Lectura metodològica i històrica de l'obra Hibbur ha-měsihá we-hatisboret (Tractat de geometria i mesurament), d'Abraham Bar Hiyya (Savasorda)

Abstract

On the occasion of the centenary of the birth of Josep Millàs Vallicrosa, I thought that, as a mathematician, it would be good to perform an analysis of the Treatise on Geometry and Measurement (1116) by Abraham Bar H. iyya (Savasorda) that the famous Arabist-Hebrewist had translated into Catalan. This work shows that in the West, before Fibonacci's Liber Abaci (1202), written in Latin, a booklet had been published in Hebrew in which the quadratic equation and its solving algorithms were introduced, based on the relations in Book II of Euclid's Elements. In addition, this booklet had a second part dedicated to the division of figures, using, however, geometric methods. Fibonacci, aware of the methodological difference between these two parts, addressed the question of the division of figures inherited from Greek mathematics in a separate treatise, The Practica Geometriæ (1220).