Arithmetic in the Thought of Gerbert of Aurillac (Philosophy and Cultural Studies Revisited / Historich-Genetische Studien Zur Philosophie Und Kulturgeschichte, 10)

The book deals with Gerbert of Aurillac (Pope Sylvester II) and his investigations in the field of theoretical (philosophy of numbers) and practical (counting) arithmetic. The book represents the comprehensive inquiry of both these aspects of arithmetic in his thought. The analysed sources are Gerbert's so-called scientific letters written to his friends, colleagues or pupils, and also including some of his other texts. On this basis, attention is paid to arithmetic as the mother of all sciences and as the path to wisdom (e.g., the so-called Saltus Gerberti , relation between arithmetic and other disciplines of the quadrivium, etc.) and also to practical arithmetic (e.g., the introduction of Hindu-Arabic numerals and the re-introduction of a new form of abacus to the Latin Christian West). Cover 1 Series Information 4 Copyright Information 6 Dedication 7 Contents 9 PREFACE 11 INTRODUCTION: ARITHMETIC AS THE SCIENCE OF NUMBERS 17 I. THEORETICAL ARITHMETIC 35 1. The Nature of Numbers: Saltus Gerberti (Letter to Constantine) 36 2. Figurative Numbers and Geometry (Letter to Adelbold) 57 3. Music and Harmony (Two Letters to Constantine) 71 4. Astronomy and Timekeeping (Letter De sphaera, Richer’s Historia, and the horological letter to Adam) 83 II. PRACTICAL ARITHMETIC 131 1. Tabula abaci, Decimal Positional Notation and Ghubar Numbers 131 2. Regulae multiplicationis 158 3. Regulae divisionis 172 CONCLUSION 187 BIBLIOGRAPHY 191 Abbreviations 191 Primary Sources 191 Secondary Sources 200 INDICES 219 List of Tables 221 List of Figures 223 Index locorum 225 Index of Personal Names (before 1700) 235 Index of Personal Names (after 1700) 239 Series index 243 The book deals with Gerbert of Aurillac (Pope Sylvester II) and his investigations in the field of theoretical and practical arithmetic. It is mainly based on an analysis of Gerbert’s so-called scientific letters. An attention is paid to the philosophy of numbers (Saltus Gerberti, quadrivium) and practical counting (Hindu-Arabic numerals, abacus).