
Contents
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1. Mathematical Treatises 1. Mathematical Treatises
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1.1 Mathematical Texts Listed in Bibliographies of Standard Histories 1.1 Mathematical Texts Listed in Bibliographies of Standard Histories
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1.2 Formation of the Corpus of Mathematical Treatises in the Early First Millennium ce 1.2 Formation of the Corpus of Mathematical Treatises in the Early First Millennium ce
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1.3 Extant Mathematical Treatises 1.3 Extant Mathematical Treatises
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1.3.1 The Jiu zhang suan shu 九章算術 (Computational Procedures of Nine Categories) 1.3.1 The Jiu zhang suan shu 九章算術 (Computational Procedures of Nine Categories)
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1.3.2 The Zhou bi suan jing 周髀算經 (Computational Treatise on the Gnomon of the Zhou [Dynasty]) 1.3.2 The Zhou bi suan jing 周髀算經 (Computational Treatise on the Gnomon of the Zhou [Dynasty])
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1.3.3 The Hai dao suan jing 海島算經 (Computational Treatise [Beginning with a Problem Concerning] a Sea Island) 1.3.3 The Hai dao suan jing 海島算經 (Computational Treatise [Beginning with a Problem Concerning] a Sea Island)
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1.3.4 The Sun zi suan jing 孫子算經 (Computational Treatise of Master Sun) 1.3.4 The Sun zi suan jing 孫子算經 (Computational Treatise of Master Sun)
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1.3.5 Zhang Qiujian suan jing 張丘建算經 (Computational Treatise of Zhang Qiujian) 1.3.5 Zhang Qiujian suan jing 張丘建算經 (Computational Treatise of Zhang Qiujian)
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1.3.6 Xiahou Yang suan jing 夏侯陽算經 (Computational Treatise of Xiahou Yang) 1.3.6 Xiahou Yang suan jing 夏侯陽算經 (Computational Treatise of Xiahou Yang)
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1.3.7 Wu cao suan jing 五曹算經 (Computational Treatise of Five [Government] Departments) 1.3.7 Wu cao suan jing 五曹算經 (Computational Treatise of Five [Government] Departments)
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1.3.8 Wu jing suan shu 五經算術 (Computational Procedures [Needed for Understanding] of the Five Classics) 1.3.8 Wu jing suan shu 五經算術 (Computational Procedures [Needed for Understanding] of the Five Classics)
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1.3.9 The Shu shu ji yi 數術記遺 (Procedures of “Numbering” Recorded to Be Preserved [for Posterity]) 1.3.9 The Shu shu ji yi 數術記遺 (Procedures of “Numbering” Recorded to Be Preserved [for Posterity])
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1.4 Recently Unearthed Treatises 1.4 Recently Unearthed Treatises
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1.4.1 Suan shu shu 筭數書 (Scripture on Computations [to Be Performed] with Counting Rods) 1.4.1 Suan shu shu 筭數書 (Scripture on Computations [to Be Performed] with Counting Rods)
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1.4.2 Suan shu 算術 ([Computational] Procedures [to Be Performed with] Counting Rods) 1.4.2 Suan shu 算術 ([Computational] Procedures [to Be Performed with] Counting Rods)
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1.4.3 Shu 數 (Numerical [Procedures (?)]) 1.4.3 Shu 數 (Numerical [Procedures (?)])
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2. Mathematical Methods of Commentators 2. Mathematical Methods of Commentators
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2.1 Area of a Circle and Approximate Values of π 2.1 Area of a Circle and Approximate Values of π
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4.2 Volume of a Pyramid 4.2 Volume of a Pyramid
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4.3 Volume of a Sphere 4.3 Volume of a Sphere
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5. Conclusions 5. Conclusions
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Bibliography Bibliography
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A4a Ancient Chinese Mathematics
Get accessAlexei Volkov, Center for General Education, National Tsing-Hua University, Hsinchu, Taiwan
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Published:10 July 2018
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Abstract
The chapter studies nine long-known extant Chinese mathematical texts, and three recently excavated texts, all composed prior to the beginning of the Sui 隋 dynasty (581–618 ce). Most of these were compiled for use as school texts. They include problems on fractions, on proportions and extraction of square and cube roots, on simultaneous linear equations and computations of areas and volumes. Among the more advanced techniques deployed in these texts are computing the area of a circle, that is, obtaining certain approximate values of π; computing the volume of a pyramid; and computing the volume of a sphere.
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