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Numerals and Arithmetic in the Middle Ages

Charles Burnett
Ashgate Variorum
Publication Date: 
Number of Pages: 
[Reviewed by
P. N. Ruane
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This book is a collection of articles on numeral forms, methods of calculation, and algebraic methods used in the early Middle Ages. There is no declaration as to the intended readership, nor are criteria for the selection of the included articles made explicit.

As is standard in the Variorum series, the articles are reproduced exactly as originally published, with the original pagination. As a result, the articles vary greatly in length and also in the format in which they appear. For example, the second article is a text in medieval French, with no translation or commentary upon its content. A much longer article, ‘The Toledan Regule (Liber Alchorismi, part II’, appears in the original medieval Latin followed by a translation into English. The varied mathematical content of this article then appears in modern notation, and the article commences with a clear introduction.

Largely focussing upon different numeral forms used in the 10th to 12th centuries, the general topic of the book is the introduction of Hindu-Arabic numerals into Western Europe. Early forms of abaci are explained, and arithmetical methods are explored. One article explains why, given that Arabic was read from right to left, our present day numbers are read from left to right (e.g. why 42 is not read as ‘two add forty’, as opposed to ‘forty add two’).

Overall, this publication could be a very useful resource book for specialists in the field of early European arithmetic. 

Peter Ruane spent 10 years at school, and left aged 15 not understanding basic arithmetic. Subsequent assiduous devotion to Pendlebury’s Shilling Arithmetic improved his computational expertise.

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.