The purpose of this paper is to consider the essence of mathematics of Takebe Katahiro (1664-1739) by investigating his method of finding the maximum in Tetsujutsu Sankei (1722). It has been said that he had first done a calculation of a derivation for finding the maximum in chapter 6 of the treatise, but that is not strictly true. A close look at the chapter will reveal that his method has nothing to do with the theory of differential.