Algebra

Abstract

The introduction referred (on p. 3) to the challenge which Jacopo’s algebra, as described by Karpinski, presents to conventional thinking about the history of pre-Renaissance algebra. Since the detailed presentation of the contents of the algebraic chapters of his treatise (pp. 100ff) did not touch on this topic, it is now time to take it up. As it turns out, the challenge is even stronger than could be guessed from Karpinski’s description. In order to see that, we shall first have to look closely at the general character of Jacopo’s own algebra compared to the Latin presentations of the topic — the translations of al-Khwārizmī prepared by Robert of Chester and Gherardo da Cremona, the anonymous fourteenth-century translation of Abū Kāmil’s algebra, and the Liber abbaci. Afterwards, we shall need to compare it both to a wide range of Arabic treatises and to a selection of Italian algebraic fourteenth-century algebraic writings.

Here and elsewhere I disregard the brief excerpts “de libro qui dicitur gleba mutabilia” in Liber Alchorizmi de pratica arismetice [ed. Boncompagni 1857b: 112f]. They are not in Allard’s partial edition of the Liber Alchorizmi [1992] but they are present in manuscripts that are as distant from each other in the stemma as possible — see [Høyrup 1998b: 16 n.7]; there is thus no doubt that they were present in the original and have not been interpolated. But the few paragraphs in question can hardly count as a presentation of the field and appear to have had no impact whatsoever.