### Abstract

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.

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 language | English |
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Number of pages | 27 |

Publication status | Published - 5 Nov 2013 |