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| { | |
| "schemaVersion": "1.0", | |
| "discourse": { | |
| "id": "euclid-elements-book-x", | |
| "name": "Euclid's Elements, Book X", | |
| "subject": "incommensurables", | |
| "variant": "classical", | |
| "description": "Incommensurables, binomials, apotomes. 16 definitions, 115 propositions. Depends on Books I, V, VI. Source: David E. Joyce.", | |
| "structure": { | |
| "books": 10, | |
| "definitions": 16, | |
| "propositions": 115, | |
| "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 X Dependency Graph. Programming Framework.", | |
| "keywords": [ | |
| "Euclid", | |
| "Elements", | |
| "Book X", | |
| "incommensurable", | |
| "binomial", | |
| "apotome", | |
| "medial" | |
| ] | |
| }, | |
| "sources": [ | |
| { | |
| "id": "joyce", | |
| "type": "digital", | |
| "authors": "Joyce, David E.", | |
| "title": "Euclid's Elements, Book X", | |
| "year": "1996", | |
| "url": "https://mathcs.clarku.edu/~djoyce/java/elements/bookX/bookX.html", | |
| "notes": "Clark University" | |
| } | |
| ], | |
| "nodes": [ | |
| { | |
| "id": "BookI", | |
| "type": "foundation", | |
| "label": "Book I — Plane geometry", | |
| "shortLabel": "Book I", | |
| "short": "Foundation", | |
| "book": 1, | |
| "colorClass": "foundation" | |
| }, | |
| { | |
| "id": "BookV", | |
| "type": "foundation", | |
| "label": "Book V — Proportions", | |
| "shortLabel": "Book V", | |
| "short": "Foundation", | |
| "book": 5, | |
| "colorClass": "foundation" | |
| }, | |
| { | |
| "id": "BookVI", | |
| "type": "foundation", | |
| "label": "Book VI — Similar figures", | |
| "shortLabel": "Book VI", | |
| "short": "Foundation", | |
| "book": 6, | |
| "colorClass": "foundation" | |
| }, | |
| { | |
| "id": "Prop1", | |
| "type": "proposition", | |
| "label": "Two unequal magnitudes: subtract more than half repeatedly; remainder less than lesser", | |
| "shortLabel": "Prop. X.1", | |
| "short": "Antenaresis for magnitudes", | |
| "book": 10, | |
| "number": 1, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop2", | |
| "type": "proposition", | |
| "label": "If less subtracted from greater repeatedly and remainder never measures prior: incommensurable", | |
| "shortLabel": "Prop. X.2", | |
| "short": "Incommensurable criterion", | |
| "book": 10, | |
| "number": 2, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop3", | |
| "type": "proposition", | |
| "label": "To find greatest common measure of two commensurable magnitudes", | |
| "shortLabel": "Prop. X.3", | |
| "short": "GCM of two commensurable", | |
| "book": 10, | |
| "number": 3, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop4", | |
| "type": "proposition", | |
| "label": "To find greatest common measure of three commensurable magnitudes", | |
| "shortLabel": "Prop. X.4", | |
| "short": "GCM of three commensurable", | |
| "book": 10, | |
| "number": 4, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop5", | |
| "type": "proposition", | |
| "label": "Commensurable magnitudes have ratio which a number has to a number", | |
| "shortLabel": "Prop. X.5", | |
| "short": "Commensurable: number ratio", | |
| "book": 10, | |
| "number": 5, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop6", | |
| "type": "proposition", | |
| "label": "If two magnitudes have number-to-number ratio, they are commensurable", | |
| "shortLabel": "Prop. X.6", | |
| "short": "Number ratio: commensurable", | |
| "book": 10, | |
| "number": 6, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop7", | |
| "type": "proposition", | |
| "label": "Incommensurable magnitudes do not have number-to-number ratio", | |
| "shortLabel": "Prop. X.7", | |
| "short": "Incommensurable: no number ratio", | |
| "book": 10, | |
| "number": 7, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop8", | |
| "type": "proposition", | |
| "label": "If magnitudes lack number-to-number ratio, they are incommensurable", | |
| "shortLabel": "Prop. X.8", | |
| "short": "No number ratio: incommensurable", | |
| "book": 10, | |
| "number": 8, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop9", | |
| "type": "proposition", | |
| "label": "Squares on commensurable lines have square-to-square ratio; converse", | |
| "shortLabel": "Prop. X.9", | |
| "short": "Squares: commensurable iff square ratio", | |
| "book": 10, | |
| "number": 9, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop10", | |
| "type": "proposition", | |
| "label": "To find two lines incommensurable with assigned: one in length, one in square", | |
| "shortLabel": "Prop. X.10", | |
| "short": "Find incommensurable lines", | |
| "book": 10, | |
| "number": 10, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop11", | |
| "type": "proposition", | |
| "label": "Four proportional: first commensurable with second iff third with fourth", | |
| "shortLabel": "Prop. X.11", | |
| "short": "Proportion preserves commensurability", | |
| "book": 10, | |
| "number": 11, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop12", | |
| "type": "proposition", | |
| "label": "Magnitudes commensurable with same magnitude are commensurable", | |
| "shortLabel": "Prop. X.12", | |
| "short": "Commensurable with same", | |
| "book": 10, | |
| "number": 12, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop13", | |
| "type": "proposition", | |
| "label": "If two commensurable, one incommensurable with third, so is the other", | |
| "shortLabel": "Prop. X.13", | |
| "short": "Commensurable: incommensurable partner", | |
| "book": 10, | |
| "number": 13, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop14", | |
| "type": "proposition", | |
| "label": "Given two lines: find square by which greater square exceeds less; find line whose square equals sum", | |
| "shortLabel": "Prop. X.14", | |
| "short": "Square difference, sum of squares", | |
| "book": 10, | |
| "number": 14, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop15", | |
| "type": "proposition", | |
| "label": "Two commensurable added: whole commensurable with each", | |
| "shortLabel": "Prop. X.15", | |
| "short": "Commensurable sum", | |
| "book": 10, | |
| "number": 15, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop16", | |
| "type": "proposition", | |
| "label": "Two incommensurable added: sum incommensurable with each", | |
| "shortLabel": "Prop. X.16", | |
| "short": "Incommensurable sum", | |
| "book": 10, | |
| "number": 16, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop17", | |
| "type": "proposition", | |
| "label": "Applied parallelogram falling short by square: parts commensurable iff square difference commensurable", | |
| "shortLabel": "Prop. X.17", | |
| "short": "Parallelogram falling short", | |
| "book": 10, | |
| "number": 17, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop18", | |
| "type": "proposition", | |
| "label": "Applied parallelogram: parts incommensurable iff square difference incommensurable", | |
| "shortLabel": "Prop. X.18", | |
| "short": "Parallelogram: incommensurable parts", | |
| "book": 10, | |
| "number": 18, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop19", | |
| "type": "proposition", | |
| "label": "Rectangle by rational lines commensurable in length is rational", | |
| "shortLabel": "Prop. X.19", | |
| "short": "Rational rectangle from rational", | |
| "book": 10, | |
| "number": 19, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop20", | |
| "type": "proposition", | |
| "label": "Rational area applied to rational line: breadth rational and commensurable", | |
| "shortLabel": "Prop. X.20", | |
| "short": "Rational area on rational", | |
| "book": 10, | |
| "number": 20, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop21", | |
| "type": "proposition", | |
| "label": "Rectangle by rational in square only is irrational; side called medial", | |
| "shortLabel": "Prop. X.21", | |
| "short": "Medial: rational in square only", | |
| "book": 10, | |
| "number": 21, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop22", | |
| "type": "proposition", | |
| "label": "Square on medial applied to rational: breadth rational, incommensurable in length", | |
| "shortLabel": "Prop. X.22", | |
| "short": "Medial applied to rational", | |
| "book": 10, | |
| "number": 22, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop23", | |
| "type": "proposition", | |
| "label": "Line commensurable with medial is medial", | |
| "shortLabel": "Prop. X.23", | |
| "short": "Commensurable with medial", | |
| "book": 10, | |
| "number": 23, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop24", | |
| "type": "proposition", | |
| "label": "Rectangle by medial lines commensurable in length is medial", | |
| "shortLabel": "Prop. X.24", | |
| "short": "Medial rectangle: commensurable length", | |
| "book": 10, | |
| "number": 24, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop25", | |
| "type": "proposition", | |
| "label": "Rectangle by medial in square only: rational or medial", | |
| "shortLabel": "Prop. X.25", | |
| "short": "Medial: square only", | |
| "book": 10, | |
| "number": 25, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop26", | |
| "type": "proposition", | |
| "label": "Medial area does not exceed medial by rational area", | |
| "shortLabel": "Prop. X.26", | |
| "short": "Medial minus medial", | |
| "book": 10, | |
| "number": 26, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop27", | |
| "type": "proposition", | |
| "label": "To find medial lines commensurable in square only containing rational rectangle", | |
| "shortLabel": "Prop. X.27", | |
| "short": "Find medial in square only, rational rect", | |
| "book": 10, | |
| "number": 27, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop28", | |
| "type": "proposition", | |
| "label": "To find medial lines commensurable in square only containing medial rectangle", | |
| "shortLabel": "Prop. X.28", | |
| "short": "Find medial in square only, medial rect", | |
| "book": 10, | |
| "number": 28, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop29", | |
| "type": "proposition", | |
| "label": "To find two rational in square only: square diff commensurable with greater", | |
| "shortLabel": "Prop. X.29", | |
| "short": "Find rational in square only, commensurable diff", | |
| "book": 10, | |
| "number": 29, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop30", | |
| "type": "proposition", | |
| "label": "To find two rational in square only: square diff incommensurable with greater", | |
| "shortLabel": "Prop. X.30", | |
| "short": "Find rational in square only, incommensurable diff", | |
| "book": 10, | |
| "number": 30, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop31", | |
| "type": "proposition", | |
| "label": "To find two medial in square only, rational rect: diff commensurable with greater", | |
| "shortLabel": "Prop. X.31", | |
| "short": "Find medial, rational rect, commensurable diff", | |
| "book": 10, | |
| "number": 31, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop32", | |
| "type": "proposition", | |
| "label": "To find two medial in square only, medial rect: diff commensurable with greater", | |
| "shortLabel": "Prop. X.32", | |
| "short": "Find medial, medial rect, commensurable diff", | |
| "book": 10, | |
| "number": 32, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop33", | |
| "type": "proposition", | |
| "label": "To find two incommensurable in square: sum of squares rational, rectangle medial", | |
| "shortLabel": "Prop. X.33", | |
| "short": "Find incommensurable: rational sum, medial rect", | |
| "book": 10, | |
| "number": 33, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop34", | |
| "type": "proposition", | |
| "label": "To find two incommensurable in square: sum medial, rectangle rational", | |
| "shortLabel": "Prop. X.34", | |
| "short": "Find incommensurable: medial sum, rational rect", | |
| "book": 10, | |
| "number": 34, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop35", | |
| "type": "proposition", | |
| "label": "To find two incommensurable in square: sum and rect medial, incommensurable", | |
| "shortLabel": "Prop. X.35", | |
| "short": "Find incommensurable: both medial", | |
| "book": 10, | |
| "number": 35, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop36", | |
| "type": "proposition", | |
| "label": "Two rational in square only added: whole irrational, called binomial", | |
| "shortLabel": "Prop. X.36", | |
| "short": "Binomial defined", | |
| "book": 10, | |
| "number": 36, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop37", | |
| "type": "proposition", | |
| "label": "Two medial in square only, rational rect added: first bimedial", | |
| "shortLabel": "Prop. X.37", | |
| "short": "First bimedial defined", | |
| "book": 10, | |
| "number": 37, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop38", | |
| "type": "proposition", | |
| "label": "Two medial in square only, medial rect added: second bimedial", | |
| "shortLabel": "Prop. X.38", | |
| "short": "Second bimedial defined", | |
| "book": 10, | |
| "number": 38, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop39", | |
| "type": "proposition", | |
| "label": "Two incommensurable in square, rational sum, medial rect added: major", | |
| "shortLabel": "Prop. X.39", | |
| "short": "Major defined", | |
| "book": 10, | |
| "number": 39, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop40", | |
| "type": "proposition", | |
| "label": "Two incommensurable in square, medial sum, rational rect added: side of rational plus medial", | |
| "shortLabel": "Prop. X.40", | |
| "short": "Side of rational plus medial", | |
| "book": 10, | |
| "number": 40, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop41", | |
| "type": "proposition", | |
| "label": "Two incommensurable in square, both medial added: side of sum of two medial", | |
| "shortLabel": "Prop. X.41", | |
| "short": "Side of sum of two medial", | |
| "book": 10, | |
| "number": 41, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop42", | |
| "type": "proposition", | |
| "label": "Binomial divided into terms at one point only", | |
| "shortLabel": "Prop. X.42", | |
| "short": "Binomial: unique division", | |
| "book": 10, | |
| "number": 42, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop43", | |
| "type": "proposition", | |
| "label": "First bimedial divided at one point only", | |
| "shortLabel": "Prop. X.43", | |
| "short": "First bimedial: unique division", | |
| "book": 10, | |
| "number": 43, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop44", | |
| "type": "proposition", | |
| "label": "Second bimedial divided at one point only", | |
| "shortLabel": "Prop. X.44", | |
| "short": "Second bimedial: unique division", | |
| "book": 10, | |
| "number": 44, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop45", | |
| "type": "proposition", | |
| "label": "Major divided at one point only", | |
| "shortLabel": "Prop. X.45", | |
| "short": "Major: unique division", | |
| "book": 10, | |
| "number": 45, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop46", | |
| "type": "proposition", | |
| "label": "Side of rational plus medial divided at one point only", | |
| "shortLabel": "Prop. X.46", | |
| "short": "Side rational+medial: unique division", | |
| "book": 10, | |
| "number": 46, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop47", | |
| "type": "proposition", | |
| "label": "Side of sum of two medial divided at one point only", | |
| "shortLabel": "Prop. X.47", | |
| "short": "Side two medial: unique division", | |
| "book": 10, | |
| "number": 47, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop48", | |
| "type": "proposition", | |
| "label": "To find the first binomial line", | |
| "shortLabel": "Prop. X.48", | |
| "short": "Find first binomial", | |
| "book": 10, | |
| "number": 48, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop49", | |
| "type": "proposition", | |
| "label": "To find the second binomial line", | |
| "shortLabel": "Prop. X.49", | |
| "short": "Find second binomial", | |
| "book": 10, | |
| "number": 49, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop50", | |
| "type": "proposition", | |
| "label": "To find the third binomial line", | |
| "shortLabel": "Prop. X.50", | |
| "short": "Find third binomial", | |
| "book": 10, | |
| "number": 50, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop51", | |
| "type": "proposition", | |
| "label": "To find the fourth binomial line", | |
| "shortLabel": "Prop. X.51", | |
| "short": "Find fourth binomial", | |
| "book": 10, | |
| "number": 51, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop52", | |
| "type": "proposition", | |
| "label": "To find the fifth binomial line", | |
| "shortLabel": "Prop. X.52", | |
| "short": "Find fifth binomial", | |
| "book": 10, | |
| "number": 52, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop53", | |
| "type": "proposition", | |
| "label": "To find the sixth binomial line", | |
| "shortLabel": "Prop. X.53", | |
| "short": "Find sixth binomial", | |
| "book": 10, | |
| "number": 53, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop54", | |
| "type": "proposition", | |
| "label": "Area by rational and first binomial: side is binomial", | |
| "shortLabel": "Prop. X.54", | |
| "short": "Rational × first binomial", | |
| "book": 10, | |
| "number": 54, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop55", | |
| "type": "proposition", | |
| "label": "Area by rational and second binomial: side is first bimedial", | |
| "shortLabel": "Prop. X.55", | |
| "short": "Rational × second binomial", | |
| "book": 10, | |
| "number": 55, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop56", | |
| "type": "proposition", | |
| "label": "Area by rational and third binomial: side is second bimedial", | |
| "shortLabel": "Prop. X.56", | |
| "short": "Rational × third binomial", | |
| "book": 10, | |
| "number": 56, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop57", | |
| "type": "proposition", | |
| "label": "Area by rational and fourth binomial: side is major", | |
| "shortLabel": "Prop. X.57", | |
| "short": "Rational × fourth binomial", | |
| "book": 10, | |
| "number": 57, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop58", | |
| "type": "proposition", | |
| "label": "Area by rational and fifth binomial: side is rational plus medial", | |
| "shortLabel": "Prop. X.58", | |
| "short": "Rational × fifth binomial", | |
| "book": 10, | |
| "number": 58, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop59", | |
| "type": "proposition", | |
| "label": "Area by rational and sixth binomial: side is sum of two medial", | |
| "shortLabel": "Prop. X.59", | |
| "short": "Rational × sixth binomial", | |
| "book": 10, | |
| "number": 59, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop60", | |
| "type": "proposition", | |
| "label": "Square on binomial applied to rational: breadth first binomial", | |
| "shortLabel": "Prop. X.60", | |
| "short": "Square on binomial", | |
| "book": 10, | |
| "number": 60, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop61", | |
| "type": "proposition", | |
| "label": "Square on first bimedial applied to rational: breadth second binomial", | |
| "shortLabel": "Prop. X.61", | |
| "short": "Square on first bimedial", | |
| "book": 10, | |
| "number": 61, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop62", | |
| "type": "proposition", | |
| "label": "Square on second bimedial applied to rational: breadth third binomial", | |
| "shortLabel": "Prop. X.62", | |
| "short": "Square on second bimedial", | |
| "book": 10, | |
| "number": 62, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop63", | |
| "type": "proposition", | |
| "label": "Square on major applied to rational: breadth fourth binomial", | |
| "shortLabel": "Prop. X.63", | |
| "short": "Square on major", | |
| "book": 10, | |
| "number": 63, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop64", | |
| "type": "proposition", | |
| "label": "Square on rational+medial applied to rational: breadth fifth binomial", | |
| "shortLabel": "Prop. X.64", | |
| "short": "Square on rational+medial", | |
| "book": 10, | |
| "number": 64, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop65", | |
| "type": "proposition", | |
| "label": "Square on sum of two medial applied to rational: breadth sixth binomial", | |
| "shortLabel": "Prop. X.65", | |
| "short": "Square on two medial", | |
| "book": 10, | |
| "number": 65, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop66", | |
| "type": "proposition", | |
| "label": "Line commensurable with binomial is binomial, same order", | |
| "shortLabel": "Prop. X.66", | |
| "short": "Commensurable with binomial", | |
| "book": 10, | |
| "number": 66, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop67", | |
| "type": "proposition", | |
| "label": "Line commensurable with bimedial is bimedial, same order", | |
| "shortLabel": "Prop. X.67", | |
| "short": "Commensurable with bimedial", | |
| "book": 10, | |
| "number": 67, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop68", | |
| "type": "proposition", | |
| "label": "Line commensurable with major is major", | |
| "shortLabel": "Prop. X.68", | |
| "short": "Commensurable with major", | |
| "book": 10, | |
| "number": 68, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop69", | |
| "type": "proposition", | |
| "label": "Line commensurable with rational+medial is rational+medial", | |
| "shortLabel": "Prop. X.69", | |
| "short": "Commensurable with rational+medial", | |
| "book": 10, | |
| "number": 69, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop70", | |
| "type": "proposition", | |
| "label": "Line commensurable with sum of two medial is sum of two medial", | |
| "shortLabel": "Prop. X.70", | |
| "short": "Commensurable with two medial", | |
| "book": 10, | |
| "number": 70, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop71", | |
| "type": "proposition", | |
| "label": "Rational and medial added: four irrationals arise", | |
| "shortLabel": "Prop. X.71", | |
| "short": "Rational + medial: four irrationals", | |
| "book": 10, | |
| "number": 71, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop72", | |
| "type": "proposition", | |
| "label": "Two medial incommensurable added: two irrationals arise", | |
| "shortLabel": "Prop. X.72", | |
| "short": "Two medial: two irrationals", | |
| "book": 10, | |
| "number": 72, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop73", | |
| "type": "proposition", | |
| "label": "Rational minus rational in square only: remainder irrational, apotome", | |
| "shortLabel": "Prop. X.73", | |
| "short": "Apotome defined", | |
| "book": 10, | |
| "number": 73, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop74", | |
| "type": "proposition", | |
| "label": "Medial minus medial, rational rect: first apotome of medial", | |
| "shortLabel": "Prop. X.74", | |
| "short": "First apotome of medial", | |
| "book": 10, | |
| "number": 74, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop75", | |
| "type": "proposition", | |
| "label": "Medial minus medial, medial rect: second apotome of medial", | |
| "shortLabel": "Prop. X.75", | |
| "short": "Second apotome of medial", | |
| "book": 10, | |
| "number": 75, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop76", | |
| "type": "proposition", | |
| "label": "Line minus incommensurable: sum rational, rect medial: remainder minor", | |
| "shortLabel": "Prop. X.76", | |
| "short": "Minor defined", | |
| "book": 10, | |
| "number": 76, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop77", | |
| "type": "proposition", | |
| "label": "Line minus incommensurable: sum medial, rect rational: produces rational+medial", | |
| "shortLabel": "Prop. X.77", | |
| "short": "Produces rational+medial", | |
| "book": 10, | |
| "number": 77, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop78", | |
| "type": "proposition", | |
| "label": "Line minus incommensurable: both medial, incommensurable: produces medial+medial", | |
| "shortLabel": "Prop. X.78", | |
| "short": "Produces medial+medial", | |
| "book": 10, | |
| "number": 78, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop79", | |
| "type": "proposition", | |
| "label": "To apotome only one rational can be annexed in square only", | |
| "shortLabel": "Prop. X.79", | |
| "short": "Apotome: unique annex", | |
| "book": 10, | |
| "number": 79, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop80", | |
| "type": "proposition", | |
| "label": "To first apotome of medial: unique medial annex, rational rect", | |
| "shortLabel": "Prop. X.80", | |
| "short": "First apotome medial: unique annex", | |
| "book": 10, | |
| "number": 80, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop81", | |
| "type": "proposition", | |
| "label": "To second apotome of medial: unique medial annex, medial rect", | |
| "shortLabel": "Prop. X.81", | |
| "short": "Second apotome medial: unique annex", | |
| "book": 10, | |
| "number": 81, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop82", | |
| "type": "proposition", | |
| "label": "To minor: unique annex incommensurable in square", | |
| "shortLabel": "Prop. X.82", | |
| "short": "Minor: unique annex", | |
| "book": 10, | |
| "number": 82, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop83", | |
| "type": "proposition", | |
| "label": "To produces rational+medial: unique annex", | |
| "shortLabel": "Prop. X.83", | |
| "short": "Rational+medial: unique annex", | |
| "book": 10, | |
| "number": 83, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop84", | |
| "type": "proposition", | |
| "label": "To produces medial+medial: unique annex", | |
| "shortLabel": "Prop. X.84", | |
| "short": "Medial+medial: unique annex", | |
| "book": 10, | |
| "number": 84, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop85", | |
| "type": "proposition", | |
| "label": "To find the first apotome", | |
| "shortLabel": "Prop. X.85", | |
| "short": "Find first apotome", | |
| "book": 10, | |
| "number": 85, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop86", | |
| "type": "proposition", | |
| "label": "To find the second apotome", | |
| "shortLabel": "Prop. X.86", | |
| "short": "Find second apotome", | |
| "book": 10, | |
| "number": 86, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop87", | |
| "type": "proposition", | |
| "label": "To find the third apotome", | |
| "shortLabel": "Prop. X.87", | |
| "short": "Find third apotome", | |
| "book": 10, | |
| "number": 87, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop88", | |
| "type": "proposition", | |
| "label": "To find the fourth apotome", | |
| "shortLabel": "Prop. X.88", | |
| "short": "Find fourth apotome", | |
| "book": 10, | |
| "number": 88, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop89", | |
| "type": "proposition", | |
| "label": "To find the fifth apotome", | |
| "shortLabel": "Prop. X.89", | |
| "short": "Find fifth apotome", | |
| "book": 10, | |
| "number": 89, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop90", | |
| "type": "proposition", | |
| "label": "To find the sixth apotome", | |
| "shortLabel": "Prop. X.90", | |
| "short": "Find sixth apotome", | |
| "book": 10, | |
| "number": 90, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop91", | |
| "type": "proposition", | |
| "label": "Area by rational and first apotome: side is apotome", | |
| "shortLabel": "Prop. X.91", | |
| "short": "Rational × first apotome", | |
| "book": 10, | |
| "number": 91, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop92", | |
| "type": "proposition", | |
| "label": "Area by rational and second apotome: side is first apotome of medial", | |
| "shortLabel": "Prop. X.92", | |
| "short": "Rational × second apotome", | |
| "book": 10, | |
| "number": 92, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop93", | |
| "type": "proposition", | |
| "label": "Area by rational and third apotome: side is second apotome of medial", | |
| "shortLabel": "Prop. X.93", | |
| "short": "Rational × third apotome", | |
| "book": 10, | |
| "number": 93, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop94", | |
| "type": "proposition", | |
| "label": "Area by rational and fourth apotome: side is minor", | |
| "shortLabel": "Prop. X.94", | |
| "short": "Rational × fourth apotome", | |
| "book": 10, | |
| "number": 94, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop95", | |
| "type": "proposition", | |
| "label": "Area by rational and fifth apotome: side produces rational+medial", | |
| "shortLabel": "Prop. X.95", | |
| "short": "Rational × fifth apotome", | |
| "book": 10, | |
| "number": 95, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop96", | |
| "type": "proposition", | |
| "label": "Area by rational and sixth apotome: side produces medial+medial", | |
| "shortLabel": "Prop. X.96", | |
| "short": "Rational × sixth apotome", | |
| "book": 10, | |
| "number": 96, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop97", | |
| "type": "proposition", | |
| "label": "Square on apotome of medial applied to rational: breadth first apotome", | |
| "shortLabel": "Prop. X.97", | |
| "short": "Square on apotome medial", | |
| "book": 10, | |
| "number": 97, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop98", | |
| "type": "proposition", | |
| "label": "Square on first apotome of medial: breadth second apotome", | |
| "shortLabel": "Prop. X.98", | |
| "short": "Square on first apotome medial", | |
| "book": 10, | |
| "number": 98, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop99", | |
| "type": "proposition", | |
| "label": "Square on second apotome of medial: breadth third apotome", | |
| "shortLabel": "Prop. X.99", | |
| "short": "Square on second apotome medial", | |
| "book": 10, | |
| "number": 99, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop100", | |
| "type": "proposition", | |
| "label": "Square on minor applied to rational: breadth fourth apotome", | |
| "shortLabel": "Prop. X.100", | |
| "short": "Square on minor", | |
| "book": 10, | |
| "number": 100, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop101", | |
| "type": "proposition", | |
| "label": "Square on produces rational+medial: breadth fifth apotome", | |
| "shortLabel": "Prop. X.101", | |
| "short": "Square on rational+medial", | |
| "book": 10, | |
| "number": 101, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop102", | |
| "type": "proposition", | |
| "label": "Square on produces medial+medial: breadth sixth apotome", | |
| "shortLabel": "Prop. X.102", | |
| "short": "Square on medial+medial", | |
| "book": 10, | |
| "number": 102, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop103", | |
| "type": "proposition", | |
| "label": "Line commensurable with apotome is apotome, same order", | |
| "shortLabel": "Prop. X.103", | |
| "short": "Commensurable with apotome", | |
| "book": 10, | |
| "number": 103, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop104", | |
| "type": "proposition", | |
| "label": "Line commensurable with apotome of medial is apotome of medial", | |
| "shortLabel": "Prop. X.104", | |
| "short": "Commensurable with apotome medial", | |
| "book": 10, | |
| "number": 104, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop105", | |
| "type": "proposition", | |
| "label": "Line commensurable with minor is minor", | |
| "shortLabel": "Prop. X.105", | |
| "short": "Commensurable with minor", | |
| "book": 10, | |
| "number": 105, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop106", | |
| "type": "proposition", | |
| "label": "Line commensurable with produces rational+medial is same", | |
| "shortLabel": "Prop. X.106", | |
| "short": "Commensurable with rational+medial", | |
| "book": 10, | |
| "number": 106, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop107", | |
| "type": "proposition", | |
| "label": "Line commensurable with produces medial+medial is same", | |
| "shortLabel": "Prop. X.107", | |
| "short": "Commensurable with medial+medial", | |
| "book": 10, | |
| "number": 107, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop108", | |
| "type": "proposition", | |
| "label": "From rational area subtract medial: side is apotome or minor", | |
| "shortLabel": "Prop. X.108", | |
| "short": "Rational minus medial", | |
| "book": 10, | |
| "number": 108, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop109", | |
| "type": "proposition", | |
| "label": "From medial subtract rational: first apotome of medial or rational+medial", | |
| "shortLabel": "Prop. X.109", | |
| "short": "Medial minus rational", | |
| "book": 10, | |
| "number": 109, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop110", | |
| "type": "proposition", | |
| "label": "From medial subtract medial incommensurable: second apotome or medial+medial", | |
| "shortLabel": "Prop. X.110", | |
| "short": "Medial minus medial", | |
| "book": 10, | |
| "number": 110, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop111", | |
| "type": "proposition", | |
| "label": "Apotome is not the same as binomial", | |
| "shortLabel": "Prop. X.111", | |
| "short": "Apotome ≠ binomial", | |
| "book": 10, | |
| "number": 111, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop112", | |
| "type": "proposition", | |
| "label": "Square on rational applied to binomial: breadth apotome, same order", | |
| "shortLabel": "Prop. X.112", | |
| "short": "Rational on binomial", | |
| "book": 10, | |
| "number": 112, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop113", | |
| "type": "proposition", | |
| "label": "Square on rational applied to apotome: breadth binomial, same order", | |
| "shortLabel": "Prop. X.113", | |
| "short": "Rational on apotome", | |
| "book": 10, | |
| "number": 113, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop114", | |
| "type": "proposition", | |
| "label": "Area by apotome and binomial (commensurable terms): side is rational", | |
| "shortLabel": "Prop. X.114", | |
| "short": "Apotome × binomial: rational", | |
| "book": 10, | |
| "number": 114, | |
| "colorClass": "proposition" | |
| }, | |
| { | |
| "id": "Prop115", | |
| "type": "proposition", | |
| "label": "From medial arise irrationals infinite in number, none same as preceding", | |
| "shortLabel": "Prop. X.115", | |
| "short": "Medial: infinite irrationals", | |
| "book": 10, | |
| "number": 115, | |
| "colorClass": "proposition" | |
| } | |
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| "to": "Prop11" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop12" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop12" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop12" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop13" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop13" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop13" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop14" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop14" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop14" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop15" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop15" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop15" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop16" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop16" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop16" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop17" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop17" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop17" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop18" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop18" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop18" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop19" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop19" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop19" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop20" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop20" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop20" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop21" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop21" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop21" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop22" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop22" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop22" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop23" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop23" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop23" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop24" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop24" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop24" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop25" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop25" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop25" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop26" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop26" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop26" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop27" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop27" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop27" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop28" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop28" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop28" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop29" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop29" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop29" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop30" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop30" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop30" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop31" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop31" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop31" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop32" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop32" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop32" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop33" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop33" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop33" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop34" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop34" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop34" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop35" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop35" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop35" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop36" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop36" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop36" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop37" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop37" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop37" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop38" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop38" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop38" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop39" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop39" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop39" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop40" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop40" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop40" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop41" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop41" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop41" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop42" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop42" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop42" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop43" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop43" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop43" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop44" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop44" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop44" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop45" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop45" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop45" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop46" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop46" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop46" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop47" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop47" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop47" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop48" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop48" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop48" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop49" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop49" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop49" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop50" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop50" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop50" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop51" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop51" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop51" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop52" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop52" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop52" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop53" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop53" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop53" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop54" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop54" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop54" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop55" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop55" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop55" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop56" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop56" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop56" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop57" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop57" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop57" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop58" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop58" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop58" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop59" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop59" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop59" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop60" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop60" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop60" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop61" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop61" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop61" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop62" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop62" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop62" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop63" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop63" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop63" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop64" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop64" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop64" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop65" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop65" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop65" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop66" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop66" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop66" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop67" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop67" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop67" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop68" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop68" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop68" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop69" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop69" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop69" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop70" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop70" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop70" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop71" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop71" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop71" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop72" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop72" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop72" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop73" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop73" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop73" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop74" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop74" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop74" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop75" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop75" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop75" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop76" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop76" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop76" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop77" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop77" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop77" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop78" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop78" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop78" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop79" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop79" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop79" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop80" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop80" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop80" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop81" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop81" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop81" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop82" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop82" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop82" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop83" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop83" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop83" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop84" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop84" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop84" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop85" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop85" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop85" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop86" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop86" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop86" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop87" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop87" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop87" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop88" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop88" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop88" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop89" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop89" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop89" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop90" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop90" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop90" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop91" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop91" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop91" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop92" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop92" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop92" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop93" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop93" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop93" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop94" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop94" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop94" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop95" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop95" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop95" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop96" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop96" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop96" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop97" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop97" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop97" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop98" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop98" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop98" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop99" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop99" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop99" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop100" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop100" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop100" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop101" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop101" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop101" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop102" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop102" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop102" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop103" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop103" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop103" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop104" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop104" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop104" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop105" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop105" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop105" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop106" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop106" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop106" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop107" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop107" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop107" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop108" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop108" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop108" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop109" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop109" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop109" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop110" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop110" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop110" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop111" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop111" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop111" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop112" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop112" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop112" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop113" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop113" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop113" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop114" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop114" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop114" | |
| }, | |
| { | |
| "from": "BookI", | |
| "to": "Prop115" | |
| }, | |
| { | |
| "from": "BookV", | |
| "to": "Prop115" | |
| }, | |
| { | |
| "from": "BookVI", | |
| "to": "Prop115" | |
| } | |
| ], | |
| "colorScheme": { | |
| "foundation": { | |
| "fill": "#95a5a6", | |
| "stroke": "#7f8c8d" | |
| }, | |
| "proposition": { | |
| "fill": "#1abc9c", | |
| "stroke": "#16a085" | |
| } | |
| } | |
| } |