The Role of Algebraic Inferences in Na`īm Ibn Mūsā's Collection of Geometrical Propositions (2008)
Na`im ibn Musa'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 Thabit ibn Qurra's school. A relevant characteristic of Na`im'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-Khwarizmi's equations.
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