ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ᠊ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ хуудасны эх кодыг харах

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= ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ‍ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ =
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|[[File:Sum_of_angles_of_triangle_dzmanto.png|alight: top|thumb|left]]
|style = "height: 100px;"|ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ‍ᠤ ᠥᠨᠴᠦᠭ ‍ᠦᠳ ‍ᠦᠨ ᠨᠡᠢᠢᠯᠡᠪᠦᠷᠢ 180°
|<math>\alpha+\beta+\gamma = 180^\circ</math><br>
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ᠬᠦᠮᠦᠨ ᠲᠥᠷᠦᠯᠬᠢᠲᠡᠨ ‍ᠢ ᠬᠦᠷᠢᠶᠡᠯᠡᠨ ᠪᠤᠢ [[Ертөнцийг үзэх үзэл|ᠶᠢᠷᠲᠢᠨᠴᠦ ‍ᠢᠢᠨ]] ᠢᠯᠡᠳᠲᠡ ᠬᠠᠷᠠᠭᠳᠠᠬᠤ ᠲᠥᠷᠬᠦ ᠪᠠᠢᠢᠳᠠᠯ ‍ᠲᠠᠢ ᠤᠶᠠᠯᠳᠠᠵᠤ ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ‍ᠦᠨ<sup>Euclid</sup> ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ<sup>geometry</sup> ᠬᠥᠭᠵᠢᠵᠡᠢ᠃ <ref>А.М.Прохоров и др. Советский энциклопедический словарь. ©Издательство “Советская энциклопедия”. Москва 1989</ref> ᠬᠣᠶᠠᠷ ᠲᠡᠢᠢᠰᠢ ᠲᠠᠲᠤᠭᠰᠠᠨ ᠴᠢᠪᠬᠠᠳᠠᠰᠤ ᠵᠠᠪᠠᠯ ᠰᠢᠯᠠᠭᠤᠨ ᠪᠠᠢᠢᠬᠤ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠢᠨᠠᠭᠤᠬᠢ ᠴᠢᠨᠠᠷ ‍ᠤᠳ ᠡᠨᠡᠬᠦ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ‍ᠦᠨ ᠲᠣᠭᠲᠠᠯᠴᠠᠭᠠᠨ ‍ᠤ ᠦᠨᠳᠦᠰᠦ ᠪᠣᠯᠵᠡᠢ᠃ 
ᠨᠡᠢᠢᠲᠡ ‍ᠢᠢᠨ ᠲᠣᠭᠠᠯᠠᠯ ‍ᠤᠨ ᠡᠮᠦᠨᠡᠬᠢ 3 ᠳ᠋ᠤᠭᠠᠷ ᠵᠠᠭᠤᠨ ‍ᠤ ᠦᠶ ‍ᠡ᠋ ‍ᠢᠢᠨ ᠶᠡᠬᠡ ᠰᠡᠳᠬᠢᠭᠴᠢ ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ‍ᠦᠨ (Εὐκλείδης) ᠨᠡᠷ ‍ᠡ᠋ ᠲᠡᠢ ᠬᠣᠯᠪᠤᠭᠳᠠᠳᠠᠭ "ᠡᠬᠢᠯᠡᠯ" (Στοιχεῖον) ᠬᠡᠮᠡᠬᠦ 13 ᠪᠣᠲᠢ ᠪᠦᠲᠦᠭᠡᠯ ᠳ᠋ᠦ  ᠮᠠᠲ᠌ᠾᠧᠮᠠᠲ᠋ᠢᠻ᠂ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ‍ᠦᠨ ᠵᠠᠷᠴᠢᠮ᠂ ᠪᠠᠷᠢᠮᠲᠠᠯᠠᠯ ‍ᠤᠳ ‍ᠢ ᠨᠢᠭᠡᠨ ᠴᠣᠭᠴᠠ  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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==ᠫᠣᠰᠲ᠋ᠦ᠋ᠯᠠᠲ==
ᠠᠻᠰᠢᠣᠮ ‍ᠤᠨ ᠠᠷᠭ᠎ ‍ᠠ᠋ ᠭᠡᠳᠡᠭ ᠨᠢ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ ‍ᠤ ᠣᠨᠤᠯ ᠪᠠᠢᠢᠭᠤᠯᠬᠤ ᠳ᠋ᠤ ᠠᠩᠬᠠᠳᠠᠭᠴᠢ ᠪᠠᠢᠷᠢᠮᠲᠠᠯᠠᠯ ‍ᠤᠳ ᠪᠤᠶᠤ ᠠᠻᠰᠢᠣᠮ᠂ ᠫᠣᠰᠲᠦ᠋ᠯᠠᠲ ‍ᠤᠳ ‍ᠢ ᠰᠠᠭᠤᠷᠢ ᠪᠣᠯᠭᠠᠨ ᠠᠪᠳᠠᠭ᠂ ᠪᠤᠰᠤᠳ ᠰᠠᠨᠠᠭ᠎ ‍ᠠ᠋ ᠨᠤᠭᠤᠳ ‍ᠢ ᠲᠡᠳᠡᠭᠡᠷ ᠠᠩᠬᠠᠳᠠᠭᠴᠢ ᠪᠠᠷᠢᠮᠲᠠᠯᠠᠯ ‍ᠤᠳ ᠳ᠋ᠤ ᠳᠤᠯᠳᠤᠢᠢᠳᠤᠨ ᠤᠴᠢᠷ ᠰᠢᠯᠲᠠᠭᠠᠨ ‍ᠢᠢᠠᠷ ᠪᠠᠲᠤᠯᠠᠵᠤ᠂ ᠨᠣᠲᠠᠯᠠᠳᠠᠭ ᠲᠣᠭᠲᠠᠯᠴᠠᠭᠠᠨ ‍ᠤ ᠠᠷᠭ᠎ ‍ᠠ᠋ ᠵᠦᠢ ᠶᠤᠮ᠃<br>
ᠢᠢᠨ ᠬᠦ ᠲᠤᠬᠠᠢ ‍ᠢᠢᠨ ᠣᠨᠤᠯ ‍ᠢ ᠦᠨᠡᠨ ᠵᠥᠪ ᠬᠡᠮᠡᠨ ᠪᠠᠲᠤᠯᠠᠬᠤ ᠶᠠᠪᠤᠴᠠ ᠳ᠋ᠤ ᠳᠤᠷ ‍ᠠ᠋ ᠵᠣᠷᠭ᠎ ‍ᠠ᠋ ᠪᠠᠷ ᠬᠠᠨᠳᠤᠬᠤ ᠶᠠᠪᠤᠳᠠᠯ ‍ᠢ ᠬᠠᠵᠠᠭᠠᠷᠯᠠᠵᠤ ᠥᠭᠭᠦᠳᠡᠭ᠃<ref>[https://www.booksite.ru/fulltext/1/001/008/007/395.htm Ю. А. Гастев, А. С. Есенин-Вольпин. Аксиоматический метод]. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/03/19</ref><br>
ᠫᠣᠰᠲᠦ᠋ᠯᠠᠲ ᠭᠡᠳᠡᠭ ‍ᠢ ᠡ᠊᠂ ᠸᠠᠩᠳᠤᠢ ‍ᠢᠢᠨ ᠣᠷᠤᠰ-ᠮᠣᠩᠭᠤᠯ ᠨᠡᠷ ‍ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠨ ‍ᠤ ᠲᠣᠯᠢ ᠳ᠋ᠤ "ᠳᠠᠯᠳᠠ ᠦᠨᠡᠨ" 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>
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{| class="wikitable"
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|[[File:Parallel_postulate_en.svg|thumb]]
|style = "height: 250px;"|ᠲᠠᠪᠤᠳᠤᠭᠠᠷ ᠫᠣᠰᠲᠦ᠋ᠯᠠᠲ᠄ ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠲᠠᠢ ᠣᠭᠲᠣᠯᠤᠯᠴᠠᠭᠰᠠᠨ ᠰᠢᠯᠤᠭᠤᠨ ᠨᠢ ᠤᠭ ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠲᠠᠢ ᠬᠣᠶᠠᠷ ᠲᠡᠭᠰᠢ ᠥᠨᠴᠥᠭ ᠡᠴᠡ ᠪᠠᠭ᠎ᠠ ᠳᠣᠲᠣᠭᠠᠳᠤ ᠥᠷᠥᠭᠡᠯ ᠥᠨᠴᠥᠭ ᠦᠳ ᠡᠭᠦᠰᠬᠡᠵᠦ ᠪᠠᠶ᠋ᠢᠭ᠎ᠠ ᠲᠣᠬᠢᠶᠠᠯᠳᠤᠯ ᠳᠤ ᠤᠭ ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠢ ᠬᠢᠵᠠᠭᠠᠷ ᠦᠭᠡᠢ ᠦᠷᠭᠦᠯᠵᠢᠯᠡᠭᠦᠯᠪᠡᠯ ᠲᠡᠳᠡᠭᠡᠷ ᠨᠢ ᠬᠣᠶᠠᠷ ᠲᠡᠭᠰᠢ ᠥᠨᠴᠥᠭ ᠦᠳ ᠡᠴᠡ ᠪᠠᠭ᠎ᠠ ᠬᠣᠶᠠᠷ ᠥᠨᠴᠥᠭ ᠲᠡᠢ ᠲᠠᠯ᠎ᠠ ᠳᠤ ᠪᠠᠨ ᠣᠭᠲᠣᠯᠤᠯᠴᠠᠨ᠎ᠠ᠃
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<span style="writing-mode: horizontal-tb; ">1.</span> ᠠᠯᠢᠪᠠ ᠳᠤᠷ᠎ᠠ ᠶᠢᠨ ᠴᠡᠭ ᠡᠴᠡ ᠳᠤᠷ᠎ᠠ ᠶᠢᠨ ᠴᠡᠭ ᠬᠦᠷᠲᠡᠯ᠎ᠡ ᠰᠢᠯᠤᠭᠤᠨ ᠲᠠᠲᠠᠵᠤ ᠪᠣᠯᠤᠨ᠎ᠠ᠃<br>
<span style="writing-mode: horizontal-tb; ">2.</span> ᠠᠯᠢᠪᠠ ᠰᠢᠯᠤᠭᠤᠨ ᠱᠤᠭᠤᠮ ᠢ ᠬᠢᠵᠠᠭᠠᠷ ᠦᠭᠡᠢ ᠦᠷᠭᠦᠯᠵᠢᠯᠡᠭᠦᠯᠵᠦ ᠪᠣᠯᠤᠨ᠎ᠠ᠃<br>
<span style="writing-mode: horizontal-tb; ">3.</span> ᠳᠤᠷ᠎ᠠ ᠶᠢᠨ ᠲᠥᠪ ᠡᠴᠡ ᠳᠤᠷ᠎ᠠ ᠶᠢᠨ ᠷᠠᠳᠢᠦ᠋ᠰ  ‍ᠢᠶ᠋ᠠᠷ<sup>radius</sup> ᠲᠣᠭᠣᠷᠢᠭ ᠲᠠᠲᠠᠵᠤ ᠪᠣᠯᠤᠨ᠎ᠠ᠃<br>
<span style="writing-mode: horizontal-tb; ">4.</span> ᠪᠦᠬᠦ ᠲᠡᠭᠰᠢ ᠥᠨᠴᠥᠭ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠲᠡᠩᠴᠡᠭᠦᠦ᠃<br>
<span style="writing-mode: horizontal-tb; ">5.</span> ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠲᠠᠢ ᠣᠭᠲᠣᠯᠤᠯᠴᠠᠭᠰᠠᠨ ᠰᠢᠯᠤᠭᠤᠨ ᠨᠢ ᠤᠭ ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠲᠠᠢ ᠬᠣᠶᠠᠷ ᠲᠡᠭᠰᠢ ᠥᠨᠴᠥᠭ ᠡᠴᠡ ᠪᠠᠭ᠎ᠠ ᠳᠣᠲᠣᠭᠠᠳᠤ ᠥᠷᠥᠭᠡᠯ ᠥᠨᠴᠥᠭ ᠦᠳ ᠡᠭᠦᠰᠬᠡᠵᠦ ᠪᠠᠶ᠋ᠢᠭ᠎ᠠ ᠲᠣᠬᠢᠶᠠᠯᠳᠤᠯ ᠳᠤ ᠤᠭ ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠢ ᠬᠢᠵᠠᠭᠠᠷ ᠦᠭᠡᠢ ᠦᠷᠭᠦᠯᠵᠢᠯᠡᠭᠦᠯᠪᠡᠯ ᠲᠡᠳᠡᠭᠡᠷ ᠨᠢ ᠬᠣᠶᠠᠷ ᠲᠡᠭᠰᠢ ᠥᠨᠴᠥᠭ ᠦᠳ ᠡᠴᠡ ᠪᠠᠭ᠎ᠠ ᠬᠣᠶᠠᠷ ᠥᠨᠴᠥᠭ ᠲᠡᠢ ᠲᠠᠯ᠎ᠠ ᠳᠤ ᠪᠠᠨ ᠣᠭᠲᠣᠯᠤᠯᠴᠠᠨ᠎ᠠ᠃<ref>[http://900igr.net/prezentatsii/geometrija/Evklid/005-Postulaty-Evklida.html Урок геометрия 39 тем. Постулаты Евклида]. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/02/09</ref><ref name=":0" />
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==ᠠᠻᠰᠢᠥᠮ==
ᠠᠻᠰᠢᠣᠮ ᠭᠡᠳᠡᠭ ‍ᠢ ᠡ᠊᠂ ᠸᠠᠩᠳᠤᠢ ‍ᠢᠢᠨ ᠣᠷᠤᠰ-ᠮᠣᠩᠭᠤᠯ ᠨᠡᠷ ‍ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠨ ‍ᠤ ᠲᠣᠯᠢ ᠳ᠋ᠤ "ᠢᠯᠡᠳᠲᠡ ᠦᠨᠡᠨ" ᠭᠡᠵᠦ᠂ ᠬᠠᠷᠢᠨ ᠲᠾᠧᠣᠷᠧᠮ ‍ᠢ "ᠮᠠᠭᠠᠳᠯᠠᠬᠤ ᠦᠨᠡᠨ" ᠭᠡᠵᠦ ᠣᠷᠴᠢᠭᠤᠯᠤᠭᠰᠠᠨ ᠪᠠᠢᠢᠳᠠᠭ᠃<ref name=":1" /><br>
ᠠᠻᠰᠢᠣᠮ ᠪᠠ ᠫᠣᠰᠲᠦ᠋ᠯᠠᠲ ᠪᠠᠲᠤᠯᠠᠭ᠎ ‍ᠠ᠋ ᠱᠠᠭᠠᠷᠳᠠᠳᠠᠭ ᠦᠭᠡᠢ᠂ ᠥᠪᠡᠷ ᠡᠴᠡ ᠪᠡᠨ ᠢᠯᠡᠷᠬᠡᠶ᠂ ᠲᠣᠳᠤᠷᠬᠠᠶ ᠮᠡᠳᠡᠭᠳᠡᠬᠦᠨ ᠨᠤᠭᠦᠳ ᠭᠡᠵᠦ ᠦᠵᠡᠳᠡᠭ᠃ <br>
ᠬᠠᠷᠢᠨ ᠲᠾᠧᠣᠷᠧᠮ ‍ᠦᠳ ‍ᠢ ᠠᠻᠰᠢᠣᠮ᠂ ᠫᠣᠰᠲᠦ᠋ᠯᠠᠲ᠋ ᠪᠣᠯᠤᠨ ᠡᠮᠦᠨ᠎ ‍ᠡ᠋ ᠨᠢ ᠠᠻᠰᠢᠣᠮ᠂ ᠫᠣᠰᠲᠦ᠋ᠯᠠᠲ᠋ ᠲᠤ ᠲᠤᠯᠭᠠᠭᠤᠷᠯᠠᠨ ᠪᠠᠲᠤᠯᠠᠭᠰᠠᠨ ᠲᠾᠧᠣᠷᠧᠮ ‍ᠦᠳ ‍ᠢᠢᠡᠷ ᠡᠰᠢ ᠪᠣᠯᠭᠠᠨ ᠪᠠᠲᠤᠯᠠᠳᠠᠭ᠃
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{| class="wikitable"
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|style = "height: 160px;"|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᠃
|<math>c^2 = a^2 + b^2</math>
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<span style="writing-mode: horizontal-tb; ">1.</span> ᠨᠢᠭᠡ ᠵᠦᠢᠯ ᠲᠡᠢ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠤᠭᠦᠳ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠴᠤ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶ᠋ᠢᠨ᠎ᠠ᠃<br>
<span style="writing-mode: horizontal-tb; ">2.</span> ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠤᠭᠦᠳ ᠳᠡᠭᠡᠷ᠎ᠡ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠤᠭᠦᠳ ᠶᠢ ᠨᠡᠮᠡᠪᠡᠯ ᠨᠡᠶ᠋ᠢᠯᠡᠪᠦᠷᠢ ‍ᠦᠳ ᠨᠢ ᠴᠤ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶ᠋ᠢᠨ᠎ᠠ᠃<br>
<span style="writing-mode: horizontal-tb; ">3.</span> ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠤᠭᠦᠳ ᠡᠴᠡ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠤᠭᠦᠳ ᠶᠢ ᠬᠠᠰᠤᠪᠠᠯ ᠦᠯᠡᠳᠡᠭᠳᠡᠯ ᠦᠳ ᠨᠢ ᠴᠤ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶ᠋ᠢᠨ᠎ᠠ᠃<br>
<span style="writing-mode: horizontal-tb; ">4.</span> ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠢᠰᠢ ᠨᠤᠭᠦᠳ ᠳᠡᠭᠡᠷ᠎ᠡ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠤᠭᠦᠳ ᠶᠢ ᠨᠡᠮᠡᠪᠡᠯ ᠨᠡᠶ᠋ᠢᠯᠡᠪᠦᠷᠢ ‍ᠦᠳ ᠨᠢ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠢᠰᠢ ᠪᠠᠶ᠋ᠢᠨ᠎ᠠ᠃<br>
<span style="writing-mode: horizontal-tb; ">5.</span> ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠤᠭᠦᠳ ᠶᠢ ᠠᠳᠠᠯᠢ ᠬᠡᠮᠵᠢᠶ᠎ᠡ ᠪᠡᠷ ᠦᠷᠡᠵᠢᠭᠦᠯᠪᠡᠯ ᠦᠷᠡᠵᠢᠪᠦᠷᠢ ᠨᠢ ᠴᠤ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶ᠋ᠢᠨ᠎ᠠ᠃<br>
<span style="writing-mode: horizontal-tb; ">6.</span> ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠤᠭᠦᠳ ᠦᠨ ᠲᠡᠩ ᠬᠠᠭᠠᠰ ᠤᠳ ᠨᠢ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶ᠋ᠢᠨ᠎ᠠ᠃<br>
<span style="writing-mode: horizontal-tb; ">7.</span> ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠳᠠᠪᠬᠤᠴᠠᠬᠤ ᠵᠦᠢᠯ ᠦᠳ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶ᠋ᠢᠨ᠎ᠠ᠃ (ᠳᠠᠪᠬᠤᠴᠠᠬᠤ ᠭᠡᠳᠡᠭ ᠨᠢ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠶᠠᠭ ᠠᠳᠠᠯᠢ ᠭᠡᠰᠡᠨ ᠤᠳᠬ᠎ᠠ ᠲᠠᠢ)<br>
<span style="writing-mode: horizontal-tb; ">8.</span> ᠪᠦᠬᠦᠯᠢ ᠨᠢ ᠬᠡᠰᠡᠭ ᠡᠴᠡ ᠪᠡᠨ ᠶᠡᠬᠡ ᠪᠠᠶ᠋ᠢᠨ᠎ᠠ᠃<br>
<span style="writing-mode: horizontal-tb; ">9.</span> ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠤ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ [[ᠣᠭᠲᠠᠷᠭᠤᠢ|ᠣᠷᠣᠨ ᠵᠠᠢ]] ᠬᠢᠵᠠᠭᠠᠷᠯᠠᠭᠳᠠᠳᠠᠭ ᠦᠭᠡᠢ᠃<ref>[https://infourok.ru/prezentaciya-evklidova-geometriya-klass-1332117.html К.Лохматова, Н.Степанова. Презентация "Евклидова геометрия" (7 класс)]. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/02/09</ref><ref name=":0">[http://www.inggu.ru/upload/lectures/%D0%9E%D0%A1%D0%9D%D0%9E%D0%92%D0%90%D0%9D%D0%98%D0%95%20%D0%93%D0%95%D0%9E%D0%9C%D0%95%D0%A2%D0%A0%D0%98%D0%98.pdf Н.Г.Подаева, Д.А.Жук. Лекции по основаниям геометрии. Елецкий Государственный Университет им. И.А.Бунина. Елец 2005]. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/02/09</ref>
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==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᠃ 

ᠡᠨᠡ ᠬᠦ 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 ᠪᠦᠷᠢ ‍ᠳᠦ ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ‍ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠠᠵᠢᠯᠯᠠᠵᠤ ᠪᠠᠢᠢᠨ᠎ ‍ᠠ᠋᠃ 

ᠠᠯᠢᠪᠠ ᠮᠠᠱᠢᠨ ᠮᠧᠻᠠᠨᠢᠰᠮ᠂ ᠭᠠᠵᠠᠷ ‍ᠤᠨ ᠵᠢᠷᠤᠭ᠂ ᠣᠳᠤᠨ ᠣᠷᠤᠨ ᠲᠡᠷᠢᠭᠦᠲᠡᠨ ᠪᠦᠭᠦᠳᠡ ᠳ᠋ᠦ ᠶᠠᠭᠤᠨ ‍ᠤ ᠡᠮᠦᠨ᠎ ‍ᠡ᠋ ᠰᠣᠩᠭᠤᠳᠠᠭ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠬᠡᠷᠡᠭ ᠲᠤᠰᠠ ᠪᠠᠨ ᠡᠷᠭᠦᠵᠦ ᠪᠠᠢᠢᠨ᠎ ‍ᠠ᠋᠃<ref>[https://www.apxu.ru/article/geoforma/hi/zna4enie_geometrii.htm Значение геометрии]. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/03/17</ref>  

ᠮᠢᠩᠭ᠎ ‍ᠠ᠋ ᠮᠢᠩᠭᠠᠨ ᠵᠢᠯ ‍ᠦᠨ ᠤᠷᠤᠰᠬᠠᠯ 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᠃
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==ᠨᠡᠷ ‍ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠯᠠᠯ==
ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋  ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ - Euclidean geometry - евклидова геометрия <br>
"ᠡᠬᠢᠯᠡᠯ" - "Elements" - "Начала"<br>
ᠴᠡᠭ - point - точка <br>
ᠰᠢᠯᠤᠭᠤᠨ - line - прямая <br>
ᠲᠣᠭᠣᠷᠢᠭ - circle - окружность<br>
ᠤᠷᠲᠤ - length - длина <br>
ᠲᠠᠯᠠᠪᠠᠢ - area - площадь <br>
ᠡᠵᠡᠯᠡᠬᠦᠨ - volume - объём <br>
ᠫᠠᠷᠠᠯᠯᠧᠯ - parallel - параллель <br>
ᠫᠧᠷᠫᠧᠨ᠍ᠳᠢᠻᠦ᠋ᠯᠠᠷ - perpendicular - перпендикуляр <br>
ᠥᠨᠴᠦᠭ - angle - угол <br>
ᠬᠡᠭᠡᠰᠦ - radius - радиус<br>
ᠣᠭᠲᠤᠯᠤᠯᠴᠠᠬᠤ - intersect - пересекаться<br>
ᠬᠠᠪᠲᠠᠭᠠᠢ - plane - плоскость<br>
ᠣᠭᠲᠠᠷᠭᠤᠢ᠂ ᠣᠷᠤᠨ ᠵᠠᠢ - space - пространство<br>
ᠭᠤᠷᠪᠠᠯᠵᠢᠨ - triangle - треугольник<br>
ᠪᠥᠮᠪᠦᠷᠴᠡᠭ ‍- sphere - сфера<br>
ᠬᠡᠮᠵᠢᠭᠳᠡᠬᠦᠨ - dimension - измерение<br>
ᠢᠯᠡᠳᠲᠡ ᠦᠨᠡᠨ - axioma - аксиома <br>
ᠳᠠᠯᠳᠠ ᠦᠨᠡᠨ - postulate - постулат <br>
ᠮᠠᠭᠠᠳᠯᠠᠬᠤ ᠦᠨᠡᠨ - theorem - теорема <br>
ᠠᠻᠰᠢᠣᠮ ‍ᠤᠨ ᠠᠷᠭ᠎ ‍ᠠ᠋ - axiomatic method - аксиоматическийн подход<br>
ᠤᠴᠢᠷ ᠰᠢᠯᠲᠠᠭᠠᠨ - logic - логика<br>
ᠪᠠᠲᠤᠯᠠᠭ᠎ ‍ᠠ᠋ - proof - доказательство<br>
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==ᠤᠶᠠᠯᠳᠤᠭ᠎ ‍ᠠ᠋ ᠨᠡᠢᠢᠲᠡᠯᠡᠯ==
[[ᠯᠣᠪᠠᠴᠧᠹᠰᠻᠢ ᠊ᠢᠢᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ]]<br>
[[ᠷᠢᠮᠠᠨ ᠊ᠤ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ]]
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==ᠡᠬᠢ ᠰᠤᠷᠪᠤᠯᠵᠢ==
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[[Ангилал:ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲᠢᠭ]]
[[Ангилал:ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ]]