programming_framework / data /euclid-elements-book-x.json
garywelz's picture
Sync programming_framework from local progframe
06e4298
{
"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"
}
],
"edges": [
{
"from": "BookI",
"to": "Prop1"
},
{
"from": "BookV",
"to": "Prop1"
},
{
"from": "BookVI",
"to": "Prop1"
},
{
"from": "BookI",
"to": "Prop2"
},
{
"from": "BookV",
"to": "Prop2"
},
{
"from": "BookVI",
"to": "Prop2"
},
{
"from": "BookI",
"to": "Prop3"
},
{
"from": "BookV",
"to": "Prop3"
},
{
"from": "BookVI",
"to": "Prop3"
},
{
"from": "BookI",
"to": "Prop4"
},
{
"from": "BookV",
"to": "Prop4"
},
{
"from": "BookVI",
"to": "Prop4"
},
{
"from": "BookI",
"to": "Prop5"
},
{
"from": "BookV",
"to": "Prop5"
},
{
"from": "BookVI",
"to": "Prop5"
},
{
"from": "BookI",
"to": "Prop6"
},
{
"from": "BookV",
"to": "Prop6"
},
{
"from": "BookVI",
"to": "Prop6"
},
{
"from": "BookI",
"to": "Prop7"
},
{
"from": "BookV",
"to": "Prop7"
},
{
"from": "BookVI",
"to": "Prop7"
},
{
"from": "BookI",
"to": "Prop8"
},
{
"from": "BookV",
"to": "Prop8"
},
{
"from": "BookVI",
"to": "Prop8"
},
{
"from": "BookI",
"to": "Prop9"
},
{
"from": "BookV",
"to": "Prop9"
},
{
"from": "BookVI",
"to": "Prop9"
},
{
"from": "BookI",
"to": "Prop10"
},
{
"from": "BookV",
"to": "Prop10"
},
{
"from": "BookVI",
"to": "Prop10"
},
{
"from": "BookI",
"to": "Prop11"
},
{
"from": "BookV",
"to": "Prop11"
},
{
"from": "BookVI",
"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"
}
}
}