#!/usr/bin/env node /** * Build Euclid's Elements Book I discourse JSON and Mermaid. * Dependencies from David E. Joyce, Clark University: * https://mathcs.clarku.edu/~djoyce/java/elements/bookI/bookI.html */ const fs = require('fs'); const path = require('path'); const PROPOSITIONS = [ { n: 1, short: "Equilateral triangle on given line", full: "To construct an equilateral triangle on a given finite straight line" }, { n: 2, short: "Place line equal to given at point", full: "To place a straight line equal to a given straight line with one end at a given point" }, { n: 3, short: "Cut off from greater segment equal to less", full: "To cut off from the greater of two given unequal straight lines a straight line equal to the less" }, { n: 4, short: "SAS congruence", full: "If two triangles have two sides equal to two sides respectively, and the angles contained equal, then bases and remaining angles equal" }, { n: 5, short: "Base angles of isosceles equal", full: "In isosceles triangles the angles at the base equal one another" }, { n: 6, short: "Sides opposite equal angles equal", full: "If in a triangle two angles equal one another, then the sides opposite the equal angles also equal one another" }, { n: 7, short: "Uniqueness of triangle from ends", full: "Given two lines from ends of a line meeting at a point, no other such pair from same ends on same side" }, { n: 8, short: "SSS congruence", full: "If two triangles have two sides equal to two sides respectively, and the base equal to the base, then the angles contained are equal" }, { n: 9, short: "Bisect angle", full: "To bisect a given rectilinear angle" }, { n: 10, short: "Bisect line", full: "To bisect a given finite straight line" }, { n: 11, short: "Perpendicular from point on line", full: "To draw a straight line at right angles to a given straight line from a given point on it" }, { n: 12, short: "Perpendicular from point not on line", full: "To draw a straight line perpendicular to a given infinite straight line from a given point not on it" }, { n: 13, short: "Angles on line sum to two right", full: "If a straight line stands on a straight line, it makes either two right angles or angles whose sum equals two right angles" }, { n: 14, short: "If angles sum to two right, straight line", full: "If with any straight line, at a point, two lines not on same side make adjacent angles equal to two right, they are in a straight line" }, { n: 15, short: "Vertical angles equal", full: "If two straight lines cut one another, they make the vertical angles equal to one another" }, { n: 16, short: "Exterior angle > interior opposite", full: "In any triangle, if one side is produced, the exterior angle is greater than either interior opposite angle" }, { n: 17, short: "Sum of two angles < two right", full: "In any triangle the sum of any two angles is less than two right angles" }, { n: 18, short: "Angle opposite greater side greater", full: "In any triangle the angle opposite the greater side is greater" }, { n: 19, short: "Side opposite greater angle greater", full: "In any triangle the side opposite the greater angle is greater" }, { n: 20, short: "Triangle inequality", full: "In any triangle the sum of any two sides is greater than the remaining one" }, { n: 21, short: "Lines from ends within triangle", full: "If from ends of one side two lines meet within the triangle, their sum < sum of other two sides" }, { n: 22, short: "Construct triangle from three lines", full: "To construct a triangle out of three straight lines which equal three given straight lines" }, { n: 23, short: "Construct angle equal to given", full: "To construct a rectilinear angle equal to a given rectilinear angle on a given straight line" }, { n: 24, short: "SAS for greater angle => greater base", full: "If two triangles have two sides equal but one contained angle greater, the base is greater" }, { n: 25, short: "SAS for greater base => greater angle", full: "If two triangles have two sides equal but base greater, the contained angle is greater" }, { n: 26, short: "AAS congruence", full: "If two triangles have two angles equal and one side equal, the remaining sides and angle equal" }, { n: 27, short: "Alternate angles equal => parallel", full: "If a line falling on two lines makes alternate angles equal, the lines are parallel" }, { n: 28, short: "Exterior = interior opposite => parallel", full: "If exterior angle equals interior opposite, or interior same-side sum to two right, lines parallel" }, { n: 29, short: "Parallel => alternate angles equal", full: "A line falling on parallel lines makes alternate angles equal, exterior = interior opposite" }, { n: 30, short: "Transitivity of parallel", full: "Straight lines parallel to the same straight line are also parallel to one another" }, { n: 31, short: "Draw parallel through point", full: "To draw a straight line through a given point parallel to a given straight line" }, { n: 32, short: "Exterior angle = sum interior opposite", full: "In any triangle, exterior angle equals sum of two interior opposite; three angles = two right" }, { n: 33, short: "Joining ends of equal parallel lines", full: "Straight lines which join the ends of equal and parallel straight lines in same directions are equal and parallel" }, { n: 34, short: "Parallelogram properties", full: "In parallelogrammic areas the opposite sides and angles equal one another, diameter bisects" }, { n: 35, short: "Parallelograms same base equal", full: "Parallelograms which are on the same base and in the same parallels equal one another" }, { n: 36, short: "Parallelograms equal bases equal", full: "Parallelograms which are on equal bases and in the same parallels equal one another" }, { n: 37, short: "Triangles same base equal", full: "Triangles which are on the same base and in the same parallels equal one another" }, { n: 38, short: "Triangles equal bases equal", full: "Triangles which are on equal bases and in the same parallels equal one another" }, { n: 39, short: "Equal triangles same base same side", full: "Equal triangles on same base and same side are in the same parallels" }, { n: 40, short: "Equal triangles equal bases same side", full: "Equal triangles on equal bases and same side are in the same parallels" }, { n: 41, short: "Parallelogram = 2× triangle", full: "If a parallelogram has same base with triangle and same parallels, parallelogram is double the triangle" }, { n: 42, short: "Construct parallelogram = triangle", full: "To construct a parallelogram equal to a given triangle in a given rectilinear angle" }, { n: 43, short: "Complements of parallelogram", full: "In any parallelogram the complements of the parallelograms about the diameter equal one another" }, { n: 44, short: "Apply parallelogram to line", full: "To a given straight line in a given angle, to apply a parallelogram equal to a given triangle" }, { n: 45, short: "Construct parallelogram = rectilinear figure", full: "To construct a parallelogram equal to a given rectilinear figure in a given rectilinear angle" }, { n: 46, short: "Construct square on line", full: "To describe a square on a given straight line" }, { n: 47, short: "Pythagorean theorem", full: "In right-angled triangles the square on the side opposite the right angle equals the sum of the squares on the sides containing the right angle" }, { n: 48, short: "Converse Pythagorean", full: "If in a triangle the square on one side equals the sum of squares on the other two, the angle contained by those sides is right" } ]; // Joyce dependency table: { prop: [deps] } const DEPS = { 1: ["P1", "P3"], 2: ["Prop1", "P1", "P2", "P3"], 3: ["Prop2", "P3"], 4: ["CN4", "CN5"], 5: ["Prop3", "Prop4"], 6: ["Prop3", "Prop4"], 7: ["Prop5"], 8: ["Prop7"], 9: ["Prop1", "Prop3", "Prop8"], 10: ["Prop1", "Prop4", "Prop9"], 11: ["Prop1", "Prop3", "Prop8"], 12: ["Prop8", "Prop10"], 13: ["Prop11"], 14: ["Prop13"], 15: ["Prop13"], 16: ["Prop3", "Prop4", "Prop10", "Prop15"], 17: ["Prop13", "Prop16"], 18: ["Prop3", "Prop5", "Prop16"], 19: ["Prop5", "Prop18"], 20: ["Prop3", "Prop5", "Prop19"], 21: ["Prop16", "Prop20"], 22: ["Prop3", "Prop20"], 23: ["Prop8", "Prop22"], 24: ["Prop3", "Prop4", "Prop5", "Prop19", "Prop23"], 25: ["Prop4", "Prop24"], 26: ["Prop3", "Prop4", "Prop16"], 27: ["Prop16"], 28: ["Prop13", "Prop15", "Prop27"], 29: ["Prop13", "Prop15", "Prop27", "P5"], 30: ["Prop29"], 31: ["Prop23", "Prop27"], 32: ["Prop13", "Prop29", "Prop31"], 33: ["Prop4", "Prop27", "Prop29"], 34: ["Prop4", "Prop26", "Prop29"], 35: ["Prop4", "Prop29", "Prop34"], 36: ["Prop33", "Prop34", "Prop35"], 37: ["Prop31", "Prop34", "Prop35"], 38: ["Prop31", "Prop34", "Prop36"], 39: ["Prop31", "Prop37"], 40: ["Prop31", "Prop38"], 41: ["Prop34", "Prop37"], 42: ["Prop10", "Prop23", "Prop31", "Prop38", "Prop41"], 43: ["Prop34"], 44: ["Prop15", "Prop29", "Prop31", "Prop42", "Prop43"], 45: ["Prop14", "Prop29", "Prop30", "Prop33", "Prop34", "Prop42", "Prop44"], 46: ["Prop3", "Prop11", "Prop29", "Prop31", "Prop34"], 47: ["Prop4", "Prop14", "Prop31", "Prop41", "Prop46"], 48: ["Prop3", "Prop8", "Prop11", "Prop47"] }; const discourse = { schemaVersion: "1.0", discourse: { id: "euclid-elements-book-i", name: "Euclid's Elements, Book I", subject: "geometry", variant: "classical", description: "The 48 propositions of Book I with dependencies on postulates (P1–P5), common notions (CN1–CN5), and prior propositions. Source: David E. Joyce, Clark University.", structure: { books: 1, propositions: 48, foundationTypes: ["postulate", "commonNotion"] } }, 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 I Dependency Graph. Programming Framework.", keywords: ["Euclid", "Elements", "Book I", "plane geometry", "constructions", "Pythagorean theorem"] }, sources: [ { id: "joyce", type: "digital", authors: "Joyce, David E.", title: "Euclid's Elements, Book I", year: "1996", url: "https://mathcs.clarku.edu/~djoyce/java/elements/bookI/bookI.html", notes: "Clark University; dependency table from Guide" }, { id: "euclid-heath", type: "primary", authors: "Heath, T.L.", title: "The Thirteen Books of Euclid's Elements", year: "1908", edition: "2nd", publisher: "Cambridge University Press", url: "https://archive.org/details/euclidheath00heatiala", notes: "Standard English translation" } ], nodes: [], edges: [], colorScheme: { postulate: { fill: "#e74c3c", stroke: "#c0392b" }, commonNotion: { fill: "#9b59b6", stroke: "#8e44ad" }, proposition: { fill: "#1abc9c", stroke: "#16a085" } } }; // Add postulates and common notions const postulates = [ { id: "P1", label: "Draw a straight line from any point to any point", shortLabel: "Post. 1" }, { id: "P2", label: "Produce a finite straight line continuously in a straight line", shortLabel: "Post. 2" }, { id: "P3", label: "Describe a circle with any center and radius", shortLabel: "Post. 3" }, { id: "P4", label: "All right angles equal one another", shortLabel: "Post. 4" }, { id: "P5", label: "Parallel postulate: if interior angles < two right, lines meet", shortLabel: "Post. 5" } ]; const commonNotions = [ { id: "CN1", label: "Things equal to the same thing are equal to each other", shortLabel: "CN 1" }, { id: "CN2", label: "If equals are added to equals, the wholes are equal", shortLabel: "CN 2" }, { id: "CN3", label: "If equals are subtracted from equals, the remainders are equal", shortLabel: "CN 3" }, { id: "CN4", label: "Things coinciding with one another are equal", shortLabel: "CN 4" }, { id: "CN5", label: "The whole is greater than the part", shortLabel: "CN 5" } ]; for (const p of postulates) { discourse.nodes.push({ id: p.id, type: "postulate", label: p.label, shortLabel: p.shortLabel, book: 1, number: parseInt(p.id.slice(1)), colorClass: "postulate" }); } for (const c of commonNotions) { discourse.nodes.push({ id: c.id, type: "commonNotion", label: c.label, shortLabel: c.shortLabel, book: 1, number: parseInt(c.id.slice(2)), colorClass: "commonNotion" }); } // Add propositions for (const prop of PROPOSITIONS) { discourse.nodes.push({ id: `Prop${prop.n}`, type: "proposition", label: prop.full, shortLabel: `Prop. I.${prop.n}`, short: prop.short, book: 1, number: prop.n, colorClass: "proposition" }); for (const dep of DEPS[prop.n] || []) { discourse.edges.push({ from: dep, to: `Prop${prop.n}` }); } } // Write JSON const dataDir = path.join(__dirname, "..", "data"); const outPath = path.join(dataDir, "euclid-elements-book-i.json"); fs.mkdirSync(dataDir, { recursive: true }); fs.writeFileSync(outPath, JSON.stringify(discourse, null, 2), "utf8"); console.log("Wrote", outPath); // Generate Mermaid (full graph - may be large) 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.length > 35 ? n.label.slice(0, 32) + "..." : n.label); const lbl = (n.shortLabel || n.id) + "\\n" + desc; lines.push(` ${n.id}["${lbl.replace(/"/g, '\\"')}"]`); } for (const e of edges) { lines.push(` ${e.from} --> ${e.to}`); } lines.push(" classDef postulate fill:#e74c3c,color:#fff,stroke:#c0392b"); lines.push(" classDef commonNotion fill:#9b59b6,color:#fff,stroke:#8e44ad"); lines.push(" classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085"); const postIds = nodes.filter(n => n.type === "postulate").map(n => n.id).join(","); const cnIds = nodes.filter(n => n.type === "commonNotion").map(n => n.id).join(","); const propIds = nodes.filter(n => n.type === "proposition").map(n => n.id).join(","); lines.push(` class ${postIds} postulate`); lines.push(` class ${cnIds} commonNotion`); lines.push(` class ${propIds} proposition`); return lines.join("\n"); } // Full graph const fullMermaid = toMermaid(); const mermaidPath = path.join(dataDir, "euclid-elements-book-i.mmd"); fs.writeFileSync(mermaidPath, fullMermaid, "utf8"); console.log("Wrote", mermaidPath); // Subgraphs: include foundations + props in range + all their dependencies (transitive) function closure(propMin, propMax) { const needed = new Set(); for (let i = propMin; i <= propMax; i++) needed.add(`Prop${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 => n.type !== "proposition" || needed.has(n.id); } function toMermaidWithCounts(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)); return { mermaid: toMermaid(filter), nodes: nodes.length, edges: edges.length }; } const subgraphData = []; const sections = [ { name: "props-1-10", min: 1, max: 10, title: "Propositions 1–10", desc: "Foundations, SAS, SSS, bisections, perpendiculars" }, { name: "props-11-20", min: 11, max: 20, title: "Propositions 11–20", desc: "Right angles, straight lines, vertical angles, triangle exterior, triangle inequality" }, { name: "props-21-30", min: 21, max: 30, title: "Propositions 21–30", desc: "Lines within triangle, construct triangle/angle, parallel lines" }, { name: "props-31-41", min: 31, max: 41, title: "Propositions 31–41", desc: "Parallelograms, triangles, areas" }, { name: "props-42-48", min: 42, max: 48, title: "Propositions 42–48", desc: "Constructions, Pythagorean theorem" } ]; for (const s of sections) { const { mermaid: sub, nodes: n, edges: e } = toMermaidWithCounts(closure(s.min, s.max)); subgraphData.push({ ...s, mermaid: sub, nodes: n, edges: e }); const subPath = path.join(dataDir, `euclid-elements-book-i-${s.name}.mmd`); fs.writeFileSync(subPath, sub, "utf8"); console.log("Wrote", subPath); } // Generate HTML pages for Mathematics Processes Database 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 Book I Index Euclid's Elements Book I (Joyce) Programming Framework

Description

${subtitle}

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

Dependency Flowchart

Note: Arrows mean "depends on" (tail → head). Edge crossing can create illusions of connections between adjacent nodes—e.g., I.47 and I.40 have no direct dependency; both depend on I.31 among others.

${mermaidEscaped}

Color Scheme

Red
Postulates
Purple
Common Notions
Teal
Propositions

Statistics

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

Keywords

  • Euclid
  • Elements
  • Book I
  • axioms
  • postulates
  • propositions
  • geometry
  • Pythagorean theorem
`; } if (fs.existsSync(GEOM_DIR)) { for (const d of subgraphData) { const html = htmlTemplate( `Euclid's Elements Book I — ${d.title}`, `Dependency graph for ${d.title} of Euclid's Elements Book I. ${d.desc}. Shows how propositions depend on postulates (P1–P5), common notions (CN1–CN5), and prior propositions.`, d.mermaid, d.nodes, d.edges ); const fileName = "geometry_topology-euclid-elements-book-i-" + d.name; fs.writeFileSync(path.join(GEOM_DIR, fileName + ".html"), html, "utf8"); console.log("Wrote", path.join(GEOM_DIR, fileName + ".html")); } // Index page const indexHtml = ` Euclid's Elements Book I - Mathematics Process
← Back to Mathematics Database Euclid's Elements Book I (Joyce)

Euclid's Elements, Book I

Full dependency graph of all 48 propositions. Dependencies from David E. Joyce, Clark University. Split into five views for clarity.

Propositions 1–10 — Foundations, SAS, SSS, bisections, perpendiculars Propositions 11–20 — Right angles, straight lines, vertical angles, triangle exterior, triangle inequality Propositions 21–30 — Lines within triangle, construct triangle/angle, parallel lines Propositions 31–41 — Parallelograms, triangles, areas Propositions 42–48 — Constructions, Pythagorean theorem
`; fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-i.html"), indexHtml, "utf8"); console.log("Wrote", path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-i.html")); } else { console.log("MATH_DB not found at", GEOM_DIR, "- skipping HTML generation. Set MATH_DB or ensure copernicus-web-public is available."); } console.log("Done. Nodes:", discourse.nodes.length, "Edges:", discourse.edges.length);