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Article ID: CBB487628776

Proofs and Algebra in al-Fārisī's Commentary (2019)

Oaks, Jeffrey A. (Author)

Historia Mathematica
Volume: 47
Pages: 106-121

DOI: 10.1016/j.hm.2018.10.008

URI: https://www.sciencedirect.com/science/article/pii/S0315086018301393

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Algebra Number theory; number concept Commentaries Mathematics 13th century Euclid al-Farisi, Kamal al-Din

The Persian mathematician al-Fārisī (late thirteenth century) wrote a commentary on a practical arithmetic book as a means of giving techniques associated with mental reckoning a foundation in proofs modeled on those in Euclid's number theory books. One problem with this intercultural project is the incompatibility of Euclidean and Arabic numbers, while another is the occasional inadequacy of Euclid's mode of representing numbers via lines labeled with letters. Like others, al-Fārisī found a partial solution to the former by identifying fractions with ratios of integers, and for the latter he turned to the algebra of polynomials to work through one proof. To properly interpret this proof, Arabic algebra is situated in its contemporary mathematical context. Sommario Alla fine del tredicesimo secolo, il matematico al-Fārisī redasse un commento riguardo a un testo di aritmetica pratica con l'intento di dare alla tecnica associata con il calcolo digitale una base di dimostrazioni modellate su quelle presenti nei libri di Teoria dei Numeri di Euclide. Uno dei problemi associati con tale approccio é l'incompatibilitá che si riscontra fra i numeri di Euclide e quelli arabi; mentre un altro e' l'inadeguatezza del sistema euclideo che etichetta linee con lettere a rappresentare numeri. Come hanno fatto altri, al-Fārisī trova una soluzione parziale al primo problema rappresentando le frazioni con rapporti fra numeri interi; e al secondo utilizzando la somma algebrica di polinomi allo scopo di elaborare la dimostrazione. Al fine di interpretare correttamente tale dimostrazione, nel presente articolo si ricorre all'uso dell'algebra dell'epoca di al-Fārisī.

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