Numerals and Arithmetic in the Middle Ages: 1st Edition (Hardback) book cover

Numerals and Arithmetic in the Middle Ages

1st Edition

By Charles Burnett


382 pages

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Hardback: 9781409403685
pub: 2010-12-28
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This volume, the third by Charles Burnett in the Variorum series, brings together articles on the different numeral forms used in the Middle Ages, and their use in mathematical and other contexts. Some pieces study the introduction of Hindu-Arabic numerals into Western Europe, documenting, in more detail than anywhere else, the different forms in which they are found, before they acquired the standard shapes with which we are familiar today. Others deal with experiments with other forms of numeration within Latin script: e.g., using the first nine Roman numerals as symbols with place value, abbreviating the Roman numerals, and using the Latin letters as numerals. The author discusses how different types of numerals are used for different purposes, and the application of numerals to the abacus, and to calculation with pen and ink. The studies include the critical edition of several Latin texts.


'The research represented by these papers is meticulous and insightful; the book should be a first point of contact for any scholar interested in the introduction of Hindu-Arabic numerals to medieval Europe. It does not provide a comprehensive narrative, but that is not the point of a Variorum volume. Rather, it gathers the scholarship together, making it more accessible than it would have been otherwise. That is a contribution for which we should be grateful.' Mathematical Reviews '… this collection of articles is immensely rich in insights… The book can be recommended to anybody working on matters which it deals with…' Aestimatio '… a wealth of information, enriched with bibliography, diagrams, a huge number of photographs of manuscript folia and relevant footnotes, as well as useful indexes on names, manuscripts and mathematical terms. The work bears witness to Burnett's mastery of manuscripts, the Latin Language and palaeography, and of the historical scientific medieval context… an impressive and exhaustive treatment of the subject from many different perspectives, which makes this volume a rigorous and invaluable instrument for scholars dealing with medieval scientific manuscripts.' Suhayl

Table of Contents

Contents: Preface; The abacus at Echternach in ca. 1000 A.D; Abbon de Fleury, abaci doctor; Algorismi vel helcep decentior est diligentia: the arithmetic of Adelard of Bath and his circle;Ten or forty? A confusing numerical symbol in the Middle Ages; Indian numerals in the Mediterranean basin in the 12th century, with special reference to the 'Eastern forms'; The use of Arabic numerals among the three language cultures of Norman Sicily; Why we read Arabic numerals backwards; The Toledan Regule (Liber Alchorismi, part II): a 12th-century arithmetical miscellany, (with Ji-Wei Zhao and Kurt Lampe); Learning Indian arithmetic in the early 13th century; Latin alphanumerical notation and annotation in Italian in the 12th century: MS London, British Library, Harley 5402; Fibonacci's 'method of the Indians'; Addenda and corrigenda; Indexes.

About the Author

Charles Burnett is Professor of the History of Islamic Influences in Europe at the Warburg Institute, University of London, UK

About the Series

Variorum Collected Studies

The first title in the Variorum Collected Studies series was published in 1970. Since then well over 1000 titles have appeared in the series, and it has established a well-earned international reputation for the publication of key research across a whole range of subjects within the fields of history.

The history of the medieval world remains central to the series, with Byzantine studies a particular speciality, but the range of titles extends from Hellenistic philosophy and the history of the Roman empire and early Christianity, through the Renaissance and Reformation, up to the 20th century. Islamic Studies forms another major strand as do the histories of science, technology and medicine.

Each title in the Variorum Collected Studies series brings together for the first time a selection of articles by a leading authority on a particular subject. These studies are reprinted from a vast range of learned journals, Festschrifts and conference proceedings. They make available research that is scattered, even inaccessible in all but the largest and most specialized libraries. With a new introduction and index, and often with new notes and previously unpublished material, they constitute an essential resource. 

For further information about contributing to the series please contact Michael Greenwood at

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Subject Categories

BISAC Subject Codes/Headings:
HISTORY / General
MATHEMATICS / History & Philosophy