. . . . "\u041A\u0430\u0441\u0430\u0301\u0442\u0435\u043B\u044C\u043D\u0430\u044F \u043F\u0440\u044F\u043C\u0430\u0301\u044F \u2014 \u043F\u0440\u044F\u043C\u0430\u044F, \u043F\u0440\u043E\u0445\u043E\u0434\u044F\u0449\u0430\u044F \u0447\u0435\u0440\u0435\u0437 \u0442\u043E\u0447\u043A\u0443 \u043A\u0440\u0438\u0432\u043E\u0439 \u0438 \u0441\u043E\u0432\u043F\u0430\u0434\u0430\u044E\u0449\u0430\u044F \u0441 \u043D\u0435\u0439 \u0432 \u044D\u0442\u043E\u0439 \u0442\u043E\u0447\u043A\u0435 \u0441 \u0442\u043E\u0447\u043D\u043E\u0441\u0442\u044C\u044E \u0434\u043E \u043F\u0435\u0440\u0432\u043E\u0433\u043E \u043F\u043E\u0440\u044F\u0434\u043A\u0430."@ru . . . "Prosta styczna do krzywej w punkcie to prosta, kt\u00F3ra jest granicznym po\u0142o\u017Ceniem siecznych przechodz\u0105cych przez punkty i gdy punkt d\u0105\u017Cy (zbli\u017Ca si\u0119) do punktu po krzywej ."@pl . "Tangent line"@en . . . "Tangente"@de . "\u0423 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0456\u0457, \u0434\u043E\u0442\u0438\u0301\u0447\u043D\u0430 \u043F\u0440\u044F\u043C\u0430\u0301 (\u0430\u0431\u043E \u043F\u0440\u043E\u0441\u0442\u043E \u0434\u043E\u0442\u0438\u0301\u0447\u043D\u0430) \u0434\u043E \u043A\u0440\u0438\u0432\u043E\u0457 \u0432 \u0442\u043E\u0447\u0446\u0456 \u2014 \u043F\u0440\u044F\u043C\u0430, \u044F\u043A\u0430 \u043F\u0440\u043E\u0445\u043E\u0434\u0438\u0442\u044C \u0447\u0435\u0440\u0435\u0437 \u0442\u043E\u0447\u043A\u0443 \u043A\u0440\u0438\u0432\u043E\u0457 \u0456 \u0437\u0431\u0456\u0433\u0430\u0454\u0442\u044C\u0441\u044F \u0437 \u043D\u0435\u044E \u0432 \u0446\u0456\u0439 \u0442\u043E\u0447\u0446\u0456 \u0437 \u0442\u043E\u0447\u043D\u0456\u0441\u0442\u044E \u0434\u043E \u043F\u0435\u0440\u0448\u043E\u0433\u043E \u043F\u043E\u0440\u044F\u0434\u043A\u0443. \u041A\u0430\u0436\u0443\u0447\u0438 \u0437\u0430\u0433\u0430\u043B\u044C\u043D\u0438\u043C\u0438 \u0441\u043B\u043E\u0432\u0430\u043C\u0438, \u0434\u043E\u0442\u0438\u0447\u043D\u0430 \u043F\u0440\u044F\u043C\u0430 \u2014 \u0446\u0435 \u043F\u0440\u044F\u043C\u0430, \u0449\u043E \u043D\u0430\u0439\u043A\u0440\u0430\u0449\u0435 \u043D\u0430\u0431\u043B\u0438\u0436\u0430\u0454 \u043A\u0440\u0438\u0432\u0443. \u041C\u043E\u0436\u043D\u0430 \u0434\u043E\u0442\u0438\u0447\u043D\u0443 \u043F\u0440\u044F\u043C\u0443 \u0432\u0438\u0437\u043D\u0430\u0447\u0438\u0442\u0438, \u044F\u043A \u0433\u0440\u0430\u043D\u0438\u0447\u043D\u0435 \u043F\u043E\u043B\u043E\u0436\u0435\u043D\u043D\u044F \u0441\u0456\u0447\u043D\u043E\u0457."@uk . . . . . . . "Tangente (g\u00E9om\u00E9trie)"@fr . . . . . . . . . "\u521D\u7B49\u5E7E\u4F55\u5B66\u306B\u304A\u3044\u3066\u63A5\u3059\u308B\uFF08\u305B\u3063\u3059\u308B\u3001\u82F1: tangent\uFF09\u3068\u306F\u3001\u305D\u306E\u540D\u3092\u300C\u89E6\u308C\u308B\u3053\u3068\u300D\u3092\u610F\u5473\u3059\u308B\u30E9\u30C6\u30F3\u8A9E: tangere \u306B\u7531\u6765\u3057\u3001\u300C\u305F\u3060\u89E6\u308C\u308B\u3060\u3051\u300D\u3068\u3044\u3046\u76F4\u89B3\u7684\u6982\u5FF5\u3092\u5B9A\u5F0F\u5316\u3059\u308B\u3082\u306E\u3067\u3042\u308B\u3002\u7279\u306B\u3001\u66F2\u7DDA\u306E\u63A5\u7DDA\uFF08\u305B\u3063\u305B\u3093\u3001\u82F1: tangent line\u3001tangent\uFF09\u306F\u3001\u5E73\u9762\u66F2\u7DDA\u306B\u5BFE\u3057\u3066\u306F\u3001\u66F2\u7DDA\u4E0A\u306E\u4E00\u70B9\u304C\u4E0E\u3048\u3089\u308C\u305F\u3068\u304D\u3001\u305D\u306E\u70B9\u306B\u304A\u3044\u3066\u66F2\u7DDA\u306B\u300C\u305F\u3060\u89E6\u308C\u308B\u3060\u3051\u300D\u306E\u76F4\u7DDA\u3092\u610F\u5473\u3059\u308B\u3002\u30E9\u30A4\u30D7\u30CB\u30C3\u30C4\u306F\u63A5\u7DDA\u3092\u3001\u66F2\u7DDA\u4E0A\u306E\u7121\u9650\u306B\u8FD1\u3044\u4E8C\u70B9\u3092\u901A\u308B\u76F4\u7DDA\u3068\u3057\u3066\u5B9A\u7FA9\u3057\u305F\u3002\u3088\u308A\u5177\u4F53\u7684\u306B\u89E3\u6790\u5E7E\u4F55\u5B66\u306B\u304A\u3044\u3066\u3001\u4E0E\u3048\u3089\u308C\u305F\u76F4\u7DDA\u304C\u66F2\u7DDA y = f(x) \u306E x = c\uFF08\u3042\u308B\u3044\u306F\u66F2\u7DDA\u4E0A\u306E\u70B9 (c, f(c)\uFF09\u306B\u304A\u3051\u308B\u63A5\u7DDA\u3067\u3042\u308B\u3068\u306F\u3001\u305D\u306E\u76F4\u7DDA\u304C\u66F2\u7DDA\u4E0A\u306E\u70B9 (c, f (c)) \u3092\u901A\u308A\u3001\u50BE\u304D\u304C f \u306E\u5FAE\u5206\u4FC2\u6570 f'(c) \u306B\u7B49\u3057\u3044\u3068\u304D\u306B\u8A00\u3046\u3002\u540C\u69D8\u306E\u5B9A\u7FA9\u306F\u7A7A\u9593\u66F2\u7DDA\u3084\u3088\u308A\u9AD8\u6B21\u306E\u30E6\u30FC\u30AF\u30EA\u30C3\u30C9\u7A7A\u9593\u5185\u306E\u66F2\u7DDA\u306B\u5BFE\u3057\u3066\u3082\u9069\u7528\u3067\u304D\u308B\u3002 \u66F2\u7DDA\u3068\u63A5\u7DDA\u304C\u76F8\u63A5\u3059\u308B\u70B9\u306F\u63A5\u70B9 (\u82F1: point of tangency) \u3068\u8A00\u3044\u3001\u66F2\u7DDA\u3068\u306E\u63A5\u70B9\u306B\u304A\u3044\u3066\u63A5\u7DDA\u306F\u66F2\u7DDA\u3068\u300C\u540C\u3058\u65B9\u5411\u3078\u300D\u9032\u3080\u3002\u305D\u306E\u610F\u5473\u306B\u304A\u3044\u3066\u63A5\u7DDA\u306F\u3001\u63A5\u70B9\u306B\u304A\u3051\u308B\u66F2\u7DDA\u306E\u6700\u9069\u76F4\u7DDA\u8FD1\u4F3C\u3067\u3042\u308B\u3002 \u540C\u69D8\u306B\u3001\u66F2\u9762\u306E\u63A5\u5E73\u9762\u306F\u3001\u63A5\u70B9\u306B\u304A\u3044\u3066\u305D\u306E\u66F2\u7DDA\u306B\u300C\u89E6\u308C\u308B\u3060\u3051\u300D\u306E\u5E73\u9762\u3067\u3042\u308B\u3002\u3053\u306E\u3088\u3046\u306A\u610F\u5473\u3067\u306E\u300C\u63A5\u3059\u308B\u300D\u3068\u3044\u3046\u6982\u5FF5\u306F\u5FAE\u5206\u5E7E\u4F55\u5B66\u306B\u304A\u3044\u3066\u6700\u3082\u57FA\u790E\u3068\u306A\u308B\u6982\u5FF5\u3067\u3042\u308A\u3001\u63A5\u7A7A\u9593\u3068\u3057\u3066\u5927\u3044\u306B\u4E00\u822C\u5316\u3055\u308C\u308B\u3002"@ja . . . . . . . . "La retta tangente assume vari significati nella geometria analitica. La parola tangente viene dal verbo latino tangere, ovvero toccare. L'idea intuitiva di una retta tangente a una curva \u00E8 quella di una retta che \"tocca\" la curva senza \"tagliarla\" o \"secarla\" (immaginando la curva come se fosse un oggetto fisico non penetrabile). Una retta che attraversa la curva \"tagliandola\" \u00E8 invece chiamata secante. Si ha un ulteriore modo di vedere il concetto di tangenza pensando che la tangente in un punto P a una curva \u03B3 \u00E8 la retta che approssima meglio \u03B3 nei dintorni di P."@it . . . . . . . "En geometrio tan\u011Danto estas rekto kiu tu\u015Das kurbon en iu punkto, kaj trapasas tiun punkton samdirekte kiel la kurbo; tan\u011Danto estas la plej bone alproksimi\u011Do de rekto al la kurbo \u0109e tiu punkto. La kurbo tie havas la saman inklinon kiel la tan\u011Danto. Oni diras ke tan\u011Danto estas tan\u011Da al la kurbo (a\u016D tan\u011Das la kurbon). En la grava kazo kiam la kurbo estas cirklo, oni povas difini la tan\u011Danton kiel iun rektan linion, kiu tu\u015Das la cirklon precize unufoje. Tamen tiu difino ne funkcias por \u011Deneralaj kurboj, \u0109ar unuflanke eblas ke ne-tan\u011Danta linio tu\u015Das kurbon nur unufoje, kaj aliflanke eblas ke tan\u011Danto tu\u015Das kurbon dufoje, kiel montras jena ekzemplo"@eo . . . . "\u0645\u0645\u0627\u0633"@ar . . . "La tangente\u2009\u200B a una curva en un punto P es una recta que toca a la curva solo en dicho punto, llamado punto de tangencia. Se puede decir que la tangente forma un \u00E1ngulo nulo con la curva en la vecindad de dicho punto. Esta noci\u00F3n se puede generalizar desde la recta tangente a un c\u00EDrculo o una curva a figuras tangentes en dos dimensiones \u2014es decir, figuras geom\u00E9tricas con un \u00FAnico punto de contacto (por ejemplo, la circunferencia inscrita)\u2014, hasta los espacios tangentes, en donde se clasifica el concepto de tangencia en m\u00E1s dimensiones."@es . . . . "Eine Tangente (von lateinisch: tangere \u201Aber\u00FChren\u2018) ist in der Geometrie eine Gerade, die eine gegebene Kurve in einem bestimmten Punkt ber\u00FChrt. Beispielsweise ist die Schiene f\u00FCr das Rad eine Tangente, da der Auflagepunkt des Rades ein Ber\u00FChrungspunkt der beiden geometrischen Objekte, Gerade und Kreis, ist. Tangente und Kurve haben im Ber\u00FChrungspunkt die gleiche Richtung. Die Tangente ist in diesem Punkt die beste lineare N\u00E4herungsfunktion f\u00FCr die Kurve."@de . "Te\u010Dna ke k\u0159ivce je p\u0159\u00EDmka, kter\u00E1 m\u00E1 v bod\u011B dotyku stejn\u00FD sm\u011Brov\u00FD vektor jako tato k\u0159ivka. K\u0159ivka m\u016F\u017Ee b\u00FDt zad\u00E1na jako graf funkce jedn\u00E9 prom\u011Bnn\u00E9. Zpravidla (pro neline\u00E1rn\u00ED funkce) m\u00E1 te\u010Dna s k\u0159ivkou lok\u00E1ln\u011B v okol\u00ED bodu dotyku spole\u010Dn\u00FD jeden bod a zpravidla (mimo inflexn\u00ED body) le\u017E\u00ED okoln\u00ED body k\u0159ivky ve stejn\u00E9 polorovin\u011B ur\u010Den\u00E9 te\u010Dnou."@cs . "Zuzen ukitzaile"@eu . "\uC811\uC120"@ko . "Tangent"@en . . . . . "Na geometria, a tangente de uma curva em um ponto P pertencente a ela, \u00E9 uma reta definida a partir de um outro ponto Q pertencente \u00E0 curva, muito pr\u00F3ximo do ponto P. Ao tra\u00E7armos uma reta r que passa pelos dois pontos, \u00E9 a posi\u00E7\u00E3o para onde a reta r tende, \u00E0 medida que Q se aproxima de P, \"caminhando\" sobre a curva. Gottfried Wilhelm Leibniz definiu-a como uma linha infinitesimal em rela\u00E7\u00E3o ao ponto da curva que ela cruza. Em linhas gerais, uma reta se torna tangente de uma curva y = f(x) no ponto x = c, se esta passar pelo par ordenado (c, f(c)) e ter inclina\u00E7\u00E3o f\u2019(c), na qual f\u2019 \u00E9 derivada de f. A reta tangente a um ponto de uma curva diferenci\u00E1vel tamb\u00E9m pode ser pensada como o gr\u00E1fico da fun\u00E7\u00E3o afim que melhor aproxima a fun\u00E7\u00E3o original no ponto dado."@pt . . . . . . . "\u521D\u7B49\u5E7E\u4F55\u5B66\u306B\u304A\u3044\u3066\u63A5\u3059\u308B\uFF08\u305B\u3063\u3059\u308B\u3001\u82F1: tangent\uFF09\u3068\u306F\u3001\u305D\u306E\u540D\u3092\u300C\u89E6\u308C\u308B\u3053\u3068\u300D\u3092\u610F\u5473\u3059\u308B\u30E9\u30C6\u30F3\u8A9E: tangere \u306B\u7531\u6765\u3057\u3001\u300C\u305F\u3060\u89E6\u308C\u308B\u3060\u3051\u300D\u3068\u3044\u3046\u76F4\u89B3\u7684\u6982\u5FF5\u3092\u5B9A\u5F0F\u5316\u3059\u308B\u3082\u306E\u3067\u3042\u308B\u3002\u7279\u306B\u3001\u66F2\u7DDA\u306E\u63A5\u7DDA\uFF08\u305B\u3063\u305B\u3093\u3001\u82F1: tangent line\u3001tangent\uFF09\u306F\u3001\u5E73\u9762\u66F2\u7DDA\u306B\u5BFE\u3057\u3066\u306F\u3001\u66F2\u7DDA\u4E0A\u306E\u4E00\u70B9\u304C\u4E0E\u3048\u3089\u308C\u305F\u3068\u304D\u3001\u305D\u306E\u70B9\u306B\u304A\u3044\u3066\u66F2\u7DDA\u306B\u300C\u305F\u3060\u89E6\u308C\u308B\u3060\u3051\u300D\u306E\u76F4\u7DDA\u3092\u610F\u5473\u3059\u308B\u3002\u30E9\u30A4\u30D7\u30CB\u30C3\u30C4\u306F\u63A5\u7DDA\u3092\u3001\u66F2\u7DDA\u4E0A\u306E\u7121\u9650\u306B\u8FD1\u3044\u4E8C\u70B9\u3092\u901A\u308B\u76F4\u7DDA\u3068\u3057\u3066\u5B9A\u7FA9\u3057\u305F\u3002\u3088\u308A\u5177\u4F53\u7684\u306B\u89E3\u6790\u5E7E\u4F55\u5B66\u306B\u304A\u3044\u3066\u3001\u4E0E\u3048\u3089\u308C\u305F\u76F4\u7DDA\u304C\u66F2\u7DDA y = f(x) \u306E x = c\uFF08\u3042\u308B\u3044\u306F\u66F2\u7DDA\u4E0A\u306E\u70B9 (c, f(c)\uFF09\u306B\u304A\u3051\u308B\u63A5\u7DDA\u3067\u3042\u308B\u3068\u306F\u3001\u305D\u306E\u76F4\u7DDA\u304C\u66F2\u7DDA\u4E0A\u306E\u70B9 (c, f (c)) \u3092\u901A\u308A\u3001\u50BE\u304D\u304C f \u306E\u5FAE\u5206\u4FC2\u6570 f'(c) \u306B\u7B49\u3057\u3044\u3068\u304D\u306B\u8A00\u3046\u3002\u540C\u69D8\u306E\u5B9A\u7FA9\u306F\u7A7A\u9593\u66F2\u7DDA\u3084\u3088\u308A\u9AD8\u6B21\u306E\u30E6\u30FC\u30AF\u30EA\u30C3\u30C9\u7A7A\u9593\u5185\u306E\u66F2\u7DDA\u306B\u5BFE\u3057\u3066\u3082\u9069\u7528\u3067\u304D\u308B\u3002 \u66F2\u7DDA\u3068\u63A5\u7DDA\u304C\u76F8\u63A5\u3059\u308B\u70B9\u306F\u63A5\u70B9 (\u82F1: point of tangency) \u3068\u8A00\u3044\u3001\u66F2\u7DDA\u3068\u306E\u63A5\u70B9\u306B\u304A\u3044\u3066\u63A5\u7DDA\u306F\u66F2\u7DDA\u3068\u300C\u540C\u3058\u65B9\u5411\u3078\u300D\u9032\u3080\u3002\u305D\u306E\u610F\u5473\u306B\u304A\u3044\u3066\u63A5\u7DDA\u306F\u3001\u63A5\u70B9\u306B\u304A\u3051\u308B\u66F2\u7DDA\u306E\u6700\u9069\u76F4\u7DDA\u8FD1\u4F3C\u3067\u3042\u308B\u3002 \u540C\u69D8\u306B\u3001\u66F2\u9762\u306E\u63A5\u5E73\u9762\u306F\u3001\u63A5\u70B9\u306B\u304A\u3044\u3066\u305D\u306E\u66F2\u7DDA\u306B\u300C\u89E6\u308C\u308B\u3060\u3051\u300D\u306E\u5E73\u9762\u3067\u3042\u308B\u3002\u3053\u306E\u3088\u3046\u306A\u610F\u5473\u3067\u306E\u300C\u63A5\u3059\u308B\u300D\u3068\u3044\u3046\u6982\u5FF5\u306F\u5FAE\u5206\u5E7E\u4F55\u5B66\u306B\u304A\u3044\u3066\u6700\u3082\u57FA\u790E\u3068\u306A\u308B\u6982\u5FF5\u3067\u3042\u308A\u3001\u63A5\u7A7A\u9593\u3068\u3057\u3066\u5927\u3044\u306B\u4E00\u822C\u5316\u3055\u308C\u308B\u3002"@ja . . . . . "p/t092170"@en . "Tangente (geometr\u00EDa)"@es . . . . . . . . "\u63A5\u7DDA"@ja . . . . . . "En tangent \u00E4r inom plangeometri en r\u00E4t linje, som tangerar en kurva i en punkt, tangeringspunkten, i vilken tangentens lutning, eller riktningskoefficient, \u00E4r lika med kurvans lutning, dess derivata. Stringent uttryckt, s\u00E4gs en r\u00E4t linje vara en tangent till kurvan f(x) i punkten (c, f(c)), om linjen g\u00E5r genom punkten och har lutningen f'(c), d\u00E4r f(x) \u00E4r derivatan av f(x). Inom geometrin kan en tangent approximeras med en sekant. Om tangeringspunkten och riktningskoefficienten f\u00F6r tangenten \u00E4r k\u00E4nd, kan tangentens ekvation best\u00E4mmas med enpunktsformen vilken \u00E4ven kan skrivas p\u00E5 k-form"@sv . "Tangente (geometria)"@pt . . "Te\u010Dna ke k\u0159ivce je p\u0159\u00EDmka, kter\u00E1 m\u00E1 v bod\u011B dotyku stejn\u00FD sm\u011Brov\u00FD vektor jako tato k\u0159ivka. K\u0159ivka m\u016F\u017Ee b\u00FDt zad\u00E1na jako graf funkce jedn\u00E9 prom\u011Bnn\u00E9. Zpravidla (pro neline\u00E1rn\u00ED funkce) m\u00E1 te\u010Dna s k\u0159ivkou lok\u00E1ln\u011B v okol\u00ED bodu dotyku spole\u010Dn\u00FD jeden bod a zpravidla (mimo inflexn\u00ED body) le\u017E\u00ED okoln\u00ED body k\u0159ivky ve stejn\u00E9 polorovin\u011B ur\u010Den\u00E9 te\u010Dnou."@cs . "In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that \"just touches\" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. More precisely, a straight line is said to be a tangent of a curve y = f(x) at a point x = c if the line passes through the point (c, f(c)) on the curve and has slope f'(c), where f' is the derivative of f. A similar definition applies to space curves and curves in n-dimensional Euclidean space. As it passes through the point where the tangent line and the curve meet, called the point of tangency, the tangent line is \"going in the same direction\" as the curve, and is thus the best straight-line approximation to the curve at that point. The tangent line to a point on a differentiable curve can also be thought of as a tangent line approximation, the graph of the affine function that best approximates the original function at the given point. Similarly, the tangent plane to a surface at a given point is the plane that \"just touches\" the surface at that point. The concept of a tangent is one of the most fundamental notions in differential geometry and has been extensively generalized; see Tangent space. The word \"tangent\" comes from the Latin tangere, \"to touch\"."@en . . "Te\u010Dna"@cs . "La tangent (del llat\u00ED tangens \"que toca\") \u00E9s una recta que toca una corba en un punt, tot i que sense tallar-la (si, contr\u00E0riament, ho fes, aleshores seria una secant)."@ca . . . "Dalam geometri, garis singgung (disebut juga garis tangen) kurva bidang pada titik yang diketahui adalah garis lurus yang \"hanya menyentuh\" kurva pada titik tersebut. Leibniz mendefinisikan garis singgung sebagai garis yang melalui sepasang titik pada kurva. Lebih tepatnya, garis lurus disebut menyinggung kurva y = f (x) di titik x = c pada kurva jika garis melalui titik (c, f (c)) pada kurva dan memiliki kemiringan f '(c) dengan f ' adalah turunan f. Definisi serupa digunakan pada kurva ruang dan kurva dalam ruang Euklides dimensi-n."@in . . . . . . "\u041A\u0430\u0441\u0430\u0442\u0435\u043B\u044C\u043D\u0430\u044F \u043F\u0440\u044F\u043C\u0430\u044F"@ru . . "Tangent"@ca . . "Tangente vient du latin tangere, toucher : en g\u00E9om\u00E9trie, la tangente \u00E0 une courbe en un de ses points est une droite qui \u00AB touche \u00BB la courbe au plus pr\u00E8s au voisinage de ce point. La courbe et sa tangente forment alors un angle nul en ce point. La notion de tangente permet d'effectuer des approximations : pour la r\u00E9solution de certains probl\u00E8mes qui demandent de conna\u00EEtre le comportement de la courbe au voisinage d'un point, on peut assimiler celle-ci \u00E0 sa tangente. Ceci explique la parent\u00E9 entre la notion de tangente et le calcul diff\u00E9rentiel."@fr . "Tangente (geometria)"@it . . . "En tangent \u00E4r inom plangeometri en r\u00E4t linje, som tangerar en kurva i en punkt, tangeringspunkten, i vilken tangentens lutning, eller riktningskoefficient, \u00E4r lika med kurvans lutning, dess derivata. Stringent uttryckt, s\u00E4gs en r\u00E4t linje vara en tangent till kurvan f(x) i punkten (c, f(c)), om linjen g\u00E5r genom punkten och har lutningen f'(c), d\u00E4r f(x) \u00E4r derivatan av f(x). Inom geometrin kan en tangent approximeras med en sekant. Om tangeringspunkten och riktningskoefficienten f\u00F6r tangenten \u00E4r k\u00E4nd, kan tangentens ekvation best\u00E4mmas med enpunktsformen vilken \u00E4ven kan skrivas p\u00E5 k-form d\u00E4r k \u00E4r riktningskoefficienten och tangeringspunkten \u00E4r (x0, y0). I det specialfall, d\u00E4r kurvan \u00E4r en cirkel, \u00E4r tangenten vinkelr\u00E4t mot radien. Inom tredimensionell geometri bildar alla tangenter till en yta i tangeringspunkten ett tangentplan. Vid fler dimensioner talar man om tangentrum."@sv . . . . . . . . . . . . . . "La retta tangente assume vari significati nella geometria analitica. La parola tangente viene dal verbo latino tangere, ovvero toccare. L'idea intuitiva di una retta tangente a una curva \u00E8 quella di una retta che \"tocca\" la curva senza \"tagliarla\" o \"secarla\" (immaginando la curva come se fosse un oggetto fisico non penetrabile). Una retta che attraversa la curva \"tagliandola\" \u00E8 invece chiamata secante. Data inoltre una secante che passa per due punti distinti P e Q di una curva, si pu\u00F2 pensare la tangente in P come la retta cui tende (eventualmente) la secante quando il punto Q si avvicina a P lungo la curva. Si ha un ulteriore modo di vedere il concetto di tangenza pensando che la tangente in un punto P a una curva \u03B3 \u00E8 la retta che approssima meglio \u03B3 nei dintorni di P. Anche da queste definizioni informali ci si rende conto che possono esistere casi in cui la retta tangente non \u00E8 definita. Ad esempio, se la curva \u00E8 costituita dal perimetro di un triangolo e P \u00E8 un vertice, nessuna delle due definizioni precedenti corrisponde univocamente a una retta passante per P. Nell'ambito della geometria sintetica si possono dare definizioni rigorose alternative di retta tangente a curve specifiche che funzionano solo per tali curve. Ad esempio la tangente ad una circonferenza di centro O e raggio r in un suo punto P pu\u00F2 essere definita come la retta passante per P e avente distanza r da O, o come l'unica retta del piano avente in comune con la circonferenza il solo punto P. In una geometria a pi\u00F9 dimensioni, si pu\u00F2 definire il piano tangente ad una superficie in modo simile e, generalizzando, lo spazio tangente. Per definire la tangente nel caso di una curva generica in genere si ricorre agli strumenti del calcolo infinitesimale."@it . . . . . . . . . . . . "Dalam geometri, garis singgung (disebut juga garis tangen) kurva bidang pada titik yang diketahui adalah garis lurus yang \"hanya menyentuh\" kurva pada titik tersebut. Leibniz mendefinisikan garis singgung sebagai garis yang melalui sepasang titik pada kurva. Lebih tepatnya, garis lurus disebut menyinggung kurva y = f (x) di titik x = c pada kurva jika garis melalui titik (c, f (c)) pada kurva dan memiliki kemiringan f '(c) dengan f ' adalah turunan f. Definisi serupa digunakan pada kurva ruang dan kurva dalam ruang Euklides dimensi-n. Karena melalui titik di mana garis singgung dan kurva bertemu, disebut titik singgung, garis singgung \"memiliki arah yang sama\" dengan kurva, dan dengan demikian merupakan pendekatan garis lurus terbaik pada kurva di titik tersebut. Serupa dengan garis singgung, bidang singgung permukaan di titik yang diketahui adalah bidang yang \"hanya menyentuh\" permukaan di titik tersebut. Konsep persinggungan adalah satu dari gagasan paling mendasar dalam geometri diferensial dan telah digeneralisasikan secara ekstensif; lihat . Kata \"tangen\" berasal dari bahasa Latin tangere, yang berarti 'menyentuh'."@in . . . . . "Tangent Line"@en . . . . . . . . . . . . . . . . "31482"^^ . . "Na geometria, a tangente de uma curva em um ponto P pertencente a ela, \u00E9 uma reta definida a partir de um outro ponto Q pertencente \u00E0 curva, muito pr\u00F3ximo do ponto P. Ao tra\u00E7armos uma reta r que passa pelos dois pontos, \u00E9 a posi\u00E7\u00E3o para onde a reta r tende, \u00E0 medida que Q se aproxima de P, \"caminhando\" sobre a curva. Gottfried Wilhelm Leibniz definiu-a como uma linha infinitesimal em rela\u00E7\u00E3o ao ponto da curva que ela cruza. Em linhas gerais, uma reta se torna tangente de uma curva y = f(x) no ponto x = c, se esta passar pelo par ordenado (c, f(c)) e ter inclina\u00E7\u00E3o f\u2019(c), na qual f\u2019 \u00E9 derivada de f. A reta tangente a um ponto de uma curva diferenci\u00E1vel tamb\u00E9m pode ser pensada como o gr\u00E1fico da fun\u00E7\u00E3o afim que melhor aproxima a fun\u00E7\u00E3o original no ponto dado."@pt . . "Tangente vient du latin tangere, toucher : en g\u00E9om\u00E9trie, la tangente \u00E0 une courbe en un de ses points est une droite qui \u00AB touche \u00BB la courbe au plus pr\u00E8s au voisinage de ce point. La courbe et sa tangente forment alors un angle nul en ce point. La notion de tangente permet d'effectuer des approximations : pour la r\u00E9solution de certains probl\u00E8mes qui demandent de conna\u00EEtre le comportement de la courbe au voisinage d'un point, on peut assimiler celle-ci \u00E0 sa tangente. Ceci explique la parent\u00E9 entre la notion de tangente et le calcul diff\u00E9rentiel. Se contenter comme on le fait parfois de d\u00E9finir la tangente comme une droite qui \u00AB touche la courbe sans la traverser \u00BB serait incorrect, puisque \n* rien n'emp\u00EAche la courbe de retraverser une de ses tangentes un peu plus loin (le concept de tangente au point M ne d\u00E9crit bien la situation que dans un petit voisinage du point M). \n* il y a des situations exceptionnelles o\u00F9 la tangente en M traverse la courbe justement au point M. On dit alors qu'il y a une inflexion en M. L'homologue de la notion de tangente pour les surfaces est celle de plan tangent. Il peut \u00EAtre d\u00E9fini en consid\u00E9rant l'ensemble des courbes trac\u00E9es sur la surface et passant par un point donn\u00E9, et en consid\u00E9rant l'ensemble des tangentes obtenu. On peut ensuite g\u00E9n\u00E9raliser \u00E0 des objets de dimension plus grande que 2."@fr . . . "24749"^^ . . . . . "\u0414\u043E\u0442\u0438\u0447\u043D\u0430"@uk . . "TangentLine"@en . . . . . . . "1092236138"^^ . . . . . "Geometrian, zuzen ukitzailea edo zuzen tangentea kurba bat puntu batean ukitu bakarrik egiten duen zuzen bat da, kurbarekiko angelu nulu bat osatuz. Horrela, kurbaren malda eta zuzen ukitzailearen malda berdinak dira puntu horretan. kurba baten funtzioa izanik, kurbaren tangentea puntu batean honela kalkulatzen da, kurbaren funtzioaren deribatuan oinarriturik: Adibidez, kurbaren zuzenaren ekuazioa puntuan honela kalkulatzen da, kurbaren deribatua dela jakinik:"@eu . . "\u5207\u7DDA\uFF08\u82F1\u8A9E\uFF1Atangent line\uFF09\uFF0C\u70BA\u4E00\u5E7E\u4F55\u540D\u8A5E\uFF0C\u61C9\u7528\u65BC\u66F2\u7DDA\u53CA\u5E73\u9762\u5713\u6642\u610F\u7FA9\u6709\u6240\u4E0D\u540C\u3002 \u8BBEL\u4E3A\u4E00\u6761\u66F2\u7EBF\uFF0CA, B\u4E3A\u6B64\u66F2\u7EBF\u4E0A\u7684\u70B9\uFF0C\u8FC7\u6B64\u4E8C\u70B9\u4F5C\u66F2\u7EBF\u7684\u5272\u7EBF\uFF0C\u4EE4B\u8D8B\u5411A\uFF0C\u5982\u679C\u5272\u7EBF\u7684\u6975\u9650\u5B58\u5728\uFF0C\u5219\u79F0\u6B64\u6781\u9650\uFF08\u4E00\u6761\u76F4\u7EBF\uFF09\u4E3A\u66F2\u7EBF\u5728A\u7684\u5207\u7EBF\uFF0C\u7A31\u9019\u689D\u76F4\u7DDA\u8207\u66F2\u7EBF\u76F8\u5207\u3002"@zh . . . . . "Prosta styczna do krzywej w punkcie to prosta, kt\u00F3ra jest granicznym po\u0142o\u017Ceniem siecznych przechodz\u0105cych przez punkty i gdy punkt d\u0105\u017Cy (zbli\u017Ca si\u0119) do punktu po krzywej ."@pl . "\u5207\u7DDA\uFF08\u82F1\u8A9E\uFF1Atangent line\uFF09\uFF0C\u70BA\u4E00\u5E7E\u4F55\u540D\u8A5E\uFF0C\u61C9\u7528\u65BC\u66F2\u7DDA\u53CA\u5E73\u9762\u5713\u6642\u610F\u7FA9\u6709\u6240\u4E0D\u540C\u3002 \u8BBEL\u4E3A\u4E00\u6761\u66F2\u7EBF\uFF0CA, B\u4E3A\u6B64\u66F2\u7EBF\u4E0A\u7684\u70B9\uFF0C\u8FC7\u6B64\u4E8C\u70B9\u4F5C\u66F2\u7EBF\u7684\u5272\u7EBF\uFF0C\u4EE4B\u8D8B\u5411A\uFF0C\u5982\u679C\u5272\u7EBF\u7684\u6975\u9650\u5B58\u5728\uFF0C\u5219\u79F0\u6B64\u6781\u9650\uFF08\u4E00\u6761\u76F4\u7EBF\uFF09\u4E3A\u66F2\u7EBF\u5728A\u7684\u5207\u7EBF\uFF0C\u7A31\u9019\u689D\u76F4\u7DDA\u8207\u66F2\u7EBF\u76F8\u5207\u3002"@zh . . . . . . "Styczna"@pl . . . . . . . . . . "\u0627\u0644\u0645\u0645\u0627\u0633\u064F\u0651 \u0623\u0648 \u0627\u0644\u0645\u0633\u062A\u0642\u064A\u0645 \u0627\u0644\u0645\u0627\u0633\u0651 \u0623\u0648 \u062E\u0637 \u0627\u0644\u0638\u0644 \u0623\u0648 \u0627\u0644\u062E\u0637 \u0627\u0644\u0645\u064F\u0645\u0627\u0633\u0651 \u0647\u0648 \u062E\u0637 \u064A\u0645\u0631 \u0628\u0646\u0642\u0637\u0629 \u0648\u062D\u064A\u062F\u0629 \u0645\u0646 \u062F\u0627\u0626\u0631\u0629\u064D \u0623\u0648 \u0645\u0646\u062D\u0646\u0649. \u0627\u0644\u0645\u0645\u0627\u0633 \u0641\u064A \u062D\u0627\u0644\u0629 \u0645\u0646\u062D\u0646\u0649 \u0639\u0627\u0645 \u064A\u064F\u0633\u062A\u062E\u062F\u0645 \u0644\u0644\u062A\u0641\u0627\u0636\u0644 (Differential Calculus). \u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u062A\u0645\u0627\u0633 \u0647\u064A \u0648\u0627\u062D\u062F \u0645\u0646 \u0623\u0643\u062B\u0631 \u0627\u0644\u0645\u0641\u0627\u0647\u064A\u0645 \u0627\u0644\u0623\u0633\u0627\u0633\u064A\u0629 \u0641\u064A \u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u062A\u0641\u0627\u0636\u0644\u064A\u0629 \u0648\u062C\u0631\u0649 \u062A\u0639\u0645\u064A\u0645\u0647 \u0639\u0644\u0649 \u0646\u0637\u0627\u0642 \u0648\u0627\u0633\u0639\u060C \u0627\u0646\u0638\u0631 (Tangent space)."@ar . "Raaklijn"@nl . "\u5207\u7EBF"@zh . . . . . . "Tangent (matematik)"@sv . . "En geometrio tan\u011Danto estas rekto kiu tu\u015Das kurbon en iu punkto, kaj trapasas tiun punkton samdirekte kiel la kurbo; tan\u011Danto estas la plej bone alproksimi\u011Do de rekto al la kurbo \u0109e tiu punkto. La kurbo tie havas la saman inklinon kiel la tan\u011Danto. Oni diras ke tan\u011Danto estas tan\u011Da al la kurbo (a\u016D tan\u011Das la kurbon)."@eo . . . "Tan\u011Danto"@eo . . . . . "La tangent (del llat\u00ED tangens \"que toca\") \u00E9s una recta que toca una corba en un punt, tot i que sense tallar-la (si, contr\u00E0riament, ho fes, aleshores seria una secant)."@ca . . "\uC811\uC120(\u63A5\u7DDA, \uBB38\uD654\uC5B4: \uB2FF\uC774\uC120(--\u7DDA), \uC601\uC5B4: tangent)\uC740 \uACE1\uC120L\uC758 \uB450\uC810 A\uC640 B\uB85C \uC815\uC758\uB418\uB294 \uD560\uC120 AB\uC5D0\uC11C \uC810 B\uAC00 \uACE1\uC120\uC744 \uB530\uB77C \uC810 A\uC5D0 \uD55C\uC5C6\uC774 \uAC00\uAE4C\uC6CC \uC9C8\uB54C, \uC774 \uC0C8\uB85C\uC6B4 \uC9C1\uC120\uC744 \uACE1\uC120L\uC758 A\uC5D0\uC11C \uB9CC\uB098\uB294 \uC811\uC120\uC774\uB77C \uD55C\uB2E4. \uBCF4\uD1B5 \uC811\uC120\uC740 \uBBF8\uBD84\uC744 \uC774\uC6A9\uD574 \uCC3E\uB294\uB2E4."@ko . . . . . . "L\u00EDne, de ghn\u00E1th l\u00EDne dh\u00EDreach, a dh\u00E9anann tadhall le cuar ag pointe ar leith, a bhfuil an gr\u00E1d\u00E1n c\u00E9anna acu araon ag an bpointe sin. Mar shampla, t\u00E1 tadhla\u00ED ciorcail ag pointe ar leith ingearach le ga an chiorcail tr\u00EDd an bpointe sin."@ga . . . . . "\u0423 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0456\u0457, \u0434\u043E\u0442\u0438\u0301\u0447\u043D\u0430 \u043F\u0440\u044F\u043C\u0430\u0301 (\u0430\u0431\u043E \u043F\u0440\u043E\u0441\u0442\u043E \u0434\u043E\u0442\u0438\u0301\u0447\u043D\u0430) \u0434\u043E \u043A\u0440\u0438\u0432\u043E\u0457 \u0432 \u0442\u043E\u0447\u0446\u0456 \u2014 \u043F\u0440\u044F\u043C\u0430, \u044F\u043A\u0430 \u043F\u0440\u043E\u0445\u043E\u0434\u0438\u0442\u044C \u0447\u0435\u0440\u0435\u0437 \u0442\u043E\u0447\u043A\u0443 \u043A\u0440\u0438\u0432\u043E\u0457 \u0456 \u0437\u0431\u0456\u0433\u0430\u0454\u0442\u044C\u0441\u044F \u0437 \u043D\u0435\u044E \u0432 \u0446\u0456\u0439 \u0442\u043E\u0447\u0446\u0456 \u0437 \u0442\u043E\u0447\u043D\u0456\u0441\u0442\u044E \u0434\u043E \u043F\u0435\u0440\u0448\u043E\u0433\u043E \u043F\u043E\u0440\u044F\u0434\u043A\u0443. \u041A\u0430\u0436\u0443\u0447\u0438 \u0437\u0430\u0433\u0430\u043B\u044C\u043D\u0438\u043C\u0438 \u0441\u043B\u043E\u0432\u0430\u043C\u0438, \u0434\u043E\u0442\u0438\u0447\u043D\u0430 \u043F\u0440\u044F\u043C\u0430 \u2014 \u0446\u0435 \u043F\u0440\u044F\u043C\u0430, \u0449\u043E \u043D\u0430\u0439\u043A\u0440\u0430\u0449\u0435 \u043D\u0430\u0431\u043B\u0438\u0436\u0430\u0454 \u043A\u0440\u0438\u0432\u0443. \u041C\u043E\u0436\u043D\u0430 \u0434\u043E\u0442\u0438\u0447\u043D\u0443 \u043F\u0440\u044F\u043C\u0443 \u0432\u0438\u0437\u043D\u0430\u0447\u0438\u0442\u0438, \u044F\u043A \u0433\u0440\u0430\u043D\u0438\u0447\u043D\u0435 \u043F\u043E\u043B\u043E\u0436\u0435\u043D\u043D\u044F \u0441\u0456\u0447\u043D\u043E\u0457."@uk . . . . "In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that \"just touches\" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. More precisely, a straight line is said to be a tangent of a curve y = f(x) at a point x = c if the line passes through the point (c, f(c)) on the curve and has slope f'(c), where f' is the derivative of f. A similar definition applies to space curves and curves in n-dimensional Euclidean space. The word \"tangent\" comes from the Latin tangere, \"to touch\"."@en . . . . . . . . . "Tadhla\u00ED"@ga . . . . . . . "\uC811\uC120(\u63A5\u7DDA, \uBB38\uD654\uC5B4: \uB2FF\uC774\uC120(--\u7DDA), \uC601\uC5B4: tangent)\uC740 \uACE1\uC120L\uC758 \uB450\uC810 A\uC640 B\uB85C \uC815\uC758\uB418\uB294 \uD560\uC120 AB\uC5D0\uC11C \uC810 B\uAC00 \uACE1\uC120\uC744 \uB530\uB77C \uC810 A\uC5D0 \uD55C\uC5C6\uC774 \uAC00\uAE4C\uC6CC \uC9C8\uB54C, \uC774 \uC0C8\uB85C\uC6B4 \uC9C1\uC120\uC744 \uACE1\uC120L\uC758 A\uC5D0\uC11C \uB9CC\uB098\uB294 \uC811\uC120\uC774\uB77C \uD55C\uB2E4. \uBCF4\uD1B5 \uC811\uC120\uC740 \uBBF8\uBD84\uC744 \uC774\uC6A9\uD574 \uCC3E\uB294\uB2E4."@ko . "Eine Tangente (von lateinisch: tangere \u201Aber\u00FChren\u2018) ist in der Geometrie eine Gerade, die eine gegebene Kurve in einem bestimmten Punkt ber\u00FChrt. Beispielsweise ist die Schiene f\u00FCr das Rad eine Tangente, da der Auflagepunkt des Rades ein Ber\u00FChrungspunkt der beiden geometrischen Objekte, Gerade und Kreis, ist. Tangente und Kurve haben im Ber\u00FChrungspunkt die gleiche Richtung. Die Tangente ist in diesem Punkt die beste lineare N\u00E4herungsfunktion f\u00FCr die Kurve. Besonders einfach sind die Verh\u00E4ltnisse beim Kreis: Alle Geraden k\u00F6nnen bez\u00FCglich eines Kreises unterschieden werden in Sekanten, Tangenten und Passanten \u2013 je nachdem, ob sie mit dem Kreis zwei Punkte, einen oder gar keinen Punkt gemeinsam haben. Die Kreistangente trifft den Kreis also in genau einem Punkt. Sie steht dort senkrecht auf dem zu diesem Punkt geh\u00F6renden Ber\u00FChrungsradius. Auch im allgemeinen Fall steht die Tangente senkrecht auf dem zum Ber\u00FChrungspunkt geh\u00F6renden Radius des Kr\u00FCmmungskreises, sofern dieser existiert. Sie kann aber mit der Ausgangskurve noch weitere Punkte gemeinsam haben. Ist ein weiterer Punkt (der Ausgangskurve oder einer anderen Kurve) ebenfalls Ber\u00FChrpunkt, so spricht man von einer Bitangente."@de . . "L\u00EDne, de ghn\u00E1th l\u00EDne dh\u00EDreach, a dh\u00E9anann tadhall le cuar ag pointe ar leith, a bhfuil an gr\u00E1d\u00E1n c\u00E9anna acu araon ag an bpointe sin. Mar shampla, t\u00E1 tadhla\u00ED ciorcail ag pointe ar leith ingearach le ga an chiorcail tr\u00EDd an bpointe sin."@ga . . . . . . "La tangente\u2009\u200B a una curva en un punto P es una recta que toca a la curva solo en dicho punto, llamado punto de tangencia. Se puede decir que la tangente forma un \u00E1ngulo nulo con la curva en la vecindad de dicho punto. Esta noci\u00F3n se puede generalizar desde la recta tangente a un c\u00EDrculo o una curva a figuras tangentes en dos dimensiones \u2014es decir, figuras geom\u00E9tricas con un \u00FAnico punto de contacto (por ejemplo, la circunferencia inscrita)\u2014, hasta los espacios tangentes, en donde se clasifica el concepto de tangencia en m\u00E1s dimensiones."@es . "De raaklijn of tangent aan een kromme in een punt van die kromme is in de meetkunde de rechte lijn door dat punt die in dat punt dezelfde richting heeft als de kromme. Het punt waarin de raaklijn de kromme raakt, heet raakpunt, soms ook tangentpunt. De raaklijn is de benadering van de kromme in het raakpunt door een rechte lijn. De raaklijn kan de kromme eventueel nog snijden in een ander punt dan het raakpunt."@nl . "Geometrian, zuzen ukitzailea edo zuzen tangentea kurba bat puntu batean ukitu bakarrik egiten duen zuzen bat da, kurbarekiko angelu nulu bat osatuz. Horrela, kurbaren malda eta zuzen ukitzailearen malda berdinak dira puntu horretan. kurba baten funtzioa izanik, kurbaren tangentea puntu batean honela kalkulatzen da, kurbaren funtzioaren deribatuan oinarriturik: Adibidez, kurbaren zuzenaren ekuazioa puntuan honela kalkulatzen da, kurbaren deribatua dela jakinik:"@eu . . "\u041A\u0430\u0441\u0430\u0301\u0442\u0435\u043B\u044C\u043D\u0430\u044F \u043F\u0440\u044F\u043C\u0430\u0301\u044F \u2014 \u043F\u0440\u044F\u043C\u0430\u044F, \u043F\u0440\u043E\u0445\u043E\u0434\u044F\u0449\u0430\u044F \u0447\u0435\u0440\u0435\u0437 \u0442\u043E\u0447\u043A\u0443 \u043A\u0440\u0438\u0432\u043E\u0439 \u0438 \u0441\u043E\u0432\u043F\u0430\u0434\u0430\u044E\u0449\u0430\u044F \u0441 \u043D\u0435\u0439 \u0432 \u044D\u0442\u043E\u0439 \u0442\u043E\u0447\u043A\u0435 \u0441 \u0442\u043E\u0447\u043D\u043E\u0441\u0442\u044C\u044E \u0434\u043E \u043F\u0435\u0440\u0432\u043E\u0433\u043E \u043F\u043E\u0440\u044F\u0434\u043A\u0430."@ru . "\u0627\u0644\u0645\u0645\u0627\u0633\u064F\u0651 \u0623\u0648 \u0627\u0644\u0645\u0633\u062A\u0642\u064A\u0645 \u0627\u0644\u0645\u0627\u0633\u0651 \u0623\u0648 \u062E\u0637 \u0627\u0644\u0638\u0644 \u0623\u0648 \u0627\u0644\u062E\u0637 \u0627\u0644\u0645\u064F\u0645\u0627\u0633\u0651 \u0647\u0648 \u062E\u0637 \u064A\u0645\u0631 \u0628\u0646\u0642\u0637\u0629 \u0648\u062D\u064A\u062F\u0629 \u0645\u0646 \u062F\u0627\u0626\u0631\u0629\u064D \u0623\u0648 \u0645\u0646\u062D\u0646\u0649. \u0627\u0644\u0645\u0645\u0627\u0633 \u0641\u064A \u062D\u0627\u0644\u0629 \u0645\u0646\u062D\u0646\u0649 \u0639\u0627\u0645 \u064A\u064F\u0633\u062A\u062E\u062F\u0645 \u0644\u0644\u062A\u0641\u0627\u0636\u0644 (Differential Calculus). \u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u062A\u0645\u0627\u0633 \u0647\u064A \u0648\u0627\u062D\u062F \u0645\u0646 \u0623\u0643\u062B\u0631 \u0627\u0644\u0645\u0641\u0627\u0647\u064A\u0645 \u0627\u0644\u0623\u0633\u0627\u0633\u064A\u0629 \u0641\u064A \u0627\u0644\u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u062A\u0641\u0627\u0636\u0644\u064A\u0629 \u0648\u062C\u0631\u0649 \u062A\u0639\u0645\u064A\u0645\u0647 \u0639\u0644\u0649 \u0646\u0637\u0627\u0642 \u0648\u0627\u0633\u0639\u060C \u0627\u0646\u0638\u0631 (Tangent space)."@ar . . "De raaklijn of tangent aan een kromme in een punt van die kromme is in de meetkunde de rechte lijn door dat punt die in dat punt dezelfde richting heeft als de kromme. Het punt waarin de raaklijn de kromme raakt, heet raakpunt, soms ook tangentpunt. De raaklijn is de benadering van de kromme in het raakpunt door een rechte lijn. De raaklijn kan de kromme eventueel nog snijden in een ander punt dan het raakpunt. De raaklijn in een punt op de kromme kan gezien worden als de limietstand van de lijn door en een ander punt van de kromme als het punt over het raakpunt nadert. Daaruit blijkt ook dat niet in elk punt van een willekeurige kromme een raaklijn bestaat. De kromme zal aan bepaalde eisen van differentieerbaarheid moeten voldoen."@nl . . "Garis singgung"@in . . .