Methods of Solving Explicit Problems, by Seki Takakazu, collated by Hikosaburo Komatsu
Abstract This is a collated text of the first of Seki’s Trilogy. The book is composed of four chapters: Chapter 1 Addition and Subtraction [加減kagen], Chapter 2 Partition and Joining [分合bungō], Chapter 3 Whole Products [全乘zenjō] and Chapter 4 Partial Products [折乘setsujō]. In Chapter 1 easiest examples are given to show how a mathematical problem is interpreted as an algorithm on a counting board. In Chapter 2 the byscript method [傍書法bōsho hō] of Seki is introduced by which we can express a polynomial as a sum of monomials represented by a numerical coefficient of counting rods and literal factors written on its right side. The heading means the distributive law of sums and products. Chapters 3 and 4 deal with the area and the volume of geometric figures. Formulas are not given by the algebraic byscript method but as algorithms on a counting board. The Pythagorean theorem and the Eudoxos formula of the volume of a pyramid are proved by figures. The volume formula of sphere segments is correct but its proof by an illustration is hard to understand.
KeywordsMathematical Problem Partial Product Geometric Figure Left Edge Conic Section
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