# Complete Book of Mathematics Vol. 10: Geometry, by Seki Takakazu, Takebe Kataakira and Takebe Katahiro, collated by Hikosaburo Komatsu

• Takakazu Seki
• Kataakira Takebe
• Katahiro Takebe
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 39)

## Abstract

Volume 10 is named Algorithms for Appearances [形法 keihō] as the first of five volumes on geometry. It consists of four chapters. Chapter 1 Algorithms for Squares [方法 hōhō] deals with squares. Chapter 2 is entitled Algorithms for Rectangles [直法 chokuhō]. The longer side of a rectangle [直 choku] is called [縦 tate] or length [長 chō] and the shorter side [横 yoko] or [平 hei] or width [闊 katsu]. Their product is the area [積 seki]. In the following Chapter 3 Algorithms for Right Triangles [勾股法 kōko hō] this is used to prove the Pythagorean theorem. The shorter leg hook [勾 kō] and the longer leg leg [股 ko] of a right triangle stand for the right triangle itself. The hypothenuse is called chord [弦 gen]. There are no formal treatments of proportions as in Euclid’s Elements but it is remarked that rectangles or right triangle with a fixed ratio of heights to widths make a straight line. There are two appendices to Chapter 3. The first one deals with Pythagorean triplets, i. e. the integral solutions of x 2 +y 2 =z 2. The second appendix is a brief introduction to the methods of survey described in Sea Islands Mathematics [海島算經 Haidao Suanjing] by Liu Hui. In the last Chapter 4 Algorothms for Polygons [斜法 shahō] the authors develop a general theory of triangles [三斜 sansha], quadrilaterals [四 斜 shisha], pentagons [五斜] and hexagons [六斜] with the use of their elimination theory

## Keywords

General Theory Priority Area Formal Treatment Integral Solution Medium Class
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Authors and Affiliations

• Takakazu Seki
• 1
• Kataakira Takebe
• 1
• Katahiro Takebe
• 1
1. 1.EdoJapan