Nine Chapters of Arithmetic

Japanese: 九章算術 - きゅうしょうさんじゅつ

This is one of the 10 surviving ancient Chinese mathematics books known as the "Sankei Jishu." It is the oldest surviving Chinese mathematics book (the older "Zhoubi Sankei" is a mathematics book about astronomy). Its author is unknown and it was written around the 1st century. It consists of a total of 9 chapters, and the contents are as follows:

(1) Akira Hoda This book describes how to calculate the area of land. It starts with the area of a rectangle and ends with the area of a circle. It also includes a detailed explanation of how to add, subtract, multiply, and divide fractions.

(2) The chapter on millet: This is a question of proportionality dealing with the exchange of grains.

(3) Chapter on Dividing: A problem of distributing with a difference. It is a proportional distribution.

(4) Shokosho: The opposite of Hodensho. A problem on finding the length of one side of a piece of land given its area. There is an explanation of square root calculation.

(5) Merit Medal for Business: A question about civil engineering. This is related to work such as building walls and digging ditches.

(6) Equal Distribution Chapter: The problem of adjusting the amount of grain collected as tax depending on the distance to the center.

(7) The chapter on excess and deficiency: “Ei” means “excess.” This refers to today’s problem of excess and deficiency, and a similar solution using the double hypothetical method (a method of using a hypothetical condition twice).

(8) Equations: How to solve simultaneous equations with two or three unknowns using modern methods of addition and subtraction. This is where calculations of positive and negative numbers come in. This is the oldest method of dealing with positive and negative numbers in the world.

(9) The Kouko chapter is a problem about right-angled triangles. The first half is a method for solving similar triangles, and the second half is an application of Pythagoras' theorem.

[Shinichi Oya]

[Reference] | Sanjing Ten Books |Pythagoras ' theorem

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

Japanese:

中国古代の数学書で現存する10種類をとって『算経十書(さんけいじっしょ)』とよぶが、そのうちの一つ。現存する中国最古の数学書（これより古い『周髀算経(しゅうひさんけい)』は天文に関する数学書）である。著者不詳で、1世紀ごろの成立。全部で9章からなり、その内容は次のとおりである。

(1)方田章　土地の面積を測る計算法を述べている。長方形の面積から始まり、円形の面積に至る。分数の加減乗除の詳しい説明がある。

(2)粟米(ぞくべい)章　穀物相互の交換を取り扱う、比例の問題である。

(3)衰分(すいぶん)章　差等をつけて分配する問題。比例配分である。

(4)少広章　方田章の逆。土地の面積から一辺の長さを求める問題。開平の計算の説明がある。

(5)商功章　土木工事に関する問題。城垣を築いたり、溝渠(こうきょ)を掘ったりする仕事に関連する。

(6)均輸章　租税として徴収される穀物を中央までの距離の遠近によって調節する問題。

(7)盈(えい)不足章　盈は過剰の意。盈不足すなわち今日の過不足算、および同様の解き方をする複仮定法（仮定法を二度使うやり方）による解法。