Ouyang, Xiaoli (Author)

Proust, Christine (Author)

Ziran Kexueshi Yanjiu (Studies in the History of Natural Sciences)

Volume: 34

Issue: 2

Pages: 201-221

The use of the sexagesimal place value notation( hereafter SPVN) is one of the most striking features of cuneiform mathematics. The earliest attestations of a systematic use of the SPVN are found in a small set of Ur III mathematical texts,but traces of positional notations also appear in about two dozen Ur III administrative texts. These notations are located outside the main text,and hence we refer to such notations as "marginal numbers. "This article studies the marginal numbers in two Ur III documents. The numbers testify to diverse practices with positional notations and sexagesimal factors in administrative contexts during this period. A close analysis of the evidence reveals a diversity of graphical systems for what has been considered until now as a uniform notion of the SPVN. Thus,in addition to the SPVN fully developed during the Old Babylonian period,we identify other systems that we label as"partially sexagesimal place value notation"( hereafter partial-SPVN). The partial-SPVNs do not appear to be floating,while the SPVN does. The partial-SPVNs convert fractions of a measurement unit into an integer number of a sexagesimal sub-unit. This transformation would facilitate subtractions of measurement values with fractions.This diversity of place value notations reflects computational methods that vary according to the operation( multiplication,reciprocal,addition,subtraction) or the context( administrative or mathematical).The observations above may lead to a reconstruction of the process of calculation behind the Ur III administrative records. Some steps in the calculation process seem to have taken place external to the tablet,as no trace of their details occurs on the tablet. The marginal numbers thus provide evidence of an intermediate step,which converts quantities noted in the main text into the input of an external device where calculations are executed,or conversely,converts the output of the device into quantities noted in the main text.

...More Citation URI

Article
Jöran Friberg;
(2019)

Three Thousand Years of Sexagesimal Numbers in Mesopotamian Mathematical Texts
(/isis/citation/CBB634644866/)

Article
Rabii, Maryam;
(2012)

Arithmetic in Astronomy: A Treatise on Sexagesimal Arithmetic
(/isis/citation/CBB001510306/)

Article
Dipak Jadhav;
(2023)

Object-numerals as listed in Nijaguṇa Śivayogī ’s Viveka-Cintāmaṇi
(/isis/citation/CBB180449604/)

Article
John M. Steele;
(2015)

Late Babylonian Metrological Tables in the British Museum
(/isis/citation/CBB416694210/)

Article
Valeria Giardino;
(2018)

Tools for Thought: The Case of Mathematics
(/isis/citation/CBB112039489/)

Article
Michael Friedman;
(2020)

How to notate a crossing of strings? On Modesto Dedò’s notation of braids
(/isis/citation/CBB083323933/)

Book
Burnett, Charles;
(2010)

Numerals and Arithmetic in the Middle Ages
(/isis/citation/CBB001252996/)

Article
Sarma, Sreeramula Rajeswara;
(2012)

The *Kaṭapayādi* System of Numerical Notation and Its Spread Outside Kerala
(/isis/citation/CBB001210557/)

Article
Simonov, R. A.;
(2010)

Archaic Numbers and Mathematical Knowledge in Rus'
(/isis/citation/CBB001211372/)

Article
Han, Wei;
Zou, Dahai;
(2015)

Modern Chinese Translation, Photographs, and Expert Commentaries on an Excerpt from the Qin Dynasty Bamboo Strips Preserved at Peking University: “Lu Jiuci Asks Chen Qi About Numbers”
(/isis/citation/CBB209592901/)

Article
Heeffer, Albrecht;
(2014)

Epistemic Justification and Operational Symbolism
(/isis/citation/CBB001201186/)

Article
Ito, Shuntaro;
(2005)

Numeral Notations in the World
(/isis/citation/CBB000630942/)

Article
Brown, Peter B.;
(2012)

Muscovite Arithmetic in Seventeenth-Century Russian Civilization: Is It Not Time to Discard the “Backwardness” Label?
(/isis/citation/CBB001200568/)

Article
Yap, Audrey;
(2011)

Gauss' Quadratic Reciprocity Theorem and Mathematical Fruitfulness
(/isis/citation/CBB001024184/)

Article
Widom, Theodore Reed;
Schlimm, Dirk;
(2012)

Methodological Reflections on Typologies for Numerical Notations
(/isis/citation/CBB001251559/)

Article
Michaela Wiesinger;
(2021)

'Als der algoriſmus ſpricht…' – Indisch‐arabische Zahlen und der Algorismus in der Geometria Culmensis ('When the algoriſmus talks...' - Indo-Arabic Numbers and the Algorism in the Geometria Culmensis)
(/isis/citation/CBB756641010/)

Book
Stephen Chrisomalis;
(2020)

Reckonings: Numerals, Cognition, and History
(/isis/citation/CBB238847386/)

Article
Raffaele Pisano;
Paolo Bussotti;
(2015)

Fibonacci and the Abacus Schools in Italy. Mathematical Conceptual Streams - Education and its Changing Relationship with Society
(/isis/citation/CBB835911573/)

Book
King, David A.;
(2001)

The Ciphers of the Monks---A Forgotten Number-Notation of the Middle Ages
(/isis/citation/CBB000100097/)

Chapter
Burnett, Charles;
(2002)

Indian Numerals in the Mediterranean Basin in the Twelfth Century, with Special Reference to the “Eastern Forms”
(/isis/citation/CBB000203456/)

Be the first to comment!