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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Shridhara ： ウィキペディア英語版 Sridhara Sridhar Acharya ((ベンガル語:শ্রীধর আচার্য); c. 750, India – c. ? India) was an Indian mathematician, Sanskrit pundit and philosopher. He was born in Bhurishresti (Bhurisristi or Bhurshut) village in South Radha (at present day Hughli) in the 8th Century AD. His father's name was Baladev Acharya and mother's name was Acchoka. His father was also a Sanskrit pundit. ==Works== He was known for two treatises: ''Trisatika'' (nitsometimes called the ''Patiganitasara'') and the ''Patiganita''. His major work ''Patiganitasara'' was named ''Trisatika'' because it was written in three hundred slokas. The book discusses counting of numbers, measures, natural number, multiplication, division, zero, squares, cubes, fraction, rule of three, interest-calculation, joint business or partnership and mensuration. *He gave an exposition on zero. He has written, "If 0(zero) is added to any number,the sum is the same number; If 0(zero) is subtracted from any number,the number remains unchanged; If 0(zero) is multiplied by any number,the product is 0(zero)". He has said nothing about division of any number by 0(zero). *In the case of dividing a fraction he has found out the method of multiplying the fraction by the reciprocal of the divisor. *He wrote on practical applications of algebra *He separated algebra from arithmetic *He was one of the first to give a formula for solving quadratic equations. Derivation: ::$ax^2\; +\; bx\; +\; c\; =\; 0$ ::Multiply both sides by 4a, ::$4a^2x^2\; +\; 4abx\; +\; 4ac\; =\; 0$ ::Subtract 4ac from both sides, ::$4a^2x^2\; +\; 4abx\; =\; -4ac$ ::Add $b^2$ to both sides, ::$4a^2x^2\; +\; 4abx\; +\; b^2=\; -\; 4ac\; +\; b^2$ ::Since ::$(m\; +\; n)^2\; =\; m^2\; +\; 2mn\; +\; n^2$ ::Complete the square on the left side, ::$(2ax\; +\; b)^2\; =\; b^2\; -\; 4ac\; =$ ::Take square roots, ::$2ax\; +\; b\; =\; \backslash pm\backslash sqrt$ ::$2ax\; =\; -b\backslash pm\backslash sqrt$ ::and, divide by 2a, ::$x=\backslash frac.$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Sridhara」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.