"absolute geometry" meaning in English

{
  "etymology_text": "From 1832; introduced by Hungarian mathematician János Bolyai (1802—1860).",
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          "name": "Non-Euclidean geometry",
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      "examples": [
        {
          "text": "1993 [Princeton University Press], Donald M. Davis, The Nature and Power of Mathematics, 2004, Dover, page 85,\nRecall that absolute geometry is the set of statements that can be deduced from Euclid's first four postulates. Then existence of parallel lines is certainly a theorem of absolute geometry, while the question being addressed by most of the mathematicians discussed in this section is whether uniqueness of parallels is also a theorem of absolute geometry."
        }
      ],
      "glosses": [
        "The single (up to logical equivalence) geometry whose axiomatic system is equivalent to that of Euclidean geometry without the parallel postulate or any alternative."
      ],
      "id": "en-absolute_geometry-en-noun-s6tCDAQP",
      "links": [
        [
          "geometry",
          "geometry"
        ],
        [
          "axiomatic system",
          "axiomatic system"
        ],
        [
          "Euclidean geometry",
          "Euclidean geometry"
        ],
        [
          "parallel postulate",
          "parallel postulate"
        ]
      ],
      "raw_glosses": [
        "(geometry) The single (up to logical equivalence) geometry whose axiomatic system is equivalent to that of Euclidean geometry without the parallel postulate or any alternative."
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "_dis1": "59 41",
          "code": "ja",
          "lang": "Japanese",
          "sense": "Euclidean geometry without the parallel postulate",
          "word": "絶対幾何学"
        },
        {
          "_dis1": "59 41",
          "code": "ru",
          "lang": "Russian",
          "roman": "absoljútnaja geométrija",
          "sense": "Euclidean geometry without the parallel postulate",
          "tags": [
            "feminine"
          ],
          "word": "абсолю́тная геоме́трия"
        }
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          "name": "Non-Euclidean geometry",
          "orig": "en:Non-Euclidean geometry",
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      "examples": [
        {
          "text": "1970, J. F. Rigby, Axioms for Absolute Geometry, III, Canadian Journal of Mathematics, Vol. XXII, No. 1, Canadian Mathematical Congress, University of Toronto Press, page 185,\nA discussion of one-dimensional absolute geometries, with examples, will be given in a separate paper."
        }
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      "glosses": [
        "Any geometry whose axiomatic system extends that of absolute geometry (in the singular sense) and neither assumes nor contradicts the parallel postulate."
      ],
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      "raw_glosses": [
        "(geometry) Any geometry whose axiomatic system extends that of absolute geometry (in the singular sense) and neither assumes nor contradicts the parallel postulate."
      ],
      "related": [
        {
          "_dis1": "41 59",
          "word": "parallel postulate"
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          "_dis1": "41 59",
          "word": "triangle postulate"
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          "_dis1": "41 59",
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          "word": "Euclidean geometry without the parallel postulate"
        }
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    "absolute geometry"
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  "word": "absolute geometry"
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  "etymology_text": "From 1832; introduced by Hungarian mathematician János Bolyai (1802—1860).",
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  "related": [
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      "word": "parallel postulate"
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      "word": "triangle postulate"
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  "senses": [
    {
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        {
          "text": "1993 [Princeton University Press], Donald M. Davis, The Nature and Power of Mathematics, 2004, Dover, page 85,\nRecall that absolute geometry is the set of statements that can be deduced from Euclid's first four postulates. Then existence of parallel lines is certainly a theorem of absolute geometry, while the question being addressed by most of the mathematicians discussed in this section is whether uniqueness of parallels is also a theorem of absolute geometry."
        }
      ],
      "glosses": [
        "The single (up to logical equivalence) geometry whose axiomatic system is equivalent to that of Euclidean geometry without the parallel postulate or any alternative."
      ],
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        ],
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          "Euclidean geometry",
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          "parallel postulate",
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      "raw_glosses": [
        "(geometry) The single (up to logical equivalence) geometry whose axiomatic system is equivalent to that of Euclidean geometry without the parallel postulate or any alternative."
      ],
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        "geometry",
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        "sciences"
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        {
          "text": "1970, J. F. Rigby, Axioms for Absolute Geometry, III, Canadian Journal of Mathematics, Vol. XXII, No. 1, Canadian Mathematical Congress, University of Toronto Press, page 185,\nA discussion of one-dimensional absolute geometries, with examples, will be given in a separate paper."
        }
      ],
      "glosses": [
        "Any geometry whose axiomatic system extends that of absolute geometry (in the singular sense) and neither assumes nor contradicts the parallel postulate."
      ],
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          "geometry",
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      ],
      "raw_glosses": [
        "(geometry) Any geometry whose axiomatic system extends that of absolute geometry (in the singular sense) and neither assumes nor contradicts the parallel postulate."
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
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      "topics": [
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      "word": "Euclidean geometry without the parallel postulate"
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    {
      "code": "ja",
      "lang": "Japanese",
      "sense": "Euclidean geometry without the parallel postulate",
      "word": "絶対幾何学"
    },
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      "roman": "absoljútnaja geométrija",
      "sense": "Euclidean geometry without the parallel postulate",
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  "word": "absolute geometry"
}