Seki, Founder of Modern Mathematics in Japan pp 441-456 | Cite as

# Methods of Solving Explicit Problems, by Seki Takakazu, collated by Hikosaburo Komatsu

## Abstract

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.

## Keywords

Mathematical Problem Partial Product Geometric Figure Left Edge Conic Section## Preview

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