ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ᠊ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ

ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ‍ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ

ᠭᠤᠷᠪᠠᠯᠵᠢᠨ ‍ᠤ ᠥᠨᠴᠦᠭ ‍ᠦᠳ ‍ᠦᠨ ᠨᠡᠢᠢᠯᠡᠪᠦᠷᠢ 180°᠃

$\alpha +\beta +\gamma =180^{\circ }$

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>B. L. Van Der Waerden. Science Awakening I, Volume 1. Noordhoff International. 1975. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/03/17</ref>

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᠃<ref>Ю. А. Гастев, А. С. Есенин-Вольпин. Аксиоматический метод. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/03/19</ref>
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>
"ᠡᠬᠢᠯᠡᠯ" ᠪᠦᠲᠦᠭᠡᠯ ᠳ᠋ᠦ ᠲᠣᠮᠢᠶᠠᠯᠠᠭᠰᠠᠨ ᠦᠨᠳᠦᠰᠦᠨ ᠫᠣᠰᠲᠦ᠋ᠯᠠᠲ ‍‍ᠤᠳ ‍ᠤᠨ ᠤᠳᠬ ‍ᠠ᠋ ᠨᠢ᠄

ᠲᠠᠪᠤᠳᠤᠭᠠᠷ ᠫᠣᠰᠲᠦ᠋ᠯᠠᠲ᠄ ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠲᠠᠢ ᠣᠭᠲᠣᠯᠤᠯᠴᠠᠭᠰᠠᠨ ᠰᠢᠯᠤᠭᠤᠨ ᠨᠢ ᠤᠭ ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠲᠠᠢ ᠬᠣᠶᠠᠷ ᠲᠡᠭᠰᠢ ᠥᠨᠴᠥᠭ ᠡᠴᠡ ᠪᠠᠭ᠎ᠠ ᠳᠣᠲᠣᠭᠠᠳᠤ ᠥᠷᠥᠭᠡᠯ ᠥᠨᠴᠥᠭ ᠦᠳ ᠡᠭᠦᠰᠬᠡᠵᠦ ᠪᠠᠶᠢᠭ᠎ᠠ ᠲᠣᠬᠢᠶᠠᠳᠠᠯ 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᠃

1. ᠠᠯᠢᠪᠠ ᠳᠤᠷ᠎ᠠ ᠶᠢᠨ ᠴᠡᠭ ᠡᠴᠡ ᠳᠤᠷ᠎ᠠ ᠶᠢᠨ ᠴᠡᠭ ᠬᠦᠷᠲᠡᠯ᠎ᠡ ᠰᠢᠯᠤᠭᠤᠨ ᠲᠠᠲᠠᠵᠤ ᠪᠣᠯᠤᠨ᠎ᠠ᠃
2. ᠠᠯᠢᠪᠠ ᠰᠢᠯᠤᠭᠤᠨ ᠱᠤᠭᠤᠮ ᠢ ᠬᠢᠵᠠᠭᠠᠷ ᠦᠭᠡᠢ ᠦᠷᠭᠦᠯᠵᠢᠯᠡᠭᠦᠯᠵᠦ ᠪᠣᠯᠤᠨ᠎ᠠ᠃
3. ᠳᠤᠷ᠎ᠠ ᠶᠢᠨ ᠲᠥᠪ ᠡᠴᠡ ᠳᠤᠷ᠎ᠠ ᠶᠢᠨ ᠷᠠᠳᠢᠦ᠋ᠰ ᠢᠶᠠᠷ ᠲᠣᠭᠣᠷᠢᠭ ᠲᠠᠲᠠᠵᠤ ᠪᠣᠯᠤᠨ᠎ᠠ᠃
4. ᠪᠦᠬᠦ ᠲᠡᠭᠰᠢ ᠥᠨᠴᠥᠭ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠲᠡᠩᠴᠡᠭᠦᠦ᠃
5. ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠲᠠᠢ ᠣᠭᠲᠣᠯᠤᠯᠴᠠᠭᠰᠠᠨ ᠰᠢᠯᠤᠭᠤᠨ ᠨᠢ ᠤᠭ ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠲᠠᠢ ᠬᠣᠶᠠᠷ ᠲᠡᠭᠰᠢ ᠥᠨᠴᠥᠭ ᠡᠴᠡ ᠪᠠᠭ᠎ᠠ ᠳᠣᠲᠣᠭᠠᠳᠤ ᠥᠷᠥᠭᠡᠯ ᠥᠨᠴᠥᠭ ᠦᠳ ᠡᠭᠦᠰᠬᠡᠵᠦ ᠪᠠᠶᠢᠭ᠎ᠠ ᠲᠣᠬᠢᠶᠠᠳᠠᠯ 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>Урок геометрия 39 тем. Постулаты Евклида. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/02/09</ref><ref name=":0" />

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" />

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᠃

$c^2=a^2+b^2$

1. ᠨᠢᠭᠡ ᠵᠦᠢᠯ ᠲᠡᠢ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠢᠭᠦᠳ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠴᠤ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶᠢᠨ᠎ᠠ᠃
2. ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠢᠭᠦᠳ ᠳᠡᠭᠡᠷ᠎ᠡ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠢᠭᠦᠳᠦ ᠶᠢ ᠨᠡᠮᠡᠪᠡᠯ ᠨᠡᠶᠢᠯᠡᠪᠦᠷᠢ ᠨᠦᠭᠦᠳ ᠨᠢ ᠴᠤ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶᠢᠨ᠎ᠠ᠃
3. ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠢᠭᠦᠭᠦᠳ ᠡᠴᠡ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠢᠭᠦᠳᠦ ᠶᠢ ᠬᠠᠰᠤᠪᠠᠯ ᠦᠯᠡᠳᠡᠭᠳᠡᠯ ᠦᠳ ᠨᠢ ᠴᠤ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶᠢᠨ᠎ᠠ᠃
4. ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠢᠰᠢ ᠨᠢᠭᠦᠳ ᠳᠡᠭᠡᠷ᠎ᠡ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠢᠭᠦᠳᠦ ᠶᠢ ᠨᠡᠮᠡᠪᠡᠯ ᠨᠡᠶᠢᠯᠡᠪᠦᠷᠢ ᠨᠦᠭᠦᠳ ᠨᠢ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠢᠰᠢ ᠪᠠᠶᠢᠨ᠎ᠠ᠃
5. ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠢᠭᠦᠳᠦ ᠶᠢ ᠠᠳᠠᠯᠢ ᠬᠡᠮᠵᠢᠶ᠎ᠡ ᠪᠡᠷ ᠦᠷᠡᠵᠢᠭᠦᠯᠪᠡᠯ ᠦᠷᠡᠵᠢᠪᠦᠷᠢ ᠨᠢ ᠴᠤ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶᠢᠨ᠎ᠠ᠃
6. ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠢᠭᠦᠭᠦᠳ ᠦᠨ ᠲᠡᠩ ᠬᠠᠭᠠᠰ ᠤᠳ ᠨᠢ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶᠢᠨ᠎ᠠ᠃
7. ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠳᠠᠪᠬᠤᠴᠠᠬᠤ ᠵᠦᠢᠯ ᠦᠳ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶᠢᠨ᠎ᠠ᠃ (ᠳᠠᠪᠬᠤᠴᠠᠬᠤ ᠭᠡᠳᠡᠭ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠶᠠᠭ ᠠᠳᠠᠯᠢ ᠭᠡᠰᠡᠨ ᠤᠳᠬ᠎ᠠ ᠲᠠᠢ)
8. ᠪᠦᠬᠦᠯᠢ ᠨᠢ ᠬᠡᠰᠡᠭ ᠡᠴᠡ ᠪᠡᠨ ᠶᠡᠬᠡ ᠪᠠᠶᠢᠨ᠎ᠠ᠃
9. ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠤ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠣᠷᠣᠨ ᠵᠠᠢ ᠬᠢᠵᠠᠭᠠᠷᠯᠠᠭᠳᠠᠳᠠᠭ ᠦᠭᠡᠢ᠃<ref>К.Лохматова, Н.Степанова. Презентация "Евклидова геометрия" (7 класс). ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/02/09</ref><ref name=":0">Н.Г.Подаева, Д.А.Жук. Лекции по основаниям геометрии. Елецкий Государственный Университет им. И.А.Бунина. Елец 2005. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/02/09</ref>

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᠃<ref>Значение геометрии. ᠬᠠᠨᠳᠤᠭᠰᠠᠨ 2021/03/17</ref>

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

<references />