Contents // PREFACE...9 // INTRODUCTION: ARITHMETIC AS THE SCIENCE // OF NUMBERS... 15 // I. THEORETICAL ARITHMETIC... 33 // 1. The Nature of Numbers: Saltus Gerberti (Letter to Constantine) . 34 // 2. Figurative Numbers and Geometry (Letter to Adelbold) ... 55 // 3. Music and Harmony (Two Letters to Constantine)... 69 // 4. Astronomy and Timekeeping (Letter De sphaera, Richer’s // Historia, and the Horological letter to Adam)... 81 // II. PRACTICAL ARITHMETIC... 129 // 1. Tabula abaci, Decimal Positional Notation and Ghubar Numbers ... 129 // 2. Regulae multiplicationis ... 156 // 3. Regulae divisionis... 170 // CONCLUSION... 185 // BIBLIOGRAPHY... 189 // Abbreviations ... 189 // Primary Sources... 189 // Secondary Sources... 198 // 8 // Contents // INDICES // 00000000000000 // 00000000000000 // 217 // List of Tables // 05000000000000000000000000000000000000000000000202 // 219 // List of Figures...221 // Index locorum...223 // Index of Personal Names (before 1700)... 233 // Index of Personal Names (after 1700) // 00000000000000