"ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ᠊ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ"-ны өөр хувилбарууд
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= ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ = | = ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ = | ||
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<span style="writing-mode: horizontal-tb">[[File:Sum_of_angles_of_triangle_dzmanto.png|thumb|<span style="padding-left: 40px; writing-mode: vertical-lr; max-height: 15vh; "><big>ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᠤ ᠥᠨᠴᠦᠭ ᠦᠳ ᠦᠨ ᠨᠡᠢᠢᠯᠡᠪᠦᠷᠢ 180°᠃</big>]]</span> | |||
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ᠬᠦᠮᠦᠨ ᠲᠥᠷᠦᠯᠬᠢᠲᠡᠨ ᠢ ᠬᠦᠷᠢᠶᠡᠯᠡᠨ ᠪᠤᠢ ᠶᠢᠷᠲᠢᠨᠴᠦ ᠢᠢᠨ ᠢᠯᠡᠳᠲᠡ ᠬᠠᠷᠠᠭᠳᠠᠬᠤ ᠲᠥᠷᠬᠦ ᠪᠠᠢᠢᠳᠠᠯ ᠲᠠᠢ ᠦᠶᠠᠯᠳᠠᠵᠤ ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠬᠥᠭᠵᠢᠵᠡᠢ᠃ <ref>А.М.Прохоров и др. Советский энциклопедический словарь. ©Издательство “Советская энциклопедия”. Москва 1989</ref> ᠬᠣᠶᠠᠷ ᠲᠠᠯ ᠠ᠋ ᠤᠷᠤᠭᠤ ᠲᠠᠲᠤᠭᠰᠠᠨ ᠴᠢᠪᠬᠠᠳᠤᠰᠤ ᠵᠠᠪᠠᠯ ᠰᠢᠯᠠᠭᠤᠨ ᠪᠠᠢᠢᠬᠤ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠢᠨᠠᠭᠤᠬᠢ ᠴᠢᠨᠠᠷ ᠤᠳ ᠡᠨᠡᠬᠦ ᠭᠧᠣᠮᠡᠡᠷ ᠦᠨ ᠲᠣᠭᠲᠠᠯᠴᠠᠭᠠᠨ ᠤ ᠦᠨᠳᠦᠰᠦ ᠪᠣᠯᠵᠡᠢ᠃ | ᠬᠦᠮᠦᠨ ᠲᠥᠷᠦᠯᠬᠢᠲᠡᠨ ᠢ ᠬᠦᠷᠢᠶᠡᠯᠡᠨ ᠪᠤᠢ ᠶᠢᠷᠲᠢᠨᠴᠦ ᠢᠢᠨ ᠢᠯᠡᠳᠲᠡ ᠬᠠᠷᠠᠭᠳᠠᠬᠤ ᠲᠥᠷᠬᠦ ᠪᠠᠢᠢᠳᠠᠯ ᠲᠠᠢ ᠦᠶᠠᠯᠳᠠᠵᠤ ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠬᠥᠭᠵᠢᠵᠡᠢ᠃ <ref>А.М.Прохоров и др. Советский энциклопедический словарь. ©Издательство “Советская энциклопедия”. Москва 1989</ref> ᠬᠣᠶᠠᠷ ᠲᠠᠯ ᠠ᠋ ᠤᠷᠤᠭᠤ ᠲᠠᠲᠤᠭᠰᠠᠨ ᠴᠢᠪᠬᠠᠳᠤᠰᠤ ᠵᠠᠪᠠᠯ ᠰᠢᠯᠠᠭᠤᠨ ᠪᠠᠢᠢᠬᠤ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠢᠨᠠᠭᠤᠬᠢ ᠴᠢᠨᠠᠷ ᠤᠳ ᠡᠨᠡᠬᠦ ᠭᠧᠣᠮᠡᠡᠷ ᠦᠨ ᠲᠣᠭᠲᠠᠯᠴᠠᠭᠠᠨ ᠤ ᠦᠨᠳᠦᠰᠦ ᠪᠣᠯᠵᠡᠢ᠃ | ||
ᠨᠡᠢᠢᠲᠡ ᠢᠢᠨ ᠲᠣᠭᠠᠯᠠᠯ ᠤᠨ ᠡᠮᠦᠨᠡᠬᠢ 3 ᠳ᠋ᠤᠭᠠᠷ ᠵᠠᠭᠤᠨ ᠤ ᠦᠶ ᠡ᠋ ᠳ᠋ᠦ ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ (Εὐκλείδης) ᠪᠡᠷ "ᠡᠬᠢᠯᠡᠯ" (Στοιχεῖον) ᠬᠡᠮᠡᠬᠦ 13 ᠪᠣᠲᠢ ᠪᠦᠲᠦᠭᠡᠯ ᠳ᠋ᠦ ᠪᠡᠨ ᠮᠠᠲ᠌ᠾᠧᠮᠠᠲ᠋ᠢᠻ᠂ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠦᠨ ᠵᠠᠷᠴᠢᠮ᠂ ᠪᠠᠷᠢᠮᠲᠠᠯᠠᠯ ᠤᠳ ᠢ ᠨᠢᠭᠡᠨ ᠴᠣᠭᠴᠠ ᠢᠵᠢ ᠪᠦᠷᠢᠳᠡᠯ ᠪᠣᠯᠭᠠᠨ ᠨᠢᠭᠡᠳᠬᠡᠵᠡᠢ᠃<ref>[https://books.google.mn/books?id=djUPAQAAMAAJ&redir_esc=y B. L. Van Der Waerden. Science Awakening I, Volume 1. Noordhoff International. 1975]. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/03/17</ref> | ᠨᠡᠢᠢᠲᠡ ᠢᠢᠨ ᠲᠣᠭᠠᠯᠠᠯ ᠤᠨ ᠡᠮᠦᠨᠡᠬᠢ 3 ᠳ᠋ᠤᠭᠠᠷ ᠵᠠᠭᠤᠨ ᠤ ᠦᠶ ᠡ᠋ ᠳ᠋ᠦ ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ (Εὐκλείδης) ᠪᠡᠷ "ᠡᠬᠢᠯᠡᠯ" (Στοιχεῖον) ᠬᠡᠮᠡᠬᠦ 13 ᠪᠣᠲᠢ ᠪᠦᠲᠦᠭᠡᠯ ᠳ᠋ᠦ ᠪᠡᠨ ᠮᠠᠲ᠌ᠾᠧᠮᠠᠲ᠋ᠢᠻ᠂ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠦᠨ ᠵᠠᠷᠴᠢᠮ᠂ ᠪᠠᠷᠢᠮᠲᠠᠯᠠᠯ ᠤᠳ ᠢ ᠨᠢᠭᠡᠨ ᠴᠣᠭᠴᠠ ᠢᠵᠢ ᠪᠦᠷᠢᠳᠡᠯ ᠪᠣᠯᠭᠠᠨ ᠨᠢᠭᠡᠳᠬᠡᠵᠡᠢ᠃<ref>[https://books.google.mn/books?id=djUPAQAAMAAJ&redir_esc=y B. L. Van Der Waerden. Science Awakening I, Volume 1. Noordhoff International. 1975]. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/03/17</ref> | ||
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ᠫᠣᠰᠲᠦ᠋ᠯᠠᠲ ᠭᠡᠳᠡᠭ ᠢ ᠡ᠊᠂ ᠸᠠᠩᠳᠤᠢ ᠢᠢᠨ ᠣᠷᠤᠰ ᠮᠣᠩᠭᠤᠯ ᠨᠡᠷ ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠨ ᠤ ᠲᠣᠯᠢ ᠳ᠋ᠤ "ᠳᠠᠯᠳᠠ ᠦᠨᠡᠨ" ᠦᠨᠡ ᠭᠡᠵᠦ ᠣᠷᠴᠢᠭᠤᠯᠤᠭᠰᠠᠨ ᠨᠢ ᠰᠣᠨᠢᠷᠬᠠᠯ ᠲᠠᠢ᠃<ref name=":1">ᠡ᠊᠂ ᠸᠠᠩᠳᠤᠢ᠃ ᠣᠷᠤᠰ-ᠮᠣᠩᠭᠤᠯ ᠨᠡᠷ ᠡ᠋ ᠮᠣᠮᠢᠶᠠᠨ ᠤ ᠲᠣᠯᠢ᠃ ᠪᠦ᠊᠂ ᠨᠠ᠊᠂ ᠮᠣ᠊᠂ ᠠ᠊᠂ ᠤ᠊᠂ ᠤᠨ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ ᠤ ᠠᠻᠠᠳᠧᠮᠢ᠃ ᠬᠡᠯᠡ ᠵᠣᠬᠢᠶᠠᠯ ᠤᠨ ᠬᠦᠷᠢᠶᠡᠯᠡᠩ᠃ ᠤᠯᠤᠰ ᠤᠨ ᠬᠡᠪᠯᠡᠯ ᠦᠨ ᠬᠡᠷᠡᠭ ᠡᠷᠬᠢᠯᠡᠬᠦ ᠬᠣᠷᠢᠶ ᠠ᠋᠃ ᠤᠯᠠᠭᠠᠨᠪᠠᠭᠠᠲᠤᠷ 1964᠃</ref><br> | ᠫᠣᠰᠲᠦ᠋ᠯᠠᠲ ᠭᠡᠳᠡᠭ ᠢ ᠡ᠊᠂ ᠸᠠᠩᠳᠤᠢ ᠢᠢᠨ ᠣᠷᠤᠰ ᠮᠣᠩᠭᠤᠯ ᠨᠡᠷ ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠨ ᠤ ᠲᠣᠯᠢ ᠳ᠋ᠤ "ᠳᠠᠯᠳᠠ ᠦᠨᠡᠨ" ᠦᠨᠡ ᠭᠡᠵᠦ ᠣᠷᠴᠢᠭᠤᠯᠤᠭᠰᠠᠨ ᠨᠢ ᠰᠣᠨᠢᠷᠬᠠᠯ ᠲᠠᠢ᠃<ref name=":1">ᠡ᠊᠂ ᠸᠠᠩᠳᠤᠢ᠃ ᠣᠷᠤᠰ-ᠮᠣᠩᠭᠤᠯ ᠨᠡᠷ ᠡ᠋ ᠮᠣᠮᠢᠶᠠᠨ ᠤ ᠲᠣᠯᠢ᠃ ᠪᠦ᠊᠂ ᠨᠠ᠊᠂ ᠮᠣ᠊᠂ ᠠ᠊᠂ ᠤ᠊᠂ ᠤᠨ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ ᠤ ᠠᠻᠠᠳᠧᠮᠢ᠃ ᠬᠡᠯᠡ ᠵᠣᠬᠢᠶᠠᠯ ᠤᠨ ᠬᠦᠷᠢᠶᠡᠯᠡᠩ᠃ ᠤᠯᠤᠰ ᠤᠨ ᠬᠡᠪᠯᠡᠯ ᠦᠨ ᠬᠡᠷᠡᠭ ᠡᠷᠬᠢᠯᠡᠬᠦ ᠬᠣᠷᠢᠶ ᠠ᠋᠃ ᠤᠯᠠᠭᠠᠨᠪᠠᠭᠠᠲᠤᠷ 1964᠃</ref><br> | ||
"ᠡᠬᠢᠯᠡᠯ" ᠪᠦᠲᠦᠭᠡᠯ ᠳ᠋ᠦ ᠲᠣᠮᠢᠶᠠᠯᠠᠭᠰᠠᠨ ᠦᠨᠳᠦᠰᠦᠨ ᠫᠣᠰᠲᠦ᠋ᠯᠠᠲ ᠤᠳ ᠤᠨ ᠤᠳᠬ ᠠ᠋ ᠨᠢ᠄ <br><br> | "ᠡᠬᠢᠯᠡᠯ" ᠪᠦᠲᠦᠭᠡᠯ ᠳ᠋ᠦ ᠲᠣᠮᠢᠶᠠᠯᠠᠭᠰᠠᠨ ᠦᠨᠳᠦᠰᠦᠨ ᠫᠣᠰᠲᠦ᠋ᠯᠠᠲ ᠤᠳ ᠤᠨ ᠤᠳᠬ ᠠ᠋ ᠨᠢ᠄ <br><br> | ||
<span style="writing-mode: horizontal-tb">[[File:Parallel_postulate_en.svg|thumb|<span style="padding-left: 40px; writing-mode: vertical-lr; max-height: 35vh; "><big>ᠲᠠᠪᠤᠳᠤᠭᠠᠷ ᠫᠣᠰᠲᠦ᠋ᠯᠠᠲ᠄ ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠲᠠᠢ ᠣᠭᠲᠣᠯᠤᠯᠴᠠᠭᠰᠠᠨ ᠰᠢᠯᠤᠭᠤᠨ ᠨᠢ ᠤᠭ ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠲᠠᠢ ᠬᠣᠶᠠᠷ ᠲᠡᠭᠰᠢ ᠥᠨᠴᠥᠭ ᠡᠴᠡ ᠪᠠᠭᠠ ᠳᠣᠲᠣᠭᠠᠳᠤ ᠥᠷᠥᠭᠡᠯ ᠥᠨᠴᠥᠭ ᠦᠳ ᠡᠭᠦᠰᠬᠡᠵᠦ ᠪᠠᠶᠢᠭᠠ ᠲᠣᠬᠢᠶᠠᠳᠠᠯ ᠳᠤ ᠤᠭ ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠢ ᠬᠢᠵᠠᠭᠠᠷ ᠦᠭᠡᠢ ᠦᠷᠭᠦᠯᠵᠢᠯᠡᠭᠦᠯᠪᠡᠯ ᠲᠡᠳᠡᠭᠡᠷ ᠨᠢ ᠬᠣᠶᠠᠷ ᠲᠡᠭᠰᠢ ᠥᠨᠴᠥᠭ ᠦᠳ ᠡᠴᠡ ᠪᠠᠭᠠ ᠬᠣᠶᠠᠷ ᠥᠨᠴᠥᠭ ᠲᠡᠢ ᠲᠠᠯᠠ ᠳᠤ ᠪᠠᠨ ᠣᠭᠲᠣᠯᠤᠯᠴᠠᠨᠠ᠃</big>]]</span> | |||
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<span style="writing-mode: horizontal-tb; ">1.</span> ᠠᠯᠢᠪᠠ ᠳᠤᠷᠠ ᠶᠢᠨ ᠴᠡᠭ ᠡᠴᠡ ᠳᠤᠷᠠ ᠶᠢᠨ ᠴᠡᠭ ᠬᠦᠷᠲᠡᠯᠡ ᠰᠢᠯᠤᠭᠤᠨ ᠲᠠᠲᠠᠵᠤ ᠪᠣᠯᠤᠨᠠ᠃<br> | <span style="writing-mode: horizontal-tb; ">1.</span> ᠠᠯᠢᠪᠠ ᠳᠤᠷᠠ ᠶᠢᠨ ᠴᠡᠭ ᠡᠴᠡ ᠳᠤᠷᠠ ᠶᠢᠨ ᠴᠡᠭ ᠬᠦᠷᠲᠡᠯᠡ ᠰᠢᠯᠤᠭᠤᠨ ᠲᠠᠲᠠᠵᠤ ᠪᠣᠯᠤᠨᠠ᠃<br> | ||
<span style="writing-mode: horizontal-tb; ">2.</span> ᠠᠯᠢᠪᠠ ᠰᠢᠯᠤᠭᠤᠨ ᠱᠤᠭᠤᠮ ᠢ ᠬᠢᠵᠠᠭᠠᠷ ᠦᠭᠡᠢ ᠦᠷᠭᠦᠯᠵᠢᠯᠡᠭᠦᠯᠵᠦ ᠪᠣᠯᠤᠨᠠ᠃<br> | <span style="writing-mode: horizontal-tb; ">2.</span> ᠠᠯᠢᠪᠠ ᠰᠢᠯᠤᠭᠤᠨ ᠱᠤᠭᠤᠮ ᠢ ᠬᠢᠵᠠᠭᠠᠷ ᠦᠭᠡᠢ ᠦᠷᠭᠦᠯᠵᠢᠯᠡᠭᠦᠯᠵᠦ ᠪᠣᠯᠤᠨᠠ᠃<br> | ||
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==ᠠᠻᠰᠢᠥᠮ== | ==ᠠᠻᠰᠢᠥᠮ== | ||
ᠠᠻᠰᠢᠣᠮ ᠭᠡᠳᠡᠭ ᠢ ᠡ᠊᠂ ᠸᠠᠩᠳᠤᠢ ᠢᠢᠨ ᠣᠷᠤᠰ ᠮᠣᠩᠭᠤᠯ ᠨᠡᠷ ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠨ ᠤ ᠲᠣᠯᠢ ᠳ᠋ᠤ "ᠢᠯᠡᠳᠲᠡ ᠦᠨᠡᠨ" ᠦᠨᠡ ᠭᠡᠵᠦ᠂ ᠬᠠᠷᠢᠮ ᠲᠾᠧᠣᠷᠧᠮ ᠢ "ᠮᠠᠭᠠᠳᠯᠠᠬᠤ ᠦᠨᠡᠨ" ᠭᠡᠵᠦ ᠣᠷᠴᠢᠭᠤᠯᠤᠭᠰᠠᠨ ᠪᠠᠢᠢᠳᠠᠭ᠃<ref name=":1" /><br><br> | ᠠᠻᠰᠢᠣᠮ ᠭᠡᠳᠡᠭ ᠢ ᠡ᠊᠂ ᠸᠠᠩᠳᠤᠢ ᠢᠢᠨ ᠣᠷᠤᠰ ᠮᠣᠩᠭᠤᠯ ᠨᠡᠷ ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠨ ᠤ ᠲᠣᠯᠢ ᠳ᠋ᠤ "ᠢᠯᠡᠳᠲᠡ ᠦᠨᠡᠨ" ᠦᠨᠡ ᠭᠡᠵᠦ᠂ ᠬᠠᠷᠢᠮ ᠲᠾᠧᠣᠷᠧᠮ ᠢ "ᠮᠠᠭᠠᠳᠯᠠᠬᠤ ᠦᠨᠡᠨ" ᠭᠡᠵᠦ ᠣᠷᠴᠢᠭᠤᠯᠤᠭᠰᠠᠨ ᠪᠠᠢᠢᠳᠠᠭ᠃<ref name=":1" /><br><br> | ||
<span style="writing-mode: horizontal-tb">[[File:Pythagorean.svg|thumb|<span style="padding-left: 40px; writing-mode: vertical-lr; max-height: 14vh; "><big>ᠲᠡᠭᠰᠢ ᠥᠨᠴᠦᠭᠲᠦ ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ᠤ ᠬᠠᠮᠤᠭ ᠤᠨ ᠤᠷᠲᠤ ᠲᠠᠯ ᠠ᠋ ᠢᠢᠨ ᠻᠸᠠᠲᠷᠠᠲ ᠨᠢ ᠦᠯᠳᠡᠭᠰᠡᠨ ᠲᠠᠯ ᠠ᠋ ᠤᠳ ᠤᠨ ᠤᠷᠲᠤ ᠢᠢᠨ ᠻᠸᠠᠲᠷᠠᠲ ᠤᠨ ᠨᠡᠢᠢᠯᠡᠪᠦᠷᠢ ᠲᠡᠢ ᠲᠡᠩᠴᠡᠨ ᠡ᠋᠃</big>]]</span> | |||
<br> | |||
<span style="writing-mode: horizontal-tb; ">1.</span> ᠨᠢᠭᠡ ᠵᠦᠢᠯ ᠲᠡᠢ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠢᠭᠦᠳ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠴᠤ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶᠢᠨᠠ᠃<br> | <span style="writing-mode: horizontal-tb; ">1.</span> ᠨᠢᠭᠡ ᠵᠦᠢᠯ ᠲᠡᠢ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠢᠭᠦᠳ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠴᠤ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶᠢᠨᠠ᠃<br> | ||
<span style="writing-mode: horizontal-tb; ">2.</span> ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠢᠭᠦᠳ ᠳᠡᠭᠡᠷᠡ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠢᠭᠦᠳᠦ ᠶᠢ ᠨᠡᠮᠡᠪᠡᠯ ᠨᠡᠶᠢᠯᠡᠪᠦᠷᠢ ᠨᠦᠭᠦᠳ ᠨᠢ ᠴᠤ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶᠢᠨᠠ᠃<br> | <span style="writing-mode: horizontal-tb; ">2.</span> ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠢᠭᠦᠳ ᠳᠡᠭᠡᠷᠡ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠢᠭᠦᠳᠦ ᠶᠢ ᠨᠡᠮᠡᠪᠡᠯ ᠨᠡᠶᠢᠯᠡᠪᠦᠷᠢ ᠨᠦᠭᠦᠳ ᠨᠢ ᠴᠤ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶᠢᠨᠠ᠃<br> | ||
21:13, 19 Гуравдугаар сар 2021-ий байдлаарх засвар
ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ
ᠬᠦᠮᠦᠨ ᠲᠥᠷᠦᠯᠬᠢᠲᠡᠨ ᠢ ᠬᠦᠷᠢᠶᠡᠯᠡᠨ ᠪᠤᠢ ᠶᠢᠷᠲᠢᠨᠴᠦ ᠢᠢᠨ ᠢᠯᠡᠳᠲᠡ ᠬᠠᠷᠠᠭᠳᠠᠬᠤ ᠲᠥᠷᠬᠦ ᠪᠠᠢᠢᠳᠠᠯ ᠲᠠᠢ ᠦᠶᠠᠯᠳᠠᠵᠤ ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠬᠥᠭᠵᠢᠵᠡᠢ᠃ [1] ᠬᠣᠶᠠᠷ ᠲᠠᠯ ᠠ᠋ ᠤᠷᠤᠭᠤ ᠲᠠᠲᠤᠭᠰᠠᠨ ᠴᠢᠪᠬᠠᠳᠤᠰᠤ ᠵᠠᠪᠠᠯ ᠰᠢᠯᠠᠭᠤᠨ ᠪᠠᠢᠢᠬᠤ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠢᠨᠠᠭᠤᠬᠢ ᠴᠢᠨᠠᠷ ᠤᠳ ᠡᠨᠡᠬᠦ ᠭᠧᠣᠮᠡᠡᠷ ᠦᠨ ᠲᠣᠭᠲᠠᠯᠴᠠᠭᠠᠨ ᠤ ᠦᠨᠳᠦᠰᠦ ᠪᠣᠯᠵᠡᠢ᠃
ᠨᠡᠢᠢᠲᠡ ᠢᠢᠨ ᠲᠣᠭᠠᠯᠠᠯ ᠤᠨ ᠡᠮᠦᠨᠡᠬᠢ 3 ᠳ᠋ᠤᠭᠠᠷ ᠵᠠᠭᠤᠨ ᠤ ᠦᠶ ᠡ᠋ ᠳ᠋ᠦ ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ (Εὐκλείδης) ᠪᠡᠷ "ᠡᠬᠢᠯᠡᠯ" (Στοιχεῖον) ᠬᠡᠮᠡᠬᠦ 13 ᠪᠣᠲᠢ ᠪᠦᠲᠦᠭᠡᠯ ᠳ᠋ᠦ ᠪᠡᠨ ᠮᠠᠲ᠌ᠾᠧᠮᠠᠲ᠋ᠢᠻ᠂ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠦᠨ ᠵᠠᠷᠴᠢᠮ᠂ ᠪᠠᠷᠢᠮᠲᠠᠯᠠᠯ ᠤᠳ ᠢ ᠨᠢᠭᠡᠨ ᠴᠣᠭᠴᠠ ᠢᠵᠢ ᠪᠦᠷᠢᠳᠡᠯ ᠪᠣᠯᠭᠠᠨ ᠨᠢᠭᠡᠳᠬᠡᠵᠡᠢ᠃[2]
ᠫᠣᠰᠲ᠋ᠦ᠋ᠯᠠᠲ
ᠠᠻᠰᠢᠣᠮ ᠤᠨ ᠠᠷᠭ ᠠ᠋ ᠭᠡᠳᠡᠭ ᠨᠢ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ ᠤ ᠣᠨᠤᠯ ᠪᠠᠢᠢᠭᠤᠯᠬᠤ ᠳ᠋ᠤ ᠪᠠᠨ ᠠᠩᠬᠠᠳᠠᠭᠴᠢ ᠪᠠᠢᠷᠢᠮᠲᠠᠯᠠᠯ ᠤᠳ ᠪᠤᠶᠤ ᠠᠻᠰᠢᠣᠮ᠂ ᠫᠣᠰᠲᠦ᠋ᠯᠠᠲ ᠤᠳ ᠢ ᠰᠠᠭᠤᠷᠢ ᠪᠣᠯᠭᠠᠨ ᠠᠪᠳᠠᠭ᠂ ᠪᠤᠰᠤᠳ ᠰᠠᠨᠠᠭ ᠠ᠋ ᠨᠤᠭᠤᠳ ᠢ ᠲᠡᠳᠡᠭᠡᠷ ᠠᠩᠬᠠᠳᠠᠭᠴᠢ ᠪᠠᠷᠢᠮᠲᠠᠯᠠᠯ ᠤᠳ ᠳ᠋ᠤ ᠳᠤᠯᠳᠤᠢᠢᠳᠠᠨ ᠤᠴᠢᠷ ᠰᠢᠯᠲᠠᠭᠠᠨ ᠢᠢᠠᠷ ᠪᠠᠲᠤᠯᠠᠵᠤ᠂ ᠨᠣᠲᠤᠯᠠᠳᠠᠭ ᠲᠣᠭᠲᠤᠯᠠᠴᠠᠭᠠᠨ ᠤ ᠠᠷᠭ ᠠ᠋ ᠵᠦᠢ ᠶᠤᠮ᠃
ᠢᠢᠨ ᠬᠦ ᠲᠤᠬᠠᠢ ᠢᠢᠨ ᠣᠨᠤᠯ ᠢ ᠦᠨᠡᠨ ᠵᠥᠪ ᠬᠡᠮᠡᠨ ᠪᠠᠲᠤᠯᠠᠬᠤ ᠳ᠋ᠤ ᠪᠠᠨ ᠳᠤᠷ ᠠ᠋ ᠵᠣᠷᠭᠤ ᠪᠠᠷ ᠬᠠᠨᠳᠤᠬᠤ ᠳ᠋ᠤ ᠬᠢᠵᠠᠭᠠᠷ ᠲᠠᠯᠪᠢᠵᠤ ᠥᠭᠭᠦᠳᠡᠭ᠃[3]
ᠫᠣᠰᠲᠦ᠋ᠯᠠᠲ ᠭᠡᠳᠡᠭ ᠢ ᠡ᠊᠂ ᠸᠠᠩᠳᠤᠢ ᠢᠢᠨ ᠣᠷᠤᠰ ᠮᠣᠩᠭᠤᠯ ᠨᠡᠷ ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠨ ᠤ ᠲᠣᠯᠢ ᠳ᠋ᠤ "ᠳᠠᠯᠳᠠ ᠦᠨᠡᠨ" ᠦᠨᠡ ᠭᠡᠵᠦ ᠣᠷᠴᠢᠭᠤᠯᠤᠭᠰᠠᠨ ᠨᠢ ᠰᠣᠨᠢᠷᠬᠠᠯ ᠲᠠᠢ᠃[4]
"ᠡᠬᠢᠯᠡᠯ" ᠪᠦᠲᠦᠭᠡᠯ ᠳ᠋ᠦ ᠲᠣᠮᠢᠶᠠᠯᠠᠭᠰᠠᠨ ᠦᠨᠳᠦᠰᠦᠨ ᠫᠣᠰᠲᠦ᠋ᠯᠠᠲ ᠤᠳ ᠤᠨ ᠤᠳᠬ ᠠ᠋ ᠨᠢ᠄
1. ᠠᠯᠢᠪᠠ ᠳᠤᠷᠠ ᠶᠢᠨ ᠴᠡᠭ ᠡᠴᠡ ᠳᠤᠷᠠ ᠶᠢᠨ ᠴᠡᠭ ᠬᠦᠷᠲᠡᠯᠡ ᠰᠢᠯᠤᠭᠤᠨ ᠲᠠᠲᠠᠵᠤ ᠪᠣᠯᠤᠨᠠ᠃
2. ᠠᠯᠢᠪᠠ ᠰᠢᠯᠤᠭᠤᠨ ᠱᠤᠭᠤᠮ ᠢ ᠬᠢᠵᠠᠭᠠᠷ ᠦᠭᠡᠢ ᠦᠷᠭᠦᠯᠵᠢᠯᠡᠭᠦᠯᠵᠦ ᠪᠣᠯᠤᠨᠠ᠃
3. ᠳᠤᠷᠠ ᠶᠢᠨ ᠲᠥᠪ ᠡᠴᠡ ᠳᠤᠷᠠ ᠶᠢᠨ ᠷᠠᠳᠢᠦ᠋ᠰ ᠢᠶᠠᠷ ᠲᠣᠭᠣᠷᠢᠭ ᠲᠠᠲᠠᠵᠤ ᠪᠣᠯᠤᠨᠠ᠃
4. ᠪᠦᠬᠦ ᠲᠡᠭᠰᠢ ᠥᠨᠴᠥᠭ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠲᠡᠩᠴᠡᠭᠦᠦ᠃
5. ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠲᠠᠢ ᠣᠭᠲᠣᠯᠤᠯᠴᠠᠭᠰᠠᠨ ᠰᠢᠯᠤᠭᠤᠨ ᠨᠢ ᠤᠭ ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠲᠠᠢ ᠬᠣᠶᠠᠷ ᠲᠡᠭᠰᠢ ᠥᠨᠴᠥᠭ ᠡᠴᠡ ᠪᠠᠭᠠ ᠳᠣᠲᠣᠭᠠᠳᠤ ᠥᠷᠥᠭᠡᠯ ᠥᠨᠴᠥᠭ ᠦᠳ ᠡᠭᠦᠰᠬᠡᠵᠦ ᠪᠠᠶᠢᠭᠠ ᠲᠣᠬᠢᠶᠠᠳᠠᠯ ᠳᠤ ᠤᠭ ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠢ ᠬᠢᠵᠠᠭᠠᠷ ᠦᠭᠡᠢ ᠦᠷᠭᠦᠯᠵᠢᠯᠡᠭᠦᠯᠪᠡᠯ ᠲᠡᠳᠡᠭᠡᠷ ᠨᠢ ᠬᠣᠶᠠᠷ ᠲᠡᠭᠰᠢ ᠥᠨᠴᠥᠭ ᠦᠳ ᠡᠴᠡ ᠪᠠᠭᠠ ᠬᠣᠶᠠᠷ ᠥᠨᠴᠥᠭ ᠲᠡᠢ ᠲᠠᠯᠠ ᠳᠤ ᠪᠠᠨ ᠣᠭᠲᠣᠯᠤᠯᠴᠠᠨᠠ᠃[5][6]
ᠠᠻᠰᠢᠥᠮ
ᠠᠻᠰᠢᠣᠮ ᠭᠡᠳᠡᠭ ᠢ ᠡ᠊᠂ ᠸᠠᠩᠳᠤᠢ ᠢᠢᠨ ᠣᠷᠤᠰ ᠮᠣᠩᠭᠤᠯ ᠨᠡᠷ ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠨ ᠤ ᠲᠣᠯᠢ ᠳ᠋ᠤ "ᠢᠯᠡᠳᠲᠡ ᠦᠨᠡᠨ" ᠦᠨᠡ ᠭᠡᠵᠦ᠂ ᠬᠠᠷᠢᠮ ᠲᠾᠧᠣᠷᠧᠮ ᠢ "ᠮᠠᠭᠠᠳᠯᠠᠬᠤ ᠦᠨᠡᠨ" ᠭᠡᠵᠦ ᠣᠷᠴᠢᠭᠤᠯᠤᠭᠰᠠᠨ ᠪᠠᠢᠢᠳᠠᠭ᠃[4]
1. ᠨᠢᠭᠡ ᠵᠦᠢᠯ ᠲᠡᠢ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠢᠭᠦᠳ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠴᠤ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶᠢᠨᠠ᠃
2. ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠢᠭᠦᠳ ᠳᠡᠭᠡᠷᠡ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠢᠭᠦᠳᠦ ᠶᠢ ᠨᠡᠮᠡᠪᠡᠯ ᠨᠡᠶᠢᠯᠡᠪᠦᠷᠢ ᠨᠦᠭᠦᠳ ᠨᠢ ᠴᠤ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶᠢᠨᠠ᠃
3. ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠢᠭᠦᠭᠦᠳ ᠡᠴᠡ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠢᠭᠦᠳᠦ ᠶᠢ ᠬᠠᠰᠤᠪᠠᠯ ᠦᠯᠡᠳᠡᠭᠳᠡᠯ ᠦᠳ ᠨᠢ ᠴᠤ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶᠢᠨᠠ᠃
4. ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠢᠰᠢ ᠨᠢᠭᠦᠳ ᠳᠡᠭᠡᠷᠡ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠢᠭᠦᠳᠦ ᠶᠢ ᠨᠡᠮᠡᠪᠡᠯ ᠨᠡᠶᠢᠯᠡᠪᠦᠷᠢ ᠨᠦᠭᠦᠳ ᠨᠢ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠢᠰᠢ ᠪᠠᠶᠢᠨᠠ᠃
5. ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠢᠭᠦᠳᠦ ᠶᠢ ᠠᠳᠠᠯᠢ ᠬᠡᠮᠵᠢᠶᠡ ᠪᠡᠷ ᠦᠷᠡᠵᠢᠭᠦᠯᠪᠡᠯ ᠦᠷᠡᠵᠢᠪᠦᠷᠢ ᠨᠢ ᠴᠤ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶᠢᠨᠠ᠃
6. ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠢᠭᠦᠭᠦᠳ ᠦᠨ ᠲᠡᠩ ᠬᠠᠭᠠᠰ ᠤᠳ ᠨᠢ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶᠢᠨᠠ᠃
7. ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠳᠠᠪᠬᠤᠴᠠᠬᠤ ᠵᠦᠢᠯ ᠦᠳ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶᠢᠨᠠ᠃ (ᠳᠠᠪᠬᠤᠴᠠᠬᠤ ᠭᠡᠳᠡᠭ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠶᠠᠭ ᠠᠳᠠᠯᠢ ᠭᠡᠰᠡᠨ ᠤᠳᠬᠠ ᠲᠠᠢ)
8. ᠪᠦᠬᠦᠯᠢ ᠨᠢ ᠬᠡᠰᠡᠭ ᠡᠴᠡ ᠪᠡᠨ ᠶᠡᠬᠡ ᠪᠠᠶᠢᠨᠠ᠃
9. ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠤ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠣᠷᠣᠨ ᠵᠠᠢ ᠬᠢᠵᠠᠭᠠᠷᠯᠠᠭᠳᠠᠳᠠᠭ ᠦᠭᠡᠢ᠃[7][6]
ᠠᠴᠢ ᠬᠣᠯᠪᠤᠭᠳᠠᠯ
ᠡᠳᠦᠭᠡ ᠶᠡᠷᠦᠩᠬᠡᠢ ᠪᠣᠯᠪᠠᠰᠤᠷᠠᠯ ᠤᠨ ᠰᠤᠷᠭᠠᠭᠤᠯᠢ ᠳ᠋ᠤ ᠴᠤᠬᠤᠮ ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠦᠵᠡᠵᠦ᠂ ᠰᠤᠳᠤᠯᠵᠤ᠂ ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲ᠋ᠢᠻ᠂ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠦᠨ ᠠᠩᠬᠠᠨ ᠤ ᠮᠡᠳᠡᠭᠳᠡᠬᠦᠨ ᠣᠯᠵᠤ᠂ ᠤᠴᠢᠷ ᠰᠢᠯᠲᠠᠭᠠᠨ᠂ ᠯᠣᠭᠢᠻ ᠰᠡᠳᠬᠢᠯᠭᠡ᠂ ᠨᠣᠲᠠᠯᠠᠬᠤᠢ ᠠᠷᠭ ᠠ᠋ ᠤᠬᠠᠭᠠᠨ ᠳ᠋ᠤ ᠰᠤᠷᠤᠯᠴᠠᠳᠠᠭ᠃
ᠡᠨᠡᠬᠦ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠡᠩ ᠦᠨ ᠠᠮᠢᠳᠤᠷᠠᠯ ᠳ᠋ᠤ ᠪᠦᠬᠦᠢ ᠯᠡ ᠰᠠᠯᠪᠤᠷᠢ ᠳ᠋ᠤ ᠬᠡᠷᠡᠭᠯᠡᠭᠳᠡᠵᠦ ᠪᠠᠢᠢᠨ ᠠ᠋᠃
ᠵᠢᠱᠢᠶ ᠡ᠋ ᠨᠢ᠂ᠬᠠᠮᠢᠭ ᠠ᠋ ᠭᠠᠵᠠᠷ ᠬᠡᠮᠵᠢᠵᠦ ᠲᠠᠯᠠᠪᠠᠢ ᠢᠢᠨ ᠬᠡᠮᠵᠢᠶ ᠡ᠋ ᠢᠢ ᠣᠯᠬᠤ ᠬᠡᠷᠡᠭ ᠲᠠᠢ ᠪᠠᠢᠢᠨ ᠠ᠋᠂ ᠬᠠᠮᠢᠭ ᠠ᠋ ᠪᠠᠷᠠᠭ ᠠ᠋ ᠡᠳ᠋ ᠶᠠᠭᠤᠮᠠᠰ ᠤᠨ ᠡᠵᠡᠯᠡᠬᠦᠨ ᠢ ᠬᠡᠮᠵᠢᠵᠦ ᠲᠣᠭᠠᠴᠠᠭᠠᠯᠬᠤ ᠬᠡᠷᠡᠭ ᠲᠡᠢ ᠪᠠᠢᠢᠨ ᠠ᠋᠂ ᠲᠡᠷᠡ ᠪᠦᠷᠦᠢ ᠳᠦ ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠠᠵᠢᠯᠯᠠᠵᠤ ᠪᠠᠢᠢᠨ ᠠ᠋᠃
ᠠᠯᠢᠪᠠ ᠮᠠᠱᠢᠨ ᠮᠡᠻᠠᠨᠢᠰᠮ᠂ ᠭᠠᠵᠠᠷ ᠤᠨ ᠵᠢᠷᠤᠭ᠂ ᠣᠳᠤᠨ ᠣᠷᠤᠨ ᠲᠡᠷᠢᠭᠦᠲᠡᠨ ᠪᠦᠭᠦᠳᠡ ᠳ᠋ᠦ ᠶᠠᠭᠤᠨ ᠤ ᠡᠮᠦᠨ ᠡ᠋ ᠰᠣᠩᠭᠤᠳᠠᠭ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠬᠡᠷᠡᠭ ᠲᠤᠰᠠ ᠪᠠᠨ ᠡᠷᠭᠦᠵᠦ ᠪᠠᠢᠢᠨ ᠠ᠋᠃[8]
ᠮᠢᠩᠭ ᠠ᠋ ᠮᠢᠩᠭᠠᠨ ᠵᠢᠯ ᠦᠨ ᠤᠷᠠᠰᠬᠠᠯ ᠳ᠋ᠤ ᠬᠦᠷᠢᠶᠡᠯᠡᠨ ᠪᠤᠢ ᠶᠢᠷᠲᠢᠨᠴᠦ ᠢᠢᠨ ᠲᠤᠬᠠᠢ ᠬᠦᠮᠦᠨ ᠲᠥᠷᠦᠯᠬᠢᠲᠡᠨ ᠦ ᠣᠢᠢᠯᠠᠭᠠᠯᠲᠤ᠂ ᠲᠥᠰᠦᠭᠡᠯᠡᠯ ᠭᠦᠨᠵᠡᠭᠡᠢᠢᠷᠡᠬᠦ ᠶᠠᠪᠤᠴᠠ ᠳ᠋ᠤ ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ᠦᠨ ᠪᠤᠰᠤ ᠰᠢᠨ ᠡ᠋ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠦᠨ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠳ ᠡᠭᠦᠰᠴᠦ ᠬᠥᠭᠵᠢᠭᠰᠡᠨ ᠪᠢᠯᠡ᠃
ᠨᠡᠷ ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠯᠠᠯ
ᠡᠬᠢ ᠰᠤᠷᠪᠤᠯᠵᠢ
- ↑ А.М.Прохоров и др. Советский энциклопедический словарь. ©Издательство “Советская энциклопедия”. Москва 1989
- ↑ B. L. Van Der Waerden. Science Awakening I, Volume 1. Noordhoff International. 1975. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/03/17
- ↑ Ю. А. Гастев, А. С. Есенин-Вольпин. Аксиоматический метод. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/03/19
- ↑ 4.0 4.1 ᠡ᠊᠂ ᠸᠠᠩᠳᠤᠢ᠃ ᠣᠷᠤᠰ-ᠮᠣᠩᠭᠤᠯ ᠨᠡᠷ ᠡ᠋ ᠮᠣᠮᠢᠶᠠᠨ ᠤ ᠲᠣᠯᠢ᠃ ᠪᠦ᠊᠂ ᠨᠠ᠊᠂ ᠮᠣ᠊᠂ ᠠ᠊᠂ ᠤ᠊᠂ ᠤᠨ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ ᠤ ᠠᠻᠠᠳᠧᠮᠢ᠃ ᠬᠡᠯᠡ ᠵᠣᠬᠢᠶᠠᠯ ᠤᠨ ᠬᠦᠷᠢᠶᠡᠯᠡᠩ᠃ ᠤᠯᠤᠰ ᠤᠨ ᠬᠡᠪᠯᠡᠯ ᠦᠨ ᠬᠡᠷᠡᠭ ᠡᠷᠬᠢᠯᠡᠬᠦ ᠬᠣᠷᠢᠶ ᠠ᠋᠃ ᠤᠯᠠᠭᠠᠨᠪᠠᠭᠠᠲᠤᠷ 1964᠃
- ↑ Урок геометрия 39 тем. Постулаты Евклида. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/02/09
- ↑ 6.0 6.1 Н.Г.Подаева, Д.А.Жук. Лекции по основаниям геометрии. Елецкий Государственный Университет им. И.А.Бунина. Елец 2005. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/02/09
- ↑ К.Лохматова, Н.Степанова. Презентация "Евклидова геометрия" (7 класс). ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/02/09
- ↑ Значение геометрии. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/03/17