The Nine Chapters on Mathematical Art


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The Jiuzhang suanshu or the Nine Chapters on Mathematical Art is the most famous Chinese mathematical text. It was written from the period of Han Dynasty - about 206 to 220 AD. It is not dissimilar to Euclid's Elements, which were written around 600 years before the Nine Chapters.

Nine Chapters is an interesting work as it sums up the mathematical knowledge of China at the time when it was written. The author of the book is not known. The book was not written for beginners as it contains a lot of assumptions of the already existing knowledge of mathematics that the possible reader would have.

The problems which are given in this book are of general nature - one can apply the same problems in various situations. They involve problems from surveying and engineering to taxation and administration.

This is the page from the First Chapter of the book. The book contains altogether 246 problems on various topics - content of the chapters follows:

1. Fang thien (land surveying)

This chapter gave correct rules for area of a triangle, rectangle, circle and trapezoid. It also stated pi to be 3. It gave the examples of addition, subtraction, multiplication and division of fractions.

2. Su mi (millet and rice)

This chapter gave simple questions on percentage and proportions . It originally contained a table which converted weights of varied grains to the weights used to measure rice.

3. Tshui fen (distribution by progression)

This chapter dealt with the problems involving taxation, partnership and arithmetic and geometrical progressions. It used proportions to solve problems of distribution.

4. Shoa kuang (diminishing breadths)

The fourth chapter showed how to find the sides of figures when areas and single sides are known. It also gave examples of square and cube roots.

5. Shang kung (consultations of engineering works)

The fifth chapter showed calculations for volumes of solid figures (prisms, cylinders, pyramids, etcetera).

6. Chun shu (important taxation)

The sixth showed the ways to deal with the distribution of taxes.

7. Ying pu tsu (excess and deficiency)

The seventh chapter dealt with the rule of false position - it showed how to solve equations by trial and error.

8. Fang ch'eng (the way of calculating by tabulation)

The eight chapter showed how to solve systems of simultaneous equations.

9. Kou ku (right angles)

Ninth, the final chapter, described the properties of right triangles and showed how to use Pythagoras theorem (although they didn't call it "Pythagoras").



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