"Pasch's axiom" meaning in All languages combined

{
  "etymology_text": "Its essential role was discovered in 1882 by the German mathematician Moritz Pasch.",
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      "glosses": [
        "A statement in plane geometry, used implicitly by Euclid, which cannot be derived from Euclid's postulates. It states that, if a line, not passing through any vertex of a triangle, meets one side of the triangle then it meets another side."
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        "(geometry) A statement in plane geometry, used implicitly by Euclid, which cannot be derived from Euclid's postulates. It states that, if a line, not passing through any vertex of a triangle, meets one side of the triangle then it meets another side."
      ],
      "related": [
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          "word": "Pasch's theorem"
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        "Moritz Pasch",
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  "etymology_text": "Its essential role was discovered in 1882 by the German mathematician Moritz Pasch.",
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        "A statement in plane geometry, used implicitly by Euclid, which cannot be derived from Euclid's postulates. It states that, if a line, not passing through any vertex of a triangle, meets one side of the triangle then it meets another side."
      ],
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        "(geometry) A statement in plane geometry, used implicitly by Euclid, which cannot be derived from Euclid's postulates. It states that, if a line, not passing through any vertex of a triangle, meets one side of the triangle then it meets another side."
      ],
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