garywelz/programming_framework
0
1{2 "schemaVersion": "1.0",3 "discourse": {4 "id": "euclid-elements-book-iv",5 "name": "Euclid's Elements, Book IV",6 "subject": "geometry",7 "variant": "classical",8 "description": "Inscribed and circumscribed figures: triangle, square, pentagon, hexagon, 15-gon. All depend on Books I and III. IV.10 uses II.11. Source: David E. Joyce.",9 "structure": {10 "books": 4,11 "definitions": 7,12 "propositions": 16,13 "foundationTypes": [14 "definition",15 "foundation"16 ]17 }18 },19 "metadata": {20 "created": "2026-03-15",21 "lastUpdated": "2026-03-15",22 "version": "1.0.0",23 "license": "CC BY 4.0",24 "authors": [25 "Welz, G."26 ],27 "methodology": "Programming Framework",28 "citation": "Welz, G. (2026). Euclid's Elements Book IV Dependency Graph. Programming Framework.",29 "keywords": [30 "Euclid",31 "Elements",32 "Book IV",33 "inscribed",34 "circumscribed",35 "pentagon",36 "hexagon"37 ]38 },39 "sources": [40 {41 "id": "joyce",42 "type": "digital",43 "authors": "Joyce, David E.",44 "title": "Euclid's Elements, Book IV",45 "year": "1996",46 "url": "https://mathcs.clarku.edu/~djoyce/java/elements/bookIV/bookIV.html",47 "notes": "Clark University; Logical structure"48 }49 ],50 "nodes": [51 {52 "id": "BookI",53 "type": "foundation",54 "label": "Book I — Fundamentals of plane geometry",55 "shortLabel": "Book I",56 "short": "Foundation",57 "book": 1,58 "colorClass": "foundation"59 },60 {61 "id": "BookIII",62 "type": "foundation",63 "label": "Book III — Theory of circles",64 "shortLabel": "Book III",65 "short": "Foundation",66 "book": 3,67 "colorClass": "foundation"68 },69 {70 "id": "PropII11",71 "type": "foundation",72 "label": "Prop. II.11 — Golden section",73 "shortLabel": "Prop. II.11",74 "short": "From Book II",75 "book": 2,76 "colorClass": "foundation"77 },78 {79 "id": "Def1",80 "type": "definition",81 "label": "Rectilinear figure inscribed in circle when each vertex on circumference",82 "shortLabel": "Def. IV.1",83 "short": "Inscribe in circle",84 "book": 4,85 "number": 1,86 "colorClass": "definition"87 },88 {89 "id": "Def2",90 "type": "definition",91 "label": "Figure circumscribed about circle when each side touches circle",92 "shortLabel": "Def. IV.2",93 "short": "Circumscribe about circle",94 "book": 4,95 "number": 2,96 "colorClass": "definition"97 },98 {99 "id": "Def3",100 "type": "definition",101 "label": "Circle inscribed in figure when each side touches circle",102 "shortLabel": "Def. IV.3",103 "short": "Inscribe circle in figure",104 "book": 4,105 "number": 3,106 "colorClass": "definition"107 },108 {109 "id": "Def4",110 "type": "definition",111 "label": "Circle circumscribed about figure when each vertex on circumference",112 "shortLabel": "Def. IV.4",113 "short": "Circumscribe circle about figure",114 "book": 4,115 "number": 4,116 "colorClass": "definition"117 },118 {119 "id": "Def5",120 "type": "definition",121 "label": "Figure inscribed in figure when each vertex of inner on sides of outer",122 "shortLabel": "Def. IV.5",123 "short": "Inscribe in figure",124 "book": 4,125 "number": 5,126 "colorClass": "definition"127 },128 {129 "id": "Def6",130 "type": "definition",131 "label": "Figure circumscribed about figure when each side of outer touches inner",132 "shortLabel": "Def. IV.6",133 "short": "Circumscribe about figure",134 "book": 4,135 "number": 6,136 "colorClass": "definition"137 },138 {139 "id": "Def7",140 "type": "definition",141 "label": "Straight line inscribed in circle when its ends on circumference",142 "shortLabel": "Def. IV.7",143 "short": "Inscribe line in circle",144 "book": 4,145 "number": 7,146 "colorClass": "definition"147 },148 {149 "id": "Prop1",150 "type": "proposition",151 "label": "To fit into given circle a straight line equal to given, not greater than diameter",152 "shortLabel": "Prop. IV.1",153 "short": "Fit line in circle",154 "book": 4,155 "number": 1,156 "colorClass": "proposition"157 },158 {159 "id": "Prop2",160 "type": "proposition",161 "label": "To inscribe in given circle a triangle equiangular with given triangle",162 "shortLabel": "Prop. IV.2",163 "short": "Inscribe triangle in circle",164 "book": 4,165 "number": 2,166 "colorClass": "proposition"167 },168 {169 "id": "Prop3",170 "type": "proposition",171 "label": "To circumscribe about given circle a triangle equiangular with given",172 "shortLabel": "Prop. IV.3",173 "short": "Circumscribe triangle about circle",174 "book": 4,175 "number": 3,176 "colorClass": "proposition"177 },178 {179 "id": "Prop4",180 "type": "proposition",181 "label": "To inscribe a circle in a given triangle",182 "shortLabel": "Prop. IV.4",183 "short": "Inscribe circle in triangle",184 "book": 4,185 "number": 4,186 "colorClass": "proposition"187 },188 {189 "id": "Prop5",190 "type": "proposition",191 "label": "To circumscribe a circle about a given triangle",192 "shortLabel": "Prop. IV.5",193 "short": "Circumscribe circle about triangle",194 "book": 4,195 "number": 5,196 "colorClass": "proposition"197 },198 {199 "id": "Prop6",200 "type": "proposition",201 "label": "To inscribe a square in a given circle",202 "shortLabel": "Prop. IV.6",203 "short": "Inscribe square in circle",204 "book": 4,205 "number": 6,206 "colorClass": "proposition"207 },208 {209 "id": "Prop7",210 "type": "proposition",211 "label": "To circumscribe a square about a given circle",212 "shortLabel": "Prop. IV.7",213 "short": "Circumscribe square about circle",214 "book": 4,215 "number": 7,216 "colorClass": "proposition"217 },218 {219 "id": "Prop8",220 "type": "proposition",221 "label": "To inscribe a circle in a given square",222 "shortLabel": "Prop. IV.8",223 "short": "Inscribe circle in square",224 "book": 4,225 "number": 8,226 "colorClass": "proposition"227 },228 {229 "id": "Prop9",230 "type": "proposition",231 "label": "To circumscribe a circle about a given square",232 "shortLabel": "Prop. IV.9",233 "short": "Circumscribe circle about square",234 "book": 4,235 "number": 9,236 "colorClass": "proposition"237 },238 {239 "id": "Prop10",240 "type": "proposition",241 "label": "To construct isosceles triangle with each base angle double the remaining",242 "shortLabel": "Prop. IV.10",243 "short": "Isosceles triangle, base angles double",244 "book": 4,245 "number": 10,246 "colorClass": "proposition"247 },248 {249 "id": "Prop11",250 "type": "proposition",251 "label": "To inscribe an equilateral equiangular pentagon in a given circle",252 "shortLabel": "Prop. IV.11",253 "short": "Inscribe pentagon in circle",254 "book": 4,255 "number": 11,256 "colorClass": "proposition"257 },258 {259 "id": "Prop12",260 "type": "proposition",261 "label": "To circumscribe an equilateral equiangular pentagon about a given circle",262 "shortLabel": "Prop. IV.12",263 "short": "Circumscribe pentagon about circle",264 "book": 4,265 "number": 12,266 "colorClass": "proposition"267 },268 {269 "id": "Prop13",270 "type": "proposition",271 "label": "To inscribe a circle in a given equilateral equiangular pentagon",272 "shortLabel": "Prop. IV.13",273 "short": "Inscribe circle in pentagon",274 "book": 4,275 "number": 13,276 "colorClass": "proposition"277 },278 {279 "id": "Prop14",280 "type": "proposition",281 "label": "To circumscribe a circle about a given equilateral equiangular pentagon",282 "shortLabel": "Prop. IV.14",283 "short": "Circumscribe circle about pentagon",284 "book": 4,285 "number": 14,286 "colorClass": "proposition"287 },288 {289 "id": "Prop15",290 "type": "proposition",291 "label": "To inscribe an equilateral equiangular hexagon in a given circle",292 "shortLabel": "Prop. IV.15",293 "short": "Inscribe hexagon in circle",294 "book": 4,295 "number": 15,296 "colorClass": "proposition"297 },298 {299 "id": "Prop16",300 "type": "proposition",301 "label": "To inscribe an equilateral equiangular fifteen-angled figure in a given circle",302 "shortLabel": "Prop. IV.16",303 "short": "Inscribe 15-gon in circle",304 "book": 4,305 "number": 16,306 "colorClass": "proposition"307 }308 ],309 "edges": [310 {311 "from": "BookI",312 "to": "Def1"313 },314 {315 "from": "BookIII",316 "to": "Def1"317 },318 {319 "from": "BookI",320 "to": "Def2"321 },322 {323 "from": "BookIII",324 "to": "Def2"325 },326 {327 "from": "BookI",328 "to": "Def3"329 },330 {331 "from": "BookIII",332 "to": "Def3"333 },334 {335 "from": "BookI",336 "to": "Def4"337 },338 {339 "from": "BookIII",340 "to": "Def4"341 },342 {343 "from": "BookI",344 "to": "Def5"345 },346 {347 "from": "BookIII",348 "to": "Def5"349 },350 {351 "from": "BookI",352 "to": "Def6"353 },354 {355 "from": "BookIII",356 "to": "Def6"357 },358 {359 "from": "BookI",360 "to": "Def7"361 },362 {363 "from": "BookIII",364 "to": "Def7"365 },366 {367 "from": "BookI",368 "to": "Prop1"369 },370 {371 "from": "BookIII",372 "to": "Prop1"373 },374 {375 "from": "BookI",376 "to": "Prop2"377 },378 {379 "from": "BookIII",380 "to": "Prop2"381 },382 {383 "from": "BookI",384 "to": "Prop3"385 },386 {387 "from": "BookIII",388 "to": "Prop3"389 },390 {391 "from": "BookI",392 "to": "Prop4"393 },394 {395 "from": "BookIII",396 "to": "Prop4"397 },398 {399 "from": "BookI",400 "to": "Prop5"401 },402 {403 "from": "BookIII",404 "to": "Prop5"405 },406 {407 "from": "BookI",408 "to": "Prop6"409 },410 {411 "from": "BookIII",412 "to": "Prop6"413 },414 {415 "from": "Prop1",416 "to": "Prop6"417 },418 {419 "from": "BookI",420 "to": "Prop7"421 },422 {423 "from": "BookIII",424 "to": "Prop7"425 },426 {427 "from": "Prop6",428 "to": "Prop7"429 },430 {431 "from": "BookI",432 "to": "Prop8"433 },434 {435 "from": "BookIII",436 "to": "Prop8"437 },438 {439 "from": "Prop7",440 "to": "Prop8"441 },442 {443 "from": "BookI",444 "to": "Prop9"445 },446 {447 "from": "BookIII",448 "to": "Prop9"449 },450 {451 "from": "Prop8",452 "to": "Prop9"453 },454 {455 "from": "BookI",456 "to": "Prop10"457 },458 {459 "from": "BookIII",460 "to": "Prop10"461 },462 {463 "from": "Prop1",464 "to": "Prop10"465 },466 {467 "from": "Prop5",468 "to": "Prop10"469 },470 {471 "from": "PropII11",472 "to": "Prop10"473 },474 {475 "from": "BookI",476 "to": "Prop11"477 },478 {479 "from": "BookIII",480 "to": "Prop11"481 },482 {483 "from": "Prop2",484 "to": "Prop11"485 },486 {487 "from": "Prop10",488 "to": "Prop11"489 },490 {491 "from": "BookI",492 "to": "Prop12"493 },494 {495 "from": "BookIII",496 "to": "Prop12"497 },498 {499 "from": "Prop11",500 "to": "Prop12"501 },502 {503 "from": "BookI",504 "to": "Prop13"505 },506 {507 "from": "BookIII",508 "to": "Prop13"509 },510 {511 "from": "Prop11",512 "to": "Prop13"513 },514 {515 "from": "BookI",516 "to": "Prop14"517 },518 {519 "from": "BookIII",520 "to": "Prop14"521 },522 {523 "from": "Prop11",524 "to": "Prop14"525 },526 {527 "from": "BookI",528 "to": "Prop15"529 },530 {531 "from": "BookIII",532 "to": "Prop15"533 },534 {535 "from": "Prop1",536 "to": "Prop15"537 },538 {539 "from": "BookI",540 "to": "Prop16"541 },542 {543 "from": "BookIII",544 "to": "Prop16"545 },546 {547 "from": "Prop1",548 "to": "Prop16"549 },550 {551 "from": "Prop2",552 "to": "Prop16"553 },554 {555 "from": "Prop11",556 "to": "Prop16"557 }558 ],559 "colorScheme": {560 "foundation": {561 "fill": "#95a5a6",562 "stroke": "#7f8c8d"563 },564 "definition": {565 "fill": "#3498db",566 "stroke": "#2980b9"567 },568 "proposition": {569 "fill": "#1abc9c",570 "stroke": "#16a085"571 }572 }573}