@prefix rdf: . @prefix dbr: . @prefix dbo: . dbr:Analytic_geometry rdf:type dbo:Book . @prefix owl: . dbr:Analytic_geometry rdf:type owl:Thing . @prefix rdfs: . dbr:Analytic_geometry rdfs:label "\u0391\u03BD\u03B1\u03BB\u03C5\u03C4\u03B9\u03BA\u03AE \u03B3\u03B5\u03C9\u03BC\u03B5\u03C4\u03C1\u03AF\u03B1"@el , "Analytick\u00E1 geometrie"@cs , "Geometria analityczna"@pl , "Analytic geometry"@en , "Analitika geometrio"@eo , "Geometria anal\u00EDtica"@pt , "Geometr\u00EDa anal\u00EDtica"@es , "Analytisk geometri"@sv , "Geometria anal\u00EDtica"@ca , "Geoim\u00E9adracht anail\u00EDseach"@ga , "\u0647\u0646\u062F\u0633\u0629 \u062A\u062D\u0644\u064A\u0644\u064A\u0629"@ar , "\u0410\u043D\u0430\u043B\u0456\u0442\u0438\u0447\u043D\u0430 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0456\u044F"@uk , "\uD574\uC11D\uAE30\uD558\uD559"@ko , "Geometria analitica"@it , "Geometri analitis"@in , "\u0410\u043D\u0430\u043B\u0438\u0442\u0438\u0447\u0435\u0441\u043A\u0430\u044F \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u044F"@ru , "G\u00E9om\u00E9trie analytique"@fr , "\u89E3\u6790\u5E7E\u4F55\u5B66"@ja , "Analytische meetkunde"@nl , "Analytische Geometrie"@de , "\u89E3\u6790\u51E0\u4F55"@zh ; rdfs:comment "\u521D\u7B49\u5E7E\u4F55\u5B66\u306B\u304A\u3051\u308B\u89E3\u6790\u5E7E\u4F55\u5B66\uFF08\u304B\u3044\u305B\u304D\u304D\u304B\u304C\u304F\u3001\u82F1: analytic geometry \uFF09\u3042\u308B\u3044\u306F\u5EA7\u6A19\u5E7E\u4F55\u5B66\uFF08\u3056\u3072\u3087\u3046\u304D\u304B\u304C\u304F\u3001\u82F1: coordinate geometry \uFF09\u3001\u30C7\u30AB\u30EB\u30C8\u5E7E\u4F55\u5B66\uFF08\u30C7\u30AB\u30EB\u30C8\u304D\u304B\u304C\u304F\u3001\u82F1: Cartesian geometry \uFF09\u306F\u3001\u5EA7\u6A19\u3092\u7528\u3044\u3066\u4EE3\u6570\u7684\u306B\u56F3\u5F62\u3092\u8ABF\u3079\u308B\u5E7E\u4F55\u5B66\u3092\u3044\u3046\u3002\u5EA7\u6A19\u3092\u7528\u3044\u308B\u3068\u3044\u3046\u70B9\u306B\u304A\u3044\u3066\u3001\uFF08\u3088\u308A\u53E4\u5178\u7684\u306A\u3001\u30E6\u30FC\u30AF\u30EA\u30C3\u30C9\u306E\u539F\u8AD6\u306B\u3082\u3042\u308B\u3088\u3046\u306A\uFF09\u70B9\u3084\u76F4\u7DDA\u306A\u3069\u304C\u3069\u306E\u3088\u3046\u306A\u516C\u7406\u306B\u5F93\u3046\u304B\u3068\u3044\u3046\u3053\u3068\u306E\u307F\u306B\u3088\u3063\u3066\u56F3\u5F62\u3092\u8ABF\u3079\u308B\u7D9C\u5408\u5E7E\u4F55\u5B66 \u3068\u306F\u5BFE\u7167\u7684\u3067\u3042\u308B\u3002\u5EA7\u6A19\u3092\u5229\u7528\u3059\u308B\u3053\u3068\u306B\u3088\u308A\u3001\u56F3\u5F62\u306E\u3082\u3064\u6027\u8CEA\u3092\u5EA7\u6A19\u306E\u3042\u3044\u3060\u306B\u3042\u3089\u308F\u308C\u308B\u95A2\u4FC2\u5F0F\u3068\u3057\u3066\u7279\u5FB4\u3065\u3051\u305F\u308A\u3001\u6570\u3084\u5F0F\u3068\u3057\u3066\u56F3\u5F62\u3092\u53D6\u308A\u6271\u3063\u305F\u308A\u3059\u308B\u3053\u3068\u304C\u3067\u304D\u308B\u3002 \u3075\u3064\u3046\u306F\uFF08\u4E8C\u6B21\u5143\uFF09\u5E73\u9762\u4E0A\u306E\u70B9\u3001\u76F4\u7DDA\u306A\u3069\u3092\u6271\u3046\uFF08\u5E73\u9762\u89E3\u6790\u5E7E\u4F55\uFF09\u304B\uFF08\u4E09\u6B21\u5143\uFF09\u7A7A\u9593\u5185\u306E\u305D\u308C\u3089\u3092\u6271\u3046\uFF08\u7ACB\u4F53\u89E3\u6790\u5E7E\u4F55\uFF09\u3002"@ja , "Analitika geometrio, anka\u016D nomata koordinata geometrio kaj pli frue nomata kartezia geometrio, estas studo de geometrio uzanta la principojn de algebro. Kutime la karteziaj koordinatoj estas aplikitaj por manipuli ekvaciojn por ebenoj, rektoj, kurboj, cirkloj, en du, tri kaj iam en pli multaj dimensioj. Kiel instruite en lernejaj libroj, analitika geometrio povas esti eksplikita pli simple: \u011Di okupi\u011Das pri difinado de geometriaj formoj en nombra vojo, kaj ekstraktante nombran informon de tiu prezento. La nombra ela\u0135o, tamen, povus anka\u016D esti vektoro a\u016D . Iuj konsideras, ke la enkonduko de analitika geometrio estis la komenco de moderna matematiko."@eo , "La geometria analitica, chiamata anche geometria cartesiana da Cartesio, \u00E8 lo studio delle figure geometriche attraverso il sistema di coordinate oggi dette cartesiane, ma gi\u00E0 studiate nel Medioevo da Nicola d'Oresme. Ogni punto del piano cartesiano \u00E8 individuato dalle sue coordinate su due assi: ascisse (x) e ordinate (y), nello spazio \u00E8 individuato da 3 coordinate (x,y,z). Le coordinate determinano un vettore rispettivamente del tipo oppure . Gli enti geometrici come rette, curve, poligoni sono definiti tramite equazioni, disequazioni o insiemi di queste, detti sistemi."@it , "De analytische meetkunde, ook wel bekend als Cartesiaanse meetkunde, is de studie van meetkunde die de principes van algebra gebruikt. Dat de algebra van de re\u00EBle getallen resultaten geeft met betrekking tot meetkundige concepten als punten en lijnen hangt af van het axioma van Cantor-Dedekind, dat stelt dat punten op een lijn een eenduidige correspondentie hebben met de re\u00EBle getallen. Gewoonlijk wordt het Cartesisch co\u00F6rdinatenstelsel toegepast om vergelijkingen voor vlakken, lijnen, krommen en cirkels te manipuleren, vaak in twee of drie, maar in principe in willekeurig veel dimensies. Sommigen zijn van mening dat de introductie van analytische meetkunde door Ren\u00E9 Descartes het begin van moderne wiskunde was."@nl , "Iarracht fadhbanna geoim\u00E9adracha a r\u00E9iteach tr\u00ED chomhordan\u00E1id\u00ED a dh\u00E1ileadh ar gach pointe. Tugtar geoim\u00E9adracht Chairt\u00E9iseach n\u00F3 geoim\u00E9adracht chomhordan\u00E1ideach uirthi freisin. Maidir leis an bpl\u00E1na, is \u00E9 an c\u00F3ras is coitianta n\u00E1 dh\u00E1 ais ingearacha, ionas gur f\u00E9idir gach pointe a lua mar ph\u00E9ire uimhreacha (x, y). I ngeoim\u00E9adracht thr\u00EDthoiseach, tr\u00EDr\u00EDn uimhreacha a \u00FAs\u00E1idtear (x, y, z). T\u00E1 c\u00F3rais comhordan\u00E1id\u00ED eile ann a bh\u00EDonn \u00E1isi\u00FAil i gc\u00E1sanna, mar shampla, comhordan\u00E1id\u00ED polacha d'fhadhbanna a bhaineann le feinim\u00E9in thr\u00EDthoiseacha, eagraithe timpeall l\u00E1rphointe. Luaitear Descartes mar cheapad\u00F3ir an ch\u00F3rais seo, b\u00EDodh is gur bhain Apall\u00F3inias feidhm as aiseanna ina staid\u00E9ar ar ch\u00F3nghearrtha\u00ED."@ga , "\u89E3\u6790\u51E0\u4F55\uFF08\u82F1\u8A9E\uFF1AAnalytic geometry\uFF09\uFF0C\u53C8\u7A31\u70BA\u5750\u6807\u51E0\u4F55\uFF08\u82F1\u8A9E\uFF1ACoordinate geometry\uFF09\u6216\u5361\u6C0F\u5E7E\u4F55\uFF08\u82F1\u8A9E\uFF1ACartesian geometry\uFF09\uFF0C\u65E9\u5148\u88AB\u53EB\u4F5C\u7B1B\u5361\u5152\u51E0\u4F55\uFF0C\u662F\u4E00\u79CD\u501F\u52A9\u4E8E\u89E3\u6790\u5F0F\u8FDB\u884C\u56FE\u5F62\u7814\u7A76\u7684\u51E0\u4F55\u5B66\u5206\u652F\u3002\u89E3\u6790\u51E0\u4F55\u901A\u5E38\u4F7F\u7528\u4E8C\u7EF4\u7684\u5E73\u9762\u76F4\u89D2\u5750\u6807\u7CFB\u7814\u7A76\u76F4\u7EBF\u3001\u5706\u3001\u5706\u9525\u66F2\u7EBF\u3001\u6446\u7EBF\u3001\u661F\u5F62\u7EBF\u7B49\u5404\u79CD\u4E00\u822C\u5E73\u9762\u66F2\u7EBF\uFF0C\u4F7F\u7528\u4E09\u7EF4\u7684\u7A7A\u95F4\u76F4\u89D2\u5750\u6807\u7CFB\u6765\u7814\u7A76\u5E73\u9762\u3001\u7403\u7B49\u5404\u79CD\u4E00\u822C\u7A7A\u95F4\u66F2\u9762\uFF0C\u540C\u65F6\u7814\u7A76\u5B83\u4EEC\u7684\u65B9\u7A0B\uFF0C\u5E76\u5B9A\u4E49\u4E00\u4E9B\u56FE\u5F62\u7684\u6982\u5FF5\u548C\u53C2\u6570\u3002 \u5728\u4E2D\u5B66\u8BFE\u672C\u4E2D\uFF0C\u89E3\u6790\u51E0\u4F55\u88AB\u7B80\u5355\u5730\u89E3\u91CA\u4E3A\uFF1A\u91C7\u7528\u6570\u503C\u7684\u65B9\u6CD5\u6765\u5B9A\u4E49\u51E0\u4F55\u5F62\u72B6\uFF0C\u5E76\u4ECE\u4E2D\u63D0\u53D6\u6570\u503C\u7684\u4FE1\u606F\u3002\u7136\u800C\uFF0C\u8FD9\u79CD\u6570\u503C\u7684\u8F93\u51FA\u53EF\u80FD\u662F\u4E00\u4E2A\u65B9\u7A0B\u6216\u8005\u662F\u4E00\u79CD\u51E0\u4F55\u5F62\u72B6\u3002 1637\u5E74\uFF0C\u7B1B\u5361\u5152\u5728\u300A\u65B9\u6CD5\u8BBA\u300B\u7684\u9644\u5F55\u201C\u51E0\u4F55\u201D\u4E2D\u63D0\u51FA\u4E86\u89E3\u6790\u51E0\u4F55\u7684\u57FA\u672C\u65B9\u6CD5\u3002\u4EE5\u54F2\u5B66\u89C2\u70B9\u5199\u6210\u7684\u8FD9\u90E8\u6CD5\u8BED\u8457\u4F5C\u4E3A\u540E\u6765\u725B\u987F\u548C\u83B1\u5E03\u5C3C\u8328\u5404\u81EA\u63D0\u51FA\u5FAE\u79EF\u5206\u5B66\u63D0\u4F9B\u4E86\u57FA\u7840\u3002 \u5BF9\u4EE3\u6570\u51E0\u4F55\u5B66\u8005\u6765\u8BF4\uFF0C\u89E3\u6790\u51E0\u4F55\u4E5F\u6307\uFF08\u5B9E\u6216\u8005\u8907\uFF09\u6D41\u5F62\uFF0C\u6216\u8005\u66F4\u5E7F\u4E49\u5730\u901A\u8FC7\u4E00\u4E9B\u8907\u8B8A\u6578\uFF08\u6216\u5BE6\u8B8A\u6578\uFF09\u7684\u89E3\u6790\u51FD\u6570\u4E3A\u96F6\u800C\u5B9A\u4E49\u7684\u89E3\u6790\u7A7A\u95F4\u7406\u8BBA\u3002\u8FD9\u4E00\u7406\u8BBA\u975E\u5E38\u63A5\u8FD1\u4EE3\u6570\u51E0\u4F55\uFF0C\u7279\u522B\u662F\u901A\u8FC7\u8BA9-\u76AE\u57C3\u5C14\u00B7\u585E\u5C14\u5728\u300A\u4EE3\u6570\u51E0\u4F55\u548C\u89E3\u6790\u51E0\u4F55\u300B\u9886\u57DF\u7684\u5DE5\u4F5C\u3002\u8FD9\u662F\u4E00\u4E2A\u6BD4\u4EE3\u6570\u51E0\u4F55\u66F4\u5927\u7684\u9886\u57DF\uFF0C\u4E0D\u8FC7\u4E5F\u53EF\u4EE5\u4F7F\u7528\u7C7B\u4F3C\u7684\u65B9\u6CD5\u3002"@zh , "Na matem\u00E1tica cl\u00E1ssica, a geometria anal\u00EDtica, tamb\u00E9m chamada geometria de coordenadas e de geometria cartesiana, \u00E9 o estudo da geometria por meio de um sistema de coordenadas e dos princ\u00EDpios da \u00E1lgebra e da an\u00E1lise. Contrasta com a abordagem sint\u00E9tica da geometria euclidiana, em que certas no\u00E7\u00F5es geom\u00E9tricas s\u00E3o consideradas primitivas, e \u00E9 utilizado o racioc\u00EDnio dedutivo a partir de axiomas e teoremas para obter proposi\u00E7\u00F5es verdadeiras."@pt , "\u0391\u03BD\u03B1\u03BB\u03C5\u03C4\u03B9\u03BA\u03AE \u03B3\u03B5\u03C9\u03BC\u03B5\u03C4\u03C1\u03AF\u03B1 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03C4\u03BF \u03B5\u03AF\u03B4\u03BF\u03C2 \u03C4\u03B7\u03C2 \u03B3\u03B5\u03C9\u03BC\u03B5\u03C4\u03C1\u03AF\u03B1\u03C2 \u03C0\u03BF\u03C5 \u03B8\u03B5\u03C9\u03C1\u03B5\u03AF \u03C4\u03BF\u03BD \u03B3\u03B5\u03C9\u03BC\u03B5\u03C4\u03C1\u03B9\u03BA\u03CC \u03C7\u03CE\u03C1\u03BF \u03B4\u03B9\u03B1\u03BD\u03C5\u03C3\u03BC\u03B1\u03C4\u03B9\u03BA\u03CC \u03C7\u03CE\u03C1\u03BF. \u039A\u03AC\u03B8\u03B5 \u03B4\u03B9\u03AC\u03BD\u03C5\u03C3\u03BC\u03B1 \u03B1\u03BD\u03C4\u03B9\u03C3\u03C4\u03BF\u03B9\u03C7\u03B5\u03AF \u03C3\u03B5 \u03AD\u03BD\u03B1 \u03C3\u03B7\u03BC\u03B5\u03AF\u03BF \u03C4\u03BF\u03C5 \u03C7\u03CE\u03C1\u03BF\u03C5, \u03B5\u03BD\u03CE \u03C4\u03B1 \u03B3\u03B5\u03C9\u03BC\u03B5\u03C4\u03C1\u03B9\u03BA\u03AC \u03C3\u03C7\u03AE\u03BC\u03B1\u03C4\u03B1 \u03BA\u03B1\u03B9 \u03BF\u03B9 \u03B3\u03B5\u03C9\u03BC\u03B5\u03C4\u03C1\u03B9\u03BA\u03AD\u03C2 \u03C3\u03C7\u03AD\u03C3\u03B5\u03B9\u03C2 \u03BC\u03B5\u03C4\u03B1\u03BE\u03CD \u03C4\u03C9\u03BD \u03C3\u03B7\u03BC\u03B5\u03AF\u03C9\u03BD \u03BA\u03B1\u03B9 \u03B4\u03B9\u03AC\u03C6\u03BF\u03C1\u03C9\u03BD \u03C3\u03C7\u03B7\u03BC\u03AC\u03C4\u03C9\u03BD \u03C0\u03B5\u03C1\u03B9\u03B3\u03C1\u03AC\u03C6\u03BF\u03BD\u03C4\u03B1\u03B9 \u03BC\u03B5 \u03B4\u03B9\u03B1\u03BD\u03C5\u03C3\u03BC\u03B1\u03C4\u03B9\u03BA\u03AD\u03C2 \u03C3\u03C7\u03AD\u03C3\u03B5\u03B9\u03C2 \u03BF\u03B9 \u03BF\u03C0\u03BF\u03AF\u03B5\u03C2 \u03BC\u03C0\u03BF\u03C1\u03BF\u03CD\u03BD \u03BD\u03B1 \u03C5\u03C0\u03BF\u03C3\u03C4\u03BF\u03CD\u03BD \u03B5\u03C0\u03B5\u03BE\u03B5\u03C1\u03B3\u03B1\u03C3\u03AF\u03B1 \u03CC\u03C0\u03C9\u03C2 \u03BA\u03B1\u03B9 \u03BF\u03B9 \u03B1\u03BB\u03B3\u03B5\u03B2\u03C1\u03B9\u03BA\u03AD\u03C2. \u0388\u03C4\u03C3\u03B9 \u03BC\u03AD\u03C3\u03C9 \u03C4\u03B7\u03C2 \u03B1\u03BD\u03B1\u03BB\u03C5\u03C4\u03B9\u03BA\u03AE\u03C2 \u03B3\u03B5\u03C9\u03BC\u03B5\u03C4\u03C1\u03AF\u03B1\u03C2 \u03AD\u03B3\u03B9\u03BD\u03B5 \u03BC\u03B9\u03B1 \u03B1\u03BB\u03B3\u03B5\u03B2\u03C1\u03BF\u03C0\u03BF\u03AF\u03B7\u03C3\u03B7 \u03C4\u03B7\u03C2 \u03B3\u03B5\u03C9\u03BC\u03B5\u03C4\u03C1\u03AF\u03B1\u03C2, \u03C3\u03B5 \u03C3\u03B7\u03BC\u03B5\u03AF\u03BF \u03CE\u03C3\u03C4\u03B5 \u03BD\u03B1 \u03C5\u03C0\u03BF\u03C3\u03C4\u03B7\u03C1\u03AF\u03B6\u03B5\u03C4\u03B1\u03B9 \u03CC\u03C4\u03B9 \u03C0\u03BB\u03AD\u03BF\u03BD \u03B7 \u03B3\u03B5\u03C9\u03BC\u03B5\u03C4\u03C1\u03AF\u03B1 \u03B4\u03B5 \u03C7\u03C1\u03B5\u03B9\u03AC\u03B6\u03B5\u03C4\u03B1\u03B9 \u03BA\u03B1\u03B8\u03CC\u03BB\u03BF\u03C5 \u03B1\u03BE\u03B9\u03C9\u03BC\u03B1\u03C4\u03B9\u03BA\u03AE \u03B8\u03B5\u03BC\u03B5\u03BB\u03AF\u03C9\u03C3\u03B7, \u03B1\u03BB\u03BB\u03AC \u03B1\u03C1\u03BA\u03B5\u03AF \u03BD\u03B1 \u03C3\u03C4\u03B7\u03C1\u03B9\u03C7\u03B8\u03B5\u03AF \u03BC\u03AD\u03C3\u03C9 \u03BA\u03B1\u03C4\u03AC\u03BB\u03BB\u03B7\u03BB\u03C9\u03BD \u03BF\u03C1\u03B9\u03C3\u03BC\u03CE\u03BD \u03C3\u03C4\u03B7\u03BD \u03AC\u03BB\u03B3\u03B5\u03B2\u03C1\u03B1."@el , "\u0410\u043D\u0430\u043B\u0438\u0442\u0438\u0301\u0447\u0435\u0441\u043A\u0430\u044F \u0433\u0435\u043E\u043C\u0435\u0301\u0442\u0440\u0438\u044F \u2014 \u0440\u0430\u0437\u0434\u0435\u043B \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0438, \u0432 \u043A\u043E\u0442\u043E\u0440\u043E\u043C \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043A\u0438\u0435 \u0444\u0438\u0433\u0443\u0440\u044B \u0438 \u0438\u0445 \u0441\u0432\u043E\u0439\u0441\u0442\u0432\u0430 \u0438\u0441\u0441\u043B\u0435\u0434\u0443\u044E\u0442\u0441\u044F \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0430\u043C\u0438 \u0430\u043B\u0433\u0435\u0431\u0440\u044B. \u0412 \u043E\u0441\u043D\u043E\u0432\u0435 \u044D\u0442\u043E\u0433\u043E \u043C\u0435\u0442\u043E\u0434\u0430 \u043B\u0435\u0436\u0438\u0442 \u0442\u0430\u043A \u043D\u0430\u0437\u044B\u0432\u0430\u0435\u043C\u044B\u0439 \u043C\u0435\u0442\u043E\u0434 \u043A\u043E\u043E\u0440\u0434\u0438\u043D\u0430\u0442, \u0432\u043F\u0435\u0440\u0432\u044B\u0435 \u043F\u0440\u0438\u043C\u0435\u043D\u0451\u043D\u043D\u044B\u0439 \u0414\u0435\u043A\u0430\u0440\u0442\u043E\u043C \u0432 1637 \u0433\u043E\u0434\u0443. \u041A\u0430\u0436\u0434\u043E\u043C\u0443 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043A\u043E\u043C\u0443 \u0441\u043E\u043E\u0442\u043D\u043E\u0448\u0435\u043D\u0438\u044E \u044D\u0442\u043E\u0442 \u043C\u0435\u0442\u043E\u0434 \u0441\u0442\u0430\u0432\u0438\u0442 \u0432 \u0441\u043E\u043E\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0438\u0435 \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u043E\u0435 \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u0435, \u0441\u0432\u044F\u0437\u044B\u0432\u0430\u044E\u0449\u0435\u0435 \u043A\u043E\u043E\u0440\u0434\u0438\u043D\u0430\u0442\u044B \u0444\u0438\u0433\u0443\u0440\u044B \u0438\u043B\u0438 \u0442\u0435\u043B\u0430. \u0422\u0430\u043A\u043E\u0439 \u043C\u0435\u0442\u043E\u0434 \u00AB\u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0437\u0430\u0446\u0438\u0438\u00BB \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u0441\u0432\u043E\u0439\u0441\u0442\u0432 \u0434\u043E\u043A\u0430\u0437\u0430\u043B \u0441\u0432\u043E\u044E \u0443\u043D\u0438\u0432\u0435\u0440\u0441\u0430\u043B\u044C\u043D\u043E\u0441\u0442\u044C \u0438 \u043F\u043B\u043E\u0434\u043E\u0442\u0432\u043E\u0440\u043D\u043E \u043F\u0440\u0438\u043C\u0435\u043D\u044F\u0435\u0442\u0441\u044F \u0432\u043E \u043C\u043D\u043E\u0433\u0438\u0445 \u0435\u0441\u0442\u0435\u0441\u0442\u0432\u0435\u043D\u043D\u044B\u0445 \u043D\u0430\u0443\u043A\u0430\u0445 \u0438 \u0432 \u0442\u0435\u0445\u043D\u0438\u043A\u0435. \u0412 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0435 \u0430\u043D\u0430\u043B\u0438\u0442\u0438\u0447\u0435\u0441\u043A\u0430\u044F \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u044F \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u0442\u0430\u043A\u0436\u0435 \u043E\u0441\u043D\u043E\u0432\u043E\u0439 \u0434\u043B\u044F \u0434\u0440\u0443\u0433\u0438\u0445 \u0440\u0430\u0437\u0434\u0435\u043B\u043E\u0432 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0438 \u2014 \u043D\u0430\u043F\u0440\u0438\u043C\u0435\u0440, \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u043E\u0439, \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u043E\u0439, \u043A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0440\u043D\u043E\u0439 \u0438 \u0432\u044B\u0447\u0438\u0441\u043B\u0438\u0442\u0435\u043B\u044C\u043D\u043E\u0439 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0438."@ru , "La geometria anal\u00EDtica \u00E9s la part de les matem\u00E0tiques que fa \u00FAs de l'\u00E0lgebra per descriure i analitzar figures geom\u00E8triques. En el seg\u00FCent exemple tenim l'expressi\u00F3: que representa, en la geometria anal\u00EDtica plana, una el\u00B7lipse centrada en l'origen d'un sistema de coordenades cartesianes, que t\u00E9 el valor a com semieix major i el valor b com semieix menor. L'eix major \u00E9s l'eix de les abscisses X. Els raonaments anteriors s\u00F3n tanmateix v\u00E0lids per un punt a l'espai i una terna ordenada de nombres."@ca , "La g\u00E9om\u00E9trie analytique est une approche de la g\u00E9om\u00E9trie dans laquelle les objets sont d\u00E9crits par des \u00E9quations ou des in\u00E9quations \u00E0 l'aide d'un syst\u00E8me de coordonn\u00E9es.Elle est fondamentale pour la physique et l'infographie. En g\u00E9om\u00E9trie analytique, le choix d'un rep\u00E8re est indispensable. Tous les objets seront d\u00E9crits relativement \u00E0 ce rep\u00E8re. Article d\u00E9taill\u00E9 : Rep\u00E9rage dans le plan et dans l'espace."@fr , "Geometria analityczna \u2013 dzia\u0142 geometrii zajmuj\u0105cy si\u0119 badaniem figur geometrycznych metodami analitycznymi (obliczeniowymi) i algebraicznymi. Z\u0142o\u017Cone rozwa\u017Cania geometryczne zostaj\u0105 w geometrii analitycznej sprowadzone do rozwi\u0105zywania uk\u0142ad\u00F3w r\u00F3wna\u0144, kt\u00F3re opisuj\u0105 badane figury. Przedmiotem bada\u0144 geometrii analitycznej jest zasadniczo przestrze\u0144 euklidesowa i w\u0142asno\u015Bci jej podzbior\u00F3w, cho\u0107 wiele wynik\u00F3w mo\u017Cna uog\u00F3lni\u0107 na dowolne, sko\u0144czenie wymiarowe przestrzenie liniowe."@pl , "\uD574\uC11D\uAE30\uD558\uD559(\u89E3\u6790\u5E7E\u4F55\u5B78, analytic geometry)\uC774\uB780 \uC5EC\uB7EC \uAC1C\uC758 \uC218\uB85C \uC774\uB904\uC9C4 \uC21C\uC11C\uC30D(\uB610\uB294 \uC88C\uD45C)\uC744 \uAE30\uD558\uD559\uC801\uC73C\uB85C \uB098\uD0C0\uB0B4\uB294 \uBC29\uBC95\uC778 \uC88C\uD45C\uAE30\uD558\uD559 \uB610\uB294 \uCE74\uD14C\uC2DC\uC548 \uAE30\uD558\uD559\uC744 \uB2EC\uB9AC \uBD80\uB974\uB294 \uC774\uB984\uC774\uB2E4. n\uAC1C\uC758 \uC218\uB97C \uC0AC\uC6A9\uD558\uC5EC \uB098\uD0C0\uB0B8 n-\uC21C\uC11C\uC30D\uC758 \uC218\uB97C \uBBF8\uC9C0\uC218\uB85C \uD558\uB294 \uBC29\uC815\uC2DD\uC758 \uD615\uD0DC\uB85C \uB3C4\uD615\uC758 \uC131\uC9C8\uC744 \uC124\uBA85\uD55C\uB2E4. \uC774\uB54C 2\uCC28\uC6D0 \uC88C\uD45C\uACC4 \uD3C9\uBA74\uC5D0\uC11C\uB294 n=2\uC774\uACE0, 3\uCC28\uC6D0 \uC88C\uD45C\uACC4 \uACF5\uAC04\uC5D0\uC11C\uB294 n=3\uC774\uB2E4. \uC77C\uBC18\uC801\uC73C\uB85C \uC218\uD559\uC790\uB4E4\uC740 \uD574\uC11D\uAE30\uD558\uD559\uC5D0\uC11C \uBC29\uC815\uC2DD\uC744 \uB300\uC218\uC801\uC73C\uB85C \uB098\uD0C0\uB0B4\uC5B4 \uB2E4\uB8F8\uC73C\uB85C\uC368 \uB3C4\uD615\uC758 \uC704\uCE58 \uBC0F \uD615\uD0DC\uB97C \uACB0\uC815\uD558\uAC70\uB098 \uBD84\uB958\uD55C\uB2E4. \uD574\uC11D\uAE30\uD558\uD559\uC740 \uC218\uD559\uC5D0\uC11C 2\uAC00\uC9C0 \uB73B\uC73C\uB85C \uD574\uC11D\uB41C\uB2E4. \uD604\uB300\uC801\uC778 \uC758\uBBF8\uC5D0\uC11C\uB294 \uC758 \uAE30\uD558\uD559\uC744 \uAC00\uB9AC\uD0A8\uB2E4. \uC774 \uAE00\uC740 \uACE0\uC804\uC801\uC774\uACE0 \uAE30\uCD08\uC801\uC778 \uC758\uBBF8 \uC704\uC8FC\uB85C \uC124\uBA85\uD55C\uB2E4. \uACE0\uC804 \uC218\uD559\uC5D0\uC11C \uD574\uC11D\uAE30\uD558\uD559\uC740 \uD574\uC11D\uD559\uACFC \uB300\uC218\uD559\uC758 \uC6D0\uCE59, \uADF8\uB9AC\uACE0 \uC88C\uD45C\uACC4\uB97C \uC774\uC6A9\uD55C \uAE30\uD558\uD559\uC774\uB2E4. \uC774\uB294 \uD2B9\uC815\uD55C \uAE30\uD558\uD559\uC801 \uAC1C\uB150\uC744 \uC73C\uB85C \uB2E4\uB8E8\uACE0\uACF5\uB9AC\uC640 \uC815\uB9AC\uC5D0 \uAE30\uBC18\uD55C \uCD94\uB860\uC744 \uC774\uC6A9\uD558\uB294 \uC720\uD074\uB9AC\uB4DC \uAE30\uD558\uD559\uC758 \uACFC \uB300\uC870\uB41C\uB2E4."@ko , "In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight. It is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry."@en , "Die analytische Geometrie (auch Vektorgeometrie) ist ein Teilgebiet der Geometrie, das algebraische Hilfsmittel (vor allem aus der linearen Algebra) zur L\u00F6sung geometrischer Probleme bereitstellt. Sie erm\u00F6glicht es in vielen F\u00E4llen, geometrische Aufgabenstellungen rein rechnerisch zu l\u00F6sen, ohne die Anschauung zu Hilfe zu nehmen. Demgegen\u00FCber wird Geometrie, die ihre S\u00E4tze ohne Bezug zu einem Zahlensystem auf einer axiomatischen Grundlage begr\u00FCndet, als synthetische Geometrie bezeichnet."@de , "La geometr\u00EDa anal\u00EDtica es una rama de las matem\u00E1ticas que estudia las figuras, sus distancias, sus \u00E1reas, puntos de intersecci\u00F3n, \u00E1ngulos de inclinaci\u00F3n, puntos de divisi\u00F3n, vol\u00FAmenes, etc\u00E9tera. Analiza con detalle los datos de las figuras geom\u00E9tricas mediante t\u00E9cnicas b\u00E1sicas del an\u00E1lisis matem\u00E1tico y del \u00E1lgebra en un determinado sistema de coordenadas. Su desarrollo hist\u00F3rico comienza con la geometr\u00EDa cartesiana, contin\u00FAa con la aparici\u00F3n de la geometr\u00EDa diferencial de Carl Friedrich Gauss y m\u00E1s tarde con el desarrollo de la geometr\u00EDa algebraica. Tiene m\u00FAltiples aplicaciones, m\u00E1s all\u00E1 de las matem\u00E1ticas y la ingenier\u00EDa, pues forma parte ahora del trabajo de administradores para la planeaci\u00F3n de estrategias y log\u00EDstica en la toma de decisiones."@es , "Analytick\u00E1 geometrie (tak\u00E9 sou\u0159adnicov\u00E1 geometrie nebo kart\u00E9zsk\u00E1 geometrie) je \u010D\u00E1st geometrie, kter\u00E1 zkoum\u00E1 geometrick\u00E9 \u00FAtvary v euklidovsk\u00E9 geometrii pomoc\u00ED algebraick\u00FDch a analytick\u00FDch metod. V analytick\u00E9 geometrii jsou geometrick\u00E9 \u00FAtvary v prostoru vyjad\u0159ov\u00E1ny \u010D\u00EDsly a rovnicemi ve zvolen\u00FDch sou\u0159adnicov\u00FDch soustav\u00E1ch.Mnoh\u00E9 probl\u00E9my analytick\u00E9 geometrie jsou \u00FAzce sv\u00E1z\u00E1ny s line\u00E1rn\u00ED algebrou."@cs , "\u0410\u043D\u0430\u043B\u0456\u0442\u0438\u0301\u0447\u043D\u0430 \u0433\u0435\u043E\u043C\u0435\u0301\u0442\u0440\u0456\u044F \u2014 \u0440\u043E\u0437\u0434\u0456\u043B \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0456\u0457, \u0432 \u044F\u043A\u043E\u043C\u0443 \u0432\u043B\u0430\u0441\u0442\u0438\u0432\u043E\u0441\u0442\u0456 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u043D\u0438\u0445 \u043E\u0431'\u0454\u043A\u0442\u0456\u0432 (\u0442\u043E\u0447\u043E\u043A, \u043B\u0456\u043D\u0456\u0439, \u043F\u043E\u0432\u0435\u0440\u0445\u043E\u043D\u044C) \u0443\u0441\u0442\u0430\u043D\u043E\u0432\u043B\u044E\u044E\u0442\u044C \u0437\u0430\u0441\u043E\u0431\u0430\u043C\u0438 \u0430\u043B\u0433\u0435\u0431\u0440\u0438 \u0437\u0430 \u0434\u043E\u043F\u043E\u043C\u043E\u0433\u043E\u044E \u043C\u0435\u0442\u043E\u0434\u0443 \u043A\u043E\u043E\u0440\u0434\u0438\u043D\u0430\u0442, \u0442\u043E\u0431\u0442\u043E \u0448\u043B\u044F\u0445\u043E\u043C \u0434\u043E\u0441\u043B\u0456\u0434\u0436\u0435\u043D\u043D\u044F \u0432\u043B\u0430\u0441\u0442\u0438\u0432\u043E\u0441\u0442\u0435\u0439 \u0440\u0456\u0432\u043D\u044F\u043D\u044C, \u044F\u043A\u0456 \u0456 \u0432\u0438\u0437\u043D\u0430\u0447\u0430\u044E\u0442\u044C \u0446\u0456 \u043E\u0431'\u0454\u043A\u0442\u0438. \u041E\u0441\u043D\u043E\u0432\u043D\u0456 \u043F\u043E\u043B\u043E\u0436\u0435\u043D\u043D\u044F \u0430\u043D\u0430\u043B\u0456\u0442\u0438\u0447\u043D\u043E\u0457 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0456\u0457 \u0432\u043F\u0435\u0440\u0448\u0435 \u0441\u0444\u043E\u0440\u043C\u0443\u043B\u044E\u0432\u0430\u0432 \u0444\u0456\u043B\u043E\u0441\u043E\u0444 \u0456 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A \u0420\u0435\u043D\u0435 \u0414\u0435\u043A\u0430\u0440\u0442 1637 \u0440\u043E\u043A\u0443. \u041B\u0435\u0439\u0431\u043D\u0456\u0446, \u0406\u0441\u0430\u0430\u043A \u041D\u044C\u044E\u0442\u043E\u043D \u0456 \u041B\u0435\u043E\u043D\u0430\u0440\u0434 \u0415\u0439\u043B\u0435\u0440 \u043D\u0430\u0434\u0430\u043B\u0438 \u0430\u043D\u0430\u043B\u0456\u0442\u0438\u0447\u043D\u0456\u0439 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0456\u0457 \u0441\u0443\u0447\u0430\u0441\u043D\u043E\u0457 \u0441\u0442\u0440\u0443\u043A\u0442\u0443\u0440\u0438."@uk , "Den analytiska geometrin \u00E4r en gren av geometrin d\u00E4r algebraiska metoder fr\u00E5n fr\u00E4mst linj\u00E4r algebra anv\u00E4nds f\u00F6r att l\u00F6sa geometriska problem. Att de reella talens algebra kan anv\u00E4ndas f\u00F6r l\u00F6sning av geometriska problem vilar p\u00E5 Cantor-Dedekinds axiom."@sv , "\u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0627\u0644\u0643\u0644\u0627\u0633\u064A\u0643\u064A\u0629\u060C \u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u062A\u062D\u0644\u064A\u0644\u064A\u0629 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Analytic geometry)\u200F \u0648\u062A\u062F\u0639\u0649 \u0623\u064A\u0636\u0627\u064B \u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u0625\u062D\u062F\u0627\u062B\u064A\u0629 \u0623\u0648 \u0627\u0644\u062A\u0646\u0633\u064A\u0642\u064A\u0629 \u0648\u0633\u0627\u0628\u0642\u0627\u064B \u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u062F\u064A\u0643\u0627\u0631\u062A\u064A\u0629\u060C \u0647\u064A \u0641\u0631\u0639 \u0627\u0644\u0645\u0639\u0631\u0641\u0629 \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0629 \u0627\u0644\u0630\u064A \u064A\u062F\u0631\u0633 \u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0628\u0627\u0633\u062A\u0639\u0645\u0627\u0644 \u0646\u0638\u0627\u0645 \u0627\u0644\u0625\u062D\u062F\u0627\u062B\u064A\u0627\u062A \u0648\u0645\u0628\u0627\u062F\u0626 \u0627\u0644\u062C\u0628\u0631 \u0648\u0627\u0644\u062A\u062D\u0644\u064A\u0644 \u0627\u0644\u0631\u064A\u0627\u0636\u064A. \u062A\u0633\u062A\u0639\u0645\u0644 \u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u062A\u062D\u0644\u064A\u0644\u064A\u0629 \u0628\u0634\u0643\u0644 \u0648\u0627\u0633\u0639 \u0641\u064A \u0627\u0644\u0641\u064A\u0632\u064A\u0627\u0621 \u0648\u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u062A\u0637\u0628\u064A\u0642\u064A\u0629 \u0643\u0645\u0627 \u062A\u0645\u062B\u0644 \u0627\u0644\u0623\u0633\u0627\u0633 \u0627\u0644\u0630\u064A \u0628\u064F\u0646\u064A \u0639\u0644\u064A\u0647 \u0628\u0627\u0642\u064A \u0645\u062C\u0627\u0644\u0627\u062A \u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0643\u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u062C\u0628\u0631\u064A\u0629 \u0648\u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u062A\u0641\u0627\u0636\u0644\u064A\u0629 \u0648\u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u0645\u062A\u0642\u0637\u0639\u0629 \u0648\u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u062D\u0627\u0633\u0648\u0628\u064A\u0629."@ar , "Geometri Analitis, juga disebut geometri koordinat dan dahulu disebut geometri Kartesius, adalah pembahasan geometri menggunakan prinsip-prinsip aljabar menggunakan bilangan riil. Biasanya, sistem koordinat Kartesius diterapkan untuk menyelesaikan persamaan , garis, garis lurus, dan persegi, yang sering dalam pengukuran 2 atau 3 dimensi. Seperti yang diajarkan di buku pelajaran sekolah, geometri analitis dapat dijelaskan dengan sederhana: terfokus pada pendefinisian bentuk bangun dalam bilangan dan menjadikan sebagai sebuah hasil perhitungan. Hasil perhitungan dapat diasumsikan sebagai sebuah vektor atau bangun. Bagaimanapun juga beberapa output numerik juga membentuk vektor. Ada anggapan bahwa lahirnya geometri analitis adalah permulaan matematika modern."@in . @prefix foaf: . dbr:Analytic_geometry foaf:depiction , , . @prefix dcterms: . @prefix dbc: . dbr:Analytic_geometry dcterms:subject dbc:Analytic_geometry ; dbo:wikiPageID 2202 ; dbo:wikiPageRevisionID 1124810809 ; dbo:wikiPageWikiLink dbr:Physics , dbr:Latin , dbr:Graph_of_a_function , dbr:Algebraic_equation , dbr:Projective_space , dbr:Differential_geometry , , dbr:Cartesian_plane , dbr:Cartesian_coordinate_system , dbr:Cartesian_coordinates , dbr:Ellipse , dbr:Discourse_on_Method , dbr:Frans_van_Schooten , dbr:Aviation , dbr:Aerospace_engineering , dbr:Mathematics_Teacher , dbr:Internet_Archive , dbr:Coordinate_system , dbr:Menaechmus , dbr:Ellipsoid , dbr:Quadratic_polynomial , , dbr:Algebraic_geometry , , dbr:Tangent_space , dbr:Calculus , dbr:Classical_mathematics , dbr:Force , dbr:Leonhard_Euler , dbr:Subset , dbr:Root_of_a_function , dbr:Space_science , , dbr:Engineering , dbr:Formula , dbr:Linear_equation , dbr:Solution_set , dbr:Dot_product , dbr:American_Mathematical_Monthly , dbr:Distance , , dbc:Analytic_geometry , dbr:Pierre_de_Fermat , dbr:Applied_mathematics , dbr:Conic_section , , dbr:Discriminant , , dbr:French_language , , dbr:Rotation_of_axes , dbr:Radius , dbr:Discrete_geometry , dbr:Real_number , , dbr:Derivative , dbr:The_Mathematical_Intelligencer , dbr:Curve , dbr:Geometric_algebra , dbr:Space_curve , dbr:Affine_coordinates , dbr:Tuple , dbr:Quadratic_equation , , dbr:Spherical_coordinates , , dbr:Omar_Khayyam , dbr:Tangent_line , dbr:Parabola , dbr:Orthogonality , dbr:Euclidean_space , dbr:Angle , dbr:Paraboloid , dbr:Circle , , dbr:Polar_coordinates , dbr:Ordered_pair , dbr:Sphere , dbr:Equation , dbr:Cones , , dbr:Hyperboloid , dbr:Apollonius_of_Perga , dbr:Vector_space , dbr:Pythagorean_theorem , dbr:Normal_vector , dbr:Infinitesimal , , dbr:Slope , , dbr:Euclidean_plane , dbr:Independent_variable , dbr:Translation_of_axes , , dbr:Euclidean_geometry , dbr:Geometry , dbr:Synthetic_geometry , dbr:Spaceflight , dbr:Parametric_equation , dbr:Computational_geometry , dbr:Y-intercept , dbr:Hyperbola , dbr:Cylindrical_coordinates , , dbr:Affine_transformations , dbr:Cross_product , dbr:Ancient_Greece , dbr:Perpendicular , dbr:Slope-intercept_form , dbr:Cubic_equation , dbr:Straight_line , dbr:Descartes . @prefix ns8: . dbr:Analytic_geometry dbo:wikiPageExternalLink ns8:historyofmathema00katz , ns8:cu31924001520455 , . @prefix dbpedia-simple: . dbr:Analytic_geometry owl:sameAs dbpedia-simple:Analytic_geometry , . @prefix wikidata: . dbr:Analytic_geometry owl:sameAs wikidata:Q134787 , . @prefix dbpedia-it: . dbr:Analytic_geometry owl:sameAs dbpedia-it:Geometria_analitica . @prefix dbpedia-nl: . dbr:Analytic_geometry owl:sameAs dbpedia-nl:Analytische_meetkunde , , , . @prefix dbpedia-als: . dbr:Analytic_geometry owl:sameAs dbpedia-als:Analytische_Geometrie , , , , . @prefix dbpedia-tr: . dbr:Analytic_geometry owl:sameAs dbpedia-tr:Analitik_geometri , . @prefix dbpedia-id: . dbr:Analytic_geometry owl:sameAs dbpedia-id:Geometri_analitis , . @prefix dbpedia-da: . dbr:Analytic_geometry owl:sameAs dbpedia-da:Analytisk_geometri , , . @prefix dbpedia-cy: . dbr:Analytic_geometry owl:sameAs dbpedia-cy:Geometreg_ddadansoddol , . @prefix ns18: . dbr:Analytic_geometry owl:sameAs ns18:Analitik_geometriya , , . @prefix dbpedia-la: . dbr:Analytic_geometry owl:sameAs dbpedia-la:Geometria_analytica , , , . @prefix dbpedia-io: . dbr:Analytic_geometry owl:sameAs dbpedia-io:Analitikala_geometrio , , , , , . @prefix ns21: . dbr:Analytic_geometry owl:sameAs ns21:Analitikong_heometriya , , , . @prefix dbpedia-nn: . dbr:Analytic_geometry owl:sameAs dbpedia-nn:Analytisk_geometri , , . @prefix ns23: . dbr:Analytic_geometry owl:sameAs ns23:Mr1F , , . @prefix dbpedia-pl: . dbr:Analytic_geometry owl:sameAs dbpedia-pl:Geometria_analityczna , , . @prefix dbpedia-de: . dbr:Analytic_geometry owl:sameAs dbpedia-de:Analytische_Geometrie , , , , , , . @prefix dbpedia-af: . dbr:Analytic_geometry owl:sameAs dbpedia-af:Analitiese_meetkunde , , , . @prefix dbpedia-fi: . dbr:Analytic_geometry owl:sameAs dbpedia-fi:Analyyttinen_geometria , . @prefix dbpedia-no: . dbr:Analytic_geometry owl:sameAs dbpedia-no:Analytisk_geometri , , . @prefix dbpedia-eo: . dbr:Analytic_geometry owl:sameAs dbpedia-eo:Analitika_geometrio . @prefix dbpedia-sv: . dbr:Analytic_geometry owl:sameAs dbpedia-sv:Analytisk_geometri , , , . @prefix ns31: . dbr:Analytic_geometry owl:sameAs ns31:Analytic_geometry . @prefix dbp: . @prefix dbt: . dbr:Analytic_geometry dbp:wikiPageUsesTemplate dbt:Spaces , dbt:Anchor , dbt:Descartes , dbt:Reflist , dbt:Main , dbt:Short_description , dbt:Cn_span , dbt:Authority_control , dbt:About , , dbt:Rp , dbt:Citation , dbt:Areas_of_mathematics , dbt:General_geometry ; dbo:thumbnail ; dbo:abstract "Den analytiska geometrin \u00E4r en gren av geometrin d\u00E4r algebraiska metoder fr\u00E5n fr\u00E4mst linj\u00E4r algebra anv\u00E4nds f\u00F6r att l\u00F6sa geometriska problem. Att de reella talens algebra kan anv\u00E4ndas f\u00F6r l\u00F6sning av geometriska problem vilar p\u00E5 Cantor-Dedekinds axiom. Metoder fr\u00E5n analytisk geometri anv\u00E4nds inom alla till\u00E4mpade vetenskaper, men s\u00E4rskilt inom fysiken, till exempel f\u00F6r beskrivningen av planeternas banor. Ursprungligen behandlade analytisk geometri endast fr\u00E5gor r\u00F6rande planet och den rumsliga (euklidiska) geometrin. Mera allm\u00E4nt beskriver den analytiska geometrin affina rum av godtyckliga dimensioner \u00F6ver godtyckliga kroppar."@sv , "\uD574\uC11D\uAE30\uD558\uD559(\u89E3\u6790\u5E7E\u4F55\u5B78, analytic geometry)\uC774\uB780 \uC5EC\uB7EC \uAC1C\uC758 \uC218\uB85C \uC774\uB904\uC9C4 \uC21C\uC11C\uC30D(\uB610\uB294 \uC88C\uD45C)\uC744 \uAE30\uD558\uD559\uC801\uC73C\uB85C \uB098\uD0C0\uB0B4\uB294 \uBC29\uBC95\uC778 \uC88C\uD45C\uAE30\uD558\uD559 \uB610\uB294 \uCE74\uD14C\uC2DC\uC548 \uAE30\uD558\uD559\uC744 \uB2EC\uB9AC \uBD80\uB974\uB294 \uC774\uB984\uC774\uB2E4. n\uAC1C\uC758 \uC218\uB97C \uC0AC\uC6A9\uD558\uC5EC \uB098\uD0C0\uB0B8 n-\uC21C\uC11C\uC30D\uC758 \uC218\uB97C \uBBF8\uC9C0\uC218\uB85C \uD558\uB294 \uBC29\uC815\uC2DD\uC758 \uD615\uD0DC\uB85C \uB3C4\uD615\uC758 \uC131\uC9C8\uC744 \uC124\uBA85\uD55C\uB2E4. \uC774\uB54C 2\uCC28\uC6D0 \uC88C\uD45C\uACC4 \uD3C9\uBA74\uC5D0\uC11C\uB294 n=2\uC774\uACE0, 3\uCC28\uC6D0 \uC88C\uD45C\uACC4 \uACF5\uAC04\uC5D0\uC11C\uB294 n=3\uC774\uB2E4. \uC77C\uBC18\uC801\uC73C\uB85C \uC218\uD559\uC790\uB4E4\uC740 \uD574\uC11D\uAE30\uD558\uD559\uC5D0\uC11C \uBC29\uC815\uC2DD\uC744 \uB300\uC218\uC801\uC73C\uB85C \uB098\uD0C0\uB0B4\uC5B4 \uB2E4\uB8F8\uC73C\uB85C\uC368 \uB3C4\uD615\uC758 \uC704\uCE58 \uBC0F \uD615\uD0DC\uB97C \uACB0\uC815\uD558\uAC70\uB098 \uBD84\uB958\uD55C\uB2E4. \uD574\uC11D\uAE30\uD558\uD559\uC740 \uC218\uD559\uC5D0\uC11C 2\uAC00\uC9C0 \uB73B\uC73C\uB85C \uD574\uC11D\uB41C\uB2E4. \uD604\uB300\uC801\uC778 \uC758\uBBF8\uC5D0\uC11C\uB294 \uC758 \uAE30\uD558\uD559\uC744 \uAC00\uB9AC\uD0A8\uB2E4. \uC774 \uAE00\uC740 \uACE0\uC804\uC801\uC774\uACE0 \uAE30\uCD08\uC801\uC778 \uC758\uBBF8 \uC704\uC8FC\uB85C \uC124\uBA85\uD55C\uB2E4. \uACE0\uC804 \uC218\uD559\uC5D0\uC11C \uD574\uC11D\uAE30\uD558\uD559\uC740 \uD574\uC11D\uD559\uACFC \uB300\uC218\uD559\uC758 \uC6D0\uCE59, \uADF8\uB9AC\uACE0 \uC88C\uD45C\uACC4\uB97C \uC774\uC6A9\uD55C \uAE30\uD558\uD559\uC774\uB2E4. \uC774\uB294 \uD2B9\uC815\uD55C \uAE30\uD558\uD559\uC801 \uAC1C\uB150\uC744 \uC73C\uB85C \uB2E4\uB8E8\uACE0\uACF5\uB9AC\uC640 \uC815\uB9AC\uC5D0 \uAE30\uBC18\uD55C \uCD94\uB860\uC744 \uC774\uC6A9\uD558\uB294 \uC720\uD074\uB9AC\uB4DC \uAE30\uD558\uD559\uC758 \uACFC \uB300\uC870\uB41C\uB2E4. \uC77C\uBC18\uC801\uC73C\uB85C \uC9C1\uAD50 \uC88C\uD45C\uACC4\uB294 2~3\uCC28\uC6D0\uC73C\uB85C \uB41C \uD3C9\uBA74, \uC9C1\uC120, \uC9C1\uC0AC\uAC01\uD615\uC5D0 \uB300\uD55C \uBC29\uC815\uC2DD\uC744 \uB2E4\uB8E8\uB294 \uB370 \uC774\uC6A9\uB41C\uB2E4. \uAE30\uD558\uD559\uC801\uC73C\uB85C\uB294 \uC720\uD074\uB9AC\uB4DC \uD3C9\uBA74 (2\uCC28\uC6D0)\uACFC \uC720\uD074\uB9AC\uB4DC \uACF5\uAC04 (3\uCC28\uC6D0)\uC744 \uC5F0\uAD6C\uD55C\uB2E4. \uAD50\uACFC\uC11C\uC5D0\uC11C \uB098\uC628 \uBC14\uC640 \uAC19\uC774 \uD574\uC11D\uAE30\uD558\uD559\uC740 \uB354 \uB2E8\uC21C\uD788 \uC124\uBA85\uD560 \uC218 \uC788\uB2E4: \uAE30\uD558\uD559\uC801 \uBAA8\uC591\uC744 \uC218\uB9CE\uC740 \uBC29\uBC95\uC73C\uB85C \uC815\uC758\uD558\uACE0 \uACB0\uACFC\uB85C\uBD80\uD130 \uC218\uCE58 \uC815\uBCF4\uB97C \uAC00\uC838\uC624\uB294 \uAC83\uACFC \uAD00\uB828\uD560 \uC218 \uC788\uB2E4. \uADF8\uB7EC\uB098 \uC218\uCE58\uC801\uC778 \uACB0\uACFC\uB294 \uBCA1\uD130\uB098 \uB3C4\uD615\uC77C \uC218\uB3C4 \uC788\uB2E4. \uC2E4\uC218\uC758 \uB300\uC218\uAC00 \uAE30\uD558\uD559\uC758 \uC120\uD615 \uC5F0\uC18D\uCCB4\uC5D0 \uB300\uD558\uC5EC \uACB0\uACFC\uB97C \uC591\uC0B0\uD558\uB294 \uB370 \uC774\uC6A9\uD560 \uC218 \uC788\uB294 \uAC83\uC740 \uC5D0 \uB2EC\uB824 \uC788\uB2E4."@ko , "In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight. It is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry. Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and circles, often in two and sometimes three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space. As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometric shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations. That the algebra of the real numbers can be employed to yield results about the linear continuum of geometry relies on the Cantor\u2013Dedekind axiom."@en , "\u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0627\u0644\u0643\u0644\u0627\u0633\u064A\u0643\u064A\u0629\u060C \u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u062A\u062D\u0644\u064A\u0644\u064A\u0629 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Analytic geometry)\u200F \u0648\u062A\u062F\u0639\u0649 \u0623\u064A\u0636\u0627\u064B \u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u0625\u062D\u062F\u0627\u062B\u064A\u0629 \u0623\u0648 \u0627\u0644\u062A\u0646\u0633\u064A\u0642\u064A\u0629 \u0648\u0633\u0627\u0628\u0642\u0627\u064B \u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u062F\u064A\u0643\u0627\u0631\u062A\u064A\u0629\u060C \u0647\u064A \u0641\u0631\u0639 \u0627\u0644\u0645\u0639\u0631\u0641\u0629 \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0629 \u0627\u0644\u0630\u064A \u064A\u062F\u0631\u0633 \u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0628\u0627\u0633\u062A\u0639\u0645\u0627\u0644 \u0646\u0638\u0627\u0645 \u0627\u0644\u0625\u062D\u062F\u0627\u062B\u064A\u0627\u062A \u0648\u0645\u0628\u0627\u062F\u0626 \u0627\u0644\u062C\u0628\u0631 \u0648\u0627\u0644\u062A\u062D\u0644\u064A\u0644 \u0627\u0644\u0631\u064A\u0627\u0636\u064A. \u062A\u0633\u062A\u0639\u0645\u0644 \u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u062A\u062D\u0644\u064A\u0644\u064A\u0629 \u0628\u0634\u0643\u0644 \u0648\u0627\u0633\u0639 \u0641\u064A \u0627\u0644\u0641\u064A\u0632\u064A\u0627\u0621 \u0648\u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u062A\u0637\u0628\u064A\u0642\u064A\u0629 \u0643\u0645\u0627 \u062A\u0645\u062B\u0644 \u0627\u0644\u0623\u0633\u0627\u0633 \u0627\u0644\u0630\u064A \u0628\u064F\u0646\u064A \u0639\u0644\u064A\u0647 \u0628\u0627\u0642\u064A \u0645\u062C\u0627\u0644\u0627\u062A \u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0643\u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u062C\u0628\u0631\u064A\u0629 \u0648\u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u062A\u0641\u0627\u0636\u0644\u064A\u0629 \u0648\u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u0645\u062A\u0642\u0637\u0639\u0629 \u0648\u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u062D\u0627\u0633\u0648\u0628\u064A\u0629. \u062A\u0647\u062A\u0645 \u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u062A\u062D\u0644\u064A\u0644\u064A\u0629 \u0628\u0627\u0644\u0645\u0648\u0627\u0636\u064A\u0639 \u0630\u0627\u062A\u0647\u0627 \u0627\u0644\u062A\u064A \u062A\u0647\u062A\u0645 \u0628\u0647\u0627 \u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u062A\u0642\u0644\u064A\u062F\u064A\u0629\u060C \u063A\u064A\u0631 \u0623\u0646\u0647\u0627 \u062A\u062A\u064A\u062D \u0637\u0631\u0642\u0627\u064B \u0623\u064A\u0633\u0631 \u0644\u0628\u0631\u0647\u0627\u0646 \u0627\u0644\u0639\u062F\u064A\u062F \u0645\u0646 \u0627\u0644\u0646\u0638\u0631\u064A\u0627\u062A \u0648\u062A\u0644\u0639\u0628 \u062F\u0648\u0631\u0627\u064B \u0645\u0647\u0645\u0627 \u0641\u064A \u062D\u0633\u0627\u0628 \u0627\u0644\u0645\u062B\u0644\u062B\u0627\u062A \u0648\u062D\u0633\u0627\u0628 \u0627\u0644\u062A\u0641\u0627\u0636\u0644 \u0648\u0627\u0644\u062A\u0643\u0627\u0645\u0644\u060C \u0648\u062A\u0647\u062A\u0645 \u0623\u064A\u0636\u0627 \u0628\u062F\u0631\u0627\u0633\u0629 \u0627\u0644\u062E\u0648\u0627\u0635 \u0627\u0644\u0647\u0646\u062F\u0633\u064A\u0629 \u0644\u0644\u0623\u0634\u0643\u0627\u0644 \u0628\u0627\u0633\u062A\u062E\u062F\u0627\u0645 \u0627\u0644\u0648\u0633\u0627\u0626\u0644 \u0627\u0644\u062C\u0628\u0631\u064A\u0629. \u0639\u0627\u062F\u0629 \u062A\u0633\u062A\u062E\u062F\u0645 \u062C\u0645\u0644 \u0625\u062D\u062F\u0627\u062B\u064A\u0627\u062A \u062F\u064A\u0643\u0627\u0631\u062A\u064A\u0629 \u0644\u0648\u0635\u0641 \u0646\u0642\u0627\u0637 \u0627\u0644\u0641\u0631\u0627\u063A \u0628\u062F\u0644\u0627\u0644\u0629 \u0623\u0639\u062F\u0627\u062F \u0647\u064A \u0627\u0644\u0625\u062D\u062F\u0627\u062B\u064A\u0627\u062A \u062B\u0645 \u064A\u062A\u0645 \u0625\u064A\u062C\u0627\u062F \u0627\u0644\u0645\u0639\u0627\u062F\u0644\u0629 \u0627\u0644\u062C\u0628\u0631\u064A\u0629 \u0627\u0644\u062A\u064A \u062A\u0635\u0641 \u0627\u0644\u062F\u0627\u0626\u0631\u0629 \u0623\u0648\u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u0642\u0635 \u0623\u0648\u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0645\u0643\u0627\u0641\u064A\u0621 \u0623\u0648 \u063A\u064A\u0631\u0647\u0627."@ar , "De analytische meetkunde, ook wel bekend als Cartesiaanse meetkunde, is de studie van meetkunde die de principes van algebra gebruikt. Dat de algebra van de re\u00EBle getallen resultaten geeft met betrekking tot meetkundige concepten als punten en lijnen hangt af van het axioma van Cantor-Dedekind, dat stelt dat punten op een lijn een eenduidige correspondentie hebben met de re\u00EBle getallen. Gewoonlijk wordt het Cartesisch co\u00F6rdinatenstelsel toegepast om vergelijkingen voor vlakken, lijnen, krommen en cirkels te manipuleren, vaak in twee of drie, maar in principe in willekeurig veel dimensies. Sommigen zijn van mening dat de introductie van analytische meetkunde door Ren\u00E9 Descartes het begin van moderne wiskunde was. Veel stellingen uit de vlakke meetkunde kunnen eenvoudig nagerekend worden met behulp van cartesische co\u00F6rdinaten. In het tegenwoordige wiskundig onderzoek is de scheidslijn tussen analytische en algebra\u00EFsche meetkunde erg vaag geworden."@nl , "La geometria anal\u00EDtica \u00E9s la part de les matem\u00E0tiques que fa \u00FAs de l'\u00E0lgebra per descriure i analitzar figures geom\u00E8triques. En el seg\u00FCent exemple tenim l'expressi\u00F3: que representa, en la geometria anal\u00EDtica plana, una el\u00B7lipse centrada en l'origen d'un sistema de coordenades cartesianes, que t\u00E9 el valor a com semieix major i el valor b com semieix menor. L'eix major \u00E9s l'eix de les abscisses X. En un sistema de coordenades cartesianes, un punt del pla queda determinat per dos nombres reals, que s\u00F3n l'abscissa i l'ordenada del punt. D'aquesta manera, a qualsevol punt del pla li corresponen sempre dos nombres reals ordenats (abscissa i ordenada) i, rec\u00EDprocament, a un parell ordenat de nombres reals ordenats, correspon un \u00FAnic punt del pla. Conseq\u00FCentment, en el sistema cartesi\u00E0 s'estableix una correspond\u00E8ncia entre un concepte geom\u00E8tric com \u00E9s un punt del pla i un concepte algebraic com \u00E9s un parell de nombres ordenat. Aquesta correspond\u00E8ncia constitueix el fonament de la geometria anal\u00EDtica. Els raonaments anteriors s\u00F3n tanmateix v\u00E0lids per un punt a l'espai i una terna ordenada de nombres."@ca , "Na matem\u00E1tica cl\u00E1ssica, a geometria anal\u00EDtica, tamb\u00E9m chamada geometria de coordenadas e de geometria cartesiana, \u00E9 o estudo da geometria por meio de um sistema de coordenadas e dos princ\u00EDpios da \u00E1lgebra e da an\u00E1lise. Contrasta com a abordagem sint\u00E9tica da geometria euclidiana, em que certas no\u00E7\u00F5es geom\u00E9tricas s\u00E3o consideradas primitivas, e \u00E9 utilizado o racioc\u00EDnio dedutivo a partir de axiomas e teoremas para obter proposi\u00E7\u00F5es verdadeiras. \u00C9 um campo matem\u00E1tico no qual s\u00E3o utilizados m\u00E9todos e s\u00EDmbolos alg\u00E9bricos para representar e resolver problemas geom\u00E9tricos. Sua import\u00E2ncia est\u00E1 presente no fato de que estabelece uma correspond\u00EAncia entre equa\u00E7\u00F5es alg\u00E9bricas e curvas geom\u00E9tricas. Tal correspond\u00EAncia torna poss\u00EDvel a reavalia\u00E7\u00E3o de problemas na geometria como problemas equivalentes em \u00E1lgebra, e vice-versa; os m\u00E9todos de um \u00E2mbito podem ser utilizados para solucionar problemas no outro. A geometria anal\u00EDtica \u00E9 muito utilizada na f\u00EDsica e na engenharia e \u00E9 o fundamento das \u00E1reas mais modernas da geometria, incluindo geometria alg\u00E9brica, diferencial, discreta e computacional. Em geral, o sistema de coordenadas cartesianas \u00E9 usado para manipular equa\u00E7\u00F5es em planos, retas, curvas e c\u00EDrculos, geralmente em duas dimens\u00F5es, mas, por vezes, tamb\u00E9m em tr\u00EAs ou mais. A geometria anal\u00EDtica ensinada nos livros escolares pode ser explicada de uma forma mais simples: diz respeito \u00E0 defini\u00E7\u00E3o e representa\u00E7\u00E3o de formas geom\u00E9tricas de modo num\u00E9rico e \u00E0 extra\u00E7\u00E3o de informa\u00E7\u00E3o num\u00E9rica dessa representa\u00E7\u00E3o. O resultado num\u00E9rico tamb\u00E9m pode, no entanto, ser um vector ou uma forma. O fato de que a \u00E1lgebra dos n\u00FAmeros reais pode ser empregada para produzir resultados sobre o cont\u00EDnuo linear da geometria baseia-se no axioma de Cantor-Dedekind."@pt , "\u0391\u03BD\u03B1\u03BB\u03C5\u03C4\u03B9\u03BA\u03AE \u03B3\u03B5\u03C9\u03BC\u03B5\u03C4\u03C1\u03AF\u03B1 \u03B5\u03AF\u03BD\u03B1\u03B9 \u03C4\u03BF \u03B5\u03AF\u03B4\u03BF\u03C2 \u03C4\u03B7\u03C2 \u03B3\u03B5\u03C9\u03BC\u03B5\u03C4\u03C1\u03AF\u03B1\u03C2 \u03C0\u03BF\u03C5 \u03B8\u03B5\u03C9\u03C1\u03B5\u03AF \u03C4\u03BF\u03BD \u03B3\u03B5\u03C9\u03BC\u03B5\u03C4\u03C1\u03B9\u03BA\u03CC \u03C7\u03CE\u03C1\u03BF \u03B4\u03B9\u03B1\u03BD\u03C5\u03C3\u03BC\u03B1\u03C4\u03B9\u03BA\u03CC \u03C7\u03CE\u03C1\u03BF. \u039A\u03AC\u03B8\u03B5 \u03B4\u03B9\u03AC\u03BD\u03C5\u03C3\u03BC\u03B1 \u03B1\u03BD\u03C4\u03B9\u03C3\u03C4\u03BF\u03B9\u03C7\u03B5\u03AF \u03C3\u03B5 \u03AD\u03BD\u03B1 \u03C3\u03B7\u03BC\u03B5\u03AF\u03BF \u03C4\u03BF\u03C5 \u03C7\u03CE\u03C1\u03BF\u03C5, \u03B5\u03BD\u03CE \u03C4\u03B1 \u03B3\u03B5\u03C9\u03BC\u03B5\u03C4\u03C1\u03B9\u03BA\u03AC \u03C3\u03C7\u03AE\u03BC\u03B1\u03C4\u03B1 \u03BA\u03B1\u03B9 \u03BF\u03B9 \u03B3\u03B5\u03C9\u03BC\u03B5\u03C4\u03C1\u03B9\u03BA\u03AD\u03C2 \u03C3\u03C7\u03AD\u03C3\u03B5\u03B9\u03C2 \u03BC\u03B5\u03C4\u03B1\u03BE\u03CD \u03C4\u03C9\u03BD \u03C3\u03B7\u03BC\u03B5\u03AF\u03C9\u03BD \u03BA\u03B1\u03B9 \u03B4\u03B9\u03AC\u03C6\u03BF\u03C1\u03C9\u03BD \u03C3\u03C7\u03B7\u03BC\u03AC\u03C4\u03C9\u03BD \u03C0\u03B5\u03C1\u03B9\u03B3\u03C1\u03AC\u03C6\u03BF\u03BD\u03C4\u03B1\u03B9 \u03BC\u03B5 \u03B4\u03B9\u03B1\u03BD\u03C5\u03C3\u03BC\u03B1\u03C4\u03B9\u03BA\u03AD\u03C2 \u03C3\u03C7\u03AD\u03C3\u03B5\u03B9\u03C2 \u03BF\u03B9 \u03BF\u03C0\u03BF\u03AF\u03B5\u03C2 \u03BC\u03C0\u03BF\u03C1\u03BF\u03CD\u03BD \u03BD\u03B1 \u03C5\u03C0\u03BF\u03C3\u03C4\u03BF\u03CD\u03BD \u03B5\u03C0\u03B5\u03BE\u03B5\u03C1\u03B3\u03B1\u03C3\u03AF\u03B1 \u03CC\u03C0\u03C9\u03C2 \u03BA\u03B1\u03B9 \u03BF\u03B9 \u03B1\u03BB\u03B3\u03B5\u03B2\u03C1\u03B9\u03BA\u03AD\u03C2. \u0388\u03C4\u03C3\u03B9 \u03BC\u03AD\u03C3\u03C9 \u03C4\u03B7\u03C2 \u03B1\u03BD\u03B1\u03BB\u03C5\u03C4\u03B9\u03BA\u03AE\u03C2 \u03B3\u03B5\u03C9\u03BC\u03B5\u03C4\u03C1\u03AF\u03B1\u03C2 \u03AD\u03B3\u03B9\u03BD\u03B5 \u03BC\u03B9\u03B1 \u03B1\u03BB\u03B3\u03B5\u03B2\u03C1\u03BF\u03C0\u03BF\u03AF\u03B7\u03C3\u03B7 \u03C4\u03B7\u03C2 \u03B3\u03B5\u03C9\u03BC\u03B5\u03C4\u03C1\u03AF\u03B1\u03C2, \u03C3\u03B5 \u03C3\u03B7\u03BC\u03B5\u03AF\u03BF \u03CE\u03C3\u03C4\u03B5 \u03BD\u03B1 \u03C5\u03C0\u03BF\u03C3\u03C4\u03B7\u03C1\u03AF\u03B6\u03B5\u03C4\u03B1\u03B9 \u03CC\u03C4\u03B9 \u03C0\u03BB\u03AD\u03BF\u03BD \u03B7 \u03B3\u03B5\u03C9\u03BC\u03B5\u03C4\u03C1\u03AF\u03B1 \u03B4\u03B5 \u03C7\u03C1\u03B5\u03B9\u03AC\u03B6\u03B5\u03C4\u03B1\u03B9 \u03BA\u03B1\u03B8\u03CC\u03BB\u03BF\u03C5 \u03B1\u03BE\u03B9\u03C9\u03BC\u03B1\u03C4\u03B9\u03BA\u03AE \u03B8\u03B5\u03BC\u03B5\u03BB\u03AF\u03C9\u03C3\u03B7, \u03B1\u03BB\u03BB\u03AC \u03B1\u03C1\u03BA\u03B5\u03AF \u03BD\u03B1 \u03C3\u03C4\u03B7\u03C1\u03B9\u03C7\u03B8\u03B5\u03AF \u03BC\u03AD\u03C3\u03C9 \u03BA\u03B1\u03C4\u03AC\u03BB\u03BB\u03B7\u03BB\u03C9\u03BD \u03BF\u03C1\u03B9\u03C3\u03BC\u03CE\u03BD \u03C3\u03C4\u03B7\u03BD \u03AC\u03BB\u03B3\u03B5\u03B2\u03C1\u03B1."@el , "Analytick\u00E1 geometrie (tak\u00E9 sou\u0159adnicov\u00E1 geometrie nebo kart\u00E9zsk\u00E1 geometrie) je \u010D\u00E1st geometrie, kter\u00E1 zkoum\u00E1 geometrick\u00E9 \u00FAtvary v euklidovsk\u00E9 geometrii pomoc\u00ED algebraick\u00FDch a analytick\u00FDch metod. V analytick\u00E9 geometrii jsou geometrick\u00E9 \u00FAtvary v prostoru vyjad\u0159ov\u00E1ny \u010D\u00EDsly a rovnicemi ve zvolen\u00FDch sou\u0159adnicov\u00FDch soustav\u00E1ch.Mnoh\u00E9 probl\u00E9my analytick\u00E9 geometrie jsou \u00FAzce sv\u00E1z\u00E1ny s line\u00E1rn\u00ED algebrou."@cs , "Geometri Analitis, juga disebut geometri koordinat dan dahulu disebut geometri Kartesius, adalah pembahasan geometri menggunakan prinsip-prinsip aljabar menggunakan bilangan riil. Biasanya, sistem koordinat Kartesius diterapkan untuk menyelesaikan persamaan , garis, garis lurus, dan persegi, yang sering dalam pengukuran 2 atau 3 dimensi. Seperti yang diajarkan di buku pelajaran sekolah, geometri analitis dapat dijelaskan dengan sederhana: terfokus pada pendefinisian bentuk bangun dalam bilangan dan menjadikan sebagai sebuah hasil perhitungan. Hasil perhitungan dapat diasumsikan sebagai sebuah vektor atau bangun. Bagaimanapun juga beberapa output numerik juga membentuk vektor. Ada anggapan bahwa lahirnya geometri analitis adalah permulaan matematika modern."@in , "\u521D\u7B49\u5E7E\u4F55\u5B66\u306B\u304A\u3051\u308B\u89E3\u6790\u5E7E\u4F55\u5B66\uFF08\u304B\u3044\u305B\u304D\u304D\u304B\u304C\u304F\u3001\u82F1: analytic geometry \uFF09\u3042\u308B\u3044\u306F\u5EA7\u6A19\u5E7E\u4F55\u5B66\uFF08\u3056\u3072\u3087\u3046\u304D\u304B\u304C\u304F\u3001\u82F1: coordinate geometry \uFF09\u3001\u30C7\u30AB\u30EB\u30C8\u5E7E\u4F55\u5B66\uFF08\u30C7\u30AB\u30EB\u30C8\u304D\u304B\u304C\u304F\u3001\u82F1: Cartesian geometry \uFF09\u306F\u3001\u5EA7\u6A19\u3092\u7528\u3044\u3066\u4EE3\u6570\u7684\u306B\u56F3\u5F62\u3092\u8ABF\u3079\u308B\u5E7E\u4F55\u5B66\u3092\u3044\u3046\u3002\u5EA7\u6A19\u3092\u7528\u3044\u308B\u3068\u3044\u3046\u70B9\u306B\u304A\u3044\u3066\u3001\uFF08\u3088\u308A\u53E4\u5178\u7684\u306A\u3001\u30E6\u30FC\u30AF\u30EA\u30C3\u30C9\u306E\u539F\u8AD6\u306B\u3082\u3042\u308B\u3088\u3046\u306A\uFF09\u70B9\u3084\u76F4\u7DDA\u306A\u3069\u304C\u3069\u306E\u3088\u3046\u306A\u516C\u7406\u306B\u5F93\u3046\u304B\u3068\u3044\u3046\u3053\u3068\u306E\u307F\u306B\u3088\u3063\u3066\u56F3\u5F62\u3092\u8ABF\u3079\u308B\u7D9C\u5408\u5E7E\u4F55\u5B66 \u3068\u306F\u5BFE\u7167\u7684\u3067\u3042\u308B\u3002\u5EA7\u6A19\u3092\u5229\u7528\u3059\u308B\u3053\u3068\u306B\u3088\u308A\u3001\u56F3\u5F62\u306E\u3082\u3064\u6027\u8CEA\u3092\u5EA7\u6A19\u306E\u3042\u3044\u3060\u306B\u3042\u3089\u308F\u308C\u308B\u95A2\u4FC2\u5F0F\u3068\u3057\u3066\u7279\u5FB4\u3065\u3051\u305F\u308A\u3001\u6570\u3084\u5F0F\u3068\u3057\u3066\u56F3\u5F62\u3092\u53D6\u308A\u6271\u3063\u305F\u308A\u3059\u308B\u3053\u3068\u304C\u3067\u304D\u308B\u3002 \u3075\u3064\u3046\u306F\uFF08\u4E8C\u6B21\u5143\uFF09\u5E73\u9762\u4E0A\u306E\u70B9\u3001\u76F4\u7DDA\u306A\u3069\u3092\u6271\u3046\uFF08\u5E73\u9762\u89E3\u6790\u5E7E\u4F55\uFF09\u304B\uFF08\u4E09\u6B21\u5143\uFF09\u7A7A\u9593\u5185\u306E\u305D\u308C\u3089\u3092\u6271\u3046\uFF08\u7ACB\u4F53\u89E3\u6790\u5E7E\u4F55\uFF09\u3002"@ja , "La geometria analitica, chiamata anche geometria cartesiana da Cartesio, \u00E8 lo studio delle figure geometriche attraverso il sistema di coordinate oggi dette cartesiane, ma gi\u00E0 studiate nel Medioevo da Nicola d'Oresme. Ogni punto del piano cartesiano \u00E8 individuato dalle sue coordinate su due assi: ascisse (x) e ordinate (y), nello spazio \u00E8 individuato da 3 coordinate (x,y,z). Le coordinate determinano un vettore rispettivamente del tipo oppure . Gli enti geometrici come rette, curve, poligoni sono definiti tramite equazioni, disequazioni o insiemi di queste, detti sistemi. Le propriet\u00E0 di questi oggetti, come le condizioni di incidenza, parallelismo e perpendicolarit\u00E0, vengono anch'esse tradotte in equazioni e quindi studiate con gli strumenti dell'algebra e dell'analisi matematica. Il termine geometria analitica \u00E8 stato usato anche da alcuni matematici moderni come Jean-Pierre Serre per definire una branca della geometria algebrica che studia le variet\u00E0 complesse determinate da funzioni analitiche. Le formule della geometria analitica possono essere agevolmente estese nello spazio a tre dimensioni. La geometria strutturale studia le propriet\u00E0 delle figure geometriche in uno spazio a quattro o pi\u00F9 dimensioni, e il loro rapporto con le figure in tre dimensioni.La geometria descrittiva \u00E8 in parte attinente poich\u00E9 rappresenta su uno o pi\u00F9 piani, oggetti bidimensionali e tridimensionali. Giuseppe Veronese tent\u00F2 una descrizione a quattro o pi\u00F9 dimensioni, priva di rigore formale logico, e fortemente criticata da Giuseppe Peano."@it , "La g\u00E9om\u00E9trie analytique est une approche de la g\u00E9om\u00E9trie dans laquelle les objets sont d\u00E9crits par des \u00E9quations ou des in\u00E9quations \u00E0 l'aide d'un syst\u00E8me de coordonn\u00E9es.Elle est fondamentale pour la physique et l'infographie. En g\u00E9om\u00E9trie analytique, le choix d'un rep\u00E8re est indispensable. Tous les objets seront d\u00E9crits relativement \u00E0 ce rep\u00E8re. Article d\u00E9taill\u00E9 : Rep\u00E9rage dans le plan et dans l'espace."@fr , "Analitika geometrio, anka\u016D nomata koordinata geometrio kaj pli frue nomata kartezia geometrio, estas studo de geometrio uzanta la principojn de algebro. Kutime la karteziaj koordinatoj estas aplikitaj por manipuli ekvaciojn por ebenoj, rektoj, kurboj, cirkloj, en du, tri kaj iam en pli multaj dimensioj. Kiel instruite en lernejaj libroj, analitika geometrio povas esti eksplikita pli simple: \u011Di okupi\u011Das pri difinado de geometriaj formoj en nombra vojo, kaj ekstraktante nombran informon de tiu prezento. La nombra ela\u0135o, tamen, povus anka\u016D esti vektoro a\u016D . Iuj konsideras, ke la enkonduko de analitika geometrio estis la komenco de moderna matematiko. Rene Descartes estas populare estimita kiel prezentinto de la fundamento por la metodoj de analitika geometrio en 1637 en apendico titolita Geometrio de verko titolita Traktato pri la metodo de \u011Dusta konduto de la ka\u016Dzo en la ser\u0109o por vero en la sciencoj, kutime mallongigita kiel Traktato pri metodo. \u0108i tiu verko, skribita en lia denaska lingvo franca lingvo, kaj \u011Dia filozofiaj principoj provizis la fundamenton por kalkulo en E\u016Dropo."@eo , "\u0410\u043D\u0430\u043B\u0456\u0442\u0438\u0301\u0447\u043D\u0430 \u0433\u0435\u043E\u043C\u0435\u0301\u0442\u0440\u0456\u044F \u2014 \u0440\u043E\u0437\u0434\u0456\u043B \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0456\u0457, \u0432 \u044F\u043A\u043E\u043C\u0443 \u0432\u043B\u0430\u0441\u0442\u0438\u0432\u043E\u0441\u0442\u0456 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u043D\u0438\u0445 \u043E\u0431'\u0454\u043A\u0442\u0456\u0432 (\u0442\u043E\u0447\u043E\u043A, \u043B\u0456\u043D\u0456\u0439, \u043F\u043E\u0432\u0435\u0440\u0445\u043E\u043D\u044C) \u0443\u0441\u0442\u0430\u043D\u043E\u0432\u043B\u044E\u044E\u0442\u044C \u0437\u0430\u0441\u043E\u0431\u0430\u043C\u0438 \u0430\u043B\u0433\u0435\u0431\u0440\u0438 \u0437\u0430 \u0434\u043E\u043F\u043E\u043C\u043E\u0433\u043E\u044E \u043C\u0435\u0442\u043E\u0434\u0443 \u043A\u043E\u043E\u0440\u0434\u0438\u043D\u0430\u0442, \u0442\u043E\u0431\u0442\u043E \u0448\u043B\u044F\u0445\u043E\u043C \u0434\u043E\u0441\u043B\u0456\u0434\u0436\u0435\u043D\u043D\u044F \u0432\u043B\u0430\u0441\u0442\u0438\u0432\u043E\u0441\u0442\u0435\u0439 \u0440\u0456\u0432\u043D\u044F\u043D\u044C, \u044F\u043A\u0456 \u0456 \u0432\u0438\u0437\u043D\u0430\u0447\u0430\u044E\u0442\u044C \u0446\u0456 \u043E\u0431'\u0454\u043A\u0442\u0438. \u041E\u0441\u043D\u043E\u0432\u043D\u0456 \u043F\u043E\u043B\u043E\u0436\u0435\u043D\u043D\u044F \u0430\u043D\u0430\u043B\u0456\u0442\u0438\u0447\u043D\u043E\u0457 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0456\u0457 \u0432\u043F\u0435\u0440\u0448\u0435 \u0441\u0444\u043E\u0440\u043C\u0443\u043B\u044E\u0432\u0430\u0432 \u0444\u0456\u043B\u043E\u0441\u043E\u0444 \u0456 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A \u0420\u0435\u043D\u0435 \u0414\u0435\u043A\u0430\u0440\u0442 1637 \u0440\u043E\u043A\u0443. \u041B\u0435\u0439\u0431\u043D\u0456\u0446, \u0406\u0441\u0430\u0430\u043A \u041D\u044C\u044E\u0442\u043E\u043D \u0456 \u041B\u0435\u043E\u043D\u0430\u0440\u0434 \u0415\u0439\u043B\u0435\u0440 \u043D\u0430\u0434\u0430\u043B\u0438 \u0430\u043D\u0430\u043B\u0456\u0442\u0438\u0447\u043D\u0456\u0439 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0456\u0457 \u0441\u0443\u0447\u0430\u0441\u043D\u043E\u0457 \u0441\u0442\u0440\u0443\u043A\u0442\u0443\u0440\u0438."@uk , "\u89E3\u6790\u51E0\u4F55\uFF08\u82F1\u8A9E\uFF1AAnalytic geometry\uFF09\uFF0C\u53C8\u7A31\u70BA\u5750\u6807\u51E0\u4F55\uFF08\u82F1\u8A9E\uFF1ACoordinate geometry\uFF09\u6216\u5361\u6C0F\u5E7E\u4F55\uFF08\u82F1\u8A9E\uFF1ACartesian geometry\uFF09\uFF0C\u65E9\u5148\u88AB\u53EB\u4F5C\u7B1B\u5361\u5152\u51E0\u4F55\uFF0C\u662F\u4E00\u79CD\u501F\u52A9\u4E8E\u89E3\u6790\u5F0F\u8FDB\u884C\u56FE\u5F62\u7814\u7A76\u7684\u51E0\u4F55\u5B66\u5206\u652F\u3002\u89E3\u6790\u51E0\u4F55\u901A\u5E38\u4F7F\u7528\u4E8C\u7EF4\u7684\u5E73\u9762\u76F4\u89D2\u5750\u6807\u7CFB\u7814\u7A76\u76F4\u7EBF\u3001\u5706\u3001\u5706\u9525\u66F2\u7EBF\u3001\u6446\u7EBF\u3001\u661F\u5F62\u7EBF\u7B49\u5404\u79CD\u4E00\u822C\u5E73\u9762\u66F2\u7EBF\uFF0C\u4F7F\u7528\u4E09\u7EF4\u7684\u7A7A\u95F4\u76F4\u89D2\u5750\u6807\u7CFB\u6765\u7814\u7A76\u5E73\u9762\u3001\u7403\u7B49\u5404\u79CD\u4E00\u822C\u7A7A\u95F4\u66F2\u9762\uFF0C\u540C\u65F6\u7814\u7A76\u5B83\u4EEC\u7684\u65B9\u7A0B\uFF0C\u5E76\u5B9A\u4E49\u4E00\u4E9B\u56FE\u5F62\u7684\u6982\u5FF5\u548C\u53C2\u6570\u3002 \u5728\u4E2D\u5B66\u8BFE\u672C\u4E2D\uFF0C\u89E3\u6790\u51E0\u4F55\u88AB\u7B80\u5355\u5730\u89E3\u91CA\u4E3A\uFF1A\u91C7\u7528\u6570\u503C\u7684\u65B9\u6CD5\u6765\u5B9A\u4E49\u51E0\u4F55\u5F62\u72B6\uFF0C\u5E76\u4ECE\u4E2D\u63D0\u53D6\u6570\u503C\u7684\u4FE1\u606F\u3002\u7136\u800C\uFF0C\u8FD9\u79CD\u6570\u503C\u7684\u8F93\u51FA\u53EF\u80FD\u662F\u4E00\u4E2A\u65B9\u7A0B\u6216\u8005\u662F\u4E00\u79CD\u51E0\u4F55\u5F62\u72B6\u3002 1637\u5E74\uFF0C\u7B1B\u5361\u5152\u5728\u300A\u65B9\u6CD5\u8BBA\u300B\u7684\u9644\u5F55\u201C\u51E0\u4F55\u201D\u4E2D\u63D0\u51FA\u4E86\u89E3\u6790\u51E0\u4F55\u7684\u57FA\u672C\u65B9\u6CD5\u3002\u4EE5\u54F2\u5B66\u89C2\u70B9\u5199\u6210\u7684\u8FD9\u90E8\u6CD5\u8BED\u8457\u4F5C\u4E3A\u540E\u6765\u725B\u987F\u548C\u83B1\u5E03\u5C3C\u8328\u5404\u81EA\u63D0\u51FA\u5FAE\u79EF\u5206\u5B66\u63D0\u4F9B\u4E86\u57FA\u7840\u3002 \u5BF9\u4EE3\u6570\u51E0\u4F55\u5B66\u8005\u6765\u8BF4\uFF0C\u89E3\u6790\u51E0\u4F55\u4E5F\u6307\uFF08\u5B9E\u6216\u8005\u8907\uFF09\u6D41\u5F62\uFF0C\u6216\u8005\u66F4\u5E7F\u4E49\u5730\u901A\u8FC7\u4E00\u4E9B\u8907\u8B8A\u6578\uFF08\u6216\u5BE6\u8B8A\u6578\uFF09\u7684\u89E3\u6790\u51FD\u6570\u4E3A\u96F6\u800C\u5B9A\u4E49\u7684\u89E3\u6790\u7A7A\u95F4\u7406\u8BBA\u3002\u8FD9\u4E00\u7406\u8BBA\u975E\u5E38\u63A5\u8FD1\u4EE3\u6570\u51E0\u4F55\uFF0C\u7279\u522B\u662F\u901A\u8FC7\u8BA9-\u76AE\u57C3\u5C14\u00B7\u585E\u5C14\u5728\u300A\u4EE3\u6570\u51E0\u4F55\u548C\u89E3\u6790\u51E0\u4F55\u300B\u9886\u57DF\u7684\u5DE5\u4F5C\u3002\u8FD9\u662F\u4E00\u4E2A\u6BD4\u4EE3\u6570\u51E0\u4F55\u66F4\u5927\u7684\u9886\u57DF\uFF0C\u4E0D\u8FC7\u4E5F\u53EF\u4EE5\u4F7F\u7528\u7C7B\u4F3C\u7684\u65B9\u6CD5\u3002"@zh , "La geometr\u00EDa anal\u00EDtica es una rama de las matem\u00E1ticas que estudia las figuras, sus distancias, sus \u00E1reas, puntos de intersecci\u00F3n, \u00E1ngulos de inclinaci\u00F3n, puntos de divisi\u00F3n, vol\u00FAmenes, etc\u00E9tera. Analiza con detalle los datos de las figuras geom\u00E9tricas mediante t\u00E9cnicas b\u00E1sicas del an\u00E1lisis matem\u00E1tico y del \u00E1lgebra en un determinado sistema de coordenadas. Su desarrollo hist\u00F3rico comienza con la geometr\u00EDa cartesiana, contin\u00FAa con la aparici\u00F3n de la geometr\u00EDa diferencial de Carl Friedrich Gauss y m\u00E1s tarde con el desarrollo de la geometr\u00EDa algebraica. Tiene m\u00FAltiples aplicaciones, m\u00E1s all\u00E1 de las matem\u00E1ticas y la ingenier\u00EDa, pues forma parte ahora del trabajo de administradores para la planeaci\u00F3n de estrategias y log\u00EDstica en la toma de decisiones. Las dos cuestiones fundamentales de la geometr\u00EDa anal\u00EDtica son: \n* Dado el lugar geom\u00E9trico de un sistema de coordenadas, para obtener su ecuaci\u00F3n. \n* Dada la ecuaci\u00F3n en un sistema de coordenadas, determinar la gr\u00E1fica o lugar geom\u00E9trico de los puntos que verifican dicha ecuaci\u00F3n. La geometr\u00EDa anal\u00EDtica representa las figuras geom\u00E9tricas mediante la ecuaci\u00F3n , donde es una funci\u00F3n u otro tipo. As\u00ED, las rectas se expresan mediante la ecuaci\u00F3n general , las circunferencias y el resto de c\u00F3nicas como ecuaciones polin\u00F3micas de grado 2 (la circunferencia, ; la hip\u00E9rbola, )."@es , "Geometria analityczna \u2013 dzia\u0142 geometrii zajmuj\u0105cy si\u0119 badaniem figur geometrycznych metodami analitycznymi (obliczeniowymi) i algebraicznymi. Z\u0142o\u017Cone rozwa\u017Cania geometryczne zostaj\u0105 w geometrii analitycznej sprowadzone do rozwi\u0105zywania uk\u0142ad\u00F3w r\u00F3wna\u0144, kt\u00F3re opisuj\u0105 badane figury. Przedmiotem bada\u0144 geometrii analitycznej jest zasadniczo przestrze\u0144 euklidesowa i w\u0142asno\u015Bci jej podzbior\u00F3w, cho\u0107 wiele wynik\u00F3w mo\u017Cna uog\u00F3lni\u0107 na dowolne, sko\u0144czenie wymiarowe przestrzenie liniowe."@pl , "Iarracht fadhbanna geoim\u00E9adracha a r\u00E9iteach tr\u00ED chomhordan\u00E1id\u00ED a dh\u00E1ileadh ar gach pointe. Tugtar geoim\u00E9adracht Chairt\u00E9iseach n\u00F3 geoim\u00E9adracht chomhordan\u00E1ideach uirthi freisin. Maidir leis an bpl\u00E1na, is \u00E9 an c\u00F3ras is coitianta n\u00E1 dh\u00E1 ais ingearacha, ionas gur f\u00E9idir gach pointe a lua mar ph\u00E9ire uimhreacha (x, y). I ngeoim\u00E9adracht thr\u00EDthoiseach, tr\u00EDr\u00EDn uimhreacha a \u00FAs\u00E1idtear (x, y, z). T\u00E1 c\u00F3rais comhordan\u00E1id\u00ED eile ann a bh\u00EDonn \u00E1isi\u00FAil i gc\u00E1sanna, mar shampla, comhordan\u00E1id\u00ED polacha d'fhadhbanna a bhaineann le feinim\u00E9in thr\u00EDthoiseacha, eagraithe timpeall l\u00E1rphointe. Luaitear Descartes mar cheapad\u00F3ir an ch\u00F3rais seo, b\u00EDodh is gur bhain Apall\u00F3inias feidhm as aiseanna ina staid\u00E9ar ar ch\u00F3nghearrtha\u00ED."@ga , "\u0410\u043D\u0430\u043B\u0438\u0442\u0438\u0301\u0447\u0435\u0441\u043A\u0430\u044F \u0433\u0435\u043E\u043C\u0435\u0301\u0442\u0440\u0438\u044F \u2014 \u0440\u0430\u0437\u0434\u0435\u043B \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0438, \u0432 \u043A\u043E\u0442\u043E\u0440\u043E\u043C \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043A\u0438\u0435 \u0444\u0438\u0433\u0443\u0440\u044B \u0438 \u0438\u0445 \u0441\u0432\u043E\u0439\u0441\u0442\u0432\u0430 \u0438\u0441\u0441\u043B\u0435\u0434\u0443\u044E\u0442\u0441\u044F \u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0430\u043C\u0438 \u0430\u043B\u0433\u0435\u0431\u0440\u044B. \u0412 \u043E\u0441\u043D\u043E\u0432\u0435 \u044D\u0442\u043E\u0433\u043E \u043C\u0435\u0442\u043E\u0434\u0430 \u043B\u0435\u0436\u0438\u0442 \u0442\u0430\u043A \u043D\u0430\u0437\u044B\u0432\u0430\u0435\u043C\u044B\u0439 \u043C\u0435\u0442\u043E\u0434 \u043A\u043E\u043E\u0440\u0434\u0438\u043D\u0430\u0442, \u0432\u043F\u0435\u0440\u0432\u044B\u0435 \u043F\u0440\u0438\u043C\u0435\u043D\u0451\u043D\u043D\u044B\u0439 \u0414\u0435\u043A\u0430\u0440\u0442\u043E\u043C \u0432 1637 \u0433\u043E\u0434\u0443. \u041A\u0430\u0436\u0434\u043E\u043C\u0443 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043A\u043E\u043C\u0443 \u0441\u043E\u043E\u0442\u043D\u043E\u0448\u0435\u043D\u0438\u044E \u044D\u0442\u043E\u0442 \u043C\u0435\u0442\u043E\u0434 \u0441\u0442\u0430\u0432\u0438\u0442 \u0432 \u0441\u043E\u043E\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0438\u0435 \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u043E\u0435 \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u0435, \u0441\u0432\u044F\u0437\u044B\u0432\u0430\u044E\u0449\u0435\u0435 \u043A\u043E\u043E\u0440\u0434\u0438\u043D\u0430\u0442\u044B \u0444\u0438\u0433\u0443\u0440\u044B \u0438\u043B\u0438 \u0442\u0435\u043B\u0430. \u0422\u0430\u043A\u043E\u0439 \u043C\u0435\u0442\u043E\u0434 \u00AB\u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0437\u0430\u0446\u0438\u0438\u00BB \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043A\u0438\u0445 \u0441\u0432\u043E\u0439\u0441\u0442\u0432 \u0434\u043E\u043A\u0430\u0437\u0430\u043B \u0441\u0432\u043E\u044E \u0443\u043D\u0438\u0432\u0435\u0440\u0441\u0430\u043B\u044C\u043D\u043E\u0441\u0442\u044C \u0438 \u043F\u043B\u043E\u0434\u043E\u0442\u0432\u043E\u0440\u043D\u043E \u043F\u0440\u0438\u043C\u0435\u043D\u044F\u0435\u0442\u0441\u044F \u0432\u043E \u043C\u043D\u043E\u0433\u0438\u0445 \u0435\u0441\u0442\u0435\u0441\u0442\u0432\u0435\u043D\u043D\u044B\u0445 \u043D\u0430\u0443\u043A\u0430\u0445 \u0438 \u0432 \u0442\u0435\u0445\u043D\u0438\u043A\u0435. \u0412 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0435 \u0430\u043D\u0430\u043B\u0438\u0442\u0438\u0447\u0435\u0441\u043A\u0430\u044F \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u044F \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u0442\u0430\u043A\u0436\u0435 \u043E\u0441\u043D\u043E\u0432\u043E\u0439 \u0434\u043B\u044F \u0434\u0440\u0443\u0433\u0438\u0445 \u0440\u0430\u0437\u0434\u0435\u043B\u043E\u0432 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0438 \u2014 \u043D\u0430\u043F\u0440\u0438\u043C\u0435\u0440, \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u043E\u0439, \u0430\u043B\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043A\u043E\u0439, \u043A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0440\u043D\u043E\u0439 \u0438 \u0432\u044B\u0447\u0438\u0441\u043B\u0438\u0442\u0435\u043B\u044C\u043D\u043E\u0439 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0438."@ru , "Die analytische Geometrie (auch Vektorgeometrie) ist ein Teilgebiet der Geometrie, das algebraische Hilfsmittel (vor allem aus der linearen Algebra) zur L\u00F6sung geometrischer Probleme bereitstellt. Sie erm\u00F6glicht es in vielen F\u00E4llen, geometrische Aufgabenstellungen rein rechnerisch zu l\u00F6sen, ohne die Anschauung zu Hilfe zu nehmen. Demgegen\u00FCber wird Geometrie, die ihre S\u00E4tze ohne Bezug zu einem Zahlensystem auf einer axiomatischen Grundlage begr\u00FCndet, als synthetische Geometrie bezeichnet. Die Verfahren der analytischen Geometrie werden in allen Naturwissenschaften angewendet, vor allem aber in der Physik, wie zum Beispiel bei der Beschreibung von Planetenbahnen. Urspr\u00FCnglich befasste sich die analytische Geometrie nur mit Fragestellungen der ebenen und der r\u00E4umlichen (euklidischen) Geometrie. Im allgemeinen Sinn jedoch beschreibt die analytische Geometrie affine R\u00E4ume beliebiger Dimension \u00FCber beliebigen K\u00F6rpern."@de . @prefix gold: . dbr:Analytic_geometry gold:hypernym dbr:Study . @prefix prov: . dbr:Analytic_geometry prov:wasDerivedFrom . @prefix xsd: . dbr:Analytic_geometry dbo:wikiPageLength "39700"^^xsd:nonNegativeInteger . @prefix wikipedia-en: . dbr:Analytic_geometry foaf:isPrimaryTopicOf wikipedia-en:Analytic_geometry .