The Digital Corpus of Cuneiform Mathematical Texts

[First posted in AWOL 25 July 2014, updated 15 May 2022]

The Digital Corpus of Cuneiform Mathematical Texts

Cuneiform writing was invented some 5000 years ago in southern Iraq for the purpose of keeping accounts - and for the next few hundred years book-keeping remained its sole use. The last datable cuneiform tablet, also from southern Iraq, is an astronomical diary for the year 75 CE. For the three millennia spanning the rise and fall of cuneiform writing, and arguably for some time after, numeracy was an inseparable and essential part of literate culture throughout the Middle East.

While the vast majority of cuneiform tablets contain numerical data, written by professional scribes, a smaller number are the outcome of teaching, learning, or communicating mathematical techniques or ideas as part of scribal education. This website presents transliterations and translations of around a thousand published cuneiform mathematical tablets; a similar number await decipherment and analysis in museums around the world.

 The text and editions on this site are by Eleanor Robson whose work on this project was supported by an Early Career Fellowship from the University of Cambridge's Centre for Research in Arts, Social Sciences and Humanities in January-March 2007.

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 The Digital Corpus of Cuneiform Mathematical Texts is a component of

 Oracc: The Open Richly Annotated Cuneiform Corpus

Exact Sciences in Antiquity

Exact Sciences in Antiquity

Auf “Exact Sciences in Antiquity” werden die Forschungsergebnisse verschiedener Institutionen vorgestellt und damit Wissen gebündelt, um den Erkenntnishorizont noch weiter zu vergrößern. Beteiligt sind das Excellenzcluster Topoi, das Max-Planck-Institut für Wissenschaftsgeschichte und die Einstein Stiftung.

Das seit 2007 existierende Excellenzlcuster Topoi ist durch die Deutsche Forschungsgemeinschaft gefördert und seit 2012 in seiner zweiten Bewilligungsphase. Zahlreiche der fast unzählbaren Forschergruppen beschäftigen sich mit den exakten Wissenschaften in der Antike, ihre Ergebnisse werden hier präsentiert. Das Max-Planck-Institut für Wissenschaftsgeschichte ist enger Kooperationspartner von Topoi und beispielsweise durch die Forschungen zu antiken Waagen bei den “Exact Sciences” vertreten. Die Einstein Stiftung ist ebenfalls ansässig in Berlin und fördert über längere Zeiträume außerordentliche Wissenschaftler mit einem Fellowship, um die Forschungsthemen voranzutreiben. Mit dem Einstein Stiftung Fellowship Liba Taub wurde eine Forscherin ausgezeichnet, deren Thema “Ancient Scientific Writing” ebenfalls hier präsentiert wird. 

Die Koordination der einzelnen Projektbeiträge und der Website hat Prof. Dr. Gerd Grasshoff inne.

The platform “Exact Sciences in Antiquity” presents the research results of different institutions and hence knowledge brought together for extending the horizon of understanding. Involved are the excellence cluster Topoi, the Max-Planck-Institite for the history of science and the Einstein Fellowship Berlin.

The excellence cluster Topoi, founded in 2007 is supported by the Deutsche Forschungsgemeinschaft and in its second phase since 2012. A range of almost uncountable research areas deal with the exact sciences in antiquity and their results are presented here. The Max-Planck institute for history of sciences is a close cooperation partner of Topoi and among other things represented by research to ancient balances within the “Exact Sciences”.

The Einstein Fellowship is also based in Berlin and supports exceptional researchers with a long-term fellowship, to push certain topics. The Einstein Fellowship Liba Taub is represented by the field of “Ancient Scientific Writing”.

The coordination of the single projects and the website is holded by Prof. Dr. Gerd Grasshoff.

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Mathematics and Mathematical Astronomy

Mathematics and Mathematical Astronomy

I hope to make available public domain materials that are essential for the study of ancient and early modern mathematics and mathematical astronomy. Google, for example, has done some things to achieve this through its books.google.com project. However, like most other efforts at digitally copying non digital materials, "mistakes were made". For example, Google currently has several (all incomplete) versions of Teubner's's edition of Euclid available for download. Most of these unfortunately contain page after page that are illegible, missing, out of order or otherwise unusable.

Most of the works available here were made by repairing the imperfect Google scans. This repairing has taken the form of replacing illegible or missing pages of one Google text with readable pages from another Google scan of the same text, splicing together readable portions of pages with Photoshop, replacing missing pages with scans from a local library, and replacing missing pages with transcriptions in TeX, a mathematical typesetting software, from copies that are too brittle to scan...

Greek	Apollonius ابلونيوس Ἀπολλώνιος	Archimedes أرخميدس ὁ Ἀρχιμήδης	Aristarchus Ἀρίσταρχος ὁ Σαμαῖος	Autolycus ὁ Αυτόλυκος
Eratosthenes ὁ Ἐρατοσθένης	Diophantus Διόφαντος ὁ Ἀλεξανδρεύς ديوفنطس	Euclid اوقليدس ὁ Εὐκλείδης Euklid von Alexandria	Geminus Γεμῖνος ὁ Ῥοδιaκός	Hero هيرون Ήρων ὁ Αλεξανδρεύς
Menelaus Μενέλαος ὁ Ἀλεξανδρεύς	Nichomachus نيكوماخوس ὁ Νικόμαχος	Pappus Πάππος ὁ Ἀλεξανδρεύς	Proclus Πρόκλος ὁ Διάδοχος Proklos	Ptolemy كتاب المجسطي لبطليموس Κλαύδιος Πτολεμαῖος
Gregory Chioniades	Serenus of Antissa	Theon of Smyrna	Hipparchus	Hypsicles
Sanskrit	Aryabhata أريابهاتا Aryabhatiya आर्यभटीयम्	Bhaskaracarya Siddhanta Siromani सिद्धान्तशिरोमणिः	Brahmagupta Brahma-Sphuta-Siddhanta ब्राह्मस्फुटसिद्धान्तः	Jagannatha Samrat Rekhaganita रेखागणितम
Minaraja Vrddhayavanjataka वृद्धयवनजातकम	Panini- Kashika, Mahabhashya महाभाष्यम् अष्टाध्यायी	Surya Siddhanta सूर्यसिद्धान्तः	Varahamihira Pancasiddhantika, Brhat Samhita, Brhat Jataka वराहमिहिरः	Rg Veda Max Müller's Edition
Rg Veda H.H. Wilson's English Translation	Aitareya Brahmana of the Rig Veda Sanskrit/English	Rāmāyāṇa of Vālmīki Sanskrit with Sanskrit Commentaries
Arabic	al-Biruni: Chronology of Ancient Nations البيروني‎	al-Farabi : On the Virtuous City الفارابي	al-Khazini:The Zij as-Sanjari الخزيني‎	al-Khwarizmi: The Algebra الخوارزمي
al-Nairizi: Commentary on Euclid's Elements النريزى	Thabit ibn Qurra: Book V of the Conic Sections of Apollonius ثابت بن قرّة	al-Kindī: Several Short Philosophical Works (Latin) الكندي‎	Omar Khayyam: The Algebra of Omar Khayyam	Abu Mashar: Intrductionum in Astronomias
Ibn al-Nadim Fihrist الكتاب الفهرست	Alkabitius Astronomie Iudiciarie Principia	al-Khwarizmi: Key to the Sciences الخوارزمي	Abu Uthman al-Dimishqi: Pappus' Commentary on Book X of Euclid
Latin	Gherardus Cremonensis (Gherard of Cremona)	Copernicus كوبرنكوس	Kepler كيبلر	Fermat فيرما
Leibniz ليبنتز	Newton نيوتن	Euler	Gauss	Robert of Chester
Regiomontanus	Alphonsine Tables	George of Trebizond: Almagest
General	Philosophical Texts	Misc.	Greek Language	Sanskrit Language
Arabic Language	Greek Astrological Texts (CCAG)	Brown University's former History of Mathematics Department

MesoCalc

MesoCalc: a Mesopotamian Calculator

MesoCalc is a Mesopotamian calculator.

People interested in Mesopotamian mathematics can use it to compute with integers in sexagesimal place-value notation. See the note about the sexagesimal place-value notation (SPVN) and the bibliography below.

The present webpage is the program itself. Its latest version can be found on the official MesoCalc page. You are free to download this page, use it offline on your own computer or smartphone, modify the source code, and even redistribute your modifications under the terms of the GNU General Public License (see the license below).

This program was written in 2013 by Baptiste MÉLÈS (Archives Henri Poincaré, Université de Lorraine) with the scientific assistance of Christine PROUST (CNRS, Université Paris-Diderot) in the framework of the SAW Project (Mathematical Sciences in the Ancient World), headed by Karine Chemla (CNRS, Université Paris-Diderot).

If you see bugs or want new features, please contact Baptiste Mélès.

Available operations:

• Conversions: from decimal to sexagesimal, from sexagesimal to decimal;
• Number properties: regularity, prime factors;
• Addition: addition, substraction;
• Multiplication: multiplication, reciprocal, quotient, rule of three;
• Powers and roots: square, square root, cube, cube root;
• Tables: multiplication tables, table of reciprocals, list of regular numbers, list of reciprocal numbers;
• Measuring units: add lengths, compute brickage and carriage (nalbalum and nazbalum).