء‬ ‫أﺟﺰاء‬ :( :( ٠٫٥ ٠٫٥ ٠٫٥ ٠٫٥ ٠٫٢ ٠٫٢ ١٫١ ١٫١ ١٫٣ ١٫٣ ٠٫٣ ٠٫٣ ٠٫٠ ٠٫٠ ٠٫٢ ٠٫٢ ٠٫٥ ٠٫٥ ٠٫٩ ٠٫٩ ٠٫٢ ٠٫٢ ٠٫٥ ٠٫٥ ٠٫٤ ٠٫٤ ٠٫٣ ٠٫٣ ١٫٠ ١٫٠ ١٫٢ ١٫٢ ١٫٥ ١٫٥ ١٫٠ ١٫٠ ١٫٧ ١٫٧ ٢٫١ ٢٫١ ١٫٥ ١٫٥ ١٫٥ ١٫٥ ‫ﺣﻔﺮ‬ ‫ﺣﻔﺮ‬ ‫ردم‬ ‫ردم‬ I I II II III III ‫ﺣﺠﻢ‬ ‫ﺣﺠﻢ‬ I I ) = ) = ١٥ ١٥ x x ٣٠ ٣٠ ( ( x x )) )) ٠٫٥ ٠٫٥ + + ٠٫٢ ٠٫٢ + + ٠٫٠ ٠٫٠ + + ٠٫٠ ٠٫٠ ( ( ٤ ٤ =( =( ٧٨٫٧٥ ٧٨٫٧٥ ‫م‬ ‫م‬ ٣ ٣ ‫ﺣﺠﻢ‬ ‫ﺣﺠﻢ‬ II II ))= ))= ١٥ ١٥ + + ٣٠ ٣٠ ( ( ٢ ٢ ( ( x x ٣٠ ٣٠ ( ( x x )) )) ٠٫٢ ٠٫٢ + + ٠٫٢ ٠٫٢ + + ٠٫٠ ٠٫٠ + + ٠٫٠ ٠٫٠ ( ( ٤ ٤ =( =( ٦٧٫٥ ٦٧٫٥ ‫م‬ ‫م‬ ٣ ٣ ‫ﺣﺠﻢ‬ ‫ﺣﺠﻢ‬ III III ))= ))= ٢٢٫٥ ٢٢٫٥ + + ٣٠ ٣٠ ( ( ٢ ٢ ( ( x x ٣٠ ٣٠ ( ( x x )) )) ٠٫٩ ٠٫٩ + + ٠٫٢ ٠٫٢ + + ٠٫٠ ٠٫٠ + + ٠٫٠ ٠٫٠ ( ( ٤ ٤ =( =( ٢١٦٫٥٦ ٢١٦٫٥٦ ‫م‬ ‫م‬ ٣ ٣ ‫اﻟﺮدم‬ ‫ﺣﺠﻢ‬ ‫اﺟﻤﺎﻟﻰ‬ ‫اﻟﺮدم‬ ‫ﺣﺠﻢ‬ ‫اﺟﻤﺎﻟﻰ‬ = = ٣٦٢٢٫٥ ٣٦٢٢٫٥ + + ٧٨٫٧٥ ٧٨٫٧٥ + + ٦٧٫٥ ٦٧٫٥ + + ٢١٦٫٥٦ ٢١٦٫٥٦ = = ٣٩٨٥٫٣١ ٣٩٨٥٫٣١ ‫م‬ ‫م‬ ٣ ٣
  • 52. ٥٢ ٥٢ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١ ١ : : - - ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺠﻢ‬ ‫ﺣﺴﺎب‬ ‫ﻳﺘﻢ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺠﻢ‬ ‫ﺣﺴﺎب‬ ‫ﻳﺘﻢ‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻟﺤﻔﺮ‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻟﺤﻔﺮ‬ ) ) ‫ﻋﺪد‬ ‫ﻋﺪد‬ ٤ ٤ ‫ﻣﺮﺑﻌﺎت‬ ‫ﻣﺮﺑﻌﺎت‬ :( :( ٠٫٥ ٠٫٥ ٠٫٥ ٠٫٥ ٠٫٢ ٠٫٢ ١٫١ ١٫١ ١٫٣ ١٫٣ ٠٫٣ ٠٫٣ ٠٫٠ ٠٫٠ ٠٫٢ ٠٫٢ ٠٫٥ ٠٫٥ ٠٫٩ ٠٫٩ ٠٫٢ ٠٫٢ ٠٫٥ ٠٫٥ ٠٫٤ ٠٫٤ ٠٫٣ ٠٫٣ ١٫٠ ١٫٠ ١٫٢ ١٫٢ ١٫٥ ١٫٥ ١٫٠ ١٫٠ ١٫٧ ١٫٧ ٢٫١ ٢٫١ ١٫٥ ١٫٥ ١٫٥ ١٫٥ ‫ﺣﻔﺮ‬ ‫ﺣﻔﺮ‬ ‫ردم‬ ‫ردم‬ ١‫ع‬ ٢‫ع‬ ٣‫ع‬ ٤‫ع‬ 0.5 0.2 1.5 0 2.1 0.3 1.3 1.5 0.5 1.1 5.4 3.6 0 0 ‫اﻟﺤﺠﻢ‬ ‫اﻟﺤﺠﻢ‬ )) = )) = ٣٠ ٣٠ x x ٣٠ ٣٠ ( ( ٤ ٤ ( ( x x ) ) ١ ١ x x ٥٫٤ ٥٫٤ + + ٢ ٢ x x ٣٫٦ ٣٫٦ = ( = ( ٢٨٣٥ ٢٨٣٥ ‫م‬ ‫م‬ ٣ ٣ I I II II III III
  • 53. ٥٣ ٥٣ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ” ” ‫ﺗﺎﺑﻊ‬ ‫ﺗﺎﺑﻊ‬ “ “ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫رﻗﻢ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١ ١ : : - - ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺠﻢ‬ ‫ﺣﺴﺎب‬ ‫ﻳﺘﻢ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﺣﺠﻢ‬ ‫ﺣﺴﺎب‬ ‫ﻳﺘﻢ‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫اﻟﺤﻔﺮ‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻟﻐﻴﺮ‬ ‫اﻟﺤﻔﺮ‬ ) ) ‫ﻋﺪد‬ ‫ﻋﺪد‬ ٣ ٣ ‫أﺟﺰاء‬ ‫أﺟﺰاء‬ :( :( ٠٫٥ ٠٫٥ ٠٫٥ ٠٫٥ ٠٫٢ ٠٫٢ ١٫١ ١٫١ ١٫٣ ١٫٣ ٠٫٣ ٠٫٣ ٠٫٠ ٠٫٠ ٠٫٢ ٠٫٢ ٠٫٥ ٠٫٥ ٠٫٩ ٠٫٩ ٠٫٢ ٠٫٢ ٠٫٥ ٠٫٥ ٠٫٤ ٠٫٤ ٠٫٣ ٠٫٣ ١٫٠ ١٫٠ ١٫٢ ١٫٢ ١٫٥ ١٫٥ ١٫٠ ١٫٠ ١٫٧ ١٫٧ ٢٫١ ٢٫١ ١٫٥ ١٫٥ ١٫٥ ١٫٥ ‫ﺣﻔﺮ‬ ‫ﺣﻔﺮ‬ ‫ردم‬ ‫ردم‬ I I II II III III ‫ﺣﺠﻢ‬ ‫ﺣﺠﻢ‬ IV IV ) = ) = ١٥ ١٥ x x ٣٠ ٣٠ ( ( x x )) )) ٠٫٥ ٠٫٥ + + ٠٫٢ ٠٫٢ + + ٠٫٠ ٠٫٠ + + ٠٫٠ ٠٫٠ ( ( ٤ ٤ =( =( ٧٨٫٧٥ ٧٨٫٧٥ ‫م‬ ‫م‬ ٣ ٣ ‫ﺣﺠﻢ‬ ‫ﺣﺠﻢ‬ V V )) = )) = ١٥ ١٥ x x ٣٠ ٣٠ ( ( ٢ ٢ ( ( x x )) )) ٠٫٢ ٠٫٢ + + ٠٫٠ ٠٫٠ + + ٠٫٠ ٠٫٠ ( ( ٣ ٣ =( =( ١٥٫٠ ١٥٫٠ ‫م‬ ‫م‬ ٣ ٣ ‫ﺣﺠﻢ‬ ‫ﺣﺠﻢ‬ VI VI )) = )) = ٧٫٥ ٧٫٥ x x ٣٠ ٣٠ ( ( ٢ ٢ ( ( x x )) )) ٠٫٣ ٠٫٣ + + ٠٫٠ ٠٫٠ + + ٠٫٠ ٠٫٠ ( ( ٣ ٣ =( =( ١١٫٢٥ ١١٫٢٥ ‫م‬ ‫م‬ ٣ ٣ ‫اﻟﺮدم‬ ‫ﺣﺠﻢ‬ ‫اﺟﻤﺎﻟﻰ‬ ‫اﻟﺮدم‬ ‫ﺣﺠﻢ‬ ‫اﺟﻤﺎﻟﻰ‬ = = ٢٨٣٥ ٢٨٣٥ + + ٧٨٫٧٥ ٧٨٫٧٥ + + ١٥٫٠ ١٥٫٠ + + ١١٫٢٥ ١١٫٢٥ = = ٢٩٤٠٫٠ ٢٩٤٠٫٠ ‫م‬ ‫م‬ ٣ ٣ IV IV V V VI VI
  • 54. ٥٤ ٥٤ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٢ ٢ : : ‫أﺑﻌﺎدﻩ‬ ‫ﺳﺒﺎﺣﺔ‬ ‫ﺣﻮض‬ ‫ﻹﻧﺸﺎء‬ ‫أﺑﻌﺎدﻩ‬ ‫ﺳﺒﺎﺣﺔ‬ ‫ﺣﻮض‬ ‫ﻹﻧﺸﺎء‬ ٢٠ ٢٠ x x ٥٠ ٥٠ ‫ﻣﻴﺰاﻧﻴﺔ‬ ‫أﺟﺮﻳﺖ‬ ‫م‬ ‫ﻣﻴﺰاﻧﻴﺔ‬ ‫أﺟﺮﻳﺖ‬ ‫م‬ ‫ﻳﻠﻰ‬ ‫آﻤﺎ‬ ‫ﻓﻜﺎﻧﺖ‬ ‫اﻟﻄﻮﻟﻰ‬ ‫اﻟﻤﺤﻮر‬ ‫ﻋﻠﻰ‬ ‫ﻃﻮﻟﻴﺔ‬ ‫ﻳﻠﻰ‬ ‫آﻤﺎ‬ ‫ﻓﻜﺎﻧﺖ‬ ‫اﻟﻄﻮﻟﻰ‬ ‫اﻟﻤﺤﻮر‬ ‫ﻋﻠﻰ‬ ‫ﻃﻮﻟﻴﺔ‬ : : ‫اﻟﻤﺴﺎﻓﺔ‬ 0 10 20 30 40 50 ‫اﻷرض‬ ‫ﻣﻨﺴﻮب‬ ‫اﻟﻄﺒﻴﻌﻴﺔ‬ 39.30 40.00 41.50 39.70 39.50 37.70 ‫اﻟﺤﻮض‬ ‫ﺑﺪاﻳﺔ‬ ‫ﻋﻨﺪ‬ ‫اﻹﻧﺸﺎء‬ ‫ﺧﻂ‬ ‫ﻣﻨﺴﻮب‬ ‫آﺎن‬ ‫ﻓﺈذا‬ ‫اﻟﺤﻮض‬ ‫ﺑﺪاﻳﺔ‬ ‫ﻋﻨﺪ‬ ‫اﻹﻧﺸﺎء‬ ‫ﺧﻂ‬ ‫ﻣﻨﺴﻮب‬ ‫آﺎن‬ ‫ﻓﺈذا‬ ٣٨٫٥ ٣٨٫٥ ‫م‬ ‫م‬ ‫اﻟﺤﻮض‬ ‫ﻗﺎع‬ ‫واﻧﺤﺪار‬ ‫اﻟﺤﻮض‬ ‫ﻗﺎع‬ ‫واﻧﺤﺪار‬ ٥ ٥ % % ‫اﻟﻰ‬ ‫ﺻﻔﺮ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫ﻣﻦ‬ ‫ﻷﺳﻔﻞ‬ ‫اﻟﻰ‬ ‫ﺻﻔﺮ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫ﻣﻦ‬ ‫ﻷﺳﻔﻞ‬ ٢٠ ٢٠ ‫م‬ ‫م‬ ‫ﺛﻢ‬ ‫ﺛﻢ‬ ٤ ٤ % % ‫ﻣﻦ‬ ‫ﻷﺳﻔﻞ‬ ‫ﻣﻦ‬ ‫ﻷﺳﻔﻞ‬ ٢٠ ٢٠ ‫اﻟﻰ‬ ‫اﻟﻰ‬ ٣٠ ٣٠ ‫ﻣﻦ‬ ‫أﻓﻘﻰ‬ ‫ﺛﻢ‬ ‫م‬ ‫ﻣﻦ‬ ‫أﻓﻘﻰ‬ ‫ﺛﻢ‬ ‫م‬ ٣٠ ٣٠ ‫اﻟﻰ‬ ‫اﻟﻰ‬ ٥٠ ٥٠ ‫م‬ ‫م‬ . . ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫وﺣﺴﺎب‬ ‫ﻃﻮﻟﻰ‬ ‫ﻗﻄﺎع‬ ‫رﺳﻢ‬ ‫واﻟﻤﻄﻠﻮب‬ ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫وﺣﺴﺎب‬ ‫ﻃﻮﻟﻰ‬ ‫ﻗﻄﺎع‬ ‫رﺳﻢ‬ ‫واﻟﻤﻄﻠﻮب‬ . .
  • 55. ٥٥ ٥٥ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ٣٧ ٣٨ ٣٩ ٤٠ ٤١ ٣٦ ٣٥ ‫ء‬‫ﺎ‬‫ﺸ‬‫ﻧ‬‫ﻹ‬‫ا‬ ‫ﻂ‬‫ﺧ‬ ‫ﺔ‬‫ﻴ‬‫ﻌ‬‫ﻴ‬‫ﺒ‬‫ﻄ‬‫ﻟ‬‫ا‬ ‫ض‬‫ر‬‫ﻷ‬‫ا‬ ‫اﻟﻤﺴﺎﻓﺔ‬ 0 10 20 30 40 50 ‫اﻟﻄﺒﻴﻌﻴﺔ‬ ‫اﻷرض‬ ‫ﻣﻨﺴﻮب‬ 39.30 40.00 41.50 39.70 39.50 37.70 ‫اﻹﻧﺸﺎء‬ ‫ﺧﻂ‬ ‫ﻣﻨﺴﻮب‬ 38.50 38.00 37.50 37.10 37.10 37.10 ‫اﻟﺤﻔﺮ‬ ‫ارﺗﻔﺎع‬ 0.80 2.00 4.00 2.60 2.40 0.60 ‫اﻟﺤﻔﺮ‬ ‫ﻣﺴﺎﺣﺔ‬ 16.00 40.00 80.00 52.00 48.00 600.00 ‫اﻟﺤﻔﺮ‬ ‫ﺣﺠﻢ‬ 1120 2400 2640 2000 12960 ‫اﻟﻜﻠﻰ‬ ‫اﻟﺤﺠﻢ‬ 21120 : :٢ ٢ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬
  • 56. ٥٦ ٥٦ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٣ ٣ : : ‫آﻞ‬ ‫ﻃﻮﻟﻴﺔ‬ ‫ﻣﻴﺰاﻧﻴﺔ‬ ‫أﺟﺮﻳﺖ‬ ‫ﻃﺮﻳﻖ‬ ‫إﻧﺸﺎء‬ ‫ﺑﻬﺪف‬ ‫آﻞ‬ ‫ﻃﻮﻟﻴﺔ‬ ‫ﻣﻴﺰاﻧﻴﺔ‬ ‫أﺟﺮﻳﺖ‬ ‫ﻃﺮﻳﻖ‬ ‫إﻧﺸﺎء‬ ‫ﺑﻬﺪف‬ ١٠٠ ١٠٠ ‫ﻋﻠﻰ‬ ‫م‬ ‫ﻋﻠﻰ‬ ‫م‬ ‫ﻳﻠﻰ‬ ‫آﻤﺎ‬ ‫ﻓﻜﺎﻧﺖ‬ ‫اﻟﻄﻮﻟﻰ‬ ‫اﻟﻤﺤﻮر‬ ‫ﻳﻠﻰ‬ ‫آﻤﺎ‬ ‫ﻓﻜﺎﻧﺖ‬ ‫اﻟﻄﻮﻟﻰ‬ ‫اﻟﻤﺤﻮر‬ : : ‫اﻟﻤﺴﺎﻓﺔ‬ 0 100 200 300 400 500 ‫اﻷرض‬ ‫ﻣﻨﺴﻮب‬ ‫اﻟﻄﺒﻴﻌﻴﺔ‬ 26.00 27.50 25.00 23.00 23.00 24.00 ‫واﺣﺪ‬ ‫ﻣﺘﺮ‬ ‫ﻳﺴﺎوى‬ ‫اﻟﻄﺮﻳﻖ‬ ‫ﺑﺪاﻳﺔ‬ ‫ﻋﻨﺪ‬ ‫اﻟﺤﻔﺮ‬ ‫ارﺗﻔﺎع‬ ‫آﺎن‬ ‫ﻓﺈذا‬ ‫واﺣﺪ‬ ‫ﻣﺘﺮ‬ ‫ﻳﺴﺎوى‬ ‫اﻟﻄﺮﻳﻖ‬ ‫ﺑﺪاﻳﺔ‬ ‫ﻋﻨﺪ‬ ‫اﻟﺤﻔﺮ‬ ‫ارﺗﻔﺎع‬ ‫آﺎن‬ ‫ﻓﺈذا‬ ، ، ‫واﻟﻄﺮﻳﻖ‬ ‫واﻟﻄﺮﻳﻖ‬ ‫ﺑﻨﺴﺒﺔ‬ ‫أﺳﻔﻞ‬ ‫اﻟﻰ‬ ‫ﻳﻨﺤﺪر‬ ‫ﺑﻨﺴﺒﺔ‬ ‫أﺳﻔﻞ‬ ‫اﻟﻰ‬ ‫ﻳﻨﺤﺪر‬ ٢٠٠:١ ٢٠٠:١ ‫ﻣﺴﺎﻓﺔ‬ ‫اﻟﻰ‬ ‫ﺻﻔﺮ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫ﻣﻦ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫اﻟﻰ‬ ‫ﺻﻔﺮ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫ﻣﻦ‬ ٢٠٠ ٢٠٠ ‫م‬ ‫م‬ ، ، ‫ﻣﺴﺎﻓﺔ‬ ‫ﻣﻦ‬ ‫أﻓﻘﻰ‬ ‫ﺛﻢ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫ﻣﻦ‬ ‫أﻓﻘﻰ‬ ‫ﺛﻢ‬ ٢٠٠ ٢٠٠ ‫اﻟﻰ‬ ‫اﻟﻰ‬ ٣٠٠ ٣٠٠ ‫م‬ ‫م‬ ، ، ‫ﺑﻨﺴﺒﺔ‬ ‫أﻋﻠﻰ‬ ‫اﻟﻰ‬ ‫ﺛﻢ‬ ‫ﺑﻨﺴﺒﺔ‬ ‫أﻋﻠﻰ‬ ‫اﻟﻰ‬ ‫ﺛﻢ‬ ١٠٠:١ ١٠٠:١ ‫اﻟﻄﺮﻳﻖ‬ ‫ﻧﻬﺎﻳﺔ‬ ‫ﺣﺘﻰ‬ ‫اﻟﻄﺮﻳﻖ‬ ‫ﻧﻬﺎﻳﺔ‬ ‫ﺣﺘﻰ‬ . . ‫اﻟﻄﺮﻳﻖ‬ ‫وﻋﺮض‬ ‫اﻟﻄﺮﻳﻖ‬ ‫وﻋﺮض‬ ١٥ ١٥ ‫وﻣﻴﻮﻟﻪ‬ ‫م‬ ‫وﻣﻴﻮﻟﻪ‬ ‫م‬ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ٢:١ ٢:١ . . ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫وﺣﺴﺎب‬ ‫ﻟﻠﻄﺮﻳﻖ‬ ‫ﻃﻮﻟﻰ‬ ‫ﻗﻄﺎع‬ ‫رﺳﻢ‬ ‫واﻟﻤﻄﻠﻮب‬ ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫وﺣﺴﺎب‬ ‫ﻟﻠﻄﺮﻳﻖ‬ ‫ﻃﻮﻟﻰ‬ ‫ﻗﻄﺎع‬ ‫رﺳﻢ‬ ‫واﻟﻤﻄﻠﻮب‬ . .
  • 57. ٥٧ ٥٧ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ٢٤ ٢٥ ٢٦ ٢٧ ٢٨ ٢٣ ٢٢ ‫ء‬‫ﺎ‬‫ﺸ‬‫ﻧ‬‫ﻹ‬‫ا‬ ‫ﻂ‬‫ﺧ‬ ‫ﺔ‬‫ﻴ‬‫ﻌ‬‫ﻴ‬‫ﺒ‬‫ﻄ‬‫ﻟ‬‫ا‬ ‫ض‬ ‫ر‬‫ﻷ‬‫ا‬ : :٣ ٣ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ٢ ١ ١٥ ‫م‬ ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻓﻰ‬ ‫اﻟﻘﻄﺎع‬ ‫ﻣﺴﺎﺣﺔ‬ ‫ﻣﻌﺎدﻟﺔ‬ = ‫ع‬ x ) ١٥ + ١٥ + ٤ ‫ع‬ ( ٢ = ‫ع‬ x ) ١٥ + ٢ ‫ع‬ ( ‫ع‬ ١٥ + ٤ ‫ع‬ ‫اﻟﺤﻔﺮ‬ ‫اﻟﺮدم‬ ‫اﻟﻔﺎﺻﻞ‬ ‫اﻟﺤﺪ‬
  • 58. ٥٨ ٥٨ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﻤﺴﺎﻓﺔ‬ 0.0 100.0 200.0 300.0 400.0 500.0 ‫اﻷرض‬ ‫ﻣﻨﺴﻮب‬ ‫اﻟﻄﺒﻴﻌﻴﺔ‬ 26.0 27.5 25.0 23.0 23.0 24.0 ‫ﺧﻂ‬ ‫ﻣﻨﺴﻮب‬ ‫اﻹﻧﺸﺎء‬ 25.0 24.5 24.0 24.0 25.0 26.0 ‫اﻟﺤﻔﺮ‬ ‫ارﺗﻔﺎع‬ 1 3 1 ‫اﻟﺮدم‬ ‫ارﺗﻔﺎع‬ 1 2 2 ‫اﻟﺤﻔﺮ‬ ‫ﻣﺴﺎﺣﺔ‬ 17 63 17 0 ‫اﻟﺮدم‬ ‫ﻣﺴﺎﺣﺔ‬ 0 17 38 38 ‫اﻟﺤﻔﺮ‬ ‫ﺣﺠﻢ‬ 4000 4000 425 ‫اﻟﺮدم‬ ‫ﺣﺠﻢ‬ 425 2750 3800 ‫اﻟﺤﻔﺮ‬ ‫إﺟﻤﺎﻟﻰ‬ ‫اﻟﺮدم‬ ‫ﺣﺠﻢ‬ 6975 8425 2 5 0 .0 : :٣ ٣ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫اﻟﻔﺎﺻﻞ‬ ‫اﻟﺤﺪ‬ ‫اﻟﻔﺎﺻﻞ‬ ‫اﻟﺤﺪ‬
  • 59. ٥٩ ٥٩ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٤ ٤ : : ‫ﻣﻘﺘﺮح‬ ‫ﻃﺮﻳﻖ‬ ‫ﻣﺤﻮر‬ ‫ﻋﻠﻰ‬ ‫واﻟﻤﻨﺎﺳﻴﺐ‬ ‫اﻟﻤﺴﺎﻓﺎت‬ ‫أﺧﺬت‬ ‫ﻣﻘﺘﺮح‬ ‫ﻃﺮﻳﻖ‬ ‫ﻣﺤﻮر‬ ‫ﻋﻠﻰ‬ ‫واﻟﻤﻨﺎﺳﻴﺐ‬ ‫اﻟﻤﺴﺎﻓﺎت‬ ‫أﺧﺬت‬ ‫ﻳﻠﻰ‬ ‫آﻤﺎ‬ ‫ﻓﻜﺎﻧﺖ‬ ‫ﻳﻠﻰ‬ ‫آﻤﺎ‬ ‫ﻓﻜﺎﻧﺖ‬ : : ‫اﻟﻤﺴﺎﻓﺔ‬ 0 100 200 300 400 500 ‫اﻷرض‬ ‫ﻣﻨﺴﻮب‬ ‫اﻟﻄﺒﻴﻌﻴﺔ‬ 23.50 24.50 25.70 23.90 21.60 21.50 ‫ﺻﻔﺮ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫ﻋﻨﺪ‬ ‫اﻹﻧﺸﺎء‬ ‫ﺧﻂ‬ ‫ﻣﻨﺴﻮب‬ ‫آﺎن‬ ‫ﻓﺈذا‬ ‫ﺻﻔﺮ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫ﻋﻨﺪ‬ ‫اﻹﻧﺸﺎء‬ ‫ﺧﻂ‬ ‫ﻣﻨﺴﻮب‬ ‫آﺎن‬ ‫ﻓﺈذا‬ ٢٣٫٣٠ ٢٣٫٣٠ ‫م‬ ‫م‬ ، ، ‫وﻋﺮض‬ ‫وﻋﺮض‬ ‫اﻟﻄﺮﻳﻖ‬ ‫اﻟﻄﺮﻳﻖ‬ ١٠ ١٠ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫وﻣﻴﻮﻟﻪ‬ ‫م‬ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫وﻣﻴﻮﻟﻪ‬ ‫م‬ ١:١ ١:١ ‫أﻋﻠﻰ‬ ‫اﻟﻰ‬ ‫ﻳﻤﻴﻞ‬ ‫واﻟﻄﺮﻳﻖ‬ ‫أﻋﻠﻰ‬ ‫اﻟﻰ‬ ‫ﻳﻤﻴﻞ‬ ‫واﻟﻄﺮﻳﻖ‬ ‫ﺑﻨﺴﺒﺔ‬ ‫ﺑﻨﺴﺒﺔ‬ ٥٠٠:١ ٥٠٠:١ ‫ﻣﺴﺎﻓﺔ‬ ‫اﻟﻰ‬ ‫ﺻﻔﺮ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫ﻣﻦ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫اﻟﻰ‬ ‫ﺻﻔﺮ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫ﻣﻦ‬ ٣٠٠ ٣٠٠ ‫م‬ ‫م‬ ، ، ‫اﻟﻰ‬ ‫ﻳﻤﻴﻞ‬ ‫ﺛﻢ‬ ‫اﻟﻰ‬ ‫ﻳﻤﻴﻞ‬ ‫ﺛﻢ‬ ‫ﺑﻨﺴﺒﺔ‬ ‫أﺳﻔﻞ‬ ‫ﺑﻨﺴﺒﺔ‬ ‫أﺳﻔﻞ‬ ٤٠٠:١ ٤٠٠:١ ‫اﻟﻄﺮﻳﻖ‬ ‫ﻧﻬﺎﻳﺔ‬ ‫ﺣﺘﻰ‬ ‫اﻟﻄﺮﻳﻖ‬ ‫ﻧﻬﺎﻳﺔ‬ ‫ﺣﺘﻰ‬ . . ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫وﺣﺴﺎب‬ ‫ﻟﻠﻄﺮﻳﻖ‬ ‫ﻃﻮﻟﻰ‬ ‫ﻗﻄﺎع‬ ‫رﺳﻢ‬ ‫واﻟﻤﻄﻠﻮب‬ ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫وﺣﺴﺎب‬ ‫ﻟﻠﻄﺮﻳﻖ‬ ‫ﻃﻮﻟﻰ‬ ‫ﻗﻄﺎع‬ ‫رﺳﻢ‬ ‫واﻟﻤﻄﻠﻮب‬ . .
  • 60. ٦٠ ٦٠ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ٢٤ ٢٥ ٢٦ ٢٧ ٢١ ٢٣ ٢٢ ‫ء‬‫ﺸﺎ‬‫ﻹﻧ‬‫ا‬ ‫ﻂ‬‫ﺧ‬ ‫ﺔ‬‫ﻴ‬‫ﻌ‬‫ﻴ‬‫ﺒ‬‫ﻄ‬‫ﻟ‬‫ا‬ ‫ض‬‫ر‬‫ﻷ‬‫ا‬ : :٤ ٤ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ١ ١ ١٠ ‫م‬ ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫ﻓﻰ‬ ‫اﻟﻘﻄﺎع‬ ‫ﻣﺴﺎﺣﺔ‬ ‫ﻣﻌﺎدﻟﺔ‬ = ‫ع‬ x ) ١٠ + ١٠ + ٢ ‫ع‬ ( ٢ = ‫ع‬ x ) ١٠ + ‫ع‬ ( ‫ع‬ ١٠ + ٢ ‫ع‬ ‫اﻟﺤﻔﺮ‬ ‫اﻟﺮدم‬ ‫اﻟﻔﺎﺻﻞ‬ ‫اﻟﺤﺪ‬
  • 61. ٦١ ٦١ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﻤﺴﺎﻓﺔ‬ 0.0 100.0 200.0 300.0 400.0 500.0 ‫اﻷرض‬ ‫ﻣﻨﺴﻮب‬ ‫اﻟﻄﺒﻴﻌﻴﺔ‬ 23.50 24.50 25.70 23.90 21.60 21.50 ‫ﺧﻂ‬ ‫ﻣﻨﺴﻮب‬ ‫اﻹﻧﺸﺎء‬ 23.30 23.50 23.70 23.90 23.65 23.40 ‫اﻟﺤﻔﺮ‬ ‫ارﺗﻔﺎع‬ 0.20 1.00 2.00 0.00 ‫اﻟﺮدم‬ ‫ارﺗﻔﺎع‬ 0.00 2.05 1.90 ‫اﻟﺤﻔﺮ‬ ‫ﻣﺴﺎﺣﺔ‬ 2.04 11.00 24.00 0.00 ‫اﻟﺮدم‬ ‫ﻣﺴﺎﺣﺔ‬ 0.00 24.70 22.61 ‫اﻟﺤﻔﺮ‬ ‫ﺣﺠﻢ‬ 652.0 1750.0 1200.0 ‫اﻟﺮدم‬ ‫ﺣﺠﻢ‬ 1235.13 2365.63 ‫اﻟﺤﻔﺮ‬ ‫إﺟﻤﺎﻟﻰ‬ ‫اﻟﺮدم‬ ‫ﺣﺠﻢ‬ 3600.75 3602.00 : :٤ ٤ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﺪ‬‫ﺤ‬‫ﻟ‬‫ا‬ ‫ﺪ‬‫ﺤ‬‫ﻟ‬‫ا‬ ‫ﻞ‬‫ﺻ‬ ‫ﺎ‬‫ﻔ‬‫ﻟ‬‫ا‬ ‫ﻞ‬‫ﺻ‬ ‫ﺎ‬‫ﻔ‬‫ﻟ‬‫ا‬
  • 62. ٦٢ ٦٢ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﻜﻨﺘﻮر‬ ‫ﺧﻂ‬ ‫رﻗﻢ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ 33 300 32 500 31 600 30 750 29 800 28 1000 27 1200 26 1720 ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٥ ٥ : : ‫ﺧﻄﻮط‬ ‫داﺧﻞ‬ ‫اﻟﻤﺤﺼﻮرة‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫ﻳﻮﺿﺢ‬ ‫اﻟﺘﺎﻟﻰ‬ ‫اﻟﺠﺪول‬ ‫ﺧﻄﻮط‬ ‫داﺧﻞ‬ ‫اﻟﻤﺤﺼﻮرة‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫ﻳﻮﺿﺢ‬ ‫اﻟﺘﺎﻟﻰ‬ ‫اﻟﺠﺪول‬ ‫اﻟﻜﻨﺘﻮر‬ ‫اﻟﻜﻨﺘﻮر‬ ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫آﻤﻴﺎت‬ ‫ﺣﺴﺎب‬ ‫واﻟﻤﻄﻠﻮب‬ ‫ﺗﻞ‬ ‫ﺑﻬﺎ‬ ‫ﻟﻤﻨﻄﻘﺔ‬ ‫واﻟﺮدم‬ ‫اﻟﺤﻔﺮ‬ ‫آﻤﻴﺎت‬ ‫ﺣﺴﺎب‬ ‫واﻟﻤﻄﻠﻮب‬ ‫ﺗﻞ‬ ‫ﺑﻬﺎ‬ ‫ﻟﻤﻨﻄﻘﺔ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻋﻠﻰ‬ ‫اﻷرض‬ ‫ﻟﺘﺴﻮﻳﺔ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻋﻠﻰ‬ ‫اﻷرض‬ ‫ﻟﺘﺴﻮﻳﺔ‬ ٣٠ ٣٠ ‫م‬ ‫م‬ . .
  • 63. ٦٣ ٦٣ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﻜﻨﺘﻮر‬ ‫ﺧﻂ‬ ‫رﻗﻢ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫اﻟﺤﺠﻢ‬ ‫ﻣﻌﺎدﻟﺔ‬ ‫اﻟﻜﻤﻴﺔ‬ 33 300 (٥٠٠+٣٠٠)١ * ٠٫٥= ‫ح‬ 400.00 32 500 (٦٠٠+٥٠٠)١ * ٠٫٥= ‫ح‬ 550.00 31 600 (٧٥٠+٦٠٠)١ * ٠٫٥ = ‫ح‬ 675.00 30 750 ‫اﻟﺤﻔﺮ‬ ‫اﺟﻤﺎﻟﻰ‬ 1625.00 30 750 3250.00 (٧٥٠-٨٠٠)١ * ٠٫٥ = ‫ح‬ 25.00 29 800 (٨٠٠ - ١٠٠٠) ١٫٥ = ‫ح‬ 300.00 28 1000 (١٠٠٠ - ١٢٠٠) ٢٫٥ = ‫ح‬ 500.00 27 1200 (١٢٠٠- ١٧٢٠) ٣٫٥ = ‫ح‬ 1820.00 26 1720 ‫اﻟﺮدم‬ ‫اﺟﻤﺎﻟﻰ‬ 2645.00 ‫اﻟﺮدم‬ ‫ﻣﻜﻌﺒﺎت‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ : :٥ ٥ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬
  • 64. ٦٤ ٦٤ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﻜﻨﺘﻮر‬ ‫ﺧﻂ‬ ‫رﻗﻢ‬ ‫ﻣﺮﺑﻊ‬ ‫ﻣﺘﺮ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ 40 22080 45 56340 50 58060 55 61940 60 68060 65 70960 ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٦ ٦ : : ‫ﺻﺨﺮﻳﺔ‬ ‫ﺑﻤﻨﻄﻘﺔ‬ ‫اﻟﻤﻴﺎﻩ‬ ‫ﻟﺤﺠﺰ‬ ‫ﺧﺰان‬ ‫ﺑﻨﺎء‬ ‫ﺗﻢ‬ ‫ﺻﺨﺮﻳﺔ‬ ‫ﺑﻤﻨﻄﻘﺔ‬ ‫اﻟﻤﻴﺎﻩ‬ ‫ﻟﺤﺠﺰ‬ ‫ﺧﺰان‬ ‫ﺑﻨﺎء‬ ‫ﺗﻢ‬ ، ، ‫اﻟﺘﺎﻟﻰ‬ ‫واﻟﺠﺪول‬ ‫اﻟﺘﺎﻟﻰ‬ ‫واﻟﺠﺪول‬ ‫ﺧﻄﻮط‬ ‫وﻣﺴﺎﺣﺔ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻳﻮﺿﺢ‬ ‫ﺧﻄﻮط‬ ‫وﻣﺴﺎﺣﺔ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻳﻮﺿﺢ‬ ‫اﻟﻜﻨﺘﻮر‬ ‫اﻟﻜﻨﺘﻮر‬ ‫اﻟﻤﻨﻄﻘﺔ‬ ‫ﻟﻬﺬﻩ‬ ‫اﻟﻤﻨﻄﻘﺔ‬ ‫ﻟﻬﺬﻩ‬ ، ، ‫واﻟﻤﻄﻠﻮب‬ ‫واﻟﻤﻄﻠﻮب‬ ‫اﻟﺨﺰان‬ ‫ﺳﻌﺔ‬ ‫ﻣﻨﺤﻨﻰ‬ ‫رﺳﻢ‬ ‫اﻟﺨﺰان‬ ‫ﺳﻌﺔ‬ ‫ﻣﻨﺤﻨﻰ‬ ‫رﺳﻢ‬ . .
  • 65. ٦٥ ٦٥ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﻣﺴﺎﺋﻞ‬ ‫ﻣﺜﻞ‬ ‫ﺗﺤﺴﺐ‬ ‫اﻟﺨﺰان‬ ‫ﺳﻌﺔ‬ ‫ﻣﺴﺎﺋﻞ‬ ‫اﻟﺤﻔﺮ‬ ‫ﻣﻜﻌﺒﺎت‬ ‫ﻣﺴﺎﺋﻞ‬ ‫ﻣﺜﻞ‬ ‫ﺗﺤﺴﺐ‬ ‫اﻟﺨﺰان‬ ‫ﺳﻌﺔ‬ ‫ﻣﺴﺎﺋﻞ‬ : :٦ ٦ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫اﻟﻜﻨﺘﻮر‬ ‫ﺧﻂ‬ ‫رﻗﻢ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫آﻨﺘﻮر‬ ‫ﺧﻄﻲ‬ ‫آﻞ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻤﻴﺎﻩ‬ ‫ﺣﺠﻢ‬ ‫ﻣﻌﺎدﻟﺔ‬ ‫اﻟﺠﺰﺋﻰ‬ ‫اﻟﺤﺠﻢ‬ ‫اﻟﻜﻠﻰ‬ ‫اﻟﺤﺠﻢ‬ 40 22080 (٥٦٣٤٠+٢٢٠٨٠)٥ * ٠٫٥= ‫ح‬ 196050 196050 45 56340 (٥٦٣٤٠+٥٨٠٦٠)٥ * ٠٫٥= ‫ح‬ 286000 482050 50 58060 (٥٨٠٦٠+٦١٩٤٠)٥ * ٠٫٥ = ‫ح‬ 300000 782050 55 61940 (٦١٩٤٠+٦٨٠٦٠)٥ * ٠٫٥ = ‫ح‬ 325000 1107050 60 68060 (٦٨٠٦٠+٧٠٩٦٠)٥ * ٠٫٥ = ‫ح‬ 347550 1454600 65 70960 ‫اﻟﻜﻠﻰ‬ ‫اﻟﺤﺠﻢ‬ 1454600
  • 66. ٦٦ ٦٦ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ٥٠ ٥٥ ٦٠ ٦٥ ٤٥ ٤٠ ‫اﻟﺴﻌﺔ‬ ‫اﻟﻤﻜﻌﺐ‬ ‫ﺑﺎﻟﻤﺘﺮ‬ ‫ﺻﻔﺮ‬ ٢٥٠٠٠٠ ٥٠٠٠٠٠ ٧٥٠٠٠٠ ١٠٠٠٠٠٠ ١٢٥٠٠٠٠ ١٥٠٠٠٠٠ ‫اﻟﻤﻨﺴﻮب‬ ‫ﺔ‬‫ﻌ‬‫ﺴ‬‫ﻟ‬‫ا‬ ‫ﻰ‬‫ﻨ‬‫ﺤ‬‫ﻨ‬‫ﻣ‬ ** ** ‫ﺑﻴﻨﻰ‬ ‫ﻣﻨﺴﻮب‬ ‫أى‬ ‫ﻋﻨﺪ‬ ‫اﻟﻤﺨﺰﻧﺔ‬ ‫اﻟﻤﻴﺎﻩ‬ ‫آﻤﻴﺔ‬ ‫ﻟﺘﺤﺪﻳﺪ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻣﻨﺤﻨﻰ‬ ‫ﻳﺴﺘﺨﺪم‬ ‫ﺑﻴﻨﻰ‬ ‫ﻣﻨﺴﻮب‬ ‫أى‬ ‫ﻋﻨﺪ‬ ‫اﻟﻤﺨﺰﻧﺔ‬ ‫اﻟﻤﻴﺎﻩ‬ ‫آﻤﻴﺔ‬ ‫ﻟﺘﺤﺪﻳﺪ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻣﻨﺤﻨﻰ‬ ‫ﻳﺴﺘﺨﺪم‬ ‫ﻣﻨﺴﻮب‬ ‫ﻋﻨﺪ‬ ‫اﻟﻤﺨﺰﻧﺔ‬ ‫اﻟﻤﻴﺎﻩ‬ ‫آﻤﻴﺔ‬ ‫ﻳﻮﺿﺢ‬ ‫اﻷﺳﻮد‬ ‫اﻟﺴﻬﻢ‬ ‫اﻟﻤﺜﺎل‬ ‫ﺳﺒﻴﻞ‬ ‫ﻋﻠﻰ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻋﻨﺪ‬ ‫اﻟﻤﺨﺰﻧﺔ‬ ‫اﻟﻤﻴﺎﻩ‬ ‫آﻤﻴﺔ‬ ‫ﻳﻮﺿﺢ‬ ‫اﻷﺳﻮد‬ ‫اﻟﺴﻬﻢ‬ ‫اﻟﻤﺜﺎل‬ ‫ﺳﺒﻴﻞ‬ ‫ﻋﻠﻰ‬ ٦٣ ٦٣ ‫م‬ ‫م‬
  • 67. ٦٧ ٦٧ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﻜﻨﺘﻮر‬ ‫ﺧﻂ‬ ‫رﻗﻢ‬ ‫ﻣﺮﺑﻊ‬ ‫ﻣﺘﺮ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ 120 4600 125 7100 130 8900 135 11200 140 12300 145 14100 ‫ﻣﺜﺎل‬ ‫ﻣﺜﺎل‬ ٧ ٧ : : ‫ﺧﻄﻮط‬ ‫داﺧﻞ‬ ‫ﺧﺮﻳﻄﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺴﺎﺣﺎت‬ ‫ﻗﻴﺴﺖ‬ ‫ﺧﻄﻮط‬ ‫داﺧﻞ‬ ‫ﺧﺮﻳﻄﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺴﺎﺣﺎت‬ ‫ﻗﻴﺴﺖ‬ ‫اﻟﻜﻨﺘﻮر‬ ‫اﻟﻜﻨﺘﻮر‬ ‫ﻟﻤﻮﻗﻊ‬ ‫ﻟﻤﻮﻗﻊ‬ ‫ﻓﻜﺎﻧﺖ‬ ‫اﻟﺨﺰاﻧﺎت‬ ‫أﺣﺪ‬ ‫ﻹﻧﺸﺎء‬ ‫ﻣﻘﺘﺮح‬ ‫ﻓﻜﺎﻧﺖ‬ ‫اﻟﺨﺰاﻧﺎت‬ ‫أﺣﺪ‬ ‫ﻹﻧﺸﺎء‬ ‫ﻣﻘﺘﺮح‬ : : ‫ﻣﻨﺴﻮب‬ ‫ﻋﻠﻰ‬ ‫ﻳﻘﻊ‬ ‫اﻟﺨﺰان‬ ‫ﻗﺎع‬ ‫أن‬ ‫ﻋﻠﻤﺖ‬ ‫ﻓﺈذا‬ ‫ﻣﻨﺴﻮب‬ ‫ﻋﻠﻰ‬ ‫ﻳﻘﻊ‬ ‫اﻟﺨﺰان‬ ‫ﻗﺎع‬ ‫أن‬ ‫ﻋﻠﻤﺖ‬ ‫ﻓﺈذا‬ ١٢٠ ١٢٠ ‫ﺑﺎﻟﺨﺰان‬ ‫اﻟﻤﻴﺎﻩ‬ ‫وﺳﻄﺢ‬ ‫م‬ ‫ﺑﺎﻟﺨﺰان‬ ‫اﻟﻤﻴﺎﻩ‬ ‫وﺳﻄﺢ‬ ‫م‬ ‫ﻣﻨﺴﻮب‬ ‫ﻋﻠﻰ‬ ‫ﻣﻨﺴﻮب‬ ‫ﻋﻠﻰ‬ ١٤٢ ١٤٢ ‫ﻓﺎﺣﺴﺐ‬ ‫م‬ ‫ﻓﺎﺣﺴﺐ‬ ‫م‬ : : ‫ا‬ ‫ا‬ ( ( ‫إرﺳﻢ‬ ‫إرﺳﻢ‬ ‫اﻟﺨﺰان‬ ‫ﺳﻌﺔ‬ ‫ﻣﻨﺤﻨﻰ‬ ‫اﻟﺨﺰان‬ ‫ﺳﻌﺔ‬ ‫ﻣﻨﺤﻨﻰ‬ ‫ب‬ ‫ب‬ ( ( ‫اﻟﺨﺰان‬ ‫داﺧﻞ‬ ‫اﻟﻤﻴﺎﻩ‬ ‫ﺣﺠﻢ‬ ‫اﻟﺨﺰان‬ ‫داﺧﻞ‬ ‫اﻟﻤﻴﺎﻩ‬ ‫ﺣﺠﻢ‬ ‫ﺟـ‬ ‫ﺟـ‬ ( ( ‫ﺳﻌﺔ‬ ‫ﻋﻨﺪ‬ ‫ﺑﺎﻟﺨﺰان‬ ‫اﻟﻤﻴﺎﻩ‬ ‫ﺳﻄﺢ‬ ‫ﻣﻨﺴﻮب‬ ‫ﺳﻌﺔ‬ ‫ﻋﻨﺪ‬ ‫ﺑﺎﻟﺨﺰان‬ ‫اﻟﻤﻴﺎﻩ‬ ‫ﺳﻄﺢ‬ ‫ﻣﻨﺴﻮب‬ ١٠٠٠٠ ١٠٠٠٠ ‫ﻣﻜﻌﺐ‬ ‫ﻣﺘﺮ‬ ‫ﻣﻜﻌﺐ‬ ‫ﻣﺘﺮ‬
  • 68. ٦٨ ٦٨ Prof. Dr. Eng. Said Elmaghraby Prof. Dr. Eng. Said Elmaghraby E_Learning courses in Engineering Surveying E_Learning courses in Engineering Surveying ‫اﻟﻜﻨﺘﻮر‬ ‫ﺧﻂ‬ ‫رﻗﻢ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫آﻨﺘﻮر‬ ‫ﺧﻄﻲ‬ ‫آﻞ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻤﻴﺎﻩ‬ ‫ﺣﺠﻢ‬ ‫ﻣﻌﺎدﻟﺔ‬ ‫اﻟﺠﺰﺋﻰ‬ ‫اﻟﺤﺠﻢ‬ ‫اﻟﻜﻠﻰ‬ ‫اﻟﺤﺠﻢ‬ 120 4600 (٧١٠٠+٤٦٠٠)٥ * ٠٫٥= ‫ح‬ 29250 29250 125 7100 (٨٩٠٠+٧١٠٠)٥ * ٠٫٥= ‫ح‬ 40000 69250 130 8900 (١١٢٠٠+٨٩٠٠)٥ * ٠٫٥ = ‫ح‬ 50250 119500 135 11200 (١٢٣٠٠+١١٢٠٠)٥ * ٠٫٥ = ‫ح‬ 58750 178250 140 12300 (١٤١٠٠+١٢٣٠٠)٥ * ٠٫٥ = ‫ح‬ 66000 244250 145 14100 ‫اﻟﻜﻠﻰ‬ ‫اﻟﺤﺠﻢ‬ 244250 : :٧ ٧ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬ ‫ﻣﺜﺎل‬ ‫ﺣﻞ‬