"Pasch's axiom" meaning in English

{
  "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."
      ],
      "related": [
        {
          "word": "Pasch's theorem"
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      ],
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        "geometry",
        "mathematics",
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        "Moritz Pasch",
        "Pasch's axiom"
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  "word": "Pasch's axiom"
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{
  "etymology_text": "Its essential role was discovered in 1882 by the German mathematician Moritz Pasch.",
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  "lang_code": "en",
  "pos": "name",
  "related": [
    {
      "word": "Pasch's theorem"
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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."
      ],
      "links": [
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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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        "sciences"
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