The Nine Chapters on the Mathematical Art (九章算術) is a Chinese mathematics book, probably composed in the 1st century AD, but perhaps as early as 200 BC. This book is the earliest surviving mathematical text from China that has come down to us by being copied by scribes and (centuries later) printed. It reveals an approach to mathematics that centres on finding the most general methods of solving problems rather than on deducing propositions from an initial set of axioms, in the manner found amongst leading ancient Greek mathematicians. Mathematics is often defined as the study of topics such as quantity, structure, space, and change. ... The 1st century was that century which lasted from 1 AD to 100 AD, or from 0 to 99 in a more scientific notation (using a year zero), as in astronomical year numbering. ... In epistemology, an axiom is a self-evident truth upon which other knowledge must rest, from which other knowledge is built up. ... Ancient Greece is the term used to describe the Greek-speaking world in ancient times. ...

Entries in the book usually take the form of a statement of a problem, followed by the statement of the solution, and an explanation of the procedure that led to the solution.

Contents of the Nine Chapters are as follows

1. Fang tian - Rectangular fields Areas of fields of various shapes; manipulation of vulgar fractions.
2. Su mi - Millet and rice Exchange of commodities at different rates; pricing.
3. Cui fen - Proportional distribution Distribution of commodities and money at proportional rates.
4. Shao guang - The lesser breadth Division by mixed numbers; extraction of square and cube roots; dimensions, area and volume of circle and sphere.
5. Shang gong - Consultations on works Volumes of solids of various shapes.
6. Jun shu - Equitable taxation More advanced problems on proportion.
7. Ying bu zu - Excess and deficit Linear problems solved using the principle known later in the West as the rule of false position.
8. Fang cheng - The rectangular array Problems with several unknowns, solved by a principle similar to Gaussian elimination.
9. Gou gu - Base and altitude Problems involving the principle known in the West as the Pythagorean theorem.

Most scholars believe that Chinese mathematics and the mathematics of the ancient Mediterranean world had developed more or less independently up to the time when the Nine Chapters reached its final form. There is therefore little historical value in speculations about who was "more advanced" at any given period. Nevertheless we may note that the method of chapter 7 was not found in Europe until the 13th century, and the method of chapter 8 is not found before the sixteenth century. Of course there are also features of ancient Western mathematics that are not found in ancient China.-1... In arithmetic, a vulgar fraction (or common fraction) consists of one integer divided by a non-zero integer. ... In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the inverse of multiplication, and sometimes it can be interpreted as repeated subtraction. ... Look up Number in Wiktionary, the free dictionary A number originally was a count or a measurement. ... In mathematics, the principal square root of a non-negative real number is denoted and represents the non-negative real number whose square (the result of multiplying the number by itself) is For example, since This example suggests how square roots can arise when solving quadratic equations such as or... Plot of y = ∛x by Mathematica. ... In common usage, the dimensions (from Latin measured out) of an object are the parameters or measurements required to define its shape and size, that is, usually, its height, width, and length. ... Volume, also called capacity, is a quantification of how much space an object occupies. ... A circle, in Euclidean geometry, is the set of all points at a fixed distance, called the radius, from a fixed point, the centre. ... A sphere is a perfectly symmetrical geometrical object. ... In jewelry, a solid gold piece is the alternative to gold-filled or gold-plated jewelry. ... In numerical analysis, the false position method or regula falsi method is a root-finding algorithm that combines features from the bisection method and the secant method. ... In mathematics, Gaussian elimination or Gauss–Jordan elimination, named after Carl Friedrich Gauss and Wilhelm Jordan (for many, Gaussian elimination is regarded as the front half of the complete Gauss–Jordan elimination), is an algorithm in linear algebra for determining the solutions of a system of linear equations, for determining... The Pythagorean theorem: The sum of the areas of the two squares on the legs equals the area of the square on the hypotenuse. ...

Liu Hui wrote a very detailed commentary on this book in 263. He analyses the procedures of the Nine Chapters step by step, in a manner which is clearly designed to give the reader confidence that they are reliable, although he is not concerned to provide formal proofs in the Euclidean manner. Liu's commentary is of great mathematical interest in its own right. Liu Hui 劉徽 was a Chinese mathematician who lived in the 200s in the Wei Kingdom. ... Events The Wei Kingdom conquered the kingdom of Shu Han, one of the Chinese Three Kingdoms. ... Euclid Euclid of Alexandria (Greek: ) (ca. ...

The Nine Chapters is an anonymous work, and its origins are not clear. Until recent years there was no substantial evidence of related mathematical writing that might have preceded it. This is no longer the case. The Suan shu shu is an ancient Chinese text on mathematics approximately seven thousand characters in length, written on 190 bamboo strips. It was discovered together with other writings in 1983 when archaeologists opened a tomb at Zhangjiashan in Hubei province. From documentary evidence this tomb is known to have been closed in 186 BC, early in the Western Han dynasty. While its relationship to the Nine Chapters is still under discussion by scholars, some of its contents are clearly paralleled there. The text of the Suan shu shu is however much less systematic than the Nine Chapters; and appears to consist of a number of more or less independent short sections of text drawn from a number of sources. 1983 (MCMLXXXIII) is a common year starting on Saturday of the Gregorian calendar. ... Archaeology or sometimes in American English archeology (from the Greek words αρχαίος = ancient and λόγος = word/speech) is the study of human cultures through the recovery, documentation and analysis of material remains, including architecture, artefacts, biofacts, human remains, and landscapes. ... Hubei (Chinese: 湖北; pinyin: ; Wade-Giles: Hu-pei; Postal System Pinyin: Hupeh) is a central province of the Peoples Republic of China. ... Han commanderies and kingdoms AD 2. ...

A full translation and study of the Nine Chapters and Liu Hui's commentary is available in SHEN Kangshen "The Nine Chapters on the Mathematical Art" Oxford 1999. ISBN 0198539363

A French translation with detailed scholarly addenda and a critical edition of the Chinese text of both the book and its commentary is Chemla, Karine, and Shuchun Guo. 2004. Les neuf chapitres: le classique mathématique de la Chine ancienne et ses commentaires. Paris: Dunod.