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Overview
Key data
| Item | Detail |
|---|---|
| Completed | Western Han, with later additions |
| Nature | One of the Ten Mathematical Classics; representative of the “heaven as a cover” cosmology |
| Core content | The right triangle, shadow measurement, the measures of the twenty-eight mansions, the sun’s path |
| Famous passage | The 3–4–5 triangle and the dialogue of the Duke of Zhou with Shang Gao |
Contents and form
The work proceeds by question and answer: through the dialogues of the Duke of Zhou with Shang Gao and of Rong Fang with Chen Zi,
it develops the right-triangle method and astronomical computation step by step.
Its core is the use of the right triangle to compute the distances and sizes of celestial bodies, building a model of the cosmos.
The “heaven as a cover” model
The book holds that heaven is like a conical hat and the earth like an upturned dish, heaven above and earth below, both flat,
with the sun, moon and stars attached to the heavenly cover and moving upon it.
From this model it computes the diameter of the sun’s path and the distances of the seven concentric circles,
and finds the “centre of the earth” from the differences of shadow length at different places.
Shadow measurement and the solar terms
The book sets out in detail the method of measuring the sun’s shadow with a gnomon: a shadow of one zhang three chi five cun at the winter solstice,
and one chi six cun at the summer solstice, deriving the length of the year from the two solstitial shadows.
Here the method of fixing the terms by shadow measurement receives systematic mathematical treatment,
making the work a foundation of ancient astronomical computation.
Value
The Zhoubi joins mathematics to astronomy, the source of the “calendrical mathematics” tradition.
For the computational basis of the twenty-four solar terms it is indispensable.
Full text
Simplified Chinese (TXT) ｜ Traditional Chinese (TXT)
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The title, date, summary and index structure compiled here are offered under CC BY 4.0 (attribution: Chujia Kuang · kuangchujia.com).
The full electronic text (about 8,194 characters) is taken from the Chinese Wikisource text of Zhoubi Suanjing; that part is offered under CC BY-SA 4.0 (attribution — share alike); source: zh.wikisource.org.
The electronic text has not been collated by us; please check the original before citing.
Compiled and arranged by Chujia Kuang.