"Hjelmslev's theorem" meaning in English

{
  "etymology_text": "Named after Johannes Hjelmslev.",
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  "lang": "English",
  "lang_code": "en",
  "pos": "name",
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      "glosses": [
        "a theorem stating that if a set of points P_i lying on a line is isometrically mapped to points P_i' on a different line, then the midpoints of the segments P_iP_i' also lie on a line."
      ],
      "id": "en-Hjelmslev's_theorem-en-name-pKJPMRTu",
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        [
          "geometry",
          "geometry"
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          "theorem",
          "theorem"
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        [
          "set",
          "set"
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        [
          "point",
          "point"
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        [
          "line",
          "line"
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        [
          "isometric",
          "isometric"
        ]
      ],
      "raw_glosses": [
        "(geometry) a theorem stating that if a set of points P_i lying on a line is isometrically mapped to points P_i' on a different line, then the midpoints of the segments P_iP_i' also lie on a line."
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "de",
          "lang": "German",
          "sense": "geometry",
          "word": "Satz von Hjelmslev"
        }
      ],
      "wikipedia": [
        "Johannes Hjelmslev",
        "en:Hjelmslev's theorem"
      ]
    }
  ],
  "word": "Hjelmslev's theorem"
}

{
  "etymology_text": "Named after Johannes Hjelmslev.",
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  "lang": "English",
  "lang_code": "en",
  "pos": "name",
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      ],
      "glosses": [
        "a theorem stating that if a set of points P_i lying on a line is isometrically mapped to points P_i' on a different line, then the midpoints of the segments P_iP_i' also lie on a line."
      ],
      "links": [
        [
          "geometry",
          "geometry"
        ],
        [
          "theorem",
          "theorem"
        ],
        [
          "set",
          "set"
        ],
        [
          "point",
          "point"
        ],
        [
          "line",
          "line"
        ],
        [
          "isometric",
          "isometric"
        ]
      ],
      "raw_glosses": [
        "(geometry) a theorem stating that if a set of points P_i lying on a line is isometrically mapped to points P_i' on a different line, then the midpoints of the segments P_iP_i' also lie on a line."
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Johannes Hjelmslev",
        "en:Hjelmslev's theorem"
      ]
    }
  ],
  "translations": [
    {
      "code": "de",
      "lang": "German",
      "sense": "geometry",
      "word": "Satz von Hjelmslev"
    }
  ],
  "word": "Hjelmslev's theorem"
}