{"id":4712,"date":"2025-11-29T19:54:09","date_gmt":"2025-11-29T19:54:09","guid":{"rendered":"https:\/\/journal.ziu-university.net\/?p=4712"},"modified":"2025-11-29T19:54:10","modified_gmt":"2025-11-29T19:54:10","slug":"%d8%a7%d9%84%d8%b7%d8%b1%d9%82-%d8%a7%d9%84%d9%85%d8%ab%d9%84%d9%89-%d9%84%d9%84%d8%aa%d8%ba%d9%84%d8%a8-%d8%b9%d9%84%d9%89-%d8%a7%d9%84%d8%a7%d8%ae%d8%b7%d8%a7%d8%a1-%d8%a7%d9%84%d8%b9%d8%b4%d9%88","status":"publish","type":"post","link":"https:\/\/journal.ziu.edu.sy\/?p=4712","title":{"rendered":"\u0627\u0644\u0637\u0631\u0642 \u0627\u0644\u0645\u062b\u0644\u0649 \u0644\u0644\u062a\u063a\u0644\u0628 \u0639\u0644\u0649 \u0627\u0644\u0627\u062e\u0637\u0627\u0621 \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064a\u0629 \u0641\u064a \u0634\u0628\u0643\u0627\u062a \u0627\u0644\u0645\u0646\u0627\u0633\u064a\u0628 \u0627\u0644\u0645\u0633\u0627\u062d\u064a\u0629"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><strong>\u0627\u0644\u0645\u0644\u062e\u0635:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u062a\u0639\u062a\u0628\u0631 \u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u0627\u0644\u0627\u0633\u0644\u0648\u0628 \u0627\u0644\u0639\u0645\u0644\u064a \u0627\u0644\u0627\u0645\u062b\u0644 \u0644\u0636\u0628\u0637 \u0627\u0644\u0634\u0628\u0643\u0627\u062a \u0627\u0644\u0645\u0633\u0627\u062d\u064a\u0629 \u0648\u0630\u0644\u0643 \u0644\u0623\u0646\u0647\u0627 \u062a\u0648\u0641\u0631 \u062d\u0644\u0627\u064b \u0627\u062d\u0635\u0627\u0626\u064a\u0627 \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u062a\u0642\u0644\u064a\u0644 \u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0627\u062e\u0637\u0627\u0621 \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064a\u0629 \u0641\u064a \u0627\u0644\u0642\u064a\u0627\u0633\u0627\u062a \u062d\u064a\u062b \u064a\u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0647\u0630\u0647 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0641\u064a \u0636\u0628\u0637 \u0627\u0644\u0634\u0628\u0643\u0627\u062a \u0627\u0644\u0645\u0633\u0627\u062d\u064a\u0629 \u0627\u0644\u0645\u0639\u0642\u062f\u0629 \u0644\u0644\u0648\u0635\u0648\u0644 \u0627\u0644\u0649 \u0627\u0639\u0644\u0649 \u0645\u0633\u062a\u0648\u0649 \u0645\u0645\u0643\u0646 \u0645\u0646 \u0627\u0644\u062f\u0642\u0629 \u0627\u0644\u0645\u0648\u062b\u0648\u0642\u0629 \u0645\u0639 \u0645\u0631\u0627\u0639\u0627\u0629 \u0627\u0644\u0627\u0648\u0632\u0627\u0646 \u0627\u0644\u0646\u0633\u0628\u064a\u0629 \u0644\u0644\u0642\u064a\u0627\u0633\u0627\u062a .\u0641\u0627\u0644\u062e\u0637\u0627\u0621 \u0628\u0635\u0641\u0629 \u0639\u0627\u0645\u0629 \u0647\u0648 \u0627\u0644\u0641\u0631\u0642 \u0628\u064a\u0646 \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u062d\u0642\u064a\u0642\u064a\u0629 \u0644\u0644\u0623\u0631\u0635\u0627\u062f \u0648\u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0645\u0631\u0635\u0648\u062f\u0629 \u060c \u0648\u0647\u0648 \u0646\u0627\u062a\u062c \u0639\u0646 \u0639\u062f\u0629 \u0627\u062e\u0637\u0627\u0621 \u0643\u0627\u0644\u0623\u063a\u0644\u0627\u0637 (Gross Error)\u060c \u0627\u0644\u062e\u0637\u0623 \u0627\u0644\u062a\u0631\u0627\u0643\u0645\u064a (Accumulative Error)\u060c\u0627\u0644\u062e\u0637\u0623 \u0627\u0644\u0645\u0646\u062a\u0638\u0645 (Systematic Error)\u060c\u0648\u0627\u0644\u062e\u0637\u0623 \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064a (Random Error). \u0641\u0627\u0644\u0623\u0648\u0644 \u064a\u0645\u0643\u0646 \u0645\u0644\u0627\u062d\u0638\u062a\u0647 \u0648 \u062d\u0630\u0641\u0647 \u0645\u0646 \u0627\u0644\u0627\u0631\u0635\u0627\u062f\u060c \u0627\u0644\u062b\u0627\u0646\u064a \u0648\u0627\u0644\u062b\u0627\u0644\u062b \u064a\u0645\u0643\u0646 \u0645\u0639\u0627\u0644\u062c\u062a\u0647 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0631\u064a\u0627\u0636\u064a\u0629 \u062b\u0627\u0628\u062a\u0629\u060c \u0627\u0645\u0627 <strong>\u0627\u0644\u0627\u062e\u064a\u0631(\u0627\u0644\u062e\u0637\u0623 \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064a)<\/strong> \u0641\u0647\u0648 \u062e\u0637\u0623 \u0635\u063a\u064a\u0631 \u064a\u062a\u0628\u0639 \u0633\u0644\u0648\u0643\u0627\u064e \u0639\u0634\u0648\u0627\u0626\u064a\u0627 \u0644\u0623\u064a\u0645\u0643\u0646 \u0627\u0644\u062a\u0646\u0628\u0624 \u0628\u0645\u0642\u062f\u0627\u0631\u0647 \u0627\u0648 \u0627\u062a\u062c\u0627\u0647\u0647 . \u062a\u0642\u062f\u0645 \u0647\u0630\u0647 \u0627\u0644\u0648\u0631\u0642\u0629 \u0634\u0631\u062d\u0627 \u0645\u0641\u0635\u0644\u0627 \u0644\u0644\u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0644\u0637\u0631\u064a\u0642\u0629 \u0627\u0642\u0644 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0648\u062a\u0637\u0628\u064a\u0642\u0627 \u0639\u0645\u0644\u064a\u0627 \u0639\u0644\u0649 \u0634\u0628\u0643\u0629 \u0645\u0646\u0627\u0633\u064a\u0628 \u0645\u0633\u0627\u062d\u064a\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646 \u0627\u0644\u0627\u0631\u0635\u0627\u062f \u0627\u0644\u0632\u0627\u0626\u062f\u0629 \u0644\u0645\u0639\u0627\u0644\u062c\u0629 \u0627\u0644\u0627\u062e\u0637\u0627\u0621 \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064a\u0629 \u0644\u0644\u0648\u0635\u0648\u0644 \u0627\u0644\u0649 \u0627\u0639\u0644\u0649 \u062f\u0642\u0629 \u0645\u0648\u062b\u0648\u0642\u0629 \u0641\u064a \u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0627\u0644\u062a\u0635\u062d\u064a\u062d\u0627\u062a \u0645\u0639 \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u062d\u0635\u0627\u0626\u064a\u0627\u064e.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0627\u0644\u0643\u0644\u0645\u0627\u062a \u0627\u0644\u0645\u0641\u062a\u0627\u062d\u064a\u0629: \u0627\u0644\u0627\u062e\u0637\u0627\u0621 \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064a\u0629, \u0637\u0631\u064a\u0642\u0629 \u0645\u062c\u0645\u0648\u0639 \u0627\u0642\u0644 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a, \u0627\u0644\u0642\u064a\u0627\u0633\u0627\u062a, \u0627\u0644\u0648\u0632\u0646<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Abstract<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;The least squares method is considered the optimal practical approach for adjusting area networks because it provides a statistical solution based on minimizing the sum of squared random errors in measurement . This method is used to adjust complex surveying networks to achieve the highest possible level of reliable accuracy while considering the relative weights of measurements. Error, in general, is the differences between the true value of the observations and the observed value, and it results from several errors such as, gross error , cumulative error and Random Error .&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The first one can be observed and eliminated&nbsp; from observations, the second and third one can be dealt with using fixed mathematical equations, while the last one <strong>(random error)<\/strong> is a small error that follows random behavior and whose magnitude or direction cannot be predicted.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This paper provides a detailed explanation of the mathematical model of the least squares method and a practical application to a surveying grid using a set of redundant observations to address random errors in order to achieve the highest reliable accuracy in deducing corrections, with statistical analysis of the results.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Keywords: Random Error, least squares method, measurements, weights.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0627\u0639\u062f\u0627\u062f : <\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th><strong>\u0648\u0644\u064a\u062f \u0627\u0645\u0631\u0627\u062c\u0639 \u0627\u062d\u0645\u064a\u062f\u0629\u00a0Walid A Ahmida<\/strong><br><strong>\u0642\u0633\u0645 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u0645\u062f\u0646\u064a\u0629- \u0627\u0644\u0645\u0639\u0647\u062f \u0627\u0644\u0639\u0627\u0644\u064a \u0644\u0644\u0639\u0644\u0648\u0645 \u0648\u0627\u0644\u062a\u0642\u0646\u064a\u0629-\u0627\u0644\u0628\u064a\u0636\u0627\u0621- \u0644\u064a\u0628\u064a\u0627\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong><\/th><th><strong>\u0639\u0628\u062f\u0627\u0644\u0644\u0637\u064a\u0641 \u0639\u0637\u064a\u0629 \u0645\u062d\u0645\u062f\u00a0Abdallatef A.M. Mohamed<\/strong><br><strong>\u0642\u0633\u0645 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u0645\u062f\u0646\u064a\u0629- \u0627\u0644\u0645\u0639\u0647\u062f \u0627\u0644\u0639\u0627\u0644\u064a \u0644\u0644\u0639\u0644\u0648\u0645 \u0648\u0627\u0644\u062a\u0642\u0646\u064a\u0629-\u00a0\u0627\u0644\u0628\u064a\u0636\u0627\u0621- \u0644\u064a\u0628\u064a\u0627\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong><\/th><\/tr><\/thead><\/table><\/figure>\n\r\n\t\t<div class=\"review_wrap\">\r\n\t\t\t<div id=\"review-box\" class=\"review-box review-bottom review-stars\">\r\n\t\t\t\t<div class=\"review-summary\">\r\n\t\t\t\t\t<div class=\"review-final-score\">\r\n\t\t\t\t\t\t<span title=\"\" class=\"post-large-rate stars-large\"><span style=\"width:0%\"><\/span><\/span>\r\n\t\t\t\t\t\t<h4><\/h4>\r\n\t\t\t\t\t<\/div>\r\n\t\t\t\t\r\n\t\t\t\t<div class=\"review-short-summary\"><a href=\"https:\/\/drive.google.com\/file\/d\/1IIenUrP3Wrzbkr0R3i_AKmoQV2tc-yS7\/view?usp=drive_link\" class=\"taq-button taq-medium taq-square taq-flat\" style=\"background-color:#a0ce4e\" target=\"_blank\"><i class=\"fa fa-download\"><\/i><span class=\"button-text\">Download<\/span><\/a>\r\n\t\t\t\t<\/div>\r\n\t\t\t<\/div>\r\n\t\t\t\r\n\t\t\t<div class=\"user-rate-wrap\">\r\n\t\t\t\t<span class=\"user-rating-text\">\r\n\t\t\t\t\t<strong>\u062a\u0642\u064a\u064a\u0645 \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645\u0648\u0646: <\/strong>\r\n\t\t\t\t\t<span class=\"taq-score\"><\/span>\r\n\t\t\t\t\t<small>\u0643\u0646 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