ᱤᱣᱠᱞᱤᱰ (Euclid) ᱫᱚ ᱜᱨᱤᱠ ᱨᱤᱱᱤᱡ ᱢᱤᱫ ᱮᱠᱠᱷᱟ ᱯᱟᱹᱨᱩᱠᱷᱤᱭᱟᱹᱭ ᱛᱟᱦᱮᱸᱠᱟᱱᱟ, ᱱᱩᱭ ᱫᱚ ᱡᱚᱢᱮᱴᱨᱤ (Geometry) ᱨᱤᱱᱤᱡ ᱟᱯᱟᱛ ᱦᱚᱸ ᱠᱚ ᱢᱮᱛᱟᱭᱟ ᱾ ᱟᱡᱟᱜ ᱠᱟᱹᱢᱤ ᱫᱚ ᱮᱞᱠᱷᱟ ᱨᱮᱱᱟᱜ ᱱᱟᱜᱟᱢ ᱨᱮ ᱠᱷᱚᱫᱟ ᱜᱟᱵᱟᱣ ᱟᱠᱟᱱᱟ ᱾ ᱩᱱᱤ ᱫᱚ ᱢᱤᱥᱚᱨ ᱨᱮᱱᱟᱜ ᱟᱞᱮᱠᱡᱟᱱᱰᱨᱤᱭᱟ ᱨᱮ ᱛᱟᱦᱮᱸᱱ ᱠᱟᱱ ᱛᱟᱦᱮᱸᱫ ᱟᱨ ᱟᱞᱮᱠᱡᱟᱱᱰᱨᱤᱭᱟ ᱨᱮᱱᱟᱜ ᱢᱤᱫ ᱯᱚᱛᱚᱵ ᱢᱩᱨᱟᱹᱭ ᱨᱮ ᱠᱟᱹᱢᱤ ᱠᱟᱱ ᱛᱟᱦᱮᱸᱫ ᱾ ᱟᱡᱟᱜ ᱠᱟᱹᱢᱤ ᱫᱚ ᱥᱟᱱᱟ ᱡᱚᱢᱮᱴᱨᱤ ᱥᱟᱶ ᱡᱚᱯᱚᱲᱟᱣ ᱛᱟᱦᱮᱸ ᱠᱟᱱᱟ, ᱚᱱᱟ ᱛᱮ ᱱᱚᱶᱟ ᱠᱚᱫᱚ ᱤᱣᱠᱞᱤᱰᱤᱭᱟᱱ ᱡᱚᱢᱮᱴᱨᱤ ᱾ ᱤᱣᱠᱞᱤᱰ ᱫᱚ ᱟᱡᱟᱜ ᱠᱟᱹᱢᱤ ᱠᱚ ᱛᱤᱢᱤᱱ ᱜᱟᱱ ᱫᱚᱭ ᱚᱞ ᱥᱚᱫᱚᱨ ᱞᱮᱜᱼᱟ, ᱚᱱᱟ ᱠᱚ ᱢᱩᱸᱫ ᱨᱮ ᱯᱟᱨᱥᱯᱮᱠᱴᱤᱵᱽ (perspective), ᱠᱚᱱᱤᱠ ᱦᱟᱹᱴᱤᱧ (conic sections), ᱜᱳᱞᱟᱹᱭ ᱡᱚᱢᱮᱴᱨᱤ (spherical geometry), ᱮᱞ ᱠᱟᱛᱷᱟ (number theory), ᱟᱨ ᱨᱤᱜᱚᱨ (rigor) ᱾ ᱟᱡᱟᱜ ᱧᱩᱛᱩᱢ ᱫᱚ ᱢᱤᱫ ᱜᱨᱤᱨ ᱟᱹᱲᱟᱹ Εὐκλείδης ᱠᱷᱚᱱ ᱠᱚ ᱟᱹᱜᱩᱣᱟᱠᱟᱫᱼᱟ, ᱡᱟᱦᱟᱸ ᱨᱮᱱᱟᱜ ᱢᱮᱱᱮᱛ ᱫᱚ ᱜᱟᱹᱠᱷᱩᱲ ᱢᱮᱱᱛᱮ ᱵᱟᱰᱟᱭᱚᱜᱼᱟ ᱾
ᱟᱡᱟᱜ ᱡᱤᱭᱚᱱ ᱨᱮᱱᱟᱜ ᱥᱚᱛ ᱥᱟᱹᱠᱷᱭᱟᱹᱛ ᱠᱚ ᱫᱚ ᱟᱹᱰᱤ ᱠᱚᱢ ᱜᱮ ᱧᱟᱢ ᱞᱮᱱᱟ ᱾ ᱟᱡᱟᱜ ᱡᱟᱱᱟᱢ ᱢᱟᱦᱟᱸ, ᱜᱩᱨ ᱢᱟᱦᱟᱸ, ᱵᱟᱥᱟ ᱴᱷᱟᱶ ᱮᱢᱟᱱ ᱠᱚ ᱫᱚ ᱵᱟᱭ ᱵᱟᱰᱟᱭ ᱟᱠᱟᱱᱟ ᱾ ᱛᱚᱵᱮ ᱢᱮᱱᱟᱠᱚ ᱟᱡ ᱫᱚ "ᱮᱛᱚᱦᱚᱵ ᱴᱚᱞᱮᱢᱤ" ᱛᱮᱠᱚ ᱛᱩᱨᱮ ᱛᱦᱮᱸ ᱠᱟᱱᱟ ᱢᱮᱱᱛᱮ ᱾ ᱤᱣᱠᱞᱤᱰ ᱫᱚ ᱡᱚᱢᱮᱴᱨᱤ ᱨᱮᱱᱟᱜ ᱥᱟᱱᱟᱢ ᱵᱟᱰᱟᱭᱟᱱ ᱠᱟᱛᱷᱟ ᱠᱚ ᱫᱚᱭ ᱥᱟᱢᱴᱟᱣ ᱢᱤᱫ ᱞᱚᱫ ᱛᱟᱦᱮᱸᱫ ᱾ ᱟᱡᱟᱜ ᱯᱚᱛᱚᱵ ᱮᱞᱤᱢᱮᱱᱴ ᱥᱮᱫᱟᱭᱟᱜ ᱨᱮᱱᱟᱜ ᱢᱤᱫ ᱛᱚᱲ ᱠᱟᱱᱟ ᱾ ᱡᱟᱦᱟᱸ ᱫᱚ ᱱᱤᱛᱚᱜ ᱦᱚᱸ ᱟᱪᱮᱫ ᱠᱚ ᱠᱚ ᱯᱟᱲᱦᱟᱣᱮᱜᱼᱟ ᱾ ᱱᱚᱶᱟ ᱯᱚᱛᱚᱵ ᱨᱮᱱᱟᱜ ᱠᱟᱛᱷᱟ ᱠᱚ ᱫᱚ ᱡᱚᱛᱚ ᱜᱮ ᱥᱟᱹᱨᱤ ᱠᱚ ᱞᱟᱹᱭᱟ ᱟᱨ ᱚᱱᱠᱟ ᱜᱮᱭ ᱯᱩᱥᱴᱟᱹᱣ ᱞᱮᱫ ᱛᱟᱦᱮᱸᱫ ᱾ ᱮᱞᱤᱢᱮᱱᱴᱥ ᱨᱮ ᱫᱚ ᱱᱟᱱᱟ-ᱦᱩᱱᱟᱹᱨ ᱡᱚᱢᱮᱴᱨᱤ ᱪᱤᱛᱟᱹᱨ ᱨᱮᱱᱟᱜ ᱨᱩᱯ ᱜᱚᱲᱦᱚᱱ ᱠᱟᱛᱷᱟ ᱠᱚᱭ ᱚᱞ ᱟᱠᱟᱫᱟ ᱾ ᱚᱱᱟ ᱵᱮᱜᱚᱨ ᱮᱞᱠᱷᱟ ᱨᱮᱦᱚᱸ ᱟᱡᱟᱜ ᱮᱱᱮᱢ ᱢᱮᱱᱟᱜᱼᱟ ᱾ ᱦᱩᱰᱤᱧ ᱥᱟᱫᱷᱟᱨᱚᱱ ᱜᱟᱵᱟᱬᱤᱭᱟᱹ (HCF) ᱠᱟᱛᱷᱟ ᱟᱡᱼᱮ ᱞᱟᱹᱭ ᱞᱮᱫ ᱛᱟᱦᱮᱸᱫ ᱾ ᱱᱚᱶᱟ ᱠᱟᱛᱷᱟ ᱫᱚ ᱮᱞᱤᱢᱮᱱᱴᱥ ᱨᱮ ᱜᱮ ᱚᱞ ᱞᱮᱫ ᱛᱟᱦᱮᱸᱫ ᱾ ᱵᱟᱨᱭᱟ ᱮᱞ ᱨᱮᱱᱟᱜ HCF ᱫᱚ ᱡᱚᱛᱚ ᱠᱷᱚᱱ ᱢᱟᱨᱟᱝᱟ, ᱡᱟᱦᱟᱸ ᱫᱚ ᱵᱟᱱᱟᱨ ᱮᱞᱮ ᱦᱟᱴᱟᱬ ᱠᱤᱱᱟ ᱾ ᱚᱞᱮᱢᱮᱱᱴᱥ ᱨᱮ ᱚᱞ ᱞᱮᱱ ᱡᱚᱢᱮᱴᱨᱤ ᱫᱚ ᱟᱹᱰᱤ ᱫᱤᱱ ᱦᱟᱹᱵᱤᱡ ᱥᱩᱢᱩᱝ ᱢᱤᱫᱴᱟᱝ ᱡᱚᱢᱮᱴᱨᱤ ᱢᱮᱱᱛᱮ ᱢᱮᱱᱚᱜ ᱠᱟᱱ ᱛᱟᱦᱮᱸᱫ ᱾
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