"generalized circle" meaning in All languages combined

{
  "forms": [
    {
      "form": "generalized circles",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "generalized circle (plural generalized circles)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Circle",
          "orig": "en:Circle",
          "parents": [
            "Curves",
            "Shapes",
            "Geometry",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Curves",
          "orig": "en:Curves",
          "parents": [
            "Shapes",
            "Geometry",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Geometry",
          "orig": "en:Geometry",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Shapes",
          "orig": "en:Shapes",
          "parents": [
            "Geometry",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "1965, H. F. Weinberger, A First Course in Partial Differential Equations with Complex Variables and Transform Methods, page 247",
          "roman": "which is a generalized circle in the ζ-plane.",
          "text": "We shall speak of lines and circles as generalized circles. A line is a generalized circle that passes through the point at infinity. Under the inversion #x5C;zeta#x3D;1#x2F;z the generalized circle (53.3) goes into\n(53-4) β|ζ|²-pζ-◌̅p◌̅ζ+α=0,",
          "type": "quotation"
        },
        {
          "ref": "1999, David A. Brannan, Matthew F. Esplen, Jeremy J. Gray, Geometry, page 252",
          "text": "For any Apollonian family of circles defined by the point circles A and B, the Coaxal Circles Theorem states that every generalized circle through A and B meets each of the Apollonian circles at right angles.",
          "type": "quotation"
        },
        {
          "ref": "2001, Elie Zahar, Poincaré's Philosophy: From Conventionalism to Phenomenology, page 84",
          "text": "This is why it makes sense to call every circle and every straight line a generalized circle. Thus the geodesics of ds consist of all arcs of generalized circles which lie wholly within Ω and are orthogonal to w (see Figure 2).",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A circle or a line, the two being regarded as types of a single form."
      ],
      "id": "en-generalized_circle-en-noun-fpMs7Czk",
      "links": [
        [
          "geometry",
          "geometry"
        ],
        [
          "circle",
          "circle"
        ],
        [
          "line",
          "line"
        ]
      ],
      "qualifier": "inversive geometry",
      "raw_glosses": [
        "(geometry, inversive geometry) A circle or a line, the two being regarded as types of a single form."
      ],
      "synonyms": [
        {
          "sense": "circle or line",
          "word": "circline"
        },
        {
          "sense": "circle or line",
          "word": "cline"
        },
        {
          "word": "generalised circle"
        }
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "generalized circle"
}

{
  "forms": [
    {
      "form": "generalized circles",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "generalized circle (plural generalized circles)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "Quotation templates to be cleaned",
        "en:Circle",
        "en:Curves",
        "en:Geometry",
        "en:Shapes"
      ],
      "examples": [
        {
          "ref": "1965, H. F. Weinberger, A First Course in Partial Differential Equations with Complex Variables and Transform Methods, page 247",
          "roman": "which is a generalized circle in the ζ-plane.",
          "text": "We shall speak of lines and circles as generalized circles. A line is a generalized circle that passes through the point at infinity. Under the inversion #x5C;zeta#x3D;1#x2F;z the generalized circle (53.3) goes into\n(53-4) β|ζ|²-pζ-◌̅p◌̅ζ+α=0,",
          "type": "quotation"
        },
        {
          "ref": "1999, David A. Brannan, Matthew F. Esplen, Jeremy J. Gray, Geometry, page 252",
          "text": "For any Apollonian family of circles defined by the point circles A and B, the Coaxal Circles Theorem states that every generalized circle through A and B meets each of the Apollonian circles at right angles.",
          "type": "quotation"
        },
        {
          "ref": "2001, Elie Zahar, Poincaré's Philosophy: From Conventionalism to Phenomenology, page 84",
          "text": "This is why it makes sense to call every circle and every straight line a generalized circle. Thus the geodesics of ds consist of all arcs of generalized circles which lie wholly within Ω and are orthogonal to w (see Figure 2).",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A circle or a line, the two being regarded as types of a single form."
      ],
      "links": [
        [
          "geometry",
          "geometry"
        ],
        [
          "circle",
          "circle"
        ],
        [
          "line",
          "line"
        ]
      ],
      "qualifier": "inversive geometry",
      "raw_glosses": [
        "(geometry, inversive geometry) A circle or a line, the two being regarded as types of a single form."
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "synonyms": [
    {
      "sense": "circle or line",
      "word": "circline"
    },
    {
      "sense": "circle or line",
      "word": "cline"
    },
    {
      "word": "generalised circle"
    }
  ],
  "word": "generalized circle"
}