In the absence of the Arabic text of al-Khw's Arithmetic, which has not yet been found, the oldest Latin adaptations from the twelfth century are the only evidence documenting the genesis and the first spreading of a decimal arithmetic that uses nine figures and zero, i.e. the Indian reckoning known in the Middle Ages as algorismus. This paper studies these texts, their content, their sources, and identifies their authors and the milieus in which they were written.

The paper studies the medieval tradition of the 9th century al-Khwarizmi’s handbook on algebra compared with its Latin translation by Gerard of Cremona, later translated in Italian vernacular by an anonymous Florentine abacus master, during the 14th century. This long journey along five centuries and three countries deals accurately with the mathematical contents; by means of analysis of explicit and implied elements in the three works, we also focus on the different historical backgrounds, the social condition of the authors, the (...) cultural, mindset-related and religious obstacles they had to take into consideration, while disseminating these calculation techniques, and, finally, their teaching style. (shrink)

Eine Reihe von mittelalterlichen Schriften zur Landmessung (vom 9. islamischen Jahrhundert bis zu Fibonacci und Pacioli) enthält eine besondere Art von „algebraischen” Aufgaben. Darin werden z.B. die Summe der Fläche und einer oder alle vier Seiten eines Quadrates beschrieben und nach der Seite gefragt. Es zeigt sich erstens, daß dieser Aufgabentyp mindestens seit dem frühesten 2. vorchristlichen Jahrtausend von geometrischen Praktikern tradiert wurde, und zweitens, daß er die Entwicklung einer „Algebra” in der altbabylonischen Schreiberschule inspirierte. Der Aufsatz untersucht, in welcher (...) Weise die Überführung der „sub-wissenschaftlichen” Praktikertradition in einen systematischen Schulunterricht den mathematischen Inhalt und den Denkstil künftiger Praktiker präge. Im letzten Kapitel wird diskutiert, inwieweit es sinnvoll ist, innerhalb dieser Schulalgebra von „Schulen” zu sprechen. (shrink)

This article describes how the decimal place value system was transmitted from India via the Arabs to the West up to the end of the fifteenth century. The arithmetical work of al-Khwārizmī's, ca. 825, is the oldest Arabic work on Indian arithmetic of which we have detailed knowledge. There is no known Arabic manuscript of this work; our knowledge of it is based on an early reworking of a Latin translation. Until some years ago, only one fragmentary manuscript of this (...) twelfth-century reworking was known. Another manuscript that transmits the complete text has made possible a more exact study of al-Khwārizmī's work. This article gives an outline of this manuscript's contents and discusses some characteristics of its presentation. (shrink)