{"id":4627,"date":"2026-08-30T09:44:41","date_gmt":"2026-08-30T09:44:41","guid":{"rendered":"https:\/\/cosmalore.com\/ar\/?p=4627"},"modified":"2026-08-30T09:44:41","modified_gmt":"2026-08-30T09:44:41","slug":"pythagorean-theory","status":"publish","type":"post","link":"https:\/\/cosmalore.com\/ar\/2026\/08\/30\/pythagorean-theory\/","title":{"rendered":"\u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629"},"content":{"rendered":"<p>\u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629\u060c \u0627\u0644\u0645\u0639\u0631\u0648\u0641\u0629 \u0639\u0644\u0649 \u0646\u0637\u0627\u0642 \u0648\u0627\u0633\u0639 \u0628\u0627\u0633\u0645 \u00ab\u0646\u0638\u0631\u064a\u0629 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633\u00bb\u060c \u0647\u064a \u0625\u062d\u062f\u0649 \u0623\u0647\u0645 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0641\u064a \u062a\u0627\u0631\u064a\u062e \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0648\u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a. \u0648\u062a\u0646\u0635 \u0639\u0644\u0649 \u0623\u0646\u0647 \u0641\u064a \u0643\u0644 \u0645\u062b\u0644\u062b \u0642\u0627\u0626\u0645 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u064a\u0643\u0648\u0646 \u0645\u0631\u0628\u0639 \u0637\u0648\u0644 \u0627\u0644\u0648\u062a\u0631 \u0645\u0633\u0627\u0648\u064a\u0627\u064b \u0644\u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u064a \u0637\u0648\u0644\u064a \u0627\u0644\u0636\u0644\u0639\u064a\u0646 \u0627\u0644\u0642\u0627\u0626\u0645\u064a\u0646. \u0648\u0625\u0630\u0627 \u0631\u0645\u0632\u0646\u0627 \u0625\u0644\u0649 \u0637\u0648\u0644\u064a \u0627\u0644\u0636\u0644\u0639\u064a\u0646 \u0627\u0644\u0642\u0627\u0626\u0645\u064a\u0646 \u0628\u0627\u0644\u0631\u0645\u0632\u064a\u0646 <i>a<\/i> \u0648<i>b<\/i>\u060c \u0648\u0625\u0644\u0649 \u0627\u0644\u0648\u062a\u0631 \u0628\u0627\u0644\u0631\u0645\u0632 <i>c<\/i>\u060c \u0641\u0625\u0646 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0647\u064a <i>a\u00b2+b\u00b2=c\u00b2<\/i>. \u0648\u0642\u062f \u0638\u0647\u0631\u062a \u0647\u0630\u0647 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0641\u064a \u0627\u0644\u0645\u0639\u0631\u0641\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0642\u0628\u0644 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633 \u0628\u0642\u0631\u0648\u0646\u060c \u0628\u064a\u0646\u0645\u0627 \u0623\u0635\u0628\u062d\u062a \u0644\u0627\u062d\u0642\u0627\u064b \u0645\u0631\u062a\u0628\u0637\u0629 \u0628\u0627\u0644\u0645\u062f\u0631\u0633\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629\u060c \u062b\u0645 \u0638\u0647\u0631\u062a \u0623\u0642\u062f\u0645 \u0635\u064a\u0627\u063a\u0629 \u0628\u0631\u0647\u0627\u0646\u064a\u0629 \u0628\u0627\u0642\u064a\u0629 \u0628\u0635\u0648\u0631\u0629 \u0648\u0627\u0636\u062d\u0629 \u0641\u064a \u0627\u0644\u0643\u062a\u0627\u0628 \u0627\u0644\u0623\u0648\u0644 \u0645\u0646 \u00ab\u0627\u0644\u0639\u0646\u0627\u0635\u0631\u00bb \u0644\u0625\u0642\u0644\u064a\u062f\u0633\u060c \u0641\u064a \u0627\u0644\u0642\u0636\u064a\u0629 47. <sup class=\"ref\"><a href=\"https:\/\/plato.stanford.edu\/entries\/pythagoras\/\" title=\"1|Pythagoras|Carl Huffman\u060c Stanford Encyclopedia of Philosophy|2023\" target=\"_blank\" rel=\"noopener\">[1]<\/a><\/sup><sup class=\"ref\"><a href=\"https:\/\/aleph0.clarku.edu\/~djoyce\/java\/elements\/bookI\/propI47.html\" title=\"2|Euclid&amp;apos;s Elements, Book I, Proposition 47|David E. Joyce\u060c Clark University|2026\" target=\"_blank\" rel=\"noopener\">[2]<\/a><\/sup><\/p>\n<div class=\"infobox\">\n<table>\n<tr class=\"ib-sec\">\n<td colspan=\"2\">\u0645\u0639\u0644\u0648\u0645\u0627\u062a \u0623\u0633\u0627\u0633\u064a\u0629<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u0627\u0633\u0645<\/td>\n<td class=\"ib-val\">\u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u0627\u0633\u0645 \u0627\u0644\u0634\u0627\u0626\u0639<\/td>\n<td class=\"ib-val\">\u0646\u0638\u0631\u064a\u0629 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0628\u0627\u0644\u0625\u0646\u062c\u0644\u064a\u0632\u064a\u0629<\/td>\n<td class=\"ib-val\">Pythagorean Theorem<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u0645\u062c\u0627\u0644<\/td>\n<td class=\"ib-val\">\u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u0625\u0642\u0644\u064a\u062f\u064a\u0629<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u0645\u062b\u0644\u062b \u0627\u0644\u0645\u0639\u0646\u064a<\/td>\n<td class=\"ib-val\">\u0627\u0644\u0645\u062b\u0644\u062b \u0627\u0644\u0642\u0627\u0626\u0645 \u0627\u0644\u0632\u0627\u0648\u064a\u0629<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u0635\u064a\u063a\u0629<\/td>\n<td class=\"ib-val\">a\u00b2 + b\u00b2 = c\u00b2<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u0648\u062a\u0631<\/td>\n<td class=\"ib-val\">\u0627\u0644\u0636\u0644\u0639 \u0627\u0644\u0645\u0642\u0627\u0628\u0644 \u0644\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0642\u0627\u0626\u0645\u0629<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0623\u0634\u0647\u0631 \u0645\u0635\u062f\u0631 \u0628\u0631\u0647\u0627\u0646\u064a \u0628\u0627\u0642\u064d<\/td>\n<td class=\"ib-val\">\u0625\u0642\u0644\u064a\u062f\u0633\u060c \u0627\u0644\u0639\u0646\u0627\u0635\u0631\u060c \u0627\u0644\u0643\u062a\u0627\u0628 \u0627\u0644\u0623\u0648\u0644\u060c \u0627\u0644\u0642\u0636\u064a\u0629 47<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u0639\u0643\u0633<\/td>\n<td class=\"ib-val\">\u0625\u0630\u0627 \u062a\u062d\u0642\u0642 a\u00b2 + b\u00b2 = c\u00b2 \u0644\u0645\u062b\u0644\u062b\u060c \u0641\u0647\u0648 \u0642\u0627\u0626\u0645 \u0627\u0644\u0632\u0627\u0648\u064a\u0629<\/td>\n<\/tr>\n<tr class=\"ib-sec\">\n<td colspan=\"2\">\u0627\u0644\u062c\u0630\u0648\u0631 \u0627\u0644\u062a\u0627\u0631\u064a\u062e\u064a\u0629<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0628\u0644\u0627\u062f \u0627\u0644\u0631\u0627\u0641\u062f\u064a\u0646<\/td>\n<td class=\"ib-val\">\u0645\u0639\u0631\u0641\u0629 \u0645\u0628\u0643\u0631\u0629 \u0628\u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u0623\u0636\u0644\u0627\u0639 \u0641\u064a \u0627\u0644\u0645\u062b\u0644\u062b\u0627\u062a \u0627\u0644\u0642\u0627\u0626\u0645\u0629<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633<\/td>\n<td class=\"ib-val\">\u0646\u062d\u0648 \u0627\u0644\u0642\u0631\u0646 \u0627\u0644\u0633\u0627\u062f\u0633 \u0642\u0628\u0644 \u0627\u0644\u0645\u064a\u0644\u0627\u062f<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0625\u0642\u0644\u064a\u062f\u0633<\/td>\n<td class=\"ib-val\">\u0627\u0644\u0642\u0631\u0646 \u0627\u0644\u062b\u0627\u0644\u062b \u0642\u0628\u0644 \u0627\u0644\u0645\u064a\u0644\u0627\u062f<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u0642\u0636\u064a\u0629 \u0627\u0644\u0625\u0642\u0644\u064a\u062f\u064a\u0629<\/td>\n<td class=\"ib-val\">\u0627\u0644\u0639\u0646\u0627\u0635\u0631 I.47<\/td>\n<\/tr>\n<tr class=\"ib-sec\">\n<td colspan=\"2\">\u0623\u0645\u062b\u0644\u0629 \u0639\u062f\u062f\u064a\u0629<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">3\u060c 4\u060c 5<\/td>\n<td class=\"ib-val\">3\u00b2 + 4\u00b2 = 5\u00b2<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">5\u060c 12\u060c 13<\/td>\n<td class=\"ib-val\">5\u00b2 + 12\u00b2 = 13\u00b2<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">8\u060c 15\u060c 17<\/td>\n<td class=\"ib-val\">8\u00b2 + 15\u00b2 = 17\u00b2<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">7\u060c 24\u060c 25<\/td>\n<td class=\"ib-val\">7\u00b2 + 24\u00b2 = 25\u00b2<\/td>\n<\/tr>\n<\/table>\n<div class=\"ib-foot\">COSMALORE \u00b7 \u0627\u0644\u0645\u0648\u0633\u0648\u0639\u0629 \u0627\u0644\u0639\u0631\u0628\u064a\u0629<\/div>\n<\/div>\n<h2>\u0635\u064a\u0627\u063a\u0629 \u0627\u0644\u0646\u0638\u0631\u064a\u0629<\/h2>\n<p>\u0644\u0646\u0641\u0631\u0636 \u0623\u0646 \u0644\u062f\u064a\u0646\u0627 \u0645\u062b\u0644\u062b\u0627\u064b \u0642\u0627\u0626\u0645\u0627\u064b <i>ABC<\/i>\u060c \u0648\u0623\u0646 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0639\u0646\u062f <i>C<\/i> \u062a\u0633\u0627\u0648\u064a 90 \u062f\u0631\u062c\u0629\u060c \u0648\u0623\u0646 \u0637\u0648\u0644\u064a \u0627\u0644\u0636\u0644\u0639\u064a\u0646 \u0627\u0644\u0642\u0627\u0626\u0645\u064a\u0646 \u0647\u0645\u0627 <i>a<\/i> \u0648<i>b<\/i>\u060c \u0628\u064a\u0646\u0645\u0627 \u0637\u0648\u0644 \u0627\u0644\u0636\u0644\u0639 \u0627\u0644\u0645\u0642\u0627\u0628\u0644 \u0644\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0642\u0627\u0626\u0645\u0629\u060c \u0623\u064a \u0627\u0644\u0648\u062a\u0631\u060c \u0647\u0648 <i>c<\/i>. \u0639\u0646\u062f\u0626\u0630 \u062a\u0643\u0648\u0646 \u0627\u0644\u0639\u0644\u0627\u0642\u0629:<\/p>\n<p><i>a\u00b2+b\u00b2=c\u00b2<\/i><\/p>\n<p>\u0648\u0647\u0630\u0647 \u0627\u0644\u0635\u064a\u063a\u0629 \u062a\u0639\u0646\u064a \u0647\u0646\u062f\u0633\u064a\u0627\u064b \u0623\u0646 \u0645\u0633\u0627\u062d\u0629 \u0627\u0644\u0645\u0631\u0628\u0639 \u0627\u0644\u0645\u0646\u0634\u0623 \u0639\u0644\u0649 \u0627\u0644\u0648\u062a\u0631 \u062a\u0633\u0627\u0648\u064a \u0645\u062c\u0645\u0648\u0639 \u0645\u0633\u0627\u062d\u062a\u064a \u0627\u0644\u0645\u0631\u0628\u0639\u064a\u0646 \u0627\u0644\u0645\u0646\u0634\u0623\u064a\u0646 \u0639\u0644\u0649 \u0627\u0644\u0636\u0644\u0639\u064a\u0646 \u0627\u0644\u0642\u0627\u0626\u0645\u064a\u0646. \u0648\u0647\u0630\u0647 \u0627\u0644\u0635\u064a\u0627\u063a\u0629 \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629 \u0647\u064a \u0627\u0644\u0623\u0642\u0631\u0628 \u0625\u0644\u0649 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u062a\u064a \u0638\u0647\u0631\u062a \u0628\u0647\u0627 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0641\u064a \u00ab\u0627\u0644\u0639\u0646\u0627\u0635\u0631\u00bb\u061b \u0625\u0630 \u0644\u0645 \u064a\u0635\u063a \u0625\u0642\u0644\u064a\u062f\u0633 \u0627\u0644\u0642\u0636\u064a\u0629 \u0641\u064a \u0635\u0648\u0631\u0629 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062c\u0628\u0631\u064a\u0629 \u0627\u0644\u062d\u062f\u064a\u062b\u0629\u060c \u0628\u0644 \u062a\u062d\u062f\u062b \u0639\u0646 \u0645\u0633\u0627\u0648\u0627\u0629 \u0627\u0644\u0645\u0631\u0628\u0639 \u0627\u0644\u0645\u0646\u0634\u0623 \u0639\u0644\u0649 \u0627\u0644\u0648\u062a\u0631 \u0644\u0645\u062c\u0645\u0648\u0639 \u0627\u0644\u0645\u0631\u0628\u0639\u064a\u0646 \u0627\u0644\u0645\u0646\u0634\u0623\u064a\u0646 \u0639\u0644\u0649 \u0627\u0644\u0636\u0644\u0639\u064a\u0646 \u0627\u0644\u0622\u062e\u0631\u064a\u0646. <sup class=\"ref\"><a href=\"https:\/\/www.perseus.tufts.edu\/hopper\/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D47\" title=\"3|Euclid, Elements, Book I, Proposition 47|Thomas L. Heath\u060c Perseus Digital Library|1910\" target=\"_blank\" rel=\"noopener\">[3]<\/a><\/sup><\/p>\n<h2>\u0644\u0645\u0627\u0630\u0627 \u0627\u0644\u0648\u062a\u0631 \u0647\u0648 \u0627\u0644\u0636\u0644\u0639 c\u061f<\/h2>\n<p>\u0627\u0644\u0648\u062a\u0631 \u0647\u0648 \u0623\u0637\u0648\u0644 \u0623\u0636\u0644\u0627\u0639 \u0627\u0644\u0645\u062b\u0644\u062b \u0627\u0644\u0642\u0627\u0626\u0645\u060c \u0648\u0647\u0648 \u0627\u0644\u0636\u0644\u0639 \u0627\u0644\u0645\u0642\u0627\u0628\u0644 \u0645\u0628\u0627\u0634\u0631\u0629 \u0644\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0642\u0627\u0626\u0645\u0629. \u0641\u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0645\u062b\u0644\u062b \u0642\u0627\u0626\u0645\u0627\u064b \u0639\u0646\u062f <i>C<\/i>\u060c \u0641\u0625\u0646 \u0627\u0644\u0636\u0644\u0639 \u0627\u0644\u0645\u0642\u0627\u0628\u0644 \u0644\u0647\u0630\u0647 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0647\u0648 <i>AB<\/i>\u060c \u0648\u0644\u0630\u0644\u0643 \u064a\u0643\u0648\u0646 \u0647\u0648 \u0627\u0644\u0648\u062a\u0631.<\/p>\n<p>\u0648\u062a\u0648\u0636\u062d \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0623\u0646 \u0645\u0631\u0628\u0639 \u0647\u0630\u0627 \u0627\u0644\u0636\u0644\u0639 \u0627\u0644\u0623\u0643\u0628\u0631 \u064a\u0633\u0627\u0648\u064a \u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u064a \u0627\u0644\u0636\u0644\u0639\u064a\u0646 \u0627\u0644\u0623\u0635\u063a\u0631. \u0648\u0645\u0646 \u062b\u0645 \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647\u0627 \u0644\u0625\u064a\u062c\u0627\u062f \u0637\u0648\u0644 \u0636\u0644\u0639 \u0645\u062c\u0647\u0648\u0644 \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 \u0637\u0648\u0644\u0627 \u0627\u0644\u0636\u0644\u0639\u064a\u0646 \u0627\u0644\u0622\u062e\u0631\u064a\u0646 \u0645\u0639\u0631\u0648\u0641\u064a\u0646\u060c \u0628\u0634\u0631\u0637 \u0623\u0646 \u064a\u0643\u0648\u0646 \u0627\u0644\u0645\u062b\u0644\u062b \u0642\u0627\u0626\u0645\u0627\u064b.<\/p>\n<h2>\u0627\u0644\u0645\u0639\u0646\u0649 \u0627\u0644\u0647\u0646\u062f\u0633\u064a \u0644\u0644\u0645\u0631\u0628\u0639<\/h2>\n<p>\u062a\u062a\u0636\u062d \u0642\u0648\u0629 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0639\u0646\u062f\u0645\u0627 \u0646\u0646\u0638\u0631 \u0625\u0644\u064a\u0647\u0627 \u0645\u0646 \u0645\u0646\u0638\u0648\u0631 \u0627\u0644\u0645\u0633\u0627\u062d\u0627\u062a. \u0641\u0625\u0630\u0627 \u0631\u0633\u0645\u0646\u0627 \u0645\u0631\u0628\u0639\u0627\u064b \u0639\u0644\u0649 \u0643\u0644 \u0636\u0644\u0639 \u0645\u0646 \u0623\u0636\u0644\u0627\u0639 \u0627\u0644\u0645\u062b\u0644\u062b \u0627\u0644\u0642\u0627\u0626\u0645\u060c \u0641\u0625\u0646 \u0645\u0633\u0627\u062d\u0629 \u0627\u0644\u0645\u0631\u0628\u0639 \u0627\u0644\u0645\u0646\u0634\u0623 \u0639\u0644\u0649 \u0627\u0644\u0648\u062a\u0631 \u062a\u0633\u0627\u0648\u064a \u0645\u062c\u0645\u0648\u0639 \u0645\u0633\u0627\u062d\u062a\u064a \u0627\u0644\u0645\u0631\u0628\u0639\u064a\u0646 \u0627\u0644\u0645\u0646\u0634\u0623\u064a\u0646 \u0639\u0644\u0649 \u0627\u0644\u0636\u0644\u0639\u064a\u0646 \u0627\u0644\u0642\u0627\u0626\u0645\u064a\u0646. \u0641\u0625\u0630\u0627 \u0643\u0627\u0646 \u0637\u0648\u0644 \u0627\u0644\u0636\u0644\u0639 \u0627\u0644\u0623\u0648\u0644 3 \u0648\u062d\u062f\u0627\u062a \u0648\u0627\u0644\u062b\u0627\u0646\u064a 4 \u0648\u062d\u062f\u0627\u062a\u060c \u0641\u0625\u0646 \u0645\u0633\u0627\u062d\u062a\u064a \u0627\u0644\u0645\u0631\u0628\u0639\u064a\u0646 \u062a\u0633\u0627\u0648\u064a\u0627\u0646 9 \u064816 \u0648\u062d\u062f\u0629 \u0645\u0631\u0628\u0639\u0629\u060c \u0648\u0645\u062c\u0645\u0648\u0639\u0647\u0645\u0627 25 \u0648\u062d\u062f\u0629 \u0645\u0631\u0628\u0639\u0629\u061b \u0648\u0644\u0630\u0644\u0643 \u064a\u0643\u0648\u0646 \u0637\u0648\u0644 \u0627\u0644\u0648\u062a\u0631 5 \u0648\u062d\u062f\u0627\u062a.<\/p>\n<p>\u0648\u0647\u0630\u0627 \u0627\u0644\u062a\u0641\u0633\u064a\u0631 \u064a\u0628\u064a\u0646 \u0623\u0646 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0644\u064a\u0633\u062a \u0645\u062c\u0631\u062f \u0642\u0627\u0639\u062f\u0629 \u0644\u062d\u0633\u0627\u0628 \u0637\u0648\u0644 \u0645\u062c\u0647\u0648\u0644\u060c \u0628\u0644 \u0647\u064a \u0639\u0644\u0627\u0642\u0629 \u0639\u0645\u064a\u0642\u0629 \u0628\u064a\u0646 \u0623\u0637\u0648\u0627\u0644 \u0627\u0644\u0623\u0636\u0644\u0627\u0639 \u0648\u0645\u0633\u0627\u062d\u0627\u062a \u0627\u0644\u0623\u0634\u0643\u0627\u0644 \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629 \u0627\u0644\u0645\u0628\u0646\u064a\u0629 \u0639\u0644\u064a\u0647\u0627.<\/p>\n<h2>\u0627\u0644\u0645\u062b\u0644\u062b 3\u20134\u20135<\/h2>\n<p>\u0623\u0634\u0647\u0631 \u0645\u062b\u0627\u0644 \u0639\u0644\u0649 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0647\u0648 \u0627\u0644\u0645\u062b\u0644\u062b \u0630\u0648 \u0627\u0644\u0623\u0636\u0644\u0627\u0639 3 \u06484 \u06485. \u0625\u0630 \u0625\u0646:<\/p>\n<p><i>3\u00b2+4\u00b2=9+16=25=5\u00b2<\/i><\/p>\n<p>\u0648\u0644\u0630\u0644\u0643 \u0641\u0625\u0646 \u0627\u0644\u0645\u062b\u0644\u062b \u0627\u0644\u0630\u064a \u0623\u0637\u0648\u0627\u0644 \u0623\u0636\u0644\u0627\u0639\u0647 3 \u06484 \u06485 \u064a\u0643\u0648\u0646 \u0642\u0627\u0626\u0645\u0627\u064b. \u0648\u062a\u0633\u0645\u0649 \u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629 \u0627\u0644\u062a\u064a \u062a\u062d\u0642\u0642 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 <i>a\u00b2+b\u00b2=c\u00b2<\/i> \u00ab\u062b\u0644\u0627\u062b\u064a\u0629 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629\u00bb.<\/p>\n<p>\u0648\u062a\u0648\u062c\u062f \u062b\u0644\u0627\u062b\u064a\u0627\u062a \u0623\u062e\u0631\u0649 \u0645\u062b\u0644 5 \u064812 \u064813\u060c \u06487 \u064824 \u064825\u060c \u06488 \u064815 \u064817. \u0648\u064a\u0645\u0643\u0646 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0639\u062f\u062f \u0644\u0627 \u0646\u0647\u0627\u0626\u064a \u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u062b\u0644\u0627\u062b\u064a\u0627\u062a\u060c \u0648\u0647\u0648 \u0645\u0627 \u064a\u062c\u0639\u0644 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0645\u0631\u062a\u0628\u0637\u0629 \u0623\u064a\u0636\u0627\u064b \u0628\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f.<\/p>\n<h2>\u0627\u0644\u062c\u0630\u0648\u0631 \u0627\u0644\u0628\u0627\u0628\u0644\u064a\u0629 \u0627\u0644\u0642\u062f\u064a\u0645\u0629<\/h2>\n<p>\u0644\u0627 \u062a\u0634\u064a\u0631 \u0627\u0644\u0623\u062f\u0644\u0629 \u0627\u0644\u062a\u0627\u0631\u064a\u062e\u064a\u0629 \u0627\u0644\u0645\u062a\u0627\u062d\u0629 \u0625\u0644\u0649 \u0623\u0646 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633 \u0643\u0627\u0646 \u0623\u0648\u0644 \u0645\u0646 \u0639\u0631\u0641 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u062a\u064a \u062a\u062d\u0645\u0644 \u0627\u0633\u0645\u0647. \u0641\u0642\u062f \u0627\u0633\u062a\u062e\u062f\u0645 \u0639\u0644\u0645\u0627\u0621 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0641\u064a \u0628\u0644\u0627\u062f \u0627\u0644\u0631\u0627\u0641\u062f\u064a\u0646 \u0627\u0644\u0642\u062f\u064a\u0645\u0629 \u0639\u0644\u0627\u0642\u0627\u062a \u0628\u064a\u0646 \u0623\u0636\u0644\u0627\u0639 \u0627\u0644\u0645\u062b\u0644\u062b\u0627\u062a \u0627\u0644\u0642\u0627\u0626\u0645\u0629 \u0642\u0628\u0644 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633 \u0628\u0623\u0643\u062b\u0631 \u0645\u0646 \u0623\u0644\u0641 \u0639\u0627\u0645 \u062a\u0642\u0631\u064a\u0628\u0627\u064b. \u0648\u062a\u0634\u064a\u0631 \u0627\u0644\u062f\u0631\u0627\u0633\u0627\u062a \u0627\u0644\u062a\u0627\u0631\u064a\u062e\u064a\u0629 \u0625\u0644\u0649 \u0623\u0646 \u0627\u0644\u0628\u0627\u0628\u0644\u064a\u064a\u0646 \u0627\u0644\u0642\u062f\u0645\u0627\u0621\u060c \u062e\u0644\u0627\u0644 \u0627\u0644\u0641\u062a\u0631\u0629 \u0646\u062d\u0648 1900\u20131600 \u0642\u0628\u0644 \u0627\u0644\u0645\u064a\u0644\u0627\u062f\u060c \u0643\u0627\u0646\u0648\u0627 \u0642\u0627\u062f\u0631\u064a\u0646 \u0639\u0644\u0649 \u0627\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0645\u0627 \u064a\u0639\u0631\u0641 \u0627\u0644\u064a\u0648\u0645 \u0628\u0627\u0644\u062b\u0644\u0627\u062b\u064a\u0627\u062a \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629\u060c \u0643\u0645\u0627 \u062a\u0631\u062a\u0628\u0637 \u0627\u0644\u0644\u0648\u062d\u0629 \u0627\u0644\u0628\u0627\u0628\u0644\u064a\u0629 \u0627\u0644\u0634\u0647\u064a\u0631\u0629 Plimpton 322 \u0628\u0645\u062b\u0644 \u0647\u0630\u0647 \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a. <sup class=\"ref\"><a href=\"https:\/\/aleph0.clarku.edu\/~djoyce\/java\/elements\/bookI\/propI47.html\" title=\"4|Euclid&amp;apos;s Elements, Book I, Proposition 47|David E. Joyce\u060c Clark University|2026\" target=\"_blank\" rel=\"noopener\">[4]<\/a><\/sup><\/p>\n<p>\u0648\u062a\u0643\u062a\u0633\u0628 \u0647\u0630\u0647 \u0627\u0644\u062d\u0642\u064a\u0642\u0629 \u0623\u0647\u0645\u064a\u0629 \u062a\u0627\u0631\u064a\u062e\u064a\u0629 \u0644\u0623\u0646\u0647\u0627 \u062a\u0645\u064a\u0632 \u0628\u064a\u0646 \u00ab\u0645\u0639\u0631\u0641\u0629 \u0627\u0644\u0639\u0644\u0627\u0642\u0629\u00bb \u0648\u00ab\u0625\u062b\u0628\u0627\u062a \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0636\u0645\u0646 \u0646\u0638\u0627\u0645 \u0627\u0633\u062a\u062f\u0644\u0627\u0644\u064a\u00bb. \u0641\u0648\u062c\u0648\u062f \u0623\u0639\u062f\u0627\u062f \u062a\u062d\u0642\u0642 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0644\u0627 \u064a\u0633\u0627\u0648\u064a \u0628\u0627\u0644\u0636\u0631\u0648\u0631\u0629 \u0627\u0645\u062a\u0644\u0627\u0643 \u0628\u0631\u0647\u0627\u0646 \u0647\u0646\u062f\u0633\u064a \u0639\u0627\u0645 \u064a\u062b\u0628\u062a\u0647\u0627 \u0644\u062c\u0645\u064a\u0639 \u0627\u0644\u0645\u062b\u0644\u062b\u0627\u062a \u0627\u0644\u0642\u0627\u0626\u0645\u0629.<\/p>\n<h2>\u0627\u0644\u0644\u0648\u062d\u0629 Plimpton 322<\/h2>\n<p>\u062a\u0639\u062f Plimpton 322 \u0645\u0646 \u0623\u0634\u0647\u0631 \u0627\u0644\u0648\u062b\u0627\u0626\u0642 \u0641\u064a \u062a\u0627\u0631\u064a\u062e \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u0628\u0627\u0628\u0644\u064a\u0629. \u0648\u062a\u0631\u062a\u0628\u0637 \u0623\u0639\u062f\u0627\u062f\u0647\u0627 \u0628\u062b\u0644\u0627\u062b\u064a\u0627\u062a \u0639\u062f\u062f\u064a\u0629 \u064a\u0645\u0643\u0646 \u062a\u0641\u0633\u064a\u0631\u0647\u0627 \u0641\u064a \u0625\u0637\u0627\u0631 \u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u0645\u062b\u0644\u062b\u0627\u062a \u0627\u0644\u0642\u0627\u0626\u0645\u0629. \u0648\u0642\u062f \u0623\u062b\u0627\u0631\u062a \u0637\u0628\u064a\u0639\u062a\u0647\u0627 \u0627\u0644\u062f\u0642\u064a\u0642\u0629 \u0646\u0642\u0627\u0634\u0627\u064b \u062a\u0627\u0631\u064a\u062e\u064a\u0627\u064b \u062d\u0648\u0644 \u0627\u0644\u063a\u0631\u0636 \u0627\u0644\u0630\u064a \u0623\u064f\u0646\u0634\u0626\u062a \u0645\u0646 \u0623\u062c\u0644\u0647 \u0648\u0643\u064a\u0641\u064a\u0629 \u0625\u0646\u062a\u0627\u062c \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0648\u0627\u0631\u062f\u0629 \u0641\u064a\u0647\u0627.<\/p>\n<p>\u0648\u062a\u0624\u0643\u062f \u0647\u0630\u0647 \u0627\u0644\u0648\u062b\u064a\u0642\u0629 \u0623\u0646 \u0645\u0639\u0631\u0641\u0629 \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0627\u0644\u0645\u0631\u062a\u0628\u0637\u0629 \u0628\u0627\u0644\u0645\u062b\u0644\u062b\u0627\u062a \u0627\u0644\u0642\u0627\u0626\u0645\u0629 \u0643\u0627\u0646\u062a \u0645\u0648\u062c\u0648\u062f\u0629 \u0641\u064a \u0628\u0644\u0627\u062f \u0627\u0644\u0631\u0627\u0641\u062f\u064a\u0646 \u0642\u0628\u0644 \u0638\u0647\u0648\u0631 \u0627\u0644\u0645\u062f\u0631\u0633\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629 \u0628\u0632\u0645\u0646 \u0637\u0648\u064a\u0644\u060c \u0644\u0643\u0646\u0647\u0627 \u0644\u0627 \u062a\u062b\u0628\u062a \u0628\u0645\u0641\u0631\u062f\u0647\u0627 \u0623\u0646 \u0627\u0644\u0628\u0627\u0628\u0644\u064a\u064a\u0646 \u0635\u0627\u063a\u0648\u0627 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0628\u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u0628\u0631\u0647\u0627\u0646\u064a\u0629 \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629 \u0627\u0644\u062a\u064a \u0623\u0635\u0628\u062d\u062a \u0646\u0645\u0648\u0630\u062c\u0627\u064b \u0644\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u064a\u0648\u0646\u0627\u0646\u064a\u0629 \u0627\u0644\u0644\u0627\u062d\u0642\u0629. <sup class=\"ref\"><a href=\"https:\/\/aleph0.clarku.edu\/~djoyce\/java\/elements\/bookI\/propI47.html\" title=\"5|Euclid&amp;apos;s Elements, Book I, Proposition 47|David E. Joyce\u060c Clark University|2026\" target=\"_blank\" rel=\"noopener\">[5]<\/a><\/sup><\/p>\n<h2>\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633 \u0648\u0627\u0644\u0646\u0638\u0631\u064a\u0629<\/h2>\n<p>\u064a\u0646\u0633\u0628 \u0627\u0633\u0645 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0625\u0644\u0649 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633\u060c \u0627\u0644\u0641\u064a\u0644\u0633\u0648\u0641 \u0648\u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0627\u0644\u064a\u0648\u0646\u0627\u0646\u064a \u0627\u0644\u0630\u064a \u0639\u0627\u0634 \u0641\u064a \u0627\u0644\u0642\u0631\u0646 \u0627\u0644\u0633\u0627\u062f\u0633 \u0642\u0628\u0644 \u0627\u0644\u0645\u064a\u0644\u0627\u062f \u062a\u0642\u0631\u064a\u0628\u0627\u064b\u060c \u0644\u0643\u0646 \u0646\u0633\u0628\u0629 \u0627\u0643\u062a\u0634\u0627\u0641\u0647\u0627 \u0623\u0648 \u0625\u062b\u0628\u0627\u062a\u0647\u0627 \u0625\u0644\u064a\u0647 \u0634\u062e\u0635\u064a\u0627\u064b \u0644\u064a\u0633\u062a \u0645\u0624\u0643\u062f\u0629 \u062a\u0627\u0631\u064a\u062e\u064a\u0627\u064b. \u0641\u0627\u0644\u0645\u0635\u0627\u062f\u0631 \u0627\u0644\u0645\u0628\u0643\u0631\u0629 \u0627\u0644\u0628\u0627\u0642\u064a\u0629 \u0644\u0627 \u062a\u0642\u062f\u0645 \u062f\u0644\u064a\u0644\u0627\u064b \u0648\u0627\u0636\u062d\u0627\u064b \u0639\u0644\u0649 \u0623\u0646 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633 \u0646\u0641\u0633\u0647 \u0623\u062b\u0628\u062a \u0627\u0644\u0646\u0638\u0631\u064a\u0629.<\/p>\n<p>\u0648\u062a\u0634\u064a\u0631 \u00ab\u0645\u0648\u0633\u0648\u0639\u0629 \u0633\u062a\u0627\u0646\u0641\u0648\u0631\u062f \u0644\u0644\u0641\u0644\u0633\u0641\u0629\u00bb \u0625\u0644\u0649 \u0623\u0646 \u0627\u0644\u0645\u0635\u0627\u062f\u0631 \u0627\u0644\u064a\u0648\u0646\u0627\u0646\u064a\u0629 \u0627\u0644\u0645\u0628\u0643\u0631\u0629\u060c \u0628\u0645\u0627 \u0641\u064a\u0647\u0627 \u0623\u0641\u0644\u0627\u0637\u0648\u0646 \u0648\u0623\u0631\u0633\u0637\u0648 \u0648\u062a\u0644\u0627\u0645\u064a\u0630\u0647\u0645\u0627\u060c \u0644\u0627 \u062a\u0642\u062f\u0645 \u062f\u0644\u064a\u0644\u0627\u064b \u0639\u0644\u0649 \u0635\u0644\u0629 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633 \u0627\u0644\u0645\u0628\u0627\u0634\u0631\u0629 \u0628\u0627\u0644\u0646\u0638\u0631\u064a\u0629\u060c \u0648\u0623\u0646 \u0627\u0644\u0631\u0648\u0627\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0631\u0628\u0637 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633 \u0628\u0647\u0627 \u062a\u0638\u0647\u0631 \u0641\u064a \u0645\u0635\u062f\u0631 \u0645\u062a\u0623\u062e\u0631 \u0647\u0648 \u0628\u0631\u0648\u0643\u0644\u0633 \u0641\u064a \u0627\u0644\u0642\u0631\u0646 \u0627\u0644\u062e\u0627\u0645\u0633 \u0627\u0644\u0645\u064a\u0644\u0627\u062f\u064a. \u0643\u0645\u0627 \u0623\u0646 \u0628\u0631\u0648\u0643\u0644\u0633 \u064a\u0646\u0633\u0628 \u0625\u0644\u0649 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633 \u0645\u0639\u0631\u0641\u0629 \u0627\u0644\u062d\u0642\u064a\u0642\u0629 \u0627\u0644\u0645\u062a\u0639\u0644\u0642\u0629 \u0628\u0627\u0644\u0646\u0638\u0631\u064a\u0629\u060c \u0644\u0643\u0646\u0647 \u0644\u0627 \u064a\u0642\u062f\u0645 \u062f\u0644\u064a\u0644\u0627\u064b \u0639\u0644\u0649 \u0623\u0646 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633 \u0642\u062f\u0645 \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0627\u0644\u0645\u0648\u062c\u0648\u062f \u0644\u062f\u0649 \u0625\u0642\u0644\u064a\u062f\u0633. <sup class=\"ref\"><a href=\"https:\/\/plato.stanford.edu\/entries\/pythagoras\/\" title=\"6|Pythagoras|Carl Huffman\u060c Stanford Encyclopedia of Philosophy|2023\" target=\"_blank\" rel=\"noopener\">[6]<\/a><\/sup><\/p>\n<h2>\u0625\u0642\u0644\u064a\u062f\u0633 \u0648\u0627\u0644\u0642\u0636\u064a\u0629 \u0627\u0644\u0633\u0627\u0628\u0639\u0629 \u0648\u0627\u0644\u0623\u0631\u0628\u0639\u0648\u0646<\/h2>\n<p>\u0623\u0642\u062f\u0645 \u0628\u0631\u0647\u0627\u0646 \u0628\u0631\u0647\u0627\u0646\u064a \u0628\u0627\u0642\u064d \u0648\u0645\u0641\u0635\u0644 \u0644\u0644\u0646\u0638\u0631\u064a\u0629 \u064a\u0638\u0647\u0631 \u0641\u064a \u00ab\u0627\u0644\u0639\u0646\u0627\u0635\u0631\u00bb \u0644\u0625\u0642\u0644\u064a\u062f\u0633\u060c \u0641\u064a \u0627\u0644\u0643\u062a\u0627\u0628 \u0627\u0644\u0623\u0648\u0644\u060c \u0627\u0644\u0642\u0636\u064a\u0629 47. \u0648\u0642\u062f \u0643\u062a\u0628 \u0625\u0642\u0644\u064a\u062f\u0633 \u00ab\u0627\u0644\u0639\u0646\u0627\u0635\u0631\u00bb \u0641\u064a \u0627\u0644\u0642\u0631\u0646 \u0627\u0644\u062b\u0627\u0644\u062b \u0642\u0628\u0644 \u0627\u0644\u0645\u064a\u0644\u0627\u062f\u060c \u0648\u0647\u0648 \u0639\u0645\u0644 \u064a\u062a\u0643\u0648\u0646 \u0645\u0646 \u062b\u0644\u0627\u062b\u0629 \u0639\u0634\u0631 \u0643\u062a\u0627\u0628\u0627\u064b \u0648\u064a\u0642\u062f\u0645 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0636\u0645\u0646 \u0646\u0638\u0627\u0645 \u0627\u0633\u062a\u062f\u0644\u0627\u0644\u064a \u064a\u0628\u062f\u0623 \u0628\u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a \u0648\u0627\u0644\u0645\u0633\u0644\u0645\u0627\u062a \u0648\u0627\u0644\u0645\u0628\u0627\u062f\u0626 \u062b\u0645 \u064a\u0628\u0646\u064a \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0628\u0631\u0627\u0647\u064a\u0646. <sup class=\"ref\"><a href=\"https:\/\/encyclopediaofmath.org\/wiki\/Elements-of-Euclid\" title=\"7|Elements of Euclid|Encyclopedia of Mathematics|2020\" target=\"_blank\" rel=\"noopener\">[7]<\/a><\/sup><\/p>\n<p>\u062a\u0646\u0635 \u0627\u0644\u0642\u0636\u064a\u0629 47\u060c \u0641\u064a \u062a\u0631\u062c\u0645\u0629 \u062d\u062f\u064a\u062b\u0629 \u0644\u0635\u064a\u0627\u063a\u0629 \u0625\u0642\u0644\u064a\u062f\u0633\u060c \u0639\u0644\u0649 \u0623\u0646 \u0627\u0644\u0645\u0631\u0628\u0639 \u0627\u0644\u0645\u0646\u0634\u0623 \u0639\u0644\u0649 \u0627\u0644\u0636\u0644\u0639 \u0627\u0644\u0645\u0642\u0627\u0628\u0644 \u0644\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0642\u0627\u0626\u0645\u0629 \u064a\u0633\u0627\u0648\u064a \u0645\u062c\u0645\u0648\u0639 \u0627\u0644\u0645\u0631\u0628\u0639\u064a\u0646 \u0627\u0644\u0645\u0646\u0634\u0623\u064a\u0646 \u0639\u0644\u0649 \u0627\u0644\u0636\u0644\u0639\u064a\u0646 \u0627\u0644\u0644\u0630\u064a\u0646 \u064a\u062d\u0635\u0631\u0627\u0646 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0642\u0627\u0626\u0645\u0629. <sup class=\"ref\"><a href=\"https:\/\/www.perseus.tufts.edu\/hopper\/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D47\" title=\"8|Euclid, Elements, Book I, Proposition 47|Thomas L. Heath\u060c Perseus Digital Library|1910\" target=\"_blank\" rel=\"noopener\">[8]<\/a><\/sup><\/p>\n<h2>\u0628\u0631\u0647\u0627\u0646 \u0625\u0642\u0644\u064a\u062f\u0633 \u0627\u0644\u0647\u0646\u062f\u0633\u064a<\/h2>\n<p>\u064a\u062e\u062a\u0644\u0641 \u0628\u0631\u0647\u0627\u0646 \u0625\u0642\u0644\u064a\u062f\u0633 \u0639\u0646 \u0627\u0644\u0635\u064a\u0627\u063a\u0629 \u0627\u0644\u062c\u0628\u0631\u064a\u0629 \u0627\u0644\u062a\u064a \u064a\u062a\u0639\u0644\u0645\u0647\u0627 \u0627\u0644\u0637\u0644\u0627\u0628 \u0627\u0644\u064a\u0648\u0645. \u0641\u0647\u0648 \u0644\u0627 \u064a\u0628\u062f\u0623 \u0628\u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 <i>a\u00b2+b\u00b2=c\u00b2<\/i>\u060c \u0648\u0625\u0646\u0645\u0627 \u064a\u0628\u0646\u064a \u0645\u0631\u0628\u0639\u0627\u062a \u0639\u0644\u0649 \u0623\u0636\u0644\u0627\u0639 \u0627\u0644\u0645\u062b\u0644\u062b \u062b\u0645 \u064a\u0633\u062a\u062e\u062f\u0645 \u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u062a\u0648\u0627\u0632\u064a \u0648\u062a\u0633\u0627\u0648\u064a \u0627\u0644\u0645\u062b\u0644\u062b\u0627\u062a \u0648\u0645\u0633\u0627\u062d\u0627\u062a \u0627\u0644\u0645\u062b\u0644\u062b\u0627\u062a \u0648\u0627\u0644\u0645\u0633\u062a\u0637\u064a\u0644\u0627\u062a \u0644\u0625\u062b\u0628\u0627\u062a \u0623\u0646 \u0645\u0633\u0627\u062d\u0629 \u0645\u0631\u0628\u0639 \u0627\u0644\u0648\u062a\u0631 \u062a\u0633\u0627\u0648\u064a \u0645\u062c\u0645\u0648\u0639 \u0645\u0633\u0627\u062d\u062a\u064a \u0627\u0644\u0645\u0631\u0628\u0639\u064a\u0646 \u0627\u0644\u0622\u062e\u0631\u064a\u0646.<\/p>\n<p>\u0641\u064a \u0627\u0644\u0628\u0646\u0627\u0621 \u0627\u0644\u0623\u0633\u0627\u0633\u064a \u0644\u0644\u0628\u0631\u0647\u0627\u0646\u060c \u064a\u0631\u0633\u0645 \u0625\u0642\u0644\u064a\u062f\u0633 \u0645\u062b\u0644\u062b\u0627\u064b \u0642\u0627\u0626\u0645\u0627\u064b\u060c \u062b\u0645 \u064a\u0646\u0634\u0626 \u0645\u0631\u0628\u0639\u0627\u064b \u0639\u0644\u0649 \u0627\u0644\u0648\u062a\u0631 \u0648\u0645\u0631\u0628\u0639\u064a\u0646 \u0639\u0644\u0649 \u0627\u0644\u0636\u0644\u0639\u064a\u0646 \u0627\u0644\u0642\u0627\u0626\u0645\u064a\u0646\u060c \u0648\u0628\u0639\u062f \u0630\u0644\u0643 \u064a\u0631\u0633\u0645 \u062e\u0637\u0648\u0637\u0627\u064b \u0645\u0633\u0627\u0639\u062f\u0629 \u062a\u0642\u0633\u0645 \u0645\u0631\u0628\u0639 \u0627\u0644\u0648\u062a\u0631 \u0625\u0644\u0649 \u0645\u0633\u062a\u0637\u064a\u0644\u064a\u0646. \u0648\u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062a\u0637\u0627\u0628\u0642 \u0645\u062b\u0644\u062b\u0627\u062a \u0648\u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u0645\u0633\u0627\u062d\u0627\u062a\u060c \u064a\u062b\u0628\u062a \u0623\u0646 \u0643\u0644 \u0645\u0633\u062a\u0637\u064a\u0644 \u0645\u0646 \u0627\u0644\u0645\u0633\u062a\u0637\u064a\u0644\u064a\u0646 \u064a\u0633\u0627\u0648\u064a \u0641\u064a \u0627\u0644\u0645\u0633\u0627\u062d\u0629 \u0623\u062d\u062f \u0627\u0644\u0645\u0631\u0628\u0639\u064a\u0646 \u0627\u0644\u0645\u0646\u0634\u0623\u064a\u0646 \u0639\u0644\u0649 \u0627\u0644\u0636\u0644\u0639\u064a\u0646 \u0627\u0644\u0642\u0627\u0626\u0645\u064a\u0646. \u0648\u0639\u0646\u062f \u062c\u0645\u0639 \u0627\u0644\u0646\u062a\u064a\u062c\u062a\u064a\u0646 \u064a\u062d\u0635\u0644 \u0639\u0644\u0649 \u0645\u0633\u0627\u0648\u0627\u0629 \u0645\u0631\u0628\u0639 \u0627\u0644\u0648\u062a\u0631 \u0628\u0645\u062c\u0645\u0648\u0639 \u0627\u0644\u0645\u0631\u0628\u0639\u064a\u0646. <sup class=\"ref\"><a href=\"https:\/\/sites.math.rutgers.edu\/~cherlin\/History\/WWW\/436-s99\/Papers1999\/lee.html\" title=\"9|Euclid&amp;apos;s proof of the Pythagorean Theorem|Rutgers University Mathematics|1999\" target=\"_blank\" rel=\"noopener\">[9]<\/a><\/sup><\/p>\n<h2>\u0623\u0647\u0645\u064a\u0629 \u0628\u0631\u0647\u0627\u0646 \u0625\u0642\u0644\u064a\u062f\u0633<\/h2>\n<p>\u062a\u0643\u0645\u0646 \u0623\u0647\u0645\u064a\u0629 \u0628\u0631\u0647\u0627\u0646 \u0625\u0642\u0644\u064a\u062f\u0633 \u0641\u064a \u0623\u0646\u0647 \u064a\u0645\u062b\u0644 \u0645\u062b\u0627\u0644\u0627\u064b \u0646\u0645\u0648\u0630\u062c\u064a\u0627\u064b \u0644\u0644\u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644\u064a\u0629 \u0641\u064a \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u0642\u062f\u064a\u0645\u0629. \u0641\u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0644\u0627 \u062a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629\u060c \u0648\u0625\u0646\u0645\u0627 \u062a\u0633\u062a\u0646\u062a\u062c \u0645\u0646 \u0646\u062a\u0627\u0626\u062c \u0647\u0646\u062f\u0633\u064a\u0629 \u0633\u0627\u0628\u0642\u0629 \u0636\u0645\u0646 \u0628\u0646\u0627\u0621 \u0645\u0646\u0637\u0642\u064a \u0645\u062a\u0633\u0644\u0633\u0644.<\/p>\n<p>\u0648\u062a\u0648\u0636\u062d \u0627\u0644\u062f\u0631\u0627\u0633\u0627\u062a \u0627\u0644\u062a\u0627\u0631\u064a\u062e\u064a\u0629 \u0644\u0628\u0631\u0647\u0627\u0646 \u0625\u0642\u0644\u064a\u062f\u0633 \u0623\u0646\u0647 \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0639\u062f\u062f \u0645\u0646 \u0627\u0644\u0642\u0636\u0627\u064a\u0627 \u0627\u0644\u0633\u0627\u0628\u0642\u0629 \u0641\u064a \u0627\u0644\u0643\u062a\u0627\u0628 \u0627\u0644\u0623\u0648\u0644\u060c \u0645\u0646 \u0628\u064a\u0646\u0647\u0627 \u0625\u0646\u0634\u0627\u0621 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a\u060c \u0648\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0645\u062b\u0644\u062b\u0627\u062a\u060c \u0648\u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u062a\u0648\u0627\u0632\u064a\u060c \u0648\u0646\u062a\u0627\u0626\u062c \u062a\u062a\u0639\u0644\u0642 \u0628\u062a\u0633\u0627\u0648\u064a \u0627\u0644\u0645\u0633\u0627\u062d\u0627\u062a. \u0648\u0644\u0630\u0644\u0643 \u0641\u0625\u0646 \u0627\u0644\u0642\u0636\u064a\u0629 47 \u0644\u064a\u0633\u062a \u0646\u062a\u064a\u062c\u0629 \u0645\u0639\u0632\u0648\u0644\u0629\u060c \u0628\u0644 \u062e\u0627\u062a\u0645\u0629 \u0644\u0633\u0644\u0633\u0644\u0629 \u0645\u0646 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u062a\u064a \u0628\u0646\u0627\u0647\u0627 \u0625\u0642\u0644\u064a\u062f\u0633 \u0642\u0628\u0644\u0647\u0627. <sup class=\"ref\"><a href=\"https:\/\/www.perseus.tufts.edu\/hopper\/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D47\" title=\"10|Euclid, Elements, Book I, Proposition 47|Thomas L. Heath\u060c Perseus Digital Library|1910\" target=\"_blank\" rel=\"noopener\">[10]<\/a><\/sup><\/p>\n<h2>\u0627\u0644\u0639\u0643\u0633 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a<\/h2>\n<p>\u0644\u0644\u0646\u0638\u0631\u064a\u0629 \u0646\u062a\u064a\u062c\u0629 \u0639\u0643\u0633\u064a\u0629 \u0645\u0647\u0645\u0629. \u0641\u0625\u0630\u0627 \u0643\u0627\u0646 \u0644\u062f\u064a\u0646\u0627 \u0645\u062b\u0644\u062b \u0623\u0637\u0648\u0627\u0644 \u0623\u0636\u0644\u0627\u0639\u0647 <i>a<\/i> \u0648<i>b<\/i> \u0648<i>c<\/i>\u060c \u0648\u0643\u0627\u0646 <i>c<\/i> \u0647\u0648 \u0623\u0637\u0648\u0644 \u0627\u0644\u0623\u0636\u0644\u0627\u0639\u060c \u0648\u062a\u062d\u0642\u0642:<\/p>\n<p><i>a\u00b2+b\u00b2=c\u00b2<\/i><\/p>\n<p>\u0641\u0625\u0646 \u0627\u0644\u0645\u062b\u0644\u062b \u064a\u0643\u0648\u0646 \u0642\u0627\u0626\u0645\u0627\u064b \u0648\u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0645\u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u0636\u0644\u0639 <i>c<\/i> \u062a\u0633\u0627\u0648\u064a 90 \u062f\u0631\u062c\u0629. \u0648\u062a\u0638\u0647\u0631 \u0647\u0630\u0647 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0641\u064a \u00ab\u0627\u0644\u0639\u0646\u0627\u0635\u0631\u00bb \u0628\u0648\u0635\u0641\u0647\u0627 \u0627\u0644\u0642\u0636\u064a\u0629 48\u060c \u0623\u064a \u0645\u0628\u0627\u0634\u0631\u0629 \u0628\u0639\u062f \u0627\u0644\u0642\u0636\u064a\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629. <sup class=\"ref\"><a href=\"https:\/\/www.ms.uky.edu\/~corso\/teaching\/math330\/02-24-06.html\" title=\"11|History of Mathematics: Proposition 47 and Proposition 48|University of Kentucky|2006\" target=\"_blank\" rel=\"noopener\">[11]<\/a><\/sup><\/p>\n<p>\u0648\u0627\u0644\u0641\u0631\u0642 \u0627\u0644\u0645\u0646\u0637\u0642\u064a \u0628\u064a\u0646 \u0627\u0644\u0646\u0638\u0631\u064a\u062a\u064a\u0646 \u0645\u0647\u0645: \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0635\u0644\u064a\u0629 \u062a\u0628\u062f\u0623 \u0645\u0646 \u062d\u0642\u064a\u0642\u0629 \u0623\u0646 \u0627\u0644\u0645\u062b\u0644\u062b \u0642\u0627\u0626\u0645 \u0648\u062a\u0633\u062a\u0646\u062a\u062c \u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u0623\u0637\u0648\u0627\u0644\u060c \u0623\u0645\u0627 \u0627\u0644\u0639\u0643\u0633 \u0641\u064a\u0628\u062f\u0623 \u0645\u0646 \u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u0623\u0637\u0648\u0627\u0644 \u0648\u064a\u0633\u062a\u0646\u062a\u062c \u0623\u0646 \u0627\u0644\u0645\u062b\u0644\u062b \u0642\u0627\u0626\u0645.<\/p>\n<h2>\u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0648\u062a\u0631<\/h2>\n<p>\u0625\u0630\u0627 \u0643\u0627\u0646 \u0637\u0648\u0644\u0627 \u0627\u0644\u0636\u0644\u0639\u064a\u0646 \u0627\u0644\u0642\u0627\u0626\u0645\u064a\u0646 \u0645\u0639\u0631\u0648\u0641\u064a\u0646\u060c \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0644\u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0648\u062a\u0631. \u0641\u0625\u0630\u0627 \u0643\u0627\u0646 <i>a=6<\/i> \u0648<i>b=8<\/i>\u060c \u0641\u0625\u0646:<\/p>\n<p><i>c\u00b2=6\u00b2+8\u00b2=36+64=100<\/i><\/p>\n<p>\u0648\u0645\u0646 \u062b\u0645:<\/p>\n<p><i>c=10<\/i><\/p>\n<p>\u0648\u0628\u0630\u0644\u0643 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0645\u062b\u0644\u062b \u0642\u0627\u0626\u0645 \u0645\u0646 \u0627\u0644\u0646\u0648\u0639 6\u20138\u201310\u060c \u0648\u0647\u0648 \u0645\u062c\u0631\u062f \u0645\u0636\u0627\u0639\u0641 \u0644\u0644\u062b\u0644\u0627\u062b\u064a\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 3\u20134\u20135.<\/p>\n<h2>\u0625\u064a\u062c\u0627\u062f \u0636\u0644\u0639 \u0642\u0627\u0626\u0645 \u0645\u062c\u0647\u0648\u0644<\/h2>\n<p>\u064a\u0645\u0643\u0646 \u0623\u064a\u0636\u0627\u064b \u0625\u0639\u0627\u062f\u0629 \u062a\u0631\u062a\u064a\u0628 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0644\u0625\u064a\u062c\u0627\u062f \u0623\u062d\u062f \u0627\u0644\u0636\u0644\u0639\u064a\u0646 \u0627\u0644\u0642\u0627\u0626\u0645\u064a\u0646. \u0641\u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0648\u062a\u0631 <i>c<\/i> \u0648\u0627\u0644\u0636\u0644\u0639 \u0627\u0644\u0622\u062e\u0631 <i>b<\/i> \u0645\u0639\u0631\u0648\u0641\u064a\u0646\u060c \u0641\u0625\u0646:<\/p>\n<p><i>a\u00b2=c\u00b2-b\u00b2<\/i><\/p>\n<p>\u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p><i>a=\u221a(c\u00b2-b\u00b2)<\/i><\/p>\n<p>\u0641\u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0648\u062a\u0631 13 \u0648\u0627\u0644\u0636\u0644\u0639 \u0627\u0644\u0622\u062e\u0631 5\u060c \u0646\u062d\u0635\u0644 \u0639\u0644\u0649:<\/p>\n<p><i>a=\u221a(13\u00b2-5\u00b2)=\u221a(169-25)=\u221a144=12<\/i><\/p>\n<p>\u0641\u062a\u0638\u0647\u0631 \u0627\u0644\u062b\u0644\u0627\u062b\u064a\u0629 5\u201312\u201313.<\/p>\n<h2>\u0627\u0644\u062b\u0644\u0627\u062b\u064a\u0627\u062a \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629<\/h2>\n<p>\u0627\u0644\u062b\u0644\u0627\u062b\u064a\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629 \u0647\u064a \u062b\u0644\u0627\u062b\u0629 \u0623\u0639\u062f\u0627\u062f \u0635\u062d\u064a\u062d\u0629 \u0645\u0648\u062c\u0628\u0629 <i>a,b,c<\/i> \u062a\u062d\u0642\u0642 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 <i>a\u00b2+b\u00b2=c\u00b2<\/i>. \u0648\u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062b\u0644\u0627\u062b\u0629 \u0644\u0627 \u062a\u0634\u062a\u0631\u0643 \u0641\u064a \u0639\u0627\u0645\u0644 \u0635\u062d\u064a\u062d \u0623\u0643\u0628\u0631 \u0645\u0646 1\u060c \u062a\u0633\u0645\u0649 \u0627\u0644\u062b\u0644\u0627\u062b\u064a\u0629 \u00ab\u0623\u0648\u0644\u064a\u0629\u00bb \u0623\u0648 \u00ab\u0628\u062f\u0627\u0626\u064a\u0629\u00bb.<\/p>\n<p>\u0645\u0646 \u0623\u0634\u0647\u0631 \u0627\u0644\u062b\u0644\u0627\u062b\u064a\u0627\u062a \u0627\u0644\u0628\u062f\u0627\u0626\u064a\u0629 3\u20134\u20135 \u06485\u201312\u201313 \u06487\u201324\u201325 \u06488\u201315\u201317. \u0648\u0625\u0630\u0627 \u0636\u0631\u0628\u0646\u0627 \u0623\u0637\u0631\u0627\u0641 \u0623\u064a \u062b\u0644\u0627\u062b\u064a\u0629 \u0641\u064a \u0639\u062f\u062f \u0635\u062d\u064a\u062d \u0645\u0648\u062c\u0628 <i>k<\/i>\u060c \u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u062b\u0644\u0627\u062b\u064a\u0629 \u0623\u062e\u0631\u0649\u061b \u0641\u0625\u0630\u0627 \u0643\u0627\u0646\u062a <i>(a,b,c)<\/i> \u062b\u0644\u0627\u062b\u064a\u0629 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629\u060c \u0641\u0625\u0646 <i>(ka,kb,kc)<\/i> \u062a\u062d\u0642\u0642 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0646\u0641\u0633\u0647\u0627.<\/p>\n<h2>\u062a\u0648\u0644\u064a\u062f \u0627\u0644\u062b\u0644\u0627\u062b\u064a\u0627\u062a \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629<\/h2>\n<p>\u064a\u0645\u0643\u0646 \u062a\u0648\u0644\u064a\u062f \u0639\u062f\u062f \u0643\u0628\u064a\u0631 \u0645\u0646 \u0627\u0644\u062b\u0644\u0627\u062b\u064a\u0627\u062a \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a\u0629:<\/p>\n<p><i>a=m\u00b2-n\u00b2<\/i><\/p>\n<p><i>b=2mn<\/i><\/p>\n<p><i>c=m\u00b2+n\u00b2<\/i><\/p>\n<p>\u062d\u064a\u062b <i>m&gt;n&gt;0<\/i> \u0639\u062f\u062f\u0627\u0646 \u0635\u062d\u064a\u062d\u0627\u0646. \u0648\u0628\u0627\u0644\u062a\u0639\u0648\u064a\u0636 \u0646\u062c\u062f:<\/p>\n<p><i>(m\u00b2-n\u00b2)\u00b2+(2mn)\u00b2=(m\u00b2+n\u00b2)\u00b2<\/i><\/p>\n<p>\u0648\u0628\u0627\u0644\u062a\u0648\u0633\u064a\u0639 \u0627\u0644\u062c\u0628\u0631\u064a \u0644\u0644\u0637\u0631\u0641 \u0627\u0644\u0623\u064a\u0633\u0631 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649:<\/p>\n<p><i>m\u2074-2m\u00b2n\u00b2+n\u2074+4m\u00b2n\u00b2=m\u2074+2m\u00b2n\u00b2+n\u2074<\/i><\/p>\n<p>\u0648\u0647\u0630\u0627 \u064a\u0633\u0627\u0648\u064a \u0628\u0627\u0644\u0641\u0639\u0644:<\/p>\n<p><i>(m\u00b2+n\u00b2)\u00b2<\/i><\/p>\n<p>\u0648\u0625\u0630\u0627 \u0643\u0627\u0646 <i>m<\/i> \u0648<i>n<\/i> \u0645\u062a\u0628\u0627\u064a\u0646\u064a\u0646 \u0623\u0648\u0644\u064a\u0627\u064b\u060c \u0648\u0623\u062d\u062f\u0647\u0645\u0627 \u0632\u0648\u062c\u064a \u0648\u0627\u0644\u0622\u062e\u0631 \u0641\u0631\u062f\u064a\u060c \u0641\u0625\u0646 \u0627\u0644\u0635\u064a\u063a\u0629 \u062a\u0639\u0637\u064a \u062b\u0644\u0627\u062b\u064a\u0629 \u0628\u062f\u0627\u0626\u064a\u0629. \u0648\u062a\u0639\u062f \u0647\u0630\u0647 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0645\u0646 \u0623\u0647\u0645 \u0627\u0644\u0631\u0648\u0627\u0628\u0637 \u0628\u064a\u0646 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0648\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f.<\/p>\n<h2>\u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0648\u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0627\u0644\u0625\u0642\u0644\u064a\u062f\u064a\u0629<\/h2>\n<p>\u062a\u062a\u062c\u0627\u0648\u0632 \u0623\u0647\u0645\u064a\u0629 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0645\u062b\u0644\u062b\u0627\u062a \u0627\u0644\u0642\u0627\u0626\u0645\u0629 \u0625\u0644\u0649 \u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0641\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u0649. \u0641\u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0646\u0642\u0637\u062a\u0627\u0646 \u0641\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a \u0647\u0645\u0627 <i>(x\u2081,y\u2081)<\/i> \u0648<i>(x\u2082,y\u2082)<\/i>\u060c \u0641\u0625\u0646 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646\u0647\u0645\u0627 \u062a\u0639\u0637\u0649 \u0628\u0627\u0644\u0639\u0644\u0627\u0642\u0629:<\/p>\n<p><i>d=\u221a((x\u2082-x\u2081)\u00b2+(y\u2082-y\u2081)\u00b2)<\/i><\/p>\n<p>\u0648\u0647\u0630\u0647 \u0627\u0644\u0635\u064a\u063a\u0629 \u0644\u064a\u0633\u062a \u0633\u0648\u0649 \u062a\u0637\u0628\u064a\u0642 \u0645\u0628\u0627\u0634\u0631 \u0644\u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629. \u0641\u0627\u0644\u0641\u0631\u0642 \u0627\u0644\u0623\u0641\u0642\u064a \u0628\u064a\u0646 \u0627\u0644\u0646\u0642\u0637\u062a\u064a\u0646 \u064a\u0645\u062b\u0644 \u0623\u062d\u062f \u0636\u0644\u0639\u064a \u0645\u062b\u0644\u062b \u0642\u0627\u0626\u0645\u060c \u0648\u0627\u0644\u0641\u0631\u0642 \u0627\u0644\u0631\u0623\u0633\u064a \u064a\u0645\u062b\u0644 \u0627\u0644\u0636\u0644\u0639 \u0627\u0644\u0622\u062e\u0631\u060c \u0648\u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0627\u0644\u0645\u0628\u0627\u0634\u0631\u0629 \u0628\u064a\u0646 \u0627\u0644\u0646\u0642\u0637\u062a\u064a\u0646 \u062a\u0645\u062b\u0644 \u0627\u0644\u0648\u062a\u0631.<\/p>\n<h2>\u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0641\u064a \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629<\/h2>\n<p>\u0623\u0635\u0628\u062d\u062a \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629 \u0623\u0633\u0627\u0633\u0627\u064b \u0645\u0647\u0645\u0627\u064b \u0641\u064a \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629. \u0641\u0645\u0646 \u062e\u0644\u0627\u0644\u0647\u0627 \u064a\u0645\u0643\u0646 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0627\u062a \u0628\u064a\u0646 \u0627\u0644\u0646\u0642\u0627\u0637\u060c \u0648\u0623\u0637\u0648\u0627\u0644 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a\u060c \u0648\u0623\u0646\u0635\u0627\u0641 \u0623\u0642\u0637\u0627\u0631 \u0627\u0644\u062f\u0648\u0627\u0626\u0631\u060c \u0648\u0627\u0644\u0645\u0633\u0627\u0641\u0627\u062a \u0641\u064a \u0627\u0644\u0623\u0634\u0643\u0627\u0644 \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a\u0629.<\/p>\n<p>\u0643\u0645\u0627 \u064a\u0645\u0643\u0646 \u062a\u0639\u0645\u064a\u0645 \u0641\u0643\u0631\u0629 \u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0645\u0631\u0643\u0628\u0627\u062a \u0639\u0644\u0649 \u0627\u0644\u0641\u0636\u0627\u0621 \u062b\u0644\u0627\u062b\u064a \u0627\u0644\u0623\u0628\u0639\u0627\u062f. \u0641\u0625\u0630\u0627 \u0643\u0627\u0646 \u0644\u062f\u064a\u0646\u0627 \u0645\u062a\u062c\u0647 \u0645\u0631\u0643\u0628\u0627\u062a\u0647 <i>(x,y,z)<\/i>\u060c \u0641\u0625\u0646 \u0637\u0648\u0644\u0647 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 \u0627\u0644\u0625\u0642\u0644\u064a\u062f\u064a \u064a\u0639\u0637\u0649 \u0628\u0627\u0644\u0639\u0644\u0627\u0642\u0629:<\/p>\n<p><i>||v||=\u221a(x\u00b2+y\u00b2+z\u00b2)<\/i><\/p>\n<p>\u0648\u0647\u064a \u0627\u0645\u062a\u062f\u0627\u062f \u0637\u0628\u064a\u0639\u064a \u0644\u0644\u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629 \u0645\u0646 \u0628\u0639\u062f\u064a\u0646 \u0625\u0644\u0649 \u062b\u0644\u0627\u062b\u0629 \u0623\u0628\u0639\u0627\u062f.<\/p>\n<h2>\u0627\u0644\u062a\u0639\u0645\u064a\u0645 \u0625\u0644\u0649 \u0623\u0628\u0639\u0627\u062f \u0623\u0639\u0644\u0649<\/h2>\n<p>\u064a\u0645\u0643\u0646 \u062a\u0639\u0645\u064a\u0645 \u0627\u0644\u0641\u0643\u0631\u0629 \u0625\u0644\u0649 \u0641\u0636\u0627\u0621 \u0625\u0642\u0644\u064a\u062f\u064a \u0630\u064a <i>n<\/i> \u0623\u0628\u0639\u0627\u062f. \u0641\u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0645\u062a\u062c\u0647:<\/p>\n<p><i>v=(x\u2081,x\u2082,&#8230;,x\u2099)<\/i><\/p>\n<p>\u0641\u0625\u0646 \u0645\u0639\u064a\u0627\u0631\u064f\u0647 \u0627\u0644\u0625\u0642\u0644\u064a\u062f\u064a \u064a\u0633\u0627\u0648\u064a:<\/p>\n<p><i>||v||=\u221a(x\u2081\u00b2+x\u2082\u00b2+&#8230;+x\u2099\u00b2)<\/i><\/p>\n<p>\u0648\u062a\u0638\u0647\u0631 \u0647\u0646\u0627 \u0627\u0644\u0628\u0646\u064a\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629 \u0628\u0635\u0648\u0631\u0629 \u0648\u0627\u0636\u062d\u0629: \u0645\u0631\u0628\u0639 \u0637\u0648\u0644 \u0627\u0644\u0645\u062a\u062c\u0647 \u064a\u0633\u0627\u0648\u064a \u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u0627\u062a \u0645\u0631\u0643\u0628\u0627\u062a\u0647 \u0627\u0644\u0645\u062a\u0639\u0627\u0645\u062f\u0629. \u0648\u0647\u0630\u0647 \u0627\u0644\u0641\u0643\u0631\u0629 \u0623\u0633\u0627\u0633\u064a\u0629 \u0641\u064a \u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u062e\u0637\u064a \u0648\u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629 \u0648\u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u062a\u0637\u0628\u064a\u0642\u064a\u0629.<\/p>\n<h2>\u0627\u0644\u0627\u0631\u062a\u0628\u0627\u0637 \u0628\u0627\u0644\u062c\u062f\u0627\u0621 \u0627\u0644\u062f\u0627\u062e\u0644\u064a<\/h2>\n<p>\u0641\u064a \u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u062e\u0637\u064a\u060c \u064a\u0645\u0643\u0646 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0628\u0635\u0648\u0631\u0629 \u0623\u0643\u062b\u0631 \u062a\u062c\u0631\u064a\u062f\u0627\u064b \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062c\u062f\u0627\u0621 \u0627\u0644\u062f\u0627\u062e\u0644\u064a. \u0641\u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u0646 <i>u<\/i> \u0648<i>v<\/i> \u0645\u062a\u0639\u0627\u0645\u062f\u064a\u0646\u060c \u0641\u0625\u0646:<\/p>\n<p><i>||u+v||\u00b2=||u||\u00b2+||v||\u00b2<\/i><\/p>\n<p>\u0648\u0627\u0644\u0633\u0628\u0628 \u0647\u0648 \u0623\u0646 \u0627\u0644\u062c\u062f\u0627\u0621 \u0627\u0644\u062f\u0627\u062e\u0644\u064a \u0628\u064a\u0646 \u0627\u0644\u0645\u062a\u062c\u0647\u064a\u0646 \u0627\u0644\u0645\u062a\u0639\u0627\u0645\u062f\u064a\u0646 \u064a\u0633\u0627\u0648\u064a \u0635\u0641\u0631\u0627\u064b. \u0648\u0628\u0630\u0644\u0643 \u062a\u0635\u0628\u062d \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629 \u062d\u0627\u0644\u0629 \u062e\u0627\u0635\u0629 \u0645\u0646 \u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0641\u0636\u0627\u0621\u0627\u062a \u0630\u0627\u062a \u0627\u0644\u062c\u062f\u0627\u0621 \u0627\u0644\u062f\u0627\u062e\u0644\u064a\u060c \u0644\u0627 \u0645\u062c\u0631\u062f \u0642\u0627\u0639\u062f\u0629 \u0647\u0646\u062f\u0633\u064a\u0629 \u0644\u0644\u0645\u062b\u0644\u062b\u0627\u062a \u0641\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u0649.<\/p>\n<h2>\u0646\u0638\u0631\u064a\u0629 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621<\/h2>\n<p>\u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0645\u0631\u062a\u064a\u0646 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0646\u0642\u0637\u062a\u064a\u0646 \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621 \u062b\u0644\u0627\u062b\u064a \u0627\u0644\u0623\u0628\u0639\u0627\u062f. \u0623\u0648\u0644\u0627\u064b \u0646\u062d\u0633\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0627\u0644\u0623\u0641\u0642\u064a\u0629 \u0641\u064a \u0645\u0633\u062a\u0648\u0649 \u0645\u0639\u064a\u0646\u060c \u062b\u0645 \u0646\u0637\u0628\u0642 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0645\u0631\u0629 \u062b\u0627\u0646\u064a\u0629 \u0645\u0639 \u0627\u0644\u0641\u0631\u0642 \u0627\u0644\u0631\u0623\u0633\u064a. \u0648\u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0647\u064a \u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u062b\u0644\u0627\u062b\u064a\u0629 \u0627\u0644\u0623\u0628\u0639\u0627\u062f:<\/p>\n<p><i>d=\u221a((x\u2082-x\u2081)\u00b2+(y\u2082-y\u2081)\u00b2+(z\u2082-z\u2081)\u00b2)<\/i><\/p>\n<p>\u0648\u0647\u0630\u0627 \u0627\u0644\u062a\u0637\u0628\u064a\u0642 \u064a\u0648\u0636\u062d \u0643\u064a\u0641 \u062a\u062a\u062d\u0648\u0644 \u0646\u062a\u064a\u062c\u0629 \u0647\u0646\u062f\u0633\u064a\u0629 \u0642\u062f\u064a\u0645\u0629 \u0625\u0644\u0649 \u0623\u062f\u0627\u0629 \u0623\u0633\u0627\u0633\u064a\u0629 \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u062b\u0629.<\/p>\n<h2>\u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0648\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062b\u0644\u062b\u0627\u062a<\/h2>\n<p>\u062a\u0631\u062a\u0628\u0637 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0623\u064a\u0636\u0627\u064b \u0628\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062b\u0644\u062b\u0627\u062a. \u0641\u0641\u064a \u0627\u0644\u0645\u062b\u0644\u062b \u0627\u0644\u0642\u0627\u0626\u0645\u060c \u064a\u0645\u0643\u0646 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0645\u062b\u0644 \u0627\u0644\u062c\u064a\u0628 \u0648\u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645 \u0648\u0627\u0644\u0638\u0644 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0646\u0633\u0628 \u0627\u0644\u0623\u0636\u0644\u0627\u0639. \u0648\u062a\u0638\u0647\u0631 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629 \u0628\u0635\u0648\u0631\u0629 \u0645\u0628\u0627\u0634\u0631\u0629 \u0641\u064a \u0627\u0644\u0647\u0648\u064a\u0629:<\/p>\n<p><i>sin\u00b2\u03b8+cos\u00b2\u03b8=1<\/i><\/p>\n<p>\u0641\u0625\u0630\u0627 \u0643\u0627\u0646 \u0646\u0635\u0641 \u0642\u0637\u0631 \u062f\u0627\u0626\u0631\u0629 \u0627\u0644\u0648\u062d\u062f\u0629 \u064a\u0633\u0627\u0648\u064a 1\u060c \u0641\u0625\u0646 \u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u0646\u0642\u0637\u0629 \u0639\u0644\u064a\u0647\u0627 \u064a\u0645\u0643\u0646 \u0643\u062a\u0627\u0628\u062a\u0647\u0627 \u0641\u064a \u0635\u0648\u0631\u0629 <i>(cos\u03b8,sin\u03b8)<\/i>\u060c \u0648\u0628\u0645\u0627 \u0623\u0646 \u0627\u0644\u0646\u0642\u0637\u0629 \u062a\u0642\u0639 \u0639\u0644\u0649 \u062f\u0627\u0626\u0631\u0629 \u0627\u0644\u0648\u062d\u062f\u0629\u060c \u0641\u0625\u0646:<\/p>\n<p><i>cos\u00b2\u03b8+sin\u00b2\u03b8=1<\/i><\/p>\n<p>\u0648\u0647\u064a \u0635\u064a\u063a\u0629 \u0645\u062b\u0644\u062b\u064a\u0629 \u0644\u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629.<\/p>\n<h2>\u0646\u0638\u0631\u064a\u0629 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633 \u0648\u0627\u0644\u062f\u0648\u0627\u0626\u0631<\/h2>\n<p>\u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0644\u0625\u062b\u0628\u0627\u062a \u0645\u062c\u0645\u0648\u0639\u0629 \u0648\u0627\u0633\u0639\u0629 \u0645\u0646 \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u0645\u062a\u0639\u0644\u0642\u0629 \u0628\u0627\u0644\u062f\u0648\u0627\u0626\u0631 \u0648\u0627\u0644\u0623\u0648\u062a\u0627\u0631 \u0648\u0627\u0644\u0645\u0645\u0627\u0633\u0651\u0627\u062a \u0648\u0627\u0644\u0645\u0633\u0627\u0641\u0627\u062a \u0645\u0646 \u0627\u0644\u0645\u0631\u0627\u0643\u0632. \u0641\u0625\u0630\u0627 \u0643\u0627\u0646 \u0646\u0635\u0641 \u0642\u0637\u0631 \u062f\u0627\u0626\u0631\u0629 \u0645\u0639\u0644\u0648\u0645\u0627\u064b \u0648\u0628\u0639\u062f \u0646\u0642\u0637\u0629 \u0639\u0646 \u0627\u0644\u0645\u0631\u0643\u0632 \u0645\u0639\u0644\u0648\u0645\u0627\u064b\u060c \u0641\u0642\u062f \u062a\u062a\u062d\u0648\u0644 \u0645\u0633\u0623\u0644\u0629 \u062a\u062d\u062f\u064a\u062f \u0637\u0648\u0644 \u0645\u0642\u0637\u0639 \u0623\u0648 \u0648\u062a\u0631 \u0625\u0644\u0649 \u0645\u0633\u0623\u0644\u0629 \u0645\u062b\u0644\u062b \u0642\u0627\u0626\u0645.<\/p>\n<p>\u0648\u0644\u0647\u0630\u0627 \u0641\u0625\u0646 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u062a\u0638\u0647\u0631 \u0628\u0635\u0648\u0631\u0629 \u0645\u062a\u0643\u0631\u0631\u0629 \u0641\u064a \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u0625\u0642\u0644\u064a\u062f\u064a\u0629\u060c \u062d\u062a\u0649 \u0639\u0646\u062f\u0645\u0627 \u0644\u0627 \u064a\u0643\u0648\u0646 \u0627\u0644\u0645\u062b\u0644\u062b \u0627\u0644\u0642\u0627\u0626\u0645 \u0647\u0648 \u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0638\u0627\u0647\u0631 \u0641\u064a \u0627\u0644\u0634\u0643\u0644 \u0627\u0644\u0623\u0648\u0644 \u0644\u0644\u0645\u0633\u0623\u0644\u0629.<\/p>\n<h2>\u0627\u0644\u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629<\/h2>\n<p>\u062a\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629 \u0641\u064a \u062d\u0633\u0627\u0628 \u0627\u0644\u0623\u0637\u0648\u0627\u0644 \u0648\u0627\u0644\u0645\u0633\u0627\u0641\u0627\u062a \u0641\u064a \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u0645\u062f\u0646\u064a\u0629 \u0648\u0627\u0644\u0645\u0639\u0645\u0627\u0631\u064a\u0629 \u0648\u0627\u0644\u0645\u0633\u0627\u062d\u0629 \u0648\u0627\u0644\u0645\u064a\u0643\u0627\u0646\u064a\u0643\u0627 \u0648\u0627\u0644\u0631\u0633\u0648\u0645 \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u064a\u0629. \u0641\u0639\u0646\u062f\u0645\u0627 \u062a\u062a\u0639\u0627\u0645\u062f \u0645\u0643\u0648\u0646\u0627\u062a \u0627\u0644\u0645\u0633\u0627\u0641\u0629\u060c \u064a\u0645\u0643\u0646 \u062f\u0645\u062c\u0647\u0627 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u0627\u062a\u0647\u0627 \u0644\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0627\u0644\u0645\u0628\u0627\u0634\u0631\u0629.<\/p>\n<p>\u0648\u0641\u064a \u0623\u0639\u0645\u0627\u0644 \u0627\u0644\u0645\u0633\u0627\u062d\u0629\u060c \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647\u0627 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0627\u062a \u0628\u064a\u0646 \u0627\u0644\u0646\u0642\u0627\u0637 \u0639\u0646\u062f\u0645\u0627 \u062a\u0643\u0648\u0646 \u0627\u0644\u0625\u0632\u0627\u062d\u0627\u062a \u0627\u0644\u0623\u0641\u0642\u064a\u0629 \u0648\u0627\u0644\u0631\u0623\u0633\u064a\u0629 \u0645\u0639\u0631\u0648\u0641\u0629. \u0648\u0641\u064a \u0627\u0644\u0647\u0646\u062f\u0633\u0629\u060c \u062a\u0633\u0627\u0639\u062f \u0639\u0644\u0649 \u062a\u062d\u062f\u064a\u062f \u0623\u0637\u0648\u0627\u0644 \u0644\u0627 \u064a\u0645\u0643\u0646 \u0642\u064a\u0627\u0633\u0647\u0627 \u0645\u0628\u0627\u0634\u0631\u0629 \u0639\u0646\u062f\u0645\u0627 \u064a\u0645\u0643\u0646 \u062a\u062d\u0648\u064a\u0644 \u0627\u0644\u0645\u0633\u0623\u0644\u0629 \u0625\u0644\u0649 \u0645\u062b\u0644\u062b \u0642\u0627\u0626\u0645.<\/p>\n<h2>\u0627\u0644\u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0641\u064a \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621<\/h2>\n<p>\u062a\u0638\u0647\u0631 \u0627\u0644\u0628\u0646\u064a\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629 \u0641\u064a \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 \u0639\u0646\u062f\u0645\u0627 \u062a\u0643\u0648\u0646 \u0627\u0644\u0643\u0645\u064a\u0627\u062a \u0627\u0644\u0645\u062a\u0639\u0627\u0645\u062f\u0629 \u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u062f\u0645\u062c \u0639\u0628\u0631 \u062c\u0645\u0639 \u0645\u0631\u0628\u0639\u0627\u062a \u0645\u0631\u0643\u0628\u0627\u062a\u0647\u0627. \u0648\u0645\u0646 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0627\u0644\u0628\u0633\u064a\u0637\u0629 \u0645\u0642\u062f\u0627\u0631 \u0645\u062a\u062c\u0647 \u0627\u0644\u0633\u0631\u0639\u0629 \u0639\u0646\u062f\u0645\u0627 \u062a\u0643\u0648\u0646 \u0644\u0647 \u0645\u0631\u0643\u0628\u0627\u062a \u0645\u062a\u0639\u0627\u0645\u062f\u0629.<\/p>\n<p>\u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u062c\u0633\u0645 \u064a\u062a\u062d\u0631\u0643 \u0628\u0645\u0631\u0643\u0628\u0629 \u0623\u0641\u0642\u064a\u0629 <i>v\u2093<\/i> \u0648\u0645\u0631\u0643\u0628\u0629 \u0631\u0623\u0633\u064a\u0629 <i>v\u1d67<\/i> \u0645\u062a\u0639\u0627\u0645\u062f\u062a\u064a\u0646\u060c \u0641\u0625\u0646 \u0645\u0642\u062f\u0627\u0631 \u0627\u0644\u0633\u0631\u0639\u0629 \u064a\u0633\u0627\u0648\u064a:<\/p>\n<p><i>v=\u221a(v\u2093\u00b2+v\u1d67\u00b2)<\/i><\/p>\n<p>\u0648\u0647\u0630\u0627 \u062a\u0637\u0628\u064a\u0642 \u0645\u0628\u0627\u0634\u0631 \u0644\u0644\u0628\u0646\u064a\u0629 \u0646\u0641\u0633\u0647\u0627 \u0627\u0644\u062a\u064a \u062a\u0635\u0641 \u0648\u062a\u0631 \u0627\u0644\u0645\u062b\u0644\u062b \u0627\u0644\u0642\u0627\u0626\u0645.<\/p>\n<h2>\u0627\u0644\u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0641\u064a \u0639\u0644\u0648\u0645 \u0627\u0644\u062d\u0627\u0633\u0648\u0628<\/h2>\n<p>\u062a\u0638\u0647\u0631 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0627\u0644\u0625\u0642\u0644\u064a\u062f\u064a\u0629 \u0641\u064a \u0639\u0644\u0648\u0645 \u0627\u0644\u062d\u0627\u0633\u0648\u0628 \u0641\u064a \u0645\u0639\u0627\u0644\u062c\u0629 \u0627\u0644\u0635\u0648\u0631 \u0648\u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u064a\u0629 \u0648\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0648\u0627\u0644\u0631\u0633\u0648\u0645 \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u064a\u0629. \u0641\u0639\u0646\u062f\u0645\u0627 \u062a\u0645\u062b\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0646\u0642\u0627\u0637\u0627\u064b \u0641\u064a \u0641\u0636\u0627\u0621 \u0625\u062d\u062f\u0627\u062b\u064a\u060c \u064a\u0645\u0643\u0646 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0627\u0644\u0625\u0642\u0644\u064a\u062f\u064a\u0629 \u0628\u064a\u0646\u0647\u0627 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062a\u0639\u0645\u064a\u0645 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a.<\/p>\n<p>\u0648\u0641\u064a \u0641\u0636\u0627\u0621 \u0630\u064a \u0623\u0628\u0639\u0627\u062f \u0645\u062a\u0639\u062f\u062f\u0629\u060c \u064a\u0645\u0643\u0646 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0646\u0642\u0637\u062a\u064a\u0646 \u0628\u062c\u0645\u0639 \u0645\u0631\u0628\u0639\u0627\u062a \u0641\u0631\u0648\u0642 \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u062b\u0645 \u0623\u062e\u0630 \u0627\u0644\u062c\u0630\u0631 \u0627\u0644\u062a\u0631\u0628\u064a\u0639\u064a. \u0648\u062a\u0639\u062f \u0647\u0630\u0647 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0648\u0627\u062d\u062f\u0629 \u0645\u0646 \u0627\u0644\u0645\u0642\u0627\u064a\u064a\u0633 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u062a\u0637\u0628\u064a\u0642\u064a\u0629 \u0648\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a.<\/p>\n<h2>\u0639\u062f\u062f \u0645\u0646 \u0627\u0644\u0628\u0631\u0627\u0647\u064a\u0646<\/h2>\n<p>\u062a\u062a\u0645\u064a\u0632 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629 \u0628\u0648\u062c\u0648\u062f \u0639\u062f\u062f \u0643\u0628\u064a\u0631 \u062c\u062f\u0627\u064b \u0645\u0646 \u0627\u0644\u0628\u0631\u0627\u0647\u064a\u0646 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629. \u0628\u0639\u0636\u0647\u0627 \u0647\u0646\u062f\u0633\u064a \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u0627\u062d\u0627\u062a \u0648\u0625\u0639\u0627\u062f\u0629 \u062a\u0631\u062a\u064a\u0628 \u0627\u0644\u0623\u0634\u0643\u0627\u0644\u060c \u0648\u0628\u0639\u0636\u0647\u0627 \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u062a\u0634\u0627\u0628\u0647 \u0627\u0644\u0645\u062b\u0644\u062b\u0627\u062a\u060c \u0648\u0628\u0639\u0636\u0647\u0627 \u062c\u0628\u0631\u064a\u060c \u0648\u0628\u0639\u0636\u0647\u0627 \u064a\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u062a\u062d\u0648\u064a\u0644\u0627\u062a \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629 \u0623\u0648 \u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0623\u0648 \u0627\u0644\u062c\u062f\u0627\u0621 \u0627\u0644\u062f\u0627\u062e\u0644\u064a.<\/p>\n<p>\u0648\u064a\u064f\u0639\u062f \u0647\u0630\u0627 \u0627\u0644\u062a\u0646\u0648\u0639 \u0645\u0647\u0645\u0627\u064b \u062a\u0631\u0628\u0648\u064a\u0627\u064b \u0648\u0631\u064a\u0627\u0636\u064a\u0627\u064b\u061b \u0644\u0623\u0646 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0627\u0644\u0648\u0627\u062d\u062f\u0629 \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u0643\u0634\u0641 \u0639\u0644\u0627\u0642\u0627\u062a \u0645\u062e\u062a\u0644\u0641\u0629 \u0628\u064a\u0646 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0648\u0627\u0644\u062c\u0628\u0631 \u0648\u0627\u0644\u0645\u0633\u0627\u062d\u0629 \u0648\u0627\u0644\u062a\u0634\u0627\u0628\u0647. \u0648\u0642\u062f \u0623\u0635\u0628\u062d\u062a \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0645\u062b\u0627\u0644\u0627\u064b \u0645\u0634\u0647\u0648\u0631\u0627\u064b \u0639\u0644\u0649 \u0625\u0645\u0643\u0627\u0646\u064a\u0629 \u0625\u062b\u0628\u0627\u062a \u062d\u0642\u064a\u0642\u0629 \u0631\u064a\u0627\u0636\u064a\u0629 \u0648\u0627\u062d\u062f\u0629 \u0628\u0637\u0631\u0642 \u0645\u0633\u062a\u0642\u0644\u0629 \u0645\u062a\u0639\u062f\u062f\u0629. <sup class=\"ref\"><a href=\"https:\/\/cage.ugent.be\/~hs\/pythagoras\/pythagorasorig.html\" title=\"12|On the proof of the Pythagorean theorem in Euclid&amp;apos;s Elements|Ghent University|2026\" target=\"_blank\" rel=\"noopener\">[12]<\/a><\/sup><\/p>\n<h2>\u0628\u0631\u0647\u0627\u0646 \u0627\u0644\u0645\u0633\u0627\u062d\u0627\u062a \u0648\u0625\u0639\u0627\u062f\u0629 \u0627\u0644\u062a\u0631\u062a\u064a\u0628<\/h2>\n<p>\u0645\u0646 \u0623\u0628\u0633\u0637 \u0627\u0644\u0623\u0641\u0643\u0627\u0631 \u0627\u0644\u0628\u0631\u0647\u0627\u0646\u064a\u0629 \u0627\u0644\u062d\u062f\u064a\u062b\u0629 \u0648\u0636\u0639 \u0639\u062f\u0629 \u0646\u0633\u062e \u0645\u062a\u0637\u0627\u0628\u0642\u0629 \u0645\u0646 \u0627\u0644\u0645\u062b\u0644\u062b \u0627\u0644\u0642\u0627\u0626\u0645 \u062f\u0627\u062e\u0644 \u0645\u0631\u0628\u0639 \u0643\u0628\u064a\u0631 \u0628\u0637\u0631\u0642 \u0645\u062e\u062a\u0644\u0641\u0629. \u0648\u0641\u064a \u062a\u0631\u062a\u064a\u0628 \u0645\u0639\u064a\u0646 \u062a\u0638\u0647\u0631 \u0645\u0633\u0627\u062d\u0629 \u0645\u0631\u062a\u0628\u0637\u0629 \u0628\u0645\u0631\u0628\u0639 \u0627\u0644\u0648\u062a\u0631\u060c \u0648\u0641\u064a \u062a\u0631\u062a\u064a\u0628 \u0622\u062e\u0631 \u064a\u0645\u0643\u0646 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646 \u0627\u0644\u0645\u0633\u0627\u062d\u0629 \u0646\u0641\u0633\u0647\u0627 \u0628\u0648\u0627\u0633\u0637\u0629 \u0645\u0631\u0628\u0639\u064a \u0627\u0644\u0636\u0644\u0639\u064a\u0646 \u0627\u0644\u0642\u0627\u0626\u0645\u064a\u0646. \u0648\u0628\u0645\u0627 \u0623\u0646 \u0645\u0633\u0627\u062d\u0629 \u0627\u0644\u0634\u0643\u0644 \u0627\u0644\u062e\u0627\u0631\u062c\u064a \u062b\u0627\u0628\u062a\u0629 \u0641\u064a \u0627\u0644\u062a\u0631\u062a\u064a\u0628\u064a\u0646\u060c \u0641\u0625\u0646 \u0645\u0633\u0627\u0648\u0627\u0629 \u0627\u0644\u0645\u0633\u0627\u062d\u062a\u064a\u0646 \u062a\u0624\u062f\u064a \u0625\u0644\u0649 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629.<\/p>\n<p>\u062a\u0643\u0634\u0641 \u0647\u0630\u0647 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0639\u0646 \u0627\u0644\u0641\u0643\u0631\u0629 \u0627\u0644\u062c\u0648\u0647\u0631\u064a\u0629 \u0644\u0644\u0646\u0638\u0631\u064a\u0629: \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u0627\u0644\u0623\u0637\u0648\u0627\u0644 \u064a\u0645\u0643\u0646 \u062a\u062d\u0648\u064a\u0644\u0647\u0627 \u0625\u0644\u0649 \u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u0627\u0644\u0645\u0633\u0627\u062d\u0627\u062a\u060c \u062b\u0645 \u0625\u062b\u0628\u0627\u062a\u0647\u0627 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0645\u062d\u0627\u0641\u0638\u0629 \u0639\u0644\u0649 \u0627\u0644\u0645\u0633\u0627\u062d\u0629.<\/p>\n<h2>\u0628\u0631\u0647\u0627\u0646 \u0627\u0644\u062a\u0634\u0627\u0628\u0647<\/h2>\n<p>\u064a\u0645\u0643\u0646 \u0625\u062b\u0628\u0627\u062a \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062a\u0634\u0627\u0628\u0647 \u0627\u0644\u0645\u062b\u0644\u062b\u0627\u062a. \u0641\u0625\u0630\u0627 \u0623\u0633\u0642\u0637\u0646\u0627 \u0639\u0645\u0648\u062f\u0627\u064b \u0645\u0646 \u0631\u0623\u0633 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0642\u0627\u0626\u0645\u0629 \u0639\u0644\u0649 \u0627\u0644\u0648\u062a\u0631\u060c \u064a\u062a\u0643\u0648\u0646 \u0645\u062b\u0644\u062b\u0627\u0646 \u0623\u0635\u063a\u0631 \u064a\u0634\u0628\u0647\u0627\u0646 \u0627\u0644\u0645\u062b\u0644\u062b \u0627\u0644\u0623\u0635\u0644\u064a. \u0648\u0645\u0646 \u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u062a\u0634\u0627\u0628\u0647 \u064a\u0645\u0643\u0646 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0639\u0644\u0627\u0642\u0627\u062a \u0628\u064a\u0646 \u0645\u0631\u0628\u0639\u0627\u062a \u0623\u0637\u0648\u0627\u0644 \u0627\u0644\u0623\u0636\u0644\u0627\u0639\u060c \u062b\u0645 \u062c\u0645\u0639\u0647\u0627 \u0644\u0644\u0648\u0635\u0648\u0644 \u0625\u0644\u0649 <i>a\u00b2+b\u00b2=c\u00b2<\/i>.<\/p>\n<p>\u0648\u0647\u0630\u0627 \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u064a\u0648\u0636\u062d \u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0628\u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u062a\u0634\u0627\u0628\u0647 \u0648\u0627\u0644\u0646\u0633\u0628\u060c \u0648\u064a\u062e\u062a\u0644\u0641 \u0641\u064a \u0628\u0646\u064a\u062a\u0647 \u0639\u0646 \u0628\u0631\u0647\u0627\u0646 \u0625\u0642\u0644\u064a\u062f\u0633 \u0627\u0644\u0642\u0627\u0626\u0645 \u0639\u0644\u0649 \u062a\u0642\u0633\u064a\u0645 \u0627\u0644\u0645\u0633\u0627\u062d\u0627\u062a.<\/p>\n<h2>\u0628\u0631\u0647\u0627\u0646 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062c\u0628\u0631<\/h2>\n<p>\u064a\u0645\u0643\u0646 \u0628\u0646\u0627\u0621 \u0628\u0631\u0647\u0627\u0646 \u062c\u0628\u0631\u064a \u0628\u0633\u064a\u0637 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0631\u0628\u0639 \u0637\u0648\u0644 \u0636\u0644\u0639\u0647 <i>a+b<\/i> \u064a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u0623\u0631\u0628\u0639\u0629 \u0645\u062b\u0644\u062b\u0627\u062a \u0642\u0627\u0626\u0645\u0629 \u0645\u062a\u0637\u0627\u0628\u0642\u0629\u060c \u0628\u062d\u064a\u062b \u064a\u0643\u0648\u0646 \u0644\u0643\u0644 \u0645\u062b\u0644\u062b \u0636\u0644\u0639\u0627\u0646 \u0642\u0627\u0626\u0645\u0627\u0646 \u0637\u0648\u0644\u0647\u0645\u0627 <i>a<\/i> \u0648<i>b<\/i>\u060c \u0648\u0648\u062a\u0631 \u0637\u0648\u0644\u0647 <i>c<\/i>. \u0639\u0646\u062f \u062d\u0633\u0627\u0628 \u0645\u0633\u0627\u062d\u0629 \u0627\u0644\u0645\u0631\u0628\u0639 \u0627\u0644\u0643\u0628\u064a\u0631 \u0628\u0637\u0631\u064a\u0642\u062a\u064a\u0646 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649:<\/p>\n<p><i>(a+b)\u00b2=4(\u00bdab)+c\u00b2<\/i><\/p>\n<p>\u0648\u0628\u062a\u0648\u0633\u064a\u0639 \u0627\u0644\u0637\u0631\u0641 \u0627\u0644\u0623\u064a\u0633\u0631:<\/p>\n<p><i>a\u00b2+2ab+b\u00b2=2ab+c\u00b2<\/i><\/p>\n<p>\u0648\u0628\u0637\u0631\u062d <i>2ab<\/i> \u0645\u0646 \u0627\u0644\u0637\u0631\u0641\u064a\u0646 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649:<\/p>\n<p><i>a\u00b2+b\u00b2=c\u00b2<\/i><\/p>\n<p>\u0648\u0647\u0630\u0627 \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u064a\u062c\u0645\u0639 \u0628\u064a\u0646 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0648\u0627\u0644\u062c\u0628\u0631 \u0648\u064a\u0638\u0647\u0631 \u0643\u064a\u0641 \u064a\u0645\u0643\u0646 \u0644\u0644\u0645\u0633\u0627\u062d\u0629 \u0623\u0646 \u062a\u062a\u062d\u0648\u0644 \u0625\u0644\u0649 \u0645\u0639\u0627\u062f\u0644\u0629 \u062c\u0628\u0631\u064a\u0629.<\/p>\n<h2>\u062d\u062f\u0648\u062f \u0627\u0644\u0646\u0638\u0631\u064a\u0629<\/h2>\n<p>\u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629 \u0628\u0635\u064a\u063a\u062a\u0647\u0627 \u0627\u0644\u062a\u0642\u0644\u064a\u062f\u064a\u0629 \u062a\u0646\u0637\u0628\u0642 \u0639\u0644\u0649 \u0627\u0644\u0645\u062b\u0644\u062b\u0627\u062a \u0627\u0644\u0642\u0627\u0626\u0645\u0629 \u0641\u064a \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u0625\u0642\u0644\u064a\u062f\u064a\u0629. \u0648\u0644\u0627 \u064a\u062c\u0648\u0632 \u062a\u0637\u0628\u064a\u0642\u0647\u0627 \u0628\u0635\u0648\u0631\u0629 \u0645\u0628\u0627\u0634\u0631\u0629 \u0639\u0644\u0649 \u0623\u064a \u0645\u062b\u0644\u062b \u0623\u0648 \u0639\u0644\u0649 \u0623\u064a \u0647\u0646\u062f\u0633\u0629 \u063a\u064a\u0631 \u0625\u0642\u0644\u064a\u062f\u064a\u0629 \u0645\u0646 \u062f\u0648\u0646 \u062a\u0639\u062f\u064a\u0644.<\/p>\n<p>\u0641\u0625\u0630\u0627 \u0644\u0645 \u062a\u0643\u0646 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u0636\u0644\u0639\u064a\u0646 \u062a\u0633\u0627\u0648\u064a 90 \u062f\u0631\u062c\u0629\u060c \u0641\u0625\u0646 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u0645\u0646\u0627\u0633\u0628\u0629 \u062a\u0643\u0648\u0646 \u0623\u0639\u0645 \u0645\u0646 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629\u060c \u0648\u062a\u062f\u062e\u0644 \u0641\u064a\u0647\u0627 \u0642\u064a\u0645\u0629 \u062c\u064a\u0628 \u062a\u0645\u0627\u0645 \u0627\u0644\u0632\u0627\u0648\u064a\u0629\u060c \u0643\u0645\u0627 \u0641\u064a \u0642\u0627\u0646\u0648\u0646 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645:<\/p>\n<p><i>c\u00b2=a\u00b2+b\u00b2\u22122ab cos C<\/i><\/p>\n<p>\u0648\u0639\u0646\u062f\u0645\u0627 \u062a\u0643\u0648\u0646 <i>C=90\u00b0<\/i>\u060c \u0641\u0625\u0646 <i>cos 90\u00b0=0<\/i>\u060c \u0641\u062a\u062a\u062d\u0648\u0644 \u0647\u0630\u0647 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0645\u0628\u0627\u0634\u0631\u0629 \u0625\u0644\u0649:<\/p>\n<p><i>c\u00b2=a\u00b2+b\u00b2<\/i><\/p>\n<p>\u0648\u0645\u0646 \u0647\u0646\u0627 \u064a\u0645\u0643\u0646 \u0627\u0644\u0646\u0638\u0631 \u0625\u0644\u0649 \u0646\u0638\u0631\u064a\u0629 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633 \u0628\u0648\u0635\u0641\u0647\u0627 \u062d\u0627\u0644\u0629 \u062e\u0627\u0635\u0629 \u0645\u0646 \u0642\u0627\u0646\u0648\u0646 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645.<\/p>\n<h2>\u0641\u064a \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u063a\u064a\u0631 \u0627\u0644\u0625\u0642\u0644\u064a\u062f\u064a\u0629<\/h2>\n<p>\u062a\u062a\u063a\u064a\u0631 \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629 \u0639\u0646\u062f\u0645\u0627 \u0646\u0646\u062a\u0642\u0644 \u0645\u0646 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0625\u0642\u0644\u064a\u062f\u064a \u0625\u0644\u0649 \u0627\u0644\u0647\u0646\u062f\u0633\u0627\u062a \u0627\u0644\u0645\u0646\u062d\u0646\u064a\u0629\u060c \u0645\u062b\u0644 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u0643\u0631\u0648\u064a\u0629 \u0623\u0648 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u0632\u0627\u0626\u062f\u064a\u0629. \u0648\u0644\u0630\u0644\u0643 \u0644\u0627 \u064a\u0645\u0643\u0646 \u0627\u0641\u062a\u0631\u0627\u0636 \u0623\u0646 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 <i>a\u00b2+b\u00b2=c\u00b2<\/i> \u062a\u0628\u0642\u0649 \u0635\u062d\u064a\u062d\u0629 \u0644\u0644\u0645\u062b\u0644\u062b\u0627\u062a \u0627\u0644\u0642\u0627\u0626\u0645\u0629 \u0639\u0644\u0649 \u0633\u0637\u062d \u0645\u0646\u062d\u0646\u064d.<\/p>\n<p>\u0648\u062a\u0648\u0636\u062d \u0647\u0630\u0647 \u0627\u0644\u062d\u0642\u064a\u0642\u0629 \u0623\u0647\u0645\u064a\u0629 \u0627\u0644\u0627\u0641\u062a\u0631\u0627\u0636\u0627\u062a \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0642\u0648\u0645 \u0639\u0644\u064a\u0647\u0627 \u0627\u0644\u0646\u0638\u0631\u064a\u0629\u061b \u0641\u0647\u064a \u0644\u064a\u0633\u062a \u0645\u062c\u0631\u062f \u062d\u0642\u064a\u0642\u0629 \u0645\u0633\u062a\u0642\u0644\u0629 \u0639\u0646 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u060c \u0648\u0625\u0646\u0645\u0627 \u0646\u062a\u064a\u062c\u0629 \u0636\u0645\u0646 \u0628\u0646\u064a\u0629 \u0647\u0646\u062f\u0633\u064a\u0629 \u0645\u062d\u062f\u062f\u0629.<\/p>\n<h2>\u0646\u0638\u0631\u064a\u0629 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633 \u0648\u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u0647\u0646\u062f\u064a\u0629 \u0648\u0627\u0644\u0635\u064a\u0646\u064a\u0629<\/h2>\n<p>\u062a\u0648\u062c\u062f \u062a\u0642\u0627\u0644\u064a\u062f \u0631\u064a\u0627\u0636\u064a\u0629 \u0645\u062a\u0639\u062f\u062f\u0629 \u0639\u0631\u0641\u062a \u0639\u0644\u0627\u0642\u0627\u062a \u0645\u0631\u062a\u0628\u0637\u0629 \u0628\u0627\u0644\u0645\u062b\u0644\u062b\u0627\u062a \u0627\u0644\u0642\u0627\u0626\u0645\u0629. \u0648\u0645\u0646 \u0627\u0644\u0635\u0639\u0628 \u062a\u0627\u0631\u064a\u062e\u064a\u0627\u064b \u0627\u062e\u062a\u0632\u0627\u0644 \u062a\u0627\u0631\u064a\u062e \u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0631\u0641\u0629 \u0641\u064a \u0645\u0643\u062a\u0634\u0641 \u0648\u0627\u062d\u062f \u0623\u0648 \u062d\u0636\u0627\u0631\u0629 \u0648\u0627\u062d\u062f\u0629. \u0641\u0627\u0644\u0623\u062f\u0644\u0629 \u0627\u0644\u0628\u0627\u0628\u0644\u064a\u0629 \u062a\u062b\u0628\u062a \u0627\u0644\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0645\u0628\u0643\u0631 \u0644\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629\u060c \u0628\u064a\u0646\u0645\u0627 \u0637\u0648\u0631\u062a \u0627\u0644\u062d\u0636\u0627\u0631\u0627\u062a \u0627\u0644\u0644\u0627\u062d\u0642\u0629 \u0623\u0633\u0627\u0644\u064a\u0628 \u0645\u062e\u062a\u0644\u0641\u0629 \u0641\u064a \u0627\u0644\u062d\u0633\u0627\u0628 \u0648\u0627\u0644\u0647\u0646\u062f\u0633\u0629.<\/p>\n<p>\u0648\u062a\u0643\u0645\u0646 \u062e\u0635\u0648\u0635\u064a\u0629 \u0627\u0644\u062a\u0642\u0644\u064a\u062f \u0627\u0644\u064a\u0648\u0646\u0627\u0646\u064a \u0641\u064a \u0627\u0644\u062a\u0637\u0648\u0631 \u0627\u0644\u062a\u062f\u0631\u064a\u062c\u064a \u0644\u0644\u0645\u0646\u0647\u062c \u0627\u0644\u0628\u0631\u0647\u0627\u0646\u064a \u0648\u0627\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644\u064a\u060c \u0627\u0644\u0630\u064a \u0638\u0647\u0631 \u0628\u0648\u0636\u0648\u062d \u0641\u064a \u00ab\u0627\u0644\u0639\u0646\u0627\u0635\u0631\u00bb \u0644\u0625\u0642\u0644\u064a\u062f\u0633. \u0644\u0630\u0644\u0643 \u064a\u0646\u0628\u063a\u064a \u0627\u0644\u062a\u0641\u0631\u064a\u0642 \u0628\u064a\u0646 \u062a\u0627\u0631\u064a\u062e \u0627\u0643\u062a\u0634\u0627\u0641 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0648\u062a\u0627\u0631\u064a\u062e \u0635\u064a\u0627\u063a\u062a\u0647\u0627 \u0648\u0625\u062b\u0628\u0627\u062a\u0647\u0627 \u0636\u0645\u0646 \u0646\u0638\u0627\u0645 \u0627\u0633\u062a\u062f\u0644\u0627\u0644\u064a.<\/p>\n<h2>\u0644\u0645\u0627\u0630\u0627 \u062a\u062d\u0645\u0644 \u0627\u0633\u0645 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633\u061f<\/h2>\n<p>\u064a\u0631\u062c\u0639 \u0625\u0637\u0644\u0627\u0642 \u0627\u0633\u0645 \u00ab\u0646\u0638\u0631\u064a\u0629 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633\u00bb \u0625\u0644\u0649 \u0627\u0644\u062a\u0642\u0644\u064a\u062f \u0627\u0644\u062a\u0627\u0631\u064a\u062e\u064a \u0627\u0644\u0630\u064a \u0631\u0628\u0637 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0628\u0627\u0644\u0645\u062f\u0631\u0633\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629\u060c \u0648\u0644\u064a\u0633 \u0625\u0644\u0649 \u062f\u0644\u064a\u0644 \u0642\u0627\u0637\u0639 \u0639\u0644\u0649 \u0623\u0646 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633 \u0634\u062e\u0635\u064a\u0627\u064b \u0643\u0627\u0646 \u0623\u0648\u0644 \u0645\u0646 \u0627\u0643\u062a\u0634\u0641\u0647\u0627. \u0648\u064a\u0634\u064a\u0631 \u0627\u0644\u0645\u0635\u062f\u0631 \u0627\u0644\u0645\u062a\u062e\u0635\u0635 \u0641\u064a \u062a\u0627\u0631\u064a\u062e \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633 \u0625\u0644\u0649 \u0623\u0646 \u0627\u0633\u0645 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0631\u062a\u0628\u0637 \u0628\u0647 \u0641\u064a \u062a\u0642\u0627\u0644\u064a\u062f \u0644\u0627\u062d\u0642\u0629\u060c \u0648\u0623\u0646 \u0627\u0644\u0623\u062f\u0644\u0629 \u0627\u0644\u0645\u0628\u0643\u0631\u0629 \u0644\u0627 \u062a\u0633\u0645\u062d \u0628\u0625\u062b\u0628\u0627\u062a \u0623\u0646\u0647 \u0642\u062f\u0645 \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0627\u0644\u0645\u0639\u0631\u0648\u0641 \u0627\u0644\u064a\u0648\u0645. <sup class=\"ref\"><a href=\"https:\/\/plato.stanford.edu\/entries\/pythagoras\/\" title=\"13|Pythagoras|Carl Huffman\u060c Stanford Encyclopedia of Philosophy|2023\" target=\"_blank\" rel=\"noopener\">[13]<\/a><\/sup><\/p>\n<p>\u0648\u0647\u0630\u0627 \u0645\u062b\u0627\u0644 \u0645\u0647\u0645 \u0639\u0644\u0649 \u0627\u0644\u0641\u0631\u0642 \u0628\u064a\u0646 \u00ab\u0627\u0633\u0645 \u0627\u0644\u0646\u0638\u0631\u064a\u0629\u00bb \u0648\u00ab\u062a\u0627\u0631\u064a\u062e\u0647\u0627 \u0627\u0644\u0641\u0639\u0644\u064a\u00bb. \u0641\u0643\u062b\u064a\u0631 \u0645\u0646 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u062a\u062d\u0645\u0644 \u0623\u0633\u0645\u0627\u0621 \u0639\u0644\u0645\u0627\u0621 \u0627\u0631\u062a\u0628\u0637\u0648\u0627 \u0628\u0647\u0627 \u0628\u0635\u0648\u0631\u0629 \u0642\u0648\u064a\u0629\u060c \u062f\u0648\u0646 \u0623\u0646 \u064a\u0639\u0646\u064a \u0630\u0644\u0643 \u062f\u0627\u0626\u0645\u0627\u064b \u0623\u0646\u0647\u0645 \u0623\u0648\u0644 \u0645\u0646 \u0639\u0631\u0641\u0647\u0627 \u0623\u0648 \u0627\u0643\u062a\u0634\u0641\u0647\u0627.<\/p>\n<h2>\u0646\u0638\u0631\u064a\u0629 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633 \u0641\u064a \u062a\u0627\u0631\u064a\u062e \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0627\u0644\u0631\u064a\u0627\u0636\u064a<\/h2>\n<p>\u062a\u062d\u062a\u0644 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0645\u0643\u0627\u0646\u0629 \u062e\u0627\u0635\u0629 \u0641\u064a \u062a\u0627\u0631\u064a\u062e \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0644\u0623\u0646\u0647\u0627 \u062a\u0648\u0636\u062d \u0643\u064a\u0641 \u064a\u0645\u0643\u0646 \u0627\u0644\u0627\u0646\u062a\u0642\u0627\u0644 \u0645\u0646 \u0645\u0644\u0627\u062d\u0638\u0629 \u0639\u062f\u062f\u064a\u0629 \u0625\u0644\u0649 \u062d\u0642\u064a\u0642\u0629 \u0639\u0627\u0645\u0629. \u0641\u0645\u0646 \u0627\u0644\u0633\u0647\u0644 \u0645\u0644\u0627\u062d\u0638\u0629 \u0623\u0646 3 \u06484 \u06485 \u062a\u062d\u0642\u0642 \u0627\u0644\u0639\u0644\u0627\u0642\u0629\u060c \u0644\u0643\u0646 \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u064a\u0647\u062f\u0641 \u0625\u0644\u0649 \u0625\u062b\u0628\u0627\u062a \u0623\u0646 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0635\u062d\u064a\u062d\u0629 \u0644\u0643\u0644 \u0645\u062b\u0644\u062b \u0642\u0627\u0626\u0645\u060c \u0648\u0644\u064a\u0633 \u0641\u0642\u0637 \u0644\u0644\u0623\u0645\u062b\u0644\u0629 \u0627\u0644\u0645\u0639\u0631\u0648\u0641\u0629.<\/p>\n<p>\u0648\u0647\u0646\u0627 \u064a\u0638\u0647\u0631 \u0627\u0644\u0641\u0631\u0642 \u0628\u064a\u0646 \u0627\u0644\u062a\u062c\u0631\u0628\u0629 \u0648\u0627\u0644\u0628\u0631\u0647\u0627\u0646: \u0641\u0627\u062e\u062a\u0628\u0627\u0631 \u0645\u0644\u0627\u064a\u064a\u0646 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u0639\u0637\u064a \u062b\u0642\u0629 \u0642\u0648\u064a\u0629 \u0641\u064a \u0635\u062d\u0629 \u0627\u0644\u062a\u062e\u0645\u064a\u0646\u060c \u0644\u0643\u0646\u0647 \u0644\u0627 \u064a\u062b\u0628\u062a \u0648\u062d\u062f\u0647 \u0627\u0644\u062d\u0642\u064a\u0642\u0629 \u0627\u0644\u0639\u0627\u0645\u0629. \u0623\u0645\u0627 \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0641\u064a\u0633\u0639\u0649 \u0625\u0644\u0649 \u062a\u0623\u0633\u064a\u0633 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0639\u0644\u0649 \u0642\u0648\u0627\u0639\u062f \u0645\u0646\u0637\u0642\u064a\u0629 \u062a\u0646\u0637\u0628\u0642 \u0639\u0644\u0649 \u062c\u0645\u064a\u0639 \u0627\u0644\u062d\u0627\u0644\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0633\u062a\u0648\u0641\u064a \u0627\u0644\u0634\u0631\u0648\u0637.<\/p>\n<h2>\u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0648\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f<\/h2>\n<p>\u0623\u062f\u062a \u0627\u0644\u0639\u0644\u0627\u0642\u0629 <i>a\u00b2+b\u00b2=c\u00b2<\/i> \u0625\u0644\u0649 \u0645\u062c\u0645\u0648\u0639\u0629 \u0648\u0627\u0633\u0639\u0629 \u0645\u0646 \u0627\u0644\u0645\u0633\u0627\u0626\u0644 \u0641\u064a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f\u060c \u062e\u0635\u0648\u0635\u0627\u064b \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u062b\u0644\u0627\u062b\u064a\u0627\u062a \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629. \u0648\u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0645\u0633\u0627\u0626\u0644 \u062a\u062d\u062f\u064a\u062f \u062c\u0645\u064a\u0639 \u0627\u0644\u062d\u0644\u0648\u0644 \u0627\u0644\u0635\u062d\u064a\u062d\u0629 \u0644\u0644\u0645\u0639\u0627\u062f\u0644\u0629:<\/p>\n<p><i>x\u00b2+y\u00b2=z\u00b2<\/i><\/p>\n<p>\u0648\u062a\u062a\u0635\u0644 \u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0628\u0645\u0633\u0627\u0626\u0644 \u0623\u0639\u0645 \u0641\u064a \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629\u060c \u0648\u0628\u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629\u060c \u0648\u0628\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0643\u0645\u062c\u0627\u0645\u064a\u0639 \u0644\u0645\u0631\u0628\u0639\u0627\u062a.<\/p>\n<h2>\u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0648\u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u064a\u0646<\/h2>\n<p>\u062a\u062a\u0635\u0644 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0623\u064a\u0636\u0627\u064b \u0628\u0645\u0633\u0623\u0644\u0629 \u062a\u0645\u062b\u064a\u0644 \u0639\u062f\u062f \u0635\u062d\u064a\u062d \u0639\u0644\u0649 \u0635\u0648\u0631\u0629 \u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u064a\u0646. \u0641\u0625\u0630\u0627 \u062a\u062d\u0642\u0642:<\/p>\n<p><i>c\u00b2-a\u00b2=b\u00b2<\/i><\/p>\n<p>\u0641\u0625\u0646\u0646\u0627 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u062b\u0644\u0627\u062b\u0629 \u0645\u0631\u0628\u0639\u0627\u062a. \u0648\u0642\u062f \u0642\u0627\u062f\u062a \u062f\u0631\u0627\u0633\u0629 \u0647\u0630\u0647 \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0625\u0644\u0649 \u0646\u062a\u0627\u0626\u062c \u0645\u0647\u0645\u0629 \u0641\u064a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f\u060c \u0648\u0645\u0646\u0647\u0627 \u0645\u0633\u0627\u0626\u0644 \u062a\u062a\u0639\u0644\u0642 \u0628\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629 \u0648\u0645\u0631\u0628\u0639\u0627\u062a\u0647\u0627.<\/p>\n<h2>\u0623\u0647\u0645\u064a\u0629 \u0627\u0644\u062b\u0644\u0627\u062b\u064a\u0629 3\u20134\u20135 \u0641\u064a \u0627\u0644\u0642\u064a\u0627\u0633<\/h2>\n<p>\u062a\u062a\u0645\u064a\u0632 \u0627\u0644\u062b\u0644\u0627\u062b\u064a\u0629 3\u20134\u20135 \u0628\u0645\u064a\u0632\u0629 \u0639\u0645\u0644\u064a\u0629 \u0645\u0647\u0645\u0629: \u0625\u0630\u0627 \u062a\u0645 \u0625\u0646\u0634\u0627\u0621 \u0645\u062b\u0644\u062b \u0623\u0637\u0648\u0627\u0644\u0647 \u0645\u062a\u0646\u0627\u0633\u0628\u0629 \u0645\u0639 3 \u06484 \u06485\u060c \u0641\u0625\u0646 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0628\u064a\u0646 \u0627\u0644\u0636\u0644\u0639\u064a\u0646 3 \u06484 \u062a\u0643\u0648\u0646 \u0642\u0627\u0626\u0645\u0629. \u0648\u0644\u0647\u0630\u0627 \u0623\u0635\u0628\u062d\u062a \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0645\u062b\u0627\u0644\u0627\u064b \u0628\u0633\u064a\u0637\u0627\u064b \u0641\u064a \u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u0642\u064a\u0627\u0633 \u0648\u0627\u0644\u0628\u0646\u0627\u0621 \u0648\u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062a\u0637\u0628\u064a\u0642\u064a\u0629.<\/p>\n<p>\u0648\u0644\u0627 \u062a\u062d\u062a\u0627\u062c \u0627\u0644\u0641\u0643\u0631\u0629 \u0625\u0644\u0649 \u0623\u0646 \u062a\u0643\u0648\u0646 \u0627\u0644\u0623\u0637\u0648\u0627\u0644 3 \u06484 \u06485 \u0628\u0627\u0644\u0636\u0628\u0637\u061b \u0641\u0643\u0644 \u0645\u0636\u0627\u0639\u0641 \u0645\u0648\u062c\u0628 \u0644\u0644\u062b\u0644\u0627\u062b\u064a\u0629 \u064a\u062d\u0627\u0641\u0638 \u0639\u0644\u0649 \u0627\u0644\u0646\u0633\u0628\u0629 \u0646\u0641\u0633\u0647\u0627\u060c \u0645\u062b\u0644 6\u20138\u201310 \u06489\u201312\u201315.<\/p>\n<h2>\u0627\u0644\u0623\u0647\u0645\u064a\u0629 \u0641\u064a \u0627\u0644\u062a\u0639\u0644\u064a\u0645 \u0627\u0644\u0631\u064a\u0627\u0636\u064a<\/h2>\n<p>\u062a\u0639\u062f \u0646\u0638\u0631\u064a\u0629 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633 \u0645\u0646 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0627\u0644\u062a\u064a \u064a\u0646\u062a\u0642\u0644 \u0641\u064a\u0647\u0627 \u0627\u0644\u0637\u0627\u0644\u0628 \u0645\u0646 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0625\u0644\u0649 \u0627\u0644\u062c\u0628\u0631. \u0641\u0647\u064a \u062a\u0628\u062f\u0623 \u0645\u0646 \u0634\u0643\u0644 \u0647\u0646\u062f\u0633\u064a\u060c \u062b\u0645 \u062a\u0639\u0628\u0631 \u0639\u0646 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u0623\u0636\u0644\u0627\u0639\u0647 \u0628\u0645\u0639\u0627\u062f\u0644\u0629\u060c \u062b\u0645 \u062a\u0633\u0645\u062d \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u062c\u0628\u0631\u064a\u0629 \u0644\u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0645\u062c\u0647\u0648\u0644.<\/p>\n<p>\u0643\u0645\u0627 \u0623\u0646\u0647\u0627 \u062a\u0642\u062f\u0645 \u0646\u0645\u0648\u0630\u062c\u0627\u064b \u0645\u0628\u0643\u0631\u0627\u064b \u0644\u0641\u0643\u0631\u0629 \u0645\u0647\u0645\u0629 \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a: \u064a\u0645\u0643\u0646 \u062a\u0645\u062b\u064a\u0644 \u062e\u0627\u0635\u064a\u0629 \u0647\u0646\u062f\u0633\u064a\u0629 \u0628\u0648\u0627\u0633\u0637\u0629 \u0639\u0644\u0627\u0642\u0629 \u0639\u062f\u062f\u064a\u0629\u060c \u062b\u0645 \u0625\u0639\u0627\u062f\u0629 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0647\u0630\u0647 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0641\u064a \u0645\u0633\u0627\u0626\u0644 \u062c\u062f\u064a\u062f\u0629 \u062a\u062e\u062a\u0644\u0641 \u0641\u064a \u0627\u0644\u0634\u0643\u0644 \u0648\u0644\u0643\u0646\u0647\u0627 \u062a\u0634\u062a\u0631\u0643 \u0641\u064a \u0627\u0644\u0628\u0646\u064a\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0646\u0641\u0633\u0647\u0627.<\/p>\n<h2>\u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0628\u0648\u0635\u0641\u0647\u0627 \u062d\u0627\u0644\u0629 \u062e\u0627\u0635\u0629 \u0645\u0646 \u0628\u0646\u064a\u0629 \u0623\u0639\u0645<\/h2>\n<p>\u0645\u0646 \u0645\u0646\u0638\u0648\u0631 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u062b\u0629\u060c \u0644\u0627 \u062a\u064f\u0641\u0647\u0645 \u0646\u0638\u0631\u064a\u0629 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633 \u0641\u0642\u0637 \u0628\u0627\u0639\u062a\u0628\u0627\u0631\u0647\u0627 \u0642\u0627\u0639\u062f\u0629 \u0644\u0644\u0645\u062b\u0644\u062b\u0627\u062a. \u0641\u0647\u064a \u0645\u0631\u062a\u0628\u0637\u0629 \u0628\u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0627\u0644\u0625\u0642\u0644\u064a\u062f\u064a\u0629\u060c \u0648\u0627\u0644\u062c\u062f\u0627\u0621 \u0627\u0644\u062f\u0627\u062e\u0644\u064a\u060c \u0648\u0627\u0644\u0645\u0639\u064a\u0627\u0631\u060c \u0648\u0627\u0644\u062a\u0639\u0627\u0645\u062f\u060c \u0648\u0642\u0627\u0646\u0648\u0646 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645\u060c \u0648\u0627\u0644\u0641\u0636\u0627\u0621\u0627\u062a \u0630\u0627\u062a \u0627\u0644\u062c\u062f\u0627\u0621 \u0627\u0644\u062f\u0627\u062e\u0644\u064a.<\/p>\n<p>\u0641\u0625\u0630\u0627 \u0643\u0627\u0646 <i>u<\/i> \u0648<i>v<\/i> \u0645\u062a\u0639\u0627\u0645\u062f\u064a\u0646\u060c \u0641\u0625\u0646:<\/p>\n<p><i>\u27e8u,v\u27e9=0<\/i><\/p>\n<p>\u0648\u0645\u0646 \u062b\u0645:<\/p>\n<p><i>||u+v||\u00b2=||u||\u00b2+||v||\u00b2<\/i><\/p>\n<p>\u0648\u0647\u0630\u0647 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u062c\u0631\u062f\u0629 \u062a\u0643\u0634\u0641 \u0623\u0646 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629 \u0644\u064a\u0633\u062a \u0645\u062c\u0631\u062f \u0646\u062a\u064a\u062c\u0629 \u0645\u062f\u0631\u0633\u064a\u0629\u060c \u0628\u0644 \u062a\u0639\u0628\u064a\u0631 \u0639\u0646 \u0627\u0644\u0628\u0646\u064a\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0644\u0644\u062a\u0639\u0627\u0645\u062f \u0641\u064a \u0627\u0644\u0641\u0636\u0627\u0621\u0627\u062a \u0627\u0644\u0625\u0642\u0644\u064a\u062f\u064a\u0629.<\/p>\n<h2>\u0623\u062b\u0631 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u062b\u0629<\/h2>\n<p>\u0645\u0646 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0625\u0644\u0649 \u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u062e\u0637\u064a \u0648\u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u060c \u0628\u0642\u064a\u062a \u0627\u0644\u0641\u0643\u0631\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629 \u062d\u0627\u0636\u0631\u0629 \u0641\u064a \u0635\u064a\u063a \u0645\u062e\u062a\u0644\u0641\u0629. \u0641\u0645\u0641\u0647\u0648\u0645 \u0637\u0648\u0644 \u0627\u0644\u0645\u062a\u062c\u0647\u060c \u0648\u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0646\u0642\u0637\u062a\u064a\u0646\u060c \u0648\u0645\u0639\u064a\u0627\u0631 \u0627\u0644\u062f\u0627\u0644\u0629 \u0641\u064a \u0628\u0639\u0636 \u0641\u0636\u0627\u0621\u0627\u062a \u0627\u0644\u062f\u0648\u0627\u0644\u060c \u0643\u0644\u0647\u0627 \u062a\u0631\u062a\u0628\u0637 \u0628\u0645\u0628\u062f\u0623 \u062c\u0645\u0639 \u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0645\u0643\u0648\u0646\u0627\u062a \u0627\u0644\u0645\u062a\u0639\u0627\u0645\u062f\u0629.<\/p>\n<p>\u0648\u0647\u0643\u0630\u0627 \u0627\u0646\u062a\u0642\u0644\u062a \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0645\u0646 \u0639\u0644\u0627\u0642\u0629 \u0647\u0646\u062f\u0633\u064a\u0629 \u0628\u064a\u0646 \u062b\u0644\u0627\u062b\u0629 \u0623\u0636\u0644\u0627\u0639 \u0625\u0644\u0649 \u0645\u0628\u062f\u0623 \u0623\u0648\u0633\u0639 \u064a\u062a\u0639\u0644\u0642 \u0628\u0627\u0644\u0628\u0646\u064a\u0629 \u0627\u0644\u0645\u062a\u0631\u064a\u0629 \u0644\u0644\u0641\u0636\u0627\u0621 \u0627\u0644\u0625\u0642\u0644\u064a\u062f\u064a.<\/p>\n<h2>\u0627\u0644\u062e\u0644\u0627\u0635\u0629<\/h2>\n<p>\u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0641\u064a\u062b\u0627\u063a\u0648\u0631\u064a\u0629 \u0647\u064a \u0648\u0627\u062d\u062f\u0629 \u0645\u0646 \u0623\u0643\u062b\u0631 \u0627\u0644\u0646\u0638\u0631\u064a\u0627\u062a \u062a\u0623\u062b\u064a\u0631\u0627\u064b \u0648\u0627\u0633\u062a\u0645\u0631\u0627\u0631\u0627\u064b \u0641\u064a \u062a\u0627\u0631\u064a\u062e \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a. \u0648\u0635\u064a\u063a\u062a\u0647\u0627 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 <i>a\u00b2+b\u00b2=c\u00b2<\/i> \u062a\u0635\u0641 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u0623\u0636\u0644\u0627\u0639 \u0627\u0644\u0645\u062b\u0644\u062b \u0627\u0644\u0642\u0627\u0626\u0645\u060c \u0644\u0643\u0646\u0647\u0627 \u0641\u064a \u062c\u0648\u0647\u0631\u0647\u0627 \u062a\u0639\u0628\u0631 \u0639\u0646 \u0639\u0644\u0627\u0642\u0629 \u0623\u0639\u0645 \u0628\u064a\u0646 \u0627\u0644\u062a\u0639\u0627\u0645\u062f \u0648\u0627\u0644\u0637\u0648\u0644 \u0648\u0627\u0644\u0645\u0633\u0627\u062d\u0629. \u0648\u0642\u062f \u0643\u0627\u0646\u062a \u0645\u0639\u0631\u0641\u0629 \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u062d\u0642\u0642\u0647\u0627 \u0645\u0648\u062c\u0648\u062f\u0629 \u0641\u064a \u0628\u0644\u0627\u062f \u0627\u0644\u0631\u0627\u0641\u062f\u064a\u0646 \u0627\u0644\u0642\u062f\u064a\u0645\u0629 \u0642\u0628\u0644 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633 \u0628\u0632\u0645\u0646 \u0637\u0648\u064a\u0644\u060c \u0641\u064a \u062d\u064a\u0646 \u0623\u0635\u0628\u062d \u0627\u0633\u0645 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633 \u0645\u0631\u062a\u0628\u0637\u0627\u064b \u0628\u0647\u0627 \u0641\u064a \u0627\u0644\u062a\u0642\u0644\u064a\u062f \u0627\u0644\u0644\u0627\u062d\u0642\u060c \u062f\u0648\u0646 \u0648\u062c\u0648\u062f \u062f\u0644\u064a\u0644 \u062a\u0627\u0631\u064a\u062e\u064a \u0642\u0627\u0637\u0639 \u064a\u062b\u0628\u062a \u0623\u0646\u0647 \u0634\u062e\u0635\u064a\u0627\u064b \u0643\u0627\u0646 \u0623\u0648\u0644 \u0645\u0646 \u0627\u0643\u062a\u0634\u0641\u0647\u0627 \u0623\u0648 \u0628\u0631\u0647\u0646\u0647\u0627. <sup class=\"ref\"><a href=\"https:\/\/aleph0.clarku.edu\/~djoyce\/java\/elements\/bookI\/propI47.html\" title=\"14|Euclid&amp;apos;s Elements, Book I, Proposition 47|David E. Joyce\u060c Clark University|2026\" target=\"_blank\" rel=\"noopener\">[14]<\/a><\/sup><sup class=\"ref\"><a href=\"https:\/\/plato.stanford.edu\/entries\/pythagoras\/\" title=\"15|Pythagoras|Carl Huffman\u060c Stanford Encyclopedia of Philosophy|2023\" target=\"_blank\" rel=\"noopener\">[15]<\/a><\/sup><\/p>\n<p>\u0623\u0645\u0627 \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0627\u0644\u0647\u0646\u062f\u0633\u064a \u0627\u0644\u0628\u0627\u0642\u064a \u0627\u0644\u0623\u0634\u0647\u0631 \u0648\u0627\u0644\u0623\u0642\u062f\u0645 \u0636\u0645\u0646 \u062a\u0642\u0644\u064a\u062f \u0628\u0631\u0647\u0627\u0646\u064a \u0643\u0627\u0645\u0644\u060c \u0641\u064a\u0638\u0647\u0631 \u0641\u064a \u00ab\u0627\u0644\u0639\u0646\u0627\u0635\u0631\u00bb \u0644\u0625\u0642\u0644\u064a\u062f\u0633\u060c \u0627\u0644\u0643\u062a\u0627\u0628 \u0627\u0644\u0623\u0648\u0644\u060c \u0627\u0644\u0642\u0636\u064a\u0629 47\u060c \u062d\u064a\u062b \u0635\u064a\u063a\u062a \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0628\u0627\u0639\u062a\u0628\u0627\u0631\u0647\u0627 \u0645\u0633\u0627\u0648\u0627\u0629 \u0628\u064a\u0646 \u0645\u0631\u0628\u0639 \u0627\u0644\u0648\u062a\u0631 \u0648\u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u064a \u0627\u0644\u0636\u0644\u0639\u064a\u0646 \u0627\u0644\u0642\u0627\u0626\u0645\u064a\u0646. <sup class=\"ref\"><a href=\"https:\/\/www.perseus.tufts.edu\/hopper\/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D47\" title=\"16|Euclid, Elements, Book I, Proposition 47|Thomas L. Heath\u060c Perseus Digital Library|1910\" target=\"_blank\" rel=\"noopener\">[16]<\/a><\/sup> \u0648\u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0646\u0634\u0623\u062a \u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0644\u0627 \u062d\u0635\u0631 \u0644\u0647\u0627 \u0641\u064a \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629\u060c \u0648\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062b\u0644\u062b\u0627\u062a\u060c \u0648\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f\u060c \u0648\u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621\u060c \u0648\u0627\u0644\u0647\u0646\u062f\u0633\u0629\u060c \u0648\u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u062e\u0637\u064a\u060c \u0648\u0627\u0644\u062d\u0648\u0633\u0628\u0629. \u0648\u0644\u0630\u0644\u0643 \u0641\u0625\u0646 \u0645\u0643\u0627\u0646\u0629 \u0646\u0638\u0631\u064a\u0629 \u0641\u064a\u062b\u0627\u063a\u0648\u0631\u0633 \u0644\u0627 \u062a\u0631\u062c\u0639 \u0625\u0644\u0649 \u0628\u0633\u0627\u0637\u0629 \u0645\u0639\u0627\u062f\u0644\u062a\u0647\u0627 \u0641\u062d\u0633\u0628\u060c \u0628\u0644 \u0625\u0644\u0649 \u0642\u062f\u0631\u062a\u0647\u0627 \u0639\u0644\u0649 \u0627\u0644\u0631\u0628\u0637 \u0628\u064a\u0646 \u0641\u0631\u0648\u0639 \u0631\u064a\u0627\u0636\u064a\u0629 \u0645\u062a\u0639\u062f\u062f\u0629 \u0648\u062a\u062d\u0648\u064a\u0644 \u0641\u0643\u0631\u0629 \u0647\u0646\u062f\u0633\u064a\u0629 \u0642\u062f\u064a\u0645\u0629 \u0625\u0644\u0649 \u0645\u0628\u062f\u0623 \u0623\u0633\u0627\u0633\u064a \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u062b\u0629.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0639\u0644\u0627\u0642\u0629 \u0623\u0636\u0644\u0627\u0639 \u0627\u0644\u0645\u062b\u0644\u062b \u0627\u0644\u0642\u0627\u0626\u0645<\/p>\n","protected":false},"author":1,"featured_media":4626,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[23],"tags":[],"class_list":["post-4627","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-basic-sciences"],"_links":{"self":[{"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/posts\/4627","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/comments?post=4627"}],"version-history":[{"count":1,"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/posts\/4627\/revisions"}],"predecessor-version":[{"id":4628,"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/posts\/4627\/revisions\/4628"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/media\/4626"}],"wp:attachment":[{"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/media?parent=4627"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/categories?post=4627"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/tags?post=4627"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}