ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ᠊ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ: Засвар хоорондын ялгаа
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= ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ = | = ᠧᠦ᠋ᠻ᠊ᠯᠢᠳ᠋ ᠦᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ = | ||
ᠬᠦᠮᠦᠨ ᠲᠥᠷᠦᠯᠬᠢᠲᠡᠨ ᠢ ᠬᠦᠷᠢᠶᠡᠯᠡᠨ ᠪᠤᠢ ᠶᠢᠷᠲᠢᠨᠴᠦ ᠢᠢᠨ ᠢᠯᠡᠳᠲᠡ ᠬᠠᠷᠠᠭᠳᠠᠬᠤ ᠲᠥᠷᠬᠦ ᠪᠠᠢᠢᠳᠠᠯ ᠲᠠᠢ | <br> | ||
ᠨᠡᠢᠢᠲᠡ ᠢᠢᠨ ᠲᠣᠭᠠᠯᠠᠯ ᠤᠨ ᠡᠮᠦᠨᠡᠬᠢ 3 ᠳ᠋ᠤᠭᠠᠷ ᠵᠠᠭᠤᠨ ᠤ ᠦᠶ ᠡ᠋ | {| class="wikitable" | ||
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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== | ==ᠫᠣᠰᠲ᠋ᠦ᠋ᠯᠠᠲ== | ||
ᠠᠻᠰᠢᠣᠮ ᠤᠨ ᠠᠷᠭ ᠠ᠋ ᠭᠡᠳᠡᠭ ᠨᠢ ᠰᠢᠨᠵᠢᠯᠡᠬᠦ ᠤᠬᠠᠭᠠᠨ ᠤ ᠣᠨᠤᠯ ᠪᠠᠢᠢᠭᠤᠯᠬᠤ ᠳ᠋ᠤ ᠠᠩᠬᠠᠳᠠᠭᠴᠢ ᠪᠠᠢᠷᠢᠮᠲᠠᠯᠠᠯ ᠤᠳ ᠪᠤᠶᠤ ᠠᠻᠰᠢᠣᠮ<sup>axiom</sup>᠂ ᠫᠣᠰᠲᠦ᠋ᠯᠠᠲ ᠤᠳ<sup>postulate</sup> 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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|style = "height: 250px;"|ᠲᠠᠪᠤᠳᠤᠭᠠᠷ ᠫᠣᠰᠲᠦ᠋ᠯᠠᠲ᠄ ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠲᠠᠢ ᠣᠭᠲᠣᠯᠤᠯᠴᠠᠭᠰᠠᠨ ᠰᠢᠯᠤᠭᠤᠨ ᠨᠢ ᠤᠭ ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠲᠠᠢ ᠬᠣᠶᠠᠷ ᠲᠡᠭᠰᠢ ᠥᠨᠴᠥᠭ ᠡᠴᠡ ᠪᠠᠭᠠ ᠳᠣᠲᠣᠭᠠᠳᠤ ᠥᠷᠥᠭᠡᠯ ᠥᠨᠴᠥᠭ ᠦᠳ ᠡᠭᠦᠰᠬᠡᠵᠦ ᠪᠠᠶ᠋ᠢᠭᠠ ᠲᠣᠬᠢᠶᠠᠯᠳᠤᠯ ᠳᠤ ᠤᠭ ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠢ ᠬᠢᠵᠠᠭᠠᠷ ᠦᠭᠡᠢ ᠦᠷᠭᠦᠯᠵᠢᠯᠡᠭᠦᠯᠪᠡᠯ ᠲᠡᠳᠡᠭᠡᠷ ᠨᠢ ᠬᠣᠶᠠᠷ ᠲᠡᠭᠰᠢ ᠥᠨᠴᠥᠭ ᠦᠳ ᠡᠴᠡ ᠪᠠᠭᠠ ᠬᠣᠶᠠᠷ ᠥᠨᠴᠥᠭ ᠲᠡᠢ ᠲᠠᠯᠠ ᠳᠤ ᠪᠠᠨ ᠣᠭᠲᠣᠯᠤᠯᠴᠠᠨᠠ᠃ | |||
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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> | ||
<span style="writing-mode: horizontal-tb; ">3.</span> ᠳᠤᠷᠠ ᠶᠢᠨ ᠲᠥᠪ ᠡᠴᠡ ᠳᠤᠷᠠ ᠶᠢᠨ | <span style="writing-mode: horizontal-tb; ">3.</span> ᠳᠤᠷᠠ ᠶᠢᠨ ᠲᠥᠪ ᠡᠴᠡ ᠳᠤᠷᠠ ᠶᠢᠨ ᠷᠠᠳᠢᠦ᠋ᠰ ᠢᠶ᠋ᠠᠷ<sup>radius</sup> ᠲᠣᠭᠣᠷᠢᠭ ᠲᠠᠲᠠᠵᠤ ᠪᠣᠯᠤᠨᠠ᠃<br> | ||
<span style="writing-mode: horizontal-tb; ">4.</span> ᠪᠦᠬᠦ ᠲᠡᠭᠰᠢ ᠥᠨᠴᠥᠭ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠲᠡᠩᠴᠡᠭᠦᠦ᠃<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 ᠪᠠᠭᠠ ᠳᠣᠲᠣᠭᠠᠳᠤ ᠥᠷᠥᠭᠡᠯ ᠥᠨᠴᠥᠭ ᠦᠳ ᠡᠭᠦᠰᠬᠡᠵᠦ | <span style="writing-mode: horizontal-tb; ">5.</span> ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠲᠠᠢ ᠣᠭᠲᠣᠯᠤᠯᠴᠠᠭᠰᠠᠨ ᠰᠢᠯᠤᠭᠤᠨ ᠨᠢ ᠤᠭ ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠲᠠᠢ ᠬᠣᠶᠠᠷ ᠲᠡᠭᠰᠢ ᠥᠨᠴᠥᠭ ᠡᠴᠡ ᠪᠠᠭᠠ ᠳᠣᠲᠣᠭᠠᠳᠤ ᠥᠷᠥᠭᠡᠯ ᠥᠨᠴᠥᠭ ᠦᠳ ᠡᠭᠦᠰᠬᠡᠵᠦ ᠪᠠᠶ᠋ᠢᠭᠠ ᠲᠣᠬᠢᠶᠠᠯᠳᠤᠯ ᠳᠤ ᠤᠭ ᠬᠣᠶᠠᠷ ᠰᠢᠯᠤᠭᠤᠨ ᠢ ᠬᠢᠵᠠᠭᠠᠷ ᠦᠭᠡᠢ ᠦᠷᠭᠦᠯᠵᠢᠯᠡᠭᠦᠯᠪᠡᠯ ᠲᠡᠳᠡᠭᠡᠷ ᠨᠢ ᠬᠣᠶᠠᠷ ᠲᠡᠭᠰᠢ ᠥᠨᠴᠥᠭ ᠦᠳ ᠡᠴᠡ ᠪᠠᠭᠠ ᠬᠣᠶᠠᠷ ᠥᠨᠴᠥᠭ ᠲᠡᠢ ᠲᠠᠯᠠ ᠳᠤ ᠪᠠᠨ ᠣᠭᠲᠣᠯᠤᠯᠴᠠᠨᠠ᠃<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== | ==ᠠᠻᠰᠢᠥᠮ== | ||
ᠠᠻᠰᠢᠣᠮ ᠭᠡᠳᠡᠭ ᠢ ᠡ᠊᠂ ᠸᠠᠩᠳᠤᠢ ᠢᠢᠨ ᠣᠷᠤᠰ-ᠮᠣᠩᠭᠤᠯ ᠨᠡᠷ ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠨ ᠤ ᠲᠣᠯᠢ ᠳ᠋ᠤ "ᠢᠯᠡᠳᠲᠡ ᠦᠨᠡᠨ" ᠭᠡᠵᠦ᠂ ᠬᠠᠷᠢᠨ ᠲᠾᠧᠣᠷᠧᠮ ᠢ<sup>theorem</sup> "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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|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 ᠪᠠᠶ᠋ᠢᠨᠠ᠃<br> | |||
<span style="writing-mode: horizontal-tb; ">2.</span> ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠤᠭᠦᠳ ᠳᠡᠭᠡᠷᠡ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠤᠭᠦᠳ ᠶᠢ ᠨᠡᠮᠡᠪᠡᠯ ᠨᠡᠶ᠋ᠢᠯᠡᠪᠦᠷᠢ ᠦᠳ ᠨᠢ ᠴᠤ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶ᠋ᠢᠨᠠ᠃<br> | |||
<span style="writing-mode: horizontal-tb; ">3.</span> ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠤᠭᠦᠳ ᠡᠴᠡ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠤᠭᠦᠳ ᠶᠢ ᠬᠠᠰᠤᠪᠠᠯ ᠦᠯᠡᠳᠡᠭᠳᠡᠯ ᠦᠳ ᠨᠢ ᠴᠤ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶ᠋ᠢᠨᠠ᠃<br> | |||
<span style="writing-mode: horizontal-tb; ">4.</span> ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠢᠰᠢ ᠨᠤᠭᠦᠳ ᠳᠡᠭᠡᠷᠡ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠤᠭᠦᠳ ᠶᠢ ᠨᠡᠮᠡᠪᠡᠯ ᠨᠡᠶ᠋ᠢᠯᠡᠪᠦᠷᠢ ᠦᠳ ᠨᠢ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠢᠰᠢ ᠪᠠᠶ᠋ᠢᠨᠠ᠃<br> | |||
<span style="writing-mode: horizontal-tb; ">5.</span> ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠤᠭᠦᠳ ᠶᠢ ᠠᠳᠠᠯᠢ ᠬᠡᠮᠵᠢᠶᠡ ᠪᠡᠷ ᠦᠷᠡᠵᠢᠭᠦᠯᠪᠡᠯ ᠦᠷᠡᠵᠢᠪᠦᠷᠢ ᠨᠢ ᠴᠤ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶ᠋ᠢᠨᠠ᠃<br> | |||
<span style="writing-mode: horizontal-tb; ">6.</span> ᠲᠡᠩᠴᠡᠭᠦᠦ ᠨᠤᠭᠦᠳ ᠦᠨ ᠲᠡᠩ ᠬᠠᠭᠠᠰ ᠤᠳ ᠨᠢ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶ᠋ᠢᠨᠠ᠃<br> | |||
<span style="writing-mode: horizontal-tb; ">7.</span> ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠳᠠᠪᠬᠤᠴᠠᠬᠤ ᠵᠦᠢᠯ ᠦᠳ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠲᠡᠩᠴᠡᠭᠦᠦ ᠪᠠᠶ᠋ᠢᠨᠠ᠃ (ᠳᠠᠪᠬᠤᠴᠠᠬᠤ ᠭᠡᠳᠡᠭ ᠨᠢ ᠬᠣᠭᠣᠷᠣᠨᠳᠣ ᠪᠠᠨ ᠶᠠᠭ ᠠᠳᠠᠯᠢ ᠭᠡᠰᠡᠨ ᠤᠳᠬᠠ ᠲᠠᠢ)<br> | |||
<span style="writing-mode: horizontal-tb; ">8.</span> ᠪᠦᠬᠦᠯᠢ ᠨᠢ ᠬᠡᠰᠡᠭ ᠡᠴᠡ ᠪᠡᠨ ᠶᠡᠬᠡ ᠪᠠᠶ᠋ᠢᠨᠠ᠃<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<sup>mathematics</sup>᠂ ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ ᠦᠨ ᠠᠩᠬᠠᠨ ᠤ ᠮᠡᠳᠡᠭᠳᠡᠬᠦᠨ ᠣᠯᠵᠤ᠂ ᠤᠴᠢᠷ ᠰᠢᠯᠲᠠᠭᠠᠨ᠂ ᠯᠣᠭᠢᠻ<sup>logic</sup> 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<sup>machine</sup> ᠮᠧᠻᠠᠨᠢᠰᠮ<sup>mechanism</sup>᠂ 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<sup>system</sup> ᠡᠭᠦᠰᠴᠦ ᠬᠥᠭᠵᠢᠭᠰᠡᠨ ᠪᠢᠯᠡ᠃ | |||
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==ᠨᠡᠷ ᠡ᠋ ᠲᠣᠮᠢᠶᠠᠯᠠᠯ== | ==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== | ==ᠡᠬᠢ ᠰᠤᠷᠪᠤᠯᠵᠢ== | ||
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[[Ангилал:ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲᠢᠭ]] | [[Ангилал:ᠮᠠᠲ᠋ᠾᠧᠮᠠᠲᠢᠭ]] | ||
[[Ангилал:ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ]] | [[Ангилал:ᠭᠧᠣᠮᠧᠲ᠋ᠧᠷ]] | ||