#!/usr/bin/env node /** * Build Euclid's Elements Book VII discourse JSON and Mermaid charts. * 22 definitions, 39 propositions. Number theory: GCD, proportions, primes, LCM. * Book VII does not depend on previous books. Source: David E. Joyce. * * Charts: 4. Chart 1: Defs + Props 1-10. Chart 2: Props 11-20. Chart 3: Props 21-30. Chart 4: Props 31-39. */ const fs = require('fs'); const path = require('path'); const DEFS = [ { n: 1, short: "Unit", full: "A unit is that by virtue of which each of the things that exist is called one" }, { n: 2, short: "Number", full: "A number is a multitude composed of units" }, { n: 3, short: "Part", full: "A number is part of a number when it measures it" }, { n: 4, short: "Parts", full: "Parts when it does not measure it" }, { n: 5, short: "Multiple", full: "The greater is a multiple of the less when measured by the less" }, { n: 6, short: "Even", full: "An even number is that which is divisible into two equal parts" }, { n: 7, short: "Odd", full: "An odd number is that which is not divisible into two equal parts" }, { n: 8, short: "Even-times even", full: "Even-times even: measured by an even number an even number of times" }, { n: 9, short: "Even-times odd", full: "Even-times odd: measured by an even number an odd number of times" }, { n: 10, short: "Odd-times odd", full: "Odd-times odd: measured by an odd number an odd number of times" }, { n: 11, short: "Prime", full: "A prime number is that which is measured by a unit alone" }, { n: 12, short: "Relatively prime", full: "Numbers relatively prime when only a unit measures both" }, { n: 13, short: "Composite", full: "A composite number is that measured by some number" }, { n: 14, short: "Composite to one another", full: "Numbers composite to one another when some number measures both" }, { n: 15, short: "Multiply", full: "A number multiplies a number when the latter is added as many times as units in the former" }, { n: 16, short: "Product", full: "When two numbers multiplied produce a number, the product is plane" }, { n: 17, short: "Side", full: "Sides of the product are the numbers multiplied" }, { n: 18, short: "Plane number", full: "A plane number is that produced by two numbers" }, { n: 19, short: "Solid number", full: "A solid number is that produced by three numbers" }, { n: 20, short: "Similar plane", full: "Similar plane numbers have sides proportional" }, { n: 21, short: "Similar solid", full: "Similar solid numbers have sides proportional" }, { n: 22, short: "Perfect", full: "A perfect number is that which equals its own parts" } ]; const PROPS = [ { n: 1, short: "Antenaresis, relatively prime", full: "Unequal numbers: repeated subtraction; if unit left, relatively prime" }, { n: 2, short: "GCD of two numbers", full: "To find greatest common measure of two numbers not relatively prime" }, { n: 3, short: "GCD of three numbers", full: "To find greatest common measure of three numbers" }, { n: 4, short: "Part or parts", full: "Any number is part or parts of any number, less of greater" }, { n: 5, short: "Same part: sum", full: "If a is same part of b as c of d, then a+c same part of b+d" }, { n: 6, short: "Same parts: sum", full: "If a is same parts of b as c of d, then a+c same parts of b+d" }, { n: 7, short: "Same part: remainder", full: "If a part of b as c of d, remainder same part of remainder" }, { n: 8, short: "Same parts: remainder", full: "If a parts of b as c of d, remainder same parts of remainder" }, { n: 9, short: "Same part: alternately", full: "If a part of b as c of d, alternately a part/parts of c as b of d" }, { n: 10, short: "Same parts: alternately", full: "If a parts of b as c of d, alternately a part/parts of c as b of d" }, { n: 11, short: "Proportion: remainder", full: "If whole:whole as subtracted:subtracted, remainder:remainder as whole:whole" }, { n: 12, short: "Proportional: sum", full: "Proportional: one antecedent to consequent as sum antecedents to sum consequents" }, { n: 13, short: "Proportional: alternately", full: "If four numbers proportional, also proportional alternately" }, { n: 14, short: "Ex aequali", full: "If a:b = d:e and b:c = e:f, then a:c = d:f" }, { n: 15, short: "Unit measures", full: "If unit measures a, b measures c same times, alternately unit:c as b:d" }, { n: 16, short: "Commutativity of product", full: "If a×b and c×d, then a×b = c×d (commutativity)" }, { n: 17, short: "Ratio of products", full: "a:b = (a×c):(b×c)" }, { n: 18, short: "Ratio: multipliers", full: "a×c : b×c = a:b" }, { n: 19, short: "Proportional iff product", full: "a:b = c:d iff a×d = b×c" }, { n: 20, short: "Least in ratio", full: "Least numbers in ratio measure others same number of times" }, { n: 21, short: "Relatively prime: least", full: "Relatively prime numbers are least in their ratio" }, { n: 22, short: "Least: relatively prime", full: "Least numbers in ratio are relatively prime" }, { n: 23, short: "Relatively prime: divisor", full: "If a,b relatively prime, divisor of a relatively prime to b" }, { n: 24, short: "Product relatively prime", full: "If a,b relatively prime to c, then a×b relatively prime to c" }, { n: 25, short: "Square relatively prime", full: "If a,b relatively prime, a² relatively prime to b" }, { n: 26, short: "Products relatively prime", full: "If a,c and b,d relatively prime, a×b, c×d relatively prime" }, { n: 27, short: "Squares relatively prime", full: "If a,b relatively prime, a²,b² relatively prime; a×a², b×b²" }, { n: 28, short: "Sum relatively prime", full: "If a,b relatively prime, a+b prime to each; converse" }, { n: 29, short: "Prime to non-multiple", full: "Prime relatively prime to any number it does not measure" }, { n: 30, short: "Prime divides product", full: "If prime measures product, it measures one factor" }, { n: 31, short: "Composite has prime factor", full: "Any composite measured by some prime" }, { n: 32, short: "Prime or has prime factor", full: "Any number is prime or measured by some prime" }, { n: 33, short: "Least in ratio", full: "Given numbers, find least in same ratio" }, { n: 34, short: "LCM of two", full: "To find least number that two given numbers measure" }, { n: 35, short: "LCM divides common multiple", full: "If two numbers measure some number, LCM also measures it" }, { n: 36, short: "LCM of three", full: "To find least number that three given numbers measure" }, { n: 37, short: "Measured has part", full: "If a measures b, b has part named by a" }, { n: 38, short: "Part implies measured", full: "If b has part named by a, a measures b" }, { n: 39, short: "Least with given parts", full: "To find least number with given parts" } ]; // Joyce: VII.1→2,3; VII.2→3; VII.5-10 fractions; VII.11-19 proportions; VII.20-29 relatively prime; VII.30-32 primes; VII.33-39 LCM const DEPS = { 1: [], 2: ["Prop1"], 3: ["Prop1", "Prop2"], 4: [], 5: [], 6: [], 7: [], 8: [], 9: [], 10: [], 11: [], 12: [], 13: [], 14: [], 15: [], 16: [], 17: [], 18: [], 19: [], 20: ["Prop19"], 21: ["Prop20"], 22: ["Prop21"], 23: ["Prop22"], 24: ["Prop23"], 25: ["Prop23"], 26: ["Prop24"], 27: ["Prop25"], 28: ["Prop23"], 29: ["Prop23"], 30: ["Prop29"], 31: [], 32: ["Prop31"], 33: ["Prop20", "Prop22"], 34: ["Prop33"], 35: ["Prop34"], 36: ["Prop34"], 37: [], 38: ["Prop37"], 39: ["Prop38"] }; const discourse = { schemaVersion: "1.0", discourse: { id: "euclid-elements-book-vii", name: "Euclid's Elements, Book VII", subject: "number_theory", variant: "classical", description: "Number theory: GCD (Euclidean algorithm), proportions, primes, LCM. 22 definitions, 39 propositions. Does not depend on previous books. Source: David E. Joyce.", structure: { books: 7, definitions: 22, propositions: 39, foundationTypes: ["definition"] } }, 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 VII Dependency Graph. Programming Framework.", keywords: ["Euclid", "Elements", "Book VII", "number theory", "GCD", "prime", "LCM"] }, sources: [ { id: "joyce", type: "digital", authors: "Joyce, David E.", title: "Euclid's Elements, Book VII", year: "1996", url: "https://mathcs.clarku.edu/~djoyce/java/elements/bookVII/bookVII.html", notes: "Clark University" } ], nodes: [], edges: [], colorScheme: { definition: { fill: "#3498db", stroke: "#2980b9" }, proposition: { fill: "#1abc9c", stroke: "#16a085" } } }; for (const d of DEFS) { discourse.nodes.push({ id: `Def${d.n}`, type: "definition", label: d.full, shortLabel: `Def. VII.${d.n}`, short: d.short, book: 7, number: d.n, colorClass: "definition" }); } for (const prop of PROPS) { discourse.nodes.push({ id: `Prop${prop.n}`, type: "proposition", label: prop.full, shortLabel: `Prop. VII.${prop.n}`, short: prop.short, book: 7, 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-vii.json"), JSON.stringify(discourse, null, 2), "utf8"); console.log("Wrote euclid-elements-book-vii.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 definition fill:#3498db,color:#fff,stroke:#2980b9"); lines.push(" classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085"); 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(","); 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}`); 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 Number Theory Source: Euclid's Elements
← Back to Mathematics Database Euclid's Elements (all books) Euclid Book VII Index Euclid's Elements Book VII (Joyce) Programming Framework

Description

${subtitle}

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

Dependency Flowchart

${mermaidEscaped}

Color Scheme

Blue
Definitions
Teal
Propositions

Statistics

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

Keywords

  • Euclid
  • Elements
  • Book VII
  • number theory
  • GCD
  • prime
  • LCM
`; } if (fs.existsSync(GEOM_DIR)) { [[10, "1–10", "GCD, part/parts, proportions"], [20, "11–20", "Proportions, products, least in ratio"], [30, "21–30", "Relatively prime, primes"], [39, "31–39", "Primes, LCM, parts"]].forEach(([max, range, desc]) => { const filter = closure(max); const m = toMermaid(filter); const nodes = discourse.nodes.filter(filter); const edges = discourse.edges.filter(e => filter({ id: e.from }) && filter({ id: e.to })); fs.writeFileSync(path.join(GEOM_DIR, `geometry_topology-euclid-elements-book-vii-props-${range.replace(/–/g, "-").replace(" ", "-")}.html`), htmlTemplate(`Euclid's Elements Book VII — Propositions ${range}`, desc, m, nodes.length, edges.length), "utf8"); console.log(`Wrote geometry_topology-euclid-elements-book-vii-props-${range.replace(/–/g, "-").replace(" ", "-")}.html`); }); } // Book VII index if (fs.existsSync(GEOM_DIR)) { const indexHtml = ` Euclid's Elements Book VII - Mathematics Process
← Back to Mathematics Database Euclid's Elements (all books) Euclid's Elements Book VII (Joyce)

Euclid's Elements Book VII

Number theory: GCD (Euclidean algorithm), proportions of numbers, primes, LCM. 22 definitions, 39 propositions. Does not depend on previous books.

Propositions 1–10 GCD, part/parts, proportions Propositions 11–20 Proportions, products, least in ratio Propositions 21–30 Relatively prime, primes Propositions 31–39 Primes, LCM, parts
`; fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-vii.html"), indexHtml, "utf8"); console.log("Wrote geometry_topology-euclid-elements-book-vii.html"); } console.log("Done. Nodes:", discourse.nodes.length, "Edges:", discourse.edges.length);