#!/usr/bin/env node /** * Build Euclid's Elements Book VI discourse JSON and Mermaid charts. * 4 definitions, 33 propositions. Similar figures. Depends on Book I and Book V. * VI.1 is basis for most of Book VI; VI.33 uses proportion def directly. Source: David E. Joyce. * * Charts: 3. Chart 1: Defs + Props 1-11. Chart 2: Props 12-22. Chart 3: Props 23-33. */ const fs = require('fs'); const path = require('path'); const DEFS = [ { n: 1, short: "Similar rectilinear", full: "Similar rectilinear figures have equal angles and proportional sides" }, { n: 2, short: "Reciprocally proportional", full: "Figures reciprocally proportional when sides are proportional inversely" }, { n: 3, short: "Mean proportional", full: "Straight line is mean proportional when first to it as it to third" }, { n: 4, short: "Duplicate ratio", full: "Duplicate ratio is the ratio of the squares on corresponding sides" } ]; const PROPS = [ { n: 1, short: "Triangles under same height", full: "Triangles and parallelograms under same height are as their bases" }, { n: 2, short: "Parallel cuts sides proportionally", full: "Line parallel to side cuts sides proportionally; converse" }, { n: 3, short: "Angle bisector divides base", full: "Angle bisector: segments of base proportionally as remaining sides" }, { n: 4, short: "Equiangular: sides proportional", full: "Equiangular triangles: sides about equal angles proportional" }, { n: 5, short: "Sides proportional: equiangular", full: "If sides proportional, triangles equiangular" }, { n: 6, short: "One angle equal, sides proportional", full: "One angle equal, sides about it proportional: equiangular" }, { n: 7, short: "One angle equal, other sides proportional", full: "One angle equal, sides about others proportional: equiangular" }, { n: 8, short: "Altitude in right triangle", full: "Perpendicular from right angle: triangles similar to whole" }, { n: 9, short: "Cut off prescribed part", full: "To cut off a prescribed part from a given straight line" }, { n: 10, short: "Cut line similarly", full: "To cut a given line similarly to a given cut line" }, { n: 11, short: "Third proportional", full: "To find a third proportional to two given lines" }, { n: 12, short: "Fourth proportional", full: "To find a fourth proportional to three given lines" }, { n: 13, short: "Mean proportional", full: "To find a mean proportional to two given lines" }, { n: 14, short: "Parallelograms reciprocally proportional", full: "Equal equiangular parallelograms: sides reciprocally proportional" }, { n: 15, short: "Triangles reciprocally proportional", full: "Equal triangles, one angle equal: sides reciprocally proportional" }, { n: 16, short: "Four lines proportional: rectangle", full: "Four lines proportional iff rectangle extremes = rectangle means" }, { n: 17, short: "Three lines proportional: rectangle", full: "Three lines proportional iff rectangle extremes = square on mean" }, { n: 18, short: "Similar figure on given line", full: "To describe figure similar to given on given line" }, { n: 19, short: "Similar triangles: duplicate ratio", full: "Similar triangles in duplicate ratio of corresponding sides" }, { n: 20, short: "Similar polygons: duplicate ratio", full: "Similar polygons in duplicate ratio of corresponding sides" }, { n: 21, short: "Similar to same: similar", full: "Figures similar to same rectilinear figure are similar" }, { n: 22, short: "Four lines proportional: figures", full: "Four lines proportional iff similar figures on them proportional" }, { n: 23, short: "Equiangular parallelograms: compound ratio", full: "Equiangular parallelograms: ratio compounded of sides" }, { n: 24, short: "Parallelograms about diameter", full: "Parallelograms about diameter similar to whole" }, { n: 25, short: "Similar and equal to another", full: "To construct figure similar to one and equal to another" }, { n: 26, short: "Parallelogram similar to difference", full: "Parallelogram similar to whole, common angle: about same diameter" }, { n: 27, short: "Greatest parallelogram applied", full: "Of parallelograms applied to line, greatest is on half" }, { n: 28, short: "Apply parallelogram: deficient", full: "To apply parallelogram equal to figure, deficient by similar" }, { n: 29, short: "Apply parallelogram: exceeding", full: "To apply parallelogram equal to figure, exceeding by similar" }, { n: 30, short: "Extreme and mean ratio", full: "To cut a given line in extreme and mean ratio" }, { n: 31, short: "Right triangle: similar figures", full: "In right triangle, figure on hypotenuse = sum of similar on sides" }, { n: 32, short: "Two triangles: sides parallel", full: "Two triangles, two sides proportional, placed with parallel sides" }, { n: 33, short: "Angles in circles: ratio of arcs", full: "Angles in equal circles have ratio of circumferences" } ]; // VI.1 uses I.3, I.38, I.41, V.Def.5, V.15, V.11. VI.1 is basis for most. VI.33 uses proportion def. const DEPS = { 1: ["BookI", "BookV"], 2: ["BookI", "BookV", "Prop1"], 3: ["BookI", "BookV", "Prop1"], 4: ["BookI", "BookV", "Prop1"], 5: ["BookI", "BookV", "Prop1"], 6: ["BookI", "BookV", "Prop1"], 7: ["BookI", "BookV", "Prop1"], 8: ["BookI", "BookV", "Prop1"], 9: ["BookI", "BookV", "Prop1"], 10: ["BookI", "BookV", "Prop1"], 11: ["BookI", "BookV", "Prop1"], 12: ["BookI", "BookV", "Prop1"], 13: ["BookI", "BookV", "Prop1"], 14: ["BookI", "BookV", "Prop1"], 15: ["BookI", "BookV", "Prop1"], 16: ["BookI", "BookV", "Prop1"], 17: ["BookI", "BookV", "Prop1"], 18: ["BookI", "BookV", "Prop1"], 19: ["BookI", "BookV", "Prop1"], 20: ["BookI", "BookV", "Prop1"], 21: ["BookI", "BookV", "Prop1"], 22: ["BookI", "BookV", "Prop1"], 23: ["BookI", "BookV", "Prop1"], 24: ["BookI", "BookV", "Prop1"], 25: ["BookI", "BookV", "Prop1"], 26: ["BookI", "BookV", "Prop1"], 27: ["BookI", "BookV", "Prop1"], 28: ["BookI", "BookV", "Prop1"], 29: ["BookI", "BookV", "Prop1"], 30: ["BookI", "BookV", "Prop1"], 31: ["BookI", "BookV", "Prop1"], 32: ["BookI", "BookV", "Prop1"], 33: ["BookI", "BookV"] }; const discourse = { schemaVersion: "1.0", discourse: { id: "euclid-elements-book-vi", name: "Euclid's Elements, Book VI", subject: "geometry", variant: "classical", description: "Similar figures. 4 definitions, 33 propositions. Depends on Book I and Book V. VI.1 is basis for most. Source: David E. Joyce.", structure: { books: 6, definitions: 4, propositions: 33, 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 VI Dependency Graph. Programming Framework.", keywords: ["Euclid", "Elements", "Book VI", "similar", "proportion", "triangles"] }, sources: [ { id: "joyce", type: "digital", authors: "Joyce, David E.", title: "Euclid's Elements, Book VI", year: "1996", url: "https://mathcs.clarku.edu/~djoyce/java/elements/bookVI/bookVI.html", notes: "Clark University; VI.1 basis for most" } ], nodes: [], edges: [], colorScheme: { foundation: { fill: "#95a5a6", stroke: "#7f8c8d" }, definition: { fill: "#3498db", stroke: "#2980b9" }, proposition: { fill: "#1abc9c", stroke: "#16a085" } } }; discourse.nodes.push( { id: "BookI", type: "foundation", label: "Book I — Fundamentals of plane geometry", shortLabel: "Book I", short: "Foundation", book: 1, colorClass: "foundation" }, { id: "BookV", type: "foundation", label: "Book V — Theory of proportions", shortLabel: "Book V", short: "Foundation", book: 5, colorClass: "foundation" } ); for (const d of DEFS) { discourse.nodes.push({ id: `Def${d.n}`, type: "definition", label: d.full, shortLabel: `Def. VI.${d.n}`, short: d.short, book: 6, number: d.n, colorClass: "definition" }); discourse.edges.push({ from: "BookI", to: `Def${d.n}` }); discourse.edges.push({ from: "BookV", to: `Def${d.n}` }); } for (const prop of PROPS) { discourse.nodes.push({ id: `Prop${prop.n}`, type: "proposition", label: prop.full, shortLabel: `Prop. VI.${prop.n}`, short: prop.short, book: 6, number: prop.n, colorClass: "proposition" }); for (const dep of DEPS[prop.n]) { discourse.edges.push({ from: dep, to: `Prop${prop.n}` }); } } const dataDir = path.join(__dirname, "..", "data"); fs.mkdirSync(dataDir, { recursive: true }); fs.writeFileSync(path.join(dataDir, "euclid-elements-book-vi.json"), JSON.stringify(discourse, null, 2), "utf8"); console.log("Wrote euclid-elements-book-vi.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("BookV"); 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 VI Index Euclid's Elements Book VI (Joyce) Programming Framework

Description

${subtitle}

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

Dependency Flowchart

${mermaidEscaped}

Color Scheme

Gray
Book I, Book V (foundation)
Blue
Definitions
Teal
Propositions

Statistics

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

Keywords

  • Euclid
  • Elements
  • Book VI
  • similar
  • proportion
  • triangles
`; } if (fs.existsSync(GEOM_DIR)) { const filter1 = closure(11); const m1 = toMermaid(filter1); const nodes1 = discourse.nodes.filter(filter1); const edges1 = discourse.edges.filter(e => filter1({ id: e.from }) && filter1({ id: e.to })); fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-vi-props-1-11.html"), htmlTemplate("Euclid's Elements Book VI — Propositions 1–11", "Similar triangles: same height, parallel cuts, equiangular, third proportional. VI.1 is basis. Depends on Book I and Book V.", m1, nodes1.length, edges1.length), "utf8"); console.log("Wrote geometry_topology-euclid-elements-book-vi-props-1-11.html"); const filter2 = closure(22); const m2 = toMermaid(filter2); const nodes2 = discourse.nodes.filter(filter2); const edges2 = discourse.edges.filter(e => filter2({ id: e.from }) && filter2({ id: e.to })); fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-vi-props-12-22.html"), htmlTemplate("Euclid's Elements Book VI — Propositions 12–22", "Fourth proportional, reciprocally proportional, similar figures on lines, duplicate ratio.", m2, nodes2.length, edges2.length), "utf8"); console.log("Wrote geometry_topology-euclid-elements-book-vi-props-12-22.html"); const m3 = toMermaid(() => true); fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-vi-props-23-33.html"), htmlTemplate("Euclid's Elements Book VI — Propositions 23–33", "Compound ratio, parallelograms about diameter, application of areas, extreme and mean ratio, angles in circles.", m3, discourse.nodes.length, discourse.edges.length), "utf8"); console.log("Wrote geometry_topology-euclid-elements-book-vi-props-23-33.html"); } // Book VI index if (fs.existsSync(GEOM_DIR)) { const indexHtml = ` Euclid's Elements Book VI - Mathematics Process
← Back to Mathematics Database Euclid's Elements (all books) Euclid's Elements Book VI (Joyce)

Euclid's Elements Book VI

Similar figures. 4 definitions, 33 propositions. Depends on Book I and Book V. VI.1 (triangles under same height) is basis for most. VI.33 uses proportion def directly.

Propositions 1–11 Similar triangles, proportionals Propositions 12–22 Reciprocally proportional, duplicate ratio Propositions 23–33 Application of areas, extreme and mean ratio
`; fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-vi.html"), indexHtml, "utf8"); console.log("Wrote geometry_topology-euclid-elements-book-vi.html"); } console.log("Done. Nodes:", discourse.nodes.length, "Edges:", discourse.edges.length);