Ten or forty? A confusing numerical symbol in the Middle Ages (Q2883421)

Gemäß: ``In the twelfth century several different systems of numeration were tried out in the West, especially by mathematicians and astronomers who needed to write high numbers and make complicated calculations.'' (p. 81) stellt Verf. zunächst hieraus folgende eigentümlichen Schreibarten einiger römischer oder indisch-arabischer Zahlen in manch mittelalterlichem westlichen Kulturland vor, bevor er sein eigentliches Vorhaben formuliert: ``This article, deals with yet another kind of numeral form, namely the ligature of `\(x\)' and `1' for the number 40. -- In this symbol, the Roman numeral `\(x\)' has a small capital `\(L\)' (often reduced to a hook or cupshape) attached to its top right-hand arm. This `\(L\)'-element can easily be confused with the termination of the right-hand arm itself, and the symbol becomes difficult to distinguish from a simple `\(x\)'. The appearance of `ten' where forty would be expected is often evidence that, at any earlier stage in the transmission of the text, the \(xl\)-ligature had been used. \dots this symbol has been recorded regularly by palaeographers working on documents written in the Iberian peninsula\dots It is a characteristic of Visigothic script, appearing especially on epigraphic monuments and in charters from the sixth century onwards. In the twelfth century it is a Visigothic feature taken over into Caroline script in Spain\dots'' (p. 82) Verf. geht wie folgt vor: ``\dots to list the texts in which the ligature appears and to draw some tentative conclusions\dots'' (p. 82). -- Gegliedert in: 1) Manuscripts of the translations of John of Seville (fl. 1120s and 1130s); 2) Manuscripts of the Toledan Tables (12th cent.); 3) Manuscripts of the works of Raymond of Marseilles (fl. 1141); 4) Manuscripts of the translations of Plato of Tivoli (fl. 1134--1145); 5) Manuscripts of the translations of Gerard of Cremona (1114--1187), werden gezielt und geschickt einschlägige Werke in westeuropäischen Bibliotheken vorgestellt, ergänzt durch drei Abbildungen. -- In der Conclusion bemerkt Verf.: ``It is most likely that the use of the \(xl\)-ligature in translations of mathematical and astronomical works reflects the usage of the wider society to which the respective translators belonged, rather than their desire to introduce a more convenient symbol for enumerating and calculating. It is unusual for Roman numerals to be combined into one ligature.'' (p. 85) Nachdem ``The strongest evidence for the use of the \(xl\)-ligature in mathematical texts is in the works of John of Seville, the Toledan Tables and the works of Raymond of Marseilles.'' (p. 85), dürfte, weil keine Originalwerke vorliegen, das Auftreten der genannten Merkmale in den derzeit zugänglichen Texten auf die Schreibart der Kopisten zurückzuführen sein, ``either because they belonged to a society in which the ligature was current, or because they scrupulously, copied the forms of numerals they found in their exemplars'' (p. 85 sq.). Gemäß: ``Nevertheless, the fact that the \(xl\)-ligature occurs more frequently in the earliest manuscripts of the texts than in later copies, points towards it being in the authors' original copies. (p. 86) folgert Verf , dass sich wohl bereits in den Autographen der genannten Autoren gegenseitige Abhängigkeiten erkennen ließen, so wie z.B. die Grüße eines ``magister R'' (p. 86), wohl ``Raymond of Marseilles''; jedoch: ``But I have found no evidence that Visigothic script and/or the \(xl\)-ligature which is distinctive of it, was ``known in Marseilles in his time.'' (p. 86) diesbezügliche Quellen könnten folglich in Spanien liegen, etwa in Barcelona.NEWLINENEWLINEFor the entire collection see [Zbl 1236.01002].