Abstract 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.

中文翻译：

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al-Fārisī 评论中的证明和代数

摘要 波斯数学家 al-Fārisī（13 世纪后期）对一本实用算术书籍进行了评论，作为一种方法，提供与心理推算相关的技术，以模仿欧几里德数论书籍中的证明。这个跨文化项目的一个问题是欧几里得数字和阿拉伯数字的不兼容，而另一个问题是欧几里得通过标有字母的线条表示数字的模式偶尔不足。像其他人一样，al-Fārisī 通过用整数比识别分数，找到了前者的部分解，而对于后者，他转向多项式的代数来完成一个证明。为了正确解释这个证明，阿拉伯代数被置于其当代数学语境中。