ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ

ᠴᠢᠯᠦᠭᠡᠲᠦ ᠨᠡᠪᠲᠡᠷᠬᠡᠢ ᠲᠣᠯᠢ — ᠸᠢᠺᠢᠫᠧᠳᠢᠶ᠎ᠠ ᠠᠴᠠ
ᠬᠠᠷᠠᠶᠢᠬᠤ: ᠤᠳᠤᠷᠢᠳᠬᠤ, ᠬᠠᠶᠢᠯᠲᠠ
ᠮᠠᠨ ᠤ ᠡᠷᠡᠨ ᠦ ᠡᠮᠦᠨ᠎ᠡ III ᠵᠠᠭᠤᠨ ᠤ ᠭᠷᠧᠺ ᠦᠨ ᠮᠠᠲ᠋ᠧᠮᠠᠲ᠋ᠢᠺᠴᠢ᠂ ᠭᠧᠣᠮᠧᠲ᠋ᠷᠢ ᠤᠨ ᠡᠴᠢᠭᠡ ᠬᠡᠮᠡᠨ ᠨᠡᠷᠡᠯᠡᠭᠳᠡᠳᠡᠭ ᠧᠦᠺᠯᠢᠳᠤᠷᠠᠹᠠᠧᠯ ᠦᠨ ᠠᠹᠢᠨ ᠤ ᠰᠤᠷᠭᠠᠭᠤᠯᠢ ᠵᠢᠷᠤᠭ ᠤᠨ ᠨᠢᠭᠡᠨ ᠬᠡᠰᠡᠭ ᠳᠡᠭᠡᠷ᠎ᠡ ᠳᠦᠷᠰᠦᠯᠡᠭᠳᠡᠭᠰᠡᠨ ᠪᠠᠶᠢᠭ᠎ᠠ ᠨᠢ᠃

ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ (ᠭᠷᠧᠺ: μάθημα᠂ ᠠᠩᠭᠯᠢ: mathematics) ᠪᠤᠶᠤ ᠲᠣᠭᠠᠨ ᠤᠬᠠᠭᠠᠨ ᠨᠢ ᠲᠣᠭ᠎ᠠ ᠬᠡᠮᠵᠢᠶ᠎ᠡᠪᠦᠲᠦᠴᠡᠣᠭᠲᠠᠷᠭᠤᠢᠥᠭᠡᠷᠡᠴᠢᠯᠡᠯᠲᠡ ᠵᠡᠷᠭᠡ ᠣᠶᠢᠯᠠᠭᠠᠯᠲᠠ ᠨᠤᠭᠤᠳ ᠳᠡᠭᠡᠷ᠎ᠡ ᠲᠥᠪᠯᠡᠷᠡᠭᠰᠡᠨ ᠮᠡᠳᠡᠯᠭᠡ ᠶᠢᠨ ᠴᠣᠭᠴᠠ᠂ ᠮᠥᠨ ᠲᠡᠳᠡᠭᠡᠷ ᠦᠨ ᠲᠤᠬᠠᠢ ᠰᠤᠳᠤᠯᠳᠠᠭ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ ᠶᠤᠮ᠃ ᠪᠧᠨ᠋ᠵᠠᠮᠢᠨ ᠫᠢᠧᠷᠰ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠢ "ᠵᠠᠶᠢᠯᠠᠰᠢ ᠦᠭᠡᠢ ᠳ᠋ᠦᠩᠨᠡᠯᠲᠡ ᠨᠦᠭᠦᠳ ᠢ ᠭᠠᠷᠭᠠᠳᠠᠭ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ" ᠬᠡᠮᠡᠭᠰᠡᠨ᠃[1] ᠯᠢᠩᠨ ᠰᠡᠲᠡ ᠶᠢᠨ[2] ᠪᠠ ᠺᠧᠢᠲ ᠳᠧᠪᠯᠢᠩ[3] ᠨᠠᠷ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠨᠢ ᠵᠦᠢ ᠲᠣᠭᠲᠠᠯ ᠤᠨ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ ᠪᠥᠭᠡᠳ ᠲᠣᠭᠠᠨ ᠨᠤᠭᠤᠳ᠂ ᠣᠭᠲᠠᠷᠭᠤᠢ᠂ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ᠂ ᠺᠣᠮᠫᠢᠦ᠋ᠲ᠋ᠧᠷ᠂ ᠡᠰᠡᠪᠡᠯ ᠬᠡᠶᠢᠰᠪᠦᠷᠢ ᠵᠦᠢᠯ ᠦᠳ ᠲᠤ ᠵᠦᠢ ᠲᠣᠭᠲᠠᠯ ᠤᠳ ᠢ ᠡᠷᠢᠳᠡᠭ ᠭᠡᠵᠦ ᠦᠵᠡᠭ᠍ᠰᠡᠨ᠃

ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠨᠢ ᠲᠣᠭᠠᠯᠠᠬᠤᠲᠣᠭᠠᠴᠠᠭᠠᠯᠠᠬᠤ ᠪᠠ ᠬᠡᠮᠵᠢᠬᠦ ᠦᠢᠯᠡᠳᠦᠯ ᠦᠳ᠂ ᠮᠥᠨ ᠹᠢᠽᠢᠺ ᠣᠪᠶᠧᠺᠲ ᠤᠳ ᠤᠨ ᠬᠡᠯᠪᠡᠷᠢ ᠳᠦᠷᠰᠦ ᠪᠠ ᠬᠥᠳᠡᠯᠭᠡᠭᠡᠨ ᠦ ᠰᠢᠰᠲ᠋ᠧᠮ ᠲᠡᠢ ᠰᠤᠳᠤᠯᠭᠠᠨ ᠳᠡᠭᠡᠷ᠎ᠡ ᠬᠡᠶᠢᠰᠪᠦᠷᠢᠯᠡᠯᠯᠣᠭᠢᠭ ᠰᠡᠳᠬᠢᠯᠭᠡ ᠶᠢ ᠬᠡᠷᠡᠭᠯᠡᠭᠰᠡᠨ ᠦ ᠦᠷ᠎ᠡ ᠳ᠋ᠦᠩ ᠳᠦ ᠡᠭᠦᠰᠦᠭᠰᠡᠨ᠃ ᠮᠠᠲ᠋ᠧᠮᠠᠲ᠋ᠢᠭᠴᠢᠳ ᠡᠳᠡᠭᠡᠷ ᠣᠶᠢᠯᠠᠭᠠᠯᠲᠠ ᠨᠤᠭᠤᠳ ᠤᠨ ᠲᠠᠯ᠎ᠠ ᠪᠠᠷ ᠰᠢᠨ᠎ᠡ ᠲᠠᠭᠠᠮᠠᠭᠯᠠᠯ ᠳᠡᠪᠰᠢᠭᠦᠯᠵᠦ᠂ ᠲᠡᠳᠡᠭᠡᠷ ᠦᠨ ᠦᠨᠡᠨ ᠪᠣᠯᠬᠤ ᠶᠢ ᠵᠣᠬᠢᠬᠤ ᠠᠺᠰᠢᠣᠮ ᠤᠳ ᠪᠠ ᠲᠣᠳᠣᠷᠬᠠᠶᠢᠯᠠᠯᠲᠠ ᠨᠤᠭᠤᠳ ᠠᠴᠠ ᠯᠣᠭᠢᠭ ᠳᠦᠷᠢᠮ ᠦᠳ ᠢ ᠴᠢᠨᠭᠭ᠎ᠠ ᠪᠠᠷᠢᠮᠲᠠᠯᠠᠨ ᠪᠠᠲᠤᠯᠠᠬᠤ ᠵᠣᠷᠢᠯᠭ᠎ᠠ ᠲᠠᠢ ᠰᠤᠳᠤᠯᠭ᠎ᠠ ᠬᠢᠳᠡᠭ᠃[4]

ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠨᠠᠭᠠᠳᠤ ᠵᠠᠬ᠎ᠠ ᠶᠢᠨ ᠬᠡᠮᠵᠢᠶᠡᠨ ᠦ ᠮᠡᠳᠡᠯᠭᠡ ᠪᠠ ᠬᠡᠷᠡᠭᠯᠡᠭᠡ ᠨᠢ ᠬᠤᠪᠢ ᠬᠦᠮᠦᠨ ᠪᠣᠯᠤᠨ ᠨᠡᠶᠢᠭᠡᠮ ᠤᠨ ᠵᠠᠶᠢᠯᠠᠰᠢ ᠦᠭᠡᠢ ᠴᠢᠬᠤᠯᠠ ᠬᠡᠰᠡᠭ ᠪᠣᠯᠤᠭᠰᠠᠭᠠᠷ ᠢᠷᠡᠭᠰᠡᠨ᠃ ᠡᠨᠡ ᠦᠨᠳᠦᠰᠦᠨ ᠰᠠᠨᠠᠭᠠᠨ ᠨᠤᠭᠤᠳ ᠤᠨ ᠰᠠᠶᠢᠵᠢᠷᠠᠭᠤᠯᠤᠭᠰᠠᠨ ᠬᠡᠯᠪᠡᠷᠢ ᠡᠷᠲᠡᠨ ᠦ ᠶᠸᠵᠠᠫᠲᠪᠠᠪᠢᠯᠤᠨᠡᠨᠡᠳᠬᠡᠭᠬᠢᠲᠠᠳ ᠪᠠ ᠭᠷᠧᠺ ᠦᠨ ᠨᠣᠮ ᠰᠤᠳᠤᠷ ᠤᠳ ᠲᠤ ᠬᠠᠳᠠᠭᠠᠯᠠᠭᠳᠠᠨ ᠦᠯᠡᠳᠡᠭᠰᠡᠨ ᠪᠠᠶᠢᠳᠠᠭ᠃ ᠬᠠᠮᠤᠭ ᠤᠨ ᠠᠩᠬ᠎ᠠ ᠧᠦᠺᠯᠢᠳᠤ "ᠡᠬᠢᠯᠡᠯ" ᠪᠦᠲᠦᠭᠡᠯ ᠳᠦ ᠪᠡᠨ ᠯᠣᠭᠢᠭ ᠤᠨ ᠬᠠᠲᠠᠭᠤ ᠬᠡᠷᠡᠭᠯᠡᠭᠡ ᠶᠠᠮᠠᠷ ᠪᠠᠶᠢᠬᠤ ᠶᠣᠰᠣᠲᠠᠢ ᠶᠢ ᠬᠠᠷᠠᠭᠤᠯᠤᠭᠰᠠᠨ᠃ ᠡᠭᠦᠨ ᠡᠴᠡ ᠬᠣᠶᠢᠰᠢ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ   ᠳᠣ ᠲᠣᠮᠣ ᠳᠡᠪᠰᠢᠯ ᠭᠠᠷᠬᠤ ᠨᠢ ᠶᠡᠬᠡ ᠴᠥᠭᠡᠨ ᠪᠠᠶᠢᠵᠤ ᠪᠠᠶᠢᠭᠠᠳ Xᠵᠢᠷᠭᠤᠳᠤᠭᠠᠷ ᠵᠠᠭᠤᠨ ᠤ ᠰᠡᠷᠭᠦᠨ ᠮᠠᠨᠳᠤᠯ ᠤᠨ ᠦᠶ᠎ᠡ ᠳᠦ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠰᠢᠨᠡᠴᠢᠯᠡᠯ ᠳᠠᠷᠠᠭ᠎ᠠ ᠳᠠᠷᠠᠭ᠎ᠠ ᠪᠠᠷ ᠢᠶᠠᠨ ᠭᠠᠷᠴᠤ ᠪᠠᠶᠢᠭᠰᠠᠨ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ ᠤ ᠨᠡᠭᠡᠭᠡᠯᠲᠡ ᠨᠦᠭᠦᠳ ᠲᠡᠢ ᠬᠠᠷᠢᠯᠴᠠᠨ ᠦᠢᠯᠡᠴᠢᠯᠡᠭᠰᠡᠨ ᠦ ᠳᠦ᠋ᠨᠭ  ᠳᠣ ᠥᠨᠥ ᠶᠢ ᠬᠦᠷᠲᠡᠯ᠎ᠡ ᠦᠷᠭᠦᠯᠵᠢᠯᠡᠭᠰᠡᠨ ᠶᠡᠬᠡ ᠬᠤᠷᠳᠤᠴᠠ ᠲᠠᠢ ᠰᠤᠳᠤᠯᠭ᠎ᠠ ᠶᠢ ᠡᠬᠢᠯᠡᠭᠦᠯᠦᠭᠰᠡᠨ ᠶᠤᠮ᠃[5]

ᠥᠨᠥᠳᠥᠷ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠨᠢ ᠪᠠᠶᠢᠭᠠᠯᠢ ᠶᠢᠨ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨᠢᠨᠵᠧᠨᠧᠷᠴᠢᠯᠡᠯᠠᠨᠠᠭᠠᠬᠤ ᠤᠬᠠᠭᠠᠨᠡᠳ᠋ ᠍ ᠦᠨ ᠵᠠᠰᠠᠭ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠣᠯᠠᠨ ᠰᠠᠯᠪᠤᠷᠢ  ᠤᠳ ᠲᠤ ᠳᠡᠯᠡᠬᠡᠢ ᠳᠠᠶᠠᠭᠠᠷ ᠬᠡᠷᠡᠭᠯᠡᠭᠳᠡᠵᠦ ᠪᠠᠶᠢᠨ᠎ᠠ᠃ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠢ ᠡᠳᠡᠭᠡᠷ ᠰᠠᠯᠪᠤᠷᠢ ᠳᠤ ᠬᠡᠷᠡᠭᠯᠡᠭᠰᠡᠨ ᠢ ᠶᠡᠬᠡᠪᠴᠢᠯᠡᠨ ᠬᠡᠷᠡᠭᠯᠡᠭᠡᠨ ᠦ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠭᠡᠳᠡᠭ ᠪᠠ ᠡᠨᠡ ᠨᠢ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠨᠡᠭᠡᠭᠡᠯᠲᠡ ᠨᠦᠭᠦᠳ ᠢ ᠬᠡᠷᠡᠭᠯᠡᠳᠡᠭ᠂ ᠤᠭ ᠨᠡᠭᠡᠭᠡᠯᠲᠡ ᠨᠦᠭᠦᠳ ᠲᠦ ᠬᠦᠷᠭᠡᠳᠡᠭ᠂ ᠵᠠᠷᠢᠮ ᠳᠤ ᠪᠠᠨ ᠴᠣ ᠰᠢᠨ᠎ᠡ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ ᠢ ᠴᠤ ᠲᠥᠷᠦᠭᠦᠯᠳᠡᠭ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠨᠢᠭᠡ ᠰᠠᠯᠪᠤᠷᠢ ᠶᠤᠮ᠃ ᠮᠠᠲ᠋ᠧᠮᠠᠲ᠋ᠢᠭᠴᠢᠳ ᠮᠥᠨ ᠴᠡᠪᠡᠷ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ᠂ ᠥᠭᠡᠷ᠎ᠡ ᠪᠡᠷ ᠬᠡᠯᠡᠪᠡᠯ ᠶᠠᠭᠤᠨ ᠳᠤ ᠬᠡᠷᠡᠭᠯᠡᠬᠦ ᠶᠢ ᠨᠢ ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠬᠤ ᠦᠭᠡᠢ ᠪᠡᠷ ᠵᠥᠪᠬᠡᠨ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠢ ᠥᠪᠡᠷ ᠢ ᠨᠢ ᠰᠤᠳᠤᠯᠬᠤ ᠰᠤᠳᠤᠯᠭ᠎ᠠ ᠬᠢᠳᠡᠭ᠃ ᠰᠣᠨᠢᠷᠬᠠᠯᠲᠠᠢ ᠨᠢ ᠴᠡᠪᠡᠷ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠶᠡᠬᠡᠩᠬᠢ ᠰᠤᠳᠤᠯᠭᠠᠨ ᠨᠤᠭᠤᠳ ᠡᠷᠲᠡ ᠣᠷᠣᠢ ᠬᠡᠵᠢᠶ᠎ᠡ ᠨᠢᠭᠡᠨ ᠴᠠᠭ ᠲᠤ ᠪᠤᠳᠠᠳᠤ ᠠᠮᠢᠳᠤᠷᠠᠯ  ᠳᠣ ᠬᠡᠷᠡᠭᠯᠡᠭᠳᠡᠳᠡᠭ ᠪᠠᠶᠢᠨ᠎ᠠ᠃[6] ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠭᠣᠸ᠎ᠠ ᠰᠠᠶᠢᠬᠠᠨ ᠴᠢᠨᠠᠷ ᠨᠢ ᠮᠠᠲ᠋ᠧᠮᠠᠲ᠋ᠢᠭᠴᠢᠳ ᠤᠨ ᠮᠡᠷᠭᠡᠵᠢᠯ ᠳᠤ ᠪᠡᠨ ᠳᠤᠷᠠᠯᠠᠬᠤ ᠭᠣᠣᠯ ᠰᠢᠯᠲᠠᠭᠠᠨ ᠪᠣᠯᠳᠠᠭ᠃

ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠬᠡᠮᠡᠬᠦ ᠨᠡᠷᠡᠨ ᠦ ᠤᠴᠢᠷ ᠨᠢ[ᠵᠠᠰᠠᠪᠤᠷᠢᠯᠠᠬᠤ | ᠺᠣᠳ᠋ ᠢᠶᠠᠷ ᠵᠠᠰᠠᠬᠣ]

ᠮᠠᠨ ᠤ ᠣᠷᠣᠨ ᠲᠡᠳᠦᠢ ᠦᠭᠡᠢ ᠳᠡᠯᠡᠬᠡᠢ ᠶᠢᠨ ᠶᠡᠬᠡᠩᠬᠢ ᠣᠷᠣᠨ ᠳᠤ ᠬᠡᠷᠡᠭᠯᠡᠭᠳᠡᠳᠡᠭ «ᠮᠠᠲ᠋ᠧᠮᠠᠲ᠋ᠢᠺ» ᠭᠡᠳᠡᠭ ᠦᠭᠡ ᠨᠢ ᠡᠷᠲᠡᠨ ᠦ ᠭᠷᠧᠺ ᠬᠡᠯᠡᠨ ᠦ μάθημα (máthema, ᠮᠣᠩᠭᠣᠯ ᠢᠶᠠᠷ: ᠰᠤᠷᠬᠤ᠂ ᠰᠤᠳᠤᠯᠬᠤ᠂ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ) ᠪᠠ ᠬᠣᠯᠪᠣᠭᠳᠠᠬᠤ ᠲᠡᠮᠳᠡᠭ ᠨᠡᠷ᠎ᠡ ᠪᠣᠯᠬᠤ μαθηματικός (mathēmatikós, ᠮᠣᠩᠭᠣᠯ ᠢᠶᠠᠷ: ᠰᠤᠷᠬᠤ᠂ ᠰᠤᠳᠤᠯᠬᠤ ᠲᠠᠢ ᠬᠣᠯᠪᠣᠭ᠎ᠠ ᠲᠠᠢ) ᠭᠡᠳᠡᠭ ᠡᠴᠡ ᠭᠠᠷᠤᠯ ᠲᠠᠢ᠃

ᠲᠡᠦᠬᠡ[ᠵᠠᠰᠠᠪᠤᠷᠢᠯᠠᠬᠤ | ᠺᠣᠳ᠋ ᠢᠶᠠᠷ ᠵᠠᠰᠠᠬᠣ]

ᠳᠤᠮᠳᠠᠳᠤ ᠡᠷᠲᠡᠨ ᠦ ᠦᠶ᠎ᠡ ᠳᠦ ᠡᠮᠦᠨᠡᠲᠦ ᠠᠮᠧᠷᠢᠺᠠ ᠳᠤ ᠣᠷᠣᠰᠢᠨ ᠲᠣᠭᠲᠠᠨᠢᠵᠤ ᠪᠠᠶᠢᠭᠰᠠᠨ ᠢᠨᠺᠦᠶ᠎ᠠ ᠶᠢᠨ ᠡᠵᠡᠨᠲᠦ ᠭᠦᠷᠦᠨ ᠳᠦ ᠲᠣᠭᠠᠯᠠᠬᠤ ᠳᠤ ᠪᠠᠨ ᠣᠯᠤᠭᠰᠠᠨ ᠵᠠᠩᠭᠢᠯᠠᠭ᠎ᠠ ᠠᠴᠠ ᠪᠦᠲᠦᠭᠰᠡᠨ "ᠺᠦ᠋ᠢᠫᠤ" ᠭᠡᠭᠳᠡᠬᠦ ᠡᠨᠡᠬᠦ ᠪᠠᠭᠠᠵᠢ ᠶᠢ ᠬᠡᠷᠡᠭᠯᠡᠳᠡᠭ ᠪᠠᠶᠢᠪᠠ

ᠪᠦᠬᠦ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠲᠡᠦᠬᠡ ᠵᠢᠨ ᠲᠥᠪᠰᠢᠨ ᠨᠢ ᠤᠯᠠᠮ ᠤᠯᠠᠮ ᠥᠨᠳᠥᠷᠵᠢᠬᠦ ᠬᠡᠶᠢᠰᠪᠦᠷᠢᠯᠡᠯ ᠦᠳ ᠦᠨ ᠳᠠᠷᠠᠭᠠᠯᠠᠯ᠂ ᠡᠰᠡᠪᠡᠯ ᠰᠤᠳᠤᠯᠬᠤ ᠵᠦᠢᠯ ᠦᠳ ᠦᠨ ᠬᠢ ᠨᠢ ᠬᠦᠷᠢᠶ᠎ᠡ ᠶᠠᠭᠠᠬᠢᠵᠤ ᠥᠷᠭᠡᠳᠰᠡᠨ ᠲᠤᠬᠠᠢ ᠲᠡᠦᠬᠡ ᠭᠡᠵᠦ ᠦᠵᠡᠵᠦ ᠪᠣᠯᠤᠨ᠎ᠠ᠃ ᠬᠠᠮᠤᠭ ᠤᠨ ᠠᠩᠬᠠᠨ ᠤ ᠬᠡᠶᠢᠰᠪᠦᠷᠢᠯᠡᠯ ᠨᠢ ᠲᠣᠭ᠎ᠠ ᠪᠠᠶᠢᠭᠰᠠᠨ ᠪᠠᠶᠢᠵᠤ ᠮᠡᠳᠡᠨ᠎ᠡ᠃ ᠭᠤᠷᠪᠠᠨ ᠦᠬᠡᠷ ᠪᠠ ᠭᠤᠷᠪᠠᠨ ᠴᠢᠯᠠᠭᠤᠨ ᠤ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠶᠠᠮᠠᠷ ᠨᠢᠭᠡ ᠶᠡᠷᠦᠩᠬᠡᠢ ᠵᠦᠢᠯ ᠪᠠᠶᠢᠭ᠎ᠠ ᠶᠢ ᠣᠶᠢᠯᠠᠭᠠᠭᠰᠠᠨ ᠶᠠᠪᠤᠳᠠᠯ ᠬᠦᠮᠦᠨ ᠦ ᠰᠡᠳᠬᠢᠬᠦᠢ ᠳᠦ ᠭᠠᠷᠤᠭᠰᠠᠨ ᠲᠣᠮᠣ ᠦᠰᠦᠷᠦᠯᠲᠡ ᠨᠦᠭᠦᠳ ᠦᠨ ᠨᠢᠭᠡ ᠪᠠᠶᠢᠭᠰᠠᠨ ᠶᠤᠮ᠃ ᠪᠣᠳᠠᠲᠤ ᠹᠢᠽᠢᠺ ᠣᠪᠶᠧᠺᠲ ᠤᠳ ᠢ ᠲᠣᠭᠠᠯᠠᠵᠤ ᠰᠤᠷᠤᠭᠠᠳ ᠵᠣᠭᠰᠣᠬᠤ ᠦᠭᠡᠢ ᠡᠷᠲᠡᠨ ᠦ ᠬᠦᠮᠦᠰ ᠬᠡᠶᠢᠰᠪᠦᠷᠢ ᠬᠡᠮᠵᠢᠭᠳᠡᠬᠦᠨ ᠨᠦᠭᠦᠳ ᠢ ᠲᠣᠭᠠᠯᠠᠵᠤ ᠡᠬᠢᠯᠡᠭᠰᠡᠨ᠃ ᠵᠢᠱᠢᠶᠡᠯᠡᠪᠡᠯ ᠴᠠᠭ ᠬᠤᠭᠤᠴᠠᠭ᠎ᠠ ᠶᠢ ᠲᠣᠭᠠᠯᠠᠬᠤ ᠶᠢᠨ ᠲᠤᠯᠠᠳᠠ ᠡᠳᠦᠷᠰᠠᠷ᠎ᠠᠵᠢᠯ ᠬᠡᠮᠡᠬᠦ ᠣᠶᠢᠯᠠᠭᠠᠯᠲᠠ ᠨᠤᠭᠤᠳ ᠢ ᠬᠡᠷᠡᠭᠯᠡᠵᠦ ᠢᠷᠡᠭᠰᠡᠨ᠃ ᠡᠭᠦᠨ ᠦ ᠳᠠᠷᠠᠭ᠎ᠠ ᠠᠷᠢᠹᠮᠧᠲ᠋ᠢᠭ (ᠨᠡᠮᠡᠬᠦᠬᠠᠰᠤᠬᠤᠦᠷᠡᠵᠢᠬᠦᠬᠤᠪᠢᠶᠠᠬᠤ) ᠬᠥᠭᠵᠢᠭᠰᠡᠨ ᠪᠠ ᠡᠷᠲᠡᠨ ᠦ ᠪᠠᠯᠭᠠᠰᠤ ᠶᠢᠨ ᠤᠯᠠ ᠮᠥᠷ ᠦᠳ ᠲᠡᠷᠡ ᠦᠶ᠎ᠡ ᠶᠢᠨ ᠬᠦᠮᠦᠰ ᠭᠧᠣᠮᠧᠲ᠋ᠷᠢ ᠦᠨ ᠮᠡᠳᠡᠯᠭᠡ ᠲᠡᠢ ᠪᠠᠶᠢᠭᠰᠠᠨ ᠢ ᠭᠡᠷᠡᠴᠢᠯᠡᠳᠡᠭ᠃

ᠴᠠᠭᠠᠰᠢᠯᠠᠪᠠᠯ ᠲᠣᠭᠠᠨ ᠨᠤᠭᠤᠳ ᠢ ᠪᠦᠷᠢᠳᠬᠡᠵᠦ ᠠᠪᠬᠤ ᠶᠠᠮᠠᠷ ᠨᠢᠭᠡ ᠠᠷᠭ᠎ᠠ᠂ ᠵᠢᠱᠢᠶᠡᠯᠡᠪᠡᠯ ᠪᠢᠴᠢᠬᠦ᠂ ᠵᠢᠵᠢᠭ ᠴᠢᠯᠠᠭᠤ ᠨᠤᠭᠤᠳ ᠠᠰᠢᠭᠯᠠᠬᠤ᠂ ᠡᠰᠡᠪᠡᠯ ᠢᠨᠺᠦᠶ᠎ᠠ ᠶᠢᠨ ᠡᠵᠡᠨᠲᠦ ᠭᠦᠷᠦᠨ ᠳᠦ ᠬᠡᠷᠡᠭᠯᠡᠳᠡᠭ ᠪᠠᠶᠢᠭᠰᠠᠨ ᠰᠢᠭ ᠺᠤᠶᠢᠫᠤ ᠭᠡᠭᠳᠡᠬᠦ ᠣᠯᠤᠭᠰᠠᠨ ᠵᠠᠩᠭᠢᠯᠠᠭ᠎ᠠ ᠬᠡᠷᠡᠭ ᠪᠣᠯᠵᠤ ᠡᠬᠢᠯᠡᠭᠰᠡᠨ ᠪᠠᠶᠢᠨ᠎ᠠ᠃ ᠡᠨᠡ ᠶᠠᠪᠤᠴᠠ ᠳᠤ ᠪᠠᠨ ᠬᠦᠮᠦᠨ ᠲᠥᠷᠥᠯᠬᠢᠲᠡᠨ ᠲᠥᠷᠥᠯ ᠪᠦᠷᠢ ᠶᠢᠨ ᠲᠣᠭᠠᠯᠠᠯ ᠤᠨ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠳ ᠢ ᠵᠣᠬᠢᠶᠠᠵᠠᠢ᠃

ᠲᠡᠦᠬᠡᠨ ᠳᠦ ᠲᠡᠮᠳᠡᠭᠯᠡᠭᠳᠡᠵᠦ ᠦᠯᠡᠳᠡᠭᠰᠡᠨ ᠢᠶᠡᠷ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠲᠤ ᠬᠠᠮᠤᠷᠠᠭᠳᠠᠬᠤ ᠭᠣᠣᠯ ᠰᠠᠯᠪᠤᠷᠢ ᠤᠳ ᠲᠠᠲᠠᠪᠤᠷᠢ ᠪᠠ ᠬᠤᠳᠠᠯᠳᠤᠭ᠎ᠠ ᠲᠠᠢ ᠬᠣᠯᠪᠣᠭ᠎ᠠ ᠲᠠᠢ ᠲᠣᠭᠠᠴᠠᠭ᠎ᠠ ᠬᠢᠬᠦ᠂ ᠲᠣᠭᠠᠨ ᠨᠤᠭᠤᠳ ᠤᠨ ᠬᠣᠭᠣᠷᠣᠨᠳᠣᠬᠢ ᠬᠠᠷᠢᠴᠠᠭ᠎ᠠ ᠬᠠᠮᠢᠶᠠᠷᠤᠯ ᠤᠳ ᠢ ᠤᠶᠢᠯᠠᠭᠠᠬᠤ᠂ ᠭᠠᠵᠠᠷ ᠢ ᠬᠡᠮᠵᠢᠬᠦᠣᠳᠣᠨ ᠣᠷᠣᠨ ᠤ ᠦᠵᠡᠭᠳᠡᠯ  ᠦᠳ ᠢ ᠤᠷᠢᠳᠴᠢᠯᠠᠨ ᠬᠡᠯᠡᠬᠦ ᠱᠠᠭᠠᠷᠳᠠᠯᠭ᠎ᠠ ᠨᠤᠭᠤᠳ ᠠᠴᠠ ᠡᠭᠦᠳᠦᠨ ᠪᠤᠢ ᠪᠣᠯᠤᠭᠰᠠᠨ ᠠᠵᠠᠢ᠃ ᠡᠳᠡᠭᠡᠷ ᠱᠠᠭᠠᠷᠳᠠᠯᠭ᠎ᠠ ᠨᠤᠭᠤᠳ ᠢ ᠪᠠᠷᠤᠭᠴᠠᠭ᠎ᠠ ᠪᠠᠷ ᠲᠣᠭ᠎ᠠ ᠬᠡᠮᠵᠢᠶ᠎ᠡᠪᠦᠲᠦᠴᠡᠣᠭᠲᠠᠷᠭᠤᠢ ᠪᠠ ᠥᠭᠡᠷᠡᠴᠢᠯᠡᠯᠲᠡᠵᠢᠨ ᠰᠤᠳᠤᠯᠭ᠎ᠠ ᠨᠤᠭᠤᠳ ᠲᠤ ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠭᠤᠯᠵᠤ ᠪᠣᠯᠵᠤ ᠪᠠᠶᠢᠭ᠎ᠠ ᠶᠢ ᠠᠩᠵᠠᠭᠠᠷᠠᠭᠠᠷᠠᠢ᠃

ᠡᠨᠡ ᠦᠶ᠎ᠡ  ᠠᠴᠠ ᠬᠣᠶᠢᠰᠢ ᠮᠠᠲ᠋ᠧᠮᠠᠲ᠋ᠢᠺ ᠠᠰᠤᠷᠤ ᠶᠡᠬᠡ ᠪᠡᠷ ᠥᠷᠭᠡᠵᠢᠭᠰᠡᠨ ᠪᠥᠭᠡᠳ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠪᠠ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ ᠨᠤᠭᠤᠳ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠨᠢᠭᠲᠠ ᠬᠣᠯᠪᠣᠭ᠎ᠠ ᠲᠠᠢ ᠪᠠᠷ ᠬᠥᠭᠵᠢᠭᠰᠡᠨ᠃ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠨᠡᠭᠡᠭᠡᠯᠲᠡ ᠨᠦᠭᠦᠳ ᠲᠡᠦᠬᠡ ᠶᠢᠨ ᠲᠤᠷᠰᠢᠳᠠ ᠬᠢᠭᠳᠡᠵᠦ ᠢᠷᠡᠭᠰᠡᠨ ᠪᠠ ᠣᠳᠣ ᠴᠤ ᠬᠢᠭᠳᠡᠭᠰᠡᠭᠡᠷ ᠪᠠᠶᠢᠭ᠎ᠠ᠃ ᠠᠮᠧᠷᠢᠺᠠ ᠶᠢᠨ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠨᠡᠶᠢᠭᠡᠮᠯᠢᠭ ᠦᠨ ᠮᠡᠳᠡᠭᠡ ᠰᠡᠳᠬᠦᠯ ᠦᠨ 2006 ᠣᠨ ᠤ 1 ᠍ ᠳᠦᠭᠡᠷ ᠰᠠᠷ᠎ᠠ ᠶᠢᠨ ᠳ᠋ᠤᠭᠠᠷ ᠲᠤ ᠮᠠᠬᠠᠶᠢᠯ ᠪ ᠂ ᠰᠧᠸᠷᠶᠢᠺ ᠤᠨ ᠪᠢᠴᠢᠭᠰᠡᠨ ᠢᠶᠡᠷ "ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠰᠤᠳᠤᠯᠭ᠎ᠠ ᠰᠠᠩ ᠳᠤ 1940 (ᠡᠨᠡ ᠰᠠᠩ ᠤᠨ ᠠᠵᠢᠯᠯᠠᠵᠤ ᠡᠬᠢᠯᠡᠭᠰᠡᠨ ᠵᠢᠯ)ᠣᠨ ᠠᠴᠠ ᠬᠣᠶᠢᠰᠢ ᠬᠠᠮᠤᠷᠠᠭᠳᠠᠭᠰᠠᠨ ᠨᠣᠮ ᠬᠡᠪᠯᠡᠯ ᠦᠳ ᠦᠨ ᠲᠣᠭ᠎ᠠ ᠨᠢ ᠣᠳᠣ 1.9 ᠰᠠᠶ᠎ᠠ ᠶᠢ ᠳᠠᠪᠠᠭᠠᠳ ᠪᠠᠶᠢᠭ᠎ᠠ ᠪᠠ ᠵᠢᠯ ᠪᠦᠷᠢ 75 ᠮᠢᠩᠭᠠᠨ ᠨᠣᠮ ᠬᠡᠪᠯᠡᠯ ᠨᠡᠮᠡᠭᠳᠡᠵᠦ ᠪᠠᠶᠢᠨ᠎ᠠ᠃ ᠡᠨᠡ ᠶᠡᠬᠡ ᠳᠠᠯᠠᠢ ᠳᠠᠬᠢ ᠠᠵᠢᠯ ᠤᠳ ᠪᠠᠷᠤᠭ ᠪᠥᠭᠥᠳᠡᠭᠡᠷ ᠢᠶᠡᠨ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠲᠧᠣᠷᠧᠮ ᠤᠳ ᠪᠠ ᠲᠡᠳᠡᠭᠡᠷ ᠦᠨ ᠪᠠᠲᠤᠯᠠᠭ᠎ᠠ ᠨᠤᠭᠤᠳ ᠢ ᠠᠭᠤᠯᠠᠳᠠᠭ᠃ [7]

ᠭᠠᠳᠠᠨ᠎ᠠ ᠶᠢᠨ ᠨᠥᠯᠥᠭᠡᠯᠡᠯ᠂ ᠴᠡᠪᠡᠷ ᠪᠠ ᠬᠡᠷᠡᠭᠯᠡᠭᠡᠨ ᠦ ᠮᠠᠲ᠋ᠧᠮᠠᠲ᠋ᠢᠺ᠂ ᠭᠣᠸ᠎ᠠ ᠰᠠᠶᠢᠬᠠᠨ[ᠵᠠᠰᠠᠪᠤᠷᠢᠯᠠᠬᠤ | ᠺᠣᠳ᠋ ᠢᠶᠠᠷ ᠵᠠᠰᠠᠬᠣ]

ᠢᠰᠠᠺ ᠨᠢᠶᠦ᠋ᠲ᠋ᠣᠨ (1643-1727), ᠪᠦᠬᠦ ᠦᠶ᠎ᠡ ᠶᠢᠨ ᠬᠠᠮᠤᠭ ᠤᠨ ᠠᠭᠤᠤ ᠹᠢᠽᠢᠺᠴᠢ᠂ ᠢᠨᠲ᠋ᠧᠭᠷᠡᠯ ᠪᠠ ᠳ᠋ᠢᠹᠹᠧᠷᠧᠨᠼᠢᠠᠯ ᠲᠣᠭᠠᠯᠠᠯ ᠢ ᠦᠨᠳᠦᠰᠦᠯᠡᠭᠴᠢᠳ ᠦᠨ ᠨᠢᠭᠡ᠃
ᠵᠢᠵᠢᠭ ᠵᠢᠷᠤᠭ ᠢ ᠡᠭᠦᠰᠭᠡᠬᠦ ᠳ᠋ᠦ ᠠᠯᠳᠠᠭ᠎ᠠ ᠭᠠᠷᠤᠯ᠎ᠠ: Unable to save thumbnail to destination

ᠬᠠᠮᠢᠭ᠎ᠠ ᠯᠠ ᠲᠣᠭ᠎ᠠ ᠬᠡᠮᠵᠢᠶ᠎ᠡ᠂ ᠪᠦᠲᠦᠴᠡ᠂ ᠣᠭᠲᠠᠷᠭᠤᠢ᠂ ᠡᠰᠡᠪᠡᠯ ᠥᠭᠡᠷᠡᠴᠢᠯᠡᠯᠲᠡ ᠣᠷᠣᠯᠴᠠᠭᠰᠠᠨ ᠬᠡᠴᠡᠭᠦᠦ ᠪᠣᠳᠣᠯᠭ᠎ᠠ ᠨᠤᠭᠤᠳ ᠪᠠᠶᠢᠪᠠᠯ ᠲᠡᠨᠳᠡ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠢᠯᠡᠷᠡᠳᠡᠭ᠃ ᠡᠶᠢᠮᠦ ᠪᠣᠳᠣᠯᠭ᠎ᠠ ᠨᠤᠭᠤᠳ ᠡᠬᠢᠯᠡᠭᠡᠳ ᠬᠤᠳᠠᠯᠳᠤᠭ᠎ᠠᠭᠠᠵᠠᠷ ᠬᠡᠮᠵᠢᠯᠲᠡ᠂ ᠰᠡᠭᠦᠯ ᠳᠦ ᠣᠳᠣᠨ ᠣᠷᠣᠨ ᠳᠤ ᠣᠯᠳᠠᠳᠠᠭ ᠪᠠᠶᠢᠭᠰᠠᠨ ᠪᠥᠭᠡᠳ ᠣᠳᠣ ᠦᠶ᠎ᠡ ᠳᠦ ᠪᠦᠬᠦ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ᠂ ᠲᠡᠭᠦᠨᠴᠢᠯᠡᠨ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠥᠪᠡᠷ ᠢᠶᠡᠨ ᠲᠥᠷᠥᠯ ᠪᠦᠷᠢ ᠶᠢᠨ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠪᠣᠳᠣᠯᠭ᠎ᠠ ᠨᠤᠭᠤᠳ ᠤᠨ ᠡᠬᠢ ᠡᠭᠦᠰᠪᠦᠷᠢ ᠪᠣᠯᠳᠠᠭ᠃ ᠲᠤᠬᠠᠶᠢᠯᠠᠪᠠᠯ ᠢᠰᠠᠺ ᠨᠢᠶᠦ᠋ᠲ᠋ᠣᠨ ᠢᠨᠲ᠋ᠧᠭᠷᠡᠯ ᠪᠠ ᠳ᠋ᠢᠹᠹᠧᠷᠧᠨᠼᠢᠠᠯ ᠲᠣᠭᠠᠯᠠᠯ ᠢ ᠦᠨᠳᠦᠰᠦᠯᠡᠭᠴᠢᠳ ᠦᠨ ᠨᠢᠭᠡ ᠪᠠᠶᠢᠭᠰᠠᠨ᠂ ᠹᠧᠢᠨᠠᠮᠠᠨ ᠤ ᠵᠠᠮ ᠤᠨ ᠢᠨᠲ᠋ᠧᠭᠷᠡᠯ ᠢ ᠹᠢᠽᠢᠺ ᠰᠡᠳᠬᠢᠯᠭᠡᠨ ᠦ ᠦᠨᠳᠦᠰᠦᠨ ᠳᠡᠭᠡᠷ᠎ᠡ ᠹᠧᠢᠨᠠᠮᠠᠨ ᠣᠷᠣᠭᠤᠯᠤᠭᠰᠠᠨ᠂ ᠮᠥᠨ ᠥᠨᠥ ᠶᠢᠨ ᠤᠲᠠᠰᠤᠨ ᠤ ᠣᠨᠣᠯ ᠰᠢᠨ᠎ᠡ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠢ ᠪᠤᠢ ᠪᠣᠯᠭᠠᠬᠤ ᠳᠤ ᠨᠥᠯᠦᠭᠡᠯᠡᠵᠦ ᠪᠠᠶᠢᠨ᠎ᠠ᠃ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠵᠠᠷᠢᠮ ᠣᠨᠣᠯ ᠤᠳ ᠵᠥᠪᠬᠡᠨ ᠲᠡᠭᠦᠨ ᠢ ᠪᠤᠢ ᠪᠣᠯᠭᠠᠬᠤ ᠳᠤ ᠨᠥᠯᠦᠭᠡᠯᠡᠭᠰᠡᠨ ᠲᠠᠯᠠᠪᠤᠷ ᠲᠤ ᠯᠠ ᠠᠰᠢᠭᠯᠠᠭᠳᠠᠳᠠᠭ ᠪᠣᠯ ᠶᠡᠬᠡᠩᠬᠢ ᠣᠨᠣᠯ ᠤᠳ ᠪᠤᠰᠤᠳ ᠣᠯᠠᠨ ᠲᠠᠯᠠᠪᠤᠷ ᠲᠤ ᠮᠥᠨ ᠠᠰᠢᠭᠯᠠᠭᠳᠠᠳᠠᠭ᠃ "ᠬᠠᠮᠤᠭ ᠤᠨ ᠴᠡᠪᠡᠷ" ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠲᠤ ᠴᠤ ᠬᠡᠵᠢᠶ᠎ᠡ ᠨᠢᠭᠡᠨ ᠴᠠᠭ ᠲᠤ ᠠᠰᠢᠭᠯᠠᠭᠳᠠᠬᠤ ᠭᠠᠵᠠᠷ ᠣᠯᠳᠠᠳᠠᠭ ᠶᠠᠪᠤᠳᠠᠯ ᠢ ᠧᠦᠢᠭᠧᠨ ᠸᠢᠩᠨᠧᠷ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠶᠡᠷᠦ ᠪᠤᠰᠤ ᠶᠢᠨ ᠬᠡᠮᠨᠡᠯᠲᠡ ᠲᠡᠢ ᠪᠠᠶᠢᠳᠠᠯ ᠭᠡᠵᠦ ᠨᠡᠷᠡᠯᠡᠭᠰᠡᠨ᠃

ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠢ ᠳᠣᠲᠣᠷ᠎ᠠ ᠨᠢ ᠪᠠᠷᠤᠭᠴᠠᠭ᠎ᠠ ᠪᠠᠷ ᠴᠡᠪᠡᠷ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠪᠠ ᠬᠡᠷᠡᠭᠯᠡᠭᠡᠨ ᠦ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠭᠡᠵᠦ ᠬᠣᠶᠠᠷ ᠲᠣᠮᠣ ᠬᠡᠰᠡᠭ ᠲᠦ ᠬᠤᠪᠢᠶᠠᠳᠠᠭ᠃ ᠬᠡᠷᠡᠭᠯᠡᠭᠡᠨ ᠦ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠣᠯᠠᠨ ᠰᠠᠯᠪᠤᠷᠢ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠭᠠᠳᠠᠨᠠᠬᠢ ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠬᠤ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ ᠨᠤᠭᠤᠳ ᠲᠠᠢ ᠨᠡᠶᠢᠯᠡᠵᠦ ᠪᠦᠷᠢᠳᠭᠡᠯᠦᠢᠯᠡᠳᠦᠯ ᠦᠨ ᠰᠤᠳᠤᠯᠭ᠎ᠠᠺᠣᠮᠫᠢᠦ᠋ᠲ᠋ᠧᠷ ᠰᠤᠳᠤᠯᠤᠯ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠪᠡᠶ᠎ᠡ ᠪᠡᠨ ᠳᠠᠭᠠᠭᠰᠠᠨ ᠰᠢᠨ᠎ᠡ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ ᠨᠤᠭᠤᠳ ᠪᠣᠯᠵᠤ ᠬᠥᠭᠵᠢᠭᠰᠡᠨ᠃

ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠲᠤ ᠡᠩ ᠦᠨ ᠪᠠᠶᠢᠳᠠᠯ ᠪᠠ ᠶᠡᠷᠦᠩᠬᠡᠢ ᠪᠠᠶᠢᠳᠠᠯ ᠴᠢᠬᠤᠯᠠ᠃ ᠮᠥᠨ ᠧᠦᠺᠯᠢᠳ ᠦᠨ ᠡᠩ ᠦᠨ ᠲᠣᠭᠠᠨ ᠤ ᠲᠣᠭ᠎ᠠ ᠶᠢ ᠬᠢᠵᠠᠭᠠᠷ ᠦᠭᠡᠢ ᠭᠡᠵᠦ ᠪᠠᠲᠤᠯᠠᠭᠰᠠᠨ ᠪᠠᠲᠤᠯᠠᠭ᠎ᠠ ᠰᠢᠭ ᠤᠷ᠎ᠠ ᠤᠬᠠᠭᠠᠨ ᠱᠠᠭᠠᠷᠳᠠᠭᠰᠠᠨ ᠪᠠᠲᠤᠯᠠᠭ᠎ᠠ᠂ ᠹᠦᠷ ᠤᠨ ᠬᠤᠷᠳᠤᠨ ᠬᠤᠪᠢᠷᠠᠭᠠᠯᠲᠠ ᠰᠢᠭ ᠲᠣᠭᠠᠴᠠᠭᠠᠯᠠᠯ ᠢ ᠬᠤᠷᠳᠤᠰᠬᠠᠬᠤ ᠠᠷᠭ᠎ᠠ  ᠤᠳ ᠲᠤ ᠭᠣᠸ᠎ᠠ ᠰᠠᠶᠢᠬᠠᠨ ᠴᠢᠨᠠᠷ ᠪᠤᠢ᠃ ᠶᠡᠬᠡᠩᠬᠢ ᠮᠠᠲ᠋ᠧᠮᠠᠲ᠋ᠢᠭᠴᠢᠳ ᠥᠪᠡᠷ ᠦᠨ ᠠᠵᠢᠯ ᠠᠴᠠ ᠪᠣᠯᠤᠨ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠠᠴᠠ ᠭᠣᠸ᠎ᠠ ᠰᠠᠶᠢᠬᠠᠨ ᠤ ᠲᠠᠭᠠᠰᠢᠶᠠᠯ ᠠᠪᠳᠠᠭ᠃ ᠵᠠᠷᠢᠮ ᠮᠠᠲ᠋ᠧᠮᠠᠲ᠋ᠢᠭᠴᠢᠳ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠢ ᠤᠷᠠᠯᠢᠭ ᠤᠨ ᠲᠥᠷᠥᠯ᠂ ᠶᠠᠳᠠᠵᠤ ᠯᠠ ᠪᠦᠲᠦᠭᠡᠯᠴᠢ ᠦᠢᠯᠡ ᠠᠵᠢᠯᠯᠠᠭ᠎ᠠ ᠭᠡᠵᠦ ᠦᠵᠡᠳᠡᠭ ᠪᠥᠭᠡᠳ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠢ ᠬᠥᠭᠵᠢᠮ ᠪᠠ ᠢᠷᠠᠭᠤ ᠨᠠᠶᠢᠷᠠᠭ ᠲᠠᠢ ᠵᠢᠱᠢᠳᠡᠭ᠃

ᠪᠧᠷᠲᠤᠷᠢᠨ ᠳᠤ ᠷᠠᠰᠰᠧᠯ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠭᠣᠸ᠎ᠠ ᠰᠠᠶᠢᠬᠠᠨ ᠢ ᠢᠩᠭᠢᠵᠦ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠵᠡᠢ:

ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠢ ᠵᠥᠪ ᠢᠶᠡᠷ ᠬᠠᠷᠠᠪᠠᠯ ᠡᠨᠡ ᠨᠢ ᠵᠥᠪᠬᠡᠨ ᠦᠨᠡᠨ ᠢ ᠠᠭᠤᠯᠠᠭᠠᠳ ᠵᠣᠭᠰᠣᠬᠤ ᠦᠭᠡᠢ ᠳᠡᠭᠡᠳᠦ ᠭᠣᠸ᠎ᠠ ᠰᠠᠶᠢᠬᠠᠨ - ᠪᠠᠷᠢᠮᠠᠯ ᠮᠡᠲᠦ ᠬᠦᠢᠲᠡᠨ ᠪᠥᠭᠡᠳ ᠬᠠᠲᠠᠭᠤ ᠴᠢᠩᠳᠠ᠂ ᠪᠢᠳᠡᠨ ᠦ ᠰᠤᠯᠠ ᠪᠠᠶᠢᠳᠠᠯ ᠤᠨ ᠠᠯᠢ ᠴᠤ ᠲᠠᠯ᠎ᠠ ᠲᠠᠢ ᠬᠣᠯᠪᠣᠭ᠎ᠠ ᠦᠭᠡᠢ᠂ ᠵᠢᠷᠤᠭ ᠡᠰᠡᠪᠡᠯ ᠬᠥᠭᠵᠢᠮ ᠰᠢᠭ ᠡᠯᠳᠡᠪ ᠭᠣᠶᠣᠯ ᠴᠢᠮᠡᠭᠯᠡᠯ ᠪᠠᠶᠢᠬᠤ ᠦᠭᠡᠢ ᠪᠣᠯᠪᠠᠴᠤ ᠭᠠᠶᠢᠬᠠᠮᠰᠢᠭᠲᠠᠢ ᠴᠡᠪᠡᠷ ᠪᠥᠭᠡᠳ ᠵᠥᠪᠬᠡᠨ ᠬᠠᠮᠤᠭ ᠤᠨ ᠰᠠᠶᠢᠨ ᠤᠷᠠᠯᠢᠭ ᠲᠠᠢ ᠵᠦᠢᠷᠯᠡᠵᠦ ᠪᠣᠯᠬᠣᠷ ᠭᠤᠶᠢᠪᠢᠰᠢ ᠦᠭᠡᠢ ᠲᠡᠭᠦᠰ ᠲᠡᠭᠦᠯᠳᠡᠷ ᠪᠠᠶᠢᠳᠠᠯ ᠲᠠᠢ ᠬᠣᠯᠪᠣᠭ᠎ᠠ ᠲᠠᠢ ᠲᠡᠶᠢᠮᠦ ᠭᠣᠸ᠎ᠠ ᠰᠠᠶᠢᠬᠠᠨ ᠢᠠᠭᠤᠯᠠᠳᠠᠭ᠃ ᠬᠠᠮᠤᠭ ᠤᠨ ᠳᠡᠭᠡᠳᠦ ᠳᠠᠪᠠᠮᠠᠭᠠᠶᠢᠯᠠᠯ ᠤᠨ ᠵᠢᠰᠢᠭ ᠪᠣᠯᠤᠭᠰᠠᠨ ᠵᠢᠩᠬᠢᠨᠢ ᠪᠠᠶᠠᠷ ᠪᠠᠬᠠᠳᠤᠯ᠂ ᠰᠡᠳᠬᠢᠯ ᠦᠨ ᠬᠥᠭᠡᠷᠦᠯ᠂ ᠮᠢᠬ᠎ᠠ ᠴᠢᠰᠤᠨ ᠠᠴᠠ ᠪᠦᠲᠦᠭᠰᠡᠨ ᠬᠦᠮᠦᠨ ᠡᠴᠡ ᠢᠯᠡᠭᠦᠦ ᠪᠣᠯᠬᠤ ᠪᠠᠨ ᠮᠡᠳᠡᠷᠡᠬᠦ ᠮᠡᠳᠡᠷᠡᠮᠵᠢ ᠶᠢ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠠᠴᠠ ᠢᠷᠠᠭᠤ ᠨᠠᠶᠢᠷᠠᠭ ᠲᠠᠢ ᠠᠳᠠᠯᠢ ᠪᠠᠷ ᠣᠯᠵᠤ ᠪᠣᠯᠤᠨ᠎ᠠ᠃

ᠫᠣᠯᠢ ᠡᠷᠳᠣᠰ ᠢᠩᠭᠢᠵᠦ ᠬᠡᠯᠡᠭᠰᠡᠨ ᠪᠠᠶᠢᠨ᠎ᠠ: "ᠲᠣᠭᠠᠨ ᠨᠤᠭᠤᠳ ᠶᠠᠭᠠᠬᠢᠭᠠᠳ ᠰᠠᠶᠢᠬᠠᠨ ᠭᠡᠵᠦ ? ᠡᠨᠡ ᠨᠢ ᠶᠠᠭᠠᠬᠢᠭᠠᠳ ᠪᠧᠲ᠋ᠬᠣᠸᠸᠨ ᠦ 9 ᠍ ᠳᠦᠭᠡᠷ ᠰᠢᠮᠹᠣᠨᠢ ᠰᠠᠶᠢᠬᠠᠨ ᠪᠤᠢ ᠭᠡᠵᠦ ᠠᠰᠠᠭᠤᠭᠰᠠᠨ ᠲᠠᠢ ᠠᠳᠠᠯᠢ᠃ ᠬᠡᠷᠪᠡ ᠴᠢ ᠶᠠᠭᠠᠬᠢᠭᠠᠳ ᠭᠡᠳᠡᠭ ᠢ ᠨᠢ ᠬᠠᠷᠠᠬᠤ ᠦᠭᠡᠢ ᠪᠠᠶᠢᠭ᠎ᠠ ᠪᠣᠯ ᠬᠡᠨ ᠴᠤ ᠴᠢᠮ᠎ᠠ ᠳᠤ ᠣᠶᠢᠯᠠᠭᠠᠭᠤᠯᠵᠤ ᠴᠢᠳᠠᠬᠤ ᠦᠭᠡᠢ᠃ ᠪᠢ ᠲᠣᠭᠠᠨ ᠨᠤᠭᠤᠳ ᠰᠠᠶᠢᠬᠠᠨ ᠭᠡᠳᠡᠭ ᠢ ᠮᠡᠳᠡᠵᠦ ᠪᠠᠶᠢᠨ᠎ᠠ᠃ ᠬᠡᠷᠪᠡ ᠲᠣᠭ᠎ᠠ ᠰᠠᠶᠢᠬᠠᠨ ᠪᠢᠰᠢ ᠪᠣᠯ ᠶᠠᠭᠤ ᠴᠤ ᠲᠡᠶᠢᠮᠦ ᠪᠢᠰᠢ᠃"

ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠰᠠᠯᠪᠤᠷᠢ ᠨᠤᠭᠤᠳ[ᠵᠠᠰᠠᠪᠤᠷᠢᠯᠠᠬᠤ | ᠺᠣᠳ᠋ ᠢᠶᠠᠷ ᠵᠠᠰᠠᠬᠣ]

ᠵᠢᠵᠢᠭ ᠵᠢᠷᠤᠭ ᠢ ᠡᠭᠦᠰᠭᠡᠬᠦ ᠳ᠋ᠦ ᠠᠯᠳᠠᠭ᠎ᠠ ᠭᠠᠷᠤᠯ᠎ᠠ: Unable to save thumbnail to destination
ᠬᠢᠲᠠᠳ ᠰᠤᠸᠠᠮᠫᠠᠨ. ᠡᠬᠢᠨ ᠦ ᠦᠶ᠎ᠡ ᠶᠢᠨ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠨᠢ ᠪᠦᠬᠦᠯᠢ ᠪᠡᠷ ᠢᠶᠡᠨ ᠫᠷᠠᠺᠲ᠋ᠢᠭ ᠲᠣᠭᠠᠴᠠᠭ᠎ᠠ ᠬᠢᠬᠦ ᠲᠡᠢ ᠬᠣᠯᠪᠣᠭ᠎ᠠ ᠲᠠᠢ ᠪᠠᠶᠢᠭᠰᠠᠨ᠃

ᠳᠡᠭᠡᠷ᠎ᠡ ᠲᠤᠷᠠᠳᠤᠭᠰᠠᠨ  ᠢᠶᠠᠷ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠭᠣᠣᠯ ᠰᠠᠯᠪᠤᠷᠢ  ᠤᠳ ᠲᠠᠲᠠᠪᠤᠷᠢ ᠪᠠ ᠬᠤᠳᠠᠯᠳᠤᠭ᠎ᠠ ᠲᠠᠢ ᠬᠣᠯᠪᠣᠭ᠎ᠠ ᠲᠠᠢ ᠲᠣᠭᠠᠴᠠᠭ᠎ᠠ ᠬᠢᠬᠦ᠂ ᠲᠣᠭᠠᠨ ᠨᠤᠭᠤᠳ ᠤᠨ ᠬᠣᠭᠣᠷᠣᠨᠳᠣᠬᠢ ᠬᠠᠷᠢᠴᠠᠭ᠎ᠠ ᠬᠠᠮᠢᠶᠠᠷᠤᠯ ᠤᠳ ᠢ ᠤᠶᠢᠯᠠᠭᠠᠬᠤ᠂ ᠭᠠᠵᠠᠷ ᠢ ᠬᠡᠮᠵᠢᠬᠦ᠂ ᠣᠳᠣᠨ ᠣᠷᠣᠨ ᠤ ᠦᠵᠡᠭᠳᠡᠯ  ᠦᠳ ᠢ ᠤᠷᠢᠳᠴᠢᠯᠠᠨ ᠬᠡᠯᠡᠬᠦ ᠱᠠᠭᠠᠷᠳᠠᠯᠭ᠎ᠠ ᠨᠤᠭᠤᠳ ᠠᠴᠠ ᠡᠭᠦᠳᠦᠨ ᠪᠤᠢ ᠪᠣᠯᠤᠭᠰᠠᠨ᠃ ᠡᠳᠡᠭᠡᠷ ᠱᠠᠭᠠᠷᠳᠠᠯᠭ᠎ᠠ ᠨᠤᠭᠤᠳ ᠢ ᠪᠠᠷᠤᠭᠴᠠᠭ᠎ᠠ ᠪᠠᠷ ᠲᠣᠭ᠎ᠠ ᠬᠡᠮᠵᠢᠶ᠎ᠡᠪᠦᠲᠦᠴᠡᠣᠭᠲᠠᠷᠭᠤᠢ ᠪᠠ ᠥᠭᠡᠷᠡᠴᠢᠯᠡᠯᠲᠡ  ᠶᠢᠨ ᠰᠤᠳᠤᠯᠭ᠎ᠠ ᠨᠤᠭᠤᠳ ᠲᠤ (ᠥ ᠂ ᠬ ᠂ ᠠᠷᠢᠹᠮᠧᠲ᠋ᠢᠭᠠᠯᠭᠧᠪᠷ᠂ [[ᠭ᠍ᠸᠣᠮᠧᠲ᠋ᠷᠢ]᠂ ᠪᠠ ᠠᠨᠠᠯᠢᠽᠢ) ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠭᠤᠯᠵᠤ ᠪᠣᠯᠤᠨ᠎ᠠ᠃ ᠡᠳᠡᠭᠡᠷ ᠭᠣᠣᠯ ᠬᠡᠰᠡᠭ ᠦᠳ ᠡᠴᠡ ᠭᠠᠳᠠᠨ᠎ᠠ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠴᠥᠮ᠎ᠡ ᠡᠴᠡ ᠪᠤᠰᠤᠳ ᠰᠠᠯᠪᠤᠷᠢ  ᠤᠳ ᠤᠷᠤᠭᠤ ᠬᠣᠯᠪᠣᠭᠳᠠᠭᠰᠠᠨ ᠬᠣᠯᠪᠣᠭ᠎ᠠ ᠶᠢ ᠰᠤᠳᠤᠯᠬᠤ ᠵᠣᠷᠢᠯᠭ᠎ᠠ ᠲᠠᠢ ᠳᠡᠳ᠋ ᠬᠡᠰᠡᠭ ᠦᠳ ᠪᠤᠢ: ᠯᠣᠭᠢᠭᠣᠯᠠᠨᠯᠢᠭ ᠤᠨ ᠣᠨᠣᠯ ᠲᠠᠢ ᠬᠣᠯᠪᠣᠭ᠎ᠠ ᠲᠠᠢ ᠲᠤᠯᠭᠠᠭᠤᠷᠢ ᠰᠠᠯᠪᠤᠷᠢ  ᠤᠳ᠂ ᠲᠥᠷᠥᠯ ᠪᠦᠷᠢ ᠶᠢᠨ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ ᠤ ᠲᠤᠷᠰᠢᠯᠭ᠎ᠠ ᠶᠢᠨ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠲᠠᠢ ᠬᠣᠯᠪᠣᠭ᠎ᠠ ᠲᠠᠢ ᠬᠡᠷᠡᠭᠯᠡᠭᠡᠨ ᠦ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠭᠡᠬᠦ ᠮᠡᠲᠦ᠃

ᠲᠣᠭ᠎ᠠ ᠬᠡᠮᠵᠢᠶ᠎ᠡ[ᠵᠠᠰᠠᠪᠤᠷᠢᠯᠠᠬᠤ | ᠺᠣᠳ᠋ ᠢᠶᠠᠷ ᠵᠠᠰᠠᠬᠣ]

ᠲᠣᠭ᠎ᠠ ᠬᠡᠮᠵᠢᠶᠡᠨ ᠦ ᠰᠤᠳᠤᠯᠤᠯ ᠨᠢ ᠪᠢᠳᠡᠨ ᠦ ᠮᠡᠳᠡᠬᠦ ᠨᠠᠲ᠋ᠦᠶᠢᠷᠠᠯ ᠲᠣᠭ᠎ᠠ ᠨᠤᠭᠤᠳᠪᠦᠬᠦᠯᠢ ᠲᠣᠭᠠᠨ ᠨᠤᠭᠤᠳ ᠪᠠ ᠲᠡᠳᠡᠭᠡᠷ ᠳᠡᠭᠡᠷ᠎ᠡ ᠬᠢᠭᠳᠡᠬᠦ ᠠᠷᠢᠹᠮᠧᠲ᠋ᠢᠭ ᠦᠢᠯᠡᠳᠦᠯ ᠦᠳ ᠢᠶᠡᠷ ᠡᠬᠢᠯᠡᠬᠦ ᠪᠥᠭᠡᠳ ᠡᠨᠡ ᠨᠢ ᠠᠷᠢᠹᠮᠧᠲ᠋ᠢᠭ ᠢ ᠲᠥᠷᠦᠭᠦᠯᠦᠨ᠎ᠡ᠃ ᠪᠦᠬᠦᠯᠢ ᠲᠣᠭᠠᠨ ᠨᠤᠭᠤᠳ ᠤᠨ ᠢᠯᠡᠭᠦᠦ ᠭᠦᠨᠵᠡᠭᠡᠢ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ  ᠨᠤᠭᠤᠳ ᠢ ᠲᠣᠭᠠᠨ ᠤ ᠣᠨᠣᠯ ᠰᠤᠳᠤᠯᠬᠤ ᠪᠠ ᠹᠧᠷᠮᠠᠭ ᠤᠨ ᠰᠡᠭᠦᠯᠴᠢ ᠶᠢᠨ ᠣᠨᠣᠯ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠦᠷ᠎ᠡ ᠳ᠋ᠦᠩ ᠨᠦᠭᠦᠳ ᠢ ᠭᠠᠷᠭᠠᠳᠠᠭ᠃ ᠲᠣᠭᠠᠨ ᠤ ᠣᠨᠣᠯ ᠤᠨ ᠠᠯᠳᠠᠷᠲᠠᠢ ᠪᠣᠳᠣᠭᠳᠠᠭ᠎ᠠ ᠦᠭᠡᠢ ᠪᠣᠳᠣᠯᠭ᠎ᠠ ᠨᠤᠭᠤᠳ ᠲᠤ ᠬᠣᠣᠰ ᠡᠩ ᠦᠨ ᠲᠣᠭᠠᠨ ᠤ ᠪᠣᠯᠤᠨ ᠭᠣᠣᠯᠳᠪᠠᠬᠤ ᠶᠢᠨ ᠲᠠᠭᠠᠮᠠᠭᠯᠠᠯ ᠤᠳ ᠣᠷᠣᠨ᠎ᠠ᠃

ᠲᠣᠭᠠᠨ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠨ ᠴᠢᠨᠠᠭᠰᠢᠳᠠ ᠶᠢᠨ ᠬᠥᠭᠵᠢᠯ ᠪᠦᠬᠦᠯᠢ ᠲᠣᠭᠠᠨ ᠨᠤᠭᠤᠳ ᠢ ᠷᠠᠼᠢᠣᠨᠠᠯᠢ ᠲᠣᠭ᠎ᠠ ᠨᠤᠭᠤᠳ ᠪᠤᠶᠤ "ᠪᠤᠲᠠᠷᠬᠠᠢ" ᠲᠣᠭᠠᠨ ᠨᠤᠭᠤᠳ ᠤᠨ ᠳᠡᠳ᠋ ᠣᠯᠠᠨᠯᠢᠭ ᠪᠣᠯᠭᠠᠬᠤ ᠳᠤ ᠬᠦᠷᠭᠡᠭᠰᠡᠨ᠃ ᠷᠠᠼᠢᠣᠨᠠᠯᠢ ᠲᠣᠭ᠎ᠠ ᠨᠤᠭᠤᠳ ᠨᠢ ᠮᠥᠨ ᠥᠪᠡᠷ ᠦᠨ ᠡᠭᠡᠯᠵᠢᠨ ᠳᠦ ᠲᠠᠰᠤᠷᠠᠯᠲᠠ ᠦᠭᠡᠢ ᠲᠣᠭ᠎ᠠ ᠬᠡᠮᠵᠢᠶ᠎ᠡ ᠶᠢ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠳᠡᠭ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭᠠᠨ ᠨᠤᠭᠤᠳ ᠲᠤ ᠠᠭᠤᠯᠤᠭᠳᠠᠨ᠎ᠠ᠃ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭ᠎ᠠ ᠨᠤᠭᠤᠳ ᠨᠢ ᠺᠣᠮᠫᠯᠧᠺᠰ ᠲᠣᠭ᠎ᠠ ᠨᠤᠭᠤᠳ ᠤᠷᠤᠭᠤ ᠥᠷᠭᠡᠳᠬᠡᠭᠳᠡᠳᠡᠭ᠃ ᠡᠨᠡ ᠱᠠᠲᠤᠯᠠᠭᠰᠠᠨ ᠳᠠᠷᠠᠭᠠᠯᠠᠯ ᠴᠠᠰᠢ ᠪᠠᠨ ᠺᠸᠠᠲ᠋ᠧᠷᠨᠢᠨ ᠪᠠ ᠣᠺᠲ᠋ᠣᠨᠢᠣᠨ ᠬᠦᠷᠲᠡᠯ᠎ᠡ ᠶᠠᠪᠤᠨ᠎ᠠ᠃ ᠨᠥᠭᠥᠭᠡ ᠲᠠᠯ᠎ᠠ ᠠᠴᠠ ᠨᠠᠲ᠋ᠦᠶᠢᠷᠠᠯ ᠲᠣᠭᠠᠨ ᠨᠤᠭᠤᠳ ᠤᠨ ᠰᠤᠳᠤᠯᠤᠯ ᠲᠡᠭᠦᠰᠬᠡᠯ ᠦᠭᠡᠢ ᠬᠦᠷᠲᠡᠯ᠎ᠡ ᠲᠣᠭᠠᠯᠠᠬᠤ ᠶᠢ ᠹᠷᠮᠠᠯᠢᠵᠢᠭᠤᠯᠳᠠᠭ ᠲᠷᠠᠨᠰᠹᠢᠨᠢ ᠳᠤ ᠲᠣᠭᠠᠨ ᠨᠤᠭᠤᠳ ᠲᠤ ᠬᠦᠷᠭᠡᠳᠡᠭ᠃ ᠬᠡᠮᠵᠢᠶᠡᠨ ᠦ ᠰᠤᠳᠤᠯᠤᠯ ᠺᠠᠷᠳ᠋ᠨᠯ ᠲᠣᠭᠠᠨ ᠨᠤᠭᠤᠳ ᠢ ᠣᠷᠣᠭᠤᠯᠳᠠᠭ ᠪᠥᠭᠡᠳ ᠡᠨᠡ ᠨᠢ ᠲᠡᠭᠦᠰᠬᠡᠯ ᠦᠭᠡᠢ ᠲᠣᠮᠣ ᠬᠡᠮᠵᠢᠶ᠎ᠡ ᠲᠡᠢ ᠣᠯᠠᠨᠯᠢᠭ ᠤᠳ ᠢ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠨᠢ ᠬᠠᠷᠢᠴᠠᠭᠤᠯᠬᠤ ᠪᠣᠯᠤᠮᠵᠢ ᠣᠯᠭᠤᠳᠠᠭ ᠠᠯᠧᠹ ᠲᠣᠭᠠᠨ ᠨᠤᠭᠤᠳ ᠲᠤ ᠬᠦᠷᠭᠡᠨ᠎ᠡ᠃

<math>1, 2, 3\,\!</math> <math>-2, -1, 0, 1, 2\,\!</math> <math> -2, \frac{2}{3}, 1.21\,\!</math> <math>\sqrt{2}, \sqrt{3}, \sqrt{5},\!</math> <math>-e, \sqrt{2}, 3, \pi\,\!</math> <math>2, i, -2+3i, 2e^{i\frac{4\pi}{3}}\,\!</math>
ᠨᠠᠲ᠋ᠦᠶᠢᠷᠠᠯ ᠲᠣᠭ᠎ᠠ ᠨᠤᠭᠤᠳ ᠪᠦᠬᠦᠯᠢ ᠲᠣᠭ᠎ᠠ ᠨᠤᠭᠤᠳ ᠷᠠᠼᠢᠣᠨᠠᠯᠢ ᠲᠣᠭ᠎ᠠ ᠨᠤᠭᠤᠳ ᠢᠷᠷᠠᠼᠢᠣᠨᠠᠯᠢ ᠲᠣᠭ᠎ᠠ ᠨᠤᠭᠤᠳ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭᠠᠨ ᠨᠤᠭᠤᠳ ᠺᠣᠮᠫᠯᠧᠺᠰ ᠲᠣᠭ᠎ᠠ ᠨᠤᠭᠤᠳ

ᠪᠦᠲᠦᠴᠡ[ᠵᠠᠰᠠᠪᠤᠷᠢᠯᠠᠬᠤ | ᠺᠣᠳ᠋ ᠢᠶᠠᠷ ᠵᠠᠰᠠᠬᠣ]

ᠣᠯᠠᠨᠯᠢᠭᠹᠦᠨᠺᠼ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠣᠯᠠᠨ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠣᠪᠶᠧᠺᠲ ᠤᠳ ᠥᠪᠡᠷ ᠦᠨ ᠳᠣᠲᠣᠭᠠᠳᠤ ᠪᠦᠲᠦᠴᠡ ᠲᠡᠢ ᠪᠠᠶᠢᠳᠠᠭ᠃ ᠡᠶᠢᠮᠦ ᠣᠪᠶᠧᠺᠲ ᠤᠳ ᠤᠨ ᠪᠦᠲᠦᠴᠡ ᠶᠢᠨ ᠰᠢᠨᠵᠢ ᠴᠢᠨᠠᠷ ᠤᠳ ᠢ ᠪᠦᠯᠦᠭᠴᠠᠭᠠᠷᠢᠭ᠂ ᠪᠠ ᠲᠠᠯᠠᠪᠤᠷ ᠪᠣᠯᠤᠨ ᠪᠤᠰᠤᠳ ᠠᠪᠰᠲᠷᠠᠺᠲ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠳ ᠦᠨ ᠲᠤᠰᠠᠯᠠᠮᠵᠢ ᠲᠠᠢ ᠰᠤᠳᠤᠯᠳᠠᠭ᠃ ᠡᠳᠡᠭᠡᠷ ᠨᠢ ᠥᠪᠡᠷᠰᠡᠳ ᠢᠶᠡᠨ ᠮᠥᠨ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠣᠪᠶᠧᠺᠲ ᠤᠳ ᠪᠣᠯᠬᠤ ᠪᠥᠭᠡᠳ ᠡᠳᠡᠭᠡᠷ ᠦᠨ ᠰᠤᠳᠤᠯᠭ᠎ᠠ ᠠᠪᠰᠲᠷᠠᠺᠲ ᠠᠯᠭᠧᠪᠷᠠ ᠢ ᠪᠦᠷᠢᠳᠦᠭᠦᠯᠦᠨ᠎ᠡ᠃ ᠨᠢᠭᠡ ᠴᠢᠬᠤᠯᠠ ᠣᠶᠢᠯᠠᠭᠠᠯᠲᠠ ᠪᠣᠯ ᠸᠧᠺᠲ᠋ᠣᠷ ᠤᠳ ᠪᠠ ᠡᠳᠡᠭᠡᠷ ᠢ ᠸᠧᠺᠲ᠋ᠣᠷ ᠣᠭᠲᠠᠷᠭᠤᠢ ᠪᠣᠯᠭᠠᠵᠤ ᠥᠷᠭᠡᠳᠬᠡᠨ ᠱᠤᠭᠤᠮᠠᠨ ᠠᠯᠭᠧᠪᠷᠠ  ᠰᠤᠳᠤᠯᠤᠨ᠎ᠠ᠃ ᠸᠧᠺᠲ᠋ᠣᠷ ᠤᠳ ᠤᠨ ᠰᠤᠳᠤᠯᠭ᠎ᠠ ᠨᠢ ᠲᠣᠭ᠎ᠠ ᠬᠡᠮᠵᠢᠶ᠎ᠡ᠂ ᠪᠦᠲᠦᠴᠡ᠂ ᠣᠭᠲᠠᠷᠭᠤᠢ ᠭᠡᠰᠡᠨ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠭᠤᠷᠪᠠᠨ ᠦᠨᠳᠦᠰᠦᠨ ᠰᠤᠳᠤᠯᠤᠭᠳᠠᠬᠤᠨ ᠢ ᠨᠢᠭᠡ ᠳᠣᠣᠷ᠎ᠠ ᠠᠪᠴᠤ ᠦᠵᠡᠳᠡᠭ᠃ ᠴᠢᠨᠠᠭᠰᠢᠯᠠᠪᠠᠯ ᠸᠧᠺᠲ᠋ᠣᠷ ᠲᠣᠭᠠᠯᠠᠯ ᠳᠤ ᠦᠨᠳᠦᠰᠦᠨ ᠰᠤᠳᠤᠯᠤᠭᠳᠠᠬᠤᠨ ᠪᠣᠯᠬᠤ ᠥᠭᠡᠷᠡᠴᠢᠯᠡᠯᠲᠡ ᠶᠢ ᠮᠥᠨ ᠠᠪᠴᠤ ᠦᠵᠡᠳᠡᠭ ᠪᠠᠶᠢᠨ᠎ᠠ᠃

Elliptic curve simple.png Rubik float.png Group diagdram D6.svg Lattice of the divisibility of 60.svg
ᠲᠣᠭᠠᠨ ᠤ ᠣᠨᠣᠯ ᠠᠪᠰᠲᠷᠠᠺᠲ ᠠᠯᠭᠧᠪᠷ ᠪᠦᠯᠦᠭ ᠦᠨ ᠣᠨᠣᠯ ᠡᠷᠡᠮᠪᠠ ᠶᠢᠨ ᠣᠨᠣᠯ

ᠣᠭᠲᠠᠷᠭᠤᠢ[ᠵᠠᠰᠠᠪᠤᠷᠢᠯᠠᠬᠤ | ᠺᠣᠳ᠋ ᠢᠶᠠᠷ ᠵᠠᠰᠠᠬᠣ]

ᠣᠭᠲᠠᠷᠭᠤᠢ ᠶᠢᠨ ᠰᠤᠳᠤᠯᠭ᠎ᠠ ᠨᠢ ᠭᠧᠣᠮᠧᠲ᠋ᠷᠢ ᠡᠴᠡ᠂ ᠲᠤᠬᠠᠶᠢᠯᠠᠪᠠᠯ ᠧᠦᠺᠯᠢᠳ ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠷᠢ ᠡᠴᠡ ᠡᠬᠢᠯᠡᠯ ᠲᠡᠢ᠃ ᠲᠷᠢᠭᠣᠨᠣᠮᠧᠲ᠋ᠷᠢ ᠨᠢ ᠣᠭᠲᠠᠷᠭᠤᠢ᠂ ᠲᠣᠭ᠎ᠠ ᠬᠣᠶᠠᠷ ᠢ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠨᠢ ᠬᠣᠯᠪᠣᠳᠠᠭ ᠪᠠ ᠪᠢᠳᠡᠨ ᠦ ᠰᠠᠶᠢᠨ ᠮᠡᠳᠡᠬᠦ ᠫᠢᠹᠠᠭᠤᠷ ᠤᠨ ᠣᠨᠣᠯ ᠳᠡᠭᠡᠷ᠎ᠡ ᠦᠨᠳᠦᠰᠦᠨ ᠳᠦ ᠪᠡᠨ ᠲᠤᠯᠭᠠᠭᠤᠷᠢᠯᠠᠳᠠᠭ᠃ ᠣᠭᠲᠠᠷᠭᠤᠢ ᠶᠢᠨ ᠲᠤᠬᠠᠢ ᠣᠷᠴᠢᠨ ᠦᠶ᠎ᠡ ᠶᠢᠨ ᠣᠨᠣᠯ ᠤᠳ ᠡᠳᠡᠭᠡᠷ ᠰᠠᠨᠠᠭᠠᠨ ᠨᠤᠭᠤᠳ ᠢ ᠥᠷᠭᠡᠳᠬᠡᠨ ᠣᠯᠠᠨ ᠬᠡᠮᠵᠢᠶᠡᠰᠦᠳᠦ ᠭᠧᠣᠮᠧᠲ᠋ᠷᠢ᠂ ᠧᠦᠺᠯᠢᠳ ᠦᠨ ᠪᠢᠰᠢ ᠭᠧᠣᠮᠧᠲ᠋ᠷᠢ ᠤᠳ (ᠡᠨᠡ ᠭᠧᠣᠮᠧᠲ᠋ᠷᠢ ᠤᠳ ᠬᠠᠷᠢᠴᠠᠩᠭᠤᠢ ᠶᠢᠨ ᠶᠡᠷᠦᠩᠬᠡᠢ ᠣᠨᠣᠯ ᠳᠤ ᠭᠣᠣᠯ ᠡᠭᠦᠷᠭᠡ ᠭᠦᠢᠴᠡᠳᠭᠡᠳᠡᠭ) ᠪᠠ ᠲᠣᠫᠣᠯᠣᠭᠢ ᠶᠢ ᠰᠤᠳᠤᠯᠳᠠᠭ᠃ [[ᠠᠨᠠᠯᠢᠲ᠋ᠢᠭ ᠭ᠍ᠸᠣᠮᠧᠲ᠋ᠷᠢ]᠂ [[ᠳ᠋ᠢᠹᠹᠧᠷᠧᠨᠼᠢᠠᠯ ᠭ᠍ᠸᠣᠮᠧᠲ᠋ᠷᠢ]᠂ ᠪᠣᠯᠤᠨ ᠠᠯᠭᠧᠪᠷᠯᠢᠭ ᠭᠧᠣᠮᠧᠲ᠋ᠷᠢ ᠲᠦ ᠲᠣᠭ᠎ᠠ ᠬᠡᠮᠵᠢᠶ᠎ᠡ ᠪᠠ ᠣᠭᠲᠠᠷᠭᠤᠢ ᠬᠣᠶᠠᠭᠤᠯᠠ ᠴᠢᠬᠤᠯᠠ ᠡᠭᠦᠷᠭᠡ ᠭᠦᠢᠴᠡᠳᠭᠡᠳᠡᠭ᠃ ᠳ᠋ᠢᠹᠹᠧᠷᠧᠨᠼᠢᠠᠯ ᠭᠧᠣᠮᠧᠲ᠋ᠷᠢ ᠨᠢ ᠰᠢᠷᠬᠡᠭ ᠪᠠᠭᠴᠠ ᠪᠠ ᠴᠣᠭᠴᠠᠰ ᠳᠡᠭᠡᠷᠡᠬᠢ ᠲᠣᠭᠠᠯᠠᠯ ᠢ ᠠᠭᠤᠯᠠᠨ᠎ᠠ᠃ ᠠᠯᠭᠧᠪᠷᠯᠢᠭ ᠭᠧᠣᠮᠧᠲ᠋ᠷᠢ ᠨᠢ ᠭᠧᠣᠮᠡᠲ᠋ᠷ ᠤᠨ ᠣᠪᠶᠧᠺᠲ ᠤᠳ ᠢ ᠣᠯᠠᠨ ᠭᠡᠰᠢᠭᠦᠨ ᠳᠦ ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠦᠳ ᠦᠨ ᠣᠯᠠᠨᠯᠢᠭ ᠢᠶᠠᠷ ᠳᠦᠷᠰᠦᠯᠡᠭᠰᠡᠨ ᠢᠶᠡᠷ ᠲᠣᠭ᠎ᠠ ᠬᠡᠮᠵᠢᠶ᠎ᠡ ᠪᠠ ᠣᠭᠲᠠᠷᠭᠤᠢ ᠶᠢ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠨᠢ ᠬᠣᠯᠪᠣᠭᠠᠳ ᠵᠣᠭᠰᠣᠬᠤ ᠦᠭᠡᠢ ᠲᠣᠫᠣᠯᠣᠭᠢ ᠪᠦᠯᠦᠭ ᠦᠨ ᠲᠤᠬᠠᠢ ᠰᠤᠳᠤᠯᠵᠤ ᠪᠦᠲᠦᠴᠡ ᠪᠠ ᠣᠭᠲᠠᠷᠭᠤᠢ ᠶᠢ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠨᠢ ᠬᠣᠯᠪᠣᠳᠠᠭ ᠪᠠᠶᠢᠨ᠎ᠠ᠃ ᠯᠢ ᠪᠦᠯᠦᠭ ᠦᠳ ᠢ ᠣᠭᠲᠠᠷᠭᠤᠢ᠂ ᠪᠦᠲᠦᠴᠡ᠂ ᠥᠭᠡᠷᠡᠴᠢᠯᠡᠯᠲᠡ ᠶᠢ ᠵᠡᠷᠭᠡ ᠰᠤᠳᠤᠯᠬᠤ ᠳᠤ ᠠᠰᠢᠭᠯᠠᠳᠠᠭ᠃ ᠲᠣᠫᠣᠯᠣᠭᠢ ᠨᠢ ᠪᠦᠬᠦ ᠳᠦᠷᠰᠦ ᠬᠤᠪᠢᠷᠠᠯ ᠤᠳ ᠤᠨ ᠢᠶᠠᠨ ᠬᠠᠮᠲᠤ ᠮᠠᠭᠠᠳ ᠦᠭᠡᠢ ᠬᠣᠷᠢᠳᠤᠭᠠᠷ ᠵᠠᠭᠤᠨ ᠳᠤ ᠬᠠᠮᠤᠭ ᠤᠨ ᠶᠡᠬᠡ ᠬᠥᠭᠵᠢᠭᠰᠡᠨ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠰᠠᠯᠪᠤᠷᠢ ᠶᠤᠮ᠃ ᠡᠨᠳᠡ ᠵᠢᠱᠢᠶᠡᠯᠡᠪᠡᠯ ᠤᠳᠠᠭᠠᠨ ᠬᠤᠭᠤᠴᠠᠭᠠᠨ ᠳᠤ ᠰᠢᠢᠳᠦᠭᠳᠡᠭᠡ ᠦᠭᠡᠢ ᠪᠠᠶᠢᠭᠰᠠᠨ ᠫᠦ᠋ᠠᠩᠺᠠᠷᠢᠶᠦᠭ ᠦᠨ ᠲᠠᠭᠠᠮᠠᠭᠯᠠᠯ ᠪᠠ ᠺᠣᠮᠫᠢᠦ᠋ᠲ᠋ᠧᠷ ᠢᠶᠡᠷ ᠪᠠᠲᠤᠯᠠᠭᠰᠠᠨ ᠪᠣᠯᠪᠠᠴᠤ ᠬᠦᠮᠦᠨ ᠬᠡᠵᠢᠶ᠎ᠡ ᠴᠤ ᠪᠠᠲᠤᠯᠠᠭ᠎ᠠ ᠶᠢ ᠨᠢ ᠰᠢᠯᠭᠠᠭ᠎ᠠ ᠦᠭᠡᠢ ᠳᠥᠷᠪᠡᠨ ᠥᠩᠭᠡ ᠶᠢᠨ ᠣᠨᠣᠯ ᠵᠡᠷᠭᠡ ᠬᠠᠮᠤᠷᠠᠭᠳᠠᠨ᠎ᠠ᠃

Pythagorean.svg Taylorsine.svg Osculating circle.svg Torus.png Von koch 6 etapes.svg
[[ᠭ᠍ᠸᠣᠮᠧᠲ᠋ᠷᠢ] ᠲᠷᠢᠭᠣᠨᠣᠮᠧᠲ᠋ᠷᠢ [[ᠳ᠋ᠢᠹᠹᠧᠷᠧᠨᠼᠢᠠᠯ ᠭ᠍ᠸᠣᠮᠧᠲ᠋ᠷᠢ] ᠲᠣᠫᠣᠯᠣᠭᠢ [[ᠹᠷᠠᠺᠲᠯᠠ ᠭ᠍ᠸᠣᠮᠧᠲ᠋ᠷᠢ]

ᠥᠭᠡᠷᠡᠴᠢᠯᠡᠯᠲᠡ[ᠵᠠᠰᠠᠪᠤᠷᠢᠯᠠᠬᠤ | ᠺᠣᠳ᠋ ᠢᠶᠠᠷ ᠵᠠᠰᠠᠬᠣ]

ᠥᠭᠡᠷᠡᠴᠢᠯᠡᠯᠲᠡ ᠬᠤᠪᠢᠰᠤᠯ ᠢ ᠣᠶᠢᠯᠠᠭᠠᠵᠤ ᠲᠠᠶᠢᠯᠪᠤᠷᠢᠯᠠᠬᠤ ᠠᠰᠠᠭᠤᠳᠠᠯ ᠨᠢ ᠪᠠᠶᠢᠭᠠᠯᠢ ᠶᠢᠨ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ ᠤ ᠨᠡᠶᠢᠲᠡᠯᠢᠭ ᠠᠰᠠᠭᠤᠳᠠᠯ ᠪᠥᠭᠡᠳ ᠢᠨᠲ᠋ᠧᠭᠷᠡᠯ ᠪᠠ ᠳ᠋ᠢᠹᠹᠧᠷᠧᠨᠼᠢᠠᠯ ᠲᠣᠭᠠᠯᠠᠯ ᠨᠢ ᠶᠠᠭ ᠡᠭᠦᠨ ᠢ ᠰᠤᠳᠤᠯᠬᠤ ᠶᠢᠨ ᠲᠤᠯᠠᠳᠠ ᠪᠤᠢ ᠪᠣᠯᠭᠠᠭᠰᠠᠨ ᠬᠦᠴᠢᠲᠡᠢ ᠬᠡᠷᠡᠭᠰᠡᠯ ᠶᠤᠮ᠃ ᠥᠭᠡᠷᠡᠴᠢᠯᠡᠭᠳᠡᠵᠦ ᠪᠠᠶᠢᠭ᠎ᠠ ᠬᠡᠮᠵᠢᠭᠳᠡᠬᠦᠨ ᠢ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠬᠦ ᠲᠤᠯᠭᠠᠭᠤᠷᠢ ᠣᠶᠢᠯᠠᠭᠠᠯᠲᠠ ᠪᠣᠯᠭᠠᠨ ᠹᠦᠨᠺᠼ ᠢ ᠡᠨᠳᠡ ᠣᠷᠣᠭᠤᠯᠵᠤ ᠢᠷᠡᠳᠡᠭ᠃ ᠪᠣᠳᠠᠲᠤ ᠲᠣᠭᠠᠨ ᠨᠤᠭᠤᠳ ᠪᠠ ᠪᠣᠳᠠᠲᠤ ᠤᠳᠬ᠎ᠠ ᠠᠪᠳᠠᠭ ᠹᠦᠨᠺᠼ ᠦᠳ ᠦᠨ ᠰᠤᠳᠤᠯᠭ᠎ᠠ ᠶᠢ ᠪᠣᠳᠠᠲᠤ ᠠᠨᠠᠯᠢᠽᠢ ᠭᠡᠳᠡᠭ ᠪᠥᠭᠡᠳ ᠺᠣᠮᠫᠯᠧᠺᠰ ᠲᠣᠭ᠎ᠠ ᠲᠠᠢ ᠬᠣᠯᠪᠣᠭ᠎ᠠ ᠲᠠᠢ ᠡᠶᠢᠮᠦ ᠰᠠᠯᠪᠤᠷᠢ ᠶᠢ ᠨᠢ ᠺᠣᠮᠫᠯᠧᠺᠰ ᠠᠨᠠᠯᠢᠽᠢ ᠭᠡᠵᠦ ᠨᠡᠷᠡᠯᠡᠳᠡᠭ᠃ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠬᠠᠮᠤᠭ ᠤᠨ ᠲᠤᠯᠭᠠᠭᠤᠷᠢ ᠰᠢᠢᠳᠦᠭᠳᠡᠭᠡ ᠦᠭᠡᠢ ᠠᠰᠠᠭᠤᠳᠠᠯ ᠤᠳ ᠤᠨ ᠨᠢᠭᠡ ᠪᠣᠯᠬᠤ ᠷᠢᠮᠠᠨ ᠤ ᠲᠠᠭᠠᠮᠠᠭᠯᠠᠯ ᠺᠣᠮᠫᠯᠧᠺᠰ ᠠᠨᠠᠯᠢᠽ ᠠᠴᠠ ᠤᠷᠭᠤᠨ ᠭᠠᠷᠤᠭᠰᠠᠨ᠃ ᠹᠦᠨᠺᠼᠢᠤᠨᠠᠯ ᠠᠨᠠᠯᠢᠽᠢ ᠨᠢ ᠹᠦᠨᠺᠼ ᠦᠳ ᠦᠨ (ᠶᠡᠷᠦᠩᠬᠡᠢ ᠳᠤ ᠪᠡᠨ ᠲᠡᠭᠦᠰᠬᠡᠯ ᠦᠭᠡᠢ ᠬᠡᠮᠵᠢᠭᠡᠰᠦᠲᠡᠢ) ᠣᠭᠲᠠᠷᠭᠤᠢ ᠳᠡᠭᠡᠷ᠎ᠡ ᠲᠥᠪᠯᠡᠷᠡᠳᠡᠭ ᠪᠥᠭᠡᠳ ᠡᠭᠦᠨ ᠦ ᠨᠢᠭᠡ ᠬᠡᠷᠡᠭᠯᠡᠭᠡ ᠨᠢ ᠺᠸᠠᠨᠲ ᠮᠧᠬᠠᠨᠢᠭ ᠶᠤᠮ᠃ ᠨᠡᠶᠢᠲᠡᠯᠢᠭ ᠢᠯᠡᠷᠡᠳᠡᠭ ᠲᠣᠭ᠎ᠠ ᠬᠡᠮᠵᠢᠶ᠎ᠡ ᠪᠣᠯᠤᠨ ᠲᠡᠭᠦᠨ ᠦ ᠥᠭᠡᠷᠡᠴᠢᠯᠡᠯᠲᠡ ᠶᠢᠨ ᠬᠣᠭᠣᠷᠣᠨᠳᠣᠬᠢ ᠬᠣᠯᠪᠣᠭ᠎ᠠ ᠶᠢ ᠳ᠋ᠢᠹᠹᠧᠷᠧᠨᠼᠢᠠᠯ ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠪᠣᠯᠭᠠᠵᠤ ᠰᠤᠳᠤᠯᠳᠠᠭ᠃ ᠪᠠᠶᠢᠭᠠᠯᠢ ᠶᠢᠨ ᠣᠯᠠᠨ ᠦᠵᠡᠭᠳᠡᠯ  ᠳ᠋ᠢᠨᠠᠮᠢᠺ ᠰᠢᠰᠲ᠋ᠧᠮ ᠢᠶᠡᠷ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠭᠳᠡᠳᠡᠭ᠃ ᠡᠳᠡᠭᠡᠷ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠳ ᠶᠠᠮᠠᠷ ᠦᠶ᠎ᠡ ᠳᠦ ᠳ᠋ᠧᠲ᠋ᠧᠷᠮᠢᠨᠢᠰᠲ᠋ᠢᠭ ᠪᠣᠯᠪᠠᠴᠤ ᠤᠷᠢᠳᠴᠢᠯᠠᠵᠤ ᠲᠠᠭᠤᠬᠤ ᠶᠢᠨ ᠠᠷᠭ᠎ᠠ ᠦᠭᠡᠢ ᠰᠢᠨᠵᠢ ᠪᠠᠶᠢᠳᠠᠯ ᠦᠵᠡᠭᠦᠯᠬᠦ ᠪᠤᠢ ᠭᠡᠳᠡᠭ ᠢ ᠬᠠᠣᠰ ᠤᠨ ᠣᠨᠣᠯ ᠳᠤ ᠰᠤᠳᠤᠯᠤᠨ᠎ᠠ᠃

Integral as region under curve.svg Vectorfield jaredwf.png Limitcycle.jpg Lorenz attractor.svg
ᠢᠨᠲ᠋ᠧᠭᠷᠡᠯ ᠪᠠ ᠳ᠋ᠢᠹᠹᠧᠷᠧᠨᠼᠢᠠᠯ ᠲᠣᠭᠠᠯᠠᠯ ᠸᠧᠺᠲ᠋ᠣᠷ ᠲᠣᠭᠠᠯᠠᠯ ᠳ᠋ᠢᠹᠹᠧᠷᠧᠨᠼᠢᠠᠯ ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠳ᠋ᠢᠨᠠᠮᠢᠺ ᠰᠢᠰᠲ᠋ᠧᠮ ᠬᠠᠣᠰ ᠤᠨ ᠣᠨᠣᠯ

ᠲᠤᠯᠭᠠᠭᠤᠷᠢ ᠰᠠᠯᠪᠤᠷᠢ ᠤᠳ ᠪᠠ ᠹᠢᠯᠣᠰᠣᠹᠢ[ᠵᠠᠰᠠᠪᠤᠷᠢᠯᠠᠬᠤ | ᠺᠣᠳ᠋ ᠢᠶᠠᠷ ᠵᠠᠰᠠᠬᠣ]

ᠪᠦᠬᠦ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠳᠡᠭᠡᠷ᠎ᠡ ᠨᠢ ᠲᠣᠭᠲᠠᠵᠤ ᠪᠠᠶᠢᠭ᠎ᠠ ᠦᠨᠳᠦᠰᠦ ᠰᠠᠭᠤᠷᠢ ᠶᠢ ᠲᠣᠳᠣᠷᠬᠠᠢ ᠪᠣᠯᠭᠠᠬᠤ ᠶᠢᠨ ᠲᠤᠯᠠᠳᠠ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠯᠣᠭᠢᠭ ᠪᠠ ᠣᠯᠠᠨᠯᠢᠭ ᠤᠨ ᠣᠨᠣᠯ᠂ ᠮᠥᠨ ᠣᠳᠣ ᠪᠠᠷ ᠪᠦᠷᠢᠨ ᠲᠡᠭᠦᠯᠳᠡᠷᠵᠢᠭᠡ ᠦᠭᠡᠢ ᠪᠠᠶᠢᠭ᠎ᠠ ᠺᠠᠲ᠋ᠧᠭᠣᠷᠢ ᠶᠢᠨ ᠣᠨᠣᠯ ᠢ ᠡᠭᠦᠰᠬᠡᠵᠡᠢ᠃

ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠯᠣᠭᠢᠭ ᠨᠢ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠢ ᠬᠠᠲᠠᠭᠤ ᠠᠺᠰᠢᠣᠮᠣᠴᠢᠯᠠᠭᠰᠠᠨ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠨ ᠬᠦᠷᠢᠶᠡᠨ ᠳᠦ ᠠᠪᠴᠤ ᠦᠵᠡᠬᠦ ᠪᠠ ᠡᠭᠦᠨ ᠡᠴᠡ ᠭᠠᠷᠬᠤ ᠦᠷ᠎ᠡ ᠳᠠᠭᠠᠪᠤᠷᠢ ᠨᠤᠭᠤᠳ ᠢ ᠰᠤᠳᠤᠯᠳᠠᠭ᠃ ᠡᠨᠳᠡ ᠵᠢᠱᠢᠶᠡᠯᠡᠪᠡᠯ ᠯᠣᠭᠢᠭ ᠤᠨ ᠬᠠᠮᠤᠭ ᠤᠨ ᠠᠯᠳᠠᠷᠲᠠᠢ ᠦᠷ᠎ᠡ ᠳ᠋ᠦᠩ ᠪᠠᠶᠢᠵᠤ ᠮᠡᠳᠡᠬᠦ ᠭᠶᠳᠧᠯ ᠤᠨ ᠭᠦᠢᠴᠡᠳ ᠪᠤᠰᠤ ᠶᠢᠨ ᠬᠣᠶᠠᠳᠤᠭᠠᠷ ᠣᠨᠣᠯ ᠬᠠᠮᠢᠶᠠᠷᠤᠭᠳᠠᠨ᠎ᠠ᠃ ᠡᠨᠡ ᠣᠨᠣᠯ ᠨᠢ (ᠪᠠᠷᠤᠭᠴᠠᠭ᠎ᠠ ᠪᠠᠷ ᠬᠡᠯᠡᠪᠡᠯ) ᠦᠨᠳᠦᠰᠦᠨ ᠠᠷᠢᠹᠮᠧᠲ᠋ᠢᠭ ᠢ ᠪᠠᠭᠲᠠᠭᠠᠭᠰᠠᠨ ᠳᠤᠷ᠎ᠠ ᠶᠢᠨ ᠹᠷᠮᠠᠯ ᠰᠢᠰᠲ᠋ᠧᠮ ᠬᠡᠷᠪᠡ ᠤᠭ ᠰᠢᠰᠲ᠋ᠧᠮ ᠳᠦ ᠪᠠᠲᠤᠯᠠᠵᠤ ᠪᠣᠯᠬᠤ ᠪᠦᠬᠦ ᠣᠨᠣᠯ ᠦᠨᠡᠨ ᠪᠣᠯ ᠤᠭ ᠰᠢᠰᠲ᠋ᠧᠮ ᠳᠣᠲᠣᠷ᠎ᠠ ᠪᠠᠲᠤᠯᠠᠬᠤ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠭᠡᠢ᠂ ᠦᠨᠡᠨ ᠣᠨᠣᠯ ᠤᠳ ᠣᠷᠣᠰᠢᠨ ᠪᠠᠶᠢᠨ᠎ᠠ ᠭᠡᠳᠡᠭ᠃ ᠭᠶᠳᠧᠯ ᠲᠣᠭᠠᠨ ᠤ ᠣᠨᠣᠯ ᠤᠨ ᠳᠤᠷ᠎ᠠ ᠶᠢᠨ ᠠᠺᠰᠢᠣᠮ ᠤᠳ ᠥᠭᠭᠦᠭᠳᠡᠭᠰᠡᠨ ᠪᠠᠶᠢᠬᠤ ᠳᠤ ᠤᠭ ᠠᠺᠰᠢᠣᠮ ᠤᠳ ᠠᠴᠠ ᠭᠠᠷᠬᠤ ᠦᠭᠡᠢ᠂ ᠲᠣᠭᠠᠨ ᠤ ᠣᠨᠣᠯ ᠤᠨ ᠦᠨᠡᠨ ᠪᠠᠷᠢᠮᠲᠠ ᠶᠢ ᠢᠯᠡᠷᠬᠡᠶᠢᠯᠡᠬᠦ ᠯᠣᠭᠢᠭ ᠥᠭᠦᠯᠡᠪᠦᠷᠢ ᠶᠢ ᠶᠠᠭᠠᠬᠢᠵᠤ ᠪᠠᠶᠢᠭᠤᠯᠬᠤ ᠶᠢ ᠵᠢᠭᠠᠵᠤ ᠥᠭᠭᠦᠭᠰᠡᠨ᠃ ᠡᠶᠢᠮᠦ ᠳᠦ ᠶᠠᠮᠠᠷ ᠴᠤ ᠹᠷᠮᠠᠯ ᠰᠢᠰᠲ᠋ᠧᠮ ᠲᠣᠭᠠᠨ ᠤ ᠣᠨᠣᠯ ᠤᠨ ᠵᠢᠩᠬᠢᠨᠢ ᠠᠺᠰᠢᠣᠮᠴᠢᠯᠠᠯ ᠪᠣᠯᠵᠤ ᠴᠢᠳᠠᠬᠤ ᠦᠭᠡᠢ ᠶᠤᠮ᠃ ᠣᠷᠴᠢᠨ ᠦᠶ᠎ᠡ ᠶᠢᠨ ᠯᠣᠭᠢᠭ ᠨᠢ ᠷᠧᠺᠦ᠋ᠷᠰ ᠤᠨ ᠣᠨᠣᠯᠮᠣᠳᠧᠯ ᠤᠨ ᠣᠨᠣᠯ᠂ ᠪᠠ ᠪᠠᠲᠤᠯᠠᠭᠠᠨ ᠤ ᠣᠨᠣᠯ ᠭᠡᠵᠦ ᠬᠤᠪᠢᠶᠠᠭᠳᠠᠳᠠᠭ ᠪᠥᠭᠡᠳ ᠣᠨᠣᠯ ᠤᠨ ᠺᠣᠮᠫᠢᠦ᠋ᠲ᠋ᠧᠷ ᠰᠤᠳᠤᠯᠤᠯ ᠲᠠᠢ ᠨᠢᠭᠳᠠ ᠬᠣᠯᠪᠣᠭ᠎ᠠ ᠲᠠᠢ ᠣᠷᠣᠰᠢᠳᠠᠭ᠃

<math> P \Rightarrow Q \,</math> Venn A intersect B.svg Commutative diagram for morphism.svg
ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠯᠣᠭᠢᠭ ᠣᠯᠠᠨᠯᠢᠭ ᠤᠨ ᠣᠨᠣᠯ ᠺᠠᠲ᠋ᠧᠭᠣᠷᠢ ᠶᠢᠨ ᠣᠨᠣᠯ

ᠳ᠋ᠢᠰᠺᠷᠧᠲ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ[ᠵᠠᠰᠠᠪᠤᠷᠢᠯᠠᠬᠤ | ᠺᠣᠳ᠋ ᠢᠶᠠᠷ ᠵᠠᠰᠠᠬᠣ]

ᠳ᠋ᠢᠰᠺᠷᠧᠲ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠨᠢ ᠶᠡᠷᠦᠩᠬᠡᠢ ᠳᠤ ᠪᠡᠨ ᠣᠨᠣᠯ ᠤᠨ ᠺᠣᠮᠫᠢᠦ᠋ᠲ᠋ᠧᠷ ᠰᠤᠳᠤᠯᠤᠯ ᠳᠤ ᠬᠡᠷᠡᠭᠯᠡᠭᠳᠡᠳᠡᠭ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠰᠠᠯᠪᠤᠷᠢ  ᠤᠳ ᠢ ᠨᠡᠷᠡᠯᠡᠭᠰᠡᠨ ᠨᠡᠷ᠎ᠡ ᠶᠤᠮ᠃ ᠡᠭᠦᠨ ᠳᠦ ᠲᠣᠭᠠᠴᠠᠭᠠᠯᠠᠭᠳᠠᠬᠤ ᠪᠠᠶᠢᠳᠠᠯ ᠤᠨ ᠣᠨᠣᠯᠲᠣᠭᠠᠴᠠᠭᠠᠯᠠᠯ ᠤᠨ ᠨᠡᠶᠢᠯᠡᠮᠡᠯ ᠪᠠᠶᠢᠳᠠᠯ ᠤᠨ ᠣᠨᠣᠯ ᠪᠠ ᠮᠡᠳᠡᠭᠡᠯᠡᠯ ᠦᠨ ᠣᠨᠣᠯ ᠪᠠᠭᠲᠠᠨ᠎ᠠ᠃ ᠲᠣᠭᠠᠴᠠᠭᠠᠯᠠᠭᠳᠠᠬᠤ ᠪᠠᠶᠢᠳᠠᠯ ᠤᠨ ᠣᠨᠣᠯ ᠨᠢ ᠣᠳᠣ ᠪᠠᠷ ᠮᠡᠳᠡᠭᠳᠡᠵᠦ ᠪᠠᠶᠢᠭ᠎ᠠ ᠬᠠᠮᠤᠭ ᠤᠨ ᠬᠦᠴᠦᠷᠬᠡᠭ ᠵᠠᠭᠪᠤᠷ ᠪᠣᠯᠬᠤ ᠲᠶᠷᠢᠩ ᠦᠨ ᠵᠠᠭᠪᠤᠷ ᠢ ᠣᠷᠤᠯᠴᠠᠭᠤᠯᠤᠨ ᠺᠣᠮᠫᠢᠦ᠋ᠲ᠋ᠧᠷ ᠦᠨ ᠲᠥᠷᠥᠯ ᠪᠦᠷᠢ ᠶᠢᠨ ᠣᠨᠣᠯ ᠤᠨ ᠵᠠᠭᠪᠤᠷ ᠤᠳ ᠤᠨ ᠪᠣᠯᠤᠮᠵᠢ ᠶᠢᠨ ᠬᠢᠵᠠᠭᠠᠷ ᠢ ᠰᠤᠳᠤᠯᠳᠠᠭ᠃ ᠨᠡᠶᠢᠯᠡᠮᠡᠯ ᠪᠠᠶᠢᠳᠠᠯ ᠤᠨ ᠣᠨᠣᠯ ᠨᠢ ᠺᠣᠮᠫᠢᠦ᠋ᠲ᠋ᠧᠷ ᠠᠰᠢᠭᠯᠠᠨ ᠪᠣᠳᠣᠯᠭ᠎ᠠ ᠨᠤᠭᠤᠳ ᠢ ᠪᠣᠳᠣᠬᠤ ᠦᠶ᠎ᠡ ᠳᠦ ᠵᠠᠷᠤᠴᠠᠭᠤᠯᠬᠤ ᠥᠷᠲᠡᠭ ᠢ ᠰᠤᠳᠤᠯᠤᠨ᠎ᠠ᠃ ᠵᠠᠷᠢᠮ ᠪᠣᠳᠣᠯᠭ᠎ᠠ ᠶᠢ ᠵᠠᠷᠴᠢᠮ ᠤᠨ ᠬᠤᠪᠢ ᠺᠣᠮᠫᠢᠦ᠋ᠲ᠋ᠧᠷ ᠢᠶᠡᠷ ᠪᠣᠳᠣᠵᠤ ᠪᠣᠯᠬᠤ ᠪᠣᠯᠪᠠᠴᠤ ᠫᠷᠠᠺᠲ᠋ᠢᠭ ᠳᠡᠭᠡᠷ᠎ᠡ ᠺᠣᠮᠫᠢᠦ᠋ᠲ᠋ᠧᠷ ᠬᠡᠴᠢᠨᠡᠨ ᠴᠤ ᠬᠥᠭᠵᠢᠯ ᠢᠶᠡᠨ ᠭᠡᠰᠡᠨ ᠪᠦᠲᠦᠭᠡᠬᠦ ᠠᠷᠭ᠎ᠠ ᠦᠭᠡᠢ ᠶᠡᠬᠡ ᠰᠠᠨᠠᠬᠤ ᠣᠢ ᠪᠣᠯᠤᠨ ᠴᠠᠭ ᠬᠤᠭᠤᠴᠠᠭ᠎ᠠ ᠱᠠᠭᠠᠷᠳᠠᠬᠤ ᠪᠠᠷ ᠪᠠᠶᠢᠵᠤ ᠪᠣᠯᠳᠠᠭ᠃ ᠥᠭᠭᠦᠭᠳᠡᠭᠰᠡᠨ ᠤᠷᠴᠢᠨ ᠳᠤ ᠬᠢᠷᠢ ᠶᠡᠬᠡ ᠬᠡᠮᠵᠢᠶᠡᠨ ᠦ ᠮᠡᠳᠡᠭᠡᠯᠡᠯ ᠬᠠᠳᠠᠭᠠᠯᠠᠵᠤ ᠪᠣᠯᠬᠤ ᠪᠤᠢ ᠭᠡᠳᠡᠭ ᠢ ᠮᠡᠳᠡᠭᠡᠯᠡᠯ ᠦᠨ ᠣᠨᠣᠯ ᠰᠤᠳᠤᠯᠬᠤ ᠪᠠ ᠥᠭᠭᠥᠭᠳᠡᠯ ᠢ ᠰᠢᠬᠠᠬᠤᠡᠩᠲᠷᠣᠫᠢ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠣᠶᠢᠯᠠᠭᠠᠯᠲᠠ ᠨᠤᠭᠤᠳ ᠢ ᠣᠷᠣᠭᠤᠯᠵᠤ ᠢᠷᠡᠳᠡᠭ᠃

ᠬᠠᠷᠢᠴᠠᠩᠭᠤᠢ ᠰᠢᠨ᠎ᠡ ᠰᠠᠯᠪᠤᠷᠢ ᠲᠤᠯᠠ ᠳ᠋ᠢᠰᠺᠷᠧᠲ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠲᠤ ᠰᠢᠢᠳᠦᠭᠳᠡᠭᠡ ᠦᠭᠡᠢ ᠲᠤᠯᠭᠠᠭᠤᠷᠢ ᠠᠰᠠᠭᠤᠳᠠᠯ ᠤᠳ ᠨᠡᠯᠢᠶᠡᠳ ᠪᠤᠢ᠃ ᠡᠳᠡᠭᠡᠷ ᠡᠴᠡ ᠬᠠᠮᠤᠭ ᠤᠨ ᠠᠯᠳᠠᠷᠲᠠᠢ ᠨᠢ ᠮᠢᠩᠭᠠᠨ ᠤ ᠱᠠᠩᠨᠠᠯᠲᠤ ᠪᠣᠳᠣᠯᠭ᠎ᠠ ᠨᠤᠭᠤᠳ ᠤᠨ ᠨᠢᠭᠡ ᠪᠣᠯᠬᠤ "P=NP?" ᠪᠣᠳᠣᠯᠭ᠎ᠠ ᠶᠤᠮ᠃

<math>\begin{matrix} (1,2,3) & (1,3,2) \\ (2,1,3) & (2,3,1) \\ (3,1,2) & (3,2,1) \end{matrix}</math> DFAexample.svg Caesar3.svg 6n-graf.svg
ᠺᠣᠮᠪᠢᠨᠠᠲ᠋ᠣᠷᠢᠺ ᠲᠣᠭᠠᠴᠠᠭᠠᠯᠠᠯ ᠤᠨ ᠣᠨᠣᠯ ᠺᠷᠢᠫᠲ᠋ᠣᠭᠷᠠᠹ ᠭᠷᠠᠹ ᠤᠨ ᠣᠨᠣᠯ

ᠬᠡᠷᠡᠭᠯᠡᠭᠡᠨ ᠦ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ[ᠵᠠᠰᠠᠪᠤᠷᠢᠯᠠᠬᠤ | ᠺᠣᠳ᠋ ᠢᠶᠠᠷ ᠵᠠᠰᠠᠬᠣ]

ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨᠪᠢᠽᠢᠨ᠋ᠧᠰ ᠪᠣᠯᠤᠨ ᠪᠤᠰᠤᠳ ᠰᠠᠯᠪᠤᠷᠢ ᠳᠤ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠠᠪᠰᠲᠷᠠᠺᠲ ᠠᠫᠫᠠᠷᠠᠲ ᠢ ᠠᠰᠢᠭᠯᠠᠬᠤ ᠶᠠᠪᠤᠳᠠᠯ ᠢ ᠬᠡᠷᠡᠭᠯᠡᠭᠡᠨ ᠦ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠲᠤ ᠠᠪᠴᠤ ᠦᠵᠡᠳᠡᠭ᠃ ᠬᠡᠷᠡᠭᠯᠡᠭᠡᠨ ᠦ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠨᠢᠭᠡ ᠴᠢᠬᠤᠯᠠ ᠰᠠᠯᠪᠤᠷᠢ ᠨᠢ ᠪᠦᠷᠢᠳᠭᠡᠯ ᠪᠥᠭᠡᠳ ᠡᠨᠳᠡ ᠮᠠᠭᠠᠳᠯᠠᠯ ᠤᠨ ᠣᠨᠣᠯ ᠢ ᠠᠰᠢᠭᠯᠠᠨ ᠲᠣᠬᠢᠶᠠᠯᠳᠣᠬᠤ ᠡᠰᠡᠬᠦ ᠨᠢ ᠲᠣᠳᠣᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠦᠵᠡᠭᠳᠡᠯ  ᠦᠳ ᠢ ᠲᠠᠶᠢᠯᠪᠤᠷᠢᠯᠠᠬᠤ᠂ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ᠂ ᠤᠷᠢᠳᠴᠢᠯᠠᠭᠰᠠᠨ ᠲᠠᠭᠠᠮᠠᠭ ᠭᠠᠷᠲᠠᠯ᠎ᠠ  ᠰᠤᠳᠤᠯᠤᠨ᠎ᠠ᠃ ᠶᠡᠬᠡᠩᠬᠢ ᠲᠤᠷᠰᠢᠯᠲᠠ᠂ ᠬᠠᠶᠢᠭᠤᠯ᠂ ᠪᠣᠯᠤᠨ ᠠᠵᠢᠭᠯᠠᠯᠳᠠ ᠨᠤᠭᠤᠳ ᠪᠦᠷᠢᠳᠭᠡᠯ ᠤᠨ ᠶᠠᠳᠠᠵᠤ ᠠᠩᠬᠠᠨ ᠱᠠᠲᠤᠨ ᠤ ᠮᠡᠳᠡᠯᠭᠡ ᠱᠠᠭᠠᠷᠳᠠᠳᠠᠭ᠃ ᠶᠡᠷᠦᠩᠬᠡᠢ ᠳᠤ ᠪᠡᠨ ᠬᠦᠮᠦᠨ ᠦ ᠲᠣᠭᠠᠴᠠᠨ ᠪᠣᠳᠣᠬᠤ ᠴᠢᠳᠠᠪᠤᠷᠢ ᠠᠴᠠ ᠬᠡᠲᠦ ᠳᠠᠪᠠᠭᠰᠠᠨ ᠲᠥᠷᠥᠯ ᠪᠦᠷᠢ ᠶᠢᠨ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠤ ᠪᠣᠳᠣᠯᠭ᠎ᠠ ᠨᠤᠭᠤᠳ ᠢ ᠬᠡᠮᠨᠡᠯᠲᠡᠲᠡᠢ ᠪᠡᠷ ᠲᠣᠭᠠᠴᠠᠭᠠᠯᠠᠬᠤ ᠠᠷᠭ᠎ᠠ ᠨᠤᠭᠤᠳ ᠢ ᠲᠣᠭᠠᠨ ᠠᠨᠠᠯᠢᠽᠢ ᠰᠤᠳᠤᠯᠳᠠᠭ᠃ ᠡᠨᠳᠡ ᠲᠤᠬᠠᠶᠢᠯᠠᠪᠠᠯ ᠲᠣᠶᠢᠮᠣᠯᠠᠯ ᠤᠨ ᠠᠯᠳᠠᠭ᠎ᠠ ᠪᠣᠯᠤᠨ ᠪᠤᠰᠤᠳ ᠠᠯᠳᠠᠭᠠᠨ ᠤ ᠡᠬᠢ ᠡᠭᠦᠰᠪᠦᠷᠢ ᠨᠦᠭᠦᠳ ᠢ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠶᠠᠪᠤᠳᠠᠯ ᠣᠷᠣᠨ᠎ᠠ᠃

ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠹᠢᠽᠢᠺᠠᠨᠠᠯᠢᠲ᠋ᠢᠭ ᠮᠧᠬᠠᠨᠢᠭᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠰᠢᠩᠭᠡᠨ ᠦ ᠳ᠋ᠢᠨᠠᠮᠢᠺᠲᠣᠭᠠᠨ ᠠᠨᠠᠯᠢᠽᠢᠣᠫᠲ᠋ᠢᠮᠢᠰᠠᠼᠢᠮᠠᠭᠠᠳᠯᠠᠯᠪᠦᠷᠢᠳᠭᠡᠯᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠡᠳ᠋ ᠍ ᠦᠨ ᠵᠠᠰᠠᠭᠰᠠᠩᠬᠦᠦ ᠶᠢᠨ ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨᠲᠣᠭᠯᠠᠭᠠᠮ ᠤᠨ ᠣᠨᠣᠯᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨ ᠪᠢᠣᠯᠣᠭᠢᠺᠷᠢᠫᠲ᠋ᠣᠭᠷᠠᠹᠦᠢᠯᠡᠳᠦᠯ ᠦᠨ ᠰᠢᠨᠵᠢᠯᠡᠭᠡ

ᠮᠥᠨ ᠦᠵᠡᠬᠦ[ᠵᠠᠰᠠᠪᠤᠷᠢᠯᠠᠬᠤ | ᠺᠣᠳ᠋ ᠢᠶᠠᠷ ᠵᠠᠰᠠᠬᠣ]

ᠲᠡᠮᠳᠡᠭᠯᠡᠯ ᠦᠳ[ᠵᠠᠰᠠᠪᠤᠷᠢᠯᠠᠬᠤ | ᠺᠣᠳ᠋ ᠢᠶᠠᠷ ᠵᠠᠰᠠᠬᠣ]

  1. Peirce, ᠬᠤᠤ ᠳᠤ᠃97
  2. Steen, L.A., (April 29, 1988). The Science of Patterns. Science, 240: 611–616. ᠲᠣᠶᠢᠮᠣ: Association for Supervision and Curriculum Development.
  3. Devlin, Keith, Mathematics: The Science of Patterns: The Search for Order in Life, Mind and the Universe (Scientific American Paperback Library) 1996, ISBN-10: 0716760223
  4. Jourdain
  5. Eves
  6. Peterson
  7. Sevryuk

ᠨᠣᠮ ᠬᠡᠪᠯᠡᠯ[ᠵᠠᠰᠠᠪᠤᠷᠢᠯᠠᠬᠤ | ᠺᠣᠳ᠋ ᠢᠶᠠᠷ ᠵᠠᠰᠠᠬᠣ]

  • Eves, Howard, An Introduction to the History of Mathematics, Sixth Edition, Saunders, 1990, ISBN 0-03-029558-0.
  • Jourdain, Philip E. B., The Nature of Mathematics, in The World of Mathematics, James R. Newman, editor, Dover, 2003, ISBN 0-486-43268-8.
  • Peirce, Benjamin. "Linear Associative Algebra". American Journal of Mathematics (Vol. 4, No. 1/4. (1881). JSTOR.
  • Peterson, Ivars, Mathematical Tourist, New and Updated Snapshots of Modern Mathematics, Owl Books, 2001, ISBN 0-8050-7159-8.
  • Sevryuk, Mikhail B. (January 2006). "Book Reviews" (PDF). Bulletin of the American Mathematical Society 43 (1): 101-109.

ᠲᠣᠭᠠᠨ ᠤ ᠣᠬᠠᠭᠠᠨᠡᠶᠢᠨ ᠲᠣᠮᠣᠬᠠᠨ ᠰᠠᠯᠪᠤᠷᠢ ᠨᠤᠭᠤᠳ

ᠠᠯᠭᠧᠪᠷᠠᠪᠰᠲᠷᠠᠺᠲ ᠠᠯᠭᠧᠪᠷᠱᠤᠭᠤᠮᠠᠨ ᠠᠯᠭᠧᠪᠷᠠᠨᠠᠯᠢᠽᠹᠦᠨᠺᠼᠢᠤᠨᠠᠯ ᠠᠨᠠᠯᠢᠽᠢᠲᠣᠭᠠᠨ ᠠᠨᠠᠯᠢᠽᠢᠢᠨᠲ᠋ᠧᠭᠷᠡᠯ ᠪᠠ ᠳ᠋ᠢᠹᠹᠧᠷᠧᠨᠼᠢᠠᠯ ᠲᠣᠭᠠᠯᠠᠯᠳ᠋ᠢᠹᠹᠧᠷᠧᠨᠼᠢᠠᠯ ᠲᠡᠭᠰᠢᠳᠬᠡᠯᠺᠠᠲ᠋ᠧᠭᠣᠷᠢ ᠶᠢᠨ ᠣᠨᠣᠯᠺᠣᠮᠪᠢᠨᠠᠲ᠋ᠣᠷᠢᠺ • [[ᠭ᠍ᠸᠣᠮᠧᠲ᠋ᠷᠢ] • [[ᠠᠯᠭᠧᠪᠷᠯᠢᠭ ᠭ᠍ᠸᠣᠮᠧᠲ᠋ᠷᠢ] • ᠯᠣᠭᠢᠭᠲᠣᠭᠠᠨ ᠤ ᠣᠨᠣᠯᠣᠯᠠᠨᠯᠢᠭ ᠤᠨ ᠣᠨᠣᠯᠣᠫᠲ᠋ᠢᠮᠢᠰᠠᠼᠢᠮᠠᠭᠠᠳᠯᠠᠯᠰᠲ᠋ᠠᠲ᠋ᠢᠰᠲ᠋ᠢᠺᠲᠣᠫᠣᠯᠣᠭᠢᠠᠯᠭᠧᠪᠷᠯᠢᠭ ᠲᠣᠫᠣᠯᠣᠭᠢᠲᠷᠢᠭᠣᠨᠣᠮᠧᠲ᠋ᠷ

ᠪᠢᠴᠢᠭᠡᠰᠦ