新編直指算法統宗 (Suanfa Tongzong: Systematic Treatise on Arithmetic) Vol 5

Name: 新編直指算法統宗 (Suanfa Tongzong: Systematic Treatise on Arithmetic) Vol 5
Author: Cheng Dawei

Cheng Dawei

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Systematic Treatise on Arithmetic, Vol. 5

新編直指算法統宗 (Suanfa Tongzong: Systematic Treatise on Arithmetic) Vol 5

Cheng Dawei

Chinese

1592

89 pages

4 images

Natural Philosophy Chinese Classics Mathematics East Asia

First Complete Translation

Only partial translations or excerpts exist. This is the first complete English translation.

While the Suanfa Tongzong is a foundational text in the history of Chinese mathematics and is extensively discussed and excerpted in English-language scholarly works (such as Martzloff's 'A History of Chinese Mathematics'), no complete, cover-to-cover English translation of the 17-volume work or specifically of Volume 5 (Shaoguang) exists. Existing publications provide only partial translations of specific problems or methods for analytical purposes.

Related translations found:

A History of Chinese Mathematics, trans. Jean-Claude Martzloff (translated by Stephen S. Wilson) (2007) [excerpts] source

And Yet It Is Heard: Musical, Multilingual and Multicultural History of the Mathematical Sciences - Volume 1, trans. Tito M. Tonietti (2014) [excerpts] source

Verified Mar 8, 2026 via local catalogs, local catalogs, open library, google books, google books, google books, open library, google books, google books · methodology

Natural Philosophy & Science Chinese Classics Mathematics & Sacred Number

About This Book

mathematics

Step into the world of the 'most illustrious Chinese arithmetician,' Cheng Dawei, as he transforms complex algebra into a visual and poetic art form. This volume reveals the secret algorithms and mnemonic songs used to solve everything from land measurements to the geometry of spherical storage, proving that ancient mathematics was as elegant as it was practical.

Index

206 terms

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Major Themes

square root extraction38pSuanfa Tongzong37p算法統宗30p初商29pCheng Dawei26p廉法26pgeometry26p次商24pquadratic equations21parea calculation20p方法19p隅法19pChinese mathematics17p開平方法16pcube root extraction16pdividend15p

3375p. 61, p. 62

abacus calculationp. 3, p. 10, p. 63

abacus mathematicsp. 14, p. 49

abacus mnemonicsp. 16, p. 17, p. 71, p. 72, p. 73, p. 74

algebraic identityp. 46, p. 47

ancient Chinese mathematicsp. 32, p. 50

areap. 2, p. 3, p. 28, p. 32

binomial coefficientsp. 6, p. 7

binomial expansionp. 8, p. 9, p. 77, p. 80

bushel constantp. 82, p. 85

Chinese geometryp. 75, p. 87

chu shangp. 76, p. 79

chu shang; the first digit of the rootp. 80, p. 81

Chu shang: The first digit of the resultp. 11, p. 13

Ci shangp. 13, p. 79, p. 80

circular granaryp. 83, p. 86

circumferencep. 30, p. 67, p. 86

circumference calculationp. 31, p. 69

Corner (Yu)p. 52, p. 53

corner methodp. 12, p. 60, p. 64

counting boardp. 11, p. 22, p. 38, p. 60

cube rootp. 7, p. 63, p. 79, p. 82

cubic feetp. 64, p. 87

Cubic Root Extractionp. 66, p. 68, p. 69, p. 70, p. 71, p. 72, p. 74, p. 75

diameterp. 30, p. 32, p. 67, p. 68

Dividend (Shi)p. 14, p. 51, p. 63, p. 64

divisorp. 21, p. 71, p. 82, p. 85

doup. 83, p. 85, p. 86

dou; one-tenth of a stonep. 83, p. 84, p. 85, p. 86

Edge Methodp. 64, p. 66

Edge Method (Lianfa)p. 63, p. 64

Extraction of a Square Root with a Subtracted Linear Component (Jiancong Kaipingfang)p. 26, p. 27

fap. 82, p. 89

Fa: the number used to divide the remainderp. 16, p. 17

Fang-fa: base divisorp. 32, p. 33

Fang-Lian-Yup. 10, p. 62

Fen-mu: denominatorp. 34, p. 35

Fen-zi: numeratorp. 34, p. 35

First Quotient: "Shang," the first digit of the root being soughtp. 48, p. 49

frustum volumep. 86, p. 87

Showing 40 of 190 entries.

Illustrations4

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diagram

Related Books

1 related

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Related works (1)

Systematic Treatise on ArithmeticCheng DaweiCheng Dawei, Cheng Dawei, Xin’an, Xin’an, Dividend (Shi)

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Systematic Treatise on Arithmetic, Vol. 5

新編直指算法統宗 (Suanfa Tongzong: Systematic Treatise on Arithmetic) Vol 5

Cheng Dawei

Chinese

1592

89 pages

4 images

Natural Philosophy Chinese Classics Mathematics East Asia

First Complete Translation

Only partial translations or excerpts exist. This is the first complete English translation.

Related translations found:

A History of Chinese Mathematics, trans. Jean-Claude Martzloff (translated by Stephen S. Wilson) (2007) [excerpts] source

And Yet It Is Heard: Musical, Multilingual and Multicultural History of the Mathematical Sciences - Volume 1, trans. Tito M. Tonietti (2014) [excerpts] source

Verified Mar 8, 2026 via local catalogs, local catalogs, open library, google books, google books, google books, open library, google books, google books · methodology

Natural Philosophy & Science Chinese Classics Mathematics & Sacred Number