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Kyokusujutsu in Wasan and Bud of Extremum Concept in Traditional Mathematics of China

The paper showed the method of maximizing and minimizing a polonomial function in Wasan ,analyzed the mathematical basis and the principle of establishment for the method of extremum in Wasan. The paper also held that Takebe Katahiro’s(1664一1739) Fermat Method of extremizing a polynomial function had stemmed from the problem of equation of the center of the sun and the moon in Shoushi Li. Through the survey and the induction,Takebe Katahiro had acquired the genetal method of solving this kind of extremum problem.Takebe Katahiro’s method of determinating a stable point of a polynomial function had been the same as the Tekijinshokyuho in Seki Takakazu’s theory of equations ,which was just a coincidence in form. Based on the above-mentioned analyses ,the paper probed further into the reasons for the bud of variate mathematics in traditional mathematics in the Orient and the reasons why it had not been developed continuously.