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Arithmetic in Nine Sections
The Arithmetic in Nine Sections (or Chiu Chang Suan Shu) is the most well known and influential Chinese mathematical text, which is dated back to the Han Dynasty
(200 BC – 220AD). It is a collection of 246 problems on agriculture, business procedures, engineering, surveying, solutions of equations, and the properties of right angles.
Below is the opening of Section 1 of The Arithmetic in Nine Sections:
The nine sections are as follows:
1. Fang Thien (land surveying)
– Rules for area of a triangle, rectangle, square and trapezium
–
taken as 3
– Addition, subtraction, multiplication and division of fractions
2. Su Mi (Millet and Rice)
– Percentage and Proportion Questions
3. Tshui Fen (Distribution by Progression)
– Problems involving tax, arithmetic and geometrical progressions
– Use of proportions, rule of three
4. Shoa Kuang (Diminishing Breadths)
– Calculating sides of figures given area and single side
– Square and cube roots
5. Shang Kung (Consultations of Engineering Works)
– Volumes of prisms, cylinders, pyramids
6. Chun Ju (Important Taxation)
– Distribution of taxes
7. Ying Pu Tsu (Excess and Deficiency)
– Rule of False Position
8. Fang Chi'eng (Calculating by Tabulation)
– Solution of systems of simultaneous linear equations
9. Kou ku (Right Angles)
– Properties of right angled triangles
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