"Pasch's theorem" meaning in English

{
  "etymology_text": "Stated in 1882 by the German mathematician Moritz Pasch.",
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      "glosses": [
        "A result in plane geometry which cannot be derived from Euclid's postulates. It states that, given points a, b, c, and d on a line, if it is known that the points are ordered as (a, b, c) and (b, c, d), then it is also true that (a, b, d)."
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          "geometry",
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          "plane geometry",
          "plane geometry"
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          "point",
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          "line",
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      "raw_glosses": [
        "(geometry) A result in plane geometry which cannot be derived from Euclid's postulates. It states that, given points a, b, c, and d on a line, if it is known that the points are ordered as (a, b, c) and (b, c, d), then it is also true that (a, b, d)."
      ],
      "related": [
        {
          "word": "Pasch's axiom"
        }
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Moritz Pasch",
        "Pasch's theorem"
      ]
    }
  ],
  "word": "Pasch's theorem"
}

{
  "etymology_text": "Stated in 1882 by the German mathematician Moritz Pasch.",
  "head_templates": [
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  "lang_code": "en",
  "pos": "name",
  "related": [
    {
      "word": "Pasch's axiom"
    }
  ],
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      "glosses": [
        "A result in plane geometry which cannot be derived from Euclid's postulates. It states that, given points a, b, c, and d on a line, if it is known that the points are ordered as (a, b, c) and (b, c, d), then it is also true that (a, b, d)."
      ],
      "links": [
        [
          "geometry",
          "geometry"
        ],
        [
          "plane geometry",
          "plane geometry"
        ],
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          "postulate",
          "postulate"
        ],
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          "point",
          "point"
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          "line",
          "line"
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      "raw_glosses": [
        "(geometry) A result in plane geometry which cannot be derived from Euclid's postulates. It states that, given points a, b, c, and d on a line, if it is known that the points are ordered as (a, b, c) and (b, c, d), then it is also true that (a, b, d)."
      ],
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        "geometry",
        "mathematics",
        "sciences"
      ],
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        "Moritz Pasch",
        "Pasch's theorem"
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