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古周髀算經

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Text ID
KR3fa002
Date
-100–250
Dynasty
漢

Gǔ Zhōubì suànjīng 古周髀算經

The Ancient Gnomon-Classic of the Zhou by 趙爽 (注)

About the work

The Gǔ Zhōubì suànjīng 古周髀算經 is the catalog’s name for the long, expanded reception of the Zhōubì suànjīng 周髀算經 (KR3f0001) — the foundational Hàn-era text on the gāitiān 蓋天 (“canopied-sky”) cosmology and the gnomon-and-shadow geometry that underpinned the early Chinese state’s astronomical practice. The label Gǔ 古 (“ancient”) distinguishes this five-juǎn received compound — the main classic plus the HòuHàn zhù 注 of Zhào Shuǎng 趙爽, the yīntú 隂圖 (“dim diagrams”) that Zhào appended, and additional later commentary layers — from the two-juàn core text alone (KR3f0001). The five-juan figure matches the Sòng-imperial reprint and the Sìkù quánshū listing, which presents the same composite: the jīng 經 plus Zhào’s zhù plus the Bèi Yīn 甄鸞 (sic, 6th-c.) and the Táng 李淳風 commentary.

Abstract

The Zhōubì is one of the most-studied and most-debated texts in the early Chinese scientific corpus. Cullen (1996) has shown convincingly that the layered text known today coalesced in the first centuries BCE / CE around an older nucleus of practical gnomonic procedures attached to a Western-Hàn cosmographical thought-experiment in which the heavens are a parallel disc above a parallel flat earth, both 81,000 lǐ across and 80,000 lǐ apart — the gāitiān model. Wilkinson summarises the position in his discussion of gāitiān: “The main source for gaitian theory is the Zhoubi suanjing” (Wilkinson, Chinese History: A New Manual, §gaitian). The text’s most-cited content is the Pythagorean-style demonstration (gōugǔ 句股) attributed to Shāng Gāo 商高 in dialogue with the Duke of Zhōu 周公, which gives the right-triangle relation gōu²+gǔ²=xián² with the canonical (3,4,5) numerical example.

The catalog meta dates the work to the Hàn dynasty; the actual composition window of the received recension extends from the late Western Hàn through the HòuHàn into the Three-Kingdoms period when 趙爽 Zhào Shuǎng of Wú wrote the zhù and the Gōugǔ yuánfāng túshuō 句股圓方圖說 essay that is normally appended. The bracket 100 BCE – 250 CE adopted here covers the nucleus through Zhào Shuǎng. The further Northern-Zhōu glosses by 甄鸞 Zhēn Luán (6th c.) and the Táng-court commentary by 李淳風 (656) are textual accretions, not part of the Gǔ Zhōubì proper. The five-juǎn division of the modern catalog reflects the SòngYuán transmission and Bào Huànzhī 鮑澣之’s 1213 printing. Duan Yucai 段玉裁 in the Qīng proposed adding the Zhōubì to the Confucian Classics, recognising the cultural status of the work (Wilkinson §1.1).

The Zhōubì was lost in independent transmission and recovered for the Sìkù quánshū by Dài Zhèn 戴震 from the Yǒnglè dàdiǎn 永樂大典; the catalog’s separate Zhōubì suànjīng jiàokān jì KR3fa003 records Dài’s collation work. The relation between the early gāitiān of the Zhōubì and the later hùntiān 渾天 (“encircled-sky” / armillary) cosmology displaced it as the orthodox model after the 1st c. CE is discussed at length in Cullen’s monograph.

Translations and research

  • Cullen, Christopher. 1996. Astronomy and Mathematics in Ancient China: The Zhou bi suan jing. Cambridge: Cambridge University Press. — the standard English-language translation, study and historical reconstruction. Indispensable.
  • Cullen, Christopher. 1993. “The Zhou bi: A Background.” In Loewe, Michael (ed.), Early Chinese Texts: A Bibliographical Guide. Berkeley: SSEC/IEAS, 33–38.
  • 錢寳琮 Qián Bǎocóng (ed.). 1963. Suànjīng shíshū 算經十書. Beijing: Zhōnghuá shūjú. — standard modern critical edition.
  • 程貞一 Chéng Zhēn-yī 1996, Zhōubì suànjīng yìzhù 周髀算經譯注. Shenyang: Liáoníng jiàoyù. — modern Chinese translation with notes.
  • Chen Cheng-Yih 程貞一. 1996. Early Chinese Work in Natural Science: A Re-examination of the Physics of Motion, Acoustics, Astronomy and Scientific Thoughts. Hong Kong: HKUP. — contains a long section on the Zhōubì.
  • Joseph Needham, Science and Civilisation in China III (Mathematics and the Sciences of the Heavens and the Earth), Cambridge 1959, 19–24, 210–224 — the classic Western survey.

Other points of interest

The Zhōubì’s gāitiān model is one of the very few cases in early Chinese science where a quantitative cosmological theory survives with its underlying gnomonic measurements and a geometrical demonstration of its key relation. The pedagogical dialogue between Duke of Zhōu and Shāng Gāo on the gōugǔ relation is one of the most-quoted passages in the entire mathematical canon. Joseph Needham was repeatedly drawn to the question of whether this constitutes an “independent” Chinese Pythagorean theorem; Cullen has provided the most careful modern treatment.

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