#!/usr/bin/env node /** * Build Euclid's Elements Book VIII discourse JSON and Mermaid charts. * 27 propositions. Continued proportions. Depends on Book VII. Source: David E. Joyce. * * Charts: 2. Chart 1: Props 1-14. Chart 2: Props 15-27. */ const fs = require('fs'); const path = require('path'); const PROPS = [ { n: 1, short: "Continued proportion, extremes prime", full: "Continued proportion, extremes relatively prime: least in ratio" }, { n: 2, short: "Find numbers in continued proportion", full: "To find numbers in continued proportion, least in given ratio" }, { n: 3, short: "Least: extremes prime", full: "Least in continued proportion: extremes relatively prime" }, { n: 4, short: "Find continued proportion from ratios", full: "Given ratios in least numbers, find least in continued proportion" }, { n: 5, short: "Plane numbers: compound ratio", full: "Plane numbers have ratio compounded of ratios of sides" }, { n: 6, short: "First does not measure second", full: "Continued proportion: if first does not measure second, none measures another" }, { n: 7, short: "First measures last", full: "Continued proportion: if first measures last, it measures second" }, { n: 8, short: "Numbers between in proportion", full: "Numbers between two in continued proportion correspond to ratios" }, { n: 9, short: "Relatively prime: numbers to unit", full: "Two relatively prime: numbers between them as between each and unit" }, { n: 10, short: "Numbers from unit", full: "Numbers between number and unit correspond to between two numbers" }, { n: 11, short: "Mean proportional of squares", full: "Between two squares one mean proportional; duplicate ratio" }, { n: 12, short: "Two means between cubes", full: "Between two cubes two mean proportionals; triplicate ratio" }, { n: 13, short: "Products proportional", full: "Continued proportion: products proportional; products of products" }, { n: 14, short: "Square measures square", full: "Square measures square iff side measures side" }, { n: 15, short: "Cube measures cube", full: "Cube measures cube iff side measures side" }, { n: 16, short: "Square does not measure square", full: "Square does not measure square iff side does not measure side" }, { n: 17, short: "Cube does not measure cube", full: "Cube does not measure cube iff side does not measure side" }, { n: 18, short: "Similar plane: mean proportional", full: "Between similar plane numbers one mean proportional; duplicate ratio" }, { n: 19, short: "Similar solid: two means", full: "Between similar solid numbers two mean proportionals; triplicate ratio" }, { n: 20, short: "One mean: similar plane", full: "If one mean between two numbers, they are similar plane" }, { n: 21, short: "Two means: similar solid", full: "If two means between two numbers, they are similar solid" }, { n: 22, short: "Three in proportion: first square", full: "Three in continued proportion, first square: third square" }, { n: 23, short: "Four in proportion: first cube", full: "Four in continued proportion, first cube: fourth cube" }, { n: 24, short: "Ratio as square to square", full: "If ratio as square to square and first square, second square" }, { n: 25, short: "Ratio as cube to cube", full: "If ratio as cube to cube and first cube, second cube" }, { n: 26, short: "Similar plane: square ratio", full: "Similar plane numbers have ratio of square to square" }, { n: 27, short: "Similar solid: cube ratio", full: "Similar solid numbers have ratio of cube to cube" } ]; const DEPS = {}; for (let i = 1; i <= 27; i++) DEPS[i] = ["BookVII"]; DEPS[2] = ["BookVII", "Prop1"]; DEPS[3] = ["BookVII", "Prop2"]; DEPS[4] = ["BookVII", "Prop2"]; DEPS[5] = ["BookVII"]; DEPS[6] = ["BookVII", "Prop1"]; DEPS[7] = ["BookVII", "Prop1"]; DEPS[8] = ["BookVII"]; DEPS[9] = ["BookVII", "Prop8"]; DEPS[10] = ["BookVII", "Prop9"]; DEPS[11] = ["BookVII", "Prop8"]; DEPS[12] = ["BookVII", "Prop8"]; DEPS[13] = ["BookVII"]; DEPS[14] = ["BookVII", "Prop11"]; DEPS[15] = ["BookVII", "Prop12"]; DEPS[16] = ["BookVII", "Prop14"]; DEPS[17] = ["BookVII", "Prop15"]; DEPS[18] = ["BookVII", "Prop8"]; DEPS[19] = ["BookVII", "Prop8"]; DEPS[20] = ["BookVII", "Prop18"]; DEPS[21] = ["BookVII", "Prop19"]; DEPS[22] = ["BookVII", "Prop1"]; DEPS[23] = ["BookVII", "Prop1"]; DEPS[24] = ["BookVII", "Prop22"]; DEPS[25] = ["BookVII", "Prop23"]; DEPS[26] = ["BookVII", "Prop18"]; DEPS[27] = ["BookVII", "Prop19"]; const discourse = { schemaVersion: "1.0", discourse: { id: "euclid-elements-book-viii", name: "Euclid's Elements, Book VIII", subject: "number_theory", variant: "classical", description: "Continued proportions. 27 propositions. Depends on Book VII. Source: David E. Joyce.", structure: { books: 8, propositions: 27, foundationTypes: ["foundation"] } }, metadata: { created: "2026-03-18", lastUpdated: "2026-03-18", version: "1.0.0", license: "CC BY 4.0", authors: ["Welz, G."], methodology: "Programming Framework", citation: "Welz, G. (2026). Euclid's Elements Book VIII Dependency Graph. Programming Framework.", keywords: ["Euclid", "Elements", "Book VIII", "continued proportion", "plane", "solid"] }, sources: [ { id: "joyce", type: "digital", authors: "Joyce, David E.", title: "Euclid's Elements, Book VIII", year: "1996", url: "https://mathcs.clarku.edu/~djoyce/java/elements/bookVIII/bookVIII.html", notes: "Clark University" } ], nodes: [], edges: [], colorScheme: { foundation: { fill: "#95a5a6", stroke: "#7f8c8d" }, proposition: { fill: "#1abc9c", stroke: "#16a085" } } }; discourse.nodes.push( { id: "BookVII", type: "foundation", label: "Book VII — Number theory", shortLabel: "Book VII", short: "Foundation", book: 7, colorClass: "foundation" } ); for (const prop of PROPS) { discourse.nodes.push({ id: `Prop${prop.n}`, type: "proposition", label: prop.full, shortLabel: `Prop. VIII.${prop.n}`, short: prop.short, book: 8, number: prop.n, colorClass: "proposition" }); for (const dep of DEPS[prop.n] || ["BookVII"]) { 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-viii.json"), JSON.stringify(discourse, null, 2), "utf8"); console.log("Wrote euclid-elements-book-viii.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 proposition fill:#1abc9c,color:#fff,stroke:#16a085"); const foundIds = nodes.filter(n => n.type === "foundation").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 ${propIds} proposition`); return lines.join("\n"); } function closure(propMax) { const needed = new Set(["BookVII"]); for (let i = 1; i <= propMax; i++) needed.add(`Prop${i}`); 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 Number Theory Source: Euclid's Elements
← Back to Mathematics Database Euclid's Elements (all books) Euclid Book VIII Index Euclid's Elements Book VIII (Joyce) Programming Framework

Description

${subtitle}

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

Dependency Flowchart

${mermaidEscaped}

Color Scheme

Gray
Book VII (foundation)
Teal
Propositions

Statistics

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

Keywords

  • Euclid
  • Elements
  • Book VIII
  • continued proportion
  • plane
  • solid
`; } if (fs.existsSync(GEOM_DIR)) { const filter1 = closure(14); 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-viii-props-1-14.html"), htmlTemplate("Euclid's Elements Book VIII — Propositions 1–14", "Continued proportion, least in ratio, square/cube. Depends on Book VII.", m1, nodes1.length, edges1.length), "utf8"); console.log("Wrote geometry_topology-euclid-elements-book-viii-props-1-14.html"); const m2 = toMermaid(() => true); fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-viii-props-15-27.html"), htmlTemplate("Euclid's Elements Book VIII — Propositions 15–27", "Similar plane/solid, mean proportionals, square/cube ratios.", m2, discourse.nodes.length, discourse.edges.length), "utf8"); console.log("Wrote geometry_topology-euclid-elements-book-viii-props-15-27.html"); } // Book VIII index if (fs.existsSync(GEOM_DIR)) { const indexHtml = ` Euclid's Elements Book VIII - Mathematics Process
← Back to Mathematics Database Euclid's Elements (all books) Euclid's Elements Book VIII (Joyce)

Euclid's Elements Book VIII

Continued proportions. 27 propositions. Depends on Book VII. Plane numbers, solid numbers, mean proportionals.

Propositions 1–14 Continued proportion, squares, cubes Propositions 15–27 Similar plane/solid, ratios
`; fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-viii.html"), indexHtml, "utf8"); console.log("Wrote geometry_topology-euclid-elements-book-viii.html"); } console.log("Done. Nodes:", discourse.nodes.length, "Edges:", discourse.edges.length);