The Definitive Bilingual Critical Edition of Imperial China’s Mathematical Canon
For more than ten centuries, the Nine Chapters on Calculation Procedures served as the reference mathematical manual of imperial China. Its 246 problems formulate practical methods for the technical administration of the empire, while establishing a constructive foundation for arithmetic, proportion, and geometry. This edition presents the Classical Chinese text mirrored in parallel English translation across its three original historical layers—the Han canon, Liu Hui’s commentary, and Li Chunfeng’s subcommentary—together with Liu Hui’s treatise Haidao Suanjing, sourced from the Southern Song Bao Hanzhi woodblock recension (1213 AD) and the Ming imperial Yongle Dadian (1408 AD).
Complementing the historical record, the volume provides a contemporary technical framework: the historical context and mathematical foundations; a synoptic summary transcribing all 255 problems and procedures into modern mathematical notation, with 66 reconstructed diagrams of the lost historical figures; and technical appendices on counting-board calculation and Han imperial metrology.
Key Features of this Edition
• Complete Critical Edition: Presents the primary Classical Chinese text and parallel English translation from its earliest surviving witnesses with its contemporary mathematical transposition, geometric proofs, and the operational apparatus of the counting board and Han metrology.
• Three Historical Layers: Distinct typography separating the Han canon, Liu Hui’s commentary (263 AD), and Li Chunfeng’s subcommentary (656 AD).
• Liu Hui’s Original Preface (263 AD): Foundational treatise on cosmology, epistemology, and the double-difference method of the Haidao.
• Tang Imperial Memorial and Decrees (656 AD): Official court records and examination statutes by Li Chunfeng codifying the canon for the civil service.
• Astronomical Records of pi (636 AD): Primary text from the Book of Sui preserving Zu Chongzhi’s register of 355/113.
• Summary of Problems and Procedures: Ninety pages systematically transcribing all 255 problems and procedures, explaining each statement and resolution with the corresponding simbolic model and numerical resolution in contemporary notation.
• Visual Reconstruction of Lost Diagrams (66 Diagrams): Restored geometric figures, including 11 dissection proofs, 14 solids, and the surveying Problem 9 in 3D.
• The Counting Board: Technical manual detailing calculating rods, the 271-rod bundle, alternating decimal notation, negative numbers, root extractions, and worked canonical problems.
• Chinese Imperial Metrology: Exhaustive statutory tables for Han linear measures, field areas, dry capacities, weights, aristocratic ranks, and commodity trade ratios.
About the Authors
Zhang Cang (c. 160–150 BC) collected surviving bamboo fragments and compiled the canonical chapters. Geng Shouchang (c. 50 BC) augmented and standardized the procedures for imperial administration. Liu Hui (263 AD) commented and established the theoretical foundations and proofs. Li Chunfeng (656 AD) subcommented the text and codified the official imperial examination syllabus.
About this Edition
Sources: Southern Song woodblock recension (1213 AD) and Ming imperial Yongle Dadian (1408 AD).
Translation: EXHIRA.
Editorial matter: EXHIRA.
Cover design: EXHIRA.
Cover art: Fuxi and Nüwa (Wu Liang Shrine, c. 151 AD).
Typeset in: TeX.
Published by: EXHIRA — Great Books of Science, Vol. 2.
