. "\u041A\u0435\u0440\u0430\u043B\u044C\u0441\u044C\u043A\u0430 \u0448\u043A\u043E\u043B\u0430 \u0437 \u0410\u0441\u0442\u0440\u043E\u043D\u043E\u043C\u0456\u0457 \u0456 \u041C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438"@uk . . "\u30B1\u30FC\u30E9\u30E9\u5B66\u6D3E\uFF08\u30B1\u30FC\u30E9\u30E9\u304C\u304F\u306F\u3001\u82F1\u8A9E\uFF1AKerala school of astronomy and mathematics\uFF09\u306F\u3001\u30A4\u30F3\u30C9\u306E\u30B1\u30FC\u30E9\u30E9\u5730\u65B9\u3067\u6D3B\u52D5\u3057\u305F\u6570\u5B66\u3068\u5929\u6587\u5B66\u306E\u5B66\u6D3E\u3002\u30B5\u30F3\u30AC\u30DE\u30B0\u30E9\u30FC\u30DE\u306E\u30DE\u30FC\u30C0\u30F4\u30A1\u304C\u59CB\u7956\u3068\u3055\u308C\u3001\u4E3B\u306B14\u4E16\u7D00\u304B\u308917\u4E16\u7D00\u306B\u304B\u3051\u3066\u6D3B\u52D5\u3057\u305F\u3002\u30DE\u30FC\u30C0\u30F4\u30A1\u5B66\u6D3E\u3068\u3082\u547C\u3070\u308C\u308B\u3002"@ja . . . . . . . . . "\u041A\u0435\u0440\u0430\u043B\u044C\u0441\u044C\u043A\u0430 \u0448\u043A\u043E\u043B\u0430 \u0437 \u0410\u0441\u0442\u0440\u043E\u043D\u043E\u043C\u0456\u0457 \u0456 \u041C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438 \u0431\u0443\u043B\u0430 \u0448\u043A\u043E\u043B\u043E\u044E \u0437 \u0456 \u0430\u0441\u0442\u0440\u043E\u043D\u043E\u043C\u0456\u0457 \u043E\u0441\u043D\u043E\u0432\u0430\u043D\u043E\u044E \u0443 \u041A\u0435\u0440\u0430\u043B\u0456 \u0449\u043E \u0432 \u0406\u043D\u0434\u0456\u0457, \u0441\u0435\u0440\u0435\u0434 \u0443\u0447\u0430\u0441\u043D\u0438\u043A\u0456\u0432 \u044F\u043A\u043E\u0457 \u0431\u0443\u043B\u0438: , , , , \u0456 . \u0428\u043A\u043E\u043B\u0430 \u043D\u0430\u0431\u0443\u043B\u0430 \u0440\u043E\u0437\u0432\u0438\u0442\u043A\u0443 \u043C\u0456\u0436 14-\u0438\u043C \u0456 16-\u0438\u043C \u0441\u0442\u043E\u043B\u0456\u0442\u0442\u044F\u043C\u0438, \u0430 \u043E\u0440\u0438\u0433\u0456\u043D\u0430\u043B\u044C\u043D\u0456 \u0432\u0456\u0434\u043A\u0440\u0438\u0442\u0442\u044F \u0448\u043A\u043E\u043B\u0438 \u0441\u0445\u043E\u0436\u0435 \u0437\u0430\u043A\u0456\u043D\u0447\u0438\u043B\u0438\u0441\u044F \u043F\u0456\u0441\u043B\u044F \u041D\u0430\u0440\u0430\u044F\u043D\u0438 \u0411\u0445\u0430\u0442\u0442\u0430\u0442\u0456\u0440\u0456 (1559\u20131632). \u041F\u0440\u0438 \u043D\u0430\u043C\u0430\u0433\u0430\u043D\u043D\u0456 \u0432\u0438\u0440\u0456\u0448\u0438\u0442\u0438 \u0430\u0441\u0442\u0440\u043E\u043D\u043E\u043C\u0456\u0447\u043D\u0456 \u0437\u0430\u0434\u0430\u0447\u0456, \u041A\u0435\u0440\u0430\u043B\u044C\u0441\u044C\u043A\u0430 \u0448\u043A\u043E\u043B\u0430 \u043D\u0435\u0437\u0430\u043B\u0435\u0436\u043D\u043E \u0432\u0456\u0434 \u0456\u043D\u0448\u0438\u0445 \u0441\u0442\u0432\u043E\u0440\u0438\u043B\u0430 \u0440\u044F\u0434 \u0432\u0430\u0436\u043B\u0438\u0432\u0438\u0445 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u043D\u0438\u0445 \u043F\u043E\u043D\u044F\u0442\u044C. \u0407\u0445\u043D\u0456\u043C \u043D\u0430\u0439\u0432\u0430\u0436\u043B\u0438\u0432\u0456\u0448\u0438\u043C \u0440\u0435\u0437\u0443\u043B\u044C\u0442\u0430\u0442\u043E\u043C \u0454 \u0440\u043E\u0437\u043A\u043B\u0430\u0434\u0430\u043D\u043D\u044F \u0432 \u0440\u044F\u0434\u0438 \u0442\u0440\u0438\u0433\u043E\u043D\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u043D\u0438\u0445 \u0444\u0443\u043D\u043A\u0446\u0456\u0439, \u043E\u043F\u0438\u0441\u0430\u043D\u0435 \u043D\u0430 \u0441\u0430\u043D\u0441\u043A\u0440\u0438\u0442\u0456 \u0432 \u043A\u043D\u0438\u0437\u0456 \u041D\u0456\u043B\u0430\u043A\u0430\u043D\u0442\u0438, \u0449\u043E \u043D\u0430\u0437\u0438\u0432\u0430\u043B\u0430\u0441\u044F \u0422\u0430\u043D\u0442\u0440\u0430\u0441\u0430\u043D\u0433\u0440\u0430\u0433\u0430 (\u0430\u043D\u0433\u043B. ), \u0456 \u0432 \u043A\u043E\u043C\u0435\u043D\u0442\u0430\u0440\u044F\u0445 \u0434\u043E \u0446\u0456\u0454\u0457 \u0440\u043E\u0431\u043E\u0442\u0438, \u0449\u043E \u043D\u0430\u0437\u0438\u0432\u0430\u043B\u0438\u0441\u044F \u0422\u0430\u043D\u0442\u0440\u0430\u0441\u0430\u043D\u0433\u0440\u0430\u0433\u0430-\u0432\u0430\u0445'\u044F, \u0430\u0432\u0442\u043E\u0440\u0441\u0442\u0432\u043E \u044F\u043A\u0438\u0445 \u043D\u0435 \u0432\u0456\u0434\u043E\u043C\u043E. \u0422\u0435\u043E\u0440\u0435\u043C\u0438 \u043E\u043F\u0438\u0441\u0443\u0432\u0430\u043B\u0438\u0441\u044F \u0431\u0435\u0437 \u0434\u043E\u0432\u0435\u0434\u0435\u043D\u043D\u044F, \u0430\u043B\u0435 \u0434\u043E\u043A\u0430\u0437\u0438 \u0434\u043B\u044F \u0440\u044F\u0434\u0456\u0432 \u0441\u0438\u043D\u0443\u0441\u0430, \u043A\u043E\u0441\u0438\u043D\u0443\u0441\u0430 \u0456 \u043E\u0431\u0435\u0440\u043D\u0435\u043D\u043E\u0433\u043E \u0442\u0430\u043D\u0433\u0435\u043D\u0441\u0430 \u0431\u0443\u043B\u0438 \u043F\u0440\u0438\u0432\u0435\u0434\u0435\u043D\u0456 \u0441\u0442\u043E\u043B\u0456\u0442\u0442\u044F\u043C \u043F\u0456\u0437\u043D\u0456\u0448\u0435 \u0443 \u0440\u043E\u0431\u043E\u0442\u0456 (\u0431\u043B\u0438\u0437\u044C"@uk . "La Escuela de Kerala fue una escuela de matem\u00E1tica y astronom\u00EDa fundada por Madhava en Kherala (sur de la India) que inclu\u00EDa como miembros destacados a Param\u00E9suara, , Jyeshtadeva, , y . Floreci\u00F3 entre los siglos XIV y XVI y las ra\u00EDces intelectuales se remontan al s. V d. C., con los trabajos de Aryabhatta. Esta Escuela tiene una evoluci\u00F3n rastreable hasta nuestros d\u00EDas, aunque los m\u00E9todos de investigaci\u00F3n finalizaron con . Estos astr\u00F3nomos, al intentar resolver algunos problemas, desarrollaron un notable n\u00FAmero de ideas, que incluyen:"@es . . . "\u30B1\u30FC\u30E9\u30E9\u5B66\u6D3E\uFF08\u30B1\u30FC\u30E9\u30E9\u304C\u304F\u306F\u3001\u82F1\u8A9E\uFF1AKerala school of astronomy and mathematics\uFF09\u306F\u3001\u30A4\u30F3\u30C9\u306E\u30B1\u30FC\u30E9\u30E9\u5730\u65B9\u3067\u6D3B\u52D5\u3057\u305F\u6570\u5B66\u3068\u5929\u6587\u5B66\u306E\u5B66\u6D3E\u3002\u30B5\u30F3\u30AC\u30DE\u30B0\u30E9\u30FC\u30DE\u306E\u30DE\u30FC\u30C0\u30F4\u30A1\u304C\u59CB\u7956\u3068\u3055\u308C\u3001\u4E3B\u306B14\u4E16\u7D00\u304B\u308917\u4E16\u7D00\u306B\u304B\u3051\u3066\u6D3B\u52D5\u3057\u305F\u3002\u30DE\u30FC\u30C0\u30F4\u30A1\u5B66\u6D3E\u3068\u3082\u547C\u3070\u308C\u308B\u3002"@ja . . . . "\uCF00\uB784\uB77C \uD559\uD30C(Kerala school)\uB294 \uC911\uC138 \uB9D0\uAE30 \uC778\uB3C4\uC758 \uCF00\uB784\uB77C \uC0AC\uB78C \uAC00 \uCC3D\uC2DC\uD55C \uC218\uD559 \uBC0F \uCC9C\uBB38\uD559 \uD559\uD30C\uB2E4. \uC8FC\uC694 \uC18C\uC18D \uD559\uC790\uB85C , \uB2D0\uB77C\uCE78\uD0C0 \uC18C\uB9C8\uC57C\uC9C0, \uC81C\uD558\uB370\uBC14, , \uB4F1\uC774 \uC788\uB2E4. \uCF00\uB784\uB77C \uD559\uD30C\uB294 14\uC138\uAE30\uC5D0\uC11C 16\uC138\uAE30 \uC0AC\uC774\uC5D0 \uBC88\uCC3D\uD558\uB2E4\uAC00, 17\uC138\uAE30\uC758 \uB098\uB77C\uC57C\uB098 \uBC14\uD0C0\uD2F0\uB9AC \uC774\uD6C4\uB85C\uB294 \uB3C5\uCC3D\uC801 \uBC1C\uACAC\uC774 \uB04A\uC5B4\uC84C\uB2E4. \uCF00\uB784\uB77C \uD559\uD30C\uB294 \uCC9C\uBB38\uD559 \uBB38\uC81C\uB4E4\uC744 \uD574\uACB0\uD558\uAE30 \uC704\uD574 \uC2DC\uB3C4\uD558\uB294 \uACFC\uC815\uC5D0\uC11C \uC0BC\uAC01\uD568\uC218\uC758 \uAE09\uC218\uC804\uAC1C\uB97C \uBE44\uB86F\uD55C \uC5EC\uB7EC \uAC00\uC9C0 \uC911\uC694\uD55C \uC218\uD559 \uAC1C\uB150\uB4E4\uC744 \uB3C5\uB9BD\uC801\uC73C\uB85C \uBC1C\uACAC\uD588\uB2E4. \uC774\uB7F0 \uB0B4\uC6A9\uB4E4\uC740 \uC0B0\uC2A4\uD06C\uB9AC\uD2B8\uC5B4\uB85C \uC4F0\uC778 \u300E\u300F(1501\uB144\uACBD)\uC5D0 \uCC98\uC74C \uC5B8\uAE09\uB418\uC9C0\uB9CC \uC774 \uCC45\uC5D0\uB294 \uC99D\uBA85\uC774 \uC5C6\uC5C8\uB2E4. \uC99D\uBA85\uC740 \uC81C\uD558\uB370\uBC14\uAC00 \uB9D0\uB808\uC774\uC5B4\uB85C \uC4F4 \u300E\u300F(1530\uB144\uACBD)\uC5D0\uC11C \uC81C\uC2DC\uB418\uC5C8\uB2E4. \uC11C\uC591\uC5D0\uC11C \uBBF8\uC801\uBD84\uD559\uC774 \uBC1C\uBA85\uB418\uAE30 \uB450 \uC138\uAE30 \uC804\uC5D0 \uC774\uB8E8\uC5B4\uC9C4 \uCF00\uB784\uB77C \uD559\uD30C\uC758 \uC791\uC5C5\uC740 \uC218\uD559\uC0AC\uC0C1 \uCD5C\uCD08\uB85C \uBA71\uAE09\uC218\uB97C \uC0AC\uC6A9\uD55C \uC0AC\uB840\uB85C \uC778\uC815\uB418\uACE0 \uC788\uB2E4.:173 \uADF8\uB7EC\uB098 \uCF00\uB784\uB77C \uD559\uD30C\uB294 \uBBF8\uBD84\uACFC \uC801\uBD84\uC758 \uCCB4\uACC4\uC801 \uC774\uB860\uC73C\uB85C\uAE4C\uC9C0\uB294 \uB098\uC544\uAC00\uC9C0 \uBABB\uD588\uACE0, \uADF8\uB4E4\uC758 \uC5C5\uC801\uC774 \uCF00\uB784\uB77C \uBC14\uAE65\uC5D0 \uC804\uD30C\uB418\uC5B4 \uC720\uC758\uBBF8\uD55C \uC601\uD5A5\uC744 \uB0A8\uACBC\uB2E4\uB294 \uC99D\uAC70\uB3C4 \uC5C6\uB2E4.:12:293:562:173\u2013174"@ko . . . . . . "L\u2019\u00E9cole du Kerala est une \u00E9cole de math\u00E9matiques et d'astronomie fond\u00E9e par Madhava de Sangamagrama dans la province du Kerala en Inde, et ayant eu entre autres pour membres (en) et Nilakantha Somayaji. Elle prosp\u00E9ra entre le XIVe et le XVIe si\u00E8cle, s'achevant avec les travaux de Melpathur Narayana Bhattathiri. Les d\u00E9couvertes math\u00E9matiques de l'\u00E9cole anticipent de deux si\u00E8cles certains des r\u00E9sultats du calcul infinit\u00E9simal de Newton et Leibniz (mais non leurs techniques), obtenant par exemple le d\u00E9veloppement en s\u00E9rie enti\u00E8re des fonctions trigonom\u00E9triques, mais il n'y a pas de preuve que ces d\u00E9couvertes se soient diffus\u00E9es en dehors du Kerala."@fr . . . "\u041A\u0435\u0440\u0430\u043B\u044C\u0441\u044C\u043A\u0430 \u0448\u043A\u043E\u043B\u0430 \u0437 \u0410\u0441\u0442\u0440\u043E\u043D\u043E\u043C\u0456\u0457 \u0456 \u041C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438 \u0431\u0443\u043B\u0430 \u0448\u043A\u043E\u043B\u043E\u044E \u0437 \u0456 \u0430\u0441\u0442\u0440\u043E\u043D\u043E\u043C\u0456\u0457 \u043E\u0441\u043D\u043E\u0432\u0430\u043D\u043E\u044E \u0443 \u041A\u0435\u0440\u0430\u043B\u0456 \u0449\u043E \u0432 \u0406\u043D\u0434\u0456\u0457, \u0441\u0435\u0440\u0435\u0434 \u0443\u0447\u0430\u0441\u043D\u0438\u043A\u0456\u0432 \u044F\u043A\u043E\u0457 \u0431\u0443\u043B\u0438: , , , , \u0456 . \u0428\u043A\u043E\u043B\u0430 \u043D\u0430\u0431\u0443\u043B\u0430 \u0440\u043E\u0437\u0432\u0438\u0442\u043A\u0443 \u043C\u0456\u0436 14-\u0438\u043C \u0456 16-\u0438\u043C \u0441\u0442\u043E\u043B\u0456\u0442\u0442\u044F\u043C\u0438, \u0430 \u043E\u0440\u0438\u0433\u0456\u043D\u0430\u043B\u044C\u043D\u0456 \u0432\u0456\u0434\u043A\u0440\u0438\u0442\u0442\u044F \u0448\u043A\u043E\u043B\u0438 \u0441\u0445\u043E\u0436\u0435 \u0437\u0430\u043A\u0456\u043D\u0447\u0438\u043B\u0438\u0441\u044F \u043F\u0456\u0441\u043B\u044F \u041D\u0430\u0440\u0430\u044F\u043D\u0438 \u0411\u0445\u0430\u0442\u0442\u0430\u0442\u0456\u0440\u0456 (1559\u20131632). \u041F\u0440\u0438 \u043D\u0430\u043C\u0430\u0433\u0430\u043D\u043D\u0456 \u0432\u0438\u0440\u0456\u0448\u0438\u0442\u0438 \u0430\u0441\u0442\u0440\u043E\u043D\u043E\u043C\u0456\u0447\u043D\u0456 \u0437\u0430\u0434\u0430\u0447\u0456, \u041A\u0435\u0440\u0430\u043B\u044C\u0441\u044C\u043A\u0430 \u0448\u043A\u043E\u043B\u0430 \u043D\u0435\u0437\u0430\u043B\u0435\u0436\u043D\u043E \u0432\u0456\u0434 \u0456\u043D\u0448\u0438\u0445 \u0441\u0442\u0432\u043E\u0440\u0438\u043B\u0430 \u0440\u044F\u0434 \u0432\u0430\u0436\u043B\u0438\u0432\u0438\u0445 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u043D\u0438\u0445 \u043F\u043E\u043D\u044F\u0442\u044C. \u0407\u0445\u043D\u0456\u043C \u043D\u0430\u0439\u0432\u0430\u0436\u043B\u0438\u0432\u0456\u0448\u0438\u043C \u0440\u0435\u0437\u0443\u043B\u044C\u0442\u0430\u0442\u043E\u043C \u0454 \u0440\u043E\u0437\u043A\u043B\u0430\u0434\u0430\u043D\u043D\u044F \u0432 \u0440\u044F\u0434\u0438 \u0442\u0440\u0438\u0433\u043E\u043D\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u043D\u0438\u0445 \u0444\u0443\u043D\u043A\u0446\u0456\u0439, \u043E\u043F\u0438\u0441\u0430\u043D\u0435 \u043D\u0430 \u0441\u0430\u043D\u0441\u043A\u0440\u0438\u0442\u0456 \u0432 \u043A\u043D\u0438\u0437\u0456 \u041D\u0456\u043B\u0430\u043A\u0430\u043D\u0442\u0438, \u0449\u043E \u043D\u0430\u0437\u0438\u0432\u0430\u043B\u0430\u0441\u044F \u0422\u0430\u043D\u0442\u0440\u0430\u0441\u0430\u043D\u0433\u0440\u0430\u0433\u0430 (\u0430\u043D\u0433\u043B. ), \u0456 \u0432 \u043A\u043E\u043C\u0435\u043D\u0442\u0430\u0440\u044F\u0445 \u0434\u043E \u0446\u0456\u0454\u0457 \u0440\u043E\u0431\u043E\u0442\u0438, \u0449\u043E \u043D\u0430\u0437\u0438\u0432\u0430\u043B\u0438\u0441\u044F \u0422\u0430\u043D\u0442\u0440\u0430\u0441\u0430\u043D\u0433\u0440\u0430\u0433\u0430-\u0432\u0430\u0445'\u044F, \u0430\u0432\u0442\u043E\u0440\u0441\u0442\u0432\u043E \u044F\u043A\u0438\u0445 \u043D\u0435 \u0432\u0456\u0434\u043E\u043C\u043E. \u0422\u0435\u043E\u0440\u0435\u043C\u0438 \u043E\u043F\u0438\u0441\u0443\u0432\u0430\u043B\u0438\u0441\u044F \u0431\u0435\u0437 \u0434\u043E\u0432\u0435\u0434\u0435\u043D\u043D\u044F, \u0430\u043B\u0435 \u0434\u043E\u043A\u0430\u0437\u0438 \u0434\u043B\u044F \u0440\u044F\u0434\u0456\u0432 \u0441\u0438\u043D\u0443\u0441\u0430, \u043A\u043E\u0441\u0438\u043D\u0443\u0441\u0430 \u0456 \u043E\u0431\u0435\u0440\u043D\u0435\u043D\u043E\u0433\u043E \u0442\u0430\u043D\u0433\u0435\u043D\u0441\u0430 \u0431\u0443\u043B\u0438 \u043F\u0440\u0438\u0432\u0435\u0434\u0435\u043D\u0456 \u0441\u0442\u043E\u043B\u0456\u0442\u0442\u044F\u043C \u043F\u0456\u0437\u043D\u0456\u0448\u0435 \u0443 \u0440\u043E\u0431\u043E\u0442\u0456 (\u0431\u043B\u0438\u0437\u044C\u043A\u043E 1500 - 1610), \u043D\u0430\u043F\u0438\u0441\u0430\u043D\u0456\u0439 \u043C\u043E\u0432\u043E\u044E \u041C\u0430\u043B\u0430\u044F\u043B\u0430\u043C, \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u043E\u043C \u042E\u0454\u0448\u0442\u0430\u0434\u0435\u0432\u0430, \u0430 \u0442\u0430\u043A\u043E\u0436 \u0443 \u043A\u043E\u043C\u0435\u043D\u0442\u0430\u0440\u044F\u0445 \u0434\u043E \u0422\u0430\u043D\u0442\u0440\u0430\u0441\u0430\u043D\u0433\u0440\u0430\u0433\u0430."@uk . . . . "La Scuola del Kerala \u00E8 stata un'importante scuola di matematici e astronomi ivi fiorita tra il XIV e il XVI secolo. Fu fondata da Madhava di Sangamagrama (ca. 1350 - ca. 1425) e tra i suoi membri vanno ricordati: Narayana Pandit, , Nilakantha Somayaji, , , e Achyuta Panikkar. Si ritiene che le scoperte originali della scuola siano terminate con (1559-1632). Nel tentativo di risolvere problemi astronomici, la scuola del Kerala svilupp\u00F2 autonomamente un gran numero di importanti concetti matematici. I loro risultati pi\u00F9 importanti, gli sviluppi in serie di funzioni trigonometriche, sono stati descritti mediante versi in sanscrito in un libro di Neelakanta chiamato Tantrasangraha, e anche in un commentario su questo lavoro, chiamato Tantrasangraha-vakhya, di autore ignoto. I teoremi vennero enunciati senza dimostrazione, ma le dimostrazioni relative alle serie per seno, coseno e tangente furono fornite un secolo pi\u00F9 tardi nel lavoro Yuktibhasa (c.1500-c.1610), scritto in malayalam da Jyesthadeva, e anche in un commentario su Tantrasangraha. La loro scoperta di queste tre importanti sviluppi in serie \u2014 molti secoli prima che fossero sviluppati in Europa da Leibniz e Newton \u2014 fu una pietra miliare per la matematica. Non si pu\u00F2 comunque dire che la scuola del Kerala abbia inventato il calcolo infinitesimale in quanto, mentre i matematici del Kerala erano in grado di sviluppare in serie di Taylor le funzioni trigonometriche, non svilupparono una teoria globale del calcolo differenziale o integrale, n\u00E9 svilupparono i teoremi fondamentali dell'analisi."@it . . . . "Chain of teachers of the Kerala school"@en . . . . "Escuela de Kerala"@es . . . . . . . "Escola de Querala de Astronomia e Matem\u00E1tica"@pt . . . . . . "\u041A\u0435\u0440\u0430\u0301\u043B\u044C\u0441\u043A\u0430\u044F \u0448\u043A\u043E\u043B\u0430 \u0430\u0441\u0442\u0440\u043E\u043D\u043E\u043C\u0438\u0438 \u0438 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438 \u2014 \u043D\u0430\u0443\u0447\u043D\u0430\u044F \u0448\u043A\u043E\u043B\u0430, \u043A\u043E\u0442\u043E\u0440\u0430\u044F \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u043E\u0432\u0430\u043B\u0430 \u0432 \u0418\u043D\u0434\u0438\u0438 \u0432 XIV\u2014XVII \u0432\u0435\u043A\u0430\u0445 \u0438 \u0432\u043D\u0435\u0441\u043B\u0430 \u0437\u0430\u043C\u0435\u0442\u043D\u044B\u0439 \u0432\u043A\u043B\u0430\u0434 \u0432 \u0430\u0441\u0442\u0440\u043E\u043D\u043E\u043C\u0438\u044E \u0438 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0443."@ru . . . . . . "26445"^^ . . "\u0645\u062F\u0631\u0633\u0629 \u0643\u064A\u0631\u0644\u0627 \u0644\u0639\u0644\u0645 \u0627\u0644\u0641\u0644\u0643 \u0648\u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0643\u0627\u0646\u062A \u0645\u062F\u0631\u0633\u0629 \u0644\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0648\u0639\u0644\u0645 \u0627\u0644\u0641\u0644\u0643 \u0641\u064A \u0643\u064A\u0631\u0644\u0627 \u0641\u064A \u0627\u0644\u0647\u0646\u062F."@ar . . . . . . . . "Mazhab astronomi dan matematika Kerala adalah mazhab matematika dan astronomi yang didirikan oleh Madhava dari Sangamagrama di Kerala, India Selatan; yang para anggotanya termasuk antara lain , , , , , dan . Mazhab ini berkembang antara abad ke-14 dan ke-16 masehi, dan penemuan orisinil terakhir mazhab ini tampaknya terdapat pada (1559-1632). Dalam upaya untuk memecahkan masalah-masalah astronomi, mazhab Kerala secara mandiri menciptakan beberapa konsep-konsep penting matematika. Hasil terpenting mereka, yaitu ekspansi untuk fungsi trigonometri, digambarkan dalam syair bahasa Sanskerta dalam sebuah buku karangan Neelakanta yang bernama Tantrasangraha, serta dalam komentar tentang karya ini yang disebut Tantrasangraha-vakhya, yang tidak diketahui penulisnya. Teorema-teorema yang ada dinyatakan tanpa bukti, tetapi bukti-bukti untuk deret sinus, kosinus, dan tangen terbalik diberikan satu abad kemudian dalam karya Yuktibhasa (k. 1500 - k. 1610), yang ditulis dalam bahasa Malayalam oleh Jyesthadeva, dan juga dalam komentar tentang Tantrasangraha. Karya mereka, yang diselesaikan dua abad sebelum penemuan kalkulus di Eropa, memberikan gambaran tentang apa yang sekarang disebut sebagai contoh pertama suatu deret pangkat (berbeda dengan deret geometri). Namun mereka tidak merumuskan teori diferensial dan integral secara sistematis, serta tidak terdapat bukti yang jelas bahwa hasil karya mereka pernah dikabarkan di luar wilayah Kerala."@in . "Kerala school of astronomy and mathematics"@en . . . . . "A Escola de Querala de Astronomia e Matem\u00E1tica foi uma escola de matem\u00E1tica e astronomia indiana fundada por Madhava de Sangamagrama na Costa do Malabar, Querala, no sul da \u00CDndia. Dentre seu membros constam: Parameshvara, Nilakantha Somayaji, , , e . A escola foi ativa entre os s\u00E9culos XIV e XVI e as descobertas originas da escola parecem ter terminado com (1559\u20131632). Na tentativa de resolver problemas de astronomia, a escola de Querala independentemente criou um n\u00FAmero significativo de conceitos matem\u00E1ticos. Seus resultados mais importantes foram as s\u00E9ries de expans\u00E3o para fun\u00E7\u00F5es trigonom\u00E9tricas, descritas em versos em s\u00E2nscrito em um livro de Neelakanta chamado Tantrasangraha, e novamente comentado no trabalho Tantrasangraha-vakhya de autoria desconhecida. Os teoremas foram enunciados sem provas, mas estas foram publicadas um s\u00E9culo depois para as s\u00E9ries do seno, cosseno e o inverso da tangente no trabalho (ca. 1500 \u2013 ca. 1610), escrito em por Jyesthadeva e tamb\u00E9m comentado no Tantrasangraha."@pt . . "A Escola de Querala de Astronomia e Matem\u00E1tica foi uma escola de matem\u00E1tica e astronomia indiana fundada por Madhava de Sangamagrama na Costa do Malabar, Querala, no sul da \u00CDndia. Dentre seu membros constam: Parameshvara, Nilakantha Somayaji, , , e . A escola foi ativa entre os s\u00E9culos XIV e XVI e as descobertas originas da escola parecem ter terminado com (1559\u20131632). Na tentativa de resolver problemas de astronomia, a escola de Querala independentemente criou um n\u00FAmero significativo de conceitos matem\u00E1ticos. Seus resultados mais importantes foram as s\u00E9ries de expans\u00E3o para fun\u00E7\u00F5es trigonom\u00E9tricas, descritas em versos em s\u00E2nscrito em um livro de Neelakanta chamado Tantrasangraha, e novamente comentado no trabalho Tantrasangraha-vakhya de autoria desconhecida. Os teoremas foram enunciado"@pt . . . . . "Mazhab astronomi dan matematika Kerala"@in . . . . "3099132"^^ . . . . "Mazhab astronomi dan matematika Kerala adalah mazhab matematika dan astronomi yang didirikan oleh Madhava dari Sangamagrama di Kerala, India Selatan; yang para anggotanya termasuk antara lain , , , , , dan . Mazhab ini berkembang antara abad ke-14 dan ke-16 masehi, dan penemuan orisinil terakhir mazhab ini tampaknya terdapat pada (1559-1632). Dalam upaya untuk memecahkan masalah-masalah astronomi, mazhab Kerala secara mandiri menciptakan beberapa konsep-konsep penting matematika. Hasil terpenting mereka, yaitu ekspansi untuk fungsi trigonometri, digambarkan dalam syair bahasa Sanskerta dalam sebuah buku karangan Neelakanta yang bernama Tantrasangraha, serta dalam komentar tentang karya ini yang disebut Tantrasangraha-vakhya, yang tidak diketahui penulisnya. Teorema-teorema yang ada dinya"@in . "\u30B1\u30FC\u30E9\u30E9\u5B66\u6D3E"@ja . "\uCF00\uB784\uB77C \uD559\uD30C"@ko . . . . . . . "Central and North Kerala"@en . "\u0645\u062F\u0631\u0633\u0629 \u0643\u064A\u0631\u0644\u0627 \u0644\u0639\u0644\u0645 \u0627\u0644\u0641\u0644\u0643 \u0648\u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0643\u0627\u0646\u062A \u0645\u062F\u0631\u0633\u0629 \u0644\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A \u0648\u0639\u0644\u0645 \u0627\u0644\u0641\u0644\u0643 \u0641\u064A \u0643\u064A\u0631\u0644\u0627 \u0641\u064A \u0627\u0644\u0647\u0646\u062F."@ar . . . . . . . "La Scuola del Kerala \u00E8 stata un'importante scuola di matematici e astronomi ivi fiorita tra il XIV e il XVI secolo. Fu fondata da Madhava di Sangamagrama (ca. 1350 - ca. 1425) e tra i suoi membri vanno ricordati: Narayana Pandit, , Nilakantha Somayaji, , , e Achyuta Panikkar. Si ritiene che le scoperte originali della scuola siano terminate con (1559-1632)."@it . . . . . . "\u0645\u062F\u0631\u0633\u0629 \u0643\u064A\u0631\u0644\u0627 \u0644\u0639\u0644\u0645 \u0627\u0644\u0641\u0644\u0643 \u0648\u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A"@ar . . . . "\u00C9cole du Kerala"@fr . "The Kerala school of astronomy and mathematics or the Kerala school was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Tirur, Malappuram, Kerala, India, which included among its members: Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar. The school flourished between the 14th and 16th centuries and the original discoveries of the school seems to have ended with Narayana Bhattathiri (1559\u20131632). In attempting to solve astronomical problems, the Kerala school independently discovered a number of important mathematical concepts. Their most important results\u2014series expansion for trigonometric functions\u2014were described in Sanskrit verse in a book by Neelakanta called Tantrasangraha, and again in a c"@en . . . . . . . . . "The Kerala school of astronomy and mathematics or the Kerala school was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Tirur, Malappuram, Kerala, India, which included among its members: Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar. The school flourished between the 14th and 16th centuries and the original discoveries of the school seems to have ended with Narayana Bhattathiri (1559\u20131632). In attempting to solve astronomical problems, the Kerala school independently discovered a number of important mathematical concepts. Their most important results\u2014series expansion for trigonometric functions\u2014were described in Sanskrit verse in a book by Neelakanta called Tantrasangraha, and again in a commentary on this work, called Tantrasangraha-vakhya, of unknown authorship. The theorems were stated without proof, but proofs for the series for sine, cosine, and inverse tangent were provided a century later in the work Yuktibhasa (c.\u20091530), written in Malayalam, by Jyesthadeva, and also in a commentary on Tantrasangraha. Their work, completed two centuries before the invention of calculus in Europe, provided what is now considered the first example of a power series (apart from geometric series)."@en . . . . . . . . . . . . . . . . "\uCF00\uB784\uB77C \uD559\uD30C(Kerala school)\uB294 \uC911\uC138 \uB9D0\uAE30 \uC778\uB3C4\uC758 \uCF00\uB784\uB77C \uC0AC\uB78C \uAC00 \uCC3D\uC2DC\uD55C \uC218\uD559 \uBC0F \uCC9C\uBB38\uD559 \uD559\uD30C\uB2E4. \uC8FC\uC694 \uC18C\uC18D \uD559\uC790\uB85C , \uB2D0\uB77C\uCE78\uD0C0 \uC18C\uB9C8\uC57C\uC9C0, \uC81C\uD558\uB370\uBC14, , \uB4F1\uC774 \uC788\uB2E4. \uCF00\uB784\uB77C \uD559\uD30C\uB294 14\uC138\uAE30\uC5D0\uC11C 16\uC138\uAE30 \uC0AC\uC774\uC5D0 \uBC88\uCC3D\uD558\uB2E4\uAC00, 17\uC138\uAE30\uC758 \uB098\uB77C\uC57C\uB098 \uBC14\uD0C0\uD2F0\uB9AC \uC774\uD6C4\uB85C\uB294 \uB3C5\uCC3D\uC801 \uBC1C\uACAC\uC774 \uB04A\uC5B4\uC84C\uB2E4. \uCF00\uB784\uB77C \uD559\uD30C\uB294 \uCC9C\uBB38\uD559 \uBB38\uC81C\uB4E4\uC744 \uD574\uACB0\uD558\uAE30 \uC704\uD574 \uC2DC\uB3C4\uD558\uB294 \uACFC\uC815\uC5D0\uC11C \uC0BC\uAC01\uD568\uC218\uC758 \uAE09\uC218\uC804\uAC1C\uB97C \uBE44\uB86F\uD55C \uC5EC\uB7EC \uAC00\uC9C0 \uC911\uC694\uD55C \uC218\uD559 \uAC1C\uB150\uB4E4\uC744 \uB3C5\uB9BD\uC801\uC73C\uB85C \uBC1C\uACAC\uD588\uB2E4. \uC774\uB7F0 \uB0B4\uC6A9\uB4E4\uC740 \uC0B0\uC2A4\uD06C\uB9AC\uD2B8\uC5B4\uB85C \uC4F0\uC778 \u300E\u300F(1501\uB144\uACBD)\uC5D0 \uCC98\uC74C \uC5B8\uAE09\uB418\uC9C0\uB9CC \uC774 \uCC45\uC5D0\uB294 \uC99D\uBA85\uC774 \uC5C6\uC5C8\uB2E4. \uC99D\uBA85\uC740 \uC81C\uD558\uB370\uBC14\uAC00 \uB9D0\uB808\uC774\uC5B4\uB85C \uC4F4 \u300E\u300F(1530\uB144\uACBD)\uC5D0\uC11C \uC81C\uC2DC\uB418\uC5C8\uB2E4. \uC11C\uC591\uC5D0\uC11C \uBBF8\uC801\uBD84\uD559\uC774 \uBC1C\uBA85\uB418\uAE30 \uB450 \uC138\uAE30 \uC804\uC5D0 \uC774\uB8E8\uC5B4\uC9C4 \uCF00\uB784\uB77C \uD559\uD30C\uC758 \uC791\uC5C5\uC740 \uC218\uD559\uC0AC\uC0C1 \uCD5C\uCD08\uB85C \uBA71\uAE09\uC218\uB97C \uC0AC\uC6A9\uD55C \uC0AC\uB840\uB85C \uC778\uC815\uB418\uACE0 \uC788\uB2E4.:173 \uADF8\uB7EC\uB098 \uCF00\uB784\uB77C \uD559\uD30C\uB294 \uBBF8\uBD84\uACFC \uC801\uBD84\uC758 \uCCB4\uACC4\uC801 \uC774\uB860\uC73C\uB85C\uAE4C\uC9C0\uB294 \uB098\uC544\uAC00\uC9C0 \uBABB\uD588\uACE0, \uADF8\uB4E4\uC758 \uC5C5\uC801\uC774 \uCF00\uB784\uB77C \uBC14\uAE65\uC5D0 \uC804\uD30C\uB418\uC5B4 \uC720\uC758\uBBF8\uD55C \uC601\uD5A5\uC744 \uB0A8\uACBC\uB2E4\uB294 \uC99D\uAC70\uB3C4 \uC5C6\uB2E4.:12:293:562:173\u2013174"@ko . . "L\u2019\u00E9cole du Kerala est une \u00E9cole de math\u00E9matiques et d'astronomie fond\u00E9e par Madhava de Sangamagrama dans la province du Kerala en Inde, et ayant eu entre autres pour membres (en) et Nilakantha Somayaji. Elle prosp\u00E9ra entre le XIVe et le XVIe si\u00E8cle, s'achevant avec les travaux de Melpathur Narayana Bhattathiri. Les d\u00E9couvertes math\u00E9matiques de l'\u00E9cole anticipent de deux si\u00E8cles certains des r\u00E9sultats du calcul infinit\u00E9simal de Newton et Leibniz (mais non leurs techniques), obtenant par exemple le d\u00E9veloppement en s\u00E9rie enti\u00E8re des fonctions trigonom\u00E9triques, mais il n'y a pas de preuve que ces d\u00E9couvertes se soient diffus\u00E9es en dehors du Kerala."@fr . "\u041A\u0435\u0440\u0430\u043B\u044C\u0441\u043A\u0430\u044F \u0448\u043A\u043E\u043B\u0430 \u0430\u0441\u0442\u0440\u043E\u043D\u043E\u043C\u0438\u0438 \u0438 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438"@ru . "Kerala school of astronomy and mathematics"@en . . . "India"@en . "\u041A\u0435\u0440\u0430\u0301\u043B\u044C\u0441\u043A\u0430\u044F \u0448\u043A\u043E\u043B\u0430 \u0430\u0441\u0442\u0440\u043E\u043D\u043E\u043C\u0438\u0438 \u0438 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0438 \u2014 \u043D\u0430\u0443\u0447\u043D\u0430\u044F \u0448\u043A\u043E\u043B\u0430, \u043A\u043E\u0442\u043E\u0440\u0430\u044F \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u043E\u0432\u0430\u043B\u0430 \u0432 \u0418\u043D\u0434\u0438\u0438 \u0432 XIV\u2014XVII \u0432\u0435\u043A\u0430\u0445 \u0438 \u0432\u043D\u0435\u0441\u043B\u0430 \u0437\u0430\u043C\u0435\u0442\u043D\u044B\u0439 \u0432\u043A\u043B\u0430\u0434 \u0432 \u0430\u0441\u0442\u0440\u043E\u043D\u043E\u043C\u0438\u044E \u0438 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0443."@ru . . . . . . . . "1121906904"^^ . . . . . "Scuola del Kerala"@it . "Kerala school of astronomy and mathematics"@en . "La Escuela de Kerala fue una escuela de matem\u00E1tica y astronom\u00EDa fundada por Madhava en Kherala (sur de la India) que inclu\u00EDa como miembros destacados a Param\u00E9suara, , Jyeshtadeva, , y . Floreci\u00F3 entre los siglos XIV y XVI y las ra\u00EDces intelectuales se remontan al s. V d. C., con los trabajos de Aryabhatta. Esta Escuela tiene una evoluci\u00F3n rastreable hasta nuestros d\u00EDas, aunque los m\u00E9todos de investigaci\u00F3n finalizaron con . Estos astr\u00F3nomos, al intentar resolver algunos problemas, desarrollaron un notable n\u00FAmero de ideas, que incluyen: \n* Ideas revolucionarias de c\u00E1lculo. \n* Teor\u00EDa de series infinitas. \n* Series de potencias. \n* Series de Taylor. \n* Pruebas de convergencia (usualmente atribuidas a Cauchy). \n* Diferenciaci\u00F3n. \n* Integraci\u00F3n t\u00E9rmino a t\u00E9rmino. \n* Integraci\u00F3n num\u00E9rica en t\u00E9rminos de series infinitas. \n* La teor\u00EDa que indica que el \u00E1rea bajo la curva es la integral de esta. \n* M\u00E9todos iterativos para solucionar ecuaciones no lineales. \n* Puntos decimales en coma flotante, sistema que permiti\u00F3 investigar y racionalizar la convergencia de series. Esta escuela matem\u00E1tica logr\u00F3 estos resultados siglos antes que los matem\u00E1ticos europeos. Jyeshtadeva consolid\u00F3 los descubrimientos de la Escuela de Kerala en el Yuktibhasa, el primer libro de c\u00E1lculo en la historia. La Escuela de Kerala tambi\u00E9n hizo contribuciones en el campo de la ling\u00FC\u00EDstica. Las tradiciones po\u00E9ticas de Kerala fueron fundadas por esta Escuela. El poema Narayaneeyam, fue escrito por ."@es . . . . . . . . . . . . .