Mu'amalat and otherwise in the Liber mahamaleth: Contribution to Le 11 ième Colloque Maghrébin sur l’histoire des mathématiques arabes, École normale Supérieure, Kouba – Alger, 26, 27, 28 octobre 2013. Preprint

Research output: Working paperResearch


The twelfth-century Iberian Liber mahamaleth was discovered and described by
Jacques Sesiano in 1986; in 2010, a critical edition of the work was produced by
Anne-Marie Vlasschaert. Both agreed that the title of the work reflects Arabic
mu'amalat, “[the mathematics of] social intercourse”; that the work goes beyond
mu'amalat mathematics by integrating its material with proofs in Euclidean style;
and that it is an independent creative compilation, not a translation of a single
work. Charles Burnett has suggested the compiler-author to be Gundisalvi.
The present paper delineates the development of the notion of mu'amalat
as a branch of practical arithmetic from the early ninth through the mid-twelfth
century and locates the contents of the Liber mahamaleth with more precision in
respect to it, using also Castilian and related early Italian abbacus material as
well as Gundisalvi’s De divisione philosophiae. Analysis of that aspect of the text
that clearly falls outside the mu mala¯t tradition leads to the conclusion that the
Liber mahamaleth is a translation of what Gundisalvi speaks of as “the book which
in Arabic is called Mahamalech”, and that the integration of mu'amalat material
with the techniques of theoretical mathematics was thus a product of al-Andalus
culture and not of the Latin translation movement.
In the end two other pieces of sophisticated theoretical arithmetic known
only from Latin and Romance vernacular sources – a systematic scrutiny of the
certain properties of the Nicomachean means and an examination of certain
complex series – are shown also to be plausible products of that phase of al-
Andalus learned culture where it influenced Hebrew and Latin much more than
later Arabic learning.
Original languageEnglish
Number of pages27
Publication statusPublished - 5 Nov 2013

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