Numerals and Arithmetic in the Middle Ages (Variorum Collected Studies)

This third volume of studies by Charles Burnett brings together articles on the different numeral forms used in the Middle Ages. Some 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. 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 abacus of 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 twelfth century, with special references to the eastern forms The use of Arabic numberals among the three language cultures of Norman Sicily Why we read Arabic numerals backwards The Toledan regule (Liber alchorismi, part II) : a twelfth-century arithmetical miscellany / with Ji-Wei Zhao and Kurt Lampe Learning Indian arithmetic in the early thirteenth century Latin alphanumerical notation, and annotation in Italian, in the twelfth century : MS London, British Library, Harley 5402 Fibonacci's method of the Indians. CONTENTS 3 1. The Abacus at Echternach 6 2. Abbon de Fleury, abaci doctor 15 3. Algorismi vel helcep decentior est diligentia 22 4. Ten or Forty?A Confusing Numerical Symbol 78 5. Indian Numerals in the Mediterranean Basin in the Twelfth Century 83 6. The use of Arabic numerals among the three language cultures of Norman Sicily 109 7. Why we read Arabic numerals backwards 114 8. The Toledan Regule (Liber Alchorismi, part II) 117 9. Learning Indian arithmetic in the early thirteenth century 163 10. Latin Alphanumerical Notation, and Annotation in Italian in the 12th c. 169 11. Fibonacci's 'method of the Indians' 177 Addenda and corrigenda 183 Index nominum 185 Index manuscriptorum 187 Index terminorum mathematicarum 189