{
  "schemaVersion": "1.0",
  "discourse": {
    "id": "euclid-elements-book-iv",
    "name": "Euclid's Elements, Book IV",
    "subject": "geometry",
    "variant": "classical",
    "description": "Inscribed and circumscribed figures: triangle, square, pentagon, hexagon, 15-gon. All depend on Books I and III. IV.10 uses II.11. Source: David E. Joyce.",
    "structure": {
      "books": 4,
      "definitions": 7,
      "propositions": 16,
      "foundationTypes": [
        "definition",
        "foundation"
      ]
    }
  },
  "metadata": {
    "created": "2026-03-15",
    "lastUpdated": "2026-03-15",
    "version": "1.0.0",
    "license": "CC BY 4.0",
    "authors": [
      "Welz, G."
    ],
    "methodology": "Programming Framework",
    "citation": "Welz, G. (2026). Euclid's Elements Book IV Dependency Graph. Programming Framework.",
    "keywords": [
      "Euclid",
      "Elements",
      "Book IV",
      "inscribed",
      "circumscribed",
      "pentagon",
      "hexagon"
    ]
  },
  "sources": [
    {
      "id": "joyce",
      "type": "digital",
      "authors": "Joyce, David E.",
      "title": "Euclid's Elements, Book IV",
      "year": "1996",
      "url": "https://mathcs.clarku.edu/~djoyce/java/elements/bookIV/bookIV.html",
      "notes": "Clark University; Logical structure"
    }
  ],
  "nodes": [
    {
      "id": "BookI",
      "type": "foundation",
      "label": "Book I — Fundamentals of plane geometry",
      "shortLabel": "Book I",
      "short": "Foundation",
      "book": 1,
      "colorClass": "foundation"
    },
    {
      "id": "BookIII",
      "type": "foundation",
      "label": "Book III — Theory of circles",
      "shortLabel": "Book III",
      "short": "Foundation",
      "book": 3,
      "colorClass": "foundation"
    },
    {
      "id": "PropII11",
      "type": "foundation",
      "label": "Prop. II.11 — Golden section",
      "shortLabel": "Prop. II.11",
      "short": "From Book II",
      "book": 2,
      "colorClass": "foundation"
    },
    {
      "id": "Def1",
      "type": "definition",
      "label": "Rectilinear figure inscribed in circle when each vertex on circumference",
      "shortLabel": "Def. IV.1",
      "short": "Inscribe in circle",
      "book": 4,
      "number": 1,
      "colorClass": "definition"
    },
    {
      "id": "Def2",
      "type": "definition",
      "label": "Figure circumscribed about circle when each side touches circle",
      "shortLabel": "Def. IV.2",
      "short": "Circumscribe about circle",
      "book": 4,
      "number": 2,
      "colorClass": "definition"
    },
    {
      "id": "Def3",
      "type": "definition",
      "label": "Circle inscribed in figure when each side touches circle",
      "shortLabel": "Def. IV.3",
      "short": "Inscribe circle in figure",
      "book": 4,
      "number": 3,
      "colorClass": "definition"
    },
    {
      "id": "Def4",
      "type": "definition",
      "label": "Circle circumscribed about figure when each vertex on circumference",
      "shortLabel": "Def. IV.4",
      "short": "Circumscribe circle about figure",
      "book": 4,
      "number": 4,
      "colorClass": "definition"
    },
    {
      "id": "Def5",
      "type": "definition",
      "label": "Figure inscribed in figure when each vertex of inner on sides of outer",
      "shortLabel": "Def. IV.5",
      "short": "Inscribe in figure",
      "book": 4,
      "number": 5,
      "colorClass": "definition"
    },
    {
      "id": "Def6",
      "type": "definition",
      "label": "Figure circumscribed about figure when each side of outer touches inner",
      "shortLabel": "Def. IV.6",
      "short": "Circumscribe about figure",
      "book": 4,
      "number": 6,
      "colorClass": "definition"
    },
    {
      "id": "Def7",
      "type": "definition",
      "label": "Straight line inscribed in circle when its ends on circumference",
      "shortLabel": "Def. IV.7",
      "short": "Inscribe line in circle",
      "book": 4,
      "number": 7,
      "colorClass": "definition"
    },
    {
      "id": "Prop1",
      "type": "proposition",
      "label": "To fit into given circle a straight line equal to given, not greater than diameter",
      "shortLabel": "Prop. IV.1",
      "short": "Fit line in circle",
      "book": 4,
      "number": 1,
      "colorClass": "proposition"
    },
    {
      "id": "Prop2",
      "type": "proposition",
      "label": "To inscribe in given circle a triangle equiangular with given triangle",
      "shortLabel": "Prop. IV.2",
      "short": "Inscribe triangle in circle",
      "book": 4,
      "number": 2,
      "colorClass": "proposition"
    },
    {
      "id": "Prop3",
      "type": "proposition",
      "label": "To circumscribe about given circle a triangle equiangular with given",
      "shortLabel": "Prop. IV.3",
      "short": "Circumscribe triangle about circle",
      "book": 4,
      "number": 3,
      "colorClass": "proposition"
    },
    {
      "id": "Prop4",
      "type": "proposition",
      "label": "To inscribe a circle in a given triangle",
      "shortLabel": "Prop. IV.4",
      "short": "Inscribe circle in triangle",
      "book": 4,
      "number": 4,
      "colorClass": "proposition"
    },
    {
      "id": "Prop5",
      "type": "proposition",
      "label": "To circumscribe a circle about a given triangle",
      "shortLabel": "Prop. IV.5",
      "short": "Circumscribe circle about triangle",
      "book": 4,
      "number": 5,
      "colorClass": "proposition"
    },
    {
      "id": "Prop6",
      "type": "proposition",
      "label": "To inscribe a square in a given circle",
      "shortLabel": "Prop. IV.6",
      "short": "Inscribe square in circle",
      "book": 4,
      "number": 6,
      "colorClass": "proposition"
    },
    {
      "id": "Prop7",
      "type": "proposition",
      "label": "To circumscribe a square about a given circle",
      "shortLabel": "Prop. IV.7",
      "short": "Circumscribe square about circle",
      "book": 4,
      "number": 7,
      "colorClass": "proposition"
    },
    {
      "id": "Prop8",
      "type": "proposition",
      "label": "To inscribe a circle in a given square",
      "shortLabel": "Prop. IV.8",
      "short": "Inscribe circle in square",
      "book": 4,
      "number": 8,
      "colorClass": "proposition"
    },
    {
      "id": "Prop9",
      "type": "proposition",
      "label": "To circumscribe a circle about a given square",
      "shortLabel": "Prop. IV.9",
      "short": "Circumscribe circle about square",
      "book": 4,
      "number": 9,
      "colorClass": "proposition"
    },
    {
      "id": "Prop10",
      "type": "proposition",
      "label": "To construct isosceles triangle with each base angle double the remaining",
      "shortLabel": "Prop. IV.10",
      "short": "Isosceles triangle, base angles double",
      "book": 4,
      "number": 10,
      "colorClass": "proposition"
    },
    {
      "id": "Prop11",
      "type": "proposition",
      "label": "To inscribe an equilateral equiangular pentagon in a given circle",
      "shortLabel": "Prop. IV.11",
      "short": "Inscribe pentagon in circle",
      "book": 4,
      "number": 11,
      "colorClass": "proposition"
    },
    {
      "id": "Prop12",
      "type": "proposition",
      "label": "To circumscribe an equilateral equiangular pentagon about a given circle",
      "shortLabel": "Prop. IV.12",
      "short": "Circumscribe pentagon about circle",
      "book": 4,
      "number": 12,
      "colorClass": "proposition"
    },
    {
      "id": "Prop13",
      "type": "proposition",
      "label": "To inscribe a circle in a given equilateral equiangular pentagon",
      "shortLabel": "Prop. IV.13",
      "short": "Inscribe circle in pentagon",
      "book": 4,
      "number": 13,
      "colorClass": "proposition"
    },
    {
      "id": "Prop14",
      "type": "proposition",
      "label": "To circumscribe a circle about a given equilateral equiangular pentagon",
      "shortLabel": "Prop. IV.14",
      "short": "Circumscribe circle about pentagon",
      "book": 4,
      "number": 14,
      "colorClass": "proposition"
    },
    {
      "id": "Prop15",
      "type": "proposition",
      "label": "To inscribe an equilateral equiangular hexagon in a given circle",
      "shortLabel": "Prop. IV.15",
      "short": "Inscribe hexagon in circle",
      "book": 4,
      "number": 15,
      "colorClass": "proposition"
    },
    {
      "id": "Prop16",
      "type": "proposition",
      "label": "To inscribe an equilateral equiangular fifteen-angled figure in a given circle",
      "shortLabel": "Prop. IV.16",
      "short": "Inscribe 15-gon in circle",
      "book": 4,
      "number": 16,
      "colorClass": "proposition"
    }
  ],
  "edges": [
    {
      "from": "BookI",
      "to": "Def1"
    },
    {
      "from": "BookIII",
      "to": "Def1"
    },
    {
      "from": "BookI",
      "to": "Def2"
    },
    {
      "from": "BookIII",
      "to": "Def2"
    },
    {
      "from": "BookI",
      "to": "Def3"
    },
    {
      "from": "BookIII",
      "to": "Def3"
    },
    {
      "from": "BookI",
      "to": "Def4"
    },
    {
      "from": "BookIII",
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    },
    {
      "from": "BookI",
      "to": "Def5"
    },
    {
      "from": "BookIII",
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      "from": "BookI",
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    {
      "from": "BookIII",
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    },
    {
      "from": "BookIII",
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    },
    {
      "from": "BookI",
      "to": "Prop1"
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    {
      "from": "BookIII",
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      "to": "Prop2"
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    {
      "from": "BookIII",
      "to": "Prop2"
    },
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    {
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      "to": "Prop4"
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      "to": "Prop5"
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    {
      "from": "BookIII",
      "to": "Prop5"
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      "to": "Prop6"
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    {
      "from": "BookIII",
      "to": "Prop6"
    },
    {
      "from": "Prop1",
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    },
    {
      "from": "BookI",
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    {
      "from": "BookIII",
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    {
      "from": "Prop6",
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    },
    {
      "from": "BookI",
      "to": "Prop8"
    },
    {
      "from": "BookIII",
      "to": "Prop8"
    },
    {
      "from": "Prop7",
      "to": "Prop8"
    },
    {
      "from": "BookI",
      "to": "Prop9"
    },
    {
      "from": "BookIII",
      "to": "Prop9"
    },
    {
      "from": "Prop8",
      "to": "Prop9"
    },
    {
      "from": "BookI",
      "to": "Prop10"
    },
    {
      "from": "BookIII",
      "to": "Prop10"
    },
    {
      "from": "Prop1",
      "to": "Prop10"
    },
    {
      "from": "Prop5",
      "to": "Prop10"
    },
    {
      "from": "PropII11",
      "to": "Prop10"
    },
    {
      "from": "BookI",
      "to": "Prop11"
    },
    {
      "from": "BookIII",
      "to": "Prop11"
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    {
      "from": "Prop2",
      "to": "Prop11"
    },
    {
      "from": "Prop10",
      "to": "Prop11"
    },
    {
      "from": "BookI",
      "to": "Prop12"
    },
    {
      "from": "BookIII",
      "to": "Prop12"
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    {
      "from": "Prop11",
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      "from": "BookI",
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    {
      "from": "Prop11",
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      "from": "BookIII",
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    {
      "from": "Prop1",
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    {
      "from": "BookI",
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      "from": "BookIII",
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    {
      "from": "Prop1",
      "to": "Prop16"
    },
    {
      "from": "Prop2",
      "to": "Prop16"
    },
    {
      "from": "Prop11",
      "to": "Prop16"
    }
  ],
  "colorScheme": {
    "foundation": {
      "fill": "#95a5a6",
      "stroke": "#7f8c8d"
    },
    "definition": {
      "fill": "#3498db",
      "stroke": "#2980b9"
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    "proposition": {
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}