From Abacus to Algorism
Theory and Practice in Medieval Arithmetic
Bibliographic Data
| ID | 8395387 |
|---|---|
| Authors | Gillian R Evans (University of Reading, corresponding author) |
| Year | 1977 |
| Volume | 10 |
| Issue | 2 |
| Pages | 114-131 |
| Publication date | 1977-07-01 |
| Peer Reviewed | Yes |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | The British Journal for the History of Science (JOURNAL) |
| Journal identifiers | ISSN: 0007-0874 • E-ISSN: 1474-001X |
| Publisher | Cambridge University Press (CUP) (PUBLISHER) |
| DOI | 10.1017/s0007087400015375 |
| OpenAlex | W2115761169 |
| Language | EN |
| Citations received | 1 |
| References cited | 7 |
Even at the level of the most elementary arithmetical operations, procedures and practices change. During the twelfth and thirteenth centuries an unusually well documented development took place: at the beginning of the period the authors of elementary manuals of computation taught the use of the abacus, whereas at the end they described the method of calculation which came to be known as the algorism. Their ideas about number, however, were still largely drawn from Boethius's rendering of Nicomachus of Gerasa's Introduction to arithmetic in the Arithmetica and there had been little progress in attempting to reconcile Boethius's teaching on the theory of number with the rather different assumptions that underlie the methods of practical calculation. Boethius and Nicomachus, for example, emphasize that one is not a number but the source of number, and they are aware of the special problems posed by ‘two’. Nicomachus questions whether ‘two’ is anything more than an embodiment of the principle of ‘otherness’; for him, it is open to dispute whether it can be rated a number in its own right. For the teacher of the skills of calculation, ‘one’ and ‘two’ are merely digits like any other. By the fourteenth century, collections of textbook material on elementary arithmetic provided the student with instruction in both theory and practice. The abacus manuals are missing from many such collections because by then the abacus has apparently been relegated to the status of a simple practical aid, but the other elements in medieval arithmetical studies are variously covered
Abacus (architecture) · Arithmetic · Arithmetic function · Discrete mathematics · Epistemology · Mathematical practice · Mathematics education · Simple (philosophy · Classics · Computer Science · Historical and Literary Studies · Historical Philosophy and Science · History · History and Theory of Mathematics · Mathematics · Philosophy
Petrus Abaelardus. Dialectica
A Catalogue of Incipits of Mediaeval Scientific Writings in Latin, 1963
A Catalogue of Incipits of Mediaeval Scientific Writings in Latin, 1963
Bibliographical Note on the "De Cifris" of Leone Battista Alberti
Two Twelfth Century Algorisms
The Invention of the Decimal Fractions and the Application of the Exponential Calculus by Immanuel Bonfils of Tarascon (c. 1350)
| Citation velocity | historical |
|---|---|
| Highly cited | No |