Marek Otisk:
Gerbert of Aurillac and Abacistic Skill of Calculation

Abstract

The paper deals with the early medieval abacus. The famous scholar Gerbert of Aurillac, teacher of kings and emperors, abbot, archbishop and Pope Sylvester II, is frequently connected with the reintroduction of the abacus to the Christian West at the end of the 10th century. For that reason the early medieval form of the abacus is often named “gerbertian” or “cloistral.” The paper describes the “gerbertian” abacus, including an explanation of the key terms needed for this kind of the calculation (arcus pythagorei, digitus, articulus, numerus simplex, numerus complex, etc.), the performance of notable mathematicians of this epoch (also called gibercisti or abacisti – for example Abbo of Fleury, Heriger of Lobbes, Byrhtferth of Ramsey, Hermannus Contractus, Turchillus Compotista, Robert of Hereford, Radulph of Laon, Adelard of Bath, Garlandus Compotista etc.), and the starting point for using Hindu-Arabic numbers in the Latin West (Gerbert’s study in the Spanish March, contact with Jews, etc.).
The historical part of the article (sections II–IV) is followed by a second part that deals with abacistic skill of calculation (sections V and VI). Addition (in accordance with early medieval rules of the calculation with help of the abacus), multiplication, and division (the most demanding mathematical operation on abacus) are described. The second part of this paper shows the rules of abacistic operations and points out similarities between “gerbertian” mathematical operations and today’s calculations.

Language: czech

Keywords: skill of calculation; Early Middle Ages; “gerbertian” abacus; medieval mathematics