#!/usr/bin/env node /** * Build Euclid's Elements Book III discourse JSON and Mermaid charts. * 11 definitions, 37 propositions. All depend on Book I. III.35 uses II.5, I.47. * Source: David E. Joyce, Clark University. * * Charts: ~16 nodes each. Chart 1: Defs + Props 1-5. Chart 2: Props 6-20. Chart 3: Props 21-37. */ const fs = require('fs'); const path = require('path'); const DEFS = [ { n: 1, short: "Equal circles", full: "Equal circles are those with equal radii" }, { n: 2, short: "Tangent", full: "A straight line touches a circle if it meets but does not cut it" }, { n: 3, short: "Circles touching", full: "Circles touch one another if they meet but do not cut" }, { n: 4, short: "Equally distant from center", full: "Lines equally distant from center when perpendiculars from center equal" }, { n: 5, short: "Greater distance", full: "Greater distance when greater perpendicular falls" }, { n: 6, short: "Segment of circle", full: "Segment of circle: figure contained by straight line and circumference" }, { n: 7, short: "Angle of segment", full: "Angle of segment: contained by straight line and circumference" }, { n: 8, short: "Angle in segment", full: "Angle in segment: contained by straight lines joining circumference" }, { n: 9, short: "Angle stands on circumference", full: "Angle stands on circumference when lines cut off that circumference" }, { n: 10, short: "Sector", full: "Sector: figure contained by two radii and circumference between them" }, { n: 11, short: "Similar segments", full: "Similar segments are those which admit equal angles" } ]; const PROPS = [ { n: 1, short: "Find center of circle", full: "To find the center of a given circle" }, { n: 2, short: "Chord falls within circle", full: "Straight line joining two points on circumference falls within circle" }, { n: 3, short: "Diameter bisects chord at right angles", full: "If diameter bisects chord not through center, it cuts at right angles" }, { n: 4, short: "Non-diameters do not bisect", full: "Two non-diameters cutting one another do not bisect" }, { n: 5, short: "Cutting circles do not share center", full: "If two circles cut one another, they do not have same center" }, { n: 6, short: "Touching circles do not share center", full: "If two circles touch, they do not have same center" }, { n: 7, short: "Greatest/shortest from point on diameter", full: "From point on diameter: greatest through center, least is remainder" }, { n: 8, short: "Lines from point outside circle", full: "From point outside: through center greatest; between point and diameter least" }, { n: 9, short: "Three equal lines imply center", full: "If more than two equal lines fall from point on circle, point is center" }, { n: 10, short: "Circles cut at most two points", full: "A circle does not cut another at more than two points" }, { n: 11, short: "Internally touching circles", full: "Line joining centers of internally touching circles passes through contact" }, { n: 12, short: "Externally touching circles", full: "Line joining centers of externally touching circles passes through contact" }, { n: 13, short: "Circles touch at most one point", full: "Circle does not touch another at more than one point" }, { n: 14, short: "Equal chords equally distant", full: "Equal chords equally distant from center, and conversely" }, { n: 15, short: "Diameter greatest", full: "Diameter greatest; nearer to center greater than more remote" }, { n: 16, short: "Tangent at end of diameter", full: "Perpendicular at end of diameter falls outside; horn angle" }, { n: 17, short: "Draw tangent from point", full: "From given point to draw straight line touching given circle" }, { n: 18, short: "Radius to tangent perpendicular", full: "Radius to point of contact perpendicular to tangent" }, { n: 19, short: "Perpendicular from contact to center", full: "Perpendicular from contact to tangent passes through center" }, { n: 20, short: "Angle at center double angle at circumference", full: "Angle at center double angle at circumference on same base" }, { n: 21, short: "Angles in same segment equal", full: "In a circle angles in same segment equal one another" }, { n: 22, short: "Opposite angles of cyclic quadrilateral", full: "Sum of opposite angles of cyclic quadrilateral equals two right angles" }, { n: 23, short: "Same line, two similar unequal segments", full: "On same line cannot construct two similar unequal segments on same side" }, { n: 24, short: "Similar segments on equal lines equal", full: "Similar segments on equal straight lines equal one another" }, { n: 25, short: "Complete circle from segment", full: "Given segment of circle, describe complete circle" }, { n: 26, short: "Equal angles stand on equal arcs", full: "In equal circles equal angles stand on equal circumferences" }, { n: 27, short: "Equal arcs imply equal angles", full: "In equal circles angles on equal circumferences equal one another" }, { n: 28, short: "Equal chords cut off equal arcs", full: "In equal circles equal chords cut off equal circumferences" }, { n: 29, short: "Equal arcs imply equal chords", full: "In equal circles chords cutting equal circumferences are equal" }, { n: 30, short: "Bisect given circumference", full: "To bisect a given circumference" }, { n: 31, short: "Angle in semicircle is right", full: "Angle in semicircle right; in greater segment less; in less greater" }, { n: 32, short: "Tangent-chord angle equals alternate segment", full: "Angle with tangent equals angle in alternate segment" }, { n: 33, short: "Segment admitting given angle", full: "On given line describe segment admitting angle equal to given" }, { n: 34, short: "Cut off segment admitting angle", full: "From given circle cut off segment admitting given angle" }, { n: 35, short: "Rectangle from chord segments equal", full: "If chords cut one another, rectangle by segments of one equals other" }, { n: 36, short: "Tangent squared = secant × external", full: "From point outside: tangent squared = secant × external part" }, { n: 37, short: "Converse: tangent if rectangle = square", full: "If rectangle equals square on line, that line touches circle" } ]; // Joyce: III.1 uses I.10, I.11, I.Def.15, I.8, I.Def.10. III.9, III.10 use III.1 cor. III.16 cor → III.17, III.33, III.37. III.35 uses III.1, I.12, III.3, II.5, I.47. // Simplified: all depend on Book I. Key within-Book: 1→2,3; 3→4,14,15,35; 16→17,33,37; 20→21,31; 21→22; 31→32; 32→33,34; 35→36; 36→37. const DEPS = { 1: ["BookI"], 2: ["BookI", "Prop1"], 3: ["BookI", "Prop1"], 4: ["BookI", "Prop3"], 5: ["BookI"], 6: ["BookI"], 7: ["BookI"], 8: ["BookI"], 9: ["BookI", "Prop1"], 10: ["BookI", "Prop1"], 11: ["BookI"], 12: ["BookI"], 13: ["BookI"], 14: ["BookI", "Prop3"], 15: ["BookI", "Prop3"], 16: ["BookI"], 17: ["BookI", "Prop16"], 18: ["BookI", "Prop1"], 19: ["BookI", "Prop18"], 20: ["BookI", "Prop1"], 21: ["BookI", "Prop20"], 22: ["BookI", "Prop21"], 23: ["BookI"], 24: ["BookI", "Prop23"], 25: ["BookI"], 26: ["BookI"], 27: ["BookI", "Prop26"], 28: ["BookI", "Prop27"], 29: ["BookI", "Prop28"], 30: ["BookI"], 31: ["BookI", "Prop20"], 32: ["BookI", "Prop31"], 33: ["BookI", "Prop16", "Prop32"], 34: ["BookI", "Prop32"], 35: ["BookI", "Prop1", "Prop3", "PropII5"], 36: ["BookI", "Prop1", "Prop18", "Prop35"], 37: ["BookI", "Prop1", "Prop16", "Prop32", "Prop36"] }; const discourse = { schemaVersion: "1.0", discourse: { id: "euclid-elements-book-iii", name: "Euclid's Elements, Book III", subject: "geometry", variant: "classical", description: "Theory of circles: 11 definitions, 37 propositions. All depend on Book I. III.35 uses II.5. Source: David E. Joyce.", structure: { books: 3, definitions: 11, propositions: 37, 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 III Dependency Graph. Programming Framework.", keywords: ["Euclid", "Elements", "Book III", "circles", "chords", "tangents"] }, sources: [ { id: "joyce", type: "digital", authors: "Joyce, David E.", title: "Euclid's Elements, Book III", year: "1996", url: "https://mathcs.clarku.edu/~djoyce/java/elements/bookIII/bookIII.html", notes: "Clark University" } ], nodes: [], edges: [], colorScheme: { foundation: { fill: "#95a5a6", stroke: "#7f8c8d" }, definition: { fill: "#3498db", stroke: "#2980b9" }, proposition: { fill: "#1abc9c", stroke: "#16a085" } } }; // Cross-book foundations discourse.nodes.push( { id: "BookI", type: "foundation", label: "Book I — Fundamentals of plane geometry", shortLabel: "Book I", short: "Foundation", book: 1, colorClass: "foundation" }, { id: "PropII5", type: "foundation", label: "Prop. II.5 — Rectangle + square = square on half", shortLabel: "Prop. II.5", short: "From Book II", book: 2, colorClass: "foundation" } ); // Definitions for (const d of DEFS) { discourse.nodes.push({ id: `Def${d.n}`, type: "definition", label: d.full, shortLabel: `Def. III.${d.n}`, short: d.short, book: 3, number: d.n, colorClass: "definition" }); discourse.edges.push({ from: "BookI", to: `Def${d.n}` }); } // Propositions for (const prop of PROPS) { discourse.nodes.push({ id: `Prop${prop.n}`, type: "proposition", label: prop.full, shortLabel: `Prop. III.${prop.n}`, short: prop.short, book: 3, number: prop.n, colorClass: "proposition" }); for (const dep of DEPS[prop.n] || ["BookI"]) { discourse.edges.push({ from: dep, to: `Prop${prop.n}` }); } } // Write JSON const dataDir = path.join(__dirname, "..", "data"); fs.mkdirSync(dataDir, { recursive: true }); fs.writeFileSync(path.join(dataDir, "euclid-elements-book-iii.json"), JSON.stringify(discourse, null, 2), "utf8"); console.log("Wrote euclid-elements-book-iii.json"); function toMermaid(filter) { const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; const nodeIds = new Set(nodes.map(n => n.id)); const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); const lines = ["graph TD"]; for (const n of nodes) { const desc = n.short || (n.label && n.label.length > 35 ? n.label.slice(0, 32) + "..." : n.label || n.id); const lbl = (n.shortLabel || n.id) + "\\n" + (desc || ""); lines.push(` ${n.id}["${String(lbl).replace(/"/g, '\\"')}"]`); } for (const e of edges) { lines.push(` ${e.from} --> ${e.to}`); } lines.push(" classDef foundation fill:#95a5a6,color:#fff,stroke:#7f8c8d"); lines.push(" classDef definition fill:#3498db,color:#fff,stroke:#2980b9"); lines.push(" classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085"); const foundIds = nodes.filter(n => n.type === "foundation").map(n => n.id).join(","); const defIds = nodes.filter(n => n.type === "definition").map(n => n.id).join(","); const propIds = nodes.filter(n => n.type === "proposition").map(n => n.id).join(","); if (foundIds) lines.push(` class ${foundIds} foundation`); lines.push(` class ${defIds} definition`); lines.push(` class ${propIds} proposition`); return lines.join("\n"); } function closure(propMax) { const needed = new Set(); for (let i = 1; i <= propMax; i++) needed.add(`Prop${i}`); needed.add("BookI"); needed.add("PropII5"); for (const d of DEFS) needed.add(`Def${d.n}`); let changed = true; while (changed) { changed = false; for (const e of discourse.edges) { if (needed.has(e.to) && !needed.has(e.from)) { needed.add(e.from); changed = true; } } } return n => needed.has(n.id); } const MATH_DB = process.env.MATH_DB || "/home/gdubs/copernicus-web-public/huggingface-space/mathematics-processes-database"; const GEOM_DIR = path.join(MATH_DB, "processes", "geometry_topology"); function htmlTemplate(title, subtitle, mermaid, nodes, edges) { const mermaidEscaped = mermaid.replace(//g, ">"); return ` ${title} - Mathematics Process

${title}

Mathematics Geometry & Topology Source: Euclid's Elements
← Back to Mathematics Database Euclid's Elements (all books) Euclid Book III Index Euclid's Elements Book III (Joyce) Programming Framework

Description

${subtitle}

Source: Euclid's Elements, Book III (David E. Joyce, Clark University)

Dependency Flowchart

${mermaidEscaped}

Color Scheme

Gray
Book I, Prop II.5 (foundation)
Blue
Definitions
Teal
Propositions

Statistics

  • Nodes: ${nodes}
  • Edges: ${edges}

Keywords

  • Euclid
  • Elements
  • Book III
  • circles
  • chords
  • tangents
`; } if (fs.existsSync(GEOM_DIR)) { // Chart 1: Book I + Prop II.5 + Defs 1-11 + Props 1-5 = 2+11+5 = 18 (slightly over) const filter1 = closure(5); const nodes1 = discourse.nodes.filter(filter1); const edges1 = discourse.edges.filter(e => filter1({ id: e.from }) && filter1({ id: e.to })); const m1 = toMermaid(filter1); const html1 = htmlTemplate( "Euclid's Elements Book III — Propositions 1–5", "Dependency graph for definitions and propositions 1–5 of Book III. Theory of circles: center, chords, diameters. All depend on Book I.", m1, nodes1.length, edges1.length ); fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-iii-props-1-5.html"), html1, "utf8"); console.log("Wrote geometry_topology-euclid-elements-book-iii-props-1-5.html"); // Chart 2: Props 6-20 const filter2 = closure(20); const nodes2 = discourse.nodes.filter(filter2); const edges2 = discourse.edges.filter(e => filter2({ id: e.from }) && filter2({ id: e.to })); const m2 = toMermaid(filter2); const html2 = htmlTemplate( "Euclid's Elements Book III — Propositions 6–20", "Dependency graph for propositions 6–20. Touching circles, distances, tangent at diameter, angles at center and circumference.", m2, nodes2.length, edges2.length ); fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-iii-props-6-20.html"), html2, "utf8"); console.log("Wrote geometry_topology-euclid-elements-book-iii-props-6-20.html"); // Chart 3: Props 21-37 const filter3 = () => true; const m3 = toMermaid(filter3); const nodes3 = discourse.nodes; const edges3 = discourse.edges; const html3 = htmlTemplate( "Euclid's Elements Book III — Propositions 21–37", "Dependency graph for propositions 21–37. Cyclic quadrilaterals, segments, chord rectangle theorem (III.35 uses Prop II.5), tangent-secant.", m3, nodes3.length, edges3.length ); fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-iii-props-21-37.html"), html3, "utf8"); console.log("Wrote geometry_topology-euclid-elements-book-iii-props-21-37.html"); } else { console.log("MATH_DB not found at", GEOM_DIR, "- skipping HTML generation."); } // Book III index page if (fs.existsSync(GEOM_DIR)) { const indexHtml = ` Euclid's Elements Book III - Mathematics Process
← Back to Mathematics Database Euclid's Elements (all books) Euclid's Elements Book III (Joyce)

Euclid's Elements Book III

Theory of circles: 11 definitions, 37 propositions. Chords, tangents, angles at center and circumference. All depend on Book I. Prop III.35 uses Prop II.5. Dependency charts split into three views (~16 nodes each).

Propositions 1–5 Defs + center, chords, diameters Propositions 6–20 Touching circles, tangent, angles Propositions 21–37 Cyclic quadrilaterals, chord rectangle, tangent-secant
`; fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-iii.html"), indexHtml, "utf8"); console.log("Wrote geometry_topology-euclid-elements-book-iii.html"); } console.log("Done. Nodes:", discourse.nodes.length, "Edges:", discourse.edges.length);