Arabic Sciences and Philosophy

Research Article

THE ROLE OF ALGEBRAIC INFERENCES IN NA‘ĪM IBN MŪSĀ’S COLLECTION OF GEOMETRICAL PROPOSITIONS

MARCO PANZAa11

a1 CNRS (REHSEIS) and University of Paris Diderot – Paris 7, UMR 7596, Univ. Paris-Diderot, Case courrier 7064, 2 place Jussieu, 75251 Paris Cedex 05, France Email: panzam@libero.it

Abstract

Na‘īm ibn Mūsā’s lived in Baghdad in the second half of the 9th century. He was probably not a major mathematician. Still his Collection of geometrical propositions – recently edited and translated in French by Roshdi Rashed and Christian Houzel – reflects quite well the mathematical practice that was common in Thābit ibn Qurra’s school. A relevant characteristic of Na‘īm’s treatise is its large use of a form of inferences that can be said ‘algebraic’ in a sense that will be explained. They occur both in proofs of theorems and in solutions of problems. In the latter case, they enter different sorts of problematic analyses that are mainly used to reduce the geometrical problems they are concerned with to al-Khwārizmī’s equations.

Footnotes

1 I thank Hélène Bellosta, Charles Burnett, Annalisa Coliva, Massimo Galuzzi, Roshdi Rashed and two anonymous referees for valuable help and comments on previous versions of my paper.

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